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Handbook of Semiconductor Technology Volume 1 Kenneth A. Jackson, Wolfgang Schroter (Eds.)

@WILEY-VCH

Handbook of Semiconductor Technology Volume 1 Kenneth A. Jackson, Wolfgang Schroter (Eds.)

BWILEY-VCH

Weinheim . New York . Chichester . Brisbane . Singapore . Toronto

Editors: Prof. K. A. Jackson The University of Arizona Arizona Materials Laboratory 4715 E. Fort Lowell Road Tucson, A 2 85712, USA

Prof. Dr. W. Schroter IV. Physikalisches Institut der Georg-August-Universitat Gottingen BunsenstraBe 13- 15 D-37073 Gottingen, Germany

This book was carefully produced. Nevertheless, authors, editors and publisher do not warrant the information contained therein to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data: applied for Deutsche Bibliothek Cataloguing-in-Publication-Data A catalogue record is available from Die Deutsche Bibliothek ISBN 3-527-29834-7

0 WILEY-VCH Verlag GmbH, D-69469 Weinheim (Federal Republic of Germany), 2000

Printed on acid-free and chlorine-free paper. All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form - by photoprinting, microfilm, or any other means - nor transmitted or translated into machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Composition, Printing and Bookbinding: Konrad Triltsch, Print und digitale Medien GmbH, D-97070 Wiirzburg Printed in the Federal Republic of Germany.

Preface

Rapid scientific and technological developments have enabled microelectronics to transform the computer industry of the sixties into today’s information technology, which is now revolutionizing communications and the information media. Larger than the car business, information technology is one of the industries most impacted by physical research and technology transfer in the 20thcentury. This will continue for at least the first two decades of the 21Stcentury. The two volumes of this Handbook describe the underlying scientific and technological bases of this unique development, with the first addressing the science, and the second the technological framework of the field. Written by experts who have made major contributions to this enterprise, the chapters span from defect physics to device processing to present a panorama of the key steps, models, and visions -in short the evolution - of microelectronics. At the same time, this Handbook can be seen as a carefully written status report, specially valuable to those engaged in the continuing interplay between semiconductor science, technology, and business, and in the creation of new markets, such as sensor arrays, power and high frequency devices, solar cells, and blue lasers. Circuit and systems design, which turn science and technology into end-user products, are not included as separate chapters, because each would need a volume in its own right. However, due to their close connection with process science and technology, they are briefly treated as the need arises. In semiconductors, science frequently develops in close interplay with technology, and fundamental investigations and technological advances cross-pollinate each other in an unprecedented fashion. The miniaturization of the transistor, begun forty years ago, is approaching dimensions, where present concepts appear to break down, and the available characterization methods may no longer function. Other devices, such as solar cells, are now entering the mass market, placing increasing demand on materials quality, process efficiency, and, of course, cost. At present, the most promising approach to addressing these challenges appears to involve fundamental understanding and modeling of highly complex nonlinear solid state phenomena, in short, physically-based, predictive simulation of complex process technological sequences. The first volume places particular emphasis on the concepts and models relevant to such issues. Starting with a description of the relevant fundamental phenomena, each chapter describes and develops the mechanisms and concepts used in current semiconductor research. Experimental details are provided in the text, or summarized in tables and diagrams to the extent needed to illustrate the models under discussion. The Handbook begins with chapters on the basic concepts of band structure formation, charge transport, and optical excitations (chapters 1 and 2), the physics of defects (point defects, impurities, dislocations, grain boundaries, and interfac-

VI

Preface

es) in crystalline semiconductors, particularly Si and GaAs (chapters 3-8, lo), special materials, such as hydrogenated amorphous Si (chapter 9), concluding with semiconductors for solar cell applications, silicon carbide, and gallium nitride (chapters l l - 13). I am very grateful to the contributors who took the trouble to write a chapter for this volume. I thank Prof. Peter Haasen, Prof. Abbas Ourmazd, PD Dr. Michael Seibt, and Prof. Helmut Feichtinger for many useful proposals and critical comments. I also thank Dr. Jorn Ritterbusch and Mrs. Renate Dotzer of WILEYVCH for their advice and very agreeable cooperation. Let me finally quote from a letter of one of the authors (A. 0.):"We wish the reader as much fun with the material as we have had - as much fun, but much less hard work". Wolfgang Schroter Gottingen, April 2000

List of Contributors

Prof. Dr. Helmut Alexander Universitat zu Koln 11. Physikalisches Institut Abteilung fur Metallphysik ZulpicherstraBe 77 D-50937 Koln Germany Chapter 6 Dr. Alain Bourret CEAIDCpartement de Recherche Fondamentale sur la Matikre CondensCe Service de Physique des MatCriaux et Microstructures 17 rue des Martyrs F-38054 Grenoble France Chapter 7 Prof. Dr. W. J. Choyke Department of Physics and Astronomy University of Pittsburgh Pittsburgh, PA 15260 USA Chapter I 1 Prof. Dr. Robert P. Devaty Department of Physics and Astronomy University of Pittsburgh Pittsburgh, PA 15260 USA Chapter 11

Prof. Dr. Helmut Feichtinger Karl-Franzens-Universitat Graz Inst. f. Experimentalphysik Universitatsplatz 5 A-801 0 Graz Austria Chapter 4 Dr. Dieter Gilles Wacker Siltronic AG Johannes-Hess-Str. 24 D-84489 Burghausen Germany Chapter I0 Prof. Dr. Ulrich M. Gosele MPI fur Mikrostrukturphysik Am Weinberg 2 D-06 120 Halle Germany Chapter 5 Dr. Martin L. Green Bell Laboratories Lucent Technologies Murray Hill, NJ 07974-2070 USA Chapter 8 Prof. Dr. Robert Hull University of Virginia Department of Materials Science and Engineering 151 Engineers Way Charlottesville, VA 22903-4745 USA Chapter 8

Vlll


Dr. Christian Kisielowski National Center for Electron Microscopy Lawrence Berkeley National Laboratory Berkeley, CA 94720 USA Chapter 13 Dr. Joachim Kruger University of California Department of Materials Science and Engineering Berkeley, CA 94720 USA Chapter 1 Prof. Dr. Michel Lannoo Institut Superieur D’Electronique du Nord 41 Boulevard Vauban 59046 Une France Chapter 1 Prof. Dr. Hans Joachim Moller Institut fur Experimentelle Physik TU Bergakademie Freiberg D-09599 Freiberg Germany Chapter 12 Prof. Dr. Abbas Ourmazd IHP Im Technologiepark 25 D-15236 Frankfurt/Oder Germany Chapter 8 Dr. W. D. Rau IHP Im Technologiepark 25 D- 15236 Frankfurt/Oder Germany Chapter 8

Dr. Jean L. Rouvikre CEAIDCpartement de Recherche Fondamentale sur la Matihre Condensee Service de Physique des MatCriaux et Microstructures 17 rue des Martyrs F-38054 Grenoble France Chapter 7 Prof. Dr. Wolfgang Schroter Georg-August-Universitat Gottingen IV. Physikalisches Institut BunsenstraDe 13- 15 D-37073 Gottingen Germany Chapter 10 Dr. P. Schwander IHP Im Technologiepark 25 D- 15236 Frankfurt/Oder Germany Chapter 8 Dr. Michael Seibt Georg-August-Universitat Gottingen IV. Physikalisches Institut Bunsenstralje 1 3 - 15 D-37073 Gottingen Germany Chapter 10 Dr. Robert A. Street Xerox Palo Alto Research Center 3333 Coyote Hill Road Palo Alto, CA 94304 USA Chapter 9


IX

Prof. Dr. Teh Y. Tan Department of Mechanical Engineering and Materials Science Duke University Durham, NC 27708 USA Chapter 5

Prof. Dr. Rainer-G. Ulbrich Georg-August-Universitat Gottingen IV. Physikalisches Institut Bunsenstrarje 13- 15 D-37073 Gottingen Germany Chapter 2

Prof. Dr. Helmar Teichler Georg-August-Universitat Gottingen Institut fur Materialphysik Hospitalstrarje 3-7 D-37073 Gottingen Germany Chapter 6

Prof. Dr. George D. Watkins Sherman Fairchild Center for Solid State Studies, Lehigh University, 16A Memorial Dr. East Bethlehem, PA 18015-3185 USA Chapter 3

Dr. Jany Thibault CEA/DCpartement de Recherche Fondamentale sur la Matibre CondensCe Service de Physique des MatCriaux et Microstructures 17 rue des Martyrs F-38054 Grenoble France Chapter 7

Prof. Dr. Eicke R. Weber University of California Department of Materials Science and Engineering Berkeley, CA 94720 USA and Lawrence Berkeley National Laboratory Material Science Division Berkeley, CA 94720 USA Chapter 13

Dr. Raymond T. Tung Bell Laboratories Lucent Technologies Murray Hill, NJ 07974-2070 USA Chapter 8

Dr. K. Winer Xerox Palo Alto Research Center 3333 Coyote Hill Road Palo Alto, CA 94304 USA Chapter 9

Contents

1 Band Theory Applied to Semiconductors

M . Lannoo

................

1

2 Optical Properties and Charge Transport . . . . . . . . . . . . . . . . 69 R. G. Ulbrich 3 Intrinsic Point Defects in Semiconductors 1999 . . . . . . . . . . . . 121 G. D. Watkins 4 Deep Centers in Semiconductors H. Feichtinger

....................

167

5 Point Defects, Diffusion, and Precipitation . . . . . . . . . . . . . . . 23 1 T I.: Tan, U. Gosele 6 Dislocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1 H. Alexander, H. Teichler

7 Grain Boundaries in Semiconductors . . . . . . . . . . . . . . . . . . 377 J. Thibault, J.-L. Rouviere, A. Bourret 8 Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 R. Hull, A. Ourmazd, W D. Rau, I? Schwandel; M. L. Green, R. i? Tung

9 Material Properties of Hydrogenated Amorphous Silicon . . . . . . . 541 R. A. Street, K. Winter 10 High-Temperature Properties of Transition Elements in Silicon . . . . 597 W Schroter, M. Seibt, D. Gilles 11 Fundamental Aspects of S i c W J. Choyke, R. l? Devaty

......................

661

12 New Materials: Semiconductors for Solar Cells . . . . . . . . . . . . 715 H. J. Moller 13 New Materials: Gallium Nitride . . . . . . . . . . . . . . . . . . . . . 77 1 E. R. Webel; J. Kriiger, C. Kisielowski Index.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809

Handbook of Semiconductor Technologj Kenneth A. Jackson, Wolfgang Schrotei CoDvriaht 0 WILEY-VCH Verlaa GrnbH. 2000

1 Band Theory Applied to Semiconductors Michel Lannoo Dkpartement Institut SupCrieur d’Electronique du Nord. Institut d’Electronique et de MicroClectronique du Nord. Villeneuve d’Ascq. France

List of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1 1.1.1 From Discrete States to Bands . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.2 Bloch Theorem for Crystalline Solids . . . . . . . . . . . . . . . . . . . . . 7 1.1.3 The Case of Disordered Systems . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.4 The Effective Mass Approximation (EMA) . . . . . . . . . . . . . . . . . . 10 1.1.4.1 Derivation of the Effective Mass Approximation for a Single Band . . . . . 10 12 1.1.4.2 Applications and Extensions . . . . . . . . . . . . . . . . . . . . . . . . . The Calculation of Crystalline Band Structures . . . . . . . . . . . . . . 14 1.2 1.2.1 Ab Initio Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 14 1.2.1.1 The Hartree Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1.2 The Hartree-Fock Approximation . . . . . . . . . . . . . . . . . . . . . . . 15 1.2.1.3 The Local Density Approximation . . . . . . . . . . . . . . . . . . . . . . 16 1.2.1.4 Beyond Local Density (the G-W Approximation) . . . . . . . . . . . . . . . 17 17 1.2.1.5 The Pseudopotential Method . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.2 Computational Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.2.2.1 Plane Wave Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 19 1.2.2.2 Localized Orbital Expansion . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.2.3 Empirical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.3.1 The Tight Binding Approximation . . . . . . . . . . . . . . . . . . . . . . 21 22 1.2.3.2 The Empirical Pseudopotential Method . . . . . . . . . . . . . . . . . . . . 1.3 Comparison with Experiments for Zinc Blende Materials . . . . . . . . 23 23 1.3.1 The General Shape of the Bands . . . . . . . . . . . . . . . . . . . . . . . 1.3.1.1 The Tight Binding Point of View . . . . . . . . . . . . . . . . . . . . . . . 23 1.3.1.2 The Empirical Pseudopotential Method . . . . . . . . . . . . . . . . . . . . 26 1.3.2 The k-p Description and Effective Masses . . . . . . . . . . . . . . . . . . 29 1.3.3 Optical Properties and Excitons . . . . . . . . . . . . . . . . . . . . . . . . 31 1.3.4 Ab Initio Calculations of the Excitonic Spectrum . . . . . . . . . . . . . . . 34 1.3.5 A Detailed Comparison with Experiments . . . . . . . . . . . . . . . . . . 34 1.4 Other Crystalline Materials with Lower Symmetry . . . . . . . . . . . . 36 1.4.1 General Results for Covalent Materials with Coordination Lower than Four . . . . . . . . . . . . . . . . . . . . . . 36 1.4.2 Chain-Like Structures Like Se and Te . . . . . . . . . . . . . . . . . . . . . 37 1.4.3 Layer Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1.4.4 New Classes of Materials: the Antimony Chalcogenides . . . . . . . . . . . 39

2 1.5 1.5.1 1.5.2 1.5.3 1.5.4 1.6 1.6.1 1.6.2 1.7 1.7.1 1.7.2 1.7.3 1.7.4 1.8

1 Band Theory Applied to

Semiconductors

Non-Crystalline Semiconductors . . . . . . . . . . . . . . . . . . . . . . 44 The Densities of States of Amorphous Semiconductors . . . . . . . . . . . . 44 Numerical Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Dangling Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 The Case of SiO. Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Disordered Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Definitions of the Different Approximations . . . . . . . . . . . . . . . . . 52 The Case of Zinc Blende Pseudobinary Alloys . . . . . . . . . . . . . . . . 54 Systems with Lower Dimensionality . . . . . . . . . . . . . . . . . . . . 57 Qualitative Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 The Envelope Function Approximation . . . . . . . . . . . . . . . . . . . . 59 Applications of the Envelope Function Approximation . . . . . . . . . . . . 61 Silicon Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

List of Symbols and Abbreviations

List of Symbols and Abbreviations lattice parameter basis vector of the unit cell bandgap energy conduction-band and valence-band energy electron charge envelope function reciprocal lattice vector resolvent operator hamiltonian Planck constant elements of the hamiltonian total angular momentum joint density of states wave vector orbital angular momentum optical matrix element effective mass density of states momentum vector momentum of electron and hole matrix element of the momentum operator spin vector kinetic energy transfer matrix Bloch's function potential crystaI volume perturbation coupling constant splitting energy energy of the state n real and imaginary part of the dielectric constant wave length frequency self-energy operator conductivity atomic states wave function volume of the unit cell atomic volume frequency

3

4

ATA a-Si, c-Si CPA DOS EMA EMT EPM EPR ESR ETB EXAFS HOMO LCAO LDA LUMO MCPA TBA UPS VCA VSEPR XPS


average t matrix approximation amorphous and crystalline silicon coherent potential approximation density of states effective mass approximation effective mass theory empirical pseudopotential method valence pair repulsion electron spin resonance empirical tight binding extended X-ray fine structure highest occupied molecular orbital linear combination of atomic orbitals local density approximation lowest unoccupied molecular orbital molecular coherent potential approximation tight binding approximation ultraviolet photoemission spectroscopy virtual crystal approximation valence shell electron pair repulsion X-ray photoemisssion spectroscopy

1.1 General Principles

1.1 General Principles The aim of this chapter is to establish the basic principles of the formation of bands in solids. To do this we start with a one-dimensional square well potential which we consider as a simplified description of an atom. We then bring two such square wells into close contact to simulate the behavior of a diatomic molecule. This can be generalized to include a large number of square wells to illustrate the concept of energy bands corresponding to the one-dimensional model of the free electron gas. These results are shown to be independent of the boundary conditions, allowing us to use Born von Karmann cyclic conditions and to classify the band states in terms of their wave vectors. Such a simple description does not take into account the spatial variations of the true potential in crystalline solids. However, the free electron gas results can be generalized through the use of Bloch's theorem which allows the classification of all energy bands in terms of their wave vectors, the periodic boundary conditions imposing that the allowed energy values be infinitely close together. This does not hold true, however, in nonperiodic systems such as amorphous solids and glasses. However, we show that, in this case, although general considerations impose the existence of bands, these can contain two types of states with localised or delocalised behavior. This represents the fundamental difference between nonperiodic systems and crystalline materials. A final situation of practical interest is the case where a slowly varying potential is superimposed on a rapidly varying crystal potential. Such cases can be treated in a simple and very efficient manner by the effective mass theory (EMT), also termed the envelope function approximation. The best known applications of the EMT correspond

5

to hydrogenic impurities in semiconductors and, more recently, to various kinds of system involving semiconductor heterojunctions, which will be discussed in Sec. 1.7.

1.1.1 From Discrete States to Bands We want to describe here in the simplest way the basic phenomena which occur when atoms are brought close to each other to form a solid. To do this, the attraction potential of the free atom is represented by a one-dimensional square well potential and the main trends concerning its energy levels and wave function are analyzed. We first consider the square well potential of Fig. 1-1, with depth V, and width a. We assume a to be of atomic dimensions (i.e., a few A)and take V, to be large enough for the energy E of the lowest states to be such that E ~ V ,In. such cases these lowest states are close to those of an infinite potential, i.e., their wave functions and energies E,, are given by:

vn

v,, - sin k,, x En

pt2 -kn2 2m

nn --

( n = 1,2, ...) a the allowed values k, of the one-dimensiona1 wave vector k practically corresponding k,,

I" Figure 1-1. One dimensional square well potential of height V , and of width a.

6


to vanishing boundary conditions at x = 0 and a. For a typical atomic dimension of a = 3 A, the distance in energy between the lowest two levels is of the order of 10 eV, typical of the values found in atoms. Of course the values of the excited states cannot correspond to what happens to true three-dimensional potentials, but this will not affect the main qualitative conclusions derived below. Let us now build the one-dimensional equivalent of a diatomic molecule by considering two such potentials at a distance R (Fig. 1-2). We can discuss qualitatively what happens by considering first the infinitely large R limit where the two cells can be treated independently. In this limit, the energy levels of the whole system are equal to those of each isolated well (i.e., E l , E2 ...) but with twofold degeneracy since the wave function can be localised on one or the other subsystem. When R is finite but large, the solutions can be obtained using the first order perturbation theory from those corresponding to the independent wells. This means that the twofold degenerate solutions at E l , E2 ... will exhibit a shift and a splitting in energy resulting in two sublevels of symmetric and antisymmetric character. This shift and splitting will increase as the distance R decreases. Such a behavior is pictured in Fig. 1-3, from R = 03 to the limiting case where R = a. This case is particularly easy to deal with since it corresponds to a single potential well but

r

a

R

0

Figure 1-2. The double well potential as a simple example of a molecule.

1

- - - - - -- - - - _ - - --------_

--- -

/

/ - -

I-

321a

-R

Figure 1-4. Formation of bands for a Kronig-Penney model where a is the well width and R the interwell distance.

of width 2 a instead of a . The consequence is that one again gets the set of solutions Eq. (1-l), but the allowed values of k, are closer together with an interval n / 2 a instead of n/a. This means that the number of levels is multiplied by two as is apparent in Fig. 1-3. The generalization to an arbitrary number N of atoms is obvious and is pictured in Fig. 1-4. At large inter-well separation R, the degeneracy of each individual level E l , E2 ... is N . At closer separation, these Ievels shift and split into N distinct components. When R = a one recovers one single well of width N u , which means that the allowed values of k, are now separated by n / N a . For a crystal, N becomes very large


(or order lo7 for a 1D system) and these allowed values form a “pseudocontinuum”, i.e., a set of discrete values extremely close to one another. The same is true of the energy levels whose pseudocontinuums can either extend over the whole range of energies (the case R = a in Fig. 1-4) or more generally ( R > a) are built from distinct groups of N levels. These groups of N levels are always contained in the same energy intervals irrespective of the value of N . They are called the allowed energy bands, the forbidden regions being called gaps. These qualitative arguments can be readily generalized to realistic atomic potentials in three dimensions. One then gets a set of allowed energy bands which contain a number of states equal to the number of atoms N times an integer. These bands are, in general, separated by forbidden energy gaps.

1.1.2 Bloch Theorem for Crystalline Solids For crystals it is possible to derive fairly general arguments concerning the the properties of the allowed energy bands. Before doing this let us come back to our simplified model of N square wells in the situation R = a where one gets a single well of width N a . We have seen that the states are completely characterized by the allowed values k, of the wave number k which are equal to n xlNa with n > 0. It is to be noted, however, that even this simple model contains complications due to the existence of boundaries or surfaces. It is the existence of these boundaries that lead to solutions having the form of stationary waves sin(kx) instead of propagating waves exp(i kx) which are mathematically simpler (the sine function is a combination of two exponentials). Of course the increased mathematical complexity of the vanishing boundary conditions is not very important for this particu-

7

lar one-dimensional problem, but it becomes prohibitive in real cases where one has to deal with the true surfaces of a threedimensional material. If one only needs information about volume properties it is possible to avoid this problem by making use of Von Laue’s theorem which states that perturbations induced by surfaces only extend a few angstroms within the bulk of the material. This means that for large systems, where the ratio of the numbers of surface to volume atoms tends to zero, volume properties can be obtained by any type of boundary conditions even if they do not seem realistic. In that respect, it is best to use Born von Karman’s periodic conditions in which one periodically reproduces the crystal under study in all directions, imposing that the wave function has the same periodicity. One then gets an infinite periodic system whose mathematical solutions are propagating waves. For instance, the linear square well problem with R = a becomes a constant potential extending from minus to plus infinity. Its solutions can be taken as:

2nn k, =L

( n% 0 integer)

They are mathematically different from Eq. (1-1) but they lead to the same answer for physical quantities. For instance, the interval between the allowed values of k is larger by a factor of two but this leads to the same density of states (number of levels per unit energy range) because the states are twofold degenerate (states with opposite values of k give the same energy). One can also show that the Fermi energy and electron density are identical in both cases.

8


The results given by Eq. (1-2) can be generalized to real crystalline solids through the use of the Bloch theorem. Such solids are characterized by a periodically repeated unit cell and, with Born von Karman boundary conditions, they have translational periodicity which greatly simplifies the mathematical formulation of the solutions. Let us then consider a three-dimensional crystal for which one has to solve the one-electron Schrodinger equation: H

3P)= E 3w

(1-3)

where r is the electron position vector. If we call aj the basis vectors of the unit cell, the fact that the system has translational symmetry imposes that:

I 3 (r+aj)12= I 3 (r)12

(1-4)

which, for the wave function itself, gives:

3 (r+ aj) = exp (i ‘pj) 3 ( r )

(1-5)

If we now consider a translation by a vector R

R = C mj aj j

mj being integers, we automatically get the condition:

which defines a new function uk (r). The direct application of a translation R to this expression leads to: (1-10)

qk(r + R ) = exp [i k (r + R ) ] uk (r + R)

and a comparison with Eq. (1-8)automati cally leads to: Uk

(r + R ) = uk ( r )

(1-11

i.e., that the function uk (r)is periodic. Equations (1-9) and (1- 11) constitute Bloch’s theorem, which states that the eigenfunctions can be classified with respect to their wave vector k and written as the product of a plane wave exp(ikr) times a periodic part. They are thus propagating waves in the crystal lattice. This is a generalization of the one-dimensional case discussed above. If one injects qk(r)into Schrodinger’s equation Eq. (1-3), then the eigenvalue will become a continuous function E ( k ) of the wave vector k . However, the vector k can only take allowed values chosen in such a way that qk(r)satisfies the boundary conditions, which are:

3k (r + Nj aj>= 3 k (r)

(1-12)

where Nj is the number of crystal cells along

aj . Using Eq. (1-9) and Eq. (1-1 1) this im-

poses the conditions:

The phase factor in Eq. (1-7) is a linear function of the components of R and can be written quite generally under the simpler form k R , leading to:

qk(r + R ) = exp (i k * R ) qk(r)

(1-8)

where k is such that k . aj is equal to (in this expression we have indexed the wave function by its wave vector k). To exploit Eq. (1-S), which is a direct consequence of translational invariance, we can write without loss of generality:

qk(r)= exp (i k - r ) uk (r)

(1-9)

(1-13) where nj is an integer. These allowed values can be expressed more directly with the help of the basis vectors of the reciprocal lattice a? defined by: a?

a, = 2 n

SjL

(1-14)

which leads to: (1-15)

1 . 1 General Principles

This again generalizes the one-dimensional situation described by Eq. (1 -2) to any real crystal in I-, 2-, or 3-dimensions. As a conclusion Bloch’s theorem leads us to write the wave function as a plane wave exp (i k .r ) modulated by a periodic part. Its energy E ( k ) is a continuous function of the wave vector k . This one takes discrete values which form a pseudocontinuum. The allowed energies will then be grouped into bands as discussed more qualitatively in the previous section. A final point is that one can show that the energy curves E ( k ) and Bloch functions qk(r)are periodic in reciprocal space. One then gets the complete information about these quantities from their calculation for k points lying in one period of the reciprocal lattice. From the symmetry properties ( E ( k )= E ( - k ) ) it is better to use the period symmetrical with respect to the origin, called the first Brillouin zone.

1.1.3 The Case of Disordered Systems Different varieties of solids exist which do not exhibit the long range order characteristic of perfect crystals. They differ qualitatively among themselves by the nature of their disorder. A simple case is the alloy system where one can find either A or B atoms on the sites of a perfect crystalline lattice. This kind of substitutional disorder is typical of the ternary semiconductor alloys Gal,A1,As where the disorder only occurs on the cationic sites. We shall deal in more detail with this problem in Sec. 1.6. Other cases correspond to amorphous semiconductors and glasses which are characterized by a short range order. For instance, in a-Si, the silicon atoms retain their normal tetrahedral bonding and bond angles (with some distortions), but there is a loss of long range order. A lot of covalently-bonded systems (with coordination numbers small than 4) can be found in the amorphous or

9

glassy state. All have a short range order and moderate fluctuations in bond length, but in some cases they can have large fluctuations in bond angles. In all these situations, even for the disordered substitional alloy, it is clear that one cannot make use of Bloch’s theorem to classify the band states. We could even ask ourselves if the concept of energy bands still exists. The simplest case demonstrating this point again corresponds to the one-dimensional system with square well potentials. We can simulate a disordered substitutional alloy by considering square wells of width a as before, and of depth VA for A atoms and VB for B atoms, with VA> VB. We also assume that the interwell distance is R = a to get the simplest situation. If the material were purely B then one would get a constant potential which we take as the origin of energies. Thus each time one substitutes an A atom for a B one this results in an extra potential well of width a a depth VA- V,. Two A neighbors lead to a well of width 2 a, and a cluster of M A neighbors gives a well of width M a (Fig. 1-5). The alloy will consist of a distribution of these potential wells separated by variable distances. It is interesting to investigate the nature of the states for such a problem. The simplest case corresponds to energies E > 0, where the states have a propagating behavior and there are solutions at any positive value of E. The existence of boundary conditions due to the fact that the system contains a finite but large number N of atoms

o

f)

P

20

Figure 1-5. Simple representation of a disordered binary alloy with square well potentials of width a for one impurity, 2a for a pair, etc.

10


will simply transform this continuum of states into a pseudocontinuum. This results in a band of “extended states’’ for E > 0. The situation for E < 0 is drastically different. An isolated impurity A, represented by a single well, gives at least one energy level at E , , or even more at E2, E,, etc. The corresponding wave function is localized and decays exponentially as exp (- k Iz I) where k =

Jg.

Clusters of M atoms

lead, as described before, to denser sets of levels in the well since the interval between allowed k values is divided by M . In particular, for a very large cluster, one obtains a pseudocontinuum of levels, the lowest one being infinitely close to the bottom of the potential well. One has thus a statistical distribution of potential wells of varying width giving rise to a corresponding distribution of levels located between E = 0 and E = - (V,- VB). Again this leads to pseudocontinuum of levels. Furthermore, there is the possibility of interaction between the potential wells when these are close enough. This also acts in favor of a spread in energy levels. The states in the potential wells can have a more or less localized character depending on the distance between the wells. We shall discuss this problem later. The conclusion of this simple model is that the occurrence of disorder, at least in somes cases, also leads to the existence of a pseudocontinuum of states, even if Bloch’s theorem does not apply. Of course we have only discussed one particular model. We shall later discuss other cases of disorder or randomness which also lead to the existence of well-defined energy bands. 1.1.4 The Effective Mass Approximation (EM4 Interesting cases that often occur in practice correspond to the application of a po-

tential slowly varying in space to a crystalline solid. Such situations can be handled relatively easily without solving the full Schrodinger equation, by using the so called “effective mass approximation“. One major field of application has been the understanding of hydrogenic impurities in semiconductors (for reviews see Bassani et al., 1974; Pantelides, 1978). More recently the same method, often called “the envelope function approximation”, has been applied to the treatment of semiconductor heterojunction and superlattices as will be discussed in Sec. 1.7.

1.1.4.1 Derivation of the Effective Mass Approximation for a Single Band Let us begin with the simplest case of a crystal whose electronic structure can be described in terms of a single energy band, the solution of the perfect crystal Schrodinger equation:

H , % (r)= E (W % (r)

(1-16)

If a perturbative potential V ( r )is applied to the system we can describe a solution of the perturbed system $J (r)as a linear combination of the perfect crystal eigenstates ( k belonging to the first Brillouin zone), (1-17) and obtain the unknown coefficients by projecting the new Schrodinger equation, (Ho + v> $J 0.1 = E $J (r)

(1-18)

onto the basis states (pk (r).This immediately leads to the set of linear equations:

E(WdW+X

(pk+w=Ea(k) (1-19) At this stage we need to simplify the matrix elements of V,otherwise it is impossible to k‘

(Vkl VI

1 . 1 General Principles

go further, except numerically. We use the fact that the % (r)are Bloch functions, cpk

(r)

( 1-20)

uk (r)

and express the potential matrix element as: (1-21)

((PkIVI Q)k’)=

=J ~

(k’ - k ) . r

(

~

1

U $ ( r ) uk* (r)d3 r

In view of the Bloch theorem the product u$ uk,is a periodic function of r and we can expand it in a Fourier series, 1

uz ( r )ukt ( r )= -

V G

c k , k * ( G )eic.r

(1-22)

where v is the crystal volume and G are the reciprocal lattice vectors. The matrix element Eq. (1-21) can thus be expressed exactly as: ( 1 -23 a) c k , k ’ ( G ) V ( k ’ + G -k) ( q k VI Q ) k ’ ) =

I

G

1

V ( q ) = - I e i q ‘ rV ( r ) d r

(1-23 b)

V

At this level we must make some assumptions about V ( r ) . The first one is that it varies slowly in space (i.e., over distances which are large compared to the size of the unit cell). This means that its Fourier transform decreases very rapidly with the modulus of the wave vector, i.e., that one can neglect terms with G#O in Eq. (1-23) and, also, that only terms with k ’ = k will effectively contribute. We now make the second central assumption of the EMA, that we look for solutions whose energy E is close to a band extremum k,. If this is so, only states with k = k , will have a ( k ) sensibly different from zero in Eq. (1-19). This means that one can rewrite Eq. (1-19) using Eq. (1-23) under the approximate form: ( 1 -24) E ( k ) a ( k ) + xC k o , k o ( 0 ) V ( k ’ - k ) a ( k ’ ) = O k’

11

However, c k o , k o ( o ) has an important property: it is given by the following integral over the crystal volume

c k o , k o ( o ) = s u i 0 ( r )uko(r) d3 r = = J qzo(r)a k o ( rd3) r = 1

( 1 -25)

in view of the fact that the wave functions % (r),are normalized. The final form of the EMA equation is thus (1-26) E ( k ) a ( k ) + xV ( k ’ - k ) a ( k ’ ) = E ~ ( k ) k’

It is interesting to derive a real space equation from this by Fourier transforming Eq. (1-26). To perform this we must take into account the fact that the function a ( k ) is strongly peaked near k,. We thus introduce the following Fourier transform:

F(r)=Cu(k)exp(i(k-ko).r)

(1-27)

k

such that F ( r ) varies slowly in space when a ( k ) only takes important values in the vicinity of k=k,. To get an equation for F ( r ) we multiply Eq. (1 -26) by exp i (k-k,) . r and sum over k , assuming that one makes a negligible error in the potential term by extending the summation over k to the whole space. This leads to the real space equation: { E(k,-i

V,)+ V ( r ) }F ( r ) = E F ( r ) (1-28)

This is a differential equation in which the operator k, -i V, has been substituted for k in the dispersion relation E ( k ) . As we have seen, the function F ( r ) is likely to vary slowly withr(ora(k) #Oonlyfork=ko)so that one can expand E ( k ) to the second order in the neighborhood of k - k,. Calling a the principal axes of this expansion we have: A2 E ( k ) -- E ( k 0 ) + -( k , - k ~ , )(1-29) ~ a 2m,

x

which defines the effective masses ma along direction a.This allows us to rewrite

12


-

scaled parameters e2 e2/e and m --z m *. This leads to a set of hydrogenic levels with

Eq. (1-28) as:

an effective Rydberg

=IE-E(ko)IF(r) which represents the usual form of the EMA equation as derived by many authors (Bassani et al., 1974; Pantelides, 1978). It is interesting to examine the meaning of the function F ( r ) .To do this we start from the expansion Eq. (1-17) of w(r), express the q k ( r ) as in Eq. (1-20) and factorize eiko.r . This gives k

As a ( k ) is peaked near k,, we approximate Uk( r ) by its value at k,, which leads us directly to:

w (r)= F ( r ) (PRO (r)

(1-32)

This means that ( r )can be rewritten as the product of the Bloch function (which varies over a length typically of the order of the interatomic distances) times a slowly varying “envelope function”. The advantage of the EMA is that one directly obtains F ( r ) from a Schrodinger-like equation involving the effective masses.

1.1.4.2 Applications and Extensions The first well known use of the EMA was for hydrogenic impurities in semiconductors. If we treat single donor substitutional impurities, like As in Si or Ge for instance, the excess electron will see an attractive potential roughly given by -e2/&r (where E is the dielectric constant), which one considers as slowly varying. This can stabilize levels in the gap in the proximity of the bottom of the conduction band E,. For a single minimum and an isotropic effective mass one gets an hydrogenic-like equation with

m*e4

which, for 2A2 E2 typical values of m*=0.1 and & = l o ,becomes of order 14 meV, i.e., fairly small compared to the band gap. This result correctly reproduces the order of magnitude found in experimental data. However, to be truly quantitative, the EMA must in many cases satisfy the following requirements: ~

- It must include the effective-mass anisotropy when necessary. This has been done in Faulkner (1968, 1969), one effect being the splitting of p states, for instance. - It must also properly include the valleyvalley interactions when there are several equivalent minima. This can be done, for instance, by first order perturbation theory on degenerate states (since there are as many identical impurity states than there are minima). With these improvements the EMA theory has achieved considerable success for single donor impurities, especially for excited states (see Bassani et al., 1974); Pantelides, 1978) and Table 1-1 for reviews. Only the ground state is found to depart significantly from the predicted levels at this stage of the theory. This is due to the deviations of the potential from its idealized form -e2/&r in the impurity cell. The corresponding correction is known as the chemical shift. It is also possible to treat more exactly the many-valley interactions by recently derived methods described in Resca and Resta (1979, 1980). The case of acceptor states derived from the valence band is more complicated. This is due to the threefold degeneracy of the top of the valence band. This means that (r) must be written as a combination of the

13


Table 1-1. Comparison between theoretical and experimental energy spacing (cm-’) for donor impurities in silicon. The theoretical values are taken from Faulkner (1968,1969). (The spacing between excited states, independent of the ground state position, is more suitable than the observed position of the transition from the ground state to perform a comparison with the theory since this ground state is not hydrogenic.) Transition

Theory

P

As

Sb

2 P, -2 Po 3 Po -2 Pi 4 Po -2 P+ 3 P, -2 P, 4 P* -2 P* 4 f, -2 f, 5 p, -2 f, 5 f, -2 p* 6 Pt -2 P i 3 s -2p* 3 43 -2 Pi 4 s -2P* 4 fo -2 P* 5 Po -2 Pi 5 Po -2 P i 6 ht -2 P,

5.11 0.92 3.07 3.29 4.22 4.5 1 4.96 5.14 5.36 0.65 2.65 3.55 4.07 4.17 4.77 5.22

5.07 0.93 3.09 3.29 4.22 4.51 4.95 5.15 5.32

5.1 1 0.92 3.10 3.28 4.21 4.49 4.94 5.14 5.32

5.12 0.91 3.07 3.29 4.21 4.46 4.92 5.31

2.64 4.08 4.17 4.76 5.52

+cV ( k ’ - k ) q ( k )= E q ( k )

Zhij ( k ) U j ( k )

k’

j

(1-34)

Now one can define slowly vaying functions F;. (r) by the Fourier transformation Eq. (1 -27) from ai(k) with k = 0 and get the generalization of Eq. (1-28):

Z hij ( - iV,)Fj(r)+ V(r)F;( r )= E 6 ( r ) .l

4.70

Bloch states ( ~ , , ~ (with ( r ) n = 1, 2, 3) belonging to each of the three energy branches E, (k).The first part of the derivation proceeds as for a single band and the generalization of Eq. (1-26) becomes:

E , , ( k ) a , ( k ) + C V ( k ’ - k ) a , ( k ’ ) =E a , ( k ) k’

the quantities that can be expanded to second order in k are the elements hjj(k)of a 3 x 3 matrix (6 x 6 if spin orbit is included (Kane, 1956, 1957; Luttinger and Kohn, 1955; Luttinger, 1956)) whose eigenvalues are the E,(k). Considering the a,(k) as the components of a 3-component column vector ( n = 1,2,3) expressed on the basis of the eigenvectors of hij(k),it is advantageous to rewrite Eq. (1-33) using the natural basis states of hij(k).This leads to

(1 -35)

As the h, are of second ord in k , this represents a set of coupled second order differential equations whose solution will lead to the expression of the envelope functions. Finally, in this approximation, the total wave function q (r)becomes, by using the basis set corresponding to h,:

(1-36) jk

which, if only k 2:0 is involved, becomes

(1-33)

(1-37)

This equation is diagonal in n and is apparently a simple to solve as for the single band extremum. However, the difficulty is to proceed further and transform it to a real space equation as in Eq. (1-28). The reason is that one can no longer define the derivatives of E,(k) near the valence band maximum at k = 0. This will be shown in detail in Section 1.3.2, following Kane’s derivation (Kane, 1956, 1957) in which it is shown that

We do not discuss here the application of the method to hydrogenic acceptor states (details can be found in Bassani et al., 1974; Pantelides, 1978). We shall later see its use in quantum wells and superlattices. In such cases, the application of the envelope function approximation is complicated by the problem of boundary conditions which we discuss in Sec. 1.7.

14


1.2 The Calculation of Crystalline Band Structures We have seen that, for crystalline solids, the use of Bloch’s theorem allows us to demonstrate quite generally the existence of energy bands. However, in its derivation we have made the implicit assumption that one could write a Schrodinger equation for each electron taken separately. Of course this is in principle not permissible in view of the existence of electron-electron interactions and one should consider the N electron system as a whole. It has been shown that one can generalize the Bloch theorem to the one particle excitations of crystalline manyelectron systems. However, when this is done there is no exact method available to calculate these excitations (which correspond to the energy bands) in practice. One is left with approximate methods which are all based on the reduction of the problem to a set of separate one particle equations whose eigenvalues are used to compare the experimental one particle excitations. First, we thus give a brief account of most one-electron theories that have been used so far: Hartree, Hartree-Fock, local density, etc. We also discuss recent advances which have allowed to considerably improve the local density results (the so-called “G-W approximation”, which consists in a first order expansion of the electron self energy in terms of the screened electron-electron interaction). Usually, it is not necessary to include core electrons in calculations involving properties of the valence electrons. To achieve this separation one replaces the true atomic potentials by “first principles pseudopotentials” of which we give a short description. All this completely defines the single particle equations and, in Sec. 1.2.2 we present some techniques that can be used for their resolution. These techniques often involve a substantial amount of computa-

tion but they can be applied to simple crystals such as the zinc-blende semiconductors. However, there is a need for simpler empirical methods, either for physical understanding or as simulation tools for more complex systems. We describe two such methods in Sec. 1.2.3: the empirical pseudopotential method (EPM) and the empirical tight binding approximation (TBA).

1.2.1 Ab Initio Theories We describe here some basic methods that lead to approximate single particle equations. We begin with the Hartree approximation which is the simplest to derive and illustrates the general principles that are applied. We then discuss the Hartree-Fock approximation, local density theory, and its recent improvements via the G-W approximation.

1.2.1.1 The Hartree Approximation The full N electron Hamiltonian (for fixed nuclei) can be written: ( 1 -38)

where the hi are independent individual Hamiltonians containing the kinetic energy operator of electron i as well as its attraction by the nuclei. The second term in Eq. ( 1-38) represents the electron-electron interactions, rG being the distance between electrons i andj. If one could neglect these, the problem would be exactly separable, i.e., one could obtain the solution of the full problem by simply solving the individual Schrodinger equations,

hi vfii(ri)= &ni vfii(ri),

( 1 -39)

the full wave function being a product of individual wave functions (if one forgets for the moment the fact that it must be anti-

1.2 The Calculation of Crystalline Band Structures

symmetric) and the total energy being the sum of individual energies. The inclusion of the electron-electron interactions prevents the problem from being separable. However, one can find approximate individual equations by using a trial wave function (in the variational sense) which is of a separated form, i.e., it is a simple product of individual functions. For N electrons this gives

v @ I . ..rN) = n q n i (c)

( 1-40)

ni

The unknown wave functions can be obtained by using the variational method, i.e., by minimizing the average value of H with respect to the qni.This leads to a set of individual equations which are the Hartree equations. However, these can be obtained directly by the following simple physical argument. If the problem can be separated, then the Hamiltonian of electron i will consist of the sum of its kinetic energy operator, its potential energy in the field of the nuclei, and its potential energy of repulsion with other electrons. This leads to the Schrodinger equation:

where the second term in the Hamiltonian represents the average electrostatic repulsion exerted on electron i by all the other electrons. There are as many equations (1-41) as there electrons, i.e., N . Each oneelectron Hamiltonian contains the wave functions of the other electrons which are unknown. One has thus to proceed by iterations until a self-consistent solution is found, i.e., the wave functions injected into the hamiltonian are the same as the solutions of Eq. (1 -41). The Hartree approxima-

15

tion has been used in understanding the basic physics of atoms. It is not refined enough to be used for actual band structure calculations.

1.2.1.2 The Hartree-Fock Approximation The main drawback of the Hartree approximation is that its wave function is not properly antisymmetrized. If one wants to use a trial function corresponding to independent electrons one cannot make use of a simple product of individual wave functions but instead one must consider a Slater determinant of the form

q ( r l ... r N ) =

(1 -42)

The variational method can be applied in exactly the same way as the Hartree method. However, it is not longer possible to get the one-electron equations using a simple argument. The application of this technique leads directly to:

=Eqn,(~.)

( 1 -43)

The result is the Hartree contribution plus a correction factor, the exchange term, due to antisymmetry in the electron permutations. It is important to notice that the qni(ri) are “spin orbitals”, i.e., products of a spatial part multiplied by a spin function (Slater, 1960). This is fundamental in order to maintain the Pauli principle.

16


The Hartree-Fock method is not very easy to apply numerically in view of the complexity of the exchange terms. Its application to covalent solids like diamond or silicon (Euwema et al., 1973; Mauger, Lannoo, 1977) leads to the overall correct shape of the energy bands, but a large overestimation of the forbidden gap. For instance, one gets 12 eV and 6 eV for diamond and silicon respectively compared to the experimental values of 5.4 eV and 1.1 eV respectively. Improvements on the Hartree-Fock approximation can be made including what are called correlation effects.

1.2.1.3 The Local Density Approximation The local density approximation is an extension of the Thomas-Fermi approximation based on the Hohenberg and Kohn theorem (Hohenberg and Kohn, 1964) which shows that the ground state properties of an electron system are entirely determined by the knowledge of its electron density @ (r).The total energy of the interacting electron system can be written: (1-44)

where T represents the kinetic energy, the second term gives the electrostatic interelectronic repulsion, Vex, is the potential due to the nuclei, and Ex,is the exchange correlation energy. A variational solution of the problem (Kohn and Sham, 1965) allows us to derive a set of one particle Schrodinger equations of the form:

with t representing the one electron kinetic energy and @(‘)=

c

I4Jk(‘)I2

(1 -46)

occupied k

The practical resolution of Eqs. (1-45, 1-46) is, as we will discuss later, usually performed by replacing the atomic potentials by pseudopotentials, avoiding the explicit consideration of atomic core states. Originally these pseudopotentials were treated empirically, but now methods exist which allow us to determine them quantitatively from the properties of the free atoms (Hamann et al., 1979).The knowledge of these pseudopotentials plus the local density treatment allows a complete determination of the solutions q k of Eq. (1-45). The wave functions q k can be calculated either using an expansion in plane waves or in orbitals localized on the atoms. Equations (1-45) and (1-46) have to be solved in a self-consistent way. Up to now this formulation has been exact, the problem is that the quantity Exc,and thus V,,, is not known in general. The local density approximation then is based on the assumption that, locally, the relation between Ex, and @(r)is the same as for a free electron gas of identical density, which is known quite accurately. This approximation turns out to give satisfactory results regarding the prediction of the structural properties of molecules and solids. For instance, in solids (either with sp bonds or d bonds, as in transition metals) the cohesive energy, the interatomic distance, and the elastic properties are predicted with a precision better than 5% in general. This remains true for diatomic molecules, except that the binding energy is overestimated by about 0.5 to 1 eV (see Cohen, 1983; Schluter, 1983 for recent reviews on the subject).

17


It is tempting to use the differences between the eigenvalues of Eq. (1-45) as particle excitation energies. This is not justified in general as seen by the predicted values for the energy gap E ~ = E ~ - E “ in semiconductors and insulators, taken as the difference in the energies cC of the first empty state and E~ of the last filled state. The local density value of E~ is always found to be substantially smaller than the experimental (Hamann, 1979). It is equal to 0.6 eV for silicon instead of 1.2 eV and even vanishes for germanium. The origin of the errors cannot be traced to the use of an overly simplified exchange and correlation potential such as LDA. This has been clearly shown by the almost identical results obtained using an improved exchange-correlation potential. The exchange-correlation term thus cannot be reduced to a simple local potential.

1.2.1.4 Beyond Local Density (the G-W Approximation) To correct for the deficiencies of local density in defect calculations, one simple approach has been to use a “scissors” operator (Baraff and Schluter, 1984) which corrects for the band gap error by using a rigid shift of the conduction band states. It was later shown (Sham and Schluter, 1985, 1986; Perdew and Levy, 1983; Lannoo and Schluter, 1985) that this procedure was closer to reality than expected, since the one electron exchange correlation potential of the local density formalism must experience a discontinuity across the gap. This is correctly handled by the scissors operator for bulk semiconductors but the applicability of the scissors operator to the defect levels is still questionable. In particular, in the case of extended defects such as surfaces, it is doubtful that the defect states are correctly obtained. The advantage of this correc-

tion is mainly that it does not add any computational requirements when compared to conventional LDA calculations. A more sophisticated way of improving the density functional theories is to evaluate the electron self-energy operator C(r,r ’, E ) (Lannoo and Schluter, 1985; Hybertsen and Louie, 1985; Godby, 1986). This Ccontains the effects of exchange and correlation. It is non-local, energy-dependent, and non-hermitian. Its non-hermiticity means that the eigenvalues of the new one particle Schrodinger equation, (t+

vest

+ V,)

W n M

+

(1-47)

+ I dr’ z(rir ’ r Erik) q n k ( r ’ ) = Erik qnk(r)

will generally be complex. The imaginary part gives the lifetime of the quasiparticle, and V , is the Hartree-potential. The self-energy operator can be estimated using the G-W approximation (Hedin and Lundquist, 1969). The self-energy is expanded in a perturbation series of the screened Coulomb interaction, W The first term of the expansion corresponds to the Hartree-Fock approximation. Details can be found in Lannoo and Schluter (1985); Hybertsen and Louie (1985); Godby et al. (1986, 1987); Hedin and Lundquist (1969). These early works have been completed by more recent calculations (Rohlfing et al., 1993; Northrup et al., 1991; Northrup, 1993; Blase et al., 1994). The results show a great improvement on the values predicted for the gap of semiconductors as evidenced in Louie (1996).

1.2.1.5 The Pseudopotential Method The full atomic potentials produce strong divergences at the atomic sites in a solid. These divergences are related to the fact that these potentials must produce the atomic core states as well as the valence states.

18


However, the core states are likely to be quite similar to what they are in the free atom. Thus the use of the full atomic potentials in a band calculation is likely to lead to unnecessary computational complexity since the basis states will have to be chosen in such a way that they describe localized states and extended states at the same time. Therefore it is of much interest to devise a method which allows us to eliminiate the core states, focusing only on the valence states of interest which are easier to describe. This is the basis of the pseudopotential theory. The pseudopotential concept started with the orthogonalized plane wave theory (Cohen et al., 1970). Writing the crystal Schrodinger equation for the valence states, ( T + V) Iq) = E

lq)

( 1 -48)

one has to recognize that the eigenstate 1111) is automatically orthogonal to the core states 1 c ) produced by the same potential V. This means that I q) will be strongly oscillating in the neighbourhood of each atomic core, which prevents its expansion in terms of smoothly varying functions, like plane waves, for instance. It is thus interesting to perform the transformation l111)=(1-P)l4

( 1-49)

where P is the projector onto the core states (1-50)

I 111) is thus automatically orthogonal to the

core states and the new unknown 19) does not have to satisfy the orthogonality requirement. The equation for the “pseudostate” 19) is: ( T + V)(1 - P ) ) q ) = E ( l - P ) ) q )

(1-51)

Because the core states Ic) are eigenstates of the Hamiltonian T + V with energy, E,,

one can rewrite Eq. ( -51) in the form

{T+ V+C(E-E,) C

4

(CI}

I d = E Id

(1-52)

The pseudo-wave function is then the solution of a Schrodinger equation with the same energy eigenvalue as 1111). This new equation is obtained by replacing the potential V by a pseudopotential V p s = V + C ( E - E J Ic)(cl c

(1-53)

This is a complex non-local operator. Furthermore, it is not unique since one can add any linear combination of core states to 1 q ) in Eq. (1-52) without changing its eigenvalues. There is a corresponding non-uniqueness in Vps since the modified 1 cp) will obey a new equation with another pseudopotential. This non-uniqueness in Vps is an interesting factor since it can then be optimized to provide the smoothest possible Iq), allowing rapid convergence of plane wave expansions for 19).This will be used directly in the empirical pseudopotential method. Recently, so-called “first principles” pseudopotentials have been derived for use in quantitative calculations (Hamann et al., 1979). First of all, they are ion pseudopotentials and not total pseudopotentials as those discussed above. They are deduced from free atom calculations and have the following desirable properties: (1) real and pseudovalence eigenvalues agree for a chosen prototype atomic configuration, (2) real and pseudo-atomic wave functions agree beyond a chosen core radius r,, (3) total integrated charges at a distance r > r, which agree (norm conservation), and (4)logarithmic derivatives of the real and pseudo wave functions and their first energy derivatives which agree for r > r,. These properties are crucial for the pseudopotential to have optimum transferability among a variety of chemical environments, allowing self-con-

19


sistent calculations of a meaningful pseudocharge density.

1.2.2 Computational Techniques We now will discuss some techniques which allow us to calculate energy bands in practice. They are simply based on an expansion of the eigenfunction of the one-electron Schrodinger equation in some suitable basis functions, plane waves, or localized atomic orbitals. These seem to be, by far, the most commonly adopted methods at this time.

obtained by mixing the plane wave eik only with other plane waves whose wave vector is k + G, where G is any reciprocal lattice vector, and not with all plane waves with arbitrary wave vectors. Of course, we are only interested in low lying states so that we can truncate the expansion of Eq. (1 -54) at some maximum value of IGI, which we label C,,,. The one particle Hamiltonian is thus expressed on this basis as a finite matrix of elements: ’

1.2.2.1 Plane Wave Expansion Plane waves form a particularly interesting basis set for crystalline band structure calculations in conjunction with the use of pseudopotentials. As we shall see below the total pseudopotential can be expressed as a sum of atomic contributions. These consists of a bare ionic part which will be screened by the valence electrons. The resulting atomic pseudopotentials are often assumed to be local, i.e. to be simple functions of the electron position. However, in general, they should be operators having a non-local nature, as discussed later. The best starting point is the expression Eq. (1-9) of the Bloch function in which one makes use of the fact that the function u k ( r ) is periodic and can thus be expanded as a Fourier series: Uk(r)

= cUk(G) eiG.r

(1-54 a)

G

where G are reciprocal lattice vectors. This leads to the natural plane wave expansion for the wave function: (pk ( r )= C U R (G) ei(k+ G ) ’ r

(1-54 b)

G

The gain due to the Bloch theorem is that ) wave vector k any Bloch state ~ ( rwith belonging to the first Brillouin zone is

which readily becomes

(1-55)

A2 2 H G , G ~= ( ~) I k + G 1 &,G* + V G , G * ( ~ ) 2m ( I -56) where the second term is the potential matrix element. In the case where Vis a simple function of r, this matrix element can be reduced to: V G , y ( k )= V(G’-G)

(1-57)

Such plane wave expansions can be used in different contexts. We will later develop an application known as the empirical pseudopotential method (EMP). One can also apply these expansions to first principles calculations. This is formally easy in the local density context where the potential takes a simple form. It becomes more complex, but still can be adapted, in the HartreeFock theory or even in the G-W approximation as used in Hybertsen and Louie (1985, 1986) and Godby et al. (1986).

1.2.2.2 Localized Orbital Expansion In this expansion the wave function is written as a combination of localized orbitals centered on each atom: ly =

c i,a

Cia Pia

(1 -58)

20


where qin is the athfree atom orbital of atom i, at position R j . As each complete set of such orbitals belonging to any given atom forms a basis for Hilbert space, the whole set of qiais complete, i.e., the viaare no longer independent and Eq. (1 -58) can yield the exact wave function of the whole system. In practice one has to truncate the sum over a in this expansion. In many simplified calculations it has been assumed that the valence states of the system can be described in terms of a “minimal basis set” which only includes free atom states up to the outer shell of the free atom (e.g., 2s and 2p in diamond). It is that description which provides the most appealing physical picture, allowing us to clearly understand the formation of bands from the atomic limit. The “minimal basis set” approximation is also used in most semi-empirical calculations. When the sum over a in Eq. (1-58) is limited to a finite number, the energy levels E of the whole system are given by the secular equation: det I H - E S I = O

(1-59)

where H is the Hamiltonian matrix in the atomic basis and S the overlap matrix of elements: Sia,j p = (Pi, I qjp)

(1 -60)

These matrix elements can be readily calculated, especially in the local density theory, and when making use of Gaussian atomic orbitals. The problem, as in the plane wave expansion, is to determine the number of basis states required for good numerical accuracy. An interesting discussion on the validity of the use of a minimal basis set has been given by Louie (1980). Starting from the minimal basis set 1 qia)one can increase the size of the basis set by adding other atomic states Ixi,), called the peripheral states,

which must lead to an improvement in the description of the energy levels and wave functions. However, this will rapidly lead to problems related to overcompleteness, i.e., the overlap of different atomic states will become more and more important. To overcome this difficulty, Louie proposes three steps to justify the use of a minimum basis set. These are the following:

1. Symmetrically orthogonalize the states I cp,) belonging to the minimal basis set between themselves. This leads to an orthogonal set 2. The peripheral states Ixip) overlap It is thus necesstrongly with the sary to orthogonalize them to these I &), which yield new states defined as:

laa). Ian). [xi,)

3. The new states I&) are then orthogonalized between themselves leading to a new set of states lfi,). Louie has shown that, at least for silicon, the average energies of these atomic states behave in such a way that, after step 3, the peripheral states lji,) are much higher in energy and their coupling to the minimal set is reduced. They only have a small (although not negligible) influence, justifying the use of the minimal set as the essential step in the calcuation. The quantitative value of LCAO (linear combination of atomic orbitals) techniques for covalent systems such as diamond and silicon was first demonstrated by Chaney et al. (197 1). They have shown that the minimal basis set gives good results for the valence bands and slightly poorer (but still meaningul) results for the lower conduction bands. Such conclusions have been confirmed by Kane (1976), Chadi (1977), and Louie (1 980) who worked with pseudopotentials instead of true atomic potentials.


The great asset of the minimal basis set LCAO calculations is that they provide a direct connection between the valence states of the system and the free atom states. This becomes still more apparent with the TBA (tight binding approximation) which we shall later discuss and which allows us to obtain extremely simple, physically sound descriptions of many systems.

1.2.3 Empirical Methods Up to very recently, first principles theories, sophisticated as they may be, could not accurately predict the band structure of semiconductors. Most of the understanding of these materials was obtained from less accurate descriptions. Among these, empirical theories have played (and still play) a very important role since they allow us to simulate the true energy bands in terms of a restricted number of adjustable parameters. There are essentially two distinct methods of achieving this goal: the tight binding approximation (TBA) and the empirical pseudopotential method (EPM).

1.2.3.1 The Tight Binding Approximation This can be understood as an approximate version of the LCAO theory. It is generally defined as the use of a minimal atomic basis set neglecting interatomic overlaps, i.e., the overlap matrix defined in Eq. ( 1 -60) is equal to the unit matrix. The secular equation thus becomes det ( H - E Z I = O

( 1 -62)

where I is the unit matrix. The resolution of the problem then requires the knowledge of the Hamiltonian matrix elements. In the empirical tight binding approximation these are obtained from a fit to the bulk band structure. For this, one always truncates the

21

Hamiltonian matrix in real space, i.e., one only includes interatomic terms up to first, second, or, at most, third nearest neighbors. Also, in most cases one makes use of a twocenter approximation as discussed by Slater and Koster (1954). In such a case, all Hamiltonian matrix elements (viaI H I qp) can be reduced to a limited number of independent terms which we can call H a b ( i , j ) for the pair of atoms (i,j) and the orbitals (a,p).On an “s, p” basis, valid for group IV, 111-V, and 11-VI semiconductors, symmetry consideration applied to the two-center approximation only give the following independent terms: Ha,p ( i * j )= Hss(i?j)*Hsu(i,j)y H u s ( i , j ) ( 1 -63) H,, H,, (U (

i

J

3

where H , is strictly zero in a two-center approximation and s stands for the s orbital, othe p orbital along axis i , j with the positive lobe in the direction of the neighboring atom, and n a p orbital perpendicular to the axis i, j . With these conventions, all matrix elements are generally negative. Similar considerations apply to transition metals with s, p, and d orbitals. Simple rules obtained for the H a b ( i , j ) in a nearest neighbor’s approximation are given in Harrison (1980). They are based on the use of free atom energies for the diagonal elements of the tight binding hamiltonian. On the other hand, the nearest neighbor’s interactions are taken to scale like d-2 (where d is the interatomic distance) as determined from the free electron picture of these materials which will be discussed later. For s, p systems, this gives

where d is expressed in A.

22


Such parameters nicely reproduce the valence bands of zinc-blende semiconductors but poorly describe the band gap and badly describe the conduction bands. Improvements on this description have been attempted by going to the second nearest neighbors (Talwar and Ting, 1982) or by keeping the nearest neighbors treatment as it is but adding one s orbital (labelled s*) to the minimal basis set (Vogl and Hjalmarson, 1983). The role of this latter orbital is to simulate the effect of higher energy d orbitals which have been shown to be essential for a correct simulation of the conduction band. The quality of such a fit can be judged from Fig. 1-6, which shows that the lowest conduction bands are reproduced much more correctly. Fairly recently it has also been shown that the replacement of s* by true d orbitals improves the simulation in a striking manner (Priester).

15

c va(r

j,a

- Rj - ra)

(1-65)

where j runs over the unit cells positioned at Rj and a is the atom index, the atomic position whithin the unit cell being given by ra. Let us first assume that the v, are ordinary functions of r, or, in other words, that we are dealing with local pseudopotentials. In that case the matrix elements [Eq. (1-57)] of V between plane waves become:

5

a -5 -1c

W

One advantage of the tight binding approximation is that it provides a natural way of relating the electronic properties of a solid to the atomic structure of its constituent atoms. As will be discussed later, it is also the most appropriate way to calculate the properties of disordered systems. However, for crystalline semiconductors the empirical pseudopotential method seems to be the most efficient way to get a good overall description of both the valence and the conduction bands. The basis of this method is the plane wave expansion of the wave function given by Eq. (1-54) plus the use of a smooth pseudopotential. The matrix to be diagonalized was derived in Eq. (1-56) but now we pay more attention to the potential matrix elements. In EPM one assumes that the selfconsistent crystal pseudopotential can be written as a sum of atomic contributions, i.e., V ( r )=

ia

-15

1.2.3.2 The Empirical Pseudopotential Method

(k+GIVIk+G’)= L

r

X U,K

(1-66)

r

Figure 1-6. Comparison of the sp3 s* description of silicon (- - -) with a more sophisticated calculation (-). The vertical axis represents energies in eV, the horizontal axis the wave vector along symmetry axes in the Brillouin zone. Note that the valence band is practically perfectly reproduced.

where i2 is the volume of the unit cell. Suppose that there can be identical atoms in the unit cell. Then the sum over a can be expressed as a sum over groups /3 of identical atoms with position specified by a second

1.3 Comparison with Experiments for Zinc-Blende Materials

index y (i.e. ra = ryB). Calling n the number of atoms in the unit cell we can write

=C Sp(G’-G)vp P

(G’-G) (1-67)

where Sp(G) and v p (G) are, respectively, the structure and form factors of the corresponding atomic species, defined by

and

5

n vp (G) = - vP ( r) eiG . rd3r 2 !

(1 -68)

In practice, the empirical pseudopotential method treats the form factors va (G)as disposable parameters. In the case where the vp (r)are smooth potentials their transforms vp (G) will rapidly decay as a function of I G I so that it may be a good approximation to truncate them at a maximum value of G,. For instance, the band structure of tetrahedral covalent semiconductors like Si can be fairly well reproduced using only the three lower Fourier components v(lG1) of the atomic pseudopotential. There are thus two cut-off values for I G I to be used in practice: one, GM,limits the number of plane waves and thus the size of the Hamiltonian matrix; the other one, G,, limits the number of Fourier components of the form factors. We shall later give some practical examples. The use of a local pseudopotential is not fully justified since, from Eq. (1.52), it involves, in principle, projection operators. It can be approximately justified for systems with s and p electrons. However, when d states become important, e.g., in the conduction band of semiconductors, it is necessary to use an operator form with a projection operator on the 1 = 2 angular components.

23

1.3 Comparison with Experiments for Zinc-Blende Materials In this section we apply methods which allow us to understand the general features of the band structure of zinc-blende materials. We detail, to some extent, simple models based on tight binding or the empirical pseudopotential. We also discuss briefly the results of the most sophisiticated recent calculations. We then concentrate on the general treatment of the band structure near the top of the valence band, using the k-p perturbation theory as in the work by Kane (1 956; 1957). In the third part, we examine the optical properties of these materials putting particular emphasis on excitonic states. Finally, we give a comparison of predicted band structures with photo-emission and inverse photo-emission data, in the light of what was done on the basis of non-local empirical pseudopotentials.

1.3.1 The General Shape of the Bands In this section we start from two points of view: (i) the molecular or bond orbital model derived from tight binding and (ii) the nearly free electron picture. We show that both give rise to similar qualitative results at least for the valence bands.

1.3.1.1 The Tight Binding Point of View Consider an A-B compound in the zinc blende structure where the atoms have tetrahedral coordination. The minimal atomic basis for such systems consists of one s and three p orbitals on each atom. One could solve the Hamiltonian matrix in this basis set and get the desired band structure directly. However, one can get much more insight into the physics by performing a basis change such that, in the new basis set, some matrix elements of the Hamiltonian

24


will be much larger than the others. This will allow us to proceed by steps, treating first the dominant elements and then looking at the corrections due to the others. This is the general basis of molecular (Harrison, 1973; Lannoo and Decarpigny, 1973) or bond orbital models, two names for the same description. The natural basis change is to build sp3 hybrids of the form

Of course these states will be strongly degenerate since their degeneracy is equal to the number N of bonds in the system. The wave function of the bonding and antibonding states will take the form, for a bond ij connecting two neighbors i and j ,

(1-72)

( 1 -69)

where ‘psi is the s orbital of atom i and qp,G is one of its p orbitals pointing from i to one of its nearest neighbors j . By doing this for each atom, each bond in the system will be characterized by a pair of strongly overlapping hybrids qQ and ‘pji as shown in Fig. 1-7. It is clear that the dominant interatomic matrix elements of the Hamiltonian are given by (cpijlHlqji)=-B

B>O

(1-70)

while the diagonal elements (qQlH I qQ)are equal to the average sp3 energies of the atoms, which we denote E A for atom A and EB for atom B. In the first step we neglect all other matrix elements. The problem is then equivalent to a set of identical diatomic molecules, each one leading to one bonding and one antibonding state of energy:

\

\

CP ij

qji

/

/

Figure 1-7. Pair of sp3 hybrids involved in one bond, as defined in Eq. (1-69).

In the following discussion we take the convention that i is an A atom a n d j a B atom. As there are two electrons per bond, the ground state of the system corresponds to completely filled bonding states and empty antibonding states. This description defines the “molecular” or “bond orbital model” in which the bonding states give a rough account of the valence band and the antibonding states, of the conduction band. This model has been extremely successful in describing semiquantitatively the trends in several physical properties of these materials: ionicity, effective charges, dielectric susceptibilities, average optical gaps, and even cohesive properties (see Harrison (1980) for more details). With such a simple starting point, the formation of the band structure is easy to describe. The inclusion of further interactions which were neglected in the molecular model will tend to lift the degeneracy of the bonding and antibonding states. Exactly the same arguments as those developed in Sec. 1.1 lead to the conclusion that there will be the formation of a bonding band from the bonding states. For this we write the wave function ?,bb as a combination of all $ J ~ , ~ : q b =

ab,ij q b , i j

pairs ij

(1-73)

25


The leading correction term in the Hamiltonian matrix will be the interaction between two adjacent bonds which takes one of two values, A, or A,, depending on the common atom. Projecting Schrodinger’s equation on these states one gets the set of equations: ( 1-74) (E- Eb) abij = AA a b f + AB abirj

x

c

i‘+i

jf# j

where the sums are over adjacent bonds having an A or B atom in common. At this stage it is interesting to introduce the following sums

+ A, + AB) Ubij = A,

Si + A,

(E-E~-~AA+AB)S~=ABCS~ jci (1 -77) (E-Eb +A, - 3 A ~ ) s j= d ~ c S i icj

where the sums are over the nearest neighbors of one given atom. Injecting the second Eq. (1-77) into the first one gives

{ ( E - Eb)2 - 4 A ( E - Eb ) - 12 = (A’ - 6’)

x

Si2

2

a2} si = (1 -78)

i2

where now the sum is over the second nearest neighbors of atom i. This set of equations on sublattice A is just the same as what would be obtained for a tight binding s band on an f.c.c. lattice. This leads to the following solutions:

E=Eb+ +2 4

(1 -79)

2

k, a k,a +cos---cos2 2

+

2

2

a being the lattice parameter, and k,, k,, and k, the components of the wave vector along the cube axes. It is clear that v, varies continuously from 12 to -4. The extrema of the bands ( q= 12) are then given by:

E = Eb + 2 4 k 4 4 = Eb

E=Eb+2A+416)

Sj

(1 -76) Summing this either overj or i, one gets two equations:

with A = AA + AB and 6 = 2

( 1-80)

2

+6 4 -24

(1-81)

while for v,= - 4 a gap is opened in the band, its limits being given by

so that one can rewrite Eq. (1-74) as

(EWE,

with

[4 A* + 12 S2 + (A2 - S2) ~

1 ~

(1-82)

Equation (1 -79) gives only two bands while we started with four bonding orbitals per atom of the A sublattice. The two bands which appear to be missing can be obtained by noting that Eq. (1-76) has a trivial solution for which all the Siare zero, with nonzero abij if

E = Eb - 2 4

(1 -83)

This is the equation of a twofold degenerate flat band with pure p character, since all Si and Sjare zero. To summarize the results, one can say that the interaction between bonding orbitals has broadened the bonding level into a valence band consisting, in the present model, of two broad bands and a twofold degenerate flat band. Exactly the same treatment can be applied to the antibonding states by changing Eb into E, and defining A, and A, describing the interactions between antibonding states. This antibonding band will thus represent the conduction band. The resulting band structure is compared in Fig. 1-8 to a more sophisticated calculation from Chaney et al. (1971) (its ’ ~


The advantage of the simple picture we have just detailed is that it can be generalized, as we shall see, to a lot of other situations such as covalent systems with lower coordination (Sec. 1.4) or to non-crystalline and amorphous semiconductors. Furthermore, all tight binding descriptions with parametrized interactions give results which are in good correspondence with those we have derived, with the minor corrections we have mentioned. One such empirical model is the sp3 s* description of Vogl et al. (1983) which leads, for GaAs, to the band structure of Fig. 1-9, which can be shown to be in good agreement with experiments for the valence band and the lowest conduction band.

1.3.1.2 The Empirical Pseudopotential Method

Figure 1-8. Comparison of the simple model description of diamond (- - -) with a more sophisticated calculation (-). The vertical axis corresponds to energies in eV.

parameters have been adjusted to give overall agreement). It can be seen that it already reproduces the essential features of the valence band. The inclusion of further matrix elements left out from the previous simple picture will have the following qualitative effects: i) the bonding-antibonding interactions lead to a slight repulsion between the valence and conduction bands, and ii) the inclusion of interactions between more distant bonds induces some dispersion into the flat bands.

A major improvement in the detailed description of the bands of tetrahedral semiconductors has been achieved with the use of empirical pseudopotentials. Let us then first discuss its application to purely covalent materials like silicon and germanium. The basis vectors of the direct zinc-blende lattice are a/2 (110), a/2 ( O l l ) , and a/2 (101). The corresponding basis vectors of the reciprocal lattice are 2xla ( l l i ) , 2nla (11 l), and 2 x / a (1 11). The reciprocal lattice vectors G which have the lowest square modulus are the following, in increasing order of magnitude:

-G U

2

[&)G2

2x

000 111 200 220 311

0 3 4 8

(1-84)

11

For elemental materials like Si and Ge there is only one form factor v(G)but we


Figure 1-9. Comparison between the sp3 s* band structure of GaAs (-) and the empirical pseudopotential one (- - -). Vertical scale: energies in eV, honzontal scale: k values.

a I

2

0

(

-'

-2

-4

-4

-6

-6

-0

-a

-10

-10

-12

-12

-14

.I4

have seen in Eq. (1.67) that the matrix element of the potential involves a structure factor which is given here by:

S(G)= cos G z

(1-85)

where the origin of the unit cell has been taken at the center of a bond in the (1 11) direction and where z i s thus the vector a/8 ( 1 11). For local pseudopotentials this matrix element ( k + G 1 V I k + G')can be written V ( G ) and is thus given by: V ( G ) = v(G) cos (G*

27

Z)

(1-86)

The structure factor part is of importance since, among the lowest values of 1 GI quoted in Eq. (1-84), it gives zero for 2 n l a (2, 0,O). If one indexes V ( G )by the value tak) ~then only the en by the quantity ( ~ / 2 nG2, values V,, V,, and V , , are different from zero. It has been shown (in Cohen and Bergstresser, 1966) that the inclusion of these three parameters alone allows us to obtain a satisfactory description of the band struc-

ture of Si and Ge. This can be understood simply by the consideration of the free electron band structure of these materials which is obtained by neglecting the potential in the matrix elements Eq. (1-56) of the Hamiltonian between plane waves. The eigenvalues are thus the free electron energies A2/2mIk + G l2 which, in the f.c.c. lattice, lead to the energy bands plotted in Fig. 1-10. The similarity is striking, showing that the free electron band structure provides a meaningful starting point. The formation of gaps in this band structure can be easily understood at least in situations where only two free electron branches cross. To the lowest order in perturbation theory, one will have to solve the 2 x 2 matrix.

L

2m

'

28


True bands

Free-electron bands

Figure 1-10. Correspondence between free-electron and empirical pseudopotential bands, showing how degeneracies are lifted by the pseudopotential.

The resulting eigenvalues are

E ( k )= 2rn

* { [ g . l k + G ’ r - l2k + G r

+ I V(G‘-

G) 12>1’2

I+

(1-88)

whose behavior as a function of k is pictured in Fig. 1-11. The conclusion is that there

is the formation of a gap at the crossing point whose value is 21 V(G’- G)(. Note that for this to occur the crossing point at G’+G k=-must lie within the first Bril2 louin zone or at its boundaries. For points where several branches cross, one will have a higher order matrix to diagonalize but this will generally also result in the formation of gaps. This explains the differences between the free electron band structure and the actual one in Fig. 1-10. The number of parameters required for fitting the band structures of compounds is different in view of the fact that there are now two different atoms in the unit cell with form factors uA(G) and v,(G). The matrix elements V(G) of the total pseudopotential will thus be expressed as (1-89)

V(G)=VS(G)cos (G-z)+iVA(G)sin(G.z)

Figure 1-11. Opening of a gap in the nearly free electron method. The full line corresponds to the two free electron branches, the dashed lines to the two branches split by the potential Fourier component.

where Vs and VA are equal to (vA+ vB)/2and (vA-u,)/2, respectively. The number of fitting parameters is then multiplied by 2, the symmetric components Vi, V;, and V,: being close to those of the covalent materials and the antisymmetric components be-

29


ing Vf, V t , and V; since the antisymmetric part of V, vanishes.

1.3.2 The k-p Description and Effective Masses We have already seen for hydrogenic impurity states (Sec. 1.1) that the concept of effective masses near a band extremum is very powerful. This will prove still more important for heterostructures which we discuss later. In any case it is desirable to provide a general framework in which to analyze this problem. This is obtained directly via the k-p method which we present in this section. The basis of the method is to take advantage of the crystalline structure which allows us to express the eigenfunctions as Bloch functions and to write a Schrodingerlike equation for its periodic part. We start from (1-90)

{g+

v}eik.r u k ( r ) = E ( k )eik’ruk( r )

where we have written the wave function in Bloch form. We can rewrite this in the following form:

i

( P + A k ) 2 + V u k ( r ) = E ( k ) u k ( r )(1-91) 1 2 m which is totally equivalent to the first form. To solve this we can expand the unknown periodic part uk(r)on the basis of the corresponding solutions at given point k,, which we label unk0(r): uk ( r )=

C cn ( k )un, kn ( r )

(1-92)

n

The corresponding solutions are the eigenvalues and eigenfunctions of the matrix with the general element (1-93)

We now use the fact that u,,ko is an eigenfunction of Eq. (1.91) for k = k,, with energy E,(k,). This allows us to rewrite the matrix element Eq. (1-93) in the simpler form:

with P n n , ( k d = (un,koi~Iun*,ko)

(1-95)

Diagonalization of the matrix A ( k )given by Eq. (1 -94) can give the exact band structure (an example of this is given in Cardona and Pollak, 1966). However, the power of the method is that it represents the most natural starting point for a perturbation expansion. Let us illustrate this first for the particular case of a single non-degenerate extremum. We thus consider a given non-degenerate energy branch E,(k) which has an extremum at k = k , and look at its values for k close to k,. The last term in Eq. (1-94) can then be considered as a small perturbation and we determine the difference En( k )En(ko)by second order perturbation theory applied to the matrix A ( k ) .This gives A2 En ( k )= E n ( k o )+ -( k - k o ) 2 + 2m A2

c [ ( k- koEn1.(Printk 1~1[En’( k (koko

+2 m

n‘zn

-

-

(1-96) ). Pn’n 1

)

which is the second order expansion near k , leading to the definition of the effective masses. The last term in Eq. (1 -96) is a tensor. Calling 0 a its principal axes, one gets the general expression for the effective masses m:

30


This shows that when the situation practically reduces to two interacting bands, the upper one has positive effective masses while the opposite is true for the lower one. This is what happens at the T point for GaAs, for instance. Another very important situation is the case of a degenerate extremum, i.e., the top of the valence band in zinc blende materials which occurs at k = 0. We still have to diagonalize the matrix Eq. (1-94) taking k , = 0 and, for k = 0, the last term can still be treated by the second order perturbation theory. By letting i a n d j be two members of the degenerate set at k = 0 and I , any other state distant in energy, we now must be apply the second order perturbation theory on a degenerate state. As shown in standard textbooks (Schiff, 1955) this leads to diagonalization of a matrix:

I

Af’(k) = Ei(0)+ -k 2 2m “

J

c$ t

The top of the valence band has threefold degeneracy and its basis states behave like atomic p states in cubic symmetry (i.e., like the simple functions x, y , and z). The second order perturbation matrix is thus a 3 x 3 matrix built from the last term in Eq. (1-98) which, from symmetry, can be reduced to (Kane, 1956, 1957; Kittel and Mitchell, 1954; Dresselhaus et al., 1955)

Lk:

+ M(ky’ + k:)

A2 k 2 It is this matrix plus the term - on its 2m diagonal wich define the h&) matrix of Sec. 1.1.4 to be applied in effective mass theory to a degeneratestate. Up to this point we have not included spin effects and in particular spinorbit coupling, which plays an important role in systems with heavier elements. If we add the spin variable, the degeneracy at the top of the valence band is double and the k ep matrix becomes a 6 x 6 matrix whose detailed form can be found in (Bassani et al., 1974;Altarelli, 1986; Bastard, 1988). One can slightly simplify its diagonalization when the spin orbit coupling becomes large, from the fact that

L S = 112 ( J 2 - L2 - S 2 )

(1-101)

where J = L + S . Because here L = l and S=1/2, J can take two values J=3/2 and J = 112. From Eq. (1-101) the J=3/2 states will lie at higher energy than the J = 1/2 ones and, if the spin orbit coupling constant is large enough, these states can be treated separately. The top of the valence band will then be described by the J =3/2 states leading to a 4 x 4 matrix whose equivalent Hamiltonian has been shown by Luttinger and Kohn (1955) to be:

-Y3

c

kakp

(J,

Jp+ Jp 2

Ja)

1

(1-102)

Nkx k, Lk,’+M(k; +k:) Lk: + M ( k ? +ky’)]

where L, M , and N are three real numbers, all of the form: h2

(Pa)il ( P P)rj

-3 m 2 I E,(o)-E,(o)

(1 -1 00)

Finally, as shown by Kane (1956, 1957), it can be interesting to treat the bottom of the conduction band and the top of the valence band at k = O as a quasi-degenerate


system, extending the above described method to a full 8 x 8 matrix which can be reduced to a 6 x 6 one if the spin orbit coupling is large enough to neglect the lower valence band,

1.3.3 Optical Properties and Excitons One of the major sources of experimental information concerning the band structure of semiconductors is provided by optical experiments. In particular fine structures in the optical spectra might reflect characteristics of the band structure. To see this in more detail let us discuss the absorption of the light which is proportional to the imaginary part of the frequency dependent dielectric constant, i.e.,

which can be expressed as an integral over the surface S(hw) in k space such that Ec(k)- Ev(k)= hw. This gives

2 dS Jvc(w)=y J (2n) S ( w ) /vk(Ec(k)-Ev(k))(S (1- 106) It is clear from this expression that important contributions will come from critical points where the denominator of Eq. (1- 106) vanishes. These can originate from k points where one has the separate conditions (1- 107) Critical points of this kind only occur at high symmetry points of the Brillouin zone (such as k = 0, for instance). Other critical points are given by vk(Ec(k) - Ev(k)) = 0

.s(Ec-E,-Ao)d3k

(1-103)

where the optical matrix element is: (1- 104)

x being the wave vector of light. From the

31

(1-108)

The behavior near such Van Hove singularities can be discussed quite generally by expanding E, - E, to the second order in k , around the singular point ko. This formally gives

E, -E, = Eo +

3 a=l

aa(k, - ko,)*

(1-109)

Bloch theorem this matrix element is nonzero only if k' is equal to k + x + G (G is the and the qualitative behavior of the joint denreciprocal lattice vector). As 1x1 is much sities of states Jvc(w)near such a point desmaller than the dimensions of the first Brilpends on the sign of the a,. Typical results louin zone, this means that the transition is are shown in Fig. 1-12, showing that, from vertical within the Brillouin zone (i.e., it the shape of the absorption spectrum, one occurs at fixed k ) . Fine structures in ~ ~ ( 0 can ) infer a part of the characteristics in the due to allowed transitions can be studied by band structures. As an illustration, we show discarding the k dependence of the optical in Fig. 1- 13 the curves E* ( w ) for silicon and matrix element Mv,(k). In a narrow energy germanium in comparison to the predicted 0 ) curves (Greenaway and Harbeke, 1968). range around such a structure, ~ ~ (becomes proportional to the joint densities of Up to now we have only discussed optistates cal transitions between one particle states in n which an electron is excited into the con(1-105) duction band, leaving a hole in the valence band. This is permissible if we treat the electron and hole as independent particles.

32


t

(@I

(a)

at hv = Eg, the energy gap, can show lines

\*

\

*

I I

we

w.

Figure 1-12. Schematic joint densities of states near the critical points for different situations (see text).

However, these quasi-particles have opposite charges and attract each other via an effective potential -e2/Er. This coulombic potential can give rise to localized gap states such as hydrogenic impurities, so that the absorption spectrum, instead of starting

m*e4 1 at E g - - - 2 2 2 ' where m* is a suitable 21i E n effective mass. Again the justification of this proceeds via the effective mass theory, but in a way slightly more complex than for impurities. To find the excitonic wave function, we can write the total wave function of the excited states in the form (Knox, 1963; Kittel, 1963):

a(ke,kh)@(k,,kh)

qexc=

(l-l1')

ke,kh

where the @correspond to the excited states obtained from the ground state by exciting a valence band electron of wave vector kh to a conduction band state k,. To use the effective mass approximation we introduce a two particle envelope function by the Fourier transform: (1-111)

ke,kh

5

Figure 1-13. Experimental and predicted e2(w) for Ge.

33


For simple band extrema with isotropic effective masses, it can be shown along the same lines as in Sec. 1.1 that F(r,, rh) obeys the effective mass equation:

{,-+-

~h2

2

Pe 2m,* 2m:

&Ire-rh

Mext

I

E = Eg + -- -2M 2&2A2 n2

= (90I Cpi I V e x c )

(1-1 16)

From the definition of the envelope function Eq. (1-1 11) we see that C a ( k , k )

(1-113)

where M and m* are the total and reduced masses respectively and k is the wave vector for the center of mass motion. From this it is clear that the lowest excited states are those for k = O and these give rise to the hydrogenic lines. It is interesting to determine the oscillator strength for exciton absorption for comparison with one particle transitions. We have seen before that, at a given frequency, the strength of the absorption is determined by the optical matrix element. For many electron states, this element is given by Mexc

=~ v c a(k,k) k

One can separate the center of mass and relative motion in this Hamiltonian in such a way that the total energy becomes:

A2k2 m * e 4 1

tions, i.e., only if k, = k h = k . This matrix element is identical to the Mvc(k) defined above and we take it to be constant over the small range of k involved. We then get

(1-114)

i

k

is equal to F(r,r)d3r where we take re-rh=r. We thus obtain the final result:

IMexc12= IM,,121 I F(r,r)d3 r l2

(1-1 17)

For the simple model we have just considered, the lowest exciton wave function is

where V is the volume of the specimen, R is the center of mass position and a the exciton Bohr radius, thus leading to (1-119) This is to be compared to the one particle spectrum which is given by (1- 120)

where C p i is the one electron sum of the I

individual momenta, % is the ground state, is one of the exciton states whose and qeXc general form is given in Eq. (1-110). One can expand qeXcand express and q ( k h k,) as Slater determinants, in which case Me,, becomes:

-

= C(kh/Plke)a(ke,kh)

where m* is the reduced mass. This sum reduces to the density of states of a 3D electron gas, so that

(1-115)

ke ,kh

We have seen that the one particle matrix elements are non-zero for vertical transi-

It is better for comparison with lMexcI2 to calculate the integrated lM(co) up to a fre-

34


quency o.One thus gets

'a'(Aw - E g ) J

]

312

=6n[

Ao - E,

(1-122)

where E l , is the exciton binding energy in the 1s state. Typical values are El, = 10 meV, Ao - Eg = 200 meV in which case the ratio, Eq. (1- 122), is of the order of 20%.

1.3.4 Ab Initio Calculations of the Excitonic Spectrum Ab initio calculations of ~ ( ofor)semiconductors have recently been reported (Albrecht et al., 1997). They generalize the G-W approximation of Sec. 1.2.1.4 to the case of electron-hole excitations. This requires the calculation of the two-particle Green's function, which obeys the BetheSalpeter equation (Nozibres, 1964; Sham and Rice, 1966; Strinati, 1984). This is equivalent to solving a Schrodinger equation for the electron-hole pairs with complex potential energy meaning that true eigenstates of the system are not obtained. The dominant potential energy term is the dynamically screened electron-hole attraction, while the smaller exchange term remains unscreened. Again, as for GW, the ) ) greatly improved over results for ~ ~ ( c r are those obtained in LDA, for which the main peak is incorrectly described (Albrecht eta]., 1997).

1.3.5 A Detailed Comparison with Experiments We give an account here of some results comparing empirical pseudopotential bands with X-ray photo-emission and inverse

photo-emission results (Chelikowsky et al., 1989). These experimental techniques combined with reflectivity data can yield nearly complete information concerning the occupied and empty states. A comparison of experimental data with theory will then provide a stringent test of the validity of the predictions. The empirical pseudopotential used by Chelikowsky et al. (1989) and Cohen and Chelikowsky (1988), was built from a local and a non-local part. The local part was, as described before, restricting the non-zero components to be V,, V,, V,, and Vll. As emphasized by Chelikowsky et al. (1989), this procedure yields and accurate description of the reflectivity and photo-emission spectra. However, for Ge, GaAs, and ZnSe, non-local corrections to the pseudopotential are necessary to produce similar accuracy. This is caused by d states within the ion core which modify the conduction band structure of these three materials and make the pseudopotential non-local. As discussed before, a simple correction for a specific I-dependent term can be written 4n

VNL( k ,G - G')= -(2 I Qa

+ 1) 4 (COS 0) .

.Id r r 2 K ( ~ M % ) j M )

(1-123)

where x = k + G,cos0 = x - x ' l x x ' , Qa is the atomic volume, P , is a Legendre polynomial, j , is a spherical Bessel function, and V,(r) is the non-local correction. In Chelikowsky et al. (1989) a simple Gaussian form has been used for V,whose parameters are fitted to experiment. The local and non-local parameters are tabulated in Chelikowsky et al. (1989). The cut-off in the plane wave expansion was taken at an energy El = 8 Ry and extra plane waves up to E, = 13 Ry were introduced by the perturbation theory. The corresponding results for Ge and GaAs are compared to experimental

35


4 r d\r n-Ge(l11)12xl

p-GaAs( 110) 1x 1

L

L

A

A

r

r

A

A

X

X

w

w

K

K

z

r

z -10

-5

0

5

10

15

r

-10

-5

0

5

10

15

20

Energy relative to Ev (eV)

Energy relative to E, (eV)

Figure 1-14. Comparison between photo-emission measurements and calculated densities of states for Ge: experimental intensities (top), theoretical density of states (middle), corresponding calculated bands (bottom) for which the vertical axis corresponds to the wave vector. The experimental data corresponds to Xray photo-emission spectroscopy (XPS) or to Bremsstrahlung isochromate spectroscopy (BIS).

Figure 1-15. Comparison between photo-emission measurements and calculated densities of states for GaAs.

data in Figs. 1-14 and 1-15. The agreement is fairly good, especially if one notes that both photo-emission and optical data are reproduced with similar accuracy.

At this point it is also interesting to measure the accuracy of the first principles G-W calculations for these materials. This must be done keeping in mind that these calculations are performed starting from local density calculations which, as we have seen, lead to large discrepancies in excitation energies. One result taken from Hybertsen

36


like structures such as Se or Te for which we use the tight binding description, comparing the results with photo-emission data. We briefly discuss the case of lamellar materials. Finally, we consider a class of semiconductors with unconventional bonding, the Sb chalcogenides.

2

Ge

0 -2

F-

-4

1.4.1 General Results for Covalent Materials with Coordination Lower than Four

$ -6 9)

C

W

-8

L

A

r

Wavevector

A

X

5;

Figure 1-16.Comparison between angular resolved photo-emission and the G-W calculation of Hybertsen and Louie (1986) showing typical experimental errror bars.

and Louie (1986) compares the valence band structure with angular resolved photoemission (see Fig. 1-16).

1.4 Other Crystalline Materials with Lower Symmetry In this section other cases of crystalline semiconductors are examined. In these the bonding is more complex than that in zincblende materials which constitute, in a sense, the prototype of covalent or partly ionic bonding. We begin by generalizing the tight binding arguments discussed for tetrahedral systems to cases with lower coordination. We then specifically consider chain-

Let us consider systems where each atom has N equivalent bonds to its neighbors. As with tetrahedral compounds, we want to build a molecular model which provides a simple basis for the understanding of their band structure. On each atom we build N equivalent orbitals which point exactly or approximately towards the nearest neighbors. We consider in all cases an sp minimal basis; this is always possible since one has four basis states from which one forms only Ndirected orbitals, with N c 4. The remaining atomic states are then chosen by taken into account the local symmetry (we shall later see specific examples of how this can be achieved). Once this is done the basic electronic structure follows almost immediately. Again the directed states strongly couple in pairs as in diatomic molecules and form a bonds with a a bonding state and a a * antibonding state. It is this coupling which dominates the Hamiltonian matrix and the cohesive properties. To the lowest degree of approximation, all other states remain uncoupled at their atomic value. The resulting level scheme then consists of N / 2 abonding and N / 2 a* antibonding states plus 4 - N non-bonding atomic states per atom at energies which depend on the specific case under consideration. Of course, these levels are all strongly degenerate and, if the molecular model is meaningful, further inter-

37

1.4 Other Crystalline Materials with Lower Symmetry

actions will lift this degeneracy to form well-defined and separate energy bands.

1.4.2 Chain-Like Structures Like Se and Te One instructive example of a chain-like structure ispicturedinFig. 1-17, whichrepresents an elemental system where each atom forms two equivalent bonds with an interbond angle of 90”. This situation does not exactly represent the crystalline structure of Se and Te but is very close and will help us in understanding the properties of these materials. We will discuss this case from the tight binding point of view, the same qualitative description of the bands being obtained with the pseudopotential approach. Let us begin the tight binding picture by starting from the molecular model. As discussed before we first have to build two directed states pointing towards the neighbors. With the local axes of Fig. 1-17, these are pure p states px and py with the positive lobe oriented towards the neighbors. Then, from symmetry, the other atomic states which do not participate in 0bonds will be the s state and the pz state, perpendicular to the plane of the two bonds. The parameters appropriate to Se and Te are such that roughly Ep -E, = 10 eV, H, = - 2 eV which from Eq. (1-64) means that H s u = - 1.3 eV and H,= - 0.6 eV. The results of the molecular model are pictured in Fig. 1-18 with the corresponding electron

Figure 1-17. Simplified chain-like structure for Se and Te.

Figure 1-18. Molecular levels for Se and Te, the energy scale being of order 15 eV between the s and u* states.

-20

-16

-12

-8

-4

Energy (eV)

0

4

8

Figure 1-19. Photo-emission results for Se (a) and Te (b) compared to the calculated densities of states: - - - (experiment), -(theory).

population per atom and the nature of the states. The upper valence band is the nonbonding pz band corresponding to the wellknown “lone pair” electrons. Comparison with the photo-emission results of Fig. 1- 19 (Shevchik et al., 1973) shows that the molecular model already gives an essential account of the results.

38


As for covalent systems, we can now study the broadening of the molecular levels into bands. We treat each band separately, which is valid to the first order in perturbation theory. We make use of a nearest neighbors tight binding Hamiltonian as defined in Sec. 1.2.3.1 with four parameters H,,, H,, H,,,, and H, (note that the H , connecting the px, py functions involved in (7 bonds are already included in the molecular model). The case of the s band is the simpler one, with an interaction H,, between nearest neighbors. We are dealing with a system containing two atoms per unit cell (Fig. 1-17) and easily get the s band dispersion relation:

1 I

ka E,(k) = E, f 2 H,, cos 2

(1-124)

The pz lone pair band can be treated in the same way since the pz orbitals are coupled together only via the interaction H., This gives:

1 1

ka E z ( k ) = E p + 2 Hnn cos 2

(1-125)

The broadening of the (7 and (7* bands is slightly more involved. Let us refer the bonding and antibonding orbitals to one sublattice whose atoms are labelled i, their neighbor in the cell being labelled i f . From Fig. 1- 17 the bonding and antibonding states can be written: (1-126)

The energies of these states are +-IHual. With our tight binding Hamiltonian there is no interaction between adjacent bonds but only with second nearest neighbor bonds. Moreover, the x-like bonds do not couple with the y-like bonds giving rise to doubly degenerate bands. It is simple to show that only the H,interaction is involved and one

gets the following dispersion relations: Eb(k)=-IH,l +IH,Icos(ka) (1-127) E,(k) = + 1H, I + IH,, I cos (k a> Of course the linear chain model of Fig. 1-17 does not exactly correspond to the real structure of Se and Te. These Materials are characterized by helicoidal chains with three atoms per unit cell (Hulin, 1966). The interbond angle is 100" for Se and 90" for Te. Under such conditions the basic features of the previous model still remain valid. When the bond angle is not exactly 90", one builds on each atom two symmetrical px and py orbitals in the plane of its two bonds, pointing only approximately towards its neighbors. One then builds a pz orbital perpendicular to the plane and, finally, the s orbital is left uncoupled. This leads to a molecular model exactly identical to the previous one except that the bonding and antibonding levels will now be sin2(8/2), where 8 is the bond at +IH,I angle. The dispersion relation will also be slightly modified with respect to those in the simple model, especially for the lone pair band since the pz orbitals are no longer parallel. However, all the basic qualitative features will remain unchanged. All conclusions of the tight binding description are confirmed by experiments (Shevchik et al., 1973) and also by empirical pseudopotential calculations (Schluter et al., 1974). The main difference is that the weak interaction between chains induces some degree of three-dimensional characters which wash out to some extent the onedimensional divergences of the density of states (Schluter et al., 1974).

1.4.3 Layer Materials It is not possible here to give a complete account of what has been done on layer materials. We thus restrict ourselves to the


case of the crystalline germanium monochalcogenides Ge-Se and Ge-Te for which we can generalize the simple model discussed above for the Se and Te chains. In these material both Ge and Se (or Te) atoms have threefold coordination with interbond angles close to 90". Furthermore, they consist of two-dimensional layers, see Fig. 1-20. We can generalize the molecular model to this kind of system in a straightforward manner. We idealize the situation by considering interbond angles of 90" and build local axes 0 x, y, z, on each atom along these bonds. The natural basis states for the molecular model will be the s states and the corresponding px, py, pz orbitals, each of these having its positive lobe pointing toward one neighbor. In the molecular model the s states remain uncoupled while all p orbitals couple by pairs, leading to abonding and (T*antibonding states. The resulting level structure is shown in Fig. 1-21. The number of electrons per GeSe unit is 10. As there are 2"s" states, 30, and 3 0 " states per unit, one concludes that all s and (T states are filled and these form the valence band. The fundamental gap then takes place between the (T bonding and (T*antibonding states. The level position in Fig. 1-21 have been calculated using the parameter values given in Bergignat et al. (1988) for GeSe. The s level of Se is much lower, followed by the Te s level, and the (T and (T*levels. The resulting valence band compares extremely Ge

Figure 1-20. Simplified layer structure for GeSe.

39

d

+% s.Ge s,se

-%-

_ct_

Figure 1-21. Molecular levels for GeSe, the energy scale between the s and u* levels being of order 15 eV.

well with the XPS measurements for crystalline GeSe, noting that the densities of states of the CJ levels are 3 times larger than for s states.

1.4.4 New Classes of Materials: the Antimony Chalcogenides One major interest of these materials is that they clearly show how band theory can clarify the understanding of the chemical bond in a class of semiconductors with fairly complex structure. This subsection is a summary of what can be found in Lefebvre et al. (1987 and 1988). Tin and antimony atoms have an electronic configuration Sn: [Kr] 4d1°5 s25p2, Sb:[Kr] 4d1'5 s25p3. Some chalcogenide compounds are insulators in which the bonds have strong covalent character while others are characterized by a lone pair, 5s2, which does not take part in the bonding but whose properties are directly correlated to the Sn or Sb coordination and to the structural packing (Gillespie and Nyholm, 1957) (for instance, such a correlation is the basis of chemical valence shell electron pair repulsion VSEPR theories (Gillespie, 1972)). These materials are characterized by a large range of electrical behaviors (insulator, semi-conductor, semi-metal). Their general formula can be expressed as B,Xx, A,BbXx, or A,&,XxIi where the atoms are alkaline or alkaline-earth or T1,

40


Pb for A, Sn or Sb for B, a chalcogen for X(S, Se, Te), and iodine for I. Until recently, systematic analyses of this family of materials have consisted of a determination of their atomic structure and their electrical conductivity and also of Mossbauer experiments performed on 19Sn and on 121Sb.This has allowed Ibanez et al. (1986) to build a simple chemical bond picture using the concepts of “asymmetry” and “delocalization” of the 5s2 lone pair. It is thus interesting to analyze the exact meaning of such notions through the combined use of photo-emission (UPS and XPS) measurements and band structure calculations. We show in the following discussion that this allows us to obtain a coherent picture of the electronic properties of this class of materials and, furthermore, that one can derive a molecular approximation of the full band structure which allows a clear understanding of the physical nature of the distortion experienced by the 5s2 lone pair electron distribution. We consider five representative elements of the Sb family chosen to exhibit the whole range of electronic properties, i.e., SbI,, Sb2Te,, SbTeI, T1SbS2, and Tl,SbS,. Let us first summarize the previous understanding of the electronic properties of these materials. First, X-ray diffraction studies have provided the bond lengths and interbond angles which have been connected to the bonding character (covalent, ionic, or Van der Waals), the distortion of the packing around antimony atoms being attributed to the stereochemical activity of the 5s2 lone pair E(Sb). Mossbauer spectroscopy gives information on the electron distribution around the Sb atom through the isomer shift 6 (directly connected to the 5 s electron density at the nucleus) and the quadrupole splitting. A which reflects the electric field gradient. Using these data plus the electrical properties (conductivity a,

’

band gap E g ) , these materials have been classified into three groups on the basis of their E(Sb) behavior: i) E(Sb) is stereochemically inactive, localized around the Sb nuclei with strong 5s2 character. This corresponds to octahedral surrounding of the Sb atoms and to insulating behavior (ex: SbI,). ii) E(Sb) is stereochemically active as is seen by the distorted surrounding of the Sb atom and the corresponding reduction of the 5 s character at the Sn nucleus, which can be attributed to s-p hybridization. These materials are semiconductors (1.2 eV 5 Eg S 2 eV) with weak conductivity (a= Q-’ cm-l). iii) E(Sb) is again stereochemically inactive, i.e., the Sb environment is again octahedral as in the first group but there is a 5s density loss at the nuclei and these compounds are semi-metals ( E g = 0.1 eV, CT = 10, Q-’ cm-’ ). The lone pair E(Sb) is then considered as partly delocalized (Ibanez et al., 1986). On the basis of these known properties a tentative description of the band structure has been proposed (Ibanez etal., 1986) whose main features are schematized in Fig. 1-22. Fig. 1-22 (1) corresponds to case (i), (2) and (3) to case (ii) with sp hybridization, and (4) to the delocalized 5s2 lone pair. The important point is that such a description assumes that the “5s” band is moving from the bottom to the top of the valence band which is relatively hard to understand on simple grounds. A better understanding of these electronic properties requires a band structure calculation which is difficult to perform in view of the large numbers of atoms per unit cell (between 6 and 24 for the materials considered here). For this reason it is necessary to use empirical tight binding theory whose simplicity allows a full calculation. The

E:

Sb atomic levels


d(Sb)

2

3

tight binding description for these materials is based on the use of an “s-p” minimal basis set and, as usual, on the neglect of interatomic overlap terms. The Hamiltonian matrix elements are taken from Harrison’s most recent set of empirical parameters (Harrison, 1981). However, the situation here is more complex since there are several close neighbor distances. To account for this, we apply Harrison’s prescription to the interatomic matrix elements Hap ( R , ) for atoms which are at the nearest neighbor’s distance R , and determine the other H a p ( R ) by the scaling law:

[ [:

I1

Hap( R )= H a p ( R l )exp - 2.5 - - 1

(1- 128)

valid for R lying between R , and a cut-off distance R, chosen to correctly represent the crystal. The use of an exponential dependence and of the parameter 2.5 is discussed in Allan and Lannoo (1983). Of course, any type of empirical theory has to be tested in several ways and, for this reason, we use XPS-UPS measurements to confirm the nature of the predictions for the valence band densities of states for which tight binding should give a reasonable description. Some characteristic results are reproduced

41

Figure 1-22. Initially proposed densities of states for the antimony chalcogenides, the energy scale being 10 to 15 eV between the lower und upper levels.

4

in Fig. 1-23 where it can be seen that the empirical tight binding calculation correctly gives the number and position of the main peaks of the valence band density of states and also gives the correct valence band width. In principle, tight binding is better suited to the description of valence bands but Table 1-2 shows that the predicted gaps also compare well with the experiments. One can then calculate the number Ns of 5s electrons on the Sb atom which is the basic quantity determining the Mossbauer isomer shift S. Fig. 1-24 shows the linear correlation between the measured 6 and the computed values of N,. This proportionality demonstrates that the band structure determination gives a completely coherent picture of the electronic structure of these compounds. A striking feature of these results is that the loss of 5s electrons is extremely small with a maximum value of about 0.1. The notion of strong or weak 5s character on Sb is thus quite relative as is the notion of delocalization since the band states are always delocalized over the whole crystal. However, if we sum up their contribution to the 5 s population on the Sb atoms we get something that is always close to N s = 2. A final comment that one can make concerning the band structure is that in all cases one finds the 5s Sb density of states at the bot-

42

1 Band Theory Applied to Semiconductors 2 4 , (calc)

0.05

0.10

TI,SbS, TISbS,

0

N 1

2

3

*

Energy (eV)

Figure 1-23. Predicted valence band densities of states for antimony chalcogenides compared to UPS and XPS spectra. The full lines correspond to theory. The vertical axis represents intensities or densities of states in arbitrary units.

Table 1-2. Predicted gaps (Eg,p) compared with experimental gaps (Eg,e ) in eV. Compound

Egr P

Eg.e

SbI, Sb2Te3 SbTeI TISbS2 Tl,SbS,

2.40 0.14 1.32 1.73 2.12

2.30 0.21 1.45 1.77 1.80

tom of the valence band in contradiction with the qualitative chemical picture of Fig. 1-22 that relates the 5s2 delocalization to a shift of this density of states towards higher energies.

Figure 1-24. The Sb Mossbauer isomer shift 6 versus 2-Ns(Nsbeing the number of Sb s electrons) and the number of N of missing neighbors.

At this level, a better understanding can only be obtained using a simple physical model. To do this we idealize the atomic structure by considering that a reasonable first order description of the immediate environment of an Sb atom consists of the perfect octahedron of Fig. 1-25. However, among the 6 possible sites i = 1 to 6, N are taken to be vacant. We then treat such a Sb-M,, unit as a molecule for which we take as basis functions: qs, px, (py, and cp, which are the s and p states of the Sb atom and xiwhich are the “p” states of the existing M atoms that point towards the Sb atom (i.e., their positive lobe is in its direction). The “p” levels of the Sb and M atoms fall in


43

Figure 1-25. Simplified molecular model of the antimony chalcogenides: a) idealized octahedron around one Sb atom, b) the two possible situations along one axis with no or one missing neighbor, c) the resulting schematic level structure.

the same energy range and, to simplify, we take them as degenerate while the s level of the Sb atom is about 10 eV lower, For this reason we first treat the coupling between the p states alone. For a given direction a = X, Y, or Z two situations can occur (see Fig. 1-25b): i) There are two M atoms i(=l, 2, or 3) and j ( = 4, 5 , or 6) . In this case the Sb p state qa only couples to the corresponding antisymmetrical combination (xi- x j ) / j h giving rise to a c~ bonding state and a c ~ * antibonding state while the symmetrical + remains at the p energy. ii) There is only one M atom i. In this case pa couples to xito give again a c ~ * and c~ state but with a smaller splitting.

(xi xi)/*

The resulting level structure is shown in Fig. 1-25c. All these molecular levels have to be filled except for the c ~ * antibonding levels. At this stage the 5s electron population on the Sb atoms is exactly N , = 2. The only factor that allows for a reduction in Ns is the coupling of (ps with the empty antibonding states c ~ * . However, in case i) these are antisymmetrical so that the coupling vanishes by symmetry. This is not true in case ii) where such coupling will exist and will induce a reduction in N,. We then arrive at the conclusion that the total reduction in

N , will be proportional to the number N of missing M atoms, if 0 S N 5 3. Fig. 1-24 b shows that the plot of the chemical shift S versus N also gives a straight line but with a reduced accuracy as compared to Fig. 1 -24a. The constant factor relating 2 - N , to N can be evaluated by the second order perturbation theory and gives a result comparable to Fig. 1-24 a. This means that the simple molecular model contains the essence of the behavior of the 5s lone pair. The combination of XPS measurements and band structure calculations thus leads to a fully coherent description of these materials allowing us, for instance, to understand the trends in the Mossbauer chemical shift related to the 5s electron density at the Sb nucleus. This gives a precise meaning to the empirical notions of asymmetry and delocalisation of the 5s2 lone pair which were previously used in solid state chemistry. Similar considerations were then applied to analyze the meaning of the chemical notion of tin oxidation number in the compounds belonging to the SnS-In,&-SnS, family (Lefebvre et al., 1991). The conclusion is that the difference between the two oxidation states Sn(I1) and Sn(1V) corresponds to a variation of about 0.7 Sn 5s electrons, the SnII atoms always being in strongly distorted sites. The ETB technique

44


is equally helpful to predict trends in the valence states of binary and ternary gallium and arsenic oxides and compare them with photoemission data (Albanesi et al., 1992). A particularly interesting application is the case of lithium insertion in three dimensional tin sulfides (Lefebvre and Lannoo, 1997), where the change in tin oxidation state was related to the fact that the lithium donor turns out to be a defect with negative correlation energy. Finally, the family of tin monochalcogenides from SnO to SnTe was also studied by ETB combined with abinitio LDA calculations, both leading to similar conclusions (Lefebvre et al., 1998).

1.5 Non-Crystalline Semiconductors In the preceding section we have discussed the properties of several crystalline covalently bonded systems with varying coordination numbers. These are usually determined in such a way that each atom satisfies its local valence requirements. In most cases this leads to the 8 - N or octet rule which links the coordination Z to atomic valence through the relation Z = 8 - N for N 2 4. However, there are a lot of exceptions to this rule, for example, the case of crystalline Ge-Se in which Z is 3 for both Ge and Se instead of being respectively 4 and 2. In all these covalently bonded materials the cohesive energy mainly results from the formation of the local bonds between nearest neighbors and not from incomplete filling of a broad band as in metals. This cohesive energy is much less sensitive to variations in interbond angles, and to long range order than to stretching of the covalent bonds. This explains why, under appropriate preparation conditions, most of these materials can be found either in the amorphous or in the glassy state character-

ized by a loss of the long range order. However, as shown by the determination of their radial distribution function, these systems still possess a well-defined short range order similar to what is observed in the crystalline phases. In this section we examine some features of non-crystalline semiconductors. We first consider some elemental amorphous systems like a-Si, a-As, and a-Se and examine possible modifications in the density of states. We then detail the properties of a typical intrinsic defect likely to be present in aSi, i.e., the isolated dangling bond. Finally we make some comments on the electronic structure of more complex systems like SiO,, Ge,Sel-, ...

1.5.1 The Densities of States of Amorphous Semiconductors From our qualitative discussion in Sec. 1.1 remember that it is likely that amorphous semiconductors will give rise to energy bands. In these cases, the pseudocontinuum of states arises no only because there are a large number of atoms but also because there is some disorder inherent to such structures which tends to spread the energy spectrum, leading to band tails. To get a more precise feeling for what happens in the amorphous state, it is necessary to build idealized models which could be mathematically tractable and be considered as reference situations. It is for such reasons that continuous random networks have been developed to model systems like a-Si, a-Ge, at a-SO,. These are constructed by representing atoms and bonds as balls and sticks and connecting them together randomly without loose ends or dangling bonds. Usually such networks lead to a predicted radial distribution function relatively close to the experimental one. However, they remain idealized descriptions since the

1.5 Non-Crystalline Semiconductors

real material can contain clusters, dangling bonds, and other eventual deviations. Assume for a moment that we are dealing with such an idealized lattice for a-Si. The first problem that arises concerns the general shape of the band structure: does it lead to a fundamental energy gap and to the same structures in the valence band as in the crystalline system? An interesting answer to such complex questions can be obtained via simplified Hamiltonians such as those offered by the empirical tight binding theory. This was achieved by Weaire and Thorpe (197 1) on the basis of an Hamiltonian first proposed by Leman and Friedel (1962). This was based on the use of sp3 hybrids and included only two parameters: the intrabond coupling between such hybrids and the coupling between any two hybrids centered on the same atom. Here we shall reproduce the same conclusions by using the more involved Hamiltonian described in Sec. 1.3.1.1 for crystalline Si. We again build bonding and antibonding orbitals which are exactly the same as for the crystal. We treat the broadening of the bonding and the antibonding band separately. Concentrating on the bonding band, we get the analog of Eq. (1-76),

(E - Eb + 2 4 ) Ubij = A(si + sj)

(1- 129)

in view of the fact that we are dealing with an elemental system ( A A= A , = A ) . We directly sum this expression over j and get ( 1- 130)

where the sum overj extends over the nearest neighbors of atom i. Equations (1-130) are the same as those one would obtain for an s band on the same lattice with unit nearest neighbors interactions &Si = C j

sj

(1-131)

45

The eigenvalues of the two matrices are thus related through

E = Eb + 2 A

+ Ae

(1-132)

The Hamiltonian matrix defined by Eq. ( 1- 13 1) is known as the connectivity matrix and general topological theorems (Ziman, 1979) allow us to show that its eigenvalues E must lie in the interval [- 4, + 41 imposed by the coordination number. This means that the energies in the bonding band must lie in the range (1-133) Eb+ 2 4 -4 E S E b + 2 4 + 4 IAl This is the same result as for the crystalline case and thus shows that the bonding band for this idealized model of a-Si must be contained in the same energy interval as for cSi. The same reasoning applies to the antibonding band. Thus the gap between these two bands is at least as large as for the crystal in the same model. Inclusion of the interactions between the bonding and antibonding states can only increase this gap by mutual repulsion of the two bands. The first conclusion of the model is thus that the gap still exists in a-Si. The second question concerns the structures in the valence band. In the crystal some characteristic structures of the density of states are due to the Van Hove singularities which are a signature of long range order, as we discussed above. In the amorphous system these should be washed out as shown by the comparison of the density of states n ( & ) of the connectivity matrix Eq. (1-131) between the crystal and a Bethe-lattice with coordination 4 (Lannoo, 1973). This is effectively what the XPS and e2(co) curves represented in Fig. 1-26 show for c-Si and a-Si. The real atomic structure in a-Si is likely to deviate from the idealized one. To satisfy the local bonding constraints, distortions in bond angles and even in bond

46


(1979) and detailed consideration about localized and extended states can be found in Ziman (1979) and Weaire (1981).

40-

c-Si

30 -

-3 v

w"

20

10

1.5.2 Numerical Computations

I

-

Improvements in computational power have now allowed numerical calculations of the electronic states in amorphous structures. Major progress in this regard has been the derivation of computer-generated random continous networks with tetrahedral

-

0

lengths are likely to occur. These will give rise to band tails. It is thus expected that the gap region will not be free of states since the conduction and valence band tails will overlap as shown schematically in Fig. 1-27. As regards the transport properties, the localized or the delocalized nature of these states is of importance. A commonly adopted view (Ziman, 1979; Weaire, 1981) is that of a mobility edge separating the two types of states as shown in Fig. 1-27. Finally, the situation is complicated further by the existence of defects in the bonding, in particular the isolated dangling bonds which are treated in the following section. A more complete review of amorphous or glassy semiconductors is given in Ziman

EC

EC

Figure 1-27. Schematic density of states in the gap region of amorphous semiconductors.

et al., 1988), the first order Raman spectrum is found to be in very good agreement with the experimental one (Marinov and Zotov, 1996). It also reproduces with good accurracy the experimental radial distribution function of amorphous silicon. Recent theoretical studies of phonons in a-Si also confirm the superiority of this model compared to others (Knief et al., 1998). The electronic structure for the WootenWiner-Weaire model has been calculated (Allan et al., 1998) in the sp3s* ETB approximation (Vogl et al., 1983) and a d-* variation of the tight binding parameters with distance d (Harrison, 1980). Application of the method to a-Si gives rise to large band tailing, which is attributed to a small number of bond angles that deviate greatly from the tetrahedral 109" value. An efficient simulation of hydrogenated amorphous silicon (a-Si :H) was obtained by removing the atoms with the most distorted bond angles and saturating the resulting dangling bonds with hydrogen atoms. The resulting gap and Urbach tails then become comparable with the experimental one (Allan et al., 1998). The same description


has allowed the study of confinement effects for quantum dots of a-Si-H (Delerue et al., 1996) and to show that doping of a-Si-H results in much larger binding energies of donors and acceptors than in the crystalline material (Allan et al., 1999).

1.5.3 Dangling Bonds A lot of physical situations in tetrahedrally coordinated materials involve the rupture of bonds. The simplest well-documented case is the Pb center at the Si-SiO, interface which corresponds to a tricoordinated silicon atom, i.e., to the isolated dangling bond. Such defects are also likely to occur in a-Si. Another well-known situation is the vacancy in silicon (and to a less extent in compounds) where there are four interacting dangling bonds. Let us first shortly recall the basic physical properties of dangling bonds. The simplest description comes from a tight binding picture based on an atomic basis consisting of sp3hybrid orbitals. The properties of the bulk material are dominated by the coupling between pairs of sp3 hybrids involved in the same nearest neighbor’s bond. This leads to bonding and antibonding states which are then broadened by weaker interbond interactions to give, respectively, the valence and conduction bands. In the bonding-antibonding picture, the rupture of a bond leaves an uncoupled or “dangling” sp3 orbital whose energy is midway between the bonding and antibonding states. When one allows for interbond coupling, this results in a dangling bond state whose energy falls in the gap region and whose wave function is no longer of pure sp3 character, but is somewhat delocalized along the backbonds. Experimentally this isolated dangling bond situation is best realized for the P b center, i.e., the tricoordinated silicon atom

47

at the Si-SiO, interface (Poindexter and Caplan, 1983; Caplan et al., 1979; Johnson et al., 1983; Brower, 1983; Henderson, 1984) but it can also occur in amorphous silicon (Jackson, 1982; Street et al., 1983) as well as in grain boundaries or dislocations. It has been identified mainly through electron spin resonance (ESR) (Poindexter and Caplan, 1983), deep level transient spectroscopy (DLTS) (Johnson et al., 1983; Cohen and Lang, 1982) and capacitance measurements versus frequency and optical experiments (Jackson, 1982; Johnson et al., 1985). The following picture emerges: i) The isolated dangling bond can exist in three charge states: positive D+, neutral Do, and negative D-. These respectively correspond to zero, one, and two electrons in the dangling bond state. ii) The effective Coulomb term UeE, i.e., the difference in energy between the acceptor and donor levels, ranges from -0.2 to 0.3 eV in a-Si (Jackson, 1982) to about 0.6 eV at the Si-SiO, interface (Johnson et al., 1983). The ESR measurements give information on the paramagnetic state Do through the g tensor and the hyperfine interaction. Their interpretation indicates that the effective “s” electron population on the trivalent atom is 7.6% and the “p” one 59.4%, which corresponds to a localization of the dangling bond state on this atom amounting to 67% and an “s” to “p” ratio of 13% instead of 25% in a pure sp3 hybrid. This last feature shows a tendency towards a planar sp2 hybridization. Several calculations have been devoted to the isolated dangling bond. However, only two of them have dealt with the tricoordinated silicon atom embedded in an infinite system other than a Bethe lattice. The first one is a self-consistent local density calculation (Bar-Yam and Joannopoulos, 1986) which concludes that the purely electronic value of the Coulomb term (i.e., in the

48


absence of atomic relaxation) is U = 0.5 eV. The second one is a tight-binding Green's function treatment in which the dangling bond levels are calculated by imposing local neutrality on the tricoordinated silicon (Petit et al., 1986). In this way the donor and acceptor levels are respectively ~ ( 0+), = 0.05 eV and ~ ( 0-), = 0.7 eV. Their difference corresponds to U = 0.65 eV, which is in good agreement with the local density result. Both values correspond to a dangling bond in a bulk system and can be understood simply in the following way: the purely intra-atomic Coulomb term is about 12 eV for a Si atom; it is first reduced by a factor of 2 since the dangling bond state is only localized at 70% on the trivalent atom; finally, dielectric screening reduces it by a further factor of E = 10. The final result 6 / ~ gives the desired order of magnitude 0.6 eV. At the Si-SiO, interface, however, the situation becomes different because screening is less efficient. A very simple argument leads to the replacement of E by ( E + 1)/2 so that the electronic Coulomb term for the P, center should be twice the previous value, i.e., U(P,) = 1.2 eV. An extremely important issue is the electron-lattice interaction. There is no reason for the tricoordinated atom to keep its tetrahedral position. A very simple tight binding model (Harrison, 1976) shows that this atom does indeed experience an axial force that depends on the population of the dangling bond state. This is confirmed by more sophistical calculations (Bar-Yam and Joannopoulos, 1986). The net result is that, when the dangling bond state is empty (D+) then the trivalent atom tends to be in the plane of its three neighbors (interbond angle 120"). On the other hand, when it is completely filled (D-) it moves away to achieve a configuration with bond angles smaller than 109" as for pentavalent atoms. Finally, the situation for Do is obviously intermediate

with a slight motion towards the plane of its neighbors. For the three charge states D+, Do, and D-, corresponding to occupation numbers n =0, 1, and 2, respectively, one can then write the total energy in the form E(n, u ) = (1-134) = n Eo + (1/2) U n2- F ( n ) u + (1/2) k u2 where u is the outward axial displacement of the tricoordinated silicon atom, F(n) the occupation dependent force, U the electronelectron interaction, and k the corresponding spring constant which should show little sensitivity to n. We linearize F ( n ) F ( n ) = Fo + FI (n - 1)

(1 -1 35)

an minimize E(n, u) with respect to u to get Emin(n). The first order derivative of Emin(n)at n = 1/2 and n = 3/2 gives the levels &(O, +) and &(-, 0). The second order derivative gives the effective correlation energy:

u,, =u--42 k

(1-136)

Theoretical estimates (Bar-Yam and Joannopoulos, 1986; Harrison, 1976) give Fl = 1.6 eV A-' and k = 4 eV (A2)-' (Lannoo and Allan, 1982) so that F:/k is of the order 0.65 eV. This has strong implications for the dangling bond in a-Si where U,, becomes slightly negative as concluded in Bar-Yam and Joannopoulos (1986) but this result should be sensitive to the local environment. On the other hand, with U= 1.2 eV, the P, center at the Si-SiO, interface would correspond to Ueff=0.6eV, in good agreement with the experiment. The theoretical finding that Ueffis slightly negative for the dangling bond in a-Si leads to an inverted order for its levels, in which case the Do state could never be stable (Bourgoin and Lannoo, 1983). This


does not agree with the experiment, in which an EPR spectrum which seems characteristic of Do has been observed. One possible reason for this discrepancy is the suggestion that a-Si may contain overcoordinated atoms (Pantelides, 1986) which might be responsible for the observed features. However, recent careful EPR measurements (Stutzmann and Biegelsen, 1989) seem to rule out this possibility, practically demonstrating that dangling bonds indeed exist and with a positive U,, This would mean that theoretical calculations have underestimated the electronic U for reasons which are still unclear. 1.5.4 The Case of SiO, Glasses

We now give a simplified analysis of the valence band structure of these glasses based on an extension of the tight binding arguments developed before. Let us first consider the case of Si02.The molecular model is essentially the one developed by Harrison and Pantelides (1976). The building Si-0-Si unit is shown in Fig. 1-28. Again one builds sp3 hybrids on the Si atoms while on the oxygen atom one keeps the natural sp basis. The oxygen “s” state is by far the lowest in energy and, to

49

the first order, its coupling with other states can be neglected. It will remain atomic-like at its atomic value E,(O). On the other hand, the oxygen p energy E,,(O) is closer to the silicon sp3 energy Eand the interaction of the corresponding states must be taken into account. The molecular states of the Si-0-Si unit of Fig. 1.28 are then built from the two sp3hybrids a and b pointing towards the oxygen atom and the px, p,,, and pz oxygen “p” states. It is clear that pz, being perpendicular to the Si-0-Si plane, will remain uncoupled at this level of approximation giving one state at the atomic value E,,(O). Thus the sp3 states a and b will only couple to px and py via the projection of these states along the axis of the corresponding nearest neighbor direction. All interactions reduce to one parameter ppdefined as the interaction between an sp3 orbital and the p orbital along the corresponding bond. By symmetry px only interacts with (a-b)/* giving rise to strong bonding and antibonding states at energies (1-137)

while py and (a + b)/* lead to weak bonding and antibonding states (1-138)

‘U-

Figure 1-28. Si-0-Si unit for building the molecular model with the two sp3 hybrids of the Si atoms and the three p states of the 0 atom, p: being perpendicular to the plane of the figure.

where 2 8 is the Si-0-Si bond angle. The resulting valence band density of states per Si-0-Si unit is pictured in Fig. 1-29. It consists of delta functions at energies E,(O), ESB, EWB, and E,(O), the

50


Figure 1-29. a) SiOz density of states calculated by Robertson (1983). b) Density of states in the molecular model with a Gaussian broadening of 0.5 eV. - The vertical axis corresponds to densities of states in arbitrary units, the horizontal axis to energies, in units of 5 eV, SB, WB and LP denote strong bonding, weak bonding and lone pair states.

-15

-10

-5

0

weight of each state per Si-0-Si unit being equal to unity. The influence of further interactions can now be analyzed as for pure Si. If we call As and Aw the interaction between strong and weak bonding states belonging to adjacent Si-0-Si units then we can repeat the treatment previously applied to Si simply by replacing A with As or A,. This means that we get densities of states in the strong and weak bonding bands that have exactly the same shape as for Si, consisting of the superposition of a broad and a narrow, almost flat band. This behavior is apparent in the calculated density of states in Fig. 1-29a. These results are in good qualitative correspondence with photo-emission data (Hollinger et al., 1977; Di Stefan0 and Eastman, 1972; Ibach and Rowe, 1974) and more sophisticated numerical calculations (Chelikowski and Schluter, 1977; O'Reilly and Robertson, 1983). Essential information provided by Eqs. ( 1 - 137) and (1-1 38) is that the splitting between the strong and weak bonding bands is a very sensitive function of the Si-0-Si angle 2 8. Any cause of randomness in Bsuch as the existence of a strained SiO, layer is then likely to induce some broadening of

5

10

these two bands and partially fill the gap between them. Note that in an extreme situation where 0 - 90", like in GeSe,, the strong and weak bonding energies become identical, leading to a qualitative change in the shape of the density of states. We are now in the position to discuss qualitatively the behavior of the SiO, layer as a function of composition. Numerical calculations have been performed that are all based on a tight binding treatment combined with a more or less refined cluster Bethe lattice approximation (Lannoo and Allan, 1978; Martinez and Yndurain, 1981). Again the molecular model gives precious information that is confirmed by the full calculation. For this, let us consider the results of Lannoo and Allan (1978) which are pictured in Fig. 1-30. In the molecular model each Si-0-Si bond corresponds to a density of states as given in Fig. 1-29b, while each Si-Si bond corresponds to one bonding state which, for the parameters corresponding to Fig. 1-30, falls at an energy slightly higher than E,(O), the energy of the SiO, non-bonding state. If we start from the SiO, limit each Si-Si bond acts like an isolated defect giving rise to a defect level at

1.6 Disordered Alloys

51

energy. At still higher Si concentrations there will be three and then four Si-Si bonds connected to each Si atom. For reasons discussed above such situations are characterized by a flat band at + 2A and a broad band at lower energies. This regime will thus exhibit a peak of increasing height at the energy of the top of the pure Si valence band. This is exactly what happens in Fig. 1-30. Note also that the strong bonding band has exactly the reverse behavior: the height of its peak and its width both decrease. The last point that is clearly seen in the figure is that, for smaller 0, the separation between the strong bonding states and the weak and non-bonding states is smaller. All these conclusions are in qualitative agreement with experimental observations concerning the valence band of the SiO, systems and of the transition layer at the Si-SiO, interface.

s! h

C

1.6 Disordered Alloys -15

-12

-9

-6

-3

E (eV)

Figure 1-30. Theoretical density of valence band states for SiO, systems for different compositions and different bond angles. The flat parts correspond to the zero of n ( E ) in each case.

the energy of the bonding state of Si, i.e., just above the SiO, valence band. When the concentration of Si-Si bonds increases this defective state will begin to broaden into a band with no defined structure at small concentrations. This corresponds to Si04,3 in Fig. 1-30. It is only when the concentration is high enough for Si chains to appear that the situation changes qualitatively. If, as before, A characterizes the interaction between two adjacent Si-Si bonding states, then the DOS of a Si-Si chain exhibits two divergences at k 2 A from the bonding

Compounds with a well-defined lattice but where there is substitutional disorder on the lattice sites compose a series of important electronic structure problems. This is, for instance, the case of pseudobinary semiconductor alloys like Ga,Al,-,As, In,Gal-,As .. . . Since such alloys are of much importance, here we give an account of the work performed on these systems. However, before doing this we must introduce general methods like the virtual crystal approximation (VCA), the average t-matrix approximation (ATA), and the coherent potential approximation (CPA). Again these methods, which correspond to complex systems, are applied within the framework of the tight binding approximation. To perform such calculations on disordered systems one must use the Green's

52


function formalism. For this we introduce the resolvent operator G ( E )of the system, defined as

where H is the Hamiltonian of the system and E is the energy. One major property of the resolvent operator is that the density of states n (E) can be expressed as 1

n ( ~=)- - Im TrG(E)

n

n(&)= - - Tr Im(G(E)) n;

(1-141)

The advantage is that the quantity (G(E)) becomes statistically homogeneous, i.e., if one has a random alloy on a given lattice, (G( E)) acquires the lattice periodicity, while the original G(E)has not. It is to be noted that (G(E))is not equal to ( E + i r] - (H))-’; instead we define a self-energy operator Z(E)such that one can write ( G ( E ) ) =( & + i r ] - ( H ) - Z ( ~ ) ) - l

We want to present different possible levels of approximation here and illustrate them on a tight binding model of a random alloy. This model will consist of a tight binding s band designed to treat a random alloy A,B,-,, the atomic sites forming a lattice with one site per unit cell. This tight binding Hamiltonian can thus be written: (1-143)

(1-140)

where Tr stands for the trace and Im means imaginary part. When considering a large disordered system, the fact that one takes the trace means that one performs an average over different local situations. One would get the same result by performing an ensemble average, i.e., by considering all configurations that the system could take and weight them by their probability. This means that n ( E ) can also be obtained by performing the average (G(E))of the resolvent operator and writing 1

1.6.1 Definitions of the Different Approximations

(1-142)

The determination of this 2 i s the aim of the following different approximations.

where V is a nearest neighbor interaction taken to be independent of disorder while the on-site terms can take two values; for an A atom, E~ for a B one. Let us begin with the simplest type of approximation: the VCA (virtual crystal approximation). As indicated by its name, this consists of assuming that the average Hamiltonian (H) = fi gives a correct account of the electronic structure. This means that the exact (G(E))is replaced by an approximate expression G(E): G(E)= ( E + i r] - R)-’

( 1 - 144)

From its definition, the expression of R in the simple tight binding model is given by: H=[xE*+(l-X)Eg]C

+ v C 10(1’1

1

Il) (ZI+

(1-145)

11’

which can be solved by using the Bloch theorem. We now want to go a step further and do the proper averaging of (G)over one site while the rest of the crystal is treated in an average field approximation. The first obvious thing to do is to start from the virtual crystal, determine G, then consider the local fluctuations on a given site as perturbations and perform the average (G1Jfor that site,

53


where G , is the diagonal element of G. Let us illustrate this with our specific model. We thus start from fi defined in Eq. (1- 145) and look at the possible fluctuations at site 1. If site 1 is occupied by an A atom, the on site perturbation will be WA

A comparison between the two expressions allows us to express EATA in the form

(1-151) I

= &A - [x &A + ( 1 - x) EB] = = ( 1 -x) (&A - &B)

(1 - 146)

while for a B atom it will be WB=&B-[x&A+

(1-x)&B]=-x(&A-&B)

I

It is customary to introduce the average t matrix f, equal to the numerator in Eq. (1-151). In this way one gets the usual form of ZATA (see Ziman, 1979, for details):

(1-147) We treat both cases at the same time by assuming that there is a perturbation Wl on site 1 with possible values WA or WB. The diagonal matrix element G f Ican be obtained by applying Dyson's equation (G = G + G WG ) ,

since has translational periodicity. We now say that the average (Gll) with GII given by Eq. (1-148) represents a good approximation. This defines the average t-matrix approximation which can be written

On the other hand, ( G ) is quite generally related to Z(E)through Eq. (1-142). To the same degree of approximation as before, one should thus write that (Gff)ATA is due to the on site perturbation ZATAapplied to site 1. This leads to

(1 -1 52)

This provides a considerable improvement on the VCA, but a definitely better approximation is given by the CPA (coherent potential approximation) which we will now discuss. The CPA uses the same basic idea as the ATA, i.e., it is a single site approximation. However, instead of using an average medium corresponding to the average Hamiltonian fi it is certainly much better to use H+E(&),where the 2 i s the unknown selfenergy. Starting with this, the perturbation at site 1 is now given by W,- E(E),Wf being defined as before. Thus the average ( G f l )is given by (1-153) -

(Glf

)CPA =

Go ( E - X E ) ) 1 - [W, - a & ) 1Goo(&- a&))

But one must note that the self-energy is assumed to be the same on each lattice site so that the average crystal resolvent is simply Goo, where E is shifted by the coherent potential Z(E).On the other hand, for Z to be consistently defined, should be equal to Goo(&-2'(~)).Applying this to Eq. (1-153) one immediately gets the condition ( 1 - 1 54)

[w,- 2(&)1 Goo ( E - a&)) )=O

1 - [% - Z(&)] G&-

Z(&))

54


which defines the expression of ZCpA(&) bond. In such a way the Hamiltonian is defined on a perfectly regular lattice, but (Ziman, 1979). even in this case it is not approximation in view of the existence of several orbitals per 1.6.2 The Case of Zinc Blende atom and of diagonal and non-diagonal disPseudobinary Alloys order. The possibility of performing an MCPA Here we summarize fairly recent calculacalculation is related to the choice of the tions performed on these disordered alloys particular unit cell shown in Fig. 1-3I. As specifically, In, -,Ga,As and ZnSe,Tel-, in the previous sections, use is made of a sp3 (Lempertet al., 1987). This work makes use energy the coupling VIA between two of an extension of the CPA called the MCPA different sp3 hybrids, and the intra bond (molecular coherent potential approximacoupling VfB. As we have seen, such terms tion) which is particularly well adapted to dominate the Hamiltonian for zinc-blende these systems. semiconductors and they are likely to give This case of alloys is of technological the dominant contribution of disorder efinterest and it is important to be able to treat fects. disorder effects accurately. This disorder As explained at the beginning of this seccan be conveniently divided into chemical tion the disordered alloy Hamiltonian will and structural components. The former is related to the different atomic potentials of be replaced by an effective Hamiltonian: the two types of atoms, while the latter is (1-155) Heff(d = (H> + a.9 associated with local lattice distortions, essentially due to differences in bond length. MCPA is based on the assumption that the Such an effect was observed by Mikkelsen self-energy Z(E)is cell-diagonal (the cell and Boyce (1982,1983) in EXAFS (extendbeing defined in Fig. 1-31). It is thus repreed X-ray fine structure) measurements on sented by an 8x8 matrix in the basis of the In,-,GaJs. There the In-As and Ga-As bond lengths were found to vary by less than 2% from their limiting perfect crystal values, despite a 7% variation in the average X-ray lattice constant. This was also found in other zinc blende alloy systems (Mikkelsen, 1984). The electronic structure of these materials is described in the tight binding approximation (extended to second nearest neighbors in the particular calculation of Lempert et al., 1987). The structural problem in an A;-fi;B alloy causes a difficulty since it leads to local distortions with respect to the .....:. ....... ...... ...%. average zinc-blende structure. This is overI Zf ..:...... ..... come by assuming that the atoms lie on the sites of the average crystal but scaling the Figure 1-31. The unit cell in the molecular coherent dominant nearest neighbor interaction to potential approximation, defining the relevant interthe value appropriate to an A'B or A"B actions between sp3 hybrids.

3' >


sp3 orbitals. With this one can obtain exactly the same expression as in ordinary CPA except that one must replace all quantities W,, ($0 by 8x8 matrices within the same sp3 basis. The consistency condition (Eq. (1- 153)) also applies but with matrix inversion and multiplication. We can rewrite it for our two component system (atoms A' and A") as:

a

(1-156) { [(WA, GO]-' - 1 }-' + + { [(wA,,GO]-' - 1 }-' = 0

a

or, since

WAe

*

(1-157)

+ WAt, = 0, to:

Z(&)=-[wA 8-

I

.-c 10-

Figure 4-3.Representation of experimental ionization energies (energy levels) ascribed to iron in silicon and demonstrating the identification problem. (After Graff and Pieper, 1981).

a

-

v

I’

I

I

I

I

I

I

\

I

I

-

-- I L-- 0.5 -

,’ /&

I ,

\\

\’ I

I

.-C

‘tu‘

\,-m

*,*,

Ol

Valence band

I

\..,b’ 9

ZI

11

I

p,b

Me’”

12& c

W

I

.,4,

-‘

al

I

I

’\ 1

k 1 -

--

-

>r

P

C

w

174

4 Deep Centers in Semiconductors

fined within the small gap region (of the order of 1 eV) of various semiconductors points to an effective screening mechanism and hence also strongly favors a delocalized model. Only the most striking features of experimental data supporting controversial models have been given here, but the puzzle can readily be outlined in more detail (Zunger, 1986). Our general understanding of the physical nature of deep impurities comes from making experimental efforts with respect to the identification problem and from successfully resolving the above-cited paradoxical behavior of deep centers within electronic-structure theory. Accordingly, after introducing some frequently used graphical representations like level schemes and configurational coordinate diagrams, the central purpose of the present article is to figure out different approaches to the electronic structure problem insofar as this is necessary for global understanding, and to emphasize what various models have in common. The remainder of the contribution is devoted to highlighting special features of selected deep center systems via their electrical, optical or kinetic properties. Examples include excited states (chalcogens in silicon), large-relaxation effects (DX centers in semiconductor alloys), metastability and trends of deep donor-shallow acceptor pairs in silicon, and oxygen-related complexes (thermal donors). Some overlap with present structure models should be achieved from these results although longlasting controversies - as in the case of thermal donors in silicon - and many other problems in deep-level physics can not yet be resolved. Finally, the role of hydrogen in the passivation of shallow acceptors and other point defects is sketched.

Wide gap materials like S i c or GaN are not included in the present article because the electronic structure of defects in these materials cannot be considered as being dominated by covalency effects. Experimental and theoretical results concerning defects in S i c and GaN are therefore discussed separately in Chaps. 1 1 and 13 of this Volume.

4.2 Deep Centers: Electronic Transitions and Concepts 4.2.1 Ionization at Thermal Equilibrium As mentioned above, deep centers often show several charge states readily accessible to experiments that induce one or more ionizing transitions on the same defect. If thermal equilibrium is maintained at a fixed temperature and pressure, the fraction of centers being in a specified formal charge state relative to an adjacent one is given by (Shockley and Last, 1957)

where AG(q’q+l) is the increase in Gibbs free energy upon ionization and & refers to the standard chemical potential for transferring an electron from the Fermi level EF to the bottom of the conduction band. The formal charge state of the defect, q, changes to q+ I, thus making the defect more positive. Electronic degeneracy has been factorized out from AG and is described by the g factors. Thus AG(q’q+l) can be seen as the standard chemical potential for the ionization process, which is the thermally activated part in a reaction like Do + D++e-. Entropy terms still included in AGcqlq+*)arise from a redistribution of phonons populating

4.2 Deep Centers: Electronic Transitions and Concepts

the vibrational levels, because ionization usually weakens the lattice modes (Van Vechten, 1982). At temperatures well above 500 “C,AG(q/qfl)may drastically change, presumably due to non-harmonic effects in the lattice vibrations, whereby the contribu) tion from entropy to ~ ~ ( q / q + lstrongly increases (Gilles et al., 1990). Entropy terms may be separated from enthalpy terms according to the well-known relation AG(4/4+1)= A H ( 9 / 4 + 1 ) - T AS(4/4+1) (4-4) in oder to define “occupancy-levels” the Fermi level EF = E c - k by relating the ionization and the chemical potenenthalpy AHH(q/q+l) tial & to the conduction band edge. With these definitions (Baraff et al., 1980), Eq. (4-3) now reads E(q/q+l)= Ec-AH(q/q+l)and

If the weight of degeneracy and entropy is dropped, or there are cases where gq/gq+l G 1, AS(q/q+l) = 0, the ratio NJNq+, will be close to unity whenever the Fermi level crosses the occupancy level E(q/q+l). In particular, for amphoteric dopants (defects showing donor and acceptor behavior) and also for “negative U” centers (see later), it is sometimes useful to extend the concept of occupancy levels to two subsequent ionizations. This means determining the Fermi level position for which Nq/Nq+2= 1 in the absence of effects due to degeneracy and entropy. For this purpose, it is necessary to simply replace the numerator in the exponent of Eq. (4-3) by AG(q‘q+2)-2 = 2 [[AG‘q/q+2’/2]-pJ, separate entropy from enthalpy terms [Eq.

175

(4-4)] and, as before, relate enthalpy [now &q/q+2)/2] and & to the conduction band. This gives

L=[z)exp[ 1. [ N

-AS(q/q+2) kB

Nq+2

exp 2 [EF- E(q/q+2)] kB

(4-5 a)

T

where E(4/4+*) = (1/2) [E(q/q+l)+E(q+l/q+2) 1 is the appropriate occupancy level for two subsequent ionizations. Occupancy levels are obtained experimentally in principle by measuring thermally activated quantities such as DLTS emission rates. These are of the form

where AGn,, is related to the thermally activated process and depends on whether an electron or a hole has been emitted from the defect to the conduction band (AG,) or to the valence band (AG,), respectively. Ionization of the defect therefore occurs according to Dq + Dq+l+e- for electron emission and Dq+’ + Dq+h+ for hole emission. Electronic degeneracy is still contained in the entropy terms of AG,,, which may be split [Eq. (4-4)] into

176


{log [e,,,(T)/A,,,(T)] over 1/T} and Eqs. (4-6a, b). The factor A,,,(T) in Eq. (4-6) is given by (4-7) and contains u,,, the thermal-capture cross t E‘”’ section for electrons (n) or holes (p), the tt E, mean thermal velocity (v),,,, and the effecI I jJh I I “”’” tive density of states Nc,vat either the bot1 v tom of the conduction band (c) or the top of the balence band (v). Since (v),,- T112and Figure 4-5. Level scheme for interstitial manganese Nc,v- ~ 3 /,2the temperature dependence of in silicon (Si:Mn,). Dashed arrows indicate the therboth is (v),,, Nc,v- T 2 ;but on,,may also mally activated processes with corresponding ionization enthalpies. Numerical values for the occupancy depend on temperature (see Sec. 4.2.2) and, levels Pqlq+’) are Ec-0.13 eV (Mn;”), Ec-0.46 eV as a rule, has to be measured separately. (Mny”) and E,+0.24 eV (Mn?”) (Czaputa et al., Equation (4-3) can also be given in terms 1983). of hole emission to the valence band accordDq+h+ i with ing to the reaction Dq+’= ,uh-AG(q+’‘q)now being the appropriate within the framework of semiconductor numerator in the exponent. Relating the statistics (Blakemore, 1962; Milnes, 1973; standard chemical potential for holes (Ph) Landsberg, 1982). and the ionization enthalpy [M9+’Iq), Eq. (4-6b)l to the valence band edge gives a Fermi level EF = Ev+yhand an occupan4.2.2 Franck-Condon Transitions cy level E(q’9+’) = Ev+&4+’/9) for hole and Relaxation emission. With these definitions, Eq. (4-5) According to the requirement of thermal holds for any equilibrium that can be estabequilibrium in the energy level scheme lished between the defect and a band at a defined above, any level involves a transifixed temperature and pressure. tion between two totally relaxed defect conOnce occupancy levels are known for a figurations. There is, however, another given center, a level scheme can be conclass of transitions that correspond to censtructed like that displayed in Fig. 4-5 for ters that have been excited or ionized optiinterstitial manganese in silicon. cally. Apart from degeneracies and entropies, it Excitation by incident light may result, can be stated that when the Fermi level is for example, in an internal transition beabout midway between the two adjacent tween two localized electronic defect states Mn-” acceptor and Mno/+donor levels (Fig. leaving the formal charge state of the cen4-5, above), the impurity will be mainly in ter unchanged. If electron-lattice coupling the neutral charge state. On the other hand, is sufficiently strong, the lattice atoms near if the Fermi level crosses the Mn+/++level the defect site may be rearranged in retoward the valence band, for instance (Fig. sponse to the changed charge distribution at 4-5, below), the double positive charge state the defect. But the corresponding relaxation of interstitial manganese will be dominant. process occurs only after the excitation Details concerning single level and multienergy has been absorbed by the defect’s level systems have been extensively treated

E

*


many-electron system, since lattice relaxations are considered to proceed at a rate about three orders of magnitude smaller than that of the involved electronic system. Figure 4-6 shows the relations between optically induced transitions and lattice relaxation in a so-called configurational coordinate diagram, which helps one to keep track of important terms even in complicated processes. In Fig. 4-6, only the two interesting quantum states are shown by their adiabatic potential energy surfaces. The underlying physical idea in such a diagram is the Born-Oppenheimer approximation (Born and Oppenheimer, 1927; Adler, 1982), which separates electronic motion from that of the nuclei or ion cores (if only outer electrons have to be considered for interaction). Adiabatic then refers to an evolution of a system of electrons and nuclei (cores), where electron eigenstates do not change suddenly on ion core dis-

I

I'

I I

1

Qo

QR

>

Q

Figure 4-6. Franck-Condon transitions for an absorption-emission cycle resulting in a Stokes shift, AEStokes= 2 S fi w. S is the Huang-Rhys factor, which is a measure of the number of phonons effectively involved in a transition and therefore also accounts for electron-lattice coupling strength.

177

placements Q but provide the potential energy for ion core motion. The corresponding vibrational states are then harmonic oscillators with phonon energies En = (n+ 1/2) A o.Each electron quantum state is represented by its own parabola derived in principle by expanding total electronic energies to second order in the configurational coordinate Q at the stable positions (Q, and QR in Fig. 4-6). But it is only for linear coupling that parabolas are of the same shape as that found in Fig. 4-6. Beyond linear coupling, spring constants my be altered in an excitation leading to a shift in mean transition energies with temperature (thereby inducing changes in enthalpies and entropies in the case of ionization) and to unsymmetrical line shapes and mean energies for absorption (E,) and emission (I&), relative to zero-phonon transitions (Ezp). Mean transition energies corresponding to the most intense lines or to the center of a smoothed-out line shape (which depends on the Huang-Rhys factors S and is Gaussian in the high-coupling and high-temperature limit) depend on the overlap of vibrational wave functions in the initial and final states (Stoneham, 1975, Bourgoin and Lannoo, 1983). According to the Franck-Condon principle, most probable absorption transitions occur between states centered at configuration Q, (Point 1 in Fig. 4-6) for the ground state and states which have their wave functions concentrated near the classical turning points of the same configuration for the excited states (Point 2). When the system has relaxed non-radiatively by phonon emission to the stable configuration at QR, the situation is reversed. Emission of light (luminescence) then proceeds again at constant configuration (Points 3 and 4) followed by non-radiative relaxation of the electronic ground state to the Q, configuration thus terminating the cycle described by

178


Fig. 4-6. This simple picture will work surprisingly well in relating energy shifts, line shapes, and spatial extensions of wave functions to electron-phonon interactions, as long as non-degenerate electronic states can be coupled linearly to phonons of average frequency o by a single representative lattice mode Q. The reason for this success emerges from the fact that strong restrictions exist on mean square displacements and mean square velocities of atoms in a harmonic solid irrespective of strongly temperature-dependent details in lattice dynamics (Johnson and Kassman, 1969; Housely and Hess, 1966). Absorption of light can cause the photoionization of a deep center. The only difference to the charge-state-conserving excitations cited above lies in the fact that either the initial states or the final states are not localized near the defect. Thus, from experimental absorption studies of optical ionizations, thresholds as well as spectra may be obtained in terms of optical cross sections that can be fitted using as parameters the Franck-Condon shift S tz o,the spatial extension of the wave function associated with the localized level, and the respective oscillator strengths of transitions toward different extrema of a given band structure (e.g., Bourgoin and Lannoo, 1983). As mentioned before, in the occurrence of a Franck-Condon shift, the equilibrium position of the lattice embedding a defect may vary with its different formal charge states, depending on electron-lattice coupling. Again, such a situation is closely tracked by a configuration diagram. Figure 4-7 depicts a hypothetical donor-type defect which undergoes a distortion in a generalized configurational mode Q, when in its neutral state. In order to include the band gap, the defect in its positive charge state and the completely filled valence band are

D'+e'+h'

I

1

I

1

I

,

OR

3

Figure 4-7. Configurational coordinate model for a deep level. (After Watkins, 1983). For the level scheme, see text.

chosen as an undistorted reference configuration. Therefore, three adiabatic energy surfaces are accounted for, whereby the two centered at Q = 0 are separated by the total energy needed for the creation of an electron-hole pair. This energy does not depend on Q since the process has practically no influence on the configuration of the atoms near the defect. The arrows at the intersection points (marked on,up)indicate capture and emission processes which have their physical origin in nonadiabatic transitions left out of the Born-Oppenheimer approximation. Transitions between two vibronic states that differ in electronic energy but have the same total energy are very important in non-radiative trapping and recombination processes. EB in Fig. 4-6 denotes the barrier height by which capture rates appear thermally activated. If lattice relaxation occurs, thermal capture cross sections (Eqs. (4-6), (4-7)) become temperature dependent (e.g., Bourgoin and Lannoo, 1983). In the high-temperature limit, o n . p takes the simple exponential form - exp (-E,IkT)). The shifted parabola at QR represents the deep center in its distorted neutral charge state after having trapped an electron from the conduction band.


One may deduce a level scheme for comparison in three ways according to the previous section: (a) ionization via thermal activation, (b) calculation of the transition energy within a rigid, undistorted lattice, and (c) ionization via the absorption of light. It is clear from Fig. 4-7 that the position of the electrical level is given correctly only by the difference in total energies of the stable configurations Do+h+ and D++hf+e-, with energies taken at Q = QR and Q = 0, respectively. If relaxation effects are neglected, the ionization energy can be calculated from the difference in electron energies of the neutral and positive charge state of the deep center, both total energies being taken from the undistorted lattice configuration at Q = 0. Finally, if the ionization energy has been obtained from an optical experiment, the initial state will be defined by the relaxed configuration of the neutral defect state at Q = QR while the final state is reached by a Franck-Condon transition at constant configuration. The three ionization energies from Fig. 4-7 therefore appear in a relation Ecalc<Eth = Afp?J9+l)< Eopt.It should be noted, however, that by the definition of any chemical potential

179

Zero phonon energies obtained by fitting the spectral dependence of optical cross sections ao(ho)to an appropriate theoretical model (e.g., Lucovsky, 1965), or by extrapolating cross section data to the optical threshold, can be directly compared to the thermal activation energies hH"7'qC'). But this is only practicable if the cross sections are almost purely electronic, which applies to cases where defect-lattice coupling can be ignored (e.g., Schmalz et al., 1994). Although quantitative insight requires appropriate line-shape fitting, weakcoupling conditions (with a Huang-Rhys factor S = 1) at least allow estimation of E t h and Eoptbecause the phonon-dependent line shape of aO(Ao)manifests itself mainly in the "phonon tail" near the photo-threshold, and unfolds to a certain degree from the electronic part of the optical cross section (e.g., Mayo and Lowney, 1986). This is no longer true in the strong coupling regime (S + l ) , where accurate information on optical and thermal ionization energies rests on fitting the parameters Eth,S , and A w to the optical line shape, which is dominated by the lattice-relaxation Gaussian. From these parameters, the optical ionization energy, Eopt,may be obtained as the sum of Eth and the Franck-Condon shift S A 0 (Legros et al., 1987; Lang, 1986; Sec. 4.4.2.1). Optical cross sections aO(ho)are usually derived experimentally from optical emission rates

(4-9) eo = a0@(ho) and its application to an optical ionization where @(ti o)is the photon flux applied. process (here N denotes the number of The dependence of ionization energies on ionizations), the crystal volume is kept symmetric (breathing mode) or symmetryconstant by virtue of the Franck-Condon lowering distortions (e.g., Jahn-Teller disprinciple, whereas entropy S is conserved at tortions, induced by electronically degenerthe change of internal energy E if no phoate defect states with partial occupation (see nons are involved in the transition. ThereChapter 3; Sturge, 1967)) may result in a fore, at low temperatures and when ionizareversed level tion entropies are small, [ A Z - P=/ ~ + ~)I~ , ~ordering in extreme cases, where, for example, in a multilevel system [AE(9/4f1)]S.V.

180


like that shown in Fig. 4-5, the first donor level (O/+) and the acceptor level (40) appear in reversed order. This corresponds to a "negative U" situation envisioned by Anderson (1973, where the relation (4-10) holds for the difference of two subsequent occupancy levels. In thermal equilibrium, the q of such a series never represents a dominant intermediate charge state, contrary to the neutral state in the normal, "positive U" level ordering of acceptor and first donor in Fig. 4-5. For the case of reversed ordering in that example, the Fermi level position relative to the occupancy level E(-'+) = (1/2) (E(-/o)+E'o'+)) [see Eq. (4-5 a)] decides which one of the two preferentially accessible charge states is adopted by the negative U correlated defect. With the Fermi level above or below this level, the defect will mainly be in the negative or positive charge state, respectively. The role of relaxation is pointed out by splitting Eq. (4-8) into

ueff=u +AER

(4-1 1)

where U = E$q-l/q)-E$q/q+l)is the vertical (Franck-Condon) Mott-Hubbard correlation energy calculated at an undistorted (Q = 0) configuration. U results from the repulsive Coulomb interaction of the electrons occupying a single-particle state and in the absence of lattice relaxation, is responsible for the separation of first donor (O/+) levels and acceptor ( 4 0 )levels in the level scheme of Fig. 4-5. The contributions of lattice relaxation, which may be considerably different for two subsequent ionizations, are given by AE, = Edq-'/q) -Edq/q+'). This can best be understood with the help of diagrams such as Fig. 4-7. In cases where AE,cO, the positive U may be outweighed to promote negative4 behavior. Wellknown examples for negative4 systems

are the vacancy in silicon (Baraff et al., 1979,1980; Watkins and Troxell, 1980) and interstitial boron in silicon (Harris et al., 1982).

4.3 Phenomenological Models and Electronic Structure In the light of more recent theoretical results, a deep center is characterized by a series of bound states and resonances produced by localized perturbation. Nevertheless, it is often useful to introduce symmetry via point charges representing ligands at an impurity site, or to qualitatively select eigenvalues or band resonances representing states that are important for modeling various interactions of the defect with the host crystal. In order to circumvent the rather opaque mathematics in presenting results of modern electronic-structure theory, two models, each in favor of either a localized or a delocalized electronic configuration of a defect, will be introduced below and used throughout the following discussion.

4.3.1 The Point-Ion Crystal Field Model The pioneering work of Ludwig and Woodbury (1962), based on EPR studies, led to a semiempirical model for the electronic structure of transition metals in silicon that successfully accounts for most of the experimental findings to date. Electron paramagnetic resonance (see, e.g., Slichter, 1980) exploits the manifold of interactions that unpaired electrons undergo in a solid. These include interactions of orbital motion and spin with each other, with an applied magnetic field and with the magnetic moments of the nuclei. Electrostatic and covalent interaction reflects the symmetry of the crystalline environment. EPR spectra

4.3 Phenomenological Models and Electronic Structure

involve the lowest-lying states of a paramagnetic ion, usually considered a rather isolated system, which can be described in terms of a so-called spin-Hamiltonian

+ A J * Z - ( y + R ) & B-Z

+ [ I ( I + 1) - m 2 +

+ m (2M-

l)] A2/2 h

m M +3/2 +1/2 *1/2 -1/2

--3/2

(4- 12)

Eq. (4-12) is appropriate for tetrahedral symmetry and effective angular momentum J2 2. The leading term describes the Zeeman splitting while the second accounts for zero-field splitting due to the crystal field; the remaining terms describe the hyperfine interaction (containing the hyperfine parameter A), and the direct interaction of the external magnetic field with a nucleus of spin I (here the parameters y and R represent the isotropic and anisotropic part, respectively). p and pN denote the Bohr magneton and the nuclear magneton, and a is the cubic field splitting parameter. In general, g , A , and R are tensor quantities (Low, 1961; Abragam and Bleaney, 1970). For JO, the deep level is again host-like, but it well as band states of the pure host that are shows some bonding character. Pinning to important for host-impurity interaction, the dangling bond energy of the host occurs often are given in terms of the “spectral but this time the deep at increasing Eimpurity, local density of states” (in the form of more level enters the gap according to a valence or less pronounced peak structures). One band threshold. No hyper-deep level exists may substitute the most important peaks by in the case of nominal acceptors. weighted delta functions in order to get an For a large number of sp-bonded impurapproximation for the defect molecule picities that substitute the cation or the anion ture. Figure 4-13 displays a standard situasite and the zincblende hosts (Si, Ge, Gap, tion as occurring for the heavier elements in GaAs, InP, InAs, InSb, Alp, AIAs, ZnSe, the 3d series in silicon according to the ZnTe), predictions were made for the relaresults (see next section) of quantitative tive ordering of ionization energies of a, theories on transition elements in sp3-bondand t, states from the semi-empirical tight ed semiconductors. Again the a, -symmetric binding method. For alloys (e.g., (s-like) and the t2-symmetric (p-like) states GaAs,-xPx), deep trap levels were predictformed from the dangling bonds and the ed and experimentally confirmed to follow atomic s and d,, states of the impurity interthe pinning energy of the Ga dangling bond act according to their relative energetic (see Fig. 4-12) rather than the r, or X I positions. Thus the antibonding impuritypoints of band edges upon varying the comlike a, level (resonant with the conduction position (Vogl, 1984).

JTpurity

186


EC

+4s

/

EV

- - - 2#f# Dangling hybri,ds

"Molecules"

3d

Atom

Figure 4-13. Simplified defect molecule picture (a further a l resonance from the backbonds of nearest neighbors (Scheffler et al., 1985) is not shown), reflecting qualitatively the interactions of s and d states of substitutional 3d transition metal impurities with the dangling bond system of the host. The single particle levels (spin polarization omitted) are shown as bound states in the gap, the nonbonding e levels and the bonding t2 resonances are populated as an example according to neutral cobalt in silicon. The occupation of the al resonance, representing the fully occupied a, singlet of the dangling bond system of the vacancy, does not change upon the modeled interaction and therefore is not marked separately. (After Beeler et al., 1990).

band) and the antibonding host-like t, state constituting the deep level in the gap are created. The resonant a, level in the conduction band remains unoccupied; however, in addition to the two electrons residing originally on the t2 gap level of the neutral dangling bond system, four electrons from the impurity are needed for filling the bonding t2 level deep within the valence band. This confirms the findings of Ludwig and Woodbury presented in Sec. 4.3.1 suggesting a transfer of s electrons into the d shell and of four electrons into the sp3bonds. The nonbonding e level is not markedly affected by host interaction since the vacancy states have practically no e character (which is the actual justification for the simple picture given in Fig. 4- 13).

However, for interstitial 3d impurities the situation is different. An interstitial atom is embedded in a host environment where all bonds are complete. Thus hybridization is expected only with the tails of sp3 hybrid orbitals on the surrounding atoms. If one compares Fig. 4-9 and Fig. 4-10 for the interstitial site, one realizes that the lobes of d,,-like (t2) orbitals point to the four nearest silicon neighbors, whereas dx2,2-like (e) orbitals point to the six next-nearest neighbors. These directions are imposed by T, symmetry for forming 0-type bonds between host p states of e, t2 representation, and d states of an impurity at the interstitial site. Local densities of states (LDOS) of the pure silicon crystal, projected Onto the interstitial site (Zunger, 1986; Beeler et a]., 1990) show the availability of both t2 states from the first (nearest) coordination sphere and e states from the second (next-nearest) coordination sphere. In principle, this is also confirmed by cluster calculations (De Leo et a]., 1981) in the form of discrete dlike levels of a Si,,H,, cluster. Figure 4-14

\-I

Host

ti a

I

Interaction host-impurity

Atom

Figure 4-14. Simplified interaction model for a transition metal occupying an interstitial site of tetrahedral symmetry. Gap levels are populated according to neutral manganese in silicon.


depicts the interaction between d-like host states (as before approximated by discrete levels) and the atomic d,,,, orbitals of the transition metal at the T, interstitial site. Since symmetric host a, states are also available at the interstitial site, by their interaction with the atomic s states a resonant antibonding impurity-like a, state is formed within the conduction band and remains unoccupied. Once again, this is in formal agreement with the Ludwig-Woodbury model, suggesting a transfer of s electrons into the d shell for interstitials as well. The p-d hybridization leads to bound states of e and t, symmetry in the gap, showing antibonding character, and to their counterpart in the form of bonding resonances deep within the valence band. Contrary to substitutional 3d atoms, the gap levels must accommodate all valence electrons of the impurity. An interesting feature of the covalently delocalized models presented so far concerns the relative ordering of the e, t, gap levels: For substitutional 3d impurities, the effective crystal field splitting, with the order being t2 above e, results from the hybridization of only the t2-symmetric states with dangling bond host states of the same symmetry, in contrast to the e-symmetric impurity states which remain nonbonding and resemble atomic states. For interstitial 3d impurities, both e- and t,-symmetric states couple to the relevant host states, but the host-like, antibonding t2 gap level is repelled by antibonding conduction band states of t, character, while the e gap level is not; hence the order is e above t, (Fig. 4-14).

4.3.3 Transition Metals: Results of Quantitative Calculations As pointed out above, the relative ordering of the crstal field splitting is also ac-

187

counted for by the covalently delocalized model of a deep center. However, many more physical properties are covered by that point of view as has been revealed by quantitative calculations. In order to emphasize the most striking results, in the following sections the most important consequences are divided into several parts which, in reality, are interrelated.

4.3.3.1 Gap Levels and High Spin-Low Spin Ordering The magnitude of the crystal field splitting (AE,,) manifests itself directly in the trends of the lowest excitation energy of a 3d impurity when multiplet corrections are of minor importance and indirectly when competition with the exchange splitting AE,, for spin-up and spin-down states results in a high-spin or low-spin electronic configuration (see Fig. 4- 11b). In Fig. 4- 15 the e-t, splitting for silicon is shown as calculated from density-functional theory in conjunction with the local-density approximation. Green’s function technique within the frame work of LMTO-ASA (Linearized-Muffin-Tin-Orbital in AtomicSpheres-Approximation) was used for solving the single particle equations (Beeler et al., 1990). Results were obtained for a rigid (unrelaxed) lattice, neglecting spin polarization (Spin-restricted calculation: The occupancy of all spin-up states is assumed to be equal to the occupancy of all corresponding spin-down states). In the main trend along the 3d series, there is also agreement with calculations based on other methods, such as the X, cluster calculations in Si and GaAs for substitutional impurities (Cartling, 1975; Hemstreet, 1980; Fazzio and Leite, 1980), and in Si for interstitial impurities (De Leo et al., 198l), the empirical tight-binding method for interstitials in Si (Pecheur and Toussaint, 1983), and in

188 eV


A

-1.5

-2.0

z:

5

10

11

Figure 4-15. Gap levels and apparent crystal field splitting through the 3d transition metal series in silicon for neutral substitutional (solid lines) and interstitial (dotted lines) impurities. Z denotes the effective core charge and is equal to the total number of 3d and 4s valence electrons forming the many-electron system of the deep center. The numbers in parentheses give the population of the levels of different symmetry in the single-particle picture, neglecting spin polarization. (After Beeler et al., 1990).

local-density Green's function calculations for interstitial and substitutional 3d atoms in silicon (Zunger and Lindefelt, 1982). A critical discussion of various approaches regarding the choice of an appropriate Hamiltonian and the technique of quantitatively calculating states and energy levels that define a deep center was given by Pantelides (1986). For substitutional transition metals, the trends of the e and t2 levels with atomic number can be easily understood by the help of Fig. 4-13. The impurity-like (d-like) levels of either symmetry will reflect the decrease of atomic de,t2orbital energy with increasing Z , but the antibonding t2-symmetric states due to hybridization and pinning to the host dangling bond system show

this trend only in a strongly attenuated fashion as compared to the nonbonding e-symmetric states. Thus the one-electron crystal field splitting is largest at the high-Z limit. Interstitial 3d states will behave in a similar manner, but in this case both e and t2 states hybridize with the host. With decreasing atomic number, as the impurity-host interaction increases, the antibonding t2symmetric states are increasingly repelled by antibonding conduction band states (Fig. 4-14) hence the e-t, splitting is largest at the low Z limit (Fig. 4-15). Interstitial copper does exist only in the single positive charge state, since the completely filled atomic d shell leads to full occupancy of the antibonding e, t2 levels, and the impurity-like al level is resonant with the conduction band (Fig. 4-14); the remaining s electron may be bound by the positive Coulomb potential of interstitial copper resulting in shallow donor behavior. By separating anisotropic many-electron effects, Zunger (1986) has fitted an average crystal field energy A,, to internal transitions (ent; + e"'t;' where n + m = n'+m') determined experimentally from excitation spectra in 111-V and 11-VI compound semiconductors; the trend in Aefi behaves like that discussed for substitutional 3d elements in the one-electron picture (Fig. 4-15), at least from the heavier atoms down to manganese. In calculations within a single-particle model all electrons populating a degenerate one-electron level (like the e or t, states of Fig. 4-15) feel the same average potential. Although average many-electron effects are contained in the various one-electron approaches by including exchange terms in effective potentials or energy functionals, this symmetrization in the case of partially occupied states does not allow for stabilizing effects of spatial correlation which may arise from the electrons occupying spatial-

189


ly separated and variationally independent orbitals (like that shown in Fig. 4-9). Highspin states are simply the result of spatial correlation, since alignment of the spins in strongly localized wave functions (for example, in e and t2 orbitals) keeps the electrons apart and minimizes electrostatic repulsion despite the higher energy of the second orbital (e or t2 for interstitial or substitutional 3d states, respectively). The effect of anisotropic contributions (multiplet corrections) to ground state and transition energies in heteropolar semiconductors was demonstrated in calculations of Fazzio et al. (1984). The spin part of the correlation energy can be included within the one-electron model by carrying out spin-unrestricted calculations, i.e., allowing electrons of different spin to experience a different potential. The available electrons may then be distributed to the resulting levels in all possible ways. From such states, the various multiplet energies can be obained by perturbation theory, taking into account residual electronic interactions (e.g., Sugano et al., 1970). Possible multiplets for transition metals have also been worked out by Hemstreet and Dimmock (1979) in combining results of one-electron calculation with ligand field theory. However, determining the lowest-energy configuration (the ground state multiplet) is often hampered by the fact that orbitally degenerate multiplets may lead to spontaneous symmetry-lowering Jahn-Teller distortions, thereby stabilizing a low-spin configuration against a nondegenerate, high-spin correlated multiplet originally lower in energy. The question as to the final result of such a competition usually has to be settled by experiment, as has been done for the singly negative vacancy in silicon (see Chapter 3 by Watkins). EPR-results on total spin of 3d impurities in most cases are confirmed by spin-polar-

ized calculations with respect to a rigid lattice. This indicates that Jahn-Teller effects are presumably suppressed by substantial exchange splitting of the gap states. But even though lattice relaxation is neglected, such calculations do not predict an overall high-spin tendency throughout the 3d series and its various charge states (Beeler et al., 1985a, Katayama-Yoshida and Zunger, 1985). Fig. 4-16 and Fig. 4-17 show the spin-polarized one-electron levels in the ground state configuration for neutral, substitutional and interstitial, 3d metals in silicon as obtained from local spin density calculations (Beeler et al., 1985a). The spin splitting depends on spin density and the localization of the defect states. As for the localization, the same qualitative arguments that were used in discussing the trends of Fig. 4- 15 hold here as

'"1 1.5

1.0-

e101':

::-i

>

0.5-

.-

Lu

-1 5

-2.0

s= 0

1

3/2

0

112

1

312

Figure 4-16. One-electron energies (spin-unrestricted) of the ground states of neutral substitutional 3d transition metals in silicon. The numbers in parentheses indicate the occupancy of gap levels and resonant states. (After Beeler et al., 1985 a).

190

4

S= 1

1/2

Deep Centers in Semiconductors

2

312

1

1/2

0

Figure 4-17. One-electron energies (spin-unrestricted) of the ground states of neutral interstitial 3d transition metals in silicon. (After Beeler et al., 1985a).

For substitutional impurities, the nonbonding impurity-like e states remain strongly localized throughout the series; when they enter the gap, thereby becoming partially occupied, the spin splitting is largest. The antibonding host-like t, states are strongly delocalized at the high Z limit, due to their largely vacancy-like character, and they become increasingly localized with decreasing atomic number as they are shifted upward toward the conduction band, This causes the e-t, splitting to decrease (see Fig. 4-15) and the e l state is then pushed above the t,? state for Mno and Cro near the center of the series, resulting in a high-spin configuration for both impurities. For Coo, Ni', and Cuo, however, the nearly constant spin splitting (the increasing magnetization is compensated by increasing delocalization in that series) is markedly overwhelmed by the e-t, splitting, the latter being largest at high Z. Therefore, from Fig. 4-16 a low-spin configuration is predicted for neutral substitutional Co, Ni, and Cu in silicon. Unfortunately, experimental evidence is lacking for that prediction,

whereas high-spin states for neutral substitutional Cr and Mn are confirmed by EPR (Fig. 4-11 a). Similar arguments hold for interstitial 3d impurities. In Fig. 4-17 low-spin configurations are indicated at the low- and high-Z limits, and only the transition elements at the center of the series should form highspin states. Essentially, this is caused by the stronger localization of the e states compared to the t, states and the increase in e-t2 splitting with decreasing atomic number (Fig. 4-15). Neutral interstitial Ni is nonmagnetic due to fully occupied states. Therefore, its spin-polarized one-electron configuration is equivalent to that in Fig. 4-15. (This is also true for substitutional Fe', where the e levels are completely filled, and the t, levels are empty.) Since in silicon 3d metals dissolve mainly on interstitial sites, all high-spin states could be identified by EPR (Fig. 4-1 1a); again no experimental information exists on the predicted low-spin ground states. For Ti and V on interstitial sites, the singly positive (Ti+) (Van Wezep and Ammerlaan, 1985) and the doubly positive charge state (V2+) (Fig. 4- 1 1 a) have been identified by EPR, but for these charge states high-spin and low-spin ordering coincide. (This is easily realized by the use of Fig. 4-17.) Another interesting fact is revealed by the calculations: The local spin density at the impurity site appears more localized than the gap states themselves; this indicates that an essential part of the local magnetization originates from the impurityinduced valence band resonances, although they (like core states) do not contribute to the total spin. A substantial part of the spin density in many cases resides outside the impurity sphere as suggested by ENDOR data. For interstitial Fe+ in silicon, experimental evidence indicates that about 80% (Greulich-Weber et al., 1984) or 72%(Van


Wezep eta]., 1985) of the spin density resides inside the impurity first neighbor shell; this value is reduced to about 60% for interstitial Ti' in silicon (Van Wezep et al., 1985). For comparison, theory yields 73% in the former case and 42% in the latter case (Beeler et al., 1985a). All these findings are also consistent with reduced spin-orbit splitting which is obvious from absorption, luminescence, and photo-EPR experiments on internal transitions (Kaufmann and Schneider, 1983; Clerjaud, 1985) and the quenching of the orbital angular momentum in the g values of EPR spectra mentioned earlier. The origin these effects share, is again the host-impurity interaction via p-d hybridization. Beeler and Scheffler (1989) have also performed spin-unrestricted self-consistent LMTO Green's function calculations of the electronic structure of 4d transition metals in silicon. Figure 4-18 shows the results for substitutional impurities in the neutral charge state. In principle, all conclusions drawn from the interaction model of Fig.

Figure 4-18. One-electron energies (spin-unrestricted) of the ground states of neutral 4d transition metals at the tetrahedral substitutional site. (After Beeler and Scheffler, 1989).

191

4- 13 which are applied to explain the trends depicted in Figs. 4-15, 4-16, and 4-17 remain valid. The only difference concerns the delocalization of both the e and t, states, which is substantially stronger in the 4d series than in the 3d series (This is even more true for the 5d shell.) Consequently, from the calculations represented by Fig. 4-1 8, low-spin ground states are predicted for substitutional 4d ions. Furthermore, at the high Z end, the t, states again resemble pure dangling bond states. This was already found to be true for the heaviest 3d elements, Cu and Ni. This remarkable property, already inherent in the simplest two-state model of Fig. 4-12 by the existence of a dangling bond pinning energy, is exploited in the so-called vacancy model (Watkins, 1983, 1995). According to this model, the electronic structure of the "heavy" substitutional transition elements can be described in terms of a closed noninteracting d" shell, with the remaining electrons residing at the dangling bond orbitals of the vacancy. One may arrive at this picture by steadily increasing the attractive impurity potential and thus lowering the atomic impurity de,t2 orbital in the defect molecule model of Fig. 4-13. Finally, the nonbonding e states and the now also strongly localized impurity-like t, states, both fully occupied, form the practically noninteracting closed-shell configuration. By now, the host-like gap levels of t, symmetry can be seen to have practically pure vacancy character and no d character. (Hemstreet, 1977). For example, Ni-, Pd-, Pt-correspond to a configuration 3d"+V-, 4d"+V-, 5d''+V-, respectively ( V vacancy). Thus a total spin S = 1/2, observed in EPR studies for the cited elements and charge states (Pd- and Pt- in silicon, Ni- in germanium), can be readily explained. As for V- (see Chap. 3 of this Volume), the

192


degeneracy of the triply occupied t2 gap level (see Fig. 4-13 for the neutral vacancy) is lifted by a tetragonal and a superimposed weaker trigonal Jahn-Teller distortion resulting in CZvsymmetry of the defect. The active electronic configuration is now determined by a spin-paired b2 symmetric and a singly occupied bl symmetric split-off state (Watkins and Williams, 1995). This characteristic Jahn-Teller induced distortion is manifested in the EPR spectra of Ptand Pd- (Woodbury and Ludwig, 1962). An analogous EPR spectrum for Ni- in silicon has been detected (Vlasenko et al., 1990). These spectra were reproduced and further resolved by ENDOR studies (Van Oosten et al., 1989; Son et al., 1991), and it has been argued that the large anisotropy in the electronic g factor for Pt- points to a nonvanishing effective angular orbital momentum, contrary to what is expected for the vacancy model. Instead, a dihedral electronic structure has been proposed, consisting of an open d9 shell and two electrons bonded to only two silicon atoms, the two other dangling silicon hybrids forming a reconstructed bond. This model was found to be applicable also to Pd- and Ni-, where an open-shell orbital momentum is possibly reflected by strong anisotropy in the nuclear g factors. On the other hand, in their recent study Watkins and Williams (1995) again interpreted and analyzed substitutional Ni-, Pd-, Pt-, and also Auo within the framework of the vacancy model and found the large anisotropy of the hyperfine interaction to be consistent with the b, symmetry of the above-mentioned singly occupied orbital.

4.3.3.2 Coulomb Induced Nonlinear Screening and Self-Regulating Response The preceding sections were intended to demonstrate qualitatively why most transi-

tion metals can support bound states in the gap of a covalent semiconductor: Large variations in the energies of the atomic d states affect the gap levels only weakly via bonding-antibonding splitting. The coexistence of various charge states of a given impurity in the semiconductor gap provides another puzzling fact if one bears in mind that energies in subsequent ionizations of the d shell differ by about 20 eV for a free-space atom. For example, for Mn the d6 to d3 ionization energies are 14.2, 33.7, 51.2, and 72.4 eV, respectively (Moore, 1959; Corliss and Sugar, 1977). The counterpart of this energy for a deep impurity is the Mott-Hubbard correlation energy U,, (U for unrelaxed lattice), which in silicon is of the order of 0.3 eV (Eqs. (4-lo), (4-11) and Fig. 4-5). This small value of U points to a nonlinear screening of the intra-d-shell repulsion, since a linear response would give a Mott-Hubbard U,, reduced only by one order of magnitude. A self-consistent dielectric function, calculated by Zunger and Lindefelt (1983) for various transition metals in silicon, reveals that the impurity-induced perturbation is screened within an atomic distance. Consequently, a neutral 3d atom in silicon, substitutional or interstitial, already attains local charge neutrality at the central cell boundary and turns out to be very stable against the build-up of an ionic charge upon ionization. This remarkable dynamic aspect of nonlinear screening was first envisioned by Haldane and Anderson (1976), who concluded that several charge states in the gap occur as a result of rehybridization between transition metal d orbitals and host sp orbitals if the gap level occupation changes upon ionization. The details of this selfregulating mechanism have been worked out extensively by Zunger and Lindefelt (1983), Singh and Zunger (1983, and Zunger (1986).


Due to the antibonding character and hence rather extended nature of the gap states, their exclusive contribution to the total charge of the impurity-host system cannot effect the localization of the impurity-induced charge perturbation to the central cell. The difference is compensated by a rearrangement of valence band charge in response to the impurity-induced perturbation. Figure 4- 19 shows the contributions of gap states and valence band states (resonances) to the net impurity charge. It can be seen that the gap states only at large distances from the impurity site produce all of the center’s net charge (normalized to unity at the neutrality limit). In addition, the valence band resumes its unperturbed density at precisely these distances. Within the central cell region, the screening response from the valence band amounts to a net charge contribution of up to 50% in the case of neutral interstitial Mn in silicon. For substitutional Mn, a “screening overshoot” occurs (Q,,,>l) very close to the impurity site, arising from the strong bonding resonances.

193

Ionizing the impurity means that an electron is removed from a gap level of a neutral center. This relieves the valence band resonances (Fig. 4-13, 4-14) from their Coulomb repulsion. As a consequence, they become lower in energy, with their coupling to the host being weakened. Dehybridization now strengthens the (localized) d character and weakens the (delocalized) p character of the impurityinduced resonances. Consequently, the resonances increasingly localize in the central cell region thus making up for practically all of the charge that has been lost in the ionization process. Inversely, if an electron is added to a gap level, the mechanism just described would lead to an increase in hybridization, where the d content of the resonances markedly decreases, giving them more p character at the same time. The impurity-induced resonances therefore delocalize, and charge leaks out from the central cell, leaving Q,,,nearly as close to neutrality as before. Therefore it appears that by this self-regulating response of the im-

;1.0 0

L 0

-0

5N 0.5 0)

I

z 0

0.0

0

2

4

6 Distance (atomic units)

(a> (b) Figure 4-19. Decomposition of the net impurity charge Qnetinto gap level contribution Qgapand the valence band configuration Qva for interstitial (a) and substitutional (b) manganese in silicon. Local charge neutrality is reached at Q,,, = 1, since Q,, is normalized by AZ,the difference in the number of valence electrons between impurity and host. In the cases (a) and (b) displayed in the figure, AZ = 7 and A2 = 3, respectively. Distances from the substitutional or interstitial impurity placed at the origin are given in atomic units (1 a.u. 4 0.53 A 0.053 nm). (After Zunger and Lindefelt, 1982).

194


purity-host system, an ionization-induced change of the charge takes place at the ligands rather than the impurity site. This remarkable stability of 3d impurities in semiconductors against the build-up of an ionic charge upon ionization has been confirmed by other calculations (Beeler et al., 1985a, Vogl and Baranowski, 1985) and explains why several charge states of a 3d metal may occur within the rather small energy limits of a semiconductor gap. It is noteworthy, however, that no comparable mechanism exists for the local magnetic moments (Zunger, 1986), so that exchangeinduced screening is not very effective. Apparently, the main effect on the magnetic polarization of valence band resonances is the change in the net spin of the gap states upon ionization, whereas the varying localization of the resonances is of minor importance. Finally, it should be clear that nonlinear Coulomb screening only works in highly covalent semiconductors. It decreases in efficiency with decreasing covalency and vanishes for ionic crystals.

4.3.4 Ionization Energies and Trends 4.3.4.1 Transition Metals in Silicon Ionization energies as well as excitation energies (Sec. 4.2) correspond to differences in the total energy of the initial and final states of a defect and must therefore include all contributions from electronic and lattice relaxation. Nevertheless, in a rigid lattice, one may approximate the ionization energy of, for instance, a deep donor, within the local density formalism by the self-consistent calculation of Slater’s transition state. This means removing half an electron from the one-electron level to be ionized (e.g., from a t2? gap level) and transferring it into the conduction band. A comparison with

experimentally determined energy levels can then indicate the relative importance of lattice relaxation effects. Figure 4-20 gives a comparison of calculated (Beeler et al., 1985a) and measured energy levels (Graff and Pieper, 1981 a) of interstitial 3d transition metals in silicon. There is excellent agreement in most cases, but some drawbacks are also evident from Fig. 4-20. While theory yields a double donor for chromium, such behavior has been excluded by experiment (Feichtinger and Czaputa, 1981). Theory has failed to reproduce the correct ground states in the high-spin configuration for Cry and Cr: Apart from reasons originating from peculiarities of the applied formalism, a key to understanding the missing double-donor activity of chromium is the Crio/+transition. In this transition, the electron is taken from the t,& level whereas the next electron for the CrT’++ ionization step has to come from the el‘-single-particle gap level (see Fig. 4-17). Lattice relaxation might cause a general lowering of the calculated e? level in this case, to give the observed high-spin ground states for Cr: and Cr;. If this lowering would amount to about 0.3 eV, the el‘ level would become resonant with the valence band due to electronic relaxation upon transferring one of its two electrons into the conduction band. Thus doubledonor behavior of Cri is suppressed without seriously affecting the single-donor energy. Unfortunately, for interstitial cobalt, the behavior of the e& level as to its sensitivity to lattice relaxation cannot be tested so far, since the very high diffusivity of interstitial cobalt (e.g., Utzig, 1989) in silicon causes the thermal stability of that species to be too low to observe any predicted energy levels. Interstitial copper has no deep levels, as mentioned before, and should be stable only in its positive charge state. This supports a very high diffusion coefficient and the abil-


Conduction band

0.0

195

Figure 4-20. Calculated (solid lines) and experimental values (dashed lines) acceptor and donor levels for interstitital 3d transition metals in silicon. For each donor or acceptor level the corresponding change in the occupancy of the single-particle state involved is indicated. Calculations include spin polarization (spin-unrestricted theory). (After Beeler et al., 1985a).

Valence band

ity of copper to form electrically inactive pairs with acceptor dopants (Mesli and Heiser, 1992). Defect reactions of copper and other fast diffusing impurities in silicon have been studied via transient ion drift experiments (Zamouche et a]., 1995). For similar reasons, nickel in silicon should only be present in the neutral charge state due to its closed d shell. The experimental single-donor levels shown in Fig. 4-20 particularly reflect the free-atom 3d ionization energies (Fig. 4-4) including the characteristic exchangeinduced jump (“Hund’s point”) between Mn and Fe (d5 and d6 in the free atom, respectively). If neutral interstitial vanadium (V:) has spin S = 5/2, the spin-related jump now should occur between the Vo’+ and the Cro’+ level and indeed does so. In case V: has spin S = 1/2 (see Fig. 4-17), this characteristic jump should be related to the increase of the spin splitting of the t, level caused by the change from low-spin to high-spin ground states. For substitutional 3d impurities in silicon, with the exception of Mnp+ (Czaputa et al., 1985), no energy levels have definitely been identified until now. 3d metals in silicon dissolve mainly on interstitial sites (Weber, 1983) and often can be transferred

to the substitutional site only by codiffusion of a highly soluble and fast-precipitating species such as Cu (for precipitation effects, see Chapter 11 of this Volume). For Mnp+ theory (Beeler et al., 1985a) predicts an energy level at Ev+0.49 eV, which is in good agreement with the experimental value of Ev+0.39 eV. A few charge states, for example, Cr:, Mn:, Mn;- (Fig. 4-11), and Fe: (Muller et al., 1982), have been identified by EPR and were found to have high-spin configuration. With the exception of the trigonal center Fe:, all the other ones show cubic symmetry. According to theory, neither Fe: nor Fe; should be a stable configuration. Therefore, Fe, is predicted to produce no deep level in the gap. But all this is based on the theoretical result that the low-spin configuration for Fe: (S = 0) is the correct ground state. A highspin ground state ( S = 2) would support both the existence of Fe: with spin S = 3/2 and a single-donor level. Theory predicts 4d metals to be dissolved in silicon, preferentially on substitutional sites (Beeler and Scheffler, 1989). Calculated total energies show for the group IB ions (Cu-Ag-Au) representing the 3d, 4d, and 5d series that the stability of the substitutional site increases significantly relative to the

196


interstitial site from Cu to Au because of the increasingly delocalized defect states. Experimental information on the energy levels of 4d metals is rather indecisive; only for Rh is there agreement with theory as to the amphoteric character and level positions. Predictions have been made for the double-donor to double-acceptor activity of substitutional Pd in silicon and for singledonor to triple-acceptor activity of substitutional Ag in silicon (Beeler and Scheffler, 1989). But only isolated interstitial silver (Ag:) has been unambiguously identified from EPR in silver-doped silicon, whereas other silver related spectra have been assigned to complexes containing one silver atom, like FeAg (Son et al., 1992). Table 4-1 shows amphoteric behavior for Rh (Czaputa, 1989), Pd (Landolt-Bornstein, 1989), and Ag (Baber et al., 1987) (compare also Sec. 4.5). The tabulated levels are assumed to be related to metals at the substitutional site, a fact which often is supported only by the high thermal stability of the species investigated. It seems clear that for the heavier 4d metals and particularly for the 5d series, Jahn-Teller distortions are no longer suppressed by exchange splitting, due to considerable delocalization of the defect states. Symmetry-lowering distortions in the resulting low-spin configurations are most naturally expected for states Table 4-1. Energy levels (experimental) of substitutional 4d and 5d transition metals in silicon. For a more complete list, see Sec. 4.5. Metal

Donor level (eV)

Acceptor level (ev> ~

4d

5d

~~~

Rh Pd Ag

Ec - 0.57 E, + 0.33 E, + 0.34

E, - 0.31 E, - 0.23 Ec - 0.54

Pt Au

E, E,

E, - 0.23 E, - 0.55

+ 0.32

+ 0.35

compatible with the above-mentioned vacancy model. In any case, there is no doubt that for the 4d and 5d series, lattice relaxation should be included in a calculation of level energies to meet the experimental values as closely as possible. Fazzio et al. (1985) have studied the theoretical aspects of the substitutional IB series in silicon. They found that these impurities form a two-level, three-chargestate amphoteric system, where both the donor and acceptor transitions emerge from the antibonding t, gap state (compare Fig. 4-18 for Ag and Fig. 4-16 for Cu). But concomitant with the substantial delocalization in this system, Jahn-Teller distortions will occur. Therefore, the expected spin states for the neutral impurities will not be those derived from the unrelaxed lattice (e.g., S = 3/2 for Ag in Fig. 4-18) but instead will follow from the occupancy of the latticedistorted split-off t, states. These should give a doubly occupied spin-paired b,-like level and a singly occupied b,-like level to give S = 1/2 (see again the vacancy model given by Watkins and Williams (1995)). From Table 4- 1, an effective Hubbard energy (Eq. 4-10) of about 0.3 eV can be derived for Ag and Au. Fazzio et al. (1985) have compared their calculated values for the Franck-Condon U (Eq. 4-1 1) with the experimental values for Uee. They found contributions from lattice relaxation of about 0.15 to 0.25 eV for both donor and acceptor transitions, which tend to cancel each other. The situation should be similar in the case of Pd and Pt. For these metals, U,, appears to be increased to about 0.5 eV (Table 4-l), and the negative charge states should have spin S = 1/2, which is in accordance with the experiment. However, there is still the problem of the correct identification of the isolated substitutional site of transition metals of the 4d and 5d series. The isolated. substitutional character of


197

Pt- which spontaneously distorts off center driven by a dynamical Jahn-Teller effect, in a (1 11) direction has been confirmed by or, preferentially, by an increased spin -orbit Anderson et al. (1992) by studying stressinteraction which competes with the Jahninduced shifts of the g tensor, which clearTeller induced off-center distortion. This ly demonstrates C,,, symmetry according to very interesting issue has been discussed in the vacancy model. The latter has been great detail by Anderson (1991) and again thoroughly discussed for the case of Ptby Watkins and Williams (1995). (Anderson et al., 1992a) in a following paper. Moreover, the defect has been found 4.3.4.2 Compound Semiconductors to reorient even at 2 K, which also strongly and Bulk References supports its isolated character. As to substitutional gold, Watkins et al. Transition metals substituting the cation (1992) presented a pioneering Zeeman site in compound semiconductors were studied theoretically by spin-polarized calculastudy on the optical transitions to shallow tions within the framework of the semiexcited states (Sec. 4.3.5.2) of the gold empirical tight-binding method (Vogl and donor and acceptor. There has been' a longlasting discussion on whether the donor Baranowski, 1985). Donors, acceptors, and double acceptors for the 111-V compounds and the acceptor transitions evolve from GaAs and GaP and for the 11-IV compounds the same center or not (e.g., Lang et al., ZnS and ZnSe were predicted to form high1980; Ledebo and Wang, 1983; Utzig and spin ground states. Their calculated energy Schroter, 1984). This study not only shows levels were found to fit closely with the existthat ground-state properties and ionization ing experimental data. (For example, properenergies correspond to the same isolated ties or iron and chromium in 111-V comgold species, but also provides a solution to pounds have been discussed very thoroughthe long outstanding puzzle concerning the missing EPR spectrum of AU' (S = ~ 2 ) . ly by Bishop (1986) and Allen (1986)). In Fig. 4-2 1, an example is given for the case of While both charge states Au+ and Au-, GaAs, from which (this time for the accepaccording to the vacancy model, are expecttors) the free-ion trend for the energy levels ed to have no unpaired spin due to an empcan again be seen in its attenuated form. Note ty or fully occupied b , state, for the partialthat the characteristic spin-related jump ly filled orbital in the Auo case a definite between Mn and Fe arises again from effecEPR signal has also never been observed. From the Zeeman spectra in the cited study, a peculiar anisotropy in the g tensor Conduction band could be established, reflected by the experic 1.5 mental values 911 = 2.8 and gl = 0 (911 is observed with the magnetic field parallel to a (100) distortion direction). For compari\ a 0.5son, these values are 911= 2.1 and g1 = 1.4 for elplatinum. With g1 3 0, no transitions (AM= Valence band +1, see Fig. 4.8) can be induced by a microTi V Cr Mn Fe Co Ni Cu wave field. The origin of this large anisotroImpurity py in the gold case is thought to result either Figure 4-21. Calculated (dashed line) and experifrom a rapid tunneling of the impurity mental (squares) acceptor levels of 3d transition metals in GaAs. (After Vogl and Baranowski, 1985). between two equivalent C,, configurations % I

/-.

198


tive d5 (Mn-) and d6 (Fe-) configurations constituting the initial states for the ionization of acceptors in GaAs. The same will be true for transition metal donors in 11-VI compounds (seeFig. 4-22 below). As long as high-spin states are involved, this jump will depend both on the formal charge states of the substitutional impurity and on the number of valence electrons of the atoms being substituted. In a further step, this trend can be generalized and unified for a whole class of semiconductors. Level energies (ionization enthalpies) can be measured relative to the valence band edge, the changes of which, at least within certain classes of semiconductor materials (e.g., 11-VI or 111-V), are known to be given approximately by the differences in the experimental photothresholds (Harrison, 1980). In Fig. 4-22 experimental valence-band-related energy levels are shown, corrected for each solid by the corresponding photo-threshold (taken relative to ZnS as a reference host). Evidently, this procedure is very successful in clearly

%

0.00) 0 CdS (+0.2L)

0 ZnS

I ?

11

A ZnSe lt0.68)

0

I

Sc Ti

I

V

I

Cr

1

I

Mn Fe

I

Co

i Ni

I

Cu

I

Figure 4-22. Experimental valence band related donor levels of the 3d series in 11-VI compounds, corrected by the corresponding photothreshold, A@. For ZnS, taken as a reference system, A@ is assumed to be zero. (After Vogl and Baranowski, 1985).

exhibiting the universal trend through the 3d transition metal series for different semiconductors (Vogl and Baranowski, 1985) and its close relation to that observed for free ions (Fig. 4-4a). Furthermore, this universal trend points to the existence of a certain reference level to which a given transition metal impurity appears pinned if one changes the host crystal. There is experimental evidence that valence-band offsets in heterojunctions are simply the difference in the energy level positions of a given transition metal in the two compounds that form the heterojunction (Langer and Heinrich, 1985; Delerue et al., 1988). From these findings, an internal (bulk) reference level may be established, circumventing the contribution from the semiconductor surface to the (external) photo-threshold energy (Zunger, 1985; Tersoff and Harrison, 1987). Caldas et a]. (1984) suggested this reference level to be related to the antibonding cationic t,-symmetric state (vacuum pinning). There are arguments, however, for the average self-energy of cation and anion dangling bonds constituting the reference in the band alignment of heterojunctions (Lefebvre et al., 1987). Both versions continue to be discussed, but for 111-V compounds, the latter average gives the closer pinning and might be more appropriate at least for this class of semiconductors (Langer et a]., 1989). Once such a reference is established, and a deep level of a given metal is characterized in one semiconductor, the energy levels in other crystals within the same class may be predicted to a certain degree of accuracy. Further general trends have been discovered in isothermal pressure coefficients of donor or acceptor levels. Deep levels as a rule show pressure coefficients two orders of magnitude larger than those of shallow levels and may therefore be used to define


deep centers experimentally (Jantsch et al., 1983). Nolte et al. (1987) linked pressure coefficients to the deformation potentials of the band edges by choosing deep centers with a vacancy-like level structure as a reference. Finally, pressure coefficients of deep levels were interpreted in terms of an isothermal change of crystal volume upon ionization to obtain a measure of symmetric (breathing mode) distortions around substitutional and interstitial deep centers (Samara and Barnes, 1986, Weider et al., 1989; Feichtinger and Prescha 1989).

4.3.5 Excited States

4.3.5.1 Internal Transitions In Sec. 4.2.2, interelectronic transitions at a fixed charge state of both the defect and the accompanying electron-phonon interaction have been discussed. For transition metals, such excitations are better known as internal d -+ d* transitions according to a change of total energy of the many-electron system &‘j’

= pJ

- E“)

t,”)

199

ter, although luminescence may be masked by other competing centers or suppressed by strong electron-phonon coupling, leading to effective radiationless recombination. Zunger ( 1 986) has compiled existing data on internal transitions studied for transition metals in various semiconductors. As a rule, only one “oxidation” state of a given species is observed. This state dN is determined by the total number N of “active” electrons (e.g., d7 for Co2+, or d9 for Ni+) and must not be confused with the charge state of an impurity relative to the given host used so far. For example, an “oxidation” state of Co2+will correspond to the formal charge state Co- in 111-V compounds, to Coo in 11-VI compounds when substituting the cation site, and to Co2- in silicon. For the interstitial site, oxidation state and formal charge state coincide. In order to relate internal transitions to ionization, Fig. 4-23 represents an example, combining experimentally observed single donor activity (Fe”’) and the charge state

(4- 14)

where ij denotes the multiplet representation indices, and em’t;‘, em t; denote the predominant one-electron configurations (Singh and Zunger, 1985). In Eq. (4-14) an excitonic electron-hole contribution is contained, since both the excited electron and remaining hole are still partially bound. Apart from ground states, interconfiguration mixing may be considerable, and therefore the one-electron level description denotes the configuration that mainly contributes to higher multiplet terms. Numerous internal transitions have been observed via absorption and luminescence spectroscopy (e.g., Landolt-Bornstein, 1989). Both can give valuable information on electronic structure and symmetries of a deep cen-

-3.0 > Q)

P Fe”’. d5

Fez’. d6

0.0

Figure 4-23. Energy level diagram, relating experimentally observed internal transitions to the single donor level of Fe in ZnS. The inserts shows the parameters (including spin J = S for the positive formal charge state) of the ground state configurations participing in the ionization (left) and internal excitations (right). (After Zunger, 1986).

200


conserving (Fe') transitions into excited states of substitutional Fe in ZnS. For all states involved, the many-electron multiplets are denoted by spin multiplicin the ity (2S+ 1) and orbital symmetry tetrahedral point group. The oxidation state changes from Fe2+to Fe3+upon ionization. But transitions to higher excited states of a dN system, occurring as resonances in the conduction band, have also been observed (Baranowski and Langer, 1971). The occurrence of a single fixed oxidation state in the d + d* spectra (a few transitions have been observed additionally from neighboring states (Zunger, 1986)) and the fact that spectra from internal transitions of a given impurity resemble each other in different semiconductors are not very surprising in light of the electronic structure of deep centers discussed in the present contribution. Since the charge state (or the oxidation state) is conserved, the dynamic aspect of screening described in Sec. 4.3.3.2 is lacking. Consequently, transition energies AE'"' (Eq. (4-14)) cover roughly the same range as found for free ions, suggesting a localized electronic structure (Sec. 4.2.1). Nevertheless, whenever an electron is excited from a nonbonding e level to a hybridized t, level, it is in fact transferred from the impurity site to the ligands. The optical cross section for the Fe-'O transition in GaAs was found to be strikingly smaller than that of similar ionizations for Cr and Cu (Kleverman et al., 1983), reflecting the different spatial extension of the initial states (e for Fe, t, for Cr and Cu). It is precisely this difference in orbital character that makes it difficult to treat the multiplet effects of transition metals within empirical ligand field theory. This was pointed out by Watanabe and Kamimura (1989) who critically reviewed earlier attempts to include multiplet effects in first-

(,'+')r

(r)

principle approaches. Figure 4-24 demonstrates the state-of-the-art accuracy of such calculations compared to experimentally detected multiplet structures. Experimental values are taken from Weakliem (1962) and Koidl et a]. (1973) for ZnS, Weber et al. (1980) for GaP, Hennel and Uba (1978) for GaAs and Baranowski et al. (1967) for ZnSe. From the upper 4A2 + transition a weak chemical trend with the increasing covalency from ZnS to GaAs becomes evident and is qualitatively reproduced by the calculations. Multiplet structures of interstitial 3d transition metals in silicon were calculated combining the X,-cluster method in a spinunrestricted form with the above-cited approach of Hemstreet and Dimmock to account for space- and spin-induced correlations (DeLeo et al., 1982). Experimentally, Kleverman and Tidlund (1997) concluded from the lack of stress splitting in the optical excitation spectrum of the orthorhombic FeIn pair that the observed lines are most likely due to internal d + d* transitions of the perturbed Fet ion (Sec. 4.4.3).

-

Calculated

Observed 2.0-

.-C

:: x

c W

1.0 .

0.0 -

'A'

- ---

ZnS ZnSe GaP GaAs

Figure 4-24. Calculated and observed multiplet structures of Co2+ (oxidation state) in 111-V compounds. Theoretical values were calculated by Watanabe and Kamimura (1989).


Internal transitions of rare-earth impurities in various semiconductors provide the possibility of applications for light-emitting devices. In this case, the very atomic-like and nearly host independent luminescence spectra arise from the compact open 4f shell which is screened by the outer 5s5p closed shells. An intensively studied system is erbium in silicon, where the prominent 1.54 pm line offers the benefit of a stable light source compatible with silicon technology [see, for example, Michel et al. (1998)l. When embedded in silicon and GaAs, erbium is observed in the Er3+ oxidation state, which is also expected for other host semiconductors, at least for substitutional erbium (Delerue and Lannoo, 1991). For silicon, however, the tetrahedral interstitial site is favored by theory (Needels et al., 1993) and experiment (Przybylinska et al., 1996; Lanzerstorfer et al., 1998). The luminescence of 1.54 pm wavelength comes from an intra 4f (41,3/2+ 41,5,2)transition between the two lowest levels separated by spin-orbit interaction. While the wavelength is essentially independent of temperature, this is unfortunately not the case for the efficiency of the luminescence, which decreases significantly with increasing temperature. This main obstacle to the application of both photoluminescence (PL) and electroluminescence (EL) results from the complex nature of the energy transfer between host and Er 4f electrons. It is now well accepted and has been directly observed (Tsimperidis et al., 1998) that the excitation of the Er 4 f shell proceeds via the recombination of a transient erbium related bound exciton (BE) state, where the electron-hole pairs are generated either optically (PL) or by carrier injection (EL). Therefore, losses of intensity may result from alternative decay channels of the intermediate BE state or via nonradiative backtransfer mechanisms that de-excite the al-

201

ready excited 4f shell, thus restoring the BE state (Palm et al., 1996). Efficiency improvements in conventional host systems have been reached by co-doping with oxygen [e.g., Takahei and Taguchi (1995)], but promising results were also obtained with Si-Ge quantum wells (Huda et al, 1998) and erbium implanted wide gap semiconductors like S i c (see Chap. 11 of this Volume). 4.3.5.2 Rydberg-Like States

In the discussion of the basic physics of a deep center in Sec. 4.1.1 and Fig. 4-2 it was mentioned, that the ground state energy of a deep center is almost exclusively determined by the short-range central cell potential. But whenever a neutral deep center is ionized by emitting either an electron into the conduction band or a hole into the valence band, the screened Coulomb potential due to the charged center should, in principle, give rise to a series of shallow excited states for which effective mass theory (EMT) should be applicable. These closely spaced energy levels near the relevant band edges play a role in the so-called cascade capture. In this process, a carrier is first captured in a highly excited state. It then goes down the ladder by emitting one or very few phonons each time. Finally, the carrier may drop from a lowest-lying cascade state (at low temperatures, re-emission from this state is negligible) into the deeplying ground state by multi-phonon emission or by a lightemitting transition. The cascade process was originally developed for shallow centers (Lax, 1960); in theory, the temperature dependence of the process is expressed in the form T-n, where the value of n is usually l < n < 4 (Grimmeis et al., 1980a, b). b a g and Zeiger (1962) studied sulfurdoped silicon via absorption and obtained from their well-resolved line spectra the binding energies for the ground state and the

202


excited states of a deep center, the latter being in perfect agreement with EMT. More recently, the chalcogen series in silicon was studied by applying different spectroscopic methods (see Sec. 4.4.1) and a He-like level structure was revealed. For transition metals in silicon, Rydberg-like series were observed from both absorption and photothermal ionization spectroscopy (PTIS) and interpreted in terms of EMT (Grimmeiss and Kleverman, 1989). For studying species of deep centers with low solubility, PTIS may be a very valuable tool, since the method was shown to be essentially independent of defect concentration (Kogan and Lifshits, 1977). PTIS operates by a twostep process: an optical excitation from the ground state into excited states followed by thermal ionization of the excited center. Since the PTIS signal is derived from the induced photocurrent or photocapacitance (in junction techniques), the sample studied acts as a photon detector itself. Under certain circumstances concerning the temperature range, the method yields a discrete line spectrum that can be obtained at a very high resolution of about 0.03 meV. Figure 4-25b shows PTIS and FTIR (Fourier Transform Infrared Transmission Spectroscopy) spectra obtained from neutral interstitial iron (Fey) in silicon. The identification of the lines in the Fey transmittance spectrum is based on three overlapping EMT series (Olajos et al., 1988), each in accordance with the EMT scheme (c) pointed out in Fig. 4-25 a. Whereas p states in a Coulomb potential are split by the anisotropic effective mass, s states are split by multi-valley interaction. For Fei the symmetry is tetrahedral, hence the s-like states should be split into an Al singlet, a T, triplet and an E doublet due to the six equivalent conduction-band minima of silicon, where the strongest splitting occurs for the 1 s states.

The degeneracy of the 1 s (T2) and 1s (E) states may sometimes be lifted by spin-valley splitting (Aggarwal and Ramdas, 1965). Clearly, the true ground state is not determined by the Coulomb tail of the potential, since it constitutes the deep level. But even higher 2s and 3 s states are systematically lower in energy than that expected from EMT, since they still feel the attractive localized central cell potential. Besides, the three series in Fig. 4-25 b involve EMT-forbidden transitions, where, on the other hand, transitions to the split 1 s (T2) states are missing. Thus the formal charge state for a deep center is easily deduced from the spacing of the p-like states in a wellresolved Rydberg series (which is proportional to Z’), whereas for the symmetry of a center, perturbation spectroscopy (e.g., FTIR under uniaxial stress) may sometimes be more helpful (Krag et al., 1986). The occurrence of three EMT series in the transmittance spectrum shown in Fig. 4-25 b may be accounted for by spin-orbit splitting in the final states. Very recently, a fourth series has been resolved, thus completing the overall picture of the Fet

-

Conduction E?and ( . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

-

-1

$4)

(a 1 @) (c1 Figure 4-25a. Effective-mass-like levels with increasingly lifted degeneracy. (a) Isotropic effective mass, (b) anisotropic effective mass, one-valley treatment and (c) anisotropic effective mass, multivalley treatment in Td symmetry.


203

Figure 4-25 b. Excitation spectra of interstitial iron (Fey) obtained from photothermal ionization (upper curve) and transmittance (lower curve and inset). (After Olajos et al., 1988).

-5

-f? 0

Q

0

C

0

c

c

5 C

2

I-

I

6250

I

3s 3d0 % 3p, I

I

6300 6350 6400 Wave numbers in cm-'

PTIS Corrected

Transmittance

I

1

6225

I

I

I

6475 Wave numbers in cm-'

core structure (Thilderkvist et al., 1998). Accordingly, any of the observed transitions occur between the deep ground-state multiplet 3A, of Feo (deriving from the e2t; electronic configuration, see Fig. 4-15) as the initial state and a shallow donor state with the Fet core left behind as the final state. The orbitally degenerate 4T1term of Fe; (deriving from e2t;) is split by spinorbit interaction with respect to the manifold of the effective angular momentum ( J = 1/2, 3/2, 5/2) with the J = 512 level doubly split due to the nonspherical environment.

I

I

6725

In addition to the line spectrum of the shallow states, which is essentially similar to that found by FTIR, the PTIS spectrum of Fig. 4-25b reveals a clearly resolved structure at higher energies. The final states of the corresponding transitions must lie well within the conduction band continuum. The lines result from a higher-order absorption process, where a direct optical no-phonon ionization becomes resonant with a transition from the ground state to a bound excited state accompanied by the emission of a bulk phonon. Therefore, details of the PTIS spectrum are repeated at higher ener-

204


gies as they are just shifted by the energy of the participating phonons. These so-called phonon-assisted Fano resonances (JanzCn et al., 1985) may be very helpful in deciding whether the studied center has donor character (electron excitation) or acceptor character (hole excitation), since in silicon, only intervalley phonons (Harrison, 1956) participate in the process for donors, and the zone-center phonon (Watkins and Fowler, 1977), in the process for acceptors. EMT-like spectra of deep neutral centers are sometimes interpreted in terms of the so-called pseudo donor, as in the case of a silver-related defect in silicon (Son et al., 1994). This bound-exciton based model leads, among other features, e.g., the explanation of spin-singlet and triplet states, to a different interpretation of selection rules in the transitions, but it has been argued that these spectral details are due to properties inherent to the normal, “molecular” groundstate structure of deep donors (Kleverman, 1997). Rydberg-like spectra were also observed for gold and platinum acceptors (Kleverman et al., 1987, 1988; Armelles et al., 1985) and were found to resemble those of shallow centers like indium in silicon, so that the compatibility of EMT with shallow excited states of deep centers can be seen as well established.

4.4 Properties of Selected Systems 4.4.1 Chalcogens in Silicon Sulfur, selenium, and tellurium constitute very interesting impurities in silicon for practical and physical reasons. First, these elements can be used in infrared detectors (Sclar, 1981; Migliorato and Elliott, 1978). Second, this group provides an electronic

structure that shows both deeply bound ground states and excited Rydberg-like states. Besides, it represents an example in which the question as to the substitutional or interstitial site was definitely decided by theory (Beeler et al., 1985b). Oxygen, one of the most important impurities in device fabrication due to its strong involvement in gettering, precipitation effects, and the formation of the so-called thermal donors (TD) (Claeys and Vanhellemont, 1989; for TD’s, see also Sec. 4.4.4), behaves quite different and does not occupy T, symmetric lattice sites. As for other semiconductors, the role of oxygen in radiative recombination, especially in Gap, has been thoroughly discussed by Dean (1986).

4.4.1.1 Sulfur, Selenium, a n d Tellurium in Silicon The electronic structure of the singleparticle ground states for substitutional chalcogens was calculated by Bernholc et al. (1982), Singh et al. (1983), and Beeler et al. (1985 b) via first-principles Green’s function methods and by the empirical tight-binding method (Vogl, 1981). The calculations agree that the one-electron ground state exists in an a,-symmetric host-like state, but they differ as to the order of binding energies compared to free ions. Figure 4-26 gives a simplified interaction scheme which should also hold for other sp-bonded impurities (compare also the introduction into such schemes given by the two-state model in Sec. 4.3.2.1). Since the t,-symmetric dangling bond state is pushed into the conduction band by the interaction with the atomic p state, and four of the six impurity electrons are needed to refill the bonding t2 states in the valence band, the remaining two must populate the a,-symmetric gap level, which can accommodate only two electrons of different spin. Accordingly,

205

4.4 Properties of Selected Systems

-'

\ \

\

\

\ \

\ \

\

'

'\ '\

. t,

\

_

#

,J-s

01

Dangling hybrids

"Molecules"

Atom

Figure 4-26. Simplified interaction model for neutral chalcogens at the substitutional site in silicon.

chalcogens can only act as double donors, a fact verified by experiment. By monitoring thermal emission rates (Eq. (4-6)) via DLTS (deep level transient spectroscopy) in Si doped with S, Se, and Te, two energy levels in the upper half of the band gap could be established (Grimmeiss et al., 1980a, 1980b; Grimmeiss et al., 1981). The detailed electronic structure of these centers was revealed via absorption studies and PTIS lines, as shown in the example of Fig. 4-27 for the deeper of the two donor levels ascribed to the Te+'++transition (absorption is therefore studied for the positive charge state of tellurium). The spectral dependence of the photo-ionization cross section (Eq. (4-9)) shows a clearly resolved structure due to photothermal ionization (see previous section), which may be expanded and found to agree with the absorption lines (upper part of Fig. 4-27) within 0.2 meV. With the assignments for the 2 po and 2 pk Rydberg-like states for Te' from an overall spectrum, the spacing for the 2p lines is that expected from EMT (Faulkner, 1969) for a doubly ionized im-

#

10-31-l

0.35

I

I

I

I

0.40

I

Photon energy in eV

I

I

0.45

Figure 4-27. Photo-ionization cross section for Te' and PTIS structure just below the onset of direct photo-ionization, marked F (lower curve). 1 s(A,) + 2p0 and 1s(A,) + 2p, absorption lines of Te+ in silicon (upper curve). (After Grimmeiss et al., 1981).

purity (2 = 2). From EMT the 2p, state for a singly positive center is located 6.4 meV below the conduction band. The optical ionization energy at 5 K from Fig. 4-27 for the second donor is therefore 385 meV + 4 x 6.4 meV, which gives Eopt= 410.8 meV. This is in excellent agreement with the ionization energy taken from the F'TIS lines. Similar studies were made for S and Se, which confirmed the picture of chalcogen double donors discussed so far (see the review of Grimmeiss and JanzCn, 1986). Table 4-2 serves to illustrate the level structure accessible to optical excitation in the case of selenium. The atomic s orbital energies for Te, Se, and S are -19.06 eV, -22.77 eV, and -23.92 eV, respectively (Fischer, 1972; Clementi and Roetti, 1974). If those values are related to the interaction model of Fig. 4-26, the s orbital goes down

206


Table 4-2. Ground state related excitation energies of Seo and Se+ in silicon (all energies in meV). (After JanZen et al., 1984).

Se0 Se+

1s (Tz)

2Po

2 s (T2)

2pk

3 Po

3 P*

Cond. band

272.2 427.3 429.5

295.1

297.4

300.3

301.2

303.5

306.6

547.2

553.9

567.6

57 1.6

58 1.O

593.2

in energy in the series Te, Se, S as does the antibonding al gap level, due to decreasing interaction between the s electrons of the impurity and the a,-symmetric orbital of the vacancy. The chemical trend in the ionization energies of the series 199 meV, 306 meV, and 318 meV for the first donor and, more distinctly, 411 meV, 593 meV, and 613 meV for the second donor confirms the model, in which the results of the cited calculations are contained qualitatively. In order to complete the overall agreement with the given electronic-structure model, an EPR spectrum of Tef is shown in Fig. 4-28, whose parameters in principle

Si : Te'

9.7L GHz

are consistent with the spin-Hamiltonian of Eq. (4-12), with spin S = 1/2. One must note, however, that none of the experiments on chalcogens in silicon (including EPR and ENDOR, Niklas and Spaeth, 1983; Greulich-Weber et al., 1984) was able to decide definitely whether these atoms occupy the substitutional or the interstitial tetrahedral site. That question thus relies solely on the consistency with the theoretical results on electronic structure for substitutional atoms. This remaining piece of the nearly completed puzzle was put in place by total energy calculations for substitutional and interstitial chalcogens (Beeler et al., 1985b). It was found that the difference in the energies of solution for both species (of the order of several eV) is strongly in favor of the substitutional site.

4.4.1.2 Oxygen and Nitrogen in Silicon (0.9%)

I

I

Te

lZSTe (7%)

(92.1%) I I I I I I I I I I I I I I 3000 3500 LOO0 Magnetic field in G

I

Figure 4-28. EPR lines of Te+ in Si. The off-center lines of much lower intensity are split by hyperfine interaction with the non-vanishing nuclear spin (I = 1/2) of the isotopes lZ3Teand lZ5Te.The center line corresponds to all isotopes ('Te) having I = 0 (relative abundances are inserted). (After Grimmeiss et al., 1981).

Both oxygen and nitrogen in silicon should be describable by the scheme of Fig. 4-26, which excludes Jahn-Teller distortions because the A, ground states are not orbitally degenerated; yet neither oxygen (Watkins and Corbett, 1961; Corbett et al., 1961) nor nitrogen (Brower, 1980, 1982) occupies T,-symmetric sites. Instead, oxygen forms the so-called A center when trapped by a vacancy. Structurally, this consists of an off-centered oxygen atom bound to two silicon atoms, the remaining two forming a reconstructed bond. Contrary to


the electrical activity of the other chalcogens, this center provides a single acceptor level 0.17 eV below the conduction band edge (Brotherton et al., 1983). Oxygen may interrupt a silicon bond to form a nonlinear bridging molecule. In this rather interstitial position (Hrostowski and Adler, 1960), oxygen is electrically inactive (Corbett et al., 1964; Pajot, 1994) but in supersaturated solution, it will be mobile at higher temperatures to form a variety of oxygen-related defects. The most intriguing of them will be discussed briefly in Sec. 4.4.4.

4.4.2 DX Centers in Al,Ga,,As Detailed studies of donors in 111-V ternary alloys have revealed a steadily increasing complexity in their electronic structures. The optical ionization energy for the deep levels was found to be drastically larger than that for thermal ionization, indicating a large lattice relaxation (Lang and Logan, 1977; Lang et al., 1979). Deep centers were thought to consist of the donor D (e.g., Si) and an unknown defect X, hence the name DX centers. The large lattice relaxation (LLR) was confirmed by very sensitive optical ionization studies (Mooney et al., 1988a; Legros et al., 1987). The view that all exciting physical features of the DX center e.g., defect metastability, persistent photoconductivity (PPC), or hot electron trapping, are simple properties of the isolated donor (gallium or aluminum site group IV impurities) is now almost generally accepted. Technologically, DX centers were made responsible for device instabilities in MODFETs (modulation field effect transistors) (Theis and Parker, 1987), and are suggested to limit the free-carrier density by self-compensation (Theis et al., 1988), but they might be promising in the development

207

of holographic storage media (Linke et al., 1998).

4.4.2.1 Large Lattice Relaxation and Metastability As discussed in Sec. 4.2.2, moderate lattice relaxation most certainly influences the positions of various donor or acceptor levels in the gap (Fig. 4-7), sometimes to the extent of negative4 level ordering. In the case of very large relaxation, additional effects can occur. This is again demonstrated by configuration coordinate diagrams (Fig. 4-29) that are typical for the DX family. Apart from charge states, which are considered separately (Sec. 4.4.2.2), two important differences appear in the LLR diagram (Fig. 4-29a) compared to the two upper parabolas of Fig. 4-7: 1) The lattice relaxation energy S A w (see Fig. 4-6), measured by the difference of the optical ionization energy, Eoptrand the thermal ionization energy, Eth, is much greater than the difference in total energies of the relaxed configurations measured by Eth. This is apparently not the case in the weak coupling regime of Fig. 4-7 (Eopt-Eth<Eth). 2) The capture barrier EB has increased, leading to a small and strongly thermally activated a,. But even more remarkable is the barrier E, to be overcome for the thermal emission of an electron from the deep center into the conduction band, which now largely surmounts Eth(E, = Eth+EB). Condition (1) represents a regime where extrinsic self-trapping may occur (Toyozawa, 1980,1983). By this phenomenon, an isolated defect, which can bind a charge carrier only by its long-range Coulomb potential, is able to form a deep bound state. This mechanism is based on the interaction of

208


€total

Etotal

t.

0 Configuration Coordinate

Configuration Coordinate

(4

(b)

Figure 4-29. Simplified configuration coordinate diagrams modeling large lattice relaxation. Diagrams display configurations of the DX-active donor in its deep and strongly localized DX-state at Q = QR where it is stable (a) or metastable (b) against a configuration in which the donor occupies an undistorted fourfold coordinated tetrahedral lattice site, represented by the parabola at Q = 0. In both diagrams do+e- denotes the total energy of the effective-mass-like donor in its neutral charge state with one electron present at the bottom of the conduction band. (After Chadi and Chang, 1989).

strong electron-phonon coupling with the weak central-cell potential of the center. Thus the same donor species should give rise to both shallow and deep level behavior, the two levels being separated by an energy barrier. Figure 4-30 displays experimental evidence for such a shallow-deep bistability. A slightly Si doped Alo,29Gao.71As sample (an A1 mole fraction x = 0.29 makes the alloy a direct semiconductor since the conduction band minimum at the rpoint is lowest in energy, see Fig. 4-31) was cooled in the dark and the Hall free-carrier concentration was determined as it was gradually warmed. During the cooling process, a cooling-rate-dependent temperature can be reached below which the electrons in the

A10.29Ga0.71AS C 0 0 0

0

0

u

C 0

0

‘0 10’4

before illumination

* L V

0,

iii

1013

I

I

I

%I on 0 I I

I

1

4.4 Properties of Selected Systems 2.20 2.10

-

n

2.00

3

a,

x

1.QO

:

1.80

(u

G

w

1.70

1.80

1.50

0.0

0.1

0.2 0.3 0.4 0.5 AlAs Mole Fraction (x)

0.6

Figure 4-31. Hydrogenic level ionization energies in Al,Ga,-,As derived from far-infrared transitions. (Data from Theis et al. (1985) and Dmochowski et al. ( 1 988)). The dashed line indicates the position of the deep DX level, with varying A1 mole fraction.

conduction band cannot longer equilibrate with the deep level due to both relaxationinduced barriers (condition (2) above). Thus most of the DX centers will be occupied in the deep-level configuration at QR (Fig. 4-29a), but a small percentage of the electrons will have been frozen-out into the shallow level, which may also be represented for simplicity by the upper parabola at Q = 0 in Fig. 4-29a. Warming the sample without any illumination will thermally activate electrons from the shallow level into the conduction band; the ionization energy will be reflected by the low temperature regime of Fig. 4-30. At higher temperatures, when the barrier E, can be overcome, the deep level participates in the ionization, and the slope of the Hall curve changes drastically. Finally, nearly all centers will be emptied, assuming the configuration at Q = 0. On the other hand, low-temperature illumination

209

results in persistent photoconductivity, which simply means that the free-carrier concentration reaches a high level under illumination and only changes slightly after the light has been turned off. In terms of Fig. 4-29, this means that by optical ionization (related to Eopt),the DX center has been switched from the deep-level configuration to the shallow-level configuration. Fig. 4-3 1 shows data from far-infrared transitions where hydrogenic energy levels have been established for direct-gap material ( ~ 0 . 3 5 (Theis ) et al., 1985) as well as indirect-gap material (x> 0.35) (Dmochowski et al., 1988). Condition (2) implies another property typical for DX centers. The deep level (Si doping) is located 160 meV below the conduction band edge at the point where the direct gap (r)becomes indirect (X), at xcrossing z 0.35. Altering the composition of the semiconductor alloy toward lower A1 mole fractions causes the ionization energy (Eth) to decrease. Finally, the deep level enters the r conduction band, a situation represented by Fig. 4-29b, at x = 0.2 (see the dashed line labeled DX in Fig. 4-31). But even at such conditions, the center retains its compact bound state since it was shown experimentally that neither relaxation nor the thermal emission barrier (E, in Fig. 4-29) depends on the host band structure (Mooney et al., 1986). In the conventional model, the stability of the barrier E, against varying of the alloy composition requires the existence of selection rules by which thermal emission is linked mainly to L conduction band states. The reason for these rules is that the deep level seems to follow the L band minimum (see Fig. 4-3 1). Thus, while thermal trapping and persistent photoconductivity at the resonant deep level tend to vanish for ~ ~ 0 . (because 2 2 the capture barrier EB increases), the level can be persistently populated by a hot-electron

21 0


process (Theis and Parker, 1987). At very high doping levels, where the Fermi level is well above the conduction band edge, thermal trapping, even in GaAs, has also been observed (Mooney et al., 1988b). 4.4.2.2 Microscopic Models

for DX Centers

While all energetic barriers modeled by LLR diagrams, as those of Fig. 4-29, can be established experimentally (Lang, 1986; Mooney, 1991), the fundamental question as to the origin of the stabilizing relaxation requires the microscopic defect structure to be successfully resolved. If the DX center is a complex, then changing the electronic structure upon ionization may result in either a molecular rearrangement (see the well-understood case of carbon-carbon pairs CiC, in Chap. 3 of this Volume) or a change of one of the constituents of the complex to a more distant lattice site (see the case of donor-acceptor pairs discussed in the next section). Most of the experiment on DXcenters indicate, however, that the DX concentration roughly equals that of the donor dopant. This was especially manifested in the hydrostatic pressure experiments of Mizuta et al. (1985) and Maude et a]. (1987) on the donor-related level in GaAs. On the other hand, the majority of donors in GaAs occupy the substitutional site, where in particular group IV (cation site) and group VI (anion site) impurities act as shallow donors (Maguire et al., 1987). Morgan (1986) suggested an interstitial displacement of the donor atom. Chadi and Chang (1988,1989) modeled DX behavior in GaAs using an ab initio pseudopotential approach. The calculated structure is shown to exhibit a very large dopant-dependent lattice relaxation resulting in donor-host bond breaking, as depicted in Fig. 4-32. This structural

B

DX -

Figure 4-32. Schematic view of the normal substitution cation (Si) and anion ( S ) sites in Si- and S-doped GaAs, respectively (a), and the corresponding broken-bond configurations (b). (After Chadi and Chang, 1989).

change involves either a group IVdonor (e.g., silicon, tin) moving from the substitutional gallium site into a threefold coordinated near-interstitial site or a gallium (or aluminum) atom moving into an interstitial site adjacent to a group VIdonor (e.g., tellurium, sulfur) in the arsenic lattice (Fig. 4-32b). However, any of these configurations is stabilized against neighboring ones only by capturing an extra electron; hence its charge state is singly negative, and it can be thought to be formed by a reaction according to 2d0 + d++DX-. Inversely, it can be seen from Fig. 4-29 a that, after ionizing the DX- state, which requires Ethin thermal equilibrium and E, in the transient regime, it will take only the ionization energy of the shallow donor to release a second electron by the reaction do + d++e-. Since this energy AH(''+) can be assumed to be small com,, represents AH-",the pared to I ! & which


two-electron process described is of the negative4 type according to Eq. (4-10). Donor-host bond breaking as the essential structural change for DX-centers was also anticipated by the density functional theory calculations of Dabrowski and Scheffler (1988, 1989) when they studied the metastability of the antisite defect AsGa with a vacancy -interstitial pair (V,,AsI) related to the well-known EL2 center in GaAs (see Chap. 3 of this Volume). Later, total energy calculations were specified to the silicon donor (D) in GaAs (Dabrowski and Scheffler, 1992), and it was shown that the on-site defect in its deep ground-state configuration is positively charged (this does not rule out simultaneous hydrogenous donor behavior), because both the Sigz level and, markedly more distinct, the Si-d," level reside within the conduction band. But for the donor in its neutral (Do) and negative charge state (D-), the stable geometry is also the undistorted tetrahedral site. Displacement of the silicon atom towards the interstitial position in a (1 1I} direction therefore naturally raises the total energy for all three charge states, but when the displacement amounts to about 20% relative to the tetrahedral interstitial position, the Dcurve crosses both D+ and Do and reaches its absolute minimum at about 60% displacement, thus creating a barrier against the undistorted on-site position. In this stable, near-interstitial geometry, the defect should be seen as a vacancy-interstitial pair VGaSi, or, more generally, VGaD, because these considerations may also apply to other group IV donors in GaAs or AlGaAs. According to Dabrowski and Scheffler (1992) and Scherz and Scheffler (1993), the barrier originates from bond rupture, leaving behind a single arsenic dangling orbital which only weakly interacts with the orbitals of the near-interstitial impurity atom. Pushing the donor back to

21 1

the vacant substitutional site would therefore compress these orbitals and a barrier would be set up due to increased electron kinetic energy if, and only if, these orbitals are occupied, as in the case of D-. Thus a situation is reached (Fig. 4-33) where the Do state may play the role of an intermediate state that takes part in capture and emission of the two-electron process, and therefore in this model no selection rules need to be specified in order to explain a composition and pressure independent emission barrier E,. However, there is evidence from experiments using high pressure freeze-out (Suski, 1994) that, at least for the germanium donor in GaAs, both the antibonding Al-symmetric Do state and the (VG,Ger)state are no longer resonant with the conduction band if the pressure is raised beyond 1 GPa (10 kbar). Normally, the DXstate in GaAs only enters the gap for all group IV donors, except germanium, when the pressure exceeds about 2 GPa. The negative-U character of the DX defect and its two-electron ground state was found to be consistent with results from local vibrational mode spectroscopy on silicon-doped GaAs under pressure (Wolk et al., 1991) by studying capture kinetics in A1GaAs:Si (Mosser et al., 1991), or using Hall measurements and EPR (Khachaturian et al., 1989). A two-step photoionization process has been observed in AlGaAs :Te (Dobaczewski and Kaczor, 1991), thus also supporting the existence of an intermediate one-electron (Do) state of the donor impurity, the total energy of which shows a relative minimum at the QR configuration (Dabrowski and Scheffler, 1992). Large distortions concomitant with the LLR models discussed should give rise to local alloy disorder effects. Such effects have been studied theoretically within the Chadi-Chang model by calculating the energy difference between silicon-doped

212


(VGaD,)-

Figure 4-33. Simplified diagram modeling results of Dabrowski and Scheffler (1992) with Do representing an intermediate one-electron state (see text). A relative minimum of the Do+e- curve at Q = QR,by which Eoptmight be subdivided according to observed two-step processes has been omitted. Eth in this case corresponds to E+'-.

Configuration Coordinate AlGaAs alloy configurations containing zero and one neighboring aluminum atom (Zhang, 1991). For GaAs, there are four equivalent (1 1 1) directions, so the energy levels of the distorted configurations are spatially fourfold degenerate. In the alloy, this degeneracy is partially lifted to give well-separated peak structures for group IV or group VI doping, as has been investigated by Laplace transform DLTS (Dobaczewski et al., 1995). These structures may be resolved with respect to local defect-alloy patterns on behalf of their relative peak intensities. Thus most of the important properties of DX centers are explained satisfactorily by microscopic models based on large lattice relaxations. However, there are exceptions, e.g., the case of heavy sulfur doping of GaAs, where the large bond length change of one of the nearest-neighbor gallium atoms (Fig. 4-32 b) is missing, as seen from EXAFS data (Sette et al., 1986). From their

calculations, Park and Chadi (1996) identified a cation-cation dimer-bond formation which combines a large lattice relaxation with small bond length changes around the S dopant atom. This DX structure, also stabilized by a two-electron occupation, should only apply to anion site dopants and is characterized by orthorhombic (C2J symmetry, contrary to the trigonal (C,,) broken-bond induced distortions discussed earlier. In an entirely different concept, the DXground state is considered as the lowestlying split state originating from a very strong Jahn-Teller coupling of the twoelectron (T2 symmetric) state of a group IV or group VI substitutional impurity (Biernacki, 1992). Spontaneous trigonal or tetragonal distortions inherent to that model occur within the arsenic sublattice, thereby leaving the dopant impurity almost invariably at its on-site position. Such Jahn-Teller driven distortions are expected


to be markedly less dramatic compared to distortions in broken-bond configurations (Biernacki, 1996), but it is questionable whether this model copes with DX behavior in all its complexity.

4.4.3 Deep Transition Metal DonorShallow Acceptor Pairs in Silicon Pairing with a shallow background dopant of proper charge state provides a possible path for the decay of a supersaturated solid solution. Such a supersaturation can be built up by diffusing an interstitial 3d metal (e.g., iron) into a silicon sample at high temperatures (>lo00 "C) and then quenching the sample to room temperature. Interstitial 3d metals such as Cri, Mn,, and Fei are still mobile at room temperature or slightly above, but in any case they are not lost to higher-order precipitates very quickly during the quenching process, as observed for Co or Cu in Si. At room temperature, the above interstitial series in p-type material is positively charged (compare the position of the donor levels in Fig. 4-20), whereas practically all substitutional shallow acceptors (B, Al, Ga, In) are occupied and exist in the negative charge state. Thus the pairing is strongly catalyzed by the Coulomb-correlated reaction cross section and may finally be complete at room temperature with no isolated interstitials left. On the other hand, the pair binding energy turns out to be largely determined by Coulomb interaction and amounts to about 0.5 eV at the nearest substitutional-interstitial distance. This leads to a low barrier for pair dissociation and for the reaction Fet+ B-

c>

(Fet B-)'

(4- 15)

equilibrium can actually be established between 30 "C and 150"C (Kimerling et al., 1981; Graff and Pieper, 1981). At higher

21 3

temperatures, the iron atoms diffuse irreversibly to other sinks and may form larger precipitates. Therefore, if pairs of this type are present in high-power semiconductor components (e.g., thyristors), they may cause thermal instability and degradation. In the electronic structure of a shallowdeep pair configuration, the deep impurity retains its localized character, so that the well-known trends for isolated 3d impurities are again reproduced in the energy levels of the pairs. However, the perturbation induced by the shallow impurity makes the pair an interesting example for chargestate-controlled metastability. Thirty ironrelated complexes have been identified by EPR including those about to be discussed (Ammerlaan, 1989). Thus one may get an impression of the problems of defect identification in cases where no defect-specific fingerprints are available from experiment.

4.4.3.1 Electronic Structure and Trends In bringing together the isolated constituents Fey and Al:, the interaction between their electronic states can be modeled after theoretical results from the local density method by Scheffler (1989). In Fig. 4-34, Fey is represented by its spin-split oneelectron levels displayed in Fig. 4-17. The single-particle t,-symmetric ground state of neutral substitutional aluminum in silicon can be placed approximately 70 meV above the valence band, which value is found experimentally for the ionization energy of the shallow-acceptor level (this is feasible because the electronic relaxation is small due to the extended nature of the shallow state). When the interaction is initiated, the iron-like levels are shifted to higher energies because of the repulsive dielectrically screened A1 potential (in this case covalent interactions are of minor importance, since strongly differing spatial

214

4 Deep Centers in Semiconductors Fe: Al,,

Algi

Conduction band 7

Fe?

Conduction band 7

Mn’\

W

Valence bond

t2

--.,,,,,, Valence band

‘2

t

Figure 4-34. Interaction model for interstitial donorshallow acceptor pairs in silicon. The e l levels for both the isolated 3d impurity and the pair are resonant with the conduction band and are not shown. (After Scheffler, 1989).

extension allows for almost no overlap between the two wave functions). The t2 levels are additionally split by the superimposed symmetry-lowering perturbation in the (1 11) pair (trigonal symmetry). One electron is transferred from the iron-like levels to the shallow t2 state, which remains essentially unaffected for the reasons noted above. In general, this is not true for pairs formed exclusively from deep centers, for example, for the AuFe complex (Assali et al., 1985). Figure 4-34 shows that in contrast to isolated Fei, the pair is likely to have two iron-like ionization transitions in the gap: (FeiA1)”+ corresponding to Fe[’++ and (FeiAI)-’’, related to Fe:”. In Fig. 4-35, energy levels of nearestneighbor (1 11) pairs are shown, together with donor and double-donor levels of the isolated interstitial impurities (Mei = Ti, V, Cr, Mn, Fe). Only MeiB pairs have been used in the figure, but their trend persists for the other pairs involving A1 and Ga, a fact

Figure 4-35. Trends in experimental energy levels of interstitial transition metal (Mei) boron pairs in silicon. Data points have been interconnected and extrapolated. The donor and double-donor levels are shown for comparison. (After Feichtinger et al., 1984).

consistent with the interaction scheme of Fig. 4-34. The main trend is derived from the double-donor levels Me+’++of the isolated 3d metals since the shallow acceptors play a rather passive role. This can be explained by the iron-like one-electronlevel structure in Fig. 4-34 and by simple tight-binding arguments (Feichtinger et al., 1984). The spin-related jump in the singledonor-level series (see 4.3.4) has now shifted and occurs between Cr and Mn. There is at least indirect evidence from pair-level trends that for Cri a second donor level (Cr:’”) does not exist, which is in agreement with more direct experiments (Feichtinger and Czaputa, 1981).

4.4.3.2 Charge State Controlled Metastability As to the pair binding energy the electronic structure of pairs discussed in the previous sections suggests a simple ionic model. From such a model, the additional energy required to produce a separation from a first to a second nearest neighbor for the 3d interstitial in a positive charge state is

21 5


(4- 16)

where rl and r2 are the distances for pairs aligned in the (1 11) direction and the (100) direction, respectively (E is the static dielectric constant for silicon). Therefore, in thermal equilibrium one would expect a fraction

f- eXp [-b?b/kT]

(4-17)

of pairs aligned along a (100) direction, with the metal sitting in the next nearest interstitial position adjacent to the substitutional acceptor. If one assumes a double positive charge for the interstitial, which also becomes stable for Fe, and Cr, when it is in a pair configuration (Mn? does exist already for the isolated atom, see Fig. 4-35), then AEb should be twice as large as before. Hence the charge state of the 3d constituent of a pair decides whether an appreciable fraction of (100) pairs can be found or not. Metastability of iron-boron pairs and its kinetics in cases where the iron occupies more distant sites in the vicinity of the boron acceptor has also been reported, and a set of trap levels has been assigned to such configurations (Nakashima et al., 1993, 1994). Further consequences may easily be seen from a configuration-coordinate diagram (Fig. 4-36), especially for the ionization energies, for which the relation E2 = El hEb should hold (note that no lattice relaxation has been included in the diagram). In their comprehensive study, Chantre and Bois (1985) not only found the energy levels related to the two pair configurations, but could establish overall agreement with the diagram in the case of FeiAl pairs. In their DLTS experiments, they could show that cooling of their samples (Schottky diodes) under reverse bias yields a fraction of pairs in the (100) configuration, and two energy levels, differing in intensity (at

I

I

1‘

I ‘2

~-

Distance from acceptor

Figure 4-36. Configurational coordinate diagram for iron-acceptor pairs in silicon, based on a purely ionic model. Em is the barrier to atomic motion (migration energy) from one configuration to the other. E , and E, denote the ionization transitions, e.g., for (FeiAl)”+ (1 11) and (FeiA1)’/+ (100). (After Chantre and Bois, 1985).

Ev+0.20 eV and Ev+0.13 eV), can be detected. Cooling with no reverse bias applied results in an almost entire suppression of the Ev+0.13 eV level. Bias off corresponds to a situation where free holes are present in the junction to occupy the pair states in favor of (Fe,Al)+ (related to Fe?), whereas bias on depletes the barrier from free carriers leaving the pairs in their neutral state (related to Fe;) thus allowing for partial reorientation. Pair configurations of trigonal symmetry (1 1 1) pairs) and orthorhombic symmetry ((100) pairs) have been identified in the case of Fe,Al (Van Kooten et al., 1984; Gehlhoff et al., 1988; Irmscher et al., 1994), and also for (100) FeiIn (Gehlhoff et al., 1993). This special type of configurational metastability apparently involves no lattice relaxation and should be observed for all

21 6


similar systems composed of deep interstitial donors and shallow acceptors, but depends on whether the interstitials are mobile enough to allow for reorientation at relatively low temperatures. On the other hand, pairing at different pair distances and in different orientations might be the only way to get experimental data on the electronic structure for an ultrafast diffusing species like cobalt in silicon (Bergholz, 1982). A more recent overview on iron-acceptor pairing including properties important for silicon processing has been given by Song Zhao et al. (1997).

4.4.4 Thermal Donors in Silicon Oxygen may well be the most-studied impurity found in silicon. A large fraction of all research efforts has been spent on the process of thermal donor (TD) formation, which works upon heat treatment in the 350-500 “C temperature range and generates complex defects which act as shallow double donors. Following the original idea of Kaiser et al. (1958), it was widely assumed that TDs are small oxygen aggregates in an early stage of oxygen precipitation. It is of technological importance to clarify any facet of oxygen in Czochralskigrown silicon crystals (CZ), as this may play an important role in silicon device technology (Patel, 1977). Thermal donors have been studied by electrical measurements, such as resistivity, Hall effect, DLTS, as well as by optical absorption, EPR, and ENDOR. But the task of synthesizing the vast amount of detailed information into a consistent whole has still not been brought to an end where any discussion has been settled. A successful model would have to cover the kinetic and electronic properties of a microscopic structure that changes steadily upon heat treatment.

Electrical measurements (Hall effect, resistivity) reveal the double-donor character of TDs with the apparent energy level positions shifted toward the conduction band upon prolonged annealing at about 450°C (Kaiser et al., 1958; Gaworzewski et al., 1979). The initial rate of donor formation was found to be proportional to the fourth power of the initial oxygen concentration (Kaiser, 1957), whereas the maximum donor concentration attainable at 450 “C is approximately proportional to the cube of the initial oxygen concentration. The donor activity of TDs is destroyed by annealing at temperatures higher than 500°C. However, a new family of defects, the so-called “new donors” (NDs) is formed in the temperature range between 550 and 8OO”C, which is closely related to oxygen precipitation. For this species, “normal” TDs of the cluster type may act as nucleation sites (Gotz et al., 1992). Electron microscopy suggests that rodlike clusters grow during TD formation. They are aligned along (1 10) directions and should consist of hexagonal covalent Si (Bourret, 1987), contrary to an earlier interpretation of these clusters as ribbons of coesite, a high-pressure form of Si02 (Bourret et al., 1984). The kinetics of TDs, which is determined from the electrical activity, is closely related to infrared (IR) absorption studies (Oeder and Wagner, 1983; Pajot et al., 1983). IR absorption spectra show clearly resolved Rydberg-like states (Sec. 4.3.5.2) of at least nine distinct double donors (Fig. 4-37). Seven further individual TDs have been identified in their neutral charge state TDo (Pajot, 1983; Gotz and Pensl, 1992), so that at present the number of well separated thermal donors amounts to sixteen. The maximum intensity within the donor series is gradually shifted to the shallower species upon heat treatment. This

217


0.64

V

C

n

0

0.52 0.46

0.40

1300

1050 925 800 675 Wave numbers in cm-'

1175

Figure 4-37. Absorption spectra of five different species of TD+ in silicon, observed after 10 minutes pre-annealing at 770°C, followed by 2 hours at 450°C.(After Oeder and Wagner, 1983).

may well reflect the precipitation of impurities such as oxygen successively occurring at the core of the defect and thereby resulting in an increasingly repulsive perturbation. Figure 4-37 shows a distribution of the intensities (related to the concentration) of five different TD species; Table 4-3 lists the ground state (A,) related ionization energies of nine donors. A correlation study between DLTS and IR spectroscopy additionally links electrical and optical properties of TDs, showing that both arise from the same defect (Benton et al., 1985). EPR seemed to be the best instrument for shedding light on the initial core structure

of TD, and two prominent EPRspectra associated with TD formation were published labeled NL8 and NLlO (Muller et al., 1978). As expected for a shallow center, the spectra show only small anisotropy in the g values (orthorhombic symmetry), which are close to that typically found for conduction band electrons. Unfortunately, no hyperfine interaction with oxygen could be resolved, since the line width of EPR evidently obscures the hyperfine structure (the samples were enriched with "0, which has a nuclear spin of I = 5/2). Thus without detailed knowledge of the microscopic nature of the TD core, a number of models have been proposed. They are compatible with the kinetics and the orthorhombic symmetry of the center. A first group of models is based on the agglomeration of oxygen atoms, either of molecular oxygen to form 0, complexes (Gosele and Tan, 1982) or of substitutional oxygen upon vacancy diffusion (Keller, 1984). The second group involves interstitial oxygen (e.g., the YLID configuration, Stavola and Snyder, 1983) as the saddle-point configuration of interstitial diffusion (Fig. 4-38 a). The Ourmazd-Schroter-Bourret (OSB) model proposes an oxygen cluster of five atoms containing a silicon atom in its center, which is pushed into a near interstitial position along the (001) direction. According to this model the cluster subsequently grows by the stepwise addition of interstitial oxygen. In this model, for example, the electrical activity results from the broken bonds of the central silicon and ceases to exist by

Table 4-3. First and second ionization energies (TDo'+ and TD+'*) of thermal donor species in silicon (After Pajot et al., 1983). Species ~~

+ TD+ TD+ + TDZ+ TDO

A

B

C

D

E

F

G

H

I

66.7 150.0

64.4 144.2

62.1 138.5

60.1 133.1

58.0 128.5

56.2 124

54.3 121

52.9 118

~~

69.1 156.3

21 8


ejection of that atom, that is, by the emission of a self-interstitial upon a stressrelieving relaxation (Fig. 4-38 b). A similar model has been proposed by Borenstein et al. (1986). A third group of models relies on the agglomeration of silicon self-interstitials (Newman, 1985; Mathiot, 1987). Accordingly, the TD core is formed by two selfinterstitials in the bond-centered position on a O3 complex and can grow by adding further self-interstitials along the (1 10) 0 the diffusivity decreases as the concentration increases. Therefore, increasingly box-like concentration profiles result for increasing y. Although in reality the diffusivity of dopants is usually composed of several such terms with different values of y (Section 5.6.4),y = 1 is approximately realized for high concentration B and As diffusion in Si, and y= 2 for high-concentration P diffusion in Si and also for indiffusion of Zn in GaAs. In the case of y=- 2 the diffusivity increases with decreasing concentration which leads to a concave profile shape in the semi-logarithmic plot of Fig. 5-5. Such concave concentration profile shapes have been observed for Au, Pt and Zn in Si (Sec. 5.6.3) and for many elements in 111-V compounds such as Cr in GaAs (Tuck, 1988). The concentration dependence of D may be determined from measured concentration profiles by means of a BoltzmannMatano analysis as described in standard treatments of diffusion (Tsai, 1983). In the following section we will deal with the atomistic diffusion mechanisms, which are the underlying cause of concentration-dependent diffusivities.

0

0.5

I.o

I

x / (4 D, t 12‘

1.5

20

Figure 5-5. Normalized diffusion profiles for different concentration dependencies as indicated. (Partly from Weisberg and Blanc, 1963).

5.5 Atomistic Diffusion Mechanisms 5.5.1 Diffusion Without Involvement

of Native Point Defects Interstitially dissolved impurity atoms may diffuse by jumping from interstitial site to interstitial site. In this direct interstitial diffusion mechanism no native point defects are involved and the diffusivities are generally very high compared to those of substitutionally dissolved atoms as can be seen in Fig. 5-6, which is a compilation of diffusion data for different elements in Si. Examples are the diffusion of Li, Fe and Cu in Si. An oxygen atom in Si occupies the bond-centered interstitial positions and is covalently bonded to two involved Si atoms. Oxygen diffuse among only such interstitial sites but a diffusion jump requires the breaking of bonds, resulting in the interstitial oxygen diffusivity being much lower than normal interstitial diffusivities but still much higher than the diffusivity of substitutionally dissolved dopants or self-diffusion. It has been suggested that Si self-diffusion as well as the diffusion of group I11 and V dopants can also be accomplished with-

242

-

5 Point Defects, Diffusion, and Precipitation

Tl’Cl

1300 1100

900 800 700

600

10‘1 T [K-’]

51

-

Figure5-6. Survey of the diffusivities of foreign atoms in silicon and of silicon self-diffusion. The lines labeled with Au:” and A@) correspond to different effective diffusivities of substitutional gold in silicon as discussed in Section 5.6.3. (Partly from Frank et al., 1984)

out the involvement of native point defects via the concerted exchange mechanism (Pandey, 1986), which is a special case of the ring-mechanism. Although the contribution of this mechanism to self- and dopant diffusion in Si cannot be totally excluded, it certainly cannot substitute for the diffusion mechanisms involving native point defects. Among many reasons, it appears sufficient to mention dislocation climb processes, which require the transport of a net amount of atoms which is not within the capability of the concerted-exchange mechanism.

5.5.2 Simple Vacancy Exchange and Interstitialcy Mechanisms

The diffusion of a substitutionally dissolved atom is facilitated by the presence of a native point defect next to this atom. In the case of a simple vacancy exchange mechanism, the substitutionally dissolved atom jumps into a vacancy on a nearest neighbor site of the lattice or sublattice. In the case of the interstitialcy or indirect interstitial mechanism, the substitutionally dissolved atom is first replaced by a self-interstitial and pushed into an interstitial position from which it changes over to a neighboring lattice site by pushing out that lattice atom. In the case of self-diffusion there is no pair formation between the lattice atom and the native point defect involved, but substitutional impurities (or dopants) normally form complexes or pairs with native point defects. These point-defect-impurity complexes are the reason for the generally higher values for the dopant diffusivities than for self-diffusion (see, e.g., Fig. 5-6 for Si). Within the simple vacancy exchange mechanism the diffusivity Dy of substitutionally dissolved atoms is proportional to the available thermal equilibrium vacancy concentration

DY

a

CGq

(5-24)

Similarly, for substitutionally dissolved atoms using self-interstitials as diffusion vehicles the diffusivity 0,’ is given by

D: cc CFq

(5-25)

Since, in principle, both vacancies and selfinterstitials can contribute to the total diffusivity D,and since the native point defect may possess various charge states xr, D,as a function of the electron concentration n may be written as

0,(n)=CC Iy‘(ni)(n/ni)-r r x

(5-26)

243

5.5 Atomistic Diffusion Mechanisms

The summation over the native point defects x for a given charge state r,

C E'(ni) Q!'(ni) X

+ @"(ni>

(5-27)

describes the self-interstitial and vacancy contributions to the diffusivity under intrinsic and thermal equilibrium conditions. If the concentrations C, of native point defects x differ from their equilibrium concentrations Ctq due to an external perturbation, D,(n) changes to a perturbed diffusivity (5-28) DY (n) = 2 (G (n)/cq (n)c DX'(ni)(n/ni)-r X

r

In Eq. (5-28) it has already been taken into account that the ratio

Cx,(n)/ Cly (n)= C, (n)/ Gees (n)

(5-29)

is independent of the charge state r. We will apply and discuss this equation in the context of oxidation and nitridation-perturbed diffusion of dopants in Si in Section 5.6.4. For compound semiconductors Eq. (5-28) has to be extended to account for the dependence of D,(n)on the pressure of the more volatile component as expressed in Eq. (5-8) (Casey, 1973; Tuck, 1988; Tan et al., 1991a).

over from interstitial to substitutional sites and vice versa requires the involvement of native point defects. For uncharged species the two basic forms of their change-over which have been suggested are the kick-out mechanism (Gosele et al., 1980; Frank et al., 1984) Ai

c>

A,+I

(5-30)

involving self-interstitials and the much earlier proposed Frank-Turnbull mechanism (Frank and Turnbull, 1956) Ai+V

e>

(5-31)

A,

involving vacancies. Both mechanisms are schematically shown in Fig. 5-7. It is worth mentioning that the kickout mechanism is just the dynamic form of the Watkins replacement mechanism (Watkins, 1975) in which a self-interstitial generated by low temperature electron irradiation pushes a substitutional atom A, into an interstitial position Ai. The kickout mechanism is closely related to the interstitialcy diffusion mechanism. The main difference is that the foreign atom, once in an interstitial position,

Ai rn

5.5.3 Interstitial-Substitutional Mechanisms

0 0 0 0 0

5.5.3.1 Uncharged Species

(a)

An appreciable number of impurities (say A) in semiconductors are interstitial-substitutional (i-s) species. They are mainly dissolved on substitutional sites (A,) but accomplish diffusion by switching over to an interstitial configuration (Ai) in which their diffusivity Diis extremely high. Examples are Au, Pt and Zn in Si, Cu in Ge, and Zn, Be, Mn, Cr and Fe in GaAs. The change-

0 0 0 0 0

FRANK-TURNBULL MECHANISM

As

Ai

0 0 010 0

01'0 0 0 0 0

0

0

0

0

0 0 0 0 0 (b)

I

~

*0 0 L

oo

0

0 0 0 0 0

KIm-OUT MECHANISM

Figure 5-7. Schematic representation of the FrankTurnbull or Longini mechanism (a) and the kick-out mechanism (b).

244


remains there for only one step in the interstitialcy mechanism and for many steps in the kickout mechanism. In contrast, the Frank-Turnbull mechanism and the vacancy exchange mechanism are qualitatively different. Within the vacancy exchange mechanism an increase in vacancy concentration enhances the diffusivity, whereas within the Frank-Turnbull mechanism an increase in vacancy concentration rather decreases the effective diffusivity of the substitutional species. A detailed description of the diffusion behavior of atoms moving via the kickout or Frank-Turnbull mechanism in general requires the solution of a coupled system of three differential equations describing diffusion and reaction of Ai, A, and the native point defect involved (V or I). Detailed discussions and methods of solutions may be found in the literature (Frank et al., 1984; Tuck, 1988; Morooka and Yoshida, 1989). Here we derive the effective diffusion coefficient Deffof A, via the kickout mechanism in a simplified manner for the case of indiffusion from the surface. We assume for simplicity that the mass action law for the concentrations Ci of Ai, C, of A, and C, of I in accordance with reaction (5-30) is fulfilled,

c, C&

=c q :

c,eq/c:q

(5-32)

where the superscript "eq" indicates the thermal equilibrium concentrations (solubilities) of the corresponding species. If the indiffusion of Ai is slow enough to allow the self-interstitials generated via the kick-out mechanism to migrate out to the surface and keep their thermal equilibrium concentration, then the effective diffusivity of A, is given by

D;Y= Di C:q/C,"q

(5-33)

provided Cseq% Crq, which is generally the case. Here the lower index in bracket indi-

cates the rate limiting species. If on the other hand the indiffusion of Ai is so fast that the generated self-interstitials can not escape quickly enough to the surface (i.e., if Di CFq%D1 Cfq) a supersaturation of self-interstitials will develop and further incorporation of A, is limited by the outdiffusion of the generated self-interstitials to the surface. This leads to an effective A, diffusivity D$ following from the approximate flux balance

D$ dC,/dx=-D, dC,/dx

(5-34)

and the mass-action law (5-32) as

D,$= (D, Cfq/C,"q)(C,"q/C,)2

(5-35)

Analogously, for the Frank-Turnbull mechanism sufficiently slow indiffusion (DiCfq 4Dv C$q) leads to the same Dty as given by Eq. (5-33). An effective A, diffusivity D;; controlled by the indiffusion of vacancies from the surface results if Di Cieq%DvCGq holds: qV eff) - Dv

Ceq/C,"q v

(5-36)

The strongly concentration-dependent effective diffusivity D$f leads to the peculiar concentration profiles shown in Fig. 5-5 for y=-2. These profiles can easily be distinguished from the erfc-type profiles which are associated with DTG. This macroscopic difference allows not only to decide between different atomistic diffusion mechanisms of the specific foreign atom involved but also to obtain information on the mechanism of self-diffusion. The effective diffusivities in Eqs. (5-35) and (5-36) have been derived under the assumption of dislocation-free crystals. The presence of a high density of dislocations in an elemental crystal maintains the equilibrium concentration of intrinsic point defects and thus an erfctype profile characterized by the constant diffusivity D$ of Eq. (5-33) will result even if Di Cfq%DIC,eq holds. For compound

5.5 Atomistic Diffusion Mechanisms

semiconductors this statement does not hold in general, since the presence of dislocations does not necessarily guarantee native point defects to attain their thermal equilibrium concentrations. If self-interstitials and vacancies co-exist, such as in the case of Si, the effective A, diffusion coefficient in dislocation-free material for Di CfqS (DI CFq+ Dv CGq) is given by (5-37) 5.5.3.2 Charged Species

For the case of 111-V compounds even regular p-type dopants such as Zn, Be or Mg diffuse via an interstitial-substitutional diffusion mechanism (Casey, 1973; Tuck, 1974; Kendall, 1968; Tuck, 1988; Yu et al., 1991a; Tan et al., 1991a). In these cases the charge states of the involved species have to be taken into account. In a generalized form the kickout mechanism now reads A{+ e Ar-+Ik++(m+j-k) h+

(5-38)

where j , k, and m are integers characterizing the charge state of the species and h+ stands for holes (Gosele and Morehead, 1981; Gosele, 1988). The self-interstitial is assumed to consist of the atomic species which forms the sublattice on which A, is dissolved, e.g., a Ga self-interstitial in the case of Zn acceptors substitutionally dissolved on the Ga sublattice in GaAs. The corresponding extension of the Frank-Turnbull mechanism, which is often called Longini mechanism in the case of 111-V compounds (Longini, 1962) may be written as A{++Vk-e A:-+

(m +j - k) h+

(5-39)

In general, the native point defects, as well as the interstitials Ai, may occur in more than one charge state. For the generalized kickout mechanism, the mass action law for local equilibrium between the vari-

245

ous species reads Ci/(C, CIpm+'-k) =constant (7')

(5-40)

where p is the hole concentration. For completely ionized substitutional acceptor impurities (m > 0) of sufficiently high concentration (above the intrinsic electron concentration ni)p may be replaced by m C,. For donor impurities (mc 0) analogously the electron concentration is given by I m I C , . For dislocation-free materials, considerations similar to those for uncharged species lead to DEy = (1 m 1 + 1 ) (DiCrq/C:q) (C,/Ciq)lml*j (5-41)

if the supply of A{+ limits the incorporation rate. The positive sign in the exponent holds for substitutional acceptors and the negative sign for substitutional donors. The factor I m J + 1 accounts for the electric field enhancement (see also Section 5.4). Equation (5-41) holds both for the generalized kickout and the Frank-Turnbull mechanisms and is independent of the charge state of the native point defects. When the diffusion of self-interstitials to the surface limits the incorporation rate of A, a supersaturation of self-interstitials will develop and the effective diffusion coefficient for the A, atoms is given by DGY=(ImI+l) (DICfq(C:q)/C:q)

. (Cs/C;q>'k-I"I-2

(5-42)

When the supply of vacancies from the surface limits the incorporation of A, an undersaturation of vacancies develops and D 7 6 = ( l m l + l ) (DvCCq(Ciq)/C;q) *

(C,/C;q)'k-m

(5-43)

holds. For both Eq. (5-42) and (5-43) the same signconvention holds as for Eq. (5-41). Equations (5-40)-(5-43) reduce to (5-33), (5-35) and (5-36) if all species involved are uncharged.

246


The quantities DICFS(Ctq) and Dv CGq (Cseq) refer to the self-diffusion transport coefficients of Ik+and Vk- under the doping conditions C,=CseS and not necessarily to the intrinsic self-diffusion coefficient. Even for charged species, constant effective diffusivities may be obtained. For example, for singly charged acceptor dopants (rn = l), 13+ ( k = 3 ) or V- ( k = 1) lead to constant effective diffusivities DdZ and D$$), respectively. Since the applicable effective diffusion coefficient may change with the depth of the profile, complicated concentration profiles may result as frequently observed in 111-V compounds (Tuck, 1988). Examples of foreign atoms diffusing via one of the interstitial-substitutional mechanisms will be discussed for silicon, germanium and GaAs, in Sections 5.6-5.8, respectively. From a basic science point of view, the importance of the interstitial-substitutional diffusion mechanisms derives mainly from the possibility to distinguish whether self-diffusion in a given semiconductor material is limited by vacancies or self-interstitials, which can hardly be conclusively accomplished by any other means.

5.5.4 Recombination-Enhanced Diffusion In semiconductors, thermally activated diffusion of defects may be enhanced by the transfer of energy associated with the recombination of electrons and holes into the vibrational modes of the defects and their surrounding as first recognized by Weeks et al. (1975) and theoretically described by Kimerling (1978) and Bourgoin and Corbett (1978) in the seventies. The presence of a concentration of electrons and holes above their thermal equilibrium values may be induced by optical excitation (Weeks et al., 1975; Chow et al., 1998), by particle irradi-

ation such as electron irradiation (Bourgoin and Corbett, 1978; Watkins, 2000), ion implantation or plasma exposure (Chen et al., 1996), as well as by carrier injection in devices (Uematsu and Wada, 1992) or via the tip of a scanning tunneling microscope (STM) (Lengel et al., 1995). As a result, the effective thermal activation energy for diffusion may be reduced considerably or may even become essentially zero. In the later case, this type of recombination-enhanced diffusion is termed “athermal diffusion”. The most famous example of athermal diffusion interpreted in terms of recombination-enhanced diffusion appears to be the long-range diffusion of radiation-induced silicon self-interstitials at liquid helium temperatures. In this case, discussed in detail by Watkins (2000) in this volume, the electron-hole excitation is thought to be caused by the particle irradiation. Of technological importance is the recombinationenhanced diffusion of defects in devices such as light-emitting diodes, lasers, or bipolar transistors, including heterobipolar transistors in which carrier injection during operation may lead to undesirable movement of defects. This movement may lead e.g. to dislocation-climb and associated “dark line defects” or other defect rearrangements affecting device performance unfavorably. Convincing direct experiments demonstrating recombination-enhanced diffusion have been reported by Chow et al. (1998). By optically induced EPR, these authors measured a single diffusion jump of a zinc interstitial in ZnSe induced by optical excitation.

5.6 Diffusion in Silicon 5.6.1 General Remarks Silicon is the most important electronic material presently used and is likely to keep

5.6 Diffusion in Silicon

that position in the future. Diffusion of dopants is one of the important steps in device processing. For sufficiently deep junctions, diffusion is required for generating the desired dopant profile. For the case of submicron devices the tail of the implantation profile is already in the submicron regime, so that diffusion occurring during the necessary annealing out of implantation-induced lattice damage may already be an undesirable effect. Methods such as rapid thermal annealing by flash lamps are investigated to gain a tighter control over the time spent at high temperatures. Still shallower junctions will probably require closely controlled diffusion processes from well-defined sources, as for example, from doped polysilicon used for certain bipolar devices. The interest in dopant diffusion will increase in this context. Historically, borrowing the knowledge from metals that vacancies are the predominant thermal equilibrium native point defects, diffusion processes in Si had been first described also in terms of vacancy-related mechanisms. In 1968 Seeger and Chik suggested that in Si both self-interstitials and vacancies contribute to self- and dopant diffusion processes. The controversy on the dominant native point defects in Si lasted for almost 20 years. Finally, it became generally accepted that both self-interstitials and vacancies have to be taken into account in order to consistently understand self- and most impurity diffusion processes in the 1980s, with the exception of a few (Bourgoin, 1985; Van Vechten, 1980; Van Vechtenet al. 1991). The main indications for the involvement of self-interstitials in diffusion processes in Si came from diffusion experiments performed under non-equilibrium native point defect conditions, such as experiments on the influence of surface oxidation or nitridation on dopant diffusion. Investigations of the diffusion properties of atoms

247

such as Au or Pt migrating via an interstitial-substitutional mechanism were also crucial in establishing the role of self-interstitials in self-diffusion in Si. What is still uncertain is the diffusivity and the thermal equilibrium concentration values of selfinterstitials and vacancies, as will be discussed in Section 5.6.6.

5.6.2 Silicon Self-Diffusion The transport of Si atoms under thermal equilibrium conditions is governed by the uncorrelated self-diffusion coefficient

DSD= D, c q ;

+ D, cg

(5-44)

As mentioned in Section 5.2, native point defects may exist in several charge states. The observed doping dependence of group 111 and V dopant diffusion (Section 5.6.4) indicates the contributions of neutral, positively charged, negatively and doubly negatively charged native point defects. It is presently not known whether all these charge states occur for both self-interstitials and vacancies. Taking all observed charge states into account we may write D, Cleq as D, cq ; =Dro CIeOg+D,- cfq + D p c;f!+ D,+ c;s

(5-45)

An analogous expression holds for vacancies. The quantity CIeq comprises the sum of the concentrations of self-interstitials in the various charge states according to c;q

= c,eo9+c;3+

c;z + c,e+s

(5-46)

Therefore, the diffusivity D, is actually an effective diffusion coefficient consisting of an weighted average of the diffusivities in the different charge states according to Eq. (5-7). The same holds analogously for C+q and D,. The most common way to investigate self-diffusion in Si is to measure the diffu-

248


-r

sion of Si tracer atoms in Si. These tracer atoms are Si isotopes which can be distinguished from the usual Si isotopes the crystal consists of by various experimental techniques. The tracer self-diffusion coefficient DT differs slightly from Eq. (5-44) since it contains geometrically defined dimensionless correlation factors& and&,

DT=fI DI CFq+fv Dv CGq

(5-47)

The vacancy correlation factorf, in the diamond lattice is 0.5. The corresponding quantityh I 1 depends on the unknown selfinterstitial configuration. Measured results for DTare shown in Fig. 5-8. Various results for DTwhich are usually fitted to an expression of the form

DT=Do exp (- Q/kBT )

self - diffusion

D,CFq=9.4X lo-* exp (-4.84eV/kB T)m2s-' (5-49)

DVcGq 6x lop5exp (-4.03 eV/kB T )m2 S-l

(5-50)

Values of D,Cfq as determined by different groups are also given in Table 5-1 in the form of a pre-exponential factor and an ac-

P:

I_

i

10-191

@ @ @ @

a

lo-=

(5-48)

are given in Table 5-1 in terms of the preexponential factor Do and the activation enthalpy Q. Tracer measurements, including extensions measuring the doping dependence of DT(Frank et al., 1984), do not allow to separate self-interstitial and vacancy contributions to self-diffusion. Such a separation became possible by investigating the diffusion of Au, Pt and Zn in silicon (as described in more detail in the subsequent Section 5.6.3). These experiments allowed a fairly accurate determination of D,CFq but only a crude estimate of Dv CGq derived from a combination of different types of experiments (Tan and Gosele, 1985). The resulting expressions shown in Fig. 5-9 are

Pcl

@

Ghashlogare ( 1 9 6 6 ) Fairfield ond Maslers (1967) Mayer. Mehrer.and Moier (1977) Kalinowski and Segum ( 1 9 8 0 ) Htrvonen Ond A n t t i l o (1979) Dernond et a1 (1983) from stacking t a u l l shrinkage

1

1

6

7

8

1 0 ' 1 ~[ K-'

-1

Figure 5-8. Tracer self-diffusion coefficients of silicon as a function of reciprocal absolute temperature. (Partly from Frank et al. 1984).

tivation enthalpy. It is worth noting that D, CFq coincides within experimental error with 1/2 DTfrom tracer measurements. The doping dependence of Si self-diffusion (Frank et al., 1984) allows to conclude that neutral as well as positively and negatively charged point defects are involved in selfdiffusion, but the data are not accurate enough to determine the individual terms of Eq. (5-45) or the analogous expression for vacancies. Since DT as well as D,CFqand Dv CGq each consist of various terms, their representation in terms of an expression of the type of Eq. (5-48) can only be an approximation holding over a limited temperature range. In Section 5.6.6 we will discuss what is known about the individual factors D,, Ctq, Dv and CGq.

249


Table 5-1. Diffusivities of various elements including self-interstitials and vacancies in silicon fitted to D=Doexp(-QlksT). -~

~

DO [lo4 m2 s-']

Q

References

Lev1

Si

1800 1200 9000 1460 8 154 20

4.77 4.12 5.13 5.02 4.1 4.65 4.4

Peart, 1966 Ghostagore, 1966 Fairfield & Masters, 1967 Mayer et al., 1977 Hirvonen and Antilla, 1974 Kalinowski and Seguin, 1980 Demond et al., 1983

Si

914 320 2000 1400

4.84 4.80 4.94 5.01

Stolwijk et al., 1984 Stolwijk et al., 1988 Hauber et al., 1989 Mantovani et al., 1986

Si

0.57

4.03

Tan and Gosele, 1985

I

1o - ~ 3.75 x 8 . 6 lo5 ~

0.4 0.13 4.0

Tan and Gosele, 1985 Bronner and Plummer 1985 Taniguchi et al., 1983

0.1 2500 32 1.9 4.4 0.07 560

2.0 4.97 4.25 3.1 0.88 2.44 4.76

Tan and Gosele, 1985 Hettich et al., 1979 Yeh et al., 1968 Newman and Wakefield, 1961 Tipping and Newman, 1987 Mikkelsen, 1986 Bracht et al., 1998

Diffusing species

V Ge Sn CS

Ci 0 Si

Description of diffusivity

5.6.3 Interstitial-SubstitutionalDiffusion: Au, Pt and Zn in Si Both Au and Pt can reduce minority carrier lifetimes in Si because their energy levels are close to the middle of the band gap. They are used in power devices to improve the device frequency behavior. In contrast, Au and to a lesser extent Pt are undesirable contaminants in integrated circuits and hence have to be avoided. For both reasons, the behavior of Au and Pt has been investigated extensively. Zinc is not a technologically important impurity in Si, but scientifically it served as an element with a diffusion behavior in between substitutional dopants and Au and Pt in Si. The indiffusion profiles of both Au and Pt in dislocation-free Si show the concave

profile shape typical for the kickout mechanism (Stolwijk et al., 1983, 1984; Frank et a]., 1984; Hauber et al., 1989; Mantovani et al., 1986). Examples are shown in Figs. 5-10 and 5-11 respectively for Au diffusion and for Pt diffusion. From profiles like these and from the measured solubility CSeq of Au, and Pt, in Si, the values of D, CIeq shown in Fig. 5-9 have been determined. Diffusion of Au into thin Si wafers leads to characteristic U-shaped profiles even if the Au has been deposited on one side only. The increase of the Au concentration in the center of the wafer has also been used to determine D,Cfq (Frank et al., 1984). In heavily dislocated Si the dislocations act as efficient sinks for self-interstitials to

250

-


T[Tl

300

1100

900

800

70

self - diffusion in S i

O P e r r e t e t 01. (1989)

Stolwijk et al. (1 983) 0 M o r e h e a d et a1.(1983)

I Wilcox et 01.(1964)

4 Kitagawa

et

aL(1982)

A Montovani et a l . (1986)

Houber e t ol (1989)

7

A\

8 9 @ l T[K-'l

10

Figure 5-9. Comparison of the contributions D, C:¶ and D, C$¶ to the self-diffusion coefficient in Si determined from the diffusion of Au, Pt, Zn and Ni in Si. Full symbols refer to D,C$.

(Perret et al., 1989). In highly dislocated material, an erfc-profile develops as expected (Fig. 5-12). In dislocation-free material only the profile part close to the surface shows the concave shape typical for the kickout diffusion mechanism. This part can be used to determine D,Ctq values as indicated in Fig. 5-9. For lower Zn concentrations, a constant diffusivity takes over. The reason for this change-over from one profile type to another is as follows: In contrast to the case of Au, the DiCeq value determined for Zn is not much higher than DI CFq so that even in dislocation-free Si only the profile close to the surface is governed by 07; of Eq. (5-35) which strongly increases with depth. For sufficiently large penetra: : and a tion depths D&I':finally exceeds 0 constant effective diffusivity begins to de1

I

I

I c

I

\

\

5)

I

1

20

50

I

Au in Si 900 "C, I h

0.5

\

3

keep CI close to CFqso that the constant effective diffusivity D;yfrom Eq. (5-33) governs the diffusion profile (Stolwijk et al., 1988). Analysis of the resulting erfc-profiles allowed to determine DiCfq=6.4~10-~exp(-3.93 eVlkBT)m2s-' (5-51)

In Fig. 5-6, DiCfqIC,"q (curve Au;*') is compared to D,CfqlCtq (curve Au$')). DiCfq turns out to be much larger than D ICfs from Eq. (5-49). This is consistent with the observation that Au concentration profiles are governed by DEy in dislocation-free silicon. Zinc diffusion has also been investigated in highly dislocated and dislocation-free Si

u*

0.1 Stolwijk (1983)

0.05

2

5

10

x[pml

100

Figure 5-10. Experimental Au concentration profile in dislocation-free Si (full circles) compared with predictions of the Frank-Turnbull and the kick-out mechanism (Stolwijk et al., 1983).


Pt in SI

I

I

251

Zn in Si

. m . c f L

.0 +

-

102'

P

t

C

a, 0

C

0

0

I0 ''

0

Mantovani et at. (1986)

0

2

4 6 xlprnl

C

1020 -

.-

N

8

Figure 5-11. Platinum concentration profiles in dislocation-free Si (Mantovani et al. 1986).

1019

I

termine the concentration profile, as shown in Fig. 5-12. A detailed analysis shows that the diffusivity in the tail region may be enhanced by the supersaturation of self-interstitials generated by the indiffusion of zinc, leading to an effective diffusivity in the tail region given by

D$f (tail) =Df"&(Ci/Cfq)

0

2oo

1

4""

x pm

I 600

Figure 5-12. Zinc concentration profiles in dislocation-free and highly dislocated Si. In highly dislocated Si the results can be fitted by a complementary error function (full line), in dislocation-free Si the region close to the surface shows a kickout type profile (Perret et al., 1989).

(5-52)

The changeover from a concave to an erfctype profile has also been observed for the diffusion of Au either into very thick Si samples (Huntley and Willoughby, 1973) or for short-time diffusions (Boit et al., 1990) into normal silicon wafers 300 - 800 ym in thickness. The diffusion profile of Au in Si is very sensitive to the presence of dislocations since dislocations may act as sinks for selfinterstitials and thus enhance the local incorporation rate of Au,. Even in dislocationfree Si the self-interstitials created in supersaturation by the indiffusion of Au may agglomerate and form interstitial-type dislocation loops which further absorb self-interstitials and lead to W-shaped instead of the

usual U-shaped profiles in Au-diffused Si wafers (Hauber et al., 1986). A detailed analysis of Au diffusion profiles at 1000°C by Morehead et al. (1983) showed the presence of a small but noticeable vacancy contribution, which is consistent with the conclusion from dopant diffusion experiments that both self-interstitials and vacancies are present under thermal equilibrium conditions, to be discussed in Section 5.6.4. Wilcox et al. (1964) observed that the Au concentration profiles at 700 "C are characterized by a constant diffusivity, which indicates that at this temperature the kickout mechanism is kinetically hampered whereas the Frank-Turnbull mechanism still

252


operates. This appears also to be the case for the incorporation of substitutional nickel (Kitagawa et al., 1982; Frank et al., 1984). Attempts to repeat the 700°C Au diffusion experiments have failed probably because of a much higher background concentration of grown-in vacancies or vacancy cluster present in nowadays much larger diameter silicon crystals. Nevertheless, the 700 "C Wilcox et al. Au data have been used to estimate D, C$q at this temperature, as indicated in Fig. 5-9.

rich, 1984; Shaw, 1973, 1975; Tuck, 1974; Tsai, 1983). We will rather concentrate on the diffusion mechanisms and native point defects involved in dopant diffusion, the effect of the Fermi level on dopant diffusion and on non-equilibrium point defect phenomena induced by high-concentration indiffusion of dopants. The diffusivities D,of all dopants in Si depend on the Fermi level. The experimentally observed doping dependencies may be described in terms of the expression

5.6.4 Dopant Diffusion

D,(n)=D:+D;(ni/n) +Dg(nlni)+D:-(nlni)2

5.6.4.1 Fermi Level Effect

which reduces to

Both n- and p-type regions in silicon devices are created by intentional doping with substitutionally dissolved, group V or 111 dopants which act as donors or acceptors, respectively. Technologically most important are the donors As, P and Sb and the acceptors B and to a lesser extent also A1 and Ga. Dopant diffusion has been studied extensively because of its importance in device fabrication. A detailed quantitative understanding of dopant diffusion is also a pre-requisite for accurate and meaningful modeling in numerical process simulation programs. It is not our intention to compile all available data on dopant diffusion in silicon, which may conveniently be found elsewhere (Casey and Pearson, 1975; Fair, 1981b; Ghandi, 1983; Hu, 1973; Langhein-

D,(ni) = Dt + D;+D,+ DZ-

(5-53)

(5-54)

for intrinsic conditions IZ = ni. Depending on the specific dopant, some of the quantities in Eq. (5-54) may be negligibly small. D,(ni) is an exponential function of inverse temperature as shown in Fig. 5-6. Values of these quantities in terms of pre-exponential factors and activation enthalpies are given in Table 5-2. Conflicting results exist on the doping dependence of Sb. The higher diffusivities of all dopants as compared to self-diffusion requires fast moving complexes formed by the dopants and native point defects. The doping dependence of D,(n)is generally explained in terms of the various charge states of the native point defects carrying dopant diffusion as dis-

Table 5-2. Diffusion of various dopants fitted to Eq. (5-53). Each term fitted to Doexp(-Q/k,T); D ivalues in lo4 m2 sC1 and Q values in eV (Fair 1981a, Ho et al. 1983). Element

B P As Sb

D:

Qo

D!

Q+

0.037 3.85 0.066 0.214

3.46 3.66 3.44 3.65

0.72

3.46

-

-

-

4.44 12.0 15.0

DO

Q-

4.00 4.05 4.08

@-

Qz-

-

-

44.20

4.37

-

-


cussed in Section 5.5.2. Since both selfinterstitials and vacancies can be involved in dopant diffusion each of the terms in Eq. (5-54) in general consists of a self-interstitial and a vacancy-related contribution, e.g.,

D;

=ox'+ D:+

(5-55)

which follows from Eq. (5-27). D,(n) may also be written in terms of a self-interstitial and a vacancy-related contribution (Hu, 1974),

D , (n)=of, (n)+ DY (n)

(5-56)

with

DX(n)= DF+ D:(ni/n) + D:(n/ni) + D:-(n/ni)*

(5-57)

and an analogous expression for DG(n). Contrary to a common opinion, the observed doping dependence expressed in Eq. (5-53) just shows that charged point defects are involved in the diffusion process, but nothing can be learned on the relative contributions of self-interstitials and vacancies in the various charge states. Strictly speaking, in contrast to the case of self-diffusion, the doping dependence of dopant diffusion does not necessarily prove the presence of charged native point defects but rather the presence of charged point-defecvdopant complexes. In Section 5.6.4.2 we will describe a possibility to determine the relative contribution of self-interstitials and vacancies to dopant diffusion by measuring the effect of non-equilibrium concentrations of native point defects on dopant diffusion.

5.6.4.2 Influence of Surface Reactions In the fabrication of silicon devices, thermal oxidation is a standard process for forming field or gate oxides or for oxides protecting certain device regions from ion implantation. The oxidation process leads to the injection of self-interstitials which can

253

enhance the diffusivity of dopants using mainly self-interstitials as diffusion vehicles or retard diffusion of dopants which diffuse mainly via a vacancy mechanism. Oxidation-enhanced diffusion (OED) has been observed for the dopants B, AI, Ga, P and As and oxidation-retarted diffusion (ORD) for Sb (Fahey et al., 1989a; Frank et al., 1984; Tan and Gosele, 1985). The influence of surface oxidation on dopant diffusion is schematically shown in Fig. 5-13. The retarded diffusion of Sb is explained in terms ofthe recombination reaction (5- 10) which, in the presence of a self-interstitial supersaturation, leads to a vacancy undersaturation. The oxidation-induced self-interstitials may also nucleate and form interstitialtype dislocation loops on (1 11) planes containing a stacking fault and are therefore termed oxidation-induced stacking faults (OSF). The growth and shrinkage kinetics of OSF will be dealt with in Section 5.9 covering precipitation phenomena. The physical reason for the point defect injection during surface oxidation is simple and schematically shown in Fig. 5-14. Oxidation occurs by the diffusion of oxygen through the oxide layer to react with the Si crystal atoms at the SiO,/Si interface. The oxidation reaction is associated with a volume expansion of about a factor of two which is mostly accommodated by viscoelastic flow of the oxide but partly also by the injection of Si self-interstitials into the Si crystal matrix which leads to a supersaturation of these point defects. The detailed reactions occurring at the interface have been the subject of numerous publications (Tan and Gosele, 1985; Fahey et al., 1989a). Oxidation can also cause vacancy injection provided the oxidation occurs at sufficiently high temperatures (typically 1150°C or higher) and the oxide is thick enough. Under these circumstances silicon, probably in the form of SiO (Tan and Gosele,

254


Oxidation-influenced diffusion Si,N

a)

b)

enhanced diffusion of B,Ga, In,Al,P,As +more 'diffusion vehicles' (self-interstitia is, diffusion via I

retarded diffusion of Sb 'diffusion vehicles' (vacancies, V ) diffusion

+(csS

c, > cl" 1982; Celler and Trimble, 1988), diffuses from the interface and reacts with oxygen in theoxideawayfromtheinterface(Fig. 5-14). The resulting supersaturation of vacancies associated with an undersaturation of selfinterstitials gives rise to retarded B and P diffusion (Francis and Dobson, 1979) and enhanced antimony diffusion (Tan and Ginsberg, 1983). Thermal nitridation of Si surfaces also causes a supersaturation of vacancies coupled with an undersaturation of self-interstitials, whereas oxynitridation (nitridation of oxides) behaves more like normal oxidation. Silicidation reactions have also been found to inject native point

Figure 5-13. Influence of surface oxidation on dopant diffusion in Si. (a) Cross-section of a Si wafer doped near the surface with B, Ga, In, Al, p, (left-hand side) or Sb (right-hand side): before oxidation. (b) Same cross-section after surface oxidation indicating enhanced diffusion for B, Ga, In, Al, P, and As. (c) Retarded diffusion for Sb. For details, see text.

defects and to cause enhanced dopant diffusion (Hu, 1987; Fahey et al., 1989a). A simple quantitative formulation of oxidation- and nitridation-influenced diffusion is based on Eq. (5-56) which changes for perturbed native point-defect concentrations C, and Cv approximately to

of' (n)= 0;( n )[cl/c;q( n ) ] + D,V(n)[ c v G q(n>I

(5-58)

For long enough times and sufficiently high temperatures (e.g., one hour at 1 100°C) local dynamical equilibrium between vacancies and self-interstitial according to Eq.

255


f

oxidatton/nitridotioninfluenced diffusion in Si

act1 Lon

XOX

I

,,' /

Figure 5-14. Schematic illustration of the injection or absorption of native point defects induced by surface oxidation of silicon according to Francis and Dobson (1979) and Tan and Gosele (1982). (a) Thin oxide layer and/or moderate temperature, (b) thick oxide layer and/or high temperature.

(5-1 1) is established and Eq. (5-58) may be reformulated in terms of CI/C,"q.Defining a normalized diffusivity enhancement

A,p"'= [D,p"'(n) - D (n)]/Ds(n)

(5-59)

a fractional interstitialcy diffusion component

( n )= D:(n>ID,( n )

9

(5-60)

and a self-interstitial supersaturation ratio SI (n) = [C,-

/

/

/

= O 85

(b)

(a)

@I

/

/

/ , / /

c;q(n)]/c;q(n)

(5-61)

we may rewrite Eq. (5-58) in the form

A,P"'(n)=[2@I(n)+ @I(n)~ 1 -1 ]/ (1 + ~ 1 ) (5-62) providedEq. (5-1 1) holds. Usually Eq. (5-62) is given for intrinsic conditions and the dependence of @ I on n is not indicated. Equation (5-62) is plotted in Fig. 5-15 for values of 0.85, 0.5 and 0.2. The left-hand side of Fig. 5-15, where sIc 0 (associated with a vacancy supersaturation) has been realized by high-temperature oxidation and thermal nitridation of silicon surfaces, as mentioned above. Another

-1 -1

0

I

1

I

2

I

3

1

4 51

1.

5

Figure 5-15. Normalized diffusion enhancement A F versus self-interstitial supersaturation sI=(CI- CEq)/ CFqfor different values of @I (Tan and Gosele, 1985).

possibility to generate a vacancy supersaturation is the oxidation in an HCl containing atmosphere at sufficiently high temperatures and for sufficiently large HCl contents (Tan and Gosele, 1985; Fair, 1989). As expected, s,0) and of thermal nitridation for generating a vacancy supersaturation (sic 0), the most accurate procedure to determine @I appears to be the following: check for the diffusion changes under oxidation and under nitridation conditions. If for sI> 0 the diffusion is enhanced and for s, 0.5 holds. Based on the largest observed retardation A r ( m i n ) (which has a negative

256


1.0- 1C +I

_ _ - 0 -6 2 -

---* -

.P

j G a , A l

\‘

0.5.-

- - - - - - - - - - - - - - \ - \A

1100 O C diffusion in St

+

group

m

o i 1 group

61

t group Y

elements elements elements

value) a lower limit of ed according to

@I

‘.-.

\

may be estimat-

> 0.5 + 0.5 [ 1- (1 + Asp”’(min))2]”2 (5-63) Analogously, an upper limit for @I may be estimated for the case when retarded diffusion occurs for sI> 0 and enhanced diffusion for s, 0 . 5 ) .Inconsistencies in the determination of @I by oxidation and nitridation experiments (Fahey et al., 1989a) have led to speculations concerning the validity of the basic starting equation (5-58), and to more detailed approaches incorporating a diffusion contribution by the concerted exchange mechanism or the Frank-Turnbull mechanism (Cowern, 1988). @I

----- -Sn

Sb. . q

Figure 5-16. Interstitial-related fractional diffusion component for group 111, IV and V elements versus their atomic radius in units of the atomic radius rsi of silicon. The values for carbon and tin are expected from theoretical considerations and limited experimental results.

5.6.4.3 Dopant-Diffusion-Induced Nonequilibrium Effects Nonequilibrium concentrations of native point defects may be induced not only by various surface reactions, as discussed in the previous section, but also by the indiffusion of some dopants starting from a high surface concentration. These nonequilibrium effects are most pronounced for high concentration P diffusion, but also present for other dopants such as B and to a lesser extent for A1 and Ga. In the case of high-concentration indiffusion of P the non-equilibrium concentrations of native point defects lead to a number of phenomena which had initially been labeled anomalous (Willoughby, 1981) before a detailed understanding of these phenomena was arrived at. We just mention the most prominent of these phenomena. Phosphorus indiffusion profiles (Fig. 5-17) show a tail in which the P diffusivity is much higher (up to a factor of 100 at 900 “C)than expected from isoconcentration studies. In n-p-n transistor structures in which high concentration P is used for the emitter diffusion, the diffusion of the base dopant B below the P diffused region is similarly enhanced. This so-called emitter-push effect is schematically shown in Fig. 5-18 a. The diffusion of B, P, or Ga in buried layers many microns away from the P diffused re-


257

electrically inactive P in precipitates X 30 0 60

0120

a5

0

1.0

1.5

OISTANCE FROM SURFACE [p]4

Figure 5-17. Concentration profiles of P diffused into Si at 900" for the times t indicated (Yoshida et al., 1974).

high conc. phosphorus -oxide/ mask

\

1

I

boron-doped region si

\ I

\

a'

\

I

\

\

B,Ga,or Asdoped buried layer

C)

1

buried layer

\

I si

\

Figure 5-18. Anomalous diffusion effects induced by high-concentration P diffusion, (a) emitter-push effect of B-doped base region, (b) enhanced diffusion of B, Ga, or As in buried layers and (c) retarded diffusion of Sb in buried layer (Gosele, 1989).

Figure 5-19. A Schematic P concentration profile (C,) and the normalized native point defect concentrations C,/Cfq and Cv/CGq (Gosele, 1989).

gion is also greatly enhanced (Fig. 5-18b). In contrast, the diffusion of Sb in buried layers is retarded under the same conditions (Fig. 5-18c). The enhanced and retarded diffusion phenomena are analogous to those occurring during surface oxidation. As has also been confirmed by dislocation-climb experiments (Strunk et al., 1979; Nishi and Antoniadis, 1986), all these phenomena are due to a supersaturation of silicon self-interstitials, associated with an undersaturation of vacancies, induced by high-concentration indiffusion of P. The basic features of high concentration P diffusion are schematically shown in Fig. 5-19, which also indicates the presence of electrically neutral precipitates at P concentrations exceeding the solubility limit at the diffusion temperature. A much less pronounced supersaturation of self-interstitials is generated by B starting from a high surface concentration as can be concluded from the B profiles and from the growth of interstitial-type stacking faults induced by B diffusion (Claeys eta]., 1978; Morehead and Lever, 1986). Many qualitative and quantitative models have been proposed to explain the phenomena associated with high concentration

258


P diffusion. The earlier models are mostly vacancy based and predict a P-induced vacancy supersaturation (Fair and Tsai, 1977; Yoshida, 1983; Mathiot and Pfister, 1984) which contradict the experimental results obtained in the meantime. Morehead and Lever (1986) presented a mathematical treatment of high-concentration dopant diffusion which is primarily based on the point defect species dominating the diffusion of the dopant, e.g., self-interstitials for P and B and vacancies for Sb. The concentration of the other native point-defect type is assumed to be determined by the dominating point defect via the local equilibrium condition (see Eq. (5-1 1)). The dopant-induced self-interstitial supersaturation sImay be estimated by the influx of dopants which release part of the self-interstitials involved in their diffusion process. These self-interstitials will diffuse to the surface where it is assumed that CI=CFq holds, and also into the Si bulk. Finally, a quasi-steady-state supersaturation of self-interstitials will develop for which the dopant-induced flux of injected self-interstitials just cancels the flux of self-interstitials to the surface. The flux of self-interstitials into the Si bulk is considered to be small compared to the flux to the surface. This flux balance may be expressed similarly as in Eq. (5-34) in the case of interstitial-substitutional diffusion as @I

h D,(n) ( ~ C , / & ) = - D I ( ~ C I / (5-64) ~X)

where 1 Ih I2 is the electric field enhancement factor and C, the substitutional dopant concentration. With a doping dependence of the dopant diffusivity in the simple form

D,(n)

ny

(5-65)

integration of Eq. (5-64) yields the resulting supersaturation s, of self-interstitials as s1=

(C, - c,"q>/c;q

=Ch

@I

D,(n,) c,Il[(y+ 1) D,CFq1(5-66)

For the derivation of Eq. (5-66) the fairly small doping dependence of D,CIeq has been neglected. In Eq. (5-66) n, is the electron concentration (at the diffusion temperature) and C, the concentration of the electrically active dopants in dimensionless atomic fractions at the surface. For P, y = 2 has to be used. By an analogous equation a vacancy supersaturation may be estimated which may be induced by a dopant diffusing mainly via the vacancy exchange mechanism. Let us briefly discuss the physical meaning of Eq. (5-66). The generation of a high supersaturation of native point defects requires not only a dopant diffusivity which is higher than self-diffusion (which holds for all dopants in Si) but also a sufficiently high dopant solubility. Further simplified, the condition for generating a high supersaturation of native point defects reads

D,(n,) C,SDSD(n)

(5-67)

which is basically the same condition as has been used for the case of generating a nonequilibrium concentration of native point defects by elements diffusing via the interstitial-substitutional mechanism (see Section 5.5.3). In short, diffusion-induced nonequilibrium concentrations of native point defects are generated if the effective flux of indiffusing substitutional atoms (which either consume or generate native point defects) is larger than the flux of migrating host crystal atoms trying to re-establish thermal equilibrium concentrations of the native point defects. We will use this principle again in the context of high-concentration Zn and Be diffusion in GaAs (Section 5.8). In accordance with experimental results, Eq. (5-66) predicts the proper high selfinterstitial supersaturation for P, a factor of up to about eight for B at 900°C and negligible effects for Sb and As. Much more elab-


orate numerical models have recently been proposed for calculating diffusion-induced non-equilibrium point defect phenomena (Orlowski, 1988; Dunham and Wu, 1995).

5.6.4.4 Recombination-Enhanced Diffusion In semiconductors, thermally activated diffusion of defects may be enhanced by the transfer of energy associated with the recombination of electrons and holes into the vibrational modes of the defects and their surrounding as first recognized by Weeks et al. (1 975) and theoretically described by Kimerling (1978) and Bourgoin and Corbett (1978) in the seventies. The presence of a concentration of electrons and holes above their thermal equilibrium values may be induced by optical excitation (Weeks et al., 1975; Chow et al., 1998), by particle irradiation such as electron irradiation (Bourgoin and Corbett, 1978; Watkins, 2000), ion implantation or plasma exposure (Chen et al., 1996), as well as by carrier injection in devices (Uematsu and Wada, 1992) or via the tip of a scanning tunneling microscope (STM) (Lengel et al., 1995). As a result, the effective thermal activation energy for diffusion may be reduced considerably or may even become essentially zero. In the later case, this type of recombination-enhanced diffusion is termed “athermal diffusion”. The most famous example of athermal diffusion interpreted in terms of recombination-enhanced diffusion appears to be the long-range diffusion of radiation-induced silicon self-interstitials at liquid helium temperatures. In this case, discussed in detail by Watkins (2000) in this volume, the electron-hole excitation is thought to be caused by the particle irradiation. Of technological importance is the recombinationenhanced diffusion of defects in devices such as light-emitting diodes, lasers, or bi-

259

polar transistors, including heterobipolar transistors in which carrier injection during operation may lead to undesirable movement of defects. This movement may lead e.g. to dislocation-climb and associated “dark line defects” or other defect rearrangements affecting device performance unfavorably. Convincing direct experiments demonstrating recombination-enhanced diffusion have been reported by Chow et al. (1998). By optically induced EPR, these authors measured a single diffusion jump of a zinc interstitial in ZnSe induced by optical excitation.

5.6.5 Diffusion of Carbon and Other Group IV Elements In Section 5.6.2 we have extensively dealt with self-diffusion of Si. The other group IV elements carbon (C), Ge and Sn are also dissolved substitutionally but knowledge on their diffusion mechanisms is incomplete. The diffusivities of C, Ge and Sn are given in Table 5-1 in terms of pre-exponential factors and activation enhalpies. Ge and Sn diffusion are similarly slow as Si self-diffusion, whereas C diffusion is much faster (Fig. 5-6). Germanium atoms are slightly larger than Si atoms. Oxidation and nitridation experiments show a @, value of Ge around 0.4 at 1100°C (Fahey et al., 1989b) which is slightly lower than that derived for Si selfdiffusion. Diffusion of the much larger Sn atoms in Si is expected to be almost entirely due to the vacancy exchanged mechanism, similar as for the group V dopant Sb. Consistent with this expectation, a nitridation-induced supersaturation of vacancies increases Sn diffusion (Marioton and Gosele, 1989), but no quantitative determination of @, is available for Sn. Indiffusion C profiles in Si are error function-shaped. Considering the atomic vol-

260


ume, it can be expected that the diffusion of C atoms, which are much smaller than Si, involves mainly Si self-interstitials. Based on EPR measurements, Watkins and Brower (1976) proposed more than 20 years ago that C diffusion is accomplished by a highly mobile carbon-self-interstitial complex (CI) according to

out to the Si surface and hence the CFq condition is basically maintained, in agreement with experimental observations (Newman and Wakefield, 1961; Rollert et al., 1989). From the C indiffusion data, the solubility of C , is given by (Newman and Wakefield, 1961; Watkins and Brower, 1976; TippingandNewman, 1987; Rollertetal., 1989)

c,+re> (CI)

(5-68)

Ctq=4x1O3' exp (-2.3 eV/k,T) m-3 (5-71)

where C , denotes substitutional carbon. This expectation is consistent with the experimental observation that self-interstitials injected by oxidation or high-concentration P indiffusion enhance C diffusion (Ladd and Kalejs, 1986).Equivalently, we may regard C as an i-s impurity, just as Au. That is, to regard the diffusion of C according to (Gosele et a]., 1996; Scholz et al., 1998b)

and the diffusion coefficient of D, is given by

(5-69)

Di=4.4x104 eXp (-0.88 eV/kBT) m2 S-' (5-74)

C,+I

e> ci

where Ci denotes an interstitial carbon atom. Since whether C, diffusion is actually carried by CI complexes or by Ci atoms have not yet been distinguished on a physical basis, and the mathematical descriptions for both cases are identical in form, in the following we will regard C, diffusion as being carried by Ci atoms in accordance with the kickout mechanism of the i-s impurities. Under this assumption, diffusion of carbon into silicon for which the substitutional C concentration is at or below the solubility of the substitutional carbon atoms, C:q, the substitutional carbon diffusivity 0,""is given by the effective diffusivity Di Cfs/Czq where Di is the diffusivity of the fast diffusing Ci atoms and Crq is the solubilities of the Ci atoms. Error function type C , indiffusion profiles obtain under indiffusion conditions, because

D,"" Cts = Di Cfq< D, Cfs

(5-70)

holds. Under this condition, C indiffusion induced Si self-interstitials migrated rapidly

D,=1.9~1O"'exp (-3.1 eV/kBT) Ill2

S-l

(5-72) Interpreted in accordance with the i-s nature of C, we obtain ~ ? = 2 ~ 1 0 ~ ~ e x p ( - 4ev/kBT) .52 m-3

(5-73)

For outdiffusion of C, pre-introduced to high concentrations, however, the situation is very different. For cases for which the C , concentration significantly exceeded its solubility, as pointed out by Sholz eta]. (1 998 b, 1999), Di Cieq>D, CFq

(5-75)

may be satisfied, leading to a severe undersaturation of Si self-interstitials in the high C , concentration region which significantly retard the outdiffusion of C, atoms from the region. Indeed, such phenomena have been observed by Riicker et al. (1998) and by Werner et al. (1998). These experiments were performed using molecular beam epitaxy (MBE) grown Si layers containing reto gions with C, concentrations in the 1026m-3 range, and hence tremendously exceeded the C , solubility of the experimental temperature. A similar retardation of the diffusion of other impurity species diffusing via primarily Si self-interstitials, e.g., B,


105

1 38 c

103 g

.-

B

s

I

101

8

U

m

2

lo-’ 0.2

E

=

0.4 0.6 0.8 depth [IJmI

Figure 5-20. SIMS profiles of a 300 nm thick carbon layer with seven boron spikes (Rucker et al., 1998). Filled and open circles are respectively data of asgrown and annealed (900W45 min) cases. Dashed fitting lines are those with only the kick-out model, and solid lines are those with the dissociative mechanism also included (Scholz et al., 1999).

in the same region is also expected. This is indeed the case of the experimental results of Rucker et al. (1998), see Fig. 5-20. In order to highly satisfactorily fit both the C , profile as well as all the B spike-region profiles, Scholz et al. (1999) found that additionally the contribution of Si vacancies must also be included. Vacancy contributes a component to C , diffusion via the dissociative mechanism as given by reaction (5-31) and a component to B diffusion via the vacancy-pairing mechanism. The vacancy contribution to C , diffusion is important in regions outside the initial C , high concentration region and to B diffusion in all regions. Using similarly grown samples containing C, and B spikes, ion implantation induced silicon self-interstitials were found to be substantially attenuated in the C, spike

261

regions so that the diffusion of B buried beneath the C, spikes were severely retarded when compared to cases of having no C, spikes (Stolk et al., 1997). The phenomenon was interpreted by the authors as due to the reaction given by (5-68) but with the so formed C,complexes assumed to be immobile, which is in contrast to the suggestion of Watkins and Brower (1 976). The assumption that immobile C, complexes are responsible for the retarded boron diffusion is not needed in the Scholz et al. ( 1 999) analysis. It is expected that ion implantation or oxidation induced silicon self-interstitial supersaturation will enhance the diffusion of C and B with C in concentrations to a moderate level, e.g., in the range of m-3.

5.6.6 Diffusion of Si Self-Interstitials and Vacancies For Si, although the product D,Cfq is known and estimates of D, C:q are available, our knowledge of the individual factors D,, D ,CTqand CGq is limited in spite of immense experimental efforts to determine these quantities. These individual quantities enter most numerical programs for simulating device processing and their elusiveness hinders progress in this area (Kump and Dutton, 1988). The most direct way of measuring D,is the injection of self-interstitials (e.g., via surface oxidation) at one location of the Si crystal and the observation of its effect on dopant diffusion or on growth or shrinkage of stacking faults at another location as a function of time and of distance between the two locations. That is, the two locations may be the front- and the backside of a Si wafer. Extensive experiments on the spread of oxidation-induced self-interstitials through wafers by Mizuo and Higuchi (1983) have shown that a supersaturation of self-inter-

262

-


T ['C]

A

lo-'-

900 9

1100

6

8

4

700

10

500

12

10 IT [K-']-

Figure 5-21. Diffusivity D,of self-interstitials in Si as a function of temperature as estimated by various authors (a-h) and compared to silicon self-diffusion and copper diffusion. (a) Tan and Gijsele, 1985; (b) Morehead, 1988, (c) Bronner and Plummer 1985; (d) Seeger et al., 1977; (e) Bronner and Plummer, 1985; (f) Griffin and Plummer, 1986; (g) Taniguchi et al., 1983; (h) Wada et al., 1983. (From Taylor et al. 1989).

stitials arrives at about the same time as a corresponding undersaturation of vacancies. Therefore, these kind of experiments at 1100°C just give information on an effective diffusivity of a perturbation in the self-intestinal and vacancy concentrations. This effective diffusivity may be expressed approximately by (Tan and Gosele, 1985) D&=(D,

c;q+D,

c;q)l(cI"q+c;q)

(5-76) and probably corresponds to the diffusivity m2 s-' in the exvalues of about 3 x periments of Mizuo and Higuchi at 1100°C. Much efforts had been expended on this approaches in the past but the results are inconsistent. In most experiments aimed at determining D,it has not been taken into ac-

count that self-interstitials may react with vacancies according to Eq. (5-10) and establish local dynamical equilibrium described by Eq. (5-11).Based on experiments on oxidation-retarded diffusion of antimony (Antoniadis and Moskowitz, 1982; Fahey et al., 1989a) it has been estimated that an astonishingly long time, about one hour, is required to establish local dynamical equilibrium at 1 100"C. This long recombination time indicates the presence of an energy or entropy barrier slowing down the recombination reaction. At lower temperatures much longer recombination times can be expected. These long recombination times hold for lightly doped material. There are indications that dopants or other foreign elements may act as recombination centers which can considerably speed up the recombination reaction, but no reliable data are available in this area. In order to demonstrate the state of affairs concerning D,so determined (and therefore indirectly also of CIeq via the known product D,C,"q),the available D,estimates as a function of inverse absolute temperature are shown in Fig. 5-21 (Taylor et al., 1989). The estimated Si self-interstitial formation enthalpy (h:) values are from 1 to 4 eV, and at 800 "C the D,values differ by up to eight orders of magnitude. The problem is further complicated by the observation that the measured effective diffusivity D;ffv, depends on the type of Si material used. In the experiments of Fahey et al. (1989a) the transport of oxidation-induced self-interstitials through epitaxially-grown Si layers was much faster than through equally thick layers of as grown float-zone (FZ) or Czochralski (CZ) Si. This difference has been attributed to the presence of vacancy-type agglomerates left from the crystal growth process which might not be present in epitaxial Si layers. These vacancy agglomerates would have to be consumed by the injected self-interstitials

-


before further spread of interstitials can occur. Nonetheless, considering the recent development involving several different categories of studies, we can now tentatively conclude that the migration enthalpies of vacancies and self-interstitials in silicon, h: and h'f respectively, are relatively small while their formation enthalpies, h l and hf respectively, are large. This means that the vacancies and self-interstitials are moving fairly fast while their thermal equilibrium concentrations are fairly small. The most probable value of h q is 0.5- 1 eV while that of hFis I eV, and the corresponding most probable values of hf, is -3.5-3 eV while that of hi is - 4 eV. Sinno et al. ( I 998) used values of 0.457 and 0.937 eV respectively for h t and h;" to satisfactorily model the formation of swirl defects (interstitialtype dislocation loops and vacancy-type clusters) in FZ Si, including the defect location, density, size, and their dependence on the crystal growth rate and the thermal gradient. Plekhanov et al. (1998) used a h f ,value of 3 - 3.4 eV to satisfactorily model the formation of voids in large diameter CZ Si. Moreover, in fitting the C and B diffusion results of Rucker et al. ( 1 998), as shown in Fig. 5-20, Scholz et al. (1999) also needed to use hy and hq values smaller than 1 eV. This knowledge is consistent with recent quantum mechanical calculations which yielded fairly high hf and hb values and corespondingly low h t and h y values (Goodwin et al., 1989;Nicholsetal., 1989; Wangetal., 1991; Zhu et al., 1996; Tang et al., 1997). With the present estimates, it becomes also possible to connect in a reasonable and consistent way the fairly high diffusivities of native point defects found after low temperature electron irradiation (Watkins, 1975) with the much lower apparent diffusivities which appear to be required to explain high temperature diffusion experiments.

-

-

-

263

5.6.7 Oxygen and Hydrogen Diffusion Oxygen is the most important electrically inactive foreign element in Si. In CZ Si oxygen is incorporated from the quartz crucible and usually present in concentrations in the order 1 024m-3 and thus exceeding the concentrations of electrically active dopants in certain device regions. An oxygen atom in Si occupies the bond-centered interstitial position of two Si atoms and forms covalent bonds with the two Si atoms. Hence, its diffusion requires the breaking of bonds. The diffusivity of interstitial oxygen, Oi, has been measured between about 300°C and the melting point of Si and is in good approximation described by

Di= 0.07 exp (- 2.44 eV/k,T) m2 s-' (5-77) as shown in Fig. 5-6 (Mikkelsen, 1986). The solubility Cfq of interstitial oxygen has been determined to be C~q=1.53x1027exp(-1.03eVlk,T) m-2 (5-78) Since in most CZ Si crystals the grown-in Oi concentration exceeds Cfs at typical processing temperatures, Oiprecipitation will occur, which will be dealt with in Section 5.9.3. Around 450°C Oi forms electrically active agglomerates, called thermal donors (Kaiseret al., 1958; Bourret, 1985). The formation kinetics of these agglomerates appears to require a fast diffusing species, for which both self-interstitials (Newman, 1985) and molecular oxygen have been suggested (Gosele and Tan, 1982). The question of molecular oxygen in Si has not yet been settled. In this context it is interesting to note that the presence of fast diffusing nitrogen molecules in s i has been demonstrated by Itoh and Abe ( 1 988). Hydrogen plays an increasingly important role in silicon device technology because of

264


its capability to passivate electrically active defects. The passivation of dislocations and grain boundaries is especially important for inexpensive multicrystalline Si used for solar cells. Both acceptors and donors can be passivated by H which is usually supplied to Si from a plasma. H in Si is assumed to diffuse as unbounded atomic H that may be present in a neutral or positively charged form. The diffusivity of H in Si has been measured by Van Wieringen and Warmoltz (1956) in the temperature range of 970- 1200°C.These results are included in Fig. 5-6. Between room temperature and 600 "C H diffusivities much lower than those extrapolated from the high temperature data have been measured. Corbett and co-workers (Pearton et al., 1987)rationalized this observation by suggesting that atomic H may form interstitially dissolved, essentially immobile H, molecules. Apparently, these molecules can then form platelike precipitates (Johnson et al., 1987). For a detailed understanding of the complex H concentration profiles, trapping at dopants has also to be taken into account (Kalejs and Rajendran, 1990). As in the case of oxygen, the existence of H molecules has not been proven experimentally.

5.7 Diffusion in Germanium Germanium has lost its leading role for electronic devices about four decades ago and is now mainly used as a detector material or in Si/Ge superlattices. Therefore, basically no papers have recently been published on diffusion in Ge. Another reason might be that diffusion in Ge can be consistently explained in terms of vacancy-related mechanisms and no self-interstitial contribution has to be taken into account. Fig. 5-22 shows the diffusivities of group I11 and V dopants and of Ge in Ge as a function of inverse absolute temperature under in-

-

1 "Cl

II diffusion in Ge

l0'IT

IK-'1

-

i

Figure 5-22. Diffusivities of various elements (including Ge) in Ge as a function of inverse absolute temperature (From Frank et al., 1984).

trinsic conditions. The doping dependence of dopant diffusion can be explained by one kind of acceptor-type native point defect. These native point defects have been assumed to be vacancies since the earliest studies of diffusion in Ge (Seeger and Chik, 1968),but a convincing experimental proof has only been given in 1985 by Stolwijk et al. based on the diffusion behavior of Cu in Ge. Copper diffuses in Ge via an interstitialsubstitutional mechanism (Frank and Turnbull, 1956). In analogy to the case of Au and Pt in Si, its diffusion behavior may be used to check diffusion profiles for any indication of a self-interstitial contribution via the kickout mechanism. A concentration profile of Cu diffusion into a germanium wafer is shown in

5.8 Diffusion in Gallium Arsenide

265

Fig. 5-23 (Stolwijk et al., 1985). The dashed U-shaped profile which is typical for the kickout mechanism obviously does not fit the experimental data. In contrast, the experimental profiles may be well described by the constant diffusivity D$,, given by Eq. (5-36). In Fig. 5-24 values of the vacancy contribution to germanium self-diffusion,

D, C$ q =2 1 .3 ~1 0 4 (5-79) . exp (- 3.1 1 eV/k, r ) m2 s-l

-

x/d

Figure 5-23. Concentration profiles of Cu into a dislocation-free Ge wafer after diffusion for 15 minutes at 878 "C. The solid line holds for the Frank-Tumbull and the dashed line for the kickout mechanism (Stolwijk et al., 1985).

I

n

€lo-"

-


self-diffusion in Ge

5.8.1 General Remarks

040

0 0

A.*

b

.* b

0 '

B

PI

te+

=-a!8

*from Cu diffusion

as determined from Cu diffusion profiles are compared with corresponding tracer measurements of self-diffusion in germanium. The agreement is excellent, which shows that any kind of self-interstitial contribution is negligible and that Ge self-diffusion appears to be entirely camed by vancancies. It is unclear why self-interstitials play such an important role in diffusion processes in Si but no noticeable role in Ge.

8.

Figure 5-24. Tracer self-diffusion data compared to the vacancy contribution D , Ccq/2 determined from Cu diffusion in Ge ( 0 )(Stolwijk et al. 1985).

Gallium arsenide is the most important compound semiconductor with applications ranging from fast electronic to optoelectronic devices such as light-emitting diodes and lasers. In combination with lattice-matched AIAs, GaAs is also the main material for the fabrication of quantum well and superlattice structures. Although the diffusion of many elements in GaAs have been investigated (Tuck, 1988), most of the diffusion studies have concentrated on the main p-type dopants Zn and Be, the main n-type dopants Si and Se, and on Cr which is used for producing semi-insulating GaAs. Since Zn, Be, Cr and a number of other elements diffuse via an interstitial-substitutional mechanism, this type of diffusion mechanism has historically received much more attention in

266


GaAs than in elemental semiconductors. Similarly as for Si and Ge, it had been assumed for a long time that only vacancies have to be taken into account to understand diffusion processes in GaAs (Tuck, 1988). This assumption has also been incorporated in early versions of process simulation programs (Deal et al., 1989). Compilation of earlier diffusion data in GaAs in general may be found elsewhere (Kendall, 1968; Casey, 1973; Tuck, 1974, 1988; Jacob and Miiller, 1984). Only a few studies of self-diffusion in GaAs are available, but with the advances in growing GaAs/AlAs-type superlattices using MBE or Metal-Organic Chemical Vapor Deposition (MOCVD) methods, A1 has served as an important foreign tracer element for elucidating Ga self-diffusion mechanisms. The observation that high concentration Zn diffusion into a GaAs/Al,Ga,-,As superlattice leads to a dramatic increase in the Al-Ga interdiffusion coefficient (Laidig et al. 1981) opened up the possibility to fabricate laterally structured optoelectronic devices by locally disordering superlattices. It turned out that this dopantenhanced superlattice disordering is a fairly general phenomena which occurs for other ptype dopants such as Mg as well as for n-type dopants such as Si, Se and Te (Deppe and Holonyak, 1988). Dopant-enhanced superlattice disordering is not only of technological importance but has also allowed to unravel the contributions of self-interstitials and vacancies to self- and dopants diffusion processes in GaAs. These superlattices with their typical period of about 10 nm allow to measure Al-Ga interdiffusion coefficients, which turned out to be close to the Ga self-diffusion coefficient, down to much lower values than had been previously possible for Ga self-diffusion in bulk GaAs using radioactive Ga tracer atoms. The dependence of diffusion processes on the As vapor pressure, which normally is more of an annoying feature of

diffusion experiments in GaAs, has helped in establishing the role of self-interstitials and vacancies. In order to understand self- and dopant diffusion processes in the Gasublattice of GaAs, it appears that both Ga vacancies and selfinterstitials have to be taken into account (Tan et al., 1991a). Their relative importance and role depends on the doping conditions, dubbed the Fermi level effect, and on the ambient As vapor phase pressure. Non-equilibrium concentrations of native point defects may be induced by the indiffusion of dopants such as Zn starting from a high surface concentration, in a similar way as has been described for high concentration P diffusion in Si (Section 5.6.4.3). Much less is known on the diffusion processes of atoms dissolved on the As sublattice, but recent experiments indicate the dominance of As self-interstitials on the diffusion of the isoelectronic group V element N (Bosker et al., 1998), P, and Sb (Egger et al., 1997, Schulz et al., 1998a, Scholz et al., 1997b), and the group VI ntype dopant S (Uematsu et al., 1995). These results imply also the dominance of As selfinterstitials on As self-diffusion, which is in contrast to the earlier radio-active tracer As self-diffusion results of Palfrey et al. (1983) favoring the dominance of As vacancies.

5.8.2 Gallium Self-Diffusion and Superlattice Disordering 5.8.2.1 Intrinsic Gallium Arsenide The self-diffusion coefficient D,, (ni) of Ga in intrinsic GaAs has been measured by Goldstein (1961) and Palfrey et al. (1981) with radioactive Ga tracer atoms (Fig. 5-25). This method allows measurements of m2 s-'. MeaDG,(ni) down to about surements of the interdiffusion of Ga and A1 in GaAs/Al,Ga, -,As superlattices extended the range to much lower values (Chang

T ("C) - 1 6 ~

PO

l\

600

:

Goldstein (1961) Chang a Koma (1976) A Petroff (1977) 1

10

*

-20

Fleming et al. (1980)

Palfrey e l al. (1981) Cibert el al. (1986)

k

,

Schlesinger 8 Kuech (1986) Derived from data of

0.6

0.7

0.8

0.9

103/T(K-')

1.0

1.1

10 1.2

267


-31

I

0.6

0.7

'

I

-

0.8

I

'

0.9

I

1.0

103/T(K-')

'

I

1.1

'

1.2

Figure 5-25. Plot of available data on Ga self-diffusion in GaAs and data on G d A l interdiffusion in GaAdAlGaAs superlattices under intrinsic conditions together with D,, derived from the data of Mei et al. (1987).

Figure5-26. Contributions of V& and 1% to Ga self-diffusion or AI-Ga interdiffusion under intrinsic conditions for As-rich ( 1 atm of As, pressure) and for Ga-rich GaAs/Al,AsGa,-,As superlattices or GaAs crystals.

and Koma, 1976; Petroff, 1977; Fleming et a]., 1980; Cibert et al., 1986; Schlesinger and Kuech, 1986). The various data points have approximately been fitted by Tan and Gosele (1988a, b) to the expression

at the Ga-rich boundary is then

V D~~ ( n i , 1 atm) = 2.9 x104

Equation (5-80)is valid for the As, pressure of 1 atm ( I .013x lo5 N m-*) or for GaAs crystals with compositions at the As-rich boundary shown in Fig. 5-4a, and the superscript V in the quantity Dxa specifies that the quantity is due to the sublattice vacancy contribution to Ga self-diffusion. This is because, at 1 atm, the disordering rate of the GaAs/Al,Ga,,As superlattices increases as the ambient As, pressure is increased (Furuya et al. 1987; Guido et al., 1987). The corresponding D& values for GaAs crystals

-

D& ( n i , Ga-rich) = 3.93 x lo*

For Eqs. (5-80) and (5-81), it turned out that the responsible vacancy species is the triply negatively charged Ga vacancies V& as will be discussed in the following. On the other hand, the AI-Ga interdiffusion coefficient also increases for very low arsenic vapor pressures (Furuya et al., 1987; Guido et al., 1987), indicating that D,, (ni) is governed by Ga self-interstitials for sufficiently low As vapor pressures (Deppe and Holonyak, 1988). The role of Ga vacancies and self-interstitialswill become clearer when Ga diffusion in doped GaAs/AI,Ga,,As superlattices is considered, and when diffusion of the p-type dopant Zn and Be is considered. Combining the Al-Ga interdiffu-

268


sion data of Hsieh et al. (1988) obtained under Ga-rich ambient conditions, and the deduced Ga self-diffusion coefficients from analyzing Zn diffusion (Yu et al., 1991a) and Cr diffusion (Yu et al., 1991b), Tan et al. (1991 b) summarized that

Dha (n ,Ga-rich) = 4.46 x 1O-*

holds for the Ga self-interstitial contribution to Ga self-diffusion in GaAs crystals with composition at the Ga-rich boundary shown in Fig. 5-4a. The corresponding values for GaAs crystals with composition at the Asrich boundary shown in Fig. 5-4a is

)

( n i , 1atm) = 6.05 x low4

k g TeV . e x p i - 4.71

m* s-1

(5-83)

For Eqs. (5-82) and (5-83), it turned out that the responsible point defect species is the doubly positively charged Ga self-interstias will be discussed in the followtials ing. The values of Eqs. (5-80)-(5-83) are plotted in Fig. 5-26. As first noticed by Tan et al. (1992), however, under intrinsic conditions, for a number of Al-Ga interdiffusion studies (Chang and Koma, 1976; Lee et al., 1987; Bracht et al., 1998) and two recent Ga self-diffusion studies using stable Ga isotopes (Tan et al., 1992; Wang et al., 1996), the results are fitted better by

Zg,

DGa(ni ,1atm) = 4.3 x lo3 .exp( - 4.24 kB eV

)

m2 s-'

(5-84)

instead of Eq. (5-80). Figure 5-27 shows the values for Eqs. (5-80) and (5-84) and the as-

sociated data. There is as yet no satisfactory explanation of the discrepancy between Eq. (5-84) and the other expressions, e.g., Eq. (5-80). On the one hand, Eq. (5-84) does offer a better fitting to the more recent data. On the other, the use of Eq. (5-84) cannot be consistent with the Al-Ga data of Mei et al. (1987) under Si doping, which are associated with a 4 eV activating enthalpy. In accordance with the Fermi-level effect, the Ga diffusion activation enthalpy decreases by about 2 eV in n-doped materials (Tan et al., 1991a), which would mean that Eq. (5-80) is more reasonable. A number of reasons, however, could affect the accuracy of the experimental results. These include accidental contamination by n-type dopants in the nominal intrinsic materials, band off-sets in the case of Al-Ga interdiffusion, and the fact that the materials did not have the As-rich composition to start with and the experimental temperature- time was not sufficient to change the materials into As-rich for most of the experimental time.

5.8.2.2 Doped Gallium Arsenide No studies of Ga self-diffusion in doped bulk GaAs have been reported, but a wealth of data on Al-Ga interdiffusion in both ntype and p-type doped GaAs/A1,Ga,-xAs superlattices is available. These interdiffusion experiments was triggered by the observation of Zn diffusion enhanced superlattice disordering due to Laidig et al. (1981). A number of disordering mechanisms have been proposed (Van Vechten, 1982, 1984; Laidig et al., 1981; Tatti et al., 1989) for an individual dopant. All of these propositions are not general enough to account for the occurrence of an enhanced AlGa interdiffusion rate for other dopants. The oberved dopant enhanced interdiffusion appears to be due to two main effects (Tan and Gosele, 1988a, b):


269

T C'C)

800 4 1200

10-l~

1000

Ga Isotope data

I Goldstein ( I 961) rn

Palfrey et al. (1981) Tan et al. (1992)

A Wang et al. (1996)

4.24 eV

0

0.6

Al-Gadata

0.7

0.8 0.9 103/T(K-')

1 .o

i) The thermal equilibrium concentration of appropriately charged point defects is enhanced by doping (Fermi level effect, Sect. 5.2). In the case of the n-type dopant Si, only the presence of the dopant is of importance, not its movement. Compensation doping, e.g., with Si and Be, should not lead to enhanced Al-Ga interdiffusion, which is in accordance with experimental results (Kawabe et al., 1985; Kobayashi et al., 1986). ii) For a dopant with high diffusivity and solubility, so that the product D,Cs%DSD (n,p) as expressed in Eq. (5-67) holds, then nonequilibrium native point defects are generated. Depending on whether a supersaturation or an undersaturation of point defects develops, the enhanced disordering rate due to the Fermi level effect may be further increased or decreased. Irrespective of the

1.1

Figure 5-27. Data and fitting lines for the intrinsic Ga or AI-Ga diffusivity under 1 atm of As, pressure. The 6 eV line is that given by Eq. (5-80) and the 4.24 eV line that given by Eq. (5.84). All Ga data are directly measured ones using nominally intrinsic GaAs. The AI-Ga data include directly measured ones using normally intrinsic GaAs/Al,AsGa,_,As superlattices as well as those deduced from the Mei et al. (1987) data obtained using Si-doped GaAs/Al,AsGa,_,As superlattices.

starting material composition, such nonequilibrium native point defects drive the dopant diffused region crystal composition first toward an appropriate allowed GaAs crystal composition; the limits are shown in Fig. 5.4a. When the super- or undersaturation of point defects becomes so large that the crystal local region exceeds the allowed composition limit, extended defects form to bring the composition of the region back to that composition limit. Afterwards, this permits the diffusion processes to be described by an equilibrium point defect process appropriate for the crystal local region, which is at an appropriate allowed composition limit. The crystal is in a nonequilibrium state because of the spatially changing composition. The diffusion of high concentration Zn and Be in GaAs (Yu et al., 1991a; Jager et al., 1993) and

270


100

10

'

nln,

lo3

102

Figure 5-28. The ( n l r ~ dependence ~)~ of the Al-Ga interdiffusion data of Mei et al. (1987). D& (ni, 1 atrn) is given by Eq. (5-80). The data cannot be analyzed to a similar degree of satisfaction via the use of Eq. (5-84) to any power law dependence on nlni. (Redrawn from Tan and Gosele, 1988a.)

their effects on GaAs/Al,Ga,,As superlattices (Tan and Gosele, 1995) appear to be such cases. Let us first discuss Al-Ga interdiffusion in n-type GaAs, and more specifically the case of Si-doped GaAs, which allows to identify the type and the charge state of the native point defect dominating Ga self-diffusion in n-type GaAs. In Fig. 5-28, the enhanced Al-Ga interdiffusion coefficients under Si-doping are plotted in a normalized form as a function of n/ni of the appropriate temperature. These data, obtained by Mei et al. (1987), show a clear doping dependence (Tan and Gosele, 1988a, b) DAI-G~ (n, 1 atm) = DGa (q 1 atm) I

(;I -

(5-85)

with D,, (ni, 1 atrn) given by Eq. (5-80). Equation (5-85) indicates the involvement

of a triply negatively charged native point defect species. Based on the pressure dependence of the interdiffusion coefficient of ndoped superlattices (Guido et al., 1987; Deppe and Holonyak, 1988), this defect has to be the gallium vacancy VEz, as predicted by Baraff and Schluter (1986). Values of D,, (ni) calculated from the Mei and coworkers data and shown in Fig. 5-24 are in good agreement with values extrapolated from higher temperatures. Thus, including the As vapor pressure dependence, we may write the Ga self-diffusion coefficient in n-type GaAs as DGa

(n, pAs4) =DV G ~(ni,latm)

ir )' -

(pAs4)lj4

(5-86)

where D:, (ni, 1 atm) is given by Eq. (5-80), for the n-doping level being sufficiently high. The much later claims that these Sidoping induced Al-Ga interdiffusion data show a quadratic dependence on n by some authors (Cohen et al., 1995; Li et al., 1997) are erroneous, because these authors used the room temperature n value as that for all high temperatures. Furthermore, the overzealous statement that there is no Fermi level effect (Jafri and Gillin, 1997) bears no credence, for the claim is based on Al-Ga interdiffusion results using extremely light Si doping, which are threshold phenomena that may be influenced by many other uncontrolled factors. Tellurium-doped GaAs based superlattices show a weaker dependence of the Al-Ga interdiffusion coefficient on the Te concentration than expected from Eq. ( 5 - 8 5 ) (Mei et al., 1989), particularly at very high concentrations. The probable cause is that, due to clustering, not all Te atoms are electrically active to contribute to the electron concentration (Tan and Gosele, 1989).

271


The available AI-Ga interdiffusion data in p-type GaAs based superlattices (Laidig et al., 1981; Lee and Laidig, 1984; Kawabe et al., 1985; Myers et al., 1984; Hirayama et al., 1985; Ralston et al., 1986; Kamata et al., 1987; Zucker et al. 1989) were first thought not to be analyzable in a manner analogous to that done for the n-doping effect (Tan and Gosele, 1988a, b). As shown in Fig. 5-29, however, some of these data were later fitted approximately by Tan and Gosele ( 1995) by

10’0

108

r^

.e

106

b : E

-0

-a 9

104

B id

DAI-G~= ( P&(q, ) Ga-rich) where (ni, Ga-rich) is given by Eq. (5-82). Equation (5-87) shows that the dominant native point defects under p-doping to a sufficient concentration are the Ga selfinterstitials, and the p 2 dependence of D,,-G,(p) shows that the Ga self-interstitials are doubly positively charged. The data shown in Fig. 5-29 (Lee and Laidig, 1984; Kawabe et al., 1985; Kamata et al., 1987; Zucker et al., 1989) are those under the dopant indiffusion conditions, while the rest are those under the dopant outdiffusion conditions involving grown-in dopants without an outside dopant source. Under outdiffusion conditions, the dopant diffusivity values are too small to be reliably measured. The fitting shown in Fig. 5-29 is fairly satisfactory, but not perfect. Even if the fitting was perfect, the essential native point defect equilibrium situation implied by Fig. 5-29 is only an apparent phenomenon, for it applies only to the p-dopant diffused region, while the whole crystal has a spatially changing composition. This point is most obvious in the data of Lee and Laidig (1984), which were obtained in a high As, vapor pressure ambient. The grossly different results for in- and outdiffusion conditions is due to nonequili-

100

loo

10’

lo2

lo3

104

105

Plni

Figure 5-29. Fits of some of the available p-dopant enhanced Al-Ga interdiffusion data. Db, (ni,Ga-rich) is given by Eq. (5-82). The data exhibit an approximate quadratic dependence on p h i , indicating that the dominant native point defect is 12.(From Tan and Gosele, 1995.)

brium concentrations of native point defects inducued by high concentration diffusion of Zn or Be. Both Zn and Be diffuse via an interstitial -substitutional mechanism, as will be discussed in more detail in the subsequent section. Historically, most authors have considered the Frank-Turnbull or Longini mechanism Eq. (5-39) involving Ga vacancies as being applicable to the diffusion of p-type dopants (Kendall, 1968; Casey, 1973; Tuck, 1988). The superlattice disordering results indicate that instead the kickout mechanism Eq. (5-38) is operating for these dopants and that Ga self-diffusion is governed by Ga self-interstitials under pdoping conditions. Within the framework of the kickout mechanism, the dopant indiffusion generates a supersaturation of I, (in analogy to the indiffusion of Au or P in Si) with a corresponding increase of dopant dif-

272


fusion and the Ga self-diffusion component involving Ga self-interstitials. Because of the I,, supersaturation, the dopant diffused region tends toward the Ga-rich composition. In the case of Zn indiffusion to very high concentrations, it will be discussed that the I,, supersaturation is so large that in a small fraction of the diffusion time extended defects form (Winteler, 1971; Jager et al. 1993), resulting in the fact that the Zn diffused region composition is at the thermodynamically allowed Ga-rich composition limit and is associated with the appropriate thermal equilibrium point defect concentrations. This is the reason for the satisfactory fitting shown in Fig. 5-27. In the case of grown-in dopants without an outside source, the kickout mechanism involves the consumption of I,,, which leads to an I, undersaturation with a corresponding decrease in dopant diffusion (Kendall, 1968; Masu et al., 1980; Tuck and Houghton, 1981; Enquist et al., 1985, 1988) and the Ga self-diffusion component involving Ga self-interstitials. The results of the superlattice disordering experiments are consistent with the expectations based on the kickout mechanism. In contrast, the Frank-Turnbull mechanism predicts an undersaturation of vacancies for indiffusion conditions and a supersaturation for outdiffusion conditions with a corresponding decrease and increase of a vacancy dominated Ga self-diffusion component, respectively. Since the predictions based on the Frank-Turnbull mechanism are just opposite to the observed superlattice disordering results, it can be concluded that: (i) Zn diffusion occurs via the kickout mechanism, and (ii) Ga self-diffusion in p-type GaAs is governed by Ga self-interstitials. In contrast to the group I1 acceptors Zn and Be, the group IV acceptor carbon (C) occupying the As sublattice sites diffuses slowly. This allows the native point defects

to be maintained at their thermal equilibrium values. The effect of C on the disordering of GaAs/Al,Ga,,As superlattices (You et al., 1993b) is described well by (5-88) where Db, (ni) is given by Eqs. (5-82) and (5-83), respectively, for data obtained under Ga-rich and As-rich ambient conditions. The pressure dependence of disordering of p-doped superlattices confirms the predominance of Ga self-interstitials in Ga selfdiffusion (Deppe et al., 1987). The magnitude of the enhancement effect, its restriction to the dopant-diffused region, and the implantation results of Zucker et al. (1989) indicate that a Fermi level effect has to be considered in addition to nonequilibrium point defects. Combining the results for the p-type and the n-type dopant induced disordering, including a self-interstitial supersaturation sI defined according to Eq. (5-61) and a possible analogous vacancy supersaturation sv, we may express the Ga self-diffusion coefficient approximately as (5-89)

/

\3

where the quantities D;, (ni, 1 atm) and DA, (ni, 1 atm) are given respectively by Eqs. (5-80) and (5-83). In writing down Eq. (5-89), the As-rich GaAs, designated by PAs4=1 atm, is chosen as the reference material state, and with GaAs crystals of all other compositions represented by an appropriate PAS4value. Equation (5-89) de-

273


scribes all presently known essential effects on GaAs/Al,Ga,,As superlattice disordering. In the case of nonequilibrium Ga vacancies injected by a Si/As cap (Kavanagh et al., 1988), s v > O holds. In the case of ionimplantation, both sI> 0 and sv>0 may hold and both quantities will be time dependent. In the case of diffusion-induced nonequilibrium point defects, the presence of dislocations will allow local equilibrium between intrinsic point defects to establish in the two sublattices according to Eq. (5-13). In this way, a large supersaturation of I,, in the Ga sublattice may lead to an undersaturation of I,, or a supersaturation of V,, in the As sublattice.

5.8.3 Arsenic Self-Diffusion and Superlattice Disordering Because there is only one stable As isotope, 75As, As self-diffusion in GaAs cannot be studied using stable As isotopes. In intrinsic GaAs, however, three arsenic selfdiffusion studies have been conducted using radioactive tracers (Goldstein, 1961; Palfrey et al., 1983; Bosker et al., 1998). In one experiment (Palfrey et al., 1983), the As, pressure dependence of As self-diffusion indicated that As vacancies may be the responsible native point defect species. This is, however, in qualitative contradiction to the conclusion reached recently from a large number of studies involving As atoms and other group V and VI elements that the responsible native point defect species should be As self-interstitials. The latter studies include: (i) As-Sb and As-P interdiffusion in intrinsic GaAs/GaSb,As,, and GaAs/GaPxAsl, type superlattices for which x is small so as to avoid a large lattice mismatch (Egger et al., 1997; Schultz et al., 1998; Scholz et al., 1998b); (ii) P and Sb indiffusion into GaAs under appropriate P and As pressures so as to avoid extended

temperature ["C] 1200 1100 1000 900

r

800

1

0.70 0.75 0.80 0.85 0.90 0.95 1IT [lOOO/K]

Figure 5-30.Data on As self-diffusion coefficient obtained using radioactive As tracers (open squares), the group V elements N, P, and Sb and the group VI donor S (filled symbols). The dashed fitting line is given by Eq. (5-90); the solid line is a better overall fit (Scholz et al., 1998b).

defect formation which leads to complications (Egger et al., 1997; Schultz et al., 1998; Scholz et al., 1998b); (iii) an extensive analysis of the S indiffusion data in GaAs (Uematsu et al., 1995); (iv) outdiffusion of N from GaAs (Bosker et al., 1998). A plot of the relevant data is shown in 5-30. From Fig. 5-30, the lower limit of the As self-diffusion coefficient, assigned to be due to the As self-interstitial contribution, is given by

D i s ( n i , 1atm) = 6 ~ 1 0 - ~

For P-As and Sb-As interdiffusion, as well as indiffusion cases (Egger et al., 1997; Schultz et al., 1998; Scholz et al., 1998b), the profiles are error function shaped. With P and Sb assumed to be interstitial-substitutional elements, such diffusion profiles are described by an effective diffusivity of the type (5-91)

274


under native point defect equilibrium conditions, which are satisfied by either the kickout reaction (5-30) involving As selfinterstitials or by the dissociative reaction (5-31) involving As vacancies. The conclusion that As self-interstitials are the responsible species is reached for this group of experiments, because the diffusion rate increases upon increasing the ambient As vapor pressure. Arsenic self-interstitials should be the responsible species in the N outdiffusion experiments (Bosker et al., 1998) because the N profile is typical of that due to the kickout mechanism reaction (5-30) under the conditions of self-interstitial undersaturation, which are qualitatively different from those obtainable from the dissociative reaction (5-31). Arsenic self-interstitials should also be the responsible species in the S indiffusion experiments, because the S profile (Uematsu et al., 1995) is typical of that due to the kickout mechanism reaction (5-30) under the conditions of selfinterstitial supersaturation, which are also qualitatively different from those obtained from the dissociative reaction (5-31). It is seen from Fig. 5-30 that the available As self-diffusion data lie close to those deduced from the P, Sb, N, and S studies, and it may thus be inferred that As self-diffusion has a component contributed by the As self-interstitials. There are yet no doping dependence studies using the isoelectronic group V elements N, P, and Sb, and hence the charge nature of the involved As self-interstitials has not yet been determined. However, S is a group VI donor occupying the As sublattice sites. In analyzing S indiffusion (Uematsu et al., 1995), it was necessary to assume that neutral As self-interstitial species were involved, which are therefore the most likely species responsible for As self-diffusion. There is also a study on the disordering of GaAs/Al,Ga,,As superlattices by the

group IV acceptor species C (You et al., 1993b) which occupy the As sublattice sites. While no information has been obtained from this study on As diffusivity, satisfactory descriptions of the C diffusion profiles themselves were also obtained with the use of the kickout reaction (5-30) involving neutral As self-interstitials. This lends further support to the interpretation that neutral As self-interstitials are responsible for As self-diffusion.

5.8.4 Impurity Diffusion in Gallium Arsenide 5.8.4.1 Silicon Diffusion

For GaAs the main n-type dopant is Si. It is an amphoteric dopant mainly dissolved on the Ga sublattice, but shows a high degree of self-compensation at high concentrations due to an increased solubility on the As sublattice. The apparent concentration dependence of Si diffusion has been modeled by a variety of mechanisms. Greiner and Gibbons (1985) proposed that Si diffusion is predominantly carried by SiAs-SiGapairs. Kavanagh et al. (1988) assumed that the concentration dependence is due to a depth-dependent vacancy concentration generated by an SUAs type capping layer. Tan and Gosele (1988 b), Yu et al. (1989), and Deppe and Holonyak (1988) suggested that silicon diffusion is dominated by negatively charged Ga vacancies, and that its apparent concentration dependence is actually a Fermi level effect. Results of Si diffusion into n-type (Sn-doped) GaAs confirm the Fermi level effect and contradict the Greiner-Gibbons pair-diffusion model. Deppe and Holonyak (1988) suggested a charge state of -1 for the Ga vacancy. Yu et al. (1989) have mainly used V& to fit the Si indiffusion profiles, which is consistent with the species dominating superlattice disordering (Sec. 5.8.2).

275


In the analysis of Yu et al. (1 989), the diffusivity of the Si donor species Si;, is shown to satisfy

k1

3

Qji

( n )= DSi (ni)

(5-92)

-

which indicates that V& governs the diffusion of Si;,. In Eq. (5-92), the quantity Dsi (ni) is the Si&, diffusivity under intrinsic conditions, identified to be

8

8 \ \

indiffusion outdiffusion

for obtaining satisfactory fits to the experimental data of Greiner and Gibbons (1985) and of Kavanagh et al. (1988). In a Si outdiffusion experiment, You et al. (1993a) found that the Si profiles also satisfy Eq. (5-92), but with the needed DSi(ni) values given by Dsi (ni , 1 atm) =

(4, Ga-rich) = =9.18x104 exp

(5-94b)

(

- 5.25 eV

m2 s-l

kBT

respectively for experiments conducted under As-rich and Ga-rich ambient conditions. The Dsi (ni) expressed by Eq. (5-94) are larger than those of Eq. (5-93) by many orders of magnitude at temperatures above - 800°C (Fig. 5-3 l), indicating the presence of an undersaturation and a supersaturation of Vi; respectively under the Si in- and outdiffusion conditions (You et al., 1993a). For the indiffusion case, the starting GaAs crystal contains V& and the neutral Ga vacancies V ,: to the thermal equilibrium concentrations of those of the intrinsic material. Upon indiffusion of Si atoms, V& (and hence also V&) become undersaturated rel-

0.7

0.8

i 0 3 / T (K-’)

\ 8

\

0.9

1 .o

Figure 5-31. Comparison of the intrinsic Si& diffusivities under indiffusion conditions (Yuet al., 1989) and under outdiffusion conditions (You et al., 1993a).

ative to the thermal equilibrium V& concentration values appropriate for the n-doping conditions, which can only be alleviated via inflow of V& from the interface of the Si source material and the GaAs crystal. It appears that the flux of V& flowing into the GaAs crystal is limited by the interface region structural and electrical behavior, which is not sufficiently effective. The reverse analogy holds for the Si outdiffusion case. Since V& diffusion should be much faster than that of the S& atoms, in either case there should be no substantial spatial ,: spevariations in the distribution of the V cies, while the spatial distribution of V& follows the local n3 value.

5.8.4.2 Interstitial-Substitutional Species The group IV element carbon (C) occupies the As sublattice sites in GaAs to constitute a shallow acceptor species, designat-


1000

T (“‘3 900 800

0, (Ga-rich)=6.5 x loV2

700

- 4.47 eV kBT

S As-rich

1 Ga-rich

i \o

A

\

\

Cunningham et al. (1989)

I3 Chiu et al. (1991)

*

\

\

\

\

\

Hofler et al. (1992)

\

c;+1:,

\

1 0 Jamal et al. (1994)

0.7

0.8

0.9

1 .o

1.1

103/T (K-’)

Figure 5-32. Available carbon diffusivity data and fittings in GaAs. (You et al., 1993b).

ed as C; to emphasize that it is most likely a interstitial- substitutional species. Grownin during MBE crystal growth, C; reaches high solubilities (Konagai et al., 1989) and diffuses slow (Cunningham et al., 1989), which are attractive features when compared to the main p-type dopants Zn and Be in GaAs. The measured C; diffusivity values of a few groups obtained under As-rich annealing conditions (Saito et al., 1988; Cunningham et al., 1989; Chiu et al., 1991; Hoffler et al., 1992; Jamel and Goodhew, 1993; You et al., 1993b) are fitted well by the expression

D,(1 atm)=4.79 x lo4 - 3.13 eV

exp(

kBT

1

,2

s-l

2,

s-l

(5-95 b)

which fits satisfactorily some available data (Jamel and Goodhew, 1993; You et al., 1993b). The values of Eq. (5-95) are shown in Fig. 5-32. In the work of You et al. (1993b) the C; diffusivity data were obtained by the individual fittings of C; profiles, which are not quite error function shaped. In order to fit these profiles well, it was necessary to use the kickout reaction

Ga-rich

0 Saito et al. (1988)

)

(5-95 a)

The corresponding D,values under Ga-rich conditions should therefore be

* c;

(5-96)

where C; is an interstitial C atom, which is also assumed to be an acceptor, and ,:I is a neutral As self-interstitial, together with a carbon precipitation process. Later, Moll et al. (1 994) identified the nature of the precipitation process as that of graphite formation. The As self-interstitials are maintained at their thermal equilibrium values during C; diffusion, because of its low diffusivity value. The main p-type dopants in GaAs based devices, Zn and Be, diffuse via an interstitial-substitutional mechanism in GaAs as well as in many other 111-V compounds. Although in most papers Zn and Be diffusion has been discussed in terms of the much earlier suggested Frank-Turnbull or Longini mechanism (Casey, 1973; Tuck, 1988), only the kickout mechanism involving Ga self-interstitials is quantitatively consistent with the superlattice disordering results (Sec. 5.8.2) as well as with the Zn diffusion results (Yu et al., 1991 a; Jager et al., 1993). Isoconcentration diffusion of Zn isotopes in GaAs predoped by Zn showed error function profiles (Chang and Pearson, 1964; Ting and Pearson, 1971; Kadhim and Tuck, 1972) with the substitutional Zn diffusivity


lo+ -4

7 10

-0"

' \\ 900

1200

n

'"1 1 -

C

1 0-22

-

600

0

KadhimBTuck

A

Ting B Pearson

A

(1972)

(1971)

Casey et(1968) al.

' CaseyBPanish (1968)

ChangBPearsor (1964) l

0.6

~

l

0.8

-

l

*

l

1 .o

103/T(K-')

.

l

.

1.2

Figure 5-33. The substitutional Zn diffusivity values under intrinsic and 1 atm As, pressure conditions (Yu et al., 1991a).

values of

T:[

0,( p , 1atm) = D,(ni , 1atm) -

(5-97)

for As-rich GaAs and an analogous expression for Ga-rich GaAs. At sufficiently high Zn concentrations, since the GaAs hole concentration p approximately equals the Zn, concentration ( p C s ) , Eq. (5-97) shows that the responsible native point defect species can only be the doubly positively charged Ga self-interstitials or vacancies, 1% or V% , Under high concentration Zn indiffusion conditions, the GaAs/AI,Ga,,As superlattices disordering rates are tremendously enhanced (Sec. 5.8.2), indicating the presence of a high supersaturation of the responsible point defects. Thus the native point defect species responsible for Zn diffusion, and also for Ga self-diffusion and AI-Ga interdiffusion under p-doping conditions, is 1% and not V Z . In the latter case, only an undersaturation of V z can be incurred by Zn indiffusion, which should then

-

277

retard Al-Ga interdiffusion rates in superlattices, in contradiction to experimental results. In the Zn isoconcentration diffusion experiments, a nonequilibrium 1% concentration is not involved. Similarly, for Zn diffusion to low concentrations below the ni value, a nonequilibrium concentration of 1% is also not present, and the Zn diffusivity values may be represented by that under intrinsic conditions, D,(ni). As analyzed by Yu et a]. (199 1a), Zn isoconcentration experiments and Zn indiffusion experiments at high concentrations yielded the value range of D, (ni,1 atm)= 1.6 x 10" exp[

- 2.98 eV kB

]

m2 s-1

(5-98 a)

0,(q,1 atm)=9.68 x

The two analogous expressions for galliumrich materials are respectively 0,(q, Ga-rich)= 1.18 x lo-''

(5-99a)

D,($, Ga-nch)=7.14 x lop7 - 2.73 eV kB

(5-99b)

The values of Eq. (5-98) and the associated data are plotted in Fig. 5-33. The correspondingly deduced 1% contribution to gallium self-diffusion has been included in Eqs. (5-82) and (5-83). Because of the lack of a proper beryllium source for indiffusion studies, and in beryllium outdiffusion studies with beryllium incorporated using MBE or MOCVD methods the beryllium diffusivity is too small, there are no reliable beryllium diffusivity data.

278


Outdiffusion of Zn or Be in GaAs doped to fairly high concentrations during crystal growth but without introducing extended defects is associated with a high 1% undersaturation, leading to Zn or Be outdiffusion rates orders of magnitude smaller than those under indiffusion conditions (Kendal, 1968; Truck and Houghton, 1981; Enquist et al., 1985). Indiffusion of high concentration Zn into GaAs induces an extremely large 1% supersaturation, because the condition

Di Cpq D z y (p)

(5-100)

holds. As first noted by Winteler (197 l),this 1% supersaturation leads to the formation of extended defects. In recent works, three kinds of extended defect have been characterized and their formation process analyzed (Luysberg et al., 1989, 1992; Tan et al., 1991a; Jager et al., 1993): (i) interstitialtype dislocation loops, which degenerate into dislocation tangles in time; (ii) voids; and (iii) Ga precipitates neighboring voids. For diffusing Zn into GaAs in a Ga-rich ambient, a Zn diffused GaAs crystal region with compositions at the allowed Ga-rich boundary shown in Fig. 5-4 a is obtained, irrespective of the GaAs starting composition. The fact that the Zn diffused region is indeed rich in Ga is evidenced by the presence of Ga precipitates in the voids (Luysberg et al., 1989, 1992; Jager et al., 1993). Formation of these defects ensures that the Zn indiffusion profile is governed by the thermal equilibrium concentrations of native point defects of the Ga-rich GaAs crystal, and the profile is box-shaped, which redependence of the subveals the p 2 (or C’,) stitutional Zn, D,. Such a profile is shown in Fig. 5-34 together with an illustration of the involved extended defects. It is, however, noted that the crystal is in a highly nonequilibrium state, for two reasons: First, extended defects are generated. Second, the

starting material may not be rich in Ga and hence the crystal will now contain regions with different compositions which is of course a highly nonequilibrium crystal. For diffusing Zn into GaAs in an As-rich ambient, the situation is more complicated. After a sufficient elapse of diffusion time, the crystal surface region becomes As-rich because of the presence of a high ambient As, pressure. But since (5-101) holds in the Zn diffusion front region, it is Ga-rich. Thus the high concentration Zn indiffusion profiles are of a kink-and-tail type resembling those of high concentration Pindiffusion profiles in Si, see Fig. 5-35. The kink-and-tail profile develops because the Zn, solubility value in the As-rich and Garich GaAs materials are different (Jager et al., 1993). In the high Zn concentration region the D,(ni) values are those given by Eq. (5-98), while in the tail or Zn diffusion front region the D,(ni) values are those given by Eq. (5-99). These profiles cannot be modeled with a high degree of self-consistency, because the extended defect formation process cannot be modeled without the use of some phenomenological parameters (Yu et al., 1991a). The evolution of the extended defects, as suggested by Tan et al. (1 991 a) and Luysberg et al. (1992), is as follows: (i) to reduce 1% supersaturation, they form interstitial-type dislocation loops containing extra GaAs molecules, with the needed As atoms taken from the surrounding As sites, which generates a V,, supersaturation; (ii) the supersaturated V,, collapses to form voids, each of an initial volume about that of a neighboring Ga precipitate formed from Ga atoms lost their neighboring As atoms to the formation of dislocation loops. The voids will be rapidly filled by subsequently generated Ga self-interstitials due to further Zn indiffusion. For cases of diffusing Zn into


10 b)

0 I

40

80

160

120 x/IPml I

279

200 1

Figure 5-34. a) Zn indiffusion profiles obtained at 900°C under Ga-rich ambient conditions. Squares are the total Zn concentration and crosses are the hole or Zn, concentration. The higher total Zn concentration indicates the formation of Zn containing precipitates caused by the use of a nonequilibrium Zn source material which diffused Zn into GaAs exceeding its solubility at 900°C. b) A schematic diagram indicating the morphologies and distributions of voids (open) and Ga precipitates (filled), also indicated by v [p]. The presence of dislocations is not shown (Jager et. al., 1993).

Figure 5-35. a) Zn indiffusion profiles obtained at 900°C under As-rich ambient conditions. Squares are the total Zn concentration and crosses are the hole or Zn, concentration. The higher total Zn concentration indicates the formation of Zn-containing precipitates caused by the use of a nonequilibrium Zn source material, which diffused Zn into GaAs exceeding its solubility at 900°C. b) A schematic diagram indicating the morphologies and distributions of voids (open) and Ga precipitates (filled). The presence of dislocations is not shown (Jager et al., 1993).

GaAs in a Ga-rich ambient, the voids contain Ga precipitates throughout the Zn indiffused region, but for cases of diffusing Zn into GaAs in an As-rich ambient, the surface region voids are empty. Chromium is a deep acceptor occupying Ga sites and is used for fabricating semi-insulating GaAs. In GaAs not deliberately doped by a shallow dopant, diffusion of Cr involves no charge effects. Indiffusion profiles of Cr are characterized by a kickout type profile from the crystal surface to a substantial depth and an erfc-type profile deeper in the material near the diffusion front (Tuck, 1988; Deal and Stevenson, 1988). Outdiffusion profiles are characterized by a constant diffusivity, which is much lower than for in-diffusion. The existence of the

two types of profile needs the description of the interstitial-substitutional diffusion mechanism in terms of the kickout mechanism (Eq. 5-30)) and the Franke-Turnbull mechanism (Eq. 5-31)). Tuck (1988) and Deal and Stevenson (1988) have discussed Cr diffusion in terms of the Frank-Turnbull mechanism. The satisfactory treatment of the diffusion behavior of Cr in intrinsic GaAs (Yu et al., 1991b), however, includes to co-existence of Ga vacancies and selfinterstitials, the dependence of Ctq and Cfq on the outside Cr vapor pressure, and a dynamical equilibrium between the native point defects in the Ga and the As sublattice at the crystal surface region. Chromium indiffusion turned out to be governed by the concentration-dependent from Eq.

280


(5-37) in the surface region and by the much faster constant diffusivity Of: from Eq. (5-52) in the tail region. In the case of outdiffusion, the Cr vapor pressure is so low that, similarly to the case of outdiffusion of Zn, a much lower diffusivity prevails. This slower outdiffusion turned out to be dominated either by the constant vacancy component of D7fV, or the constant D$, which can be lower than D7Fv, for low outside chromium vapor pressure. The deduced D,CIeq value from Cr indiffusion profiles (Yu et al., 1991b) has been included in Eq. (5-82). The group VI donor S occupies As sites. With lower surface concentrations, the S indiffusion profiles (Young and Pearson, 1970; Tuck and Powell, 1981; Uematsu et al., 1995) resemble the erfc-function, but a concave shape develops in the surface region for higher concentration cases. The latter cases are indicative of the operation of the kickout mechanism for an interstitial -substitutional impurity. The available S indiffusion profiles have been quantitatively explained (Uematsu et al., 1995) using the kickout mechanism assuming the involvement of the neutral As self-interstitials, I:,. The deduced D i s (ni, 1 atm) Values were included in Eq. (5-90).

5.8.5 Comparison to Diffusion in Other 111-V Compounds Gallium arsenide is certainly the one 111-V compound in which self- and impurity diffusion processes have been studied most extensively. The available results on self-diffusion in 111-V compounds have been summarized by Willoughby (1983). The Group 111and the Group V diffusivities appear to be so close in some compounds that a common defect mechanism involving multiple native point defects appears to be the case, although no definite conclusion

has been reached. There are hardly any experimental results available which would allow conclusions to be drawn on the type and charge states of the native point defects involved in self-diffusion processes. Zinc is an important p-type dopant also for other 111-V compounds, and its diffusion behavior appears to be governed by an interstitial-substitutional mechanism as well. No information is available on whether the FrankTurnbull mechanism or the kickout mechanism is operating. It is to be expected that dopant diffusion induced superlattice disordering may rapidly advance our understanding of diffusion mechanisms in other 111-V compounds similarly as has been accomplished in GaAs. The state of understanding of diffusion mechanisms in 11-VI compounds has been discussed by Shaw (1988).

5.9 Agglomeration and Precipitation In semiconductors, agglomeration and precipitation of an impurity or native point defect species are general phenomena which exist in an excess of an appropriate thermal equilibrium concentration or solubility. Due to the supersaturation of native point defects developed during cooling, swirl defects form in Si during crystal growth. The solubility of an impurity species is defined by the thermal equilibrium coexistence of the semiconductor and a unique compound phase of material composed of the impurity atoms and elements of the semiconductor. For practical reasons, however, a nonequilibrium source material is usually used to indiffuse dopants into the semiconductor. Thus high concentration P indiffusion into Si is associated with the formation of Sip precipitates near the surface region, and high concentration Zn indiffusion into GaAs is also associated with the formation of Zn

281

5.9 Agglomeration and Precipitation

containing precipitates. In this sections we discuss the agglomeration phenomena of native point defects and impurity precipitation phenomena. For the latter category, those associated with the use of nonequilibrium diffusion source matrials will not be included for they appear to be relatively trivial cases.

5.9.1 Agglomerates of Native Point Defects in Silicon Nonequilibrium concentrations of native point defects develop in Si during crystal growth, ion-implantation, and surface processes such as oxidation or nitridation. The nonequilibrium native point defects associated with crystal growth may agglomerate to generate various types of so-called swirl defects. A-swirl defects consist of interstitial-type dislocation loops resulting from a supersaturation of Si self-interstitials. Bswirl defects are considered as a precursor of A-swirl defects, probably consisting of three-dimensional agglomerates of selfinterstitials and carbon atoms (deKock, 1981; Foll et al., 1981). Agglomerates of vacancies have been termed "D-swirl" defects (Abe and Harada, 1983). Voids to sizes of - 100 nm have been found in recently available large diameter (30 cm) CZ Si crystals (Kato et al., 1996; Ueki et al., 1997), which are apparently D-swirl defects grown to large sizes. These voids are supposed to be responsible for low gate break-down voltages in MOSFET devices (Parket al., 1994). The formation of swirl defects results from a supersaturation of Si self-interstitials or vacancies, due to cooling in crystal regions moving away from the crystal-melt interface wherein the native point defects are at their thermal equilibrium values at the Si melting temperature of 1412"C.The formation of swirl defects depends on the growth speed and the temperature gradient in the

crystal. After the way having been paved by many previous attempts (Voronkov, 1982; Tan and Gosele, 1985; Brown et al., 1994; Habu et al., 1993a, b, c), a seemingly satisfactory quantitative model on the swirl-defect formation process is now available (Sinno et al., 1998). As a function of the crystal growth rate and the temperature gradient, this model fits fairly well the experimentally observed swirl-defect type, size, and distribution. In the model, basically Eqs. (5-49) and (5-50) are used for the Si self-interstitial and vacancy contributions to Si self-diffusion, with the appropriate point defect thermal equilibrium concentration and diffusivity values already discussed in Sec. 5.6.2. An important aspect to note is that the used Si vacancy migration enthalpy is less than 1 eV. In a simplified model describing the void growth process from supersaturated Si vacancies, Plekhanov et al. (1998) also needed to use a Si vacancy migration enthalpy value of less than 1 eV. Due to the complexities involved, a detailed discussion of the swirl-defect formation process appears to be beyond the scope of the present chapter. In the following, we will deal with the much simpler case of the growth or shrinkage of dislocation loops containing a stacking fault on (1 11) planes. Such dislocation loops may be formed by the agglomeration of oxidation-induced self-interstitials, and have been termed oxidation-induced stacking faults (OSFs). These stacking faults may either nucleate at the surface (surface stacking faults) or in the bulk (bulk stacking faults). Approximating the shape of the stacking faults as semicircular at the surface with radius rSF in the bulk, we may write their growth rate as

-

n (5-102)

- Q Cq : SI +& CGq s v ] A

282


In Eq. (5-102), aeffis a dimensionless factor which can be approximated as about 0.5, ySF(= 0.026 eV atom-') denotes the extrinsic stacking fault energy, m2) the stacking fault area 2(=6.38 x m3) the per atom, and SZ (= 2.0 x atomic volume. In the derivation of Eq. (5-102) it has been assumed that y s F / k B T e l and that the line tension of the Frank partial dislocation surrounding the stacking fault may be neglected in comparison to the stacking fault energy. The first condition is always fulfilled (e.g., Y s ~ / k ~ T = 0 at . 2 1300 K), the second for rSF21 ym. The quantities sI and sv denote self-interstitial and vacancy supersaturations, respectively, defined analogously to Eq. (5-61). In an inert atmosphere, native point defect equilibrium is maintained (sI= 0, sv = 0) and Eq. (5-102) reduces to

(5-103) which describes a linear shrinkage of stacking faults, as has been observed experimentally (Fair, 1981a; Frank et al., 1984). From measured data of (drsF/dt)in, the uncorrelated self-diffusion coefficient DSDmay be determined. The results are included in Fig. 5-8. Quantitative information on sIhas been extracted from the growth rate (drsF/dt)ox of OSF under oxidation conditions, together with the shrinkage rate (drsF/dt)in in an inert atmosphere at the same temperature

Equation (5-104) yields for dry oxidation of a { 100) Si surface at temperatures in the vi-

cinity of 1100°C sI = 6.6 x

2.53 eV kB T

t-1'4 exp -

(5-105)

(Antoniadis, 1982; Tan and Gosele, 1982, 1985). For { 111 } surfaces, the right-hand side of Eq. (5-105) has to be multiplied by a factor of 0.6-0.7 (Leroy, 1986). For wet oxidation, multiplication factors larger than unity have to be used. The supersaturation ratios sIcalculated based on Eq. (5-105) appear to overestimate sIby 20-50%.

5.9.2 Void and Gallium Precipitate Formation During Zinc Diffusion into GaAs In elemental crystals, a supersaturation of native point defects may be eliminated by the nucleation and growth of dislocation loops. In this way, Czq may be established by dislocation climb processes. As discussed in Sec. 5.3, in compound semiconductors dislocation climb involves point defects in both sublattices. A supersaturation of Ga self-interstitials, as induced by high concentration Zn diffusion into GaAs, can be reduced by dislocation climb processes under the simultaneous generation of As vacancies or the consumption of As self-interstitials. Dislocation climb will stop when local point defect equilibrium according to Eq. (5-13) has been reached (Petroff and Kimerling, 1976; Marioton et al., 1989). Therefore dislocation climb alone does not generally establish the thermal equilibrium concentration of native point defects. Thermal equilibrium concentrations in both sublattices may be reached if the As vacancies generated in the As sublattice via dislocation climb agglomerate and form voids. These voids will be in close contact with Ga precipitates (in a liquid form) of about the same volume. The Ga precipitates form

283

5.9 Agglomeration and Precipitation

€€a Carbon

Oxygen

4 SiO2

9.

C

Volume increase (factor 2)

-

I agglomemtes if

Sic or agglomerate

I in supersaturation cepncipitotion I and C

.cg ‘%-swirls”

Figure 5-36. Schematic representation of volume changes during oxygen precipitation (left) and carbon precipitation (right), and the respective role of Si selfinterstitials (Gosele and Ast, 1983).

from those lattice Ga atoms that lost their neighboring As atoms to the dislocation climb process. Subsequently, the voids may act a sinks for more Ga interstitials by continued Zn indiffusion. With the combination of the growth of interstitial-type dislocation loops and of voids neighboring Ga precipitates, supersaturations of I, will be completely relieved and thermal equilibrium concentrations of native point defects in both sublattices establish, in accordance with those for a GaAs crystal with a composition at the thermodynamically allowed Ga-rich crystal limit. Such a defect structure has in fact been observed in transmission electron microscopy studies of Zn-diffused GaAs (Luysberg et al., 1989).

5.9.3 Precipitation with Volume Changes in Silicon

Oxygen and carbon are the main electrically inactive impurities in CZ Si. Oxygen is incorporated from the quartz crucible during the CZ crystal growth process in the form of oxygen interstitials Oi. The concentration Ci of these interstitial oxygen atoms at typical processing temperatures is higher than their solubility C:q at these temperatures. Therefore there is a thermodynamic driving force for Oi precipitation to occur. An unusual feature associated with oxygen precipitation, when compared to wellknown precipitation phenomena in metals or most dopants in semiconductors, is the presence of a large volume shortage. This results from the interstitial nature of Oi atoms in Si, which is not associated with a lattice volume. Thus only the Si atoms supply their atomic volumes to the formation of a Si02 precipitate. Since the molecular volume of Si02 is 2.2 times that of the Si atomic volume, there is a shortage of 1 Si atomic volume associated with the formation of each Si02 molecule. During the nucleation stage with a small number of SiOz molecules for each precipitate, this volume shortage is accommodated by elastic deformation of the Si matrix. Further growth of the precipitate will be prevented by the increase of elastic energy unless the elastic strain is relieved by plastic deformation, the emission or absorption of native point defects, and/or the incorporation of volume shrinking impurities such as carbon atoms (Fig. 5-36). In the following, we will deal with the two latter processes in a dislocation-free Si matrix, which may cause a supersaturation or undersaturation of the appropriate native point defects and impurities, which in turn may influence the nucleation and growth kinetics of precipitates. Let us first discuss the simple case that Si selfinterstitials relieve the

-

284


elastic stress completely. In terms of SiO, formation, this requires 2 O , + ( l + P ) Si e Si02+PI

(5- 106)

where p= 1.2. Assuming spherical SiO, nuclei and neglecting the influence of vacancies, we obtain the critical radius t-, above which precipitates will grow as rcrit =

052

2 k, Tln [(Ci/C:q ) (C,"q/CI)1'2 ]

(5- 107)

(Gosele and Tan, 1982). In Eq. (5-107), (J is the SiOJSi interface energy for which 0.09-0.5 J m-* has been reported, and SZ ( = 2 ~ 1 0 m-3) - ~ ~ is the volume of one Si atom in the silicon lattice. For the derivationofEq. (5-102),P= 1 hasbeenused.During precipitation a supersaturation of selfinterstitials will be produced ( C > C;q), which in turn will increase the critical radius for further nucleation. This may also cause shrinkage of already existing precipitates to occur if their radius is surpassed by the increased rCri,(Ogino, 1982; Tan and Kung, 1986; Rogers et al., 1989). After a sufficiently long time and for a sufficiently high supersaturation, the self-interstitials will nucleate interstitial-type dislocation loops (usually containing a stacking fault, the bulk stacking faults), which will reduce the self-interstitial concentration back to its thermal equilibrium value. For C = CFq,Eq. (5-107) reduces to the classical expression for the critical radius. Vanhellemont and Claeys (1987) have given an expression for the critical radius in which besides selfinterstitials also vacancies and elastic stresses have been taken into account. A more detailed look at oxygen precipitates shows that their shape, ranging from rod-like, to plate-like, to being almost spherical, depends on the detailed precipitation conditions. The different shapes can be explained by a balance between minimizing the elastic energy and the point-defect

supersaturation (Tiller et al., 1986). The growth of oxygen pricipitates is limited by the diffusivity Di of oxygen interstitials given by Eq. (5-72). The growth kinetics of Si02 platelets has been measured by Wada et al. (1983) and Livingston et al. (1984), and theoretically analyzed by Hu (1986). Carbon precipitation is associated with a decrease of about one silicon atomic volume for each carbon atom incorporated in a S i c precipitate, The same volume decrease holds for carbon agglomerates without compound formation. The volume requirements during carbon precipitation, which are opposite to those during oxygen precipitation may be fulfilled by the absorption of one self-interstitial for each carbon incorporated (Fig. 5-36). When both carbon and self-interstitials are present in supersaturation, co-precipitation is a likely process to occur. B-swirl defects are thought to have formed in this way during Si crystal growth (Foll eta]., 1981). If both carbon and oxygen are present simultaneously, it is obvious that co-precipitation of carbon and oxygen in the ratio 1 :2 will avoid stress and point-defect generation or absorption. Co-precipitation of carbon and oxygen in this ratio has been observed by Zulehner (1983), Hahn et al. (1988), and Shimura (1986). Hahn et al. (1988) also showed that the Si crystal remains essentially stress free in spite of a fairly large amount of co-precipitated carbon and oxygen. In a long time isochronal annealing experiment of CZ Si wafers containing a high supersaturation of both carbon and oxygen, intriguing features were observed (Shimura, 1986). Co-precipitation of oxygen and carbon, to a substantial amount and at the approximate ratio of 1 :2, occurred at temperatures lower than 850°C. At still higher temperatures, however, only a significant precipitation of oxygen has occurred. Based on a method developed using the principle

-

5.1 0 References

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-

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6 Dislocations Helmut Alexander I1. Physikalisches Institut der Universitat Koln. Koln. Federal Republic of Germany

Helmar Teichler Institut fur Materialphysik der Universitat Gottingen. Gottingen. Federal Republic of Germany Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . 293 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Experimental Results on the Electronic Properties of Dislocations and Deformation-InducedPoint Defects . . . . . . . . . . . . . . . . . 302 6.3.1 Electron Paramagnetic Resonance (EPR) Spectroscopy 308 of Plastically Deformed Silicon . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Information on Dislocations and Point Defects from Electrical Measurements . . . . . . . . . . . . . . . . . . . . . . . . 313 6.3.3 Phenomena Indicating Shallow Dislocation-Related States . . . . . . . . . 322 6.3.3.1 Photoluminescence (PL) . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 6.3.3.2 Optical Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 324 6.3.3.3 Microwave Conductivity (MWC) . . . . . . . . . . . . . . . . . . . . . . 6.3.3.4 Electric Dipole Spin Resonance (EDSR) . . . . . . . . . . . . . . . . . . . 326 6.3.3.5 Electron Beam Induced Current (EBIC) . . . . . . . . . . . . . . . . . . . 327 328 6.3.4 Germanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 6.3.5 Gallium Arsenide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AI1BVI Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 6.3.6 Theoretical Investigations about Electronic Levels of Dislocations . . . 334 6.4 334 6.4.1 Core Structure Calculations . . . . . . . . . . . . . . . . . . . . . . . . . 336 6.4.2 Deep Electron Levels at Dislocations . . . . . . . . . . . . . . . . . . . . 6.4.3 Core Bond Reconstruction and Reconstruction Defects . . . . . . . . . . . 338 Kinks, Reconstruction Defects, Vacancies, and Impurities 6.4.4 340 in the Dislocation Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.5 Shallow Dislocation Levels . . . . . . . . . . . . . . . . . . . . . . . . . 344 6.4.6 Deep Dislocation Levels in Compounds . . . . . . . . . . . . . . . . . . . 344 6.5 Dislocation Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 6.5.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Measurements of the Velocity of Perfect Dislocations 6.5.2 347 in Elemental Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Kink Formation and Kink Motion . . . . . . . . . . . . . . . . . . . . . . 350 6.5.4 Experiments on the Mobility of Partial Dislocations . . . . . . . . . . . . 352 List of 6.1 6.2 6.3

2 92

6.5.5 6.6 6.6.1 6.6.2 6.7 6.7.1 6.7.2 6.7.3 6.7.4 6.8 6.9

6 Dislocations

Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Theory of Dislocation Motion . . . . . . . . . . . . . . . . . . . . . . . 358 Dislocation Motion in Undoped Material . . . . . . . . . . . . . . . . . . 358 Dislocation Motion in Doped Semiconductors . . . . . . . . . . . . . . . . 362 Dislocation Generation and Plastic Deformation . . . . . . . . . . . . . 365 Dislocation Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365 Dislocation Multiplication (Plastic Deformation) . . . . . . . . . . . . . . 368 Generation of Misfit Dislocations . . . . . . . . . . . . . . . . . . . . . . 370 Gettering with the Help of Dislocations . . . . . . . . . . . . . . . . . . . 371 Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371


List of Symbols and Abbreviations lattice parameter Burgers vector, Burgers modulus kink diffusivity dipole-dipole interaction between nearest- and next-nearest-neighbor vacancies along the dislocation line dissociation widths on cross slip plane and primary glide plane conduction and valence band edge critical activation energy formation energy for a critical double kink energy height of weak obstacles dangling bond energy Fermi energy formation energy dislocation level electron charge electron effective charge glide force normal component of Peach-Kohler force geometrical factor relating glide force difference and shear force nucleation rate and effective nucleation rate Boltzmann constant distribution coefficient stress exponent of dislocation velocity dislocation density density of chargeable sites acceptor density, donor density density of states at the conduction (valence) band edge activation energy of dislocation velocity activation energy of dislocation velocity at 1 MPa shear stress activation enthalpy charge line charge critical radius friction stress ratio of friction stress critical length capture cross section for electrons capture cross section for holes temperature absolute melting temperature spin-lattice relaxation time critical thickness

293

294

6 Dislocations

pulse length, pause length critical pulse length, critical pause length mean lifetime of a double kink activation energy of the lower yield stress intraatomic Coulomb integral formation energy of a single kink kink velocity, mean kink velocity activation enthalpy activation energy migration energy stacking fault energy lattice mismatch relative and vacuum permittivity strain rate plastic strain plastic strain rate shear modulus mobility Debye frequency kink attempt frequency applied compression stress excess stress shear stress threshold stress yield stress of CRSS band bending energy in the dislocation core Coulomb potential of a screened dislocation AD CL CRSS

cs cz

DK DLTS EBIC EDSR EPR FZ HFS HREM L LCAO LEC

antisite defect cathodo luminescence critical resolved shear stress constrictions Czochralski double kink deep level transient spectroscopy electron-beam-induced current electric dipole spin resonance electron paramagnetic resonance floating zone grown hyperfine structure high-resolution electron microscope luminescence linear combination of atomic orbitals liquid encapsulation Czochralski

List of Symbols a n d Abbreviations

MWC PD PL PPE RD REDG SEM SF SI TSCAP V VVF

microwave conductivity point defect p hotoluminescence photoplastic effect reconstruction defect radiation-enhanced dislocation glide scanning electron microscope stacking fault self-interstitial thermally stimulated capacitance vacancy valence force field

295

296

6 Dislocations

6.1 Introduction At first glance the subject “dislocation in semiconductors’’ seems to be well defined. However, since dislocations in these materials are generated at elevated temperatures, their formation is always connected with a change in the number and distribution of point defects (intrinsic and extrinsic) in the crystal. Therefore, any change of a physical quantity measured at crystals with and without dislocations, respectively, has to be carefully analyzed as to which part of the change might be due to the dislocations themselves. The intricacy of this problem is illustrated by the current discussion of the extent to which clean dislocations are centers for carrier recombination. At present it is extremely difficult to arrive at a final answer to this question since methods for measuring the degree of decoration of dislocations with impurity atoms are lacking. In theory, the determination of the minimum energy core structure of straight partial dislocations has reached a state where fundamental changes are not to be expected. Regarding the electronic levels of straight dislocations, the theory indicates that no deep states exist (except perhaps for shallow levels due to extremely deformed bonds) for the so-called reconstructed variants of the dislocation cores, which seems to be the energetically stable configuration of the predominating partials in silicon. In the case of compounds, even more problems are unsolved than for the elemental semiconductors. Nevertheless, during the last few years considerable progress has been made in dislocation research. Extended application of EPR spectroscopy to plastically deformed silicon has led to a clear distinction between point defects in the bulk and defects introduced into the core of dislocations when they move. Moreover, a thermal procedure could be worked out which strongly reduc-

es the number of bulk defects after plastic deformation. As already mentioned, the core of straight partials in its ground state in silicon is reconstructed; after some motion it contains paramagnetic defects as (mainly) vacancies and other singularities as kinks and jogs. Theoretical calculations indicate that deep states in the gap arise mainly from broken bond centers. Accordingly, the intensity of the DLTS signals of deformed silicon is also greatly reduced by moderate annealing. Recently, shallow states in the gap connected to dislocations have come to the fore. Here, shallow is defined as being within 200 meV from the band edges. These states are responsible for near edge optical absorption, photoluminescence and transport phenomena such as microwave conductivity and combined resonance. Their nature is not yet clear and will be of central interest in the near future. Dislocations are extended defects, i.e., their charge state may vary in wide limits. Consequently there is Coulomb interaction between charges confined to the dislocation which shifts the dislocation level with respect to the Fermi level (band bending around extended defects). The dependence of the EBIC contrast of dislocations on temperature and injection is analyzed along these lines. Careful analysis of the ionization of shallow donors (phosphorus) in plastically deformed n-type silicon by EPR clearly evidenced another source of band bending: The inhomogeneous distribution of deep acceptors (point defects) leads to inhomogeneous compensation of doping. Analysis of DLTS spectra under these conditions is not straightforward. For semiconductor technology the most interesting properties of dislocations are their activity as a recombination center and as a sink for self-interstitials. Research is active with respect to both these effects.

6.2 Geometry

In summary, it should be emphasized that in examining dislocations, the dislocation density does not satisfactorily characterize a crystal. Instead, its whole thermal history and the process which generated the dislocations have to be taken into account. Inhomogeneity after dislocation movement is unavoidable and may have a strong influence on physical properties. This message should be delivered before going into details. In this chapter we comment on both mechanical and electronic properties of dislocations, which are often dealt with in separate reviews. We felt that there is encouraging convergence of theory and experiment but that the field is far from being well-rounded. Thus separate presentation of experimental and theoretical results seemed most helpful for the reader to form an unbiased opinion.

6.2 Geometry The reader is assumed here to be familiar with the general conception of a dislocation (Friedel, 1964). As the most important semiconductors belong to the tetrahedrally coordinated crystals with diamond or sphalerite (cubic zinc blende) structure we have to deal primarily with dislocations in crystals with the face-centered-cubic (f.c.c.) Bravais lattice. As in f.c.c. metals, the Burgers vector of perfect dislocations is of the type a/2 (110). Also, the (close-packed) glide planes, determined by the Bravais lattice, correspond in diamond-like semiconductors as in f.c.c. metals to ( 1 1 1 ] planes. However, the existence of two sublattices in the diamond as well as in the sphalerite structure brings about two types of glide planes. Figure 6-1 shows a projection of the diamond structure onto a ( 110) plane; obviously the ( 1 11) planes are arranged in

297

Iiiil

Figure 6-1. Projection of the diamond structure onto a (1 10) plane.

pairs, the distance within one pair being three times shorter than between pairs. Thus at first glance the relative shift (shear) of one part of the crystal with respect to the other could proceed either in the wide space between two neighboring pairs of ( 1 1 1 ) planes or between the two planes of one pair. Since this shift is accomplished by the motion of dislocations those two possibilities result in dislocations with quite different core structures called “shuffle-set” and “glide-set” dislocations by Hirth and Lothe (1982). In one of the first papers considering plastic deformation of germanium Seitz ( 1 952) came to the conclusion that dislocations in diamond-like crystals should belong to the shuffle-set (Fig. 6-2). For a long period of time that opinion was generally accepted because it was in agreement with two principles: First, the shear stress needed for displacement of two neighboring lattice planes, one against the other, is generally smaller, the wider the distance is between these planes; second, in the case of covalent bonding, it is reasonable to assume that cutting one bond (per unit cell of the plane) would be easier than cutting three bonds. In 1953 William Shockley gave a remarkable speech, documented as a short abstract (Shockley, 1953), in which he left open the question of whether dislocations in

298

6 Dislocations

dislocation moves one part of the crystal against the other by a Burgers vector which is not a translation vector of the space lattice; this partial dislocation (abbreviated as "partial") leaves the stacking sequence disturbed; it is followed by a stacking fault ribbon. This region of wrong stacking sequence is closed by a second partial, whose Burgers vector completes the first Burgers vector to a space lattice vector a/2 [Oll] + a/6 [121] + a/6 [I121 Figure 6-2. 60" shuffle-set dislocation.

diamond-like crystals were of shuffle or glide type. He noticed that only in the second case is splitting of perfect dislocations into two (Shockley) partial dislocations possible, as in f.c.c. metals. This reaction, also called dissociation, consists of a decomposition of the elementary step of shearing into two steps: an initial partial

(6-1)

Considering a model of the structure, it can easily be understood that only the two (1 i 1) planes constituting a narrow pair can be rebound by tetrahedral bonds after a relative displacement by a16 [121]. This means that only glide-set dislocations are able to dissociate (Fig. 6-3). Thus the clear proof of the then new weak-beam technique of transmission electron microscopy that glissile dislocations in silicon on most of their length are dissociated initiated a fun-

*

4 0

Figure 6-3. Dissociated 60" glide-set dislocation. A stacking fault ribbon is bound by the two partials: on the left side the 30" partial, on the right side the 90" partial. (Partials are shown unreconstructed).

6.2 Geometry

damental change of dislocation models and theory (Ray and Cockayne, 1970, 1971). Speculation about the association of a shuffle-set dislocation with a stacking fault ribbon in a neighboring narrow pair of planes (Haasen and Seeger, 1958) made clear that the only difference between a dissociated glide-set dislocation and a shuffle-set dislocation which is associated with a stacking fault bound by a dipole of partials is one row of atoms (Fig. 6-4) (Alexander, 1974). EPR spectroscopy (Sec. 6.3.1) brings to light that when screw dislocations in silicon move, they introduce vacancies into the core of their partials. Thus an equilibrium between (dominant) glide segments and shuffle segments must be considered (Blanc, 1975). This equilibrium appears to be influenced by the tensor of stress acting on the dislocation as well as by the concentration of native point defects and possibly certain impurity species like carbon and oxygen (Kisielowski-Kemmerich, 1990). One may ask why the former decision in favor of the shuffle-set dislocation was a wrong decision. This becomes clear from Fig. 6.3. Admittedly, the number of "dangling" bonds is larger in this structure than in Fig. 6-2 by a factor of three. But the

P?

0

I7

I?

0

Figure 6-4. Replacing the row of atoms in the core of a 30" partial by vacancies generates the core of a shuffle-set 60" dislocation associated to a stacking fault between a neighboring close pair of ( 1 1 1) planes (from Alexander, 1974).

299

arrangement of the orbitals containing the unpaired electrons is more suitable for pairwise rebonding ("reconstruction") in the partials of glide-set dislocations because the orbitals show much more overlap than in the core of shuffle-set dislocations (Fig. 6-2). Reconstruction of the core of the basic types of partials has been studied theoretically, as described in Sec. 6.4.3.The idea that this reconstruction is realized at least in silicon is in satisfactory agreement with the results of EPR spectroscopy which always came out with a much smaller number of unpaired electron spins than geometrically possible dangling bonds (Sec. 6.3.1). In summary, one may state that dissociated glide-set dislocations are favored over shuffle-set dislocations because in glide-set dislocations, both elastic energy and energy of unsaturated bonds are saved. For germanium, however, the situation is not as clear. Proceeding from elements to compounds with sphalerite structure (A"'BV compounds and cubic A"BV' compounds) an interesting complication arises: the two f.c.c. sublattices now are occupied by different atomic species. Nevertheless, in those compounds the overwhelming majority of mobile dislocations are also found dissociated into Shockley partials. Figure 6-3 can be used again, but the "black" and "white" atoms are now chemically different, and the bonding has an ionic contribution depending on the constituents. Obviously, all atoms which are seats of dangling bonds before reconstruction along a certain partial are of the same species. This makes reconstruction by pairwise rebonding more difficult; in fact, it is doubtful whether dislocations in compounds are reconstructed although without reconstruction, the preference for glide-set dislocations can no longer be easily understood. A further consequence of the uniformity of atoms occupying the core sites of a par-

300

6 Dislocations

tial is the doubling of the number of dislocation types when compared with elemental semiconductors: a 30"partial is conceivable with A atoms in its very core or with B atoms; the same holds for any dislocation. The naming of those chemical types is not uniform in the literature; there has been an attempt to remain independent from the decision whether the dislocations belong to the glide-set or to the shuffle-set. We take the view that dissociation into partials proves a dislocation to be of the glide-set type. Thus we call a dislocation with an extra half plane ending with A atoms (cations) /3dislocation and its negative counterpart with anions in the center of the core a dislocation (Fig. 6-5). A more extended name would be A(g) and B (g), respectively. A B ( s ) dislocation would be of the same sign as A(g), but ending between widely spaced { 111} planes. a-60" dislocations dissociate into an a-30" and an a-90" partial (Fig. 6-3), screw dislocations always consist of an a-30"and a p30" partial. The cubic sphalerite structure is assumed (at room temperature) by several AI1Bv1 compounds as well: cubic ZnS, ZnSe, ZnTe, CdTe. But a second group (ZnO, hexagonal ZnS, CdS, CdSe) belongs to the (hexagonal)

BY

Y

3 s )

Y

A" BY

A(@. ,

i

A=

-

-

B(g)

wurtzite structure. This structure also is composed of tetrahedral groups of atoms, but the stacking sequence of those tetrahedra is ABAB ... instead of ABCABC ... Here the basal plane (0001) it the only close-packed glide plane. It is equivalent to the four (1 11) planes in the cubic structures. The Burgers vectors of perfect dislocations are of the type b = (d3) (2110). Dislocations with these Burgers vectors may also glide on prismatic planes { l O i O } and this secondary glide is indeed observed (Ossipyan et al., 1986). Since the { lOTO} planes are chemically "mixed", there is no distinction between a and /3 dislocations on these planes. But there are two different distances between two (1010) planes in analogy to shuffle and glide planes in the case of (1 11). Information describing which one is activated in wurtzite-type crystals is lacking (Ossipyan et al., 1986). Stacking faults (SF) generated by dissociation of glissile dislocations on close packed planes are of intrinsic type in all semiconductors investigated so far. An SF locally converts a thin layer from sphalerite into wurtzite structure and vice versa (Fig. 6-6). This is observed for ZnS, where one modification is transformed into the other by sweeping a partial over every second close-packed plane (Pirouz, 1989). Similarly, microtwinning of cubic crystals is equivalent to sweeping every plane by a Shockley partial (Pirouz, 1987). The stacking fault energy y in A"'BV compounds

c

-

c

B A

c

A

B

A

c

B

c

A

B

A

c

B

c

+-=

A

c

A

c

B

B

B

B

B

B

c

B

A

A

c

A

A

c

A

Figure 6-6. An intrinsic stacking fault generates a thin layer of hexagonal wurtzite (B C B C) in the cubic lattice.

6.2 Geometry

decreases systematically with increasing ionicity of the compound (Gottschalk et al., 1978). This becomes clear as soon as y is related to the area of a unit cell in the stacking fault plane and it can be understood from the local neighborhood of ions on both sides of the SF plane: here a 13th neighbor of opposite sign enters the shell of 12 next-nearest-neighbor ions, in this way reducing the Coulomb energy. Takeuchi et al. (1984; Takeuchi and Suzuki, 1999) extended this consideration to A"BV' compounds and showed good correlation of y to the charge redistribution coefficient s, wich accounts for the dependence of the effective ionic charge on the strain. Where a wurtzite phase exists the c/a ratio also is correlated to y. An interesting feature typical for dislocations in semiconductors are constrictions (CS) where the dissociation into partials locally is withdrawn (Fig. 6-7). CS can be point-like on weak-beam micrographs (i.e., shorter than 1.5 nm) or segments on the dislocation line. It is well established that most CS are projections of jogs (Packeiser and Haasen, 1977; Tillmann, 1976). Consider-

301

ing density and distribution of CS in silicon after various deformation and annealing procedures we come to the conclusion that the majority of CS are products of climb events and not of dislocation cutting processes (Jebasinski, 1989). Point-like CS are jogs limiting a longer segment which redissociated after a climb on a new glide plane. Some of them may also be close pairs of jogs. Packeiser (1 980) was able to measure the height of jogs in germanium and found them rather short (between 2 and 7 plane distances; elementary jogs were beyond the resolution of the technique). We recently measured the average distance L between two neighboring CS in p-type silicon and found that L = 0.6 pm for a strain of 1.6%, irrespective of whether the deformation was carried out at 650°C or at 800°C. Annealing after deformation leads to an increase of L for annealing below the deformation temperature, but to a decrease of L above Tdef, exactly as was found previously for Ge (Haasen, 1979). But only above T,,, (= 650°C) equilibrium was reached within the annealing time (16 h). It must be concluded that a fast process of annihilation of

Figure 6-7. Silicon. Transmission electron micrograph of a dipole of dissociated edge dislocations with constrictions. Left image: stacking fault contrast (g= (3ii)). Right image: weak beam contrast (022/066) (from Jebasinski, 1989).

302

6 Dislocations

CS (climb of jogs along dislocations) is superimposed to a slow process of generation of new CS (net climb of the dislocation). It is noteworthy that Farber and Gottschalk (1991) in CZ-Si observed only very few CS. There are extensive investigations of climbing of dissociated dislocations carried out with the help of high resolution electron microscopy (Thibault-Desseaux et al., 1989). The authors analyzed silicon bicrystals grown by the Czochralski technique and plastically deformed at 850 "C. Climb proceeds by nucleation of a perfect interstitial loop on the 90" partial (Fig. 6-8). These loops may or may not dissociate. It is interesting that the climb events are found at dislocations which are trapped by formation of a dipole or near the grain boundary. Slowly moving or resting dislocations are preferentially concerned when interaction with point defects is considered, irrespective of whether this involves impurity atoms (Sumino, 1989) or native defects. ThibaultDesseaux et al. (1989) estimate the concentration of interstitials necessary for the first step of climb as 10-4-10-2 and believe that such a supersaturation (lo6) is the consequence of plastic deformation. The above-mentioned mechanism of climb via constrictions is not excluded by Thibault-Desseaux et al. (1989), but it is not particularly suited for investigation by HREM. It would be worthwhile to investigate whether climb in FZ-Si proceeds due to a supersaturation of vacancies, and in such a case CS would be prevalent. Dislocation core structures are studied by HREM in end-on orientation, i.e., the electron beam is parallel to the dislocation line (see Spence, 1988). The micrograph shows a projection of the atom colums (Fig. 6-8). Jogs as well as kinks cannot be resolved in this orientation. Recently, dissociated dislocations have been imaged in plane-view

Figure 6-8. Silicon: Climb by formation of a complete dislocation (high-resolution TEM). (a) dissociated 60" dislocation (Ah: 90" partial, 6B: 30" partial); (b) The partial A6 has decomposed into a complete dislocation AC (which has climbed by 7 atomic planes) and the partial C 6 (from Thibault-Desseaux et al., 1989).

orientation with high resolution (Alexander et al., 1986; Kolar et al., 1996; Spence et al., 1997). Here the electron beam is perpendicular to the glide plane, the stacking fault ribbon between the partials shows up as an area with hexagonal arrangement of the atom columns. The boundaries of that area marks the core of the partials (for application see Sec. 6.5.4).

6.3 Experimental Results on the Electronic Properties of Dislocations and DeformationInduced Point Defects Dislocations in semiconductors act as electrically active defects: they can be

6.3 Experimental Results on the Electronic Properties of Dislocations

“structural dopants” (acceptors and/or donors), recombination centers reducing the lifetime of minority carriers, or scattering centers. In the low-temperature region, dislocations are linear conductors. In addition to this direct influence on carrier density, lifetime, and mobility, there are indirect influences: electrically charged dislocations are surrounded by a screening space charge which causes local band bending and therefore may change the charge state of point defects in this region. This multitude of electrical effects has attracted considerable research activity for a long time; however, on account of some special problems, understanding has developed rather slowly. The first problem, which had not been realized immediately, concerns the superposition of the electrical effects of point defects also produced by plastic deformation with that of dislocations (plastic deformation is the usual method to produce a sufficiently high density of welldefined dislocations). As revealed mainly by EPR spectroscopy, but also by Hall effect measurements, deformation produces a surprisingly high concentration of point defect clusters contributing to and sometimes dominating the electrical properties of deformed crystals. The second problem arises from the character of dislocations as extended defects: While a point defect may change its charge state by one or two elementary charges, dislocations act as traps for majority carriers along their line; i.e., they may concentrate a considerable charge along their line. In this section we will first give a short summary of the most elaborate theories on the effects of an electrically charged dislocation on the distribution of the electron states in the band scheme. Plastic deformation of semiconductor crystals introduces deep states into the gap. It has been a major research goal for

303

decades to establish whether these states are due to dislocations and, if the answer is yes, whether they are due to the dislocations themselves or due to their decoration by point defects including impurity atoms. Experiments are aimed at measurements of the carrier density (Hall effect), and the effects of the states as traps (DLTS) and as recombination centers (EBIC). Interpretation of the experimental results requires comparison with theoretical concepts concerning the electrical properties expected for a linear arrangement of deep states. In the following we give a survey of some important models proposed so far. The pioneering work in this field was published in 1954 by Read. At that time, the structure proposed for the dislocation core in diamond-like crystals was as shown in Fig. 6-2. The distance c between neighboring dangling bonds varies between 0.4 nm and infinity depending on the dislocation character. Read ascribed to those sites with unpaired electrons a single acceptor level, i.e., they are neutral when occupied by one electron and negative with two electrons. Dislocations, therefore, are lines of variable negative charge (model I). Since the distance c between chargeable sites is much smaller than the distance between pointlike acceptors in the bulk, the electrostatic interaction between charged sites prevents degrees of high occupation: in practice the ratio between c and the distance a of neighboring charges is of the orderf= clu I0.15. Lattice defects with the peculiar property that the occupation of their chargeable sites is limited by charge interaction are called extended defects (ED). Read calculates the actual occupation f of the dislocation for a given doping (IND-NA)) and temperature from the energy minimum of the system. This approach is exact only at T = 0; at a higher temperature a certain probability for electron hopping along the dislocation must

304

6 Dislocations

be taken into account, and entropy will lead to a minimum of free enthalpy at a nonequidistant arrangement of the charges. Starting from the same structure of the dislocation core Schroter and Labusch (1969) came to a different theoretical approach (model 11). As proposed by Shockley (1953), these authors took the periodical arrangement of equal electron states seriously and proposed a one-dimensional band which is half full (f’= 1/2) when the dislocation is electrically neutral (f=0 in model I). This band can give up ( 0 5 f’< 1/2) or accept electrons (1/2 c f’l1); correspondingly, the dislocation can be positively or negatively charged. In this model, each site carries on an average the same (not necessarily integer) charge (fe) with f= 2 f’- 1. Both electron hopping and completely smeared out charge are possible. Here, treating the charged dislocation as a continuously charged line is obvious. Veth and Lannoo (1984) took a mid-position between the two models: on the one hand, they also assumed each core atom to carry the same noninteger charge ( - p e), where p can be positive or negative. On the other hand, they rejected the continuous charge approximation. Their main goal was a self-consistent calculation of the potential in the vicinity of the dislocation. They point to an intraatomic Coulomb term J and treat screening in the dislocation core as dielectric perturbation (due to polarized bond charges). Outside the core, classical screening by ionized dopant atoms or free carriers takes place. The transition between the two screening mechanisms is analyzed. From this analysis follows a parameter-free formula for the total shift * of the dislocation

* For p=O.1 and 1OI6 ~ 1 1 donors, 3 ~ ~ the contribution of the long-range potential is of the order of 0.35 eV and the contribution of the dielectric perturbation is slightly less than p eV.

level with respect to the edge of the undisturbed valence band

where a is the distance between two core atoms and J is of the order of 10 eV. Veth and Lannoo (1984) stress that this expression is strictly linear with p , which fits the experimental data (Hall effect) better than Read’s model and corresponds to the line charge model by Labusch and Schroter (1980). There are several problems that have to be solved by any model of the charged dislocation core. In both models, the electrostatic potential 1v around a charged dislocation may be calculated using the approximation for a continuously charged line qY(r)=Alnr+-rQ 4E

2

+C

(6-3)

where Q is the space charge around the line. The divergence for r + 0 can be overcome in model I by taking into account in the vicinity ( r I a ) of the dislocation line the discrete nature of the charges (Read, 1954; Langenkamp, 1995). The screening of a charged line by a space charge cylinder of opposite sign (just mentioned) prevents the divergency of the potential for r +00. For T = 0, screening by ionized donors (for negatively charged dislocations) contained in a cylindrical region with a sharp radius R can be assumed [R = (a JT lND-NAl)-”2, where R is the Read radius]. Outside R the potential 91, of the screened dislocation vanishes. Likewise the electrical field E disappears for r 2 R . From these boundary conditions, q!~can be determined as

305


At temperatures above absolute zero, free carriers exist and take part in the screening, and the local carrier density depends on the local potential, so the problem has to be solved self-consistently (Labusch and Schroter, 1980). Another problem is mobility of the charges on the dislocation line. Model I1 assumes delocalization of the charge from the start. In model I, the electrons are fixed at T = 0; at higher temperatures, a certain probability of hopping from one site to the next has to be allowed for. The equilibrium state is then characterized by unequal distances between neighboring charges and is no longer determined by minimizing the energy of the system but by minimizing the free enthalpy (Read, 1954;Figielski, 1990). While Read comes to the conclusion that the minimum energy approximation “may be good over a range of temperature in which experimental measurements could be made and compared with theory”, Figielski (1990) shows that entropy is important, especially for smallf. This author treats the kinetics of capture and emission of charges to the dislocation in the framework of the free enthalpy of the system. Two energies are of importance for any model: first the total electrostatic energy Eel of the system, comprising the charged dislocation plus space charge, and second the energy of a point charge (electron) in the dislocation core. For model I, Read (1954) has calculated Eel per electron

(converted to the Int. Unit System). It is convenient to introduce the parameter f, = c (nlND-NA1)%, so that ( M a ) =

(f/f)3’2.

The electrostatic energy per site

(fE,,)varies roughly asf2. Eel(site) =

e2f

[3 [$1

4JdEgEC 2

In

- 0.8661

(6-6) Labusch and Schroter (1980) in a certain approximation get (screening by free carriers) Eel(site)= -[In e2f2 4nec

]+-I:[

(6-7)

with A Debyes’s screening distance, ro = c/f= a. To show the principle, we calculate for Read’s model the occupation degree f that is reached at T + 0 (the chemical dopants will still be ionized). Let ETbe the local distance of the level of the uncharged dislocation from the valence band at the dislocation and EF the Fermi level. Then the free energy F ( f ) (per electron) that is due to the dislocation is given by

F(f) = E T - E, + E,,(f)

(6-8)

We find the equilibrium value offby minimizing (fF)with respect to f . The result is

= Eof

[

3 In - -0.232

1

(6-9)

with Eo= e2/(4 n E c) the interaction energy of two electrons at adjacent sites. Plotting the right side of Eq. (6-9) against f gives the occupation ratio for a given distance between the Fermi level and the level of the (uncharged) dislocation. The idea is clear: when the dislocation states by band bending reach the Fermi level, any addition of electrons from E F to the dislocation core would enhance the free energy of the

306

6 Dislocations

system. When for n-type material (with increasing temperature) the Fermi level decreases, the equilibrium charge of the dislocation also diminishes. [For T > 0, EF(T) = E,-kT In (C, T3'2/(n))for n-type, where ( ) means averaging over large volumes.] The potential q0of an electron within the chain of electrons along the dislocation can be determined by adding the interaction of the electron with the other electrons and with the positive screening charge (Read, 1954)

-

-e 4JGEoEC

[

f 31n

El 1 -

-1.232 (6-10)

The next step in constructing a model of the charged dislocation concerns the role of (configurational) entropy as soon as the temperature is clearly above zero (as in experiments). Read (1954) states that at T > 0 the nonequidistant arrangement of electrons will bring an increase of the interaction energy as well the appearance of an entropy term AS. Both contributions to free enthalpy at least partly cancel, so that the minimum energy approximation (MEA) (referred to earlier) should be adequate as long as kTis small compared tofEo. Read then deduces a different model which underestimates the free energy - in contrast to MEA. We have no space to follow the discussion further (Read, 1954; Labusch and Schroter, 1980; Figielski, 1990). At a low occupation ratio the entropy plays an important role if a full band is considered. In conclusion we will give a quantitative example: Consider n-type silicon (E = 12) with an effective doping IND-NAI = 10l6~ m - Read's ~. "standard" (60") dislocation is characterized by 0.385 nm between dangling bonds. We assume the dislocation

level ET at 0.23 eV below the edge of the conduction band E,, and the Fermi level EF (at 0 K) at 0.03 eV below E,. Consequently, the dislocation level is shifted in equilibrium by 200 meV upwards. From Eq. (6-9) we calculate the (equilibrium) occupation ratio, f=O. 107. In other words, the distance between two neighboring excess electrons u = 3.6 nm, and the dislocation line charge q L= 4.44 x lo-'' A s m-I. The Read radius R turns out to be 94 nm. The electrostatic energy of the screened dislocation E,, = 80 meV per excess electron. As shown in Fig. 6-9 the shift of the dislocation level with respect to the undisturbed valence band edge is the sum of Eel and the bending of the band edges (-e qlg) at the dislocation line. From this we calculate -eqB=(200-80)meV= 120meV. This value is confirmed by numerically computing (Langenkamp, 1995) the potential qB in the center between two charges within a chain of equidistant point charges: = -e/(4 JG c0 E a ) [In (Rlu)+ 0.2721. The energy e qBindicates the energy bamer that electrons have to overcome on their way to the dislocation in the conduction band. However, the potential q0of an excess electron in the dislocation is -176 mV; this value is smaller than the total energy shift of the dislocation level (200 mV). Read explains the latter difference by a gedanken experiment: Take one electron from a charged dislocation without moving the other electrons. Since the energy of an electron in the dislocation is higher than at r +=, the system looses the energy e q0.If we add the rearrangement of the remaining electrons to equal distances, the energy of the system decreases further. The work released by the combined action is d/df(fE,,)=&-&, i.e., the shift of the dislocation level. Therefore, the latter quantity must exceed e q0.


R

0

vB:

307

R

Figure 6-9. Band bending at a charged dislocation. e band bending and energy barrier; Eel: electrostatic energy of the system consisting of the charged dislocation plus screening charge; EF:Fermi level (after Langenkamp, 1995).

For comparison with experiments, the activation energy AE for lifting an electron from the charged dislocation into the conduction band will be important, and is given by the energetical distance of the conduction band edge E, from the dislocation level ET, both taken at the dislocation. As demonstrated by Fig. 6-9 (6-1 1) (Ec-ET)la = A E (a) = AE (U + CO)- E,,(u) This means that the activation energy depends on the charge of the defect. This statement is equivalent to the following: It is impossible to think of the dislocation level ET and the local band edges as moving rigidly together (“rigid band model”). Touching on experimental examination of the various models proposed so far, we have to first mention extended measurements of the carrier density of deformed germanium and silicon, both n-type and p-type, as a function of temperature using the Hall effect (Schroter, 1967; Schroter and

Labusch, 1969; Weberet al., 1968; Labusch and Schettler, 1972; Labusch and Schroter, 1980). From the Hall effect, the carrier density n ( T )or p ( T ) can be determined. Comparing crystals before and after deformation, the change of the carrier density can be measured, which is assumed here to be due to dislocations. If the dislocation density N is known, the average occupation ratio f can be calculated. [Problems that arise due to the influence of point defects and impurities, as well as concerning measurements of N , are discussed by Labusch and Schroter (1980).] The strongest argument in favor of model I1 (half-full band at the neutral dislocation) is delivered by measurements of p-type material. In model I, the dislocation can only accept electrons, whereas model I1 looks at the dislocation as an amphoteric center: f can be both positive and negative. Because of this difference, main efforts has been directed at p-type germanium. Lowdoped material with a relatively small dis-

308

6 Dislocations

location density is used. Qualitative observation shows the hole density p of deformed crystals to decrease over the exhaustion range (p = const) of the undeformed crystal. At high temperature, ( ~ 2 0 0 K) Pdef>Pu&f; Pdef decreases to a low temperature and crosses the value Pu&f at a certain temperature To. Obviously here the dislocations are neutral ( f = 0). The position of the Fermi level at Tocoincides with the dislocation level ET of the neutral dislocation. For germanium, ET was found 0.09 eV above the valence band. Further details can be found in Labusch and Schroter (1980). In summary, model I1 was proven to be much better at describing experimental results than model I. In spite of this success, it must be held in mind that the structural model of the dislocation core taken as the basis of all theories described above has several weaknesses. Some of them are trivial, some came to light after the “golden age” of these theories. It is well known that there is no way to introduce dislocations all belonging to the same type into a crystal. So a whole spectrum of densities of chargeable sites has to be expected. More important is dislocation splitting: TEM shows that practically all dislocations in (elemental) semiconductors are dissociated into two parallel partial dislocations with a stacking fault* in between. Most importantly: Theory and experiment suggest that most of the topological dangling bonds are reconstructed forming covalent bonds without deep states in the gap. It is highly probable that dislocations (additionally to shallow bands) contain deep states, but these are not periodically arranged along the (partial) dislocations. Rather they belong to localized secondary

* It is possible that the stacking fault also carries states in the gap.

defects (reconstruction defects, kinks, vacancies, etc.), of which apparently many more types are conceivable than hitherto known (Bulatov et al., 1995). Another effect which would obscure results is the inhomogeneity of effective doping arising from the inhomogeneous production of (electrically active) point defects by plastic deformation (Kisielowski et a]., 1991). So future research on the theoretical side will be directed to ab initio calculations of defect models revealing the presence and position of deep states (Csinyi et al., 1998), and on the experimental side to local tests of single dislocations, e.g., by EBIC (Kittler and Seifert, 1993b). The next section will show what information on the existence of unpaired electrons (and their surroundings) comes from electromagnetic paramagnetic spin resonance (EPR). After that, in Sec. 6.3.2 we will go on to discuss some of the modern electrical measurements of plastically deformed semiconductors (DLTS, EBIC).

6.3.1 Electron Paramagnetic Resonance (EPR) Spectroscopy of Plastically Deformed Silicon Where EPR spectroscopy is applicable, it yields more information on the defect under investigation than any other experimental method, because it reveals the symmetry of the defect. Via hyperfine structure (HFS) of the spectrum it also provides a hint as to the chemical species of atoms involved. Moreover, EPR spectroscopy can be calibrated to give numbers of defects. Admittedly, EPR concerns only paramagnetic centers; this means that there may be electrically active defects not detectable by EPR. Other defects will be traced only in a certain charge state. The charge state may reveal something about the position of the defect in the energy gap by observing EPR


spectra under illumination and of doped crystals. Fortunately, silicon is one of the most suitable substances for EPR. Thus we will begin with a summary of what is known about the EPR of plastically deformed silicon crystals (Kisielowski-Kemmerich and Alexander, 1988). So-called standard deformation by single slip (T = 650°C t = 30 MPa, Al/Z = 5%) resulting in a dislocation density N = 3 x lo9 cm-* produces about 10l6cm-3 paramagnetic centers. The majority (65-80%) are point defect clusters of high thermal stability. The remaining defects are related to the dislocation geometry by their anisotropy. A clear distinction between the two classes of defects can be made by several methods: (a) As mentioned before, the dislocation-related defects show anisotropy with respect to the (total) Burgers vector of

I

900

604

V, Voand

f

V vth

XI XI1

x, y, z

Z

CY

Y9 Yo

&

Ex, &y5

e, e,, eB el

P Y

e e

0 0X.y

.z t

t @B

AY, Az b.c.c. BV CBED CSL CVD dcc dCP DIGM DLTS DSC

vectors measuring the length of a SU respectively in crystals I and I1 displacement of the CSL in grains I and I1 time a vector of the DSC lattice temperature melting temperature a vector of lattice I zone axis indices crystal symmetry operator voltages GB velocity thermal velocity coordinate vector of a lattice point of crystal I expressed in lattice I base coordinate vector of a lattice point of crystal I1 expressed in lattice I axes. y z is the GB plane mean atomic number inverse of a power of two (generally 1 or W) GB energy per unit of interface area and energy coefficient dielectric constant integers equal to -1, 0 or 1 rotation angles natural rotation in the SU-dislocation analysis shear modulus Poisson's ratio rotation axis modulus of the rotation axis vector conductivity shear component coincidence index; surface energy rigid body translation relaxation time activation energy relaxation parameters body-centered cubic Burgers vector convergent beam electron diffraction coincidence site lattice chemical vapor deposition dichromatic complex dichromatic pattern diffusion-induced grain boundary migration deep level transient spectroscopy displacement shift complete or displacement symmetry consensing


EBIC EELS ELNES ESR f.c.c. FIM FS/RH GB GBD HREM IBIC IDB LBIC LCAO RBT STEBIC STEM STM

su

TDB TEM

Tm

UHV

electron beam induced current electron energy loss spectroscopy energy loss near edge spectroscopy electron spin resonance face-centered cubic field ion microscopy final stadright hand grain boundary grain boundary dislocation high resolution electron microscopy ion beam induced current inversion domain boundary light beam induced current linear combination of atomic orbitals rigid body translation scanning transmission electron beam induced current scanning transmission electron microscope scanning tunneling microscopy structural unit translation domain boundary transmission electron microscopy thin-film transistor ultrahigh vacuum

381

382

7 Grain Boundaries in Semiconductors

7.1 Introduction Grain boundaries (GBs), which are interfaces between two crystals that differ only by their orientation, are almost always present in natural crystalline materials. They can greatly influence the properties (mechanical, electrical conductivity, optical emission, etc.) of the material in which they lie. Consequently, most of the semiconductor industries have initially tried to avoid them, and worked either with single crystals elaborated by techniques such as Czochralski growth, fusion zone, etc., or with monocrystalline thin films of low defect density. However, such crystals or layers are expensive and it turned out that polycrystalline materials could also play an important role in the semiconductor industry, either due to their low cost (as in solar cells) or due to their specific properties (for instance, the preferential diffusion and doping in polycrystalline regions of transistors), or because of the impossibility to do something else (in diamond thin films). It is forecast that in future years the production of polycrystalline silicon could be as high as the production of monocrystalline silicon. Thus silicon polycrystals were an important material to study but it turned out that they contain a lot of impurities. Consequently, the academic studies on semiconductor grain boundaries really started in the 1980s with the elaboration of pure silicon or germanium bicrystals (essential tilt GBs) and the use of electron microscopy. Beside important topics such impurity segregation and deformation, the big academic issues were: Is the interface amorphous or crystalline? Is the grain boundary itself electrically active? As we will see, clear answers have been given to these questions for high coincidence tilt GBs in silicon. However, new studies on twist GBs or nanocrystals have argued whether these conclusions could be extended to “general GBs”.

In this chapter, we will focus on academic studies of GBs in semiconductors. The chapter has five main parts. Sections 7.2 and 7.3 cover the GB structure, Secs. 7.4, 7.5, and 7.6 deal with the electrical activity, the impurities, and the mechanical deformation of semiconductor GBs, respectively. Section 7.2 is devoted to the different theories or tools that can be used to analyze or determine the GB structure. Thus after some definitions, we introduce some geometrical tools, which are based essentially on the symmetry relationship between two lattices of the same material. These tools are powerful means to describe periodical interfaces, symmetry breaks, and defects associated within GBs, although they provide no information about stress fields or atomic positions. Then, the description of a GB in terms of dislocations is presented. This was the first approach to ascertain the stress fields around a GB, and the application of elastic theory was of great help in explaining a lot of GB behavior (migration, interaction of GBs with other defects). However, this elastic approach does not work for high-angle GBs. We follow this with a description of GBs in terms of structural units, which are based on atomistic structures, but can be related to dislocations. This approach allows the construction of many atomic models of a given GB and can predict, through the principle of continuity, the most probable structure. It can be applied to any low or high angle GBs. Then there is a quick presentation of the numerical and experimental tools that have been used in the study of GB structures. Atomistic computer simulations have become one of the most powerful tools to analyze both the GB atomistic and electronic structures. High resolution electron microscopy (HREM) has been the major experimental tool to study the atomic structure of GBs, but new possibilities have emerged with the advent

7.2 Grain Boundary Structure: Concepts and Tools

of scanning tunneling microscopy (STM), atom probe field ion microscopy (FIM), and EELS (electron energy-loss spectrosCOPY1. Section 7.3 onwards summarizes the experimental and simulation results obtained on different GB atomic structures in different semiconductors. Each semiconductor is treated in turn. Silicon has been studied the most. Recently, new studies on silicon have emerged with the possibility to form nanocrystals or develop wafer bonding (which stimulates twist GB studies). But GBs in other semiconductors such as ionic semiconductors (NiO) or wide band semiconductors (diamond, silicon carbide and to a lesser extent GaN and A1N) have appeared. The last few years have seen an increase of GB simulations. Whereas for years in metals most GB simulations were calculated with only a few experimental HREM results being available for comparison, the reverse situation was true for tilt GBs in elemental semiconductors. However, simulations have again taken the lead as far as twist GBs and nanocrystals are concerned. This part of the chapter ends with a discussion on the validity and generalization of all these results. Section 7.4 onwards is devoted to the electrical properties of GBs in semiconductors. These GBs may drastically affect the electronic response of semiconductor materials, and special attention is put on additional defects or impurities segregated at the GB, since these are the most likely origin of GB electrical activity. Section 7.5 onwards is devoted to new results available on the segregation occurring at GBs, and Sec. 7.6 onwards describes the deformation of crystals containing GBs and the subsequent GB modifications. The strong interaction between point and linear defects is shown to have a major influence on the behavior of GBs. Emphasis is placed

383

on some of the consequences of these events, such as GB migration, enhanced diffusion along migrated GBs, and GB recovery and cavitation. It should be pointed out that at the end of this chapter several general references are provided to which the reader is invited to refer for completeness. They provide an overview of GBs in materials in general and in semiconductors in particular.

7.2 Grain Boundary Structure: Concepts and Tools Grain boundaries (GBs) can be studied for their specific properties in diffusion, impurity absorption, deformation, and electronic properties. But a thorough analysis starts with a full description of the defect itself its definition and its structure. So in this section, after some basic definitions, we present different concepts or tools, both theoretical and experimental ones which can be used to analyze the GB’s structure. The theoretical concepts are separated into three types: the geometrical concepts, the dislocation model, and the structural unit descriptions. Historically, these different approaches have been developed to describe GBs, and predict or understand some of their properties. However, we will see that there is a strong correlation between these approaches (for instance, the structural unit model with the dislocation approach, and the simulations with the 0-lattice and the dislocation content). All of them bring specific information on the GB structure, and they are in fact greatly correlated and complementary. This part ends with sections recalling the simulation techniques and the experimental tools that have been used to study the GB’s structure.

384


7.2.1 Grain Boundary Definitions

A grain boundary is a two-dimensional defect that separates two disoriented grains of the same crystalline material (see Fig. 7-1). These two grains can be related by an affine transformation (G, Z), where G is a punctual operation and z is a rigid body translation (RBT). Thus each lattice point of crystal 11, whose coordinate vector in lattice I base is XI,, is the image of a lattice point of crystal I (XI) X,,=GX,+Z

(7- 1)

This affine transformation is not unique. In symmorphic material (with neither glide nor screw operation), G can be chosen to be a proper rotation, which we will designate R in this chapter. In nonsymmorphic material, G can be broken down into the product of a proper rotation and an inversion (Znt. Tables of Crystallography, 1983). When the punctual operation can be reduced to the identity operation, these defects have been called stacking faults or antiphase

Figure 7-1. Scheme illustrating the creation of a grain boundary (GB). The GB plane is gray. The two dotted parallelograms are references for, respectively, the front face of crystal I1 and for the interface; they make it possible to visualize the nine parameters that define the GB. Crystal I1 is deduced from crystal I by a rotation R (determined by its rotation axis e and its angle 6 :3 parameters) followed by a translation r (3 parameters). The planar interface is defined by its normal n ( 2 parameters) and its location h along its normal (1 parameter).

domain boundaries or stacking mismatch boundaries depending on their atomic structure or on their origin. They should be better designated under the generic term translation domain boundaries (TDBs) (Rouvikre et al., 1997), as the only operation linking the two crystals is a translation. Generally, these TDBs are not considered as “real” GBs, perhaps because some of them can be obtained in a unique grain by the dissociation of a dislocation. Thus we will not consider them in this chapter. When the simplest punctual operation relating the two crystals is an inversion operation, the defect is designated as an inversion domain boundary (IDB). In that case, two grains exist and IDB must be considered as a special type of GB . Depending on the geometry of the interface, a GB can be flat, faceted, or curved, although it must be noted that these latter characteristics generally depend on the scale of observation. In this chapter, we will consider only flat GBs. Thus, in addition to the affine transformation, a flat grain boundary is defined if the normal n of the boundary (n points from crystal I to crystal 11: throughout the paper, crystal I is the reference lattice) and the location h along n of its interface are known (Fig. 7.1). Thus there are nine parameters to describe a GB. Five parameters may be varied independent of the others and define the macroscopic degrees of freedom (Rand n). The four other ones (t,h ) are called the microscopic parameters, because they are determined by relaxation processes and are thus a function of the macroscopic ones if we assume that there is only one energy minima for a given set of macroscopic parameters. When n is perpendicular to the rotation axis, the GB is called a tilt GB, whereas if n is parallel to the rotation axis, it is called a twist GB. Mixed GBs have both a tilt and a twist component.


385

A symmetrical GB has its interface in a symmetrical position with respect to both grains, that is to say, if the interface normal n is equal to the vector [ k , , k,, k,], in grain I, it will be represented by a vector ( k , , k Z , k,),, in grain 11.

volumes of the unit cell of the CSL and of the crystal lattice. In other words, considering one of the two original lattices, l/.Z'represents the density of lattice sites that are coincident to both lattices. In the following, a symmetrical GB will be denoted in the form

7.2.2 Geometrical Concepts

(h k l ) ( u uw)Z=N

The several important geometric concepts presented in this part can be put into three categories. Some, like the coincidence site lattice or the coincidence index, determine the type of disorientation between the two grains and can be regarded as an extra set of definitions for the GB. Some, like the 0-lattice, will be useful in the description of the GB in terms of dislocations. Some define the symmetry of a bicrystal and are useful in determining all the possible variants of a GB and analyzing the appearance of GB defects arising from a break in the different levels of symmetry. Of course, all these geometrical concepts say nothing about the atomic local relaxations at the interface or about the energy of the GBs. The coincidence site lattice (CSL) is the intersection of the lattices of the two adjoining crystals. Friedel (1926) first introduced this concept in order to describe twins. Brandon et al. (1 964) confirmed the validity of the CSL idea with the use of field ion microscopy. This approach was first applied to cubic lattices and then extended to nonexact coincidence positions and to noncubic structures in which the dimension of the common lattice might be reduced, leading to a 1 D, 2 D, or 3 D CSL. If lattice vectors are considered, there is no problem of origin. However, if lattice points are considered, the origins of the two lattices should be common. For some rotations R a threedimensional CSL exists and it can be described by an integer called the coincidence index Z,which is defined as the ratio of the

where N is the Zvalue (integer), 8 = (u v w) represents the rotation axis of the proper rotation R and ( h k I ) refers to the GB plane, both expressed in crystal I. In the case of an asymmetrical GB, the coordinates of the GB plane in crystal I and crystal I1 will be given. In the cubic system, Z is always an odd integer and Ranganathan (1966) showed that the Zvalue, the rotation axis Q = (u u w) and the rotation angle 6 are linked by the following formulas

(7-2)

e

cot-=- k1 Z = a ( k : + k z 2 k2 @

Q2)

(7-3)

@=I QI

= d m , and a is the inverse of a power of two (generally 1 or 0.5) calculated such that Z is odd. Equations (7-3) entirely determine the rotation matrix R . In a base where the third basis vector is parallel to 0 , the matrix R is given by where k , , k2 are prime integers,

R=

1

k:

(7-4)

+ k z p2 k f - k ; p2 - 2 k l k 2 p 0

k f + k$ p2

Tables giving the coincidence indexes, the CSLs, and the associated rotations of GBs in cubic systems have been established by Grimmer et al. (1974), and by Mykura (1980). Bleris et al. (1982) studied hexagonal systems and generated tables where the

386


c/u ratio was taken into account, and proposed a method to determine the exact relationship experimentally (Bleris et al., 1981). A complete treatment of CSLs in hexagonal materials has been given by Grimmer (1989), and this was extended to rhombohedral and tetragonal lattices by Grimmer and Bonnet (1990). For some families of symmetrical tilt GBs in the diamond structure, GBs have been described by a set of two signed prime integers ( k , , k2), which verifies Eqs. (7-3) and (7-4) (Moller, 1982; Koyhama, 1987; Rouvikre and Bourret, 1990a).Here we adopt what we think is the simplest convention. To every prime integer ( k , ,k2), we associate a unique symmetrical tilt GB (where Q is the rotation axis) whose normal in lattice I is [ w k , , wk2, - u k l - v k 2 ] , . For the [0, 0, 11 and [0, 1, 11 tilt GBs, this formula reduces to [ k , , k,, 01, and [ k , , k2, -k2],, respectively. This formulation synthesizes all the behavior of a series of GBs in a few formulas and, as we will see, helps in determining all the different types of GBs in a given series. Moreover, it shows that, for a given rotation axis, the macroscopic degrees of freedom of a high-coincidence symmetrical tilt GB are reduced from five to two parameters k , and k2.

For the asymmetrical GBs, Paidar (1992) developed a systematic geometrical classification depending on the disorientation angle and the inclination of the GB plane. Bollmann (1 970) introduced several important lattice definitions which are very useful when the GB is analyzed in terms of dislocations. The 0-lattice, which is an extension of the CSL, is the set of points - and not only lattice points - that have an equivalent position in the two crystals. The O-elements are given as a solution of the basic equation

( 1 4 r 1 )rO=tl

(7-5)

where t, describes all the possible translation vectors of lattice I and I is the identity. Here, this equation defines the 0-lattice. It can also be used to define the dislocation content of a GB. Bollmann developed this approach for a general interface, where 0elements can be points, lines, or planes. In the simple case of a GB described by rotation (we neglect here the case of noncentrosymmetric crystals), the 0-elements exist for any disorientation angle 8,even when no CSL exists and they are lines parallel to the rotation axis. In the case of a cubic crystal, the 2D lattice of these 0-lines in the plane normal to Q can be simply determined by applying Eqs. (7-4) and (7-5) (Bollmann, 1970; Christian, 1981). The 0-elements can be considered as regions of good fit between the two adjoining lattices. These 0-element regions are separated by cell walls whose intersections with the GB plane represent the dislocation lines of the primary dislocation network [this is the b-net introduced by Bollmann (1970)l. For high-angle boundaries (characterized by a rotation R), with a small deviation from an exact coincidence position (characterized by a rotation R,), Bollmann (1970) also introduced the DSClattice and the 02-lattice. The DSC-lattice is obtained by considering all the linear combinations of the vectors belonging to the two lattices I and 11. The original meaning of the DSC acronym, which is Displacement Shift Complete, is not straightforward. As pointed out by Pond and Bollmann (1979), it should be replaced by Displacement Symmetry Conserving, as any translation of lattice I by any vector of the DSC-lattice conserves the original CSL-lattice. Originally, the 02-lattice acronym, which means second order 0-lattice, was defined as the 0lattice between the two 0-lattices (and not between the two crystal lattices) obtained by using Eq. (7-5) once with R (0-lattice of the studied GB) and once with R, (0-lattice of


the reference high coincidence GB near the studied GB). However, the 02-lattice can also be defined as the 0-lattice between the two DSC-lattices associated respectively with the rotations R, and R , which we respectively designate DSC, and DSC. To obtain the equation verified by the 02-elements, it is then only necessary to determine the rotation matrix 6R linking the DSC, to the DSC (6R = R R;’) and apply Eq. (7-5). The 02-elements are thus the solutions of the equation

(Z-6R-l) ro2=(Z-R,R-’) r o 2 = t D S C

(7-6)

where tDsc describes all the vectors of the DSC lattice. We will see in Secs. 7.2.3.2 and 7.2.4.3 that Eq. (7-6) is useful to analyze the secondary dislocations. Grimmer and Bonnet (1990) applied the DSC approach in their treatment of rhombohedra1 and tetragonal materials. Pond and Bollmann (1979) introduced the concept of the dichromatic pattern (dcp), which is constructed using two interpenetrating lattices, ignoring any interfacial planes. The term dichromatic refers to the black and white dots conferred on the two lattices. The most symmetrical pattern is called the precursor (Fig. 7-2 a). Any modification induced by the introduction of firstly an interface and secondly an interfacial defect leads at each step to a loss of symmetry elements, and consequently to the creation of crystallographic equivalent variants related by the lost symmetry operations. These variants may be found along the same interface. GB dislocations separating such energetically degenerated variants have been observed by Pond and Smith (1976) and Bacmann et al. (1981) in 2 = 5 and Z = 2 5 germanium bicrystals. The Burgers vector of these dislocations does not belong to the DSC lattice and as such is called a partial DSC dislocation.

387

Using group theory, these concepts have been extended to crystal coincidence by Gratias and Portier (1982) and Kalonji and Cahn (1982). In addition, these authors showed that symmetry constraints might explain some interfacial properties, such as the morphology of a crystal growing (during precipitation or solidification) in a crystalline environment. Pond (1989) reformulated this notion and introduced the dichromatic complex (dcc) which is the superposition of the two crystals with all their atoms (Fig. 7-2b). This allowed him to propose a unified description of all possible bulk and interfacial defects arising from the symmetry break of the bicrystal complex. A real bicrystallography has been defined to describe all the symmetries of an interface. Sagalowicz and Clark (1995, 1996) applied this bicrystallography to determine all the Burgers vectors that can be found in a Z=13 GB.

a

b

Figure 7-2. Projection on the (001) plane of a) dichromatic pattern (dcp) and b) the dichromatic complex (dcc) corresponding to [Ool] 2 = 5 GB in a cubic diamond crystal. Circles refer to lattice sites of crystal I (black circles) and crystal I1 (white circles). Large circles are at the 0 level, and the small circles are at the %_ level along the [OOl] axis. Squares refer to the additional atomic sites of the lattice. Large squares are at level !4 and small circles are at level %. The two interpenetrating f.c.c. lattices make up the dcp which has a space group ( I 4lm m’m’) where “”’ denotes an antisymmetry element, i.e., a change in color. The two interpenetrating cubic diamond crystals make up the dcc which has a ( I 4,lam’d’) space group. White and black dots refer to lattice sites I and 11, respectively. The square dots refer to the additional crystal sites.

388


7.2.3 Dislocation Model Historically, the modeling of interfacial structure in terms of dislocations was developed before the geometrical concepts (Burgers, 1940; Bragg, 1940; Read and Shockley, 1950, 1952). The first experimental evidence of the validity of the dislocation model was given by Vogel et al. (1953). They were able to correlate the spacings of etch pits in low angle germanium GBs with the spacings of dislocations predicted by the Burgers model from the measured misorientations between the grains. The most direct evidence for the presence of dislocations in GBs came with the first observations by TEM of dislocations in aluminum (Hirsch et al., 1956). The complete treatment was reviewed by Christian (198l), Forwood and Clarebrough (1991), and Sutton and Balluffi (1995).

7.2.3.1 Primary Dislocation Network Frank (1950) was the first to develop a theory that provides the dislocation density of a general GB. The demonstration was realized by making a Burgers circuit using the FS/RH (final start/right hand) convention with the closure failure being done in good crystal (Hirth and Lothe, 1968). Bilby et al. (1955) extended the formula to heterophase boundaries and demonstrated it using the concept of a continuous 2D distribution of dislocations at the interface. This concept of a continuous distribution of dislocations was independently defined in the 3D-case by Kroner (198 1, which is an updated English version of a 1958 paper). We give here the Frank-Bilby formula reformulated in matrix notation by Christian (198 1). The total Burgers vector S of the dislocations cut by an arbitrary vectorp of the GB is given by S=(Rf'-R,')p

=pI-pII

(7-7)

where R, and RII are the rotation matrices defining the orientation of the crystals I and I1 with respect to a reference lattice (where all the vectors and matrixes are expressed). S can be considered as the difference between the same vector p expressed once in the crystal I lattice base (pI) and once in the crystal I1 lattice base (pI1).If one of the two crystals, crystal I for instance, is chosen as the reference lattice, R, and RIIbecome respectively the identity Z and the matrix rotation R, and Eq. (7-7) simplifies to

S = (Z-R-') pI

(7-8)

If p is now considered as an O-lattice element, this equation is identical to Eq. (7-5): S is consequently a lattice vector, which is always the case for a Burgers vector of a perfect dislocation. Thus Eq. (7-8) corresponds to the O-lattice treatment presented in Sec. 7.2.2: regions of best fit (O-elements) are separated by regions of worst fit, whose dislocation content is given by Eq. (7-8). This dislocation distribution is called the primary dislocation network, because the reference is a perfect lattice crystal. If the reference lattice is taken to be the median lattice, which is obtained from lattice I (respectively, 11) by a rotation Ron of axis Q and angle 8/2 (respectively, R-e,z), Eq. (7-7) simplifies to the original Frank's formula

e e ~p S = 2sin -2 lel

(7-9)

Equation (7.9) is particularly interesting when p is a vector perpendicular to the rotation axis. In this case, the modulus of Eq. (7-9) gives

e 1p I I S I= 2 sin 2

(7-10)

Equations (7-7), (7-8), (7-9), and (7-10) are geometrically valid for any kind of GB, but


their physical meanings were more satisfactory in the case of low angle GBs. Indeed, in the case of low-angle GBs, these formulas give a low density of dislocations. Dislocation cores do not overlap: individual dislocations can be clearly defined and, as we will see in the next part, the elastic theory can be simply applied to determine the stress field and Eq. (7-10) can be approxiI = 8. mated by 1 S J l ( p However, in the case of high-angle GBs, as we will see in Sec. 7.2.4.3, these formulas can be very useful to determine the number of SU-dislocations that can be assembled in a GB model. One of the difficulties with these Frank-Bilby/O-lattice descriptions is that the relationship R between the crystal lattices is not unique: any operator U of the original crystal face group gives a new relationship U- ‘RU, which gives a different dislocation content. In practice, the relationship R is chosen in order to reproduce the experimental data. Rouvi2re and Bourret (1990a) found that the rotation R leading to a minimum b2 value, where b is the total Burgers vector associated with a GB period, reproduced well the experimental observations of [OOl] tilt GBs.

7.2.3.2 Secondary Dislocation Network In high angle GBs, it is sometimes more interesting to consider the GB (rotation R ) as a deviation from a reference high coincidence GB (rotation R,). In this case, the reference lattice is not the perfect lattice crystal, but a lattice reflecting all the translations of the high-coincidence bicrystal, that is, the DSC-lattice of the high coincidence GB, which is denoted DSC, in Sec. 7.2.2. Bollmann (1970) showed that this deviation can be accommodated by aperiodic network of dislocations, which are called sec-

389

ondary dislocations, and whose distribution is superimposed on the coincident GB. Similarly to the primary dislocation case, the secondary dislocations are located in-between the 02-elements, which are determined from Eq. (7-6). The density of the secondary dislocations is also deduced from Eq. (7-6) by substitution of the period p of the GB in place of ro2:the obtained Burgers vector b, of the secondary dislocations is thus a DSC, vector. As the disorientation 66 (associated with 6R) is small, Eq. (7-10) (with 68instead of 8)can be used to estimate b,. The Burgers vector of these dislocations can also be determined by “circuit mapping’’, as defined by Pond ( 1 989). A closed circuit is realized in the GB and is repeated in the DSC, lattice: the closure failure gives the Burgers vector. Thibault et al. (1994b) applied this method directly on HREM images and characterized the primary and secondary dislocation content of any part of a GB . Generally, these secondary grain boundary dislocations (GBDs) are linked to the GB and cannot move in one or the other adjoining grain. In addition, they are generally, but not necessarily, associated with a GB step. The height h of the step associated with one particular GBD is geometrically determined by the CSL. Determination of the Burgers vector can be done in a conventional manner using the two beams extinction condition in a TEM. If the dislocation density is too high or if the Burgers vector is too small, this method is not very sensitive. If HREM is applicable, the projection on the observation plane of the Burgers vector can be extracted and the perpendicular component can be obtained by symmetry considerations. An example of such a determination (Fig. 7-3) directly on an HREM image of a DSC dislocation in (122) (01 l)Z=9 is shown

390


Figure 7-3.Determination of the (b, h ) pair directly from an HREM micrograph. The case presented here is the one of a GBD in (122) (001)2=9. s,= 112 [OI 111 and s2=1/4 [211II1;s2 is the projection of 1/2 [110II1 or 1/2 [IOl],, and b = s , - s , can be expressed simply in grain I as 1/6 [121], or 1/6 [112],. h is the projection on the GB normal of (sl +s2)/2 and is equal to the absolute value of 1/9 [ 1221, = a/3 (El Kajbaji and Thibault-Desseaux, 1988).

in El Kajbaji and Thibault-Desseaux (1988). The (b, h ) pair is determined using the method given by King and Smith (1980) in the following way: If s1 and s2 are the displacements of the CSL due to the GB defect (b, h) respectively in grain I and grain 11, then b is given by the difference between s1 and s2 and h is the projection parallel to the GB plane of the half sum of s1 ands2.

7.2.3.3 Stress Field Associated with Grain Boundaries Predicting the stress field of a GB is of prime importance, because the stress field can induce the attraction of impurities or lattice defects (point or linear defects) to the GB.

A general expression for the stress field of a low angle periodic tilt GB in an isotropic material was published by Hirth and Lothe in 1968 [Hirth and Lothe (1982) is the new edition of this book]. The elastic stress field is calculated by adding the stress field of each individual dislocation of Burger vector b separated by a distance D. It is found that, with increasing distance x perpendicular to the GB, the stress field decays exponentially to zero over a distance comparable to the period D of the dislocation array. That is, contrary to an isolated dislocation, there are no long-range stresses in a periodic array of edge dislocations with b perpendicular to the GB. For instance, we give, respectively inEq. (7-1 1) and(7-12), theexof an pressions of the shear component ax.?, edge dislocation array (for regions where x %0/2 n) and of a single edge dislocation. The other stress components behave similarly. As usual in this section, yz is the GB plane and the dislocation lines are along z. The p and vare, respectively, the shear modulus and the Poisson's ratio.

oxy

3

Pb

a.

(1 - v) D D

(

'exp --2 y ) c o s ( % )

axy=

pb

x(x2-y2)

2n(1- v) (x2+y2)

(7-11) (7-12)

From these two equations, it can then be seen that at a distance x = D (y=O), the stress field of the periodic GB dislocations is 0.07 times the stress field of the corresponding isolated dislocation. Near the GB (x 1 cm-* s-l) will require an activation energy of the order of 5 eV or less at a temperature of 600 "C. The energetics of nucleation of complete dislocation loops within a layer, or half loops at the free surface, has been discussed by a number of authors [e.g., Eaglesham et al. (1989), Fitzgerald et al. (1989), Hull and Bean (1989a), Kamat and Hirth (1990), Matthews et al. (1976), Perovic and Houghton (1992)l. The latter case of surface nucleation is generally expected to dominate due to the lower line length (and hence self energy) of a half versus a full loop. The total system energy is calculated by balancing the dislocation self energy with strain energy relaxed and the energy of surface steps created or destroyed as a function of the loop radius R (8-18a) =AR lnR-BR2ACR

(8-I8 b)

Here, A, B and C are compound elastic and geometrical constants. The dislocation self-energy, EIoop,varies as R 1nR and dominates at low R, while the strain energy revaries as R2 and thus dominalaxed, Estrain, tes at high R. As illustrated in Fig. 8-3 1, the passes through a total system energy, Etotal, maximum, 6E, at a critical loop radius R, and then monotonically decreases. The quantity 6E thus represents an activation barrier to loop nucleation, and depending upon the elastic constants of the particular system under consideration, is typically very high (tens to hundreds of electron Volts) for strains c 0.01. It becomes physically plausible as a surmountable barrier at typical crystal growth temperatures for strains of the order of 2% or greater. Thus, homogeneous surface half loop nucleation can act as a very efficient source in systems with high lattice mismatch, but will not operate at lower mismatches. The final generic class of dislocation nucleation source to consider is heterogeneous sources. These dominate in the low mismatch regime, where homogeneous nuclea-

c

400

-600;

a* 2 X* 0.3

\

100

R

tk

200

\

300

Figure 8-31. Illustration of the energy of a glide dislocation half loop nucleating at a step on a free surface in a Ge,,,Si,,,/Si (100) heterostructure vs. the loop radius R. The total loop energy passes through a maximum, 6 E , at a critical loop radius, R,.

8.4 Interfaces Between Lattice-Mismatched, lsostructural Systems

tion cannot operate. Heterogeneous sources are also required to generate the necessary background dislocation density to allow dislocation interactions to occur and therefore to fuel multiplication sources. They occur as a result of local stress/strain fields at growth nonuniformities such as particulates, residual substrate surface contamination, precipitates, stacking faults, etc. The density of such sources is relatively low for high quality heteroepitaxy (say in the range lo2- lo4 cm-*), although each source could produce a number of dislocations. This paucity of available nucleation sites at low strain is the primary reason for large metastable regions of strained growth often observed at low lattice mismatches [e.g., in the GexSi,,/Si(lOO) system, Fig. 8-29]. In Fig. 8-32, we summarize the expected regimes in which the three different generic nucleation mechanisms (i.e., heterogeneous, homogeneous, and nucleation) will dominate as functions of strain and epilayer thickness in a lattice-mismatched heteroepitaxial system.

t pvonel

Figure 8-32. Schematic illustrations of the regimes in which heterogeneous nucleation, homogeneous nucleation, and multiplication are expected to dominate as functions of epilayer strain, E , and thickness, h, in a lattice-mismatched heteroepitaxial system.

497

8.4.3.3 Propagation of Misfit Dislocations Propagation measurements of misfit dislocations in bulk semiconductors have been well documented by several authors (e.g., Alexander, 1986; George and Rabier, 1987; Imai and Sumino, 1983), and form the basic framework for propagation velocity measurements in strained layer epitaxial systems. The usual expression for dislocation glide velocities in semiconductors is of the form (8-19) Here v, is an experimentally determined prefactor and E, is the glide activation energy. E, is high for semiconductors compared to metals, e.g., E,=2.2 eV in bulk silicon and 1.6 eV in bulk germanium at moderate stresses (Alexander, 1986; George and Rabier, 1987; Imai and Sumino, 1983). This is due to the high interatomic barriers in fully or partially covalently bonded semiconductors. The form of Eq. (8-19) also applies well to measurements of dislocation velocities in strained layer semiconductors. The most widely studied system for these measurements has been the Ge,Si,,/Si (100) system (Houghton, 1991; Hull et al., 1991 a; Hull and Bean, 1993; Tuppen and Gibbings, 1990; Nix et al., 1990; Yamashita et al., 1993). A compilation of these measurements from several groups is presented in Fig. 8-33. Note that all of these measurements are recorded from post-growth annealing of metastably strained structures, either by in situ TEM observations (Hull et al., 1991; Hull and Bean, 1993; Nix et al., 1990) or by defect-revealing etching (Houghton, 1991; Tuppen and Gibbings, 1990; Yamashita et al., 1993). The sets of measurements in Fig. 8-33 agree relatively

498

8 Interfaces

-

cap

..*.. uncap

m

loll '0l"bl

-41

.

** 102 Qex

103

I

104

well with each other. Even the relatively small range of variation that exists at a given a,, is probably not due primarily to experimental uncertainty, but rather to factors other than aex(primarily the compositional dependence of the activation energy in Ge,Si,,) contributing to the dislocation velocity. In Fig. 8-34, we show the normalization of velocity measurements made at different temperatures, compositions, and excess stresses in the GexSil,/Si( 100) system (Hull and Bean, 1993) according to the relation (Jex

0.6 x (eV) kT

. [.- (7.8k1.4)e

y*=ygO.C(aVYLT

8

9

10

1

l/kT (J-lxlO19)

(ma)

Figure 8-33. Comparison of misfit dislocation velocities measured by different groups in the Ge,Si,,/ Si (100) system normalized to equivalent velocities at 550°C.

L = e

-43-4s7

(8-20) - (2.03f0.10eV k~ 'lm2skg-l

Note again that the dislocation velocity dramatically decreases with decreasing germanium concentration, further enhancing the metastable regime at low strains in Fig. 8-29. Hull and co-workers (Hull and Bean, 1993; Hull et al., 1994) have also extended the measurements of Eq. (8-20) to dislocation velocities in GexSi,,/Ge (100) and GexSil,/Si(llO) systems. Recently, dislocation velocity observations have been made during the epitaxial

Figure 8.34. Measurement of misfit dislocation velocities in capped (300nm silicon) and uncapped (Si)/h nm Ge,Si,,/Si (100) structures by in situ TEM, normalized according the factor uexe[-o.6x(eV)'kTl in Eq. (8-20). The plotted velocities are thus normalized as equivalent velocities at an excess stress of 1 pA in pure silicon.

growth process. Whitehouse et al. (1995) observed dislocation motion during growth of In,Ga,,As/GaAs ( 100)heterostructures, and compared it to the motion observed during pauses in growth, but with the sample maintained at the growth temperature. It was observed that dislocation motion was virtually terminated during growth interruption. A similar observation was made earlier by Whaley and Cohen ( 1 990) using in situ RHEED observations; they observed that lattice relaxation was much more sluggish during growth interruption than during growth in the In,Ga,,As/GaAs (100) system. In the Ge,Si,,/Si system, however, Stach et al. (1998) observed no significant difference in misfit dislocation velocities during growth and during growth interruption. These observations were made using a TEM modified for ultrahigh vacuum and in situ chemical vapor deposition from digermane and disilane growth. However, as illustrated in Fig. 8-35, a systematic difference was observed for dislocation velocities with a "clean" surface in UHV compared to those measured with a native oxide on the GexSil, surface. It was observed that the


499

Figure 8-35. Comparison of misfit dislocation velocities (normalized according to the factor e[-0.6x(W/kTl, as eg in Fig. 8-34) for Ge,Si,,/ Si (100) during growth, during growth interruption with a clean surface, and with a native oxide on the surface (Stach, 1998).

'.. 7

8

10

9

11

l/kT (J-' x 10'9

oxide significantly enhanced dislocation motion. This may be understood in terms of stress enhanced kink nucleation arising from local stresses at asperities in the oxide-semiconductor interface (Stach, 1998).

8.4.3.4 Interactions of Misfit Dislocations The final generic kinetic misfit dislocation process that must be considered is that of dislocation interactions. In general, these will act so as to limit relaxation of the interface, and may be the dominant factor in the later stages ofrelaxation of low misfit systems. The elastic strain field around a dislocation core exerts a stress on another dislocation producing a general inter-dislocation force per unit length of F;j

- ke biR .bj

(8-21)

Here ke is a constant containing elastic and geometrical factors, b, and bj are the individual dislocations' Burgers vectors, and R is the separation between the interacting segments. For the case of infinitely long

parallel screw dislocations, for example, k,= GI2 JC. This inter-dislocation force is maximally repulsive for parallel Burgers vectors, maximally attractive for anti-parallel Burgers vectors, and zero for orthogonal Burgers vectors. The inter-dislocation force may be of sufficient magnitude to cancel the excess stress driving dislocation motion when dislocations approach each other. Thus dislocations may pin each other, as illustrated for the intersection of orthogonal dislocations in Fig. 8-36. We note that as Fij is inversely proportional to R, dislocation pinning events are more likely in thinner than in thicker films. This is because the magnitude of Fii is more likely to counterbalance the excess stress along the entire threading defect arm.For fuller discussions of these concepts, including experimental investigations and evaluation of the relevant elastic integrals as functions of epilayer thickness and strain, see Hull and Bean ( 1989b), Freund (1990), Gosling et al. (1994), Schwarz (1997), and Stach (1998). A corollary of these dislocation pinning mechanisms is that much higher threading defect densities can be expected in higher

500

8 Interfaces

Figure 8-36.Illustration by plan view TEM of the pinning of misfit dislocations by pre-existing orthogonal defects in a Si/Ge,Si,,/Se(lOO) heterostructure.

mismatch systems. This is because, for a given materials’ system, the higher the lattice mismatch the lower the epilayer thickness at which strain relaxation begins. Dislocation pinning events are therefore more likely, and the average length to which a misfit dislocation can grow is substantially reduced. To effect a given amount of strain relaxation (i.e., to attain a given amount of interfacial dislocation line length for given wafer dimensions) requires a higher number of individual dislocation segments, and the threading defect densities therefore increase accordingly (Hull and Bean, 1989b; Kvam, 1990).

8.4.4 Techniques for Reducing Interfacial and Threading Dislocation Densities Although some heteroepitaxial devices, for example, heterojunction bipolar transistors in Ge,Si,,/Si (Harame et al., 1995),

can be fabricated with layer dimensions below the appropriate critical thickness such that the interface remains undislocated, it is often necessary to exceed the critical thickness. The question then becomes not how to avoid misfit and threading dislocations, but how to minimize their impact. The primary technique for reducing interfacial dislocation densities at given interfaces within a structure is the approach of growing a “sacrificial” template upon the substrate. For example, in the work of Kasper et al. (1989), ultrathin superlattices consisting of pure germanium and silicon bilayers were grown onto buffer layers of the average superlattice composition, and the buffer layers in turn were grown onto a Si(100) substrate. The intent was thereby to grow the superlattice onto a relaxed buffer layer with the same lattice parameter as the average superlattice lattice parameter. If all misfit dislocations could be confined to the substratehuffer layer interface, the superlattice could in principle be defect free. This buffer layer approach can be adapted to most practical device structures, so the salient questions then become: how many threading dislocations remain; how many can be tolerated; and how can their density be reduced? As a general rule-of-thumb, electronic devices relying upon majority carrier transport can tolerate perhaps as many as 1O6 - 1O7 cmP2dislocations, whereas for minority carrier and optoelectronic devices, defect densities less than 1O3 - 1O4 cm-2 are necessary. The integration of heteroepitaxial materials into large circuits and wafer-scale engineering will probably require still lower defect densities. At present, threading defect densities in the highest structural quality GaAs/Si (loo), for example, which is a system with a lattice mismatch of about 4%, and which has been exhaustively studied for well over a decade, are of the order of lo6- lo7 cm-2.

-


The techniques adopted for reducing threading dislocation densities are: (i) Increasing epilayer thicknesses: Once a structure has reached its equilibrium strain state at the growth temperature, threading dislocations actually increase the system energy due to their own self-energy. In the lowest energy state of the system, there would thus be no threading defects. As the layer grows thicker, threading dislocations can then interact and annihilate each other. The major problem here, as with thermal annealing and strained layer superlattice filtering (to be discussed below), is that these annihilation processes are effective only at high defect densities. This because as the dislocation density decreases, the average distance between threading dislocations increases, and the probability of dislocations meeting and annihilating eventually becomes vanishingly small. Dislocation interactions can also impede (and eventually arrest) dislocation motion at lower strains (i.e., later stages of the relaxation process), as discussed in Sec. 8.4.3.4. This will further reduce the probability of dislocation annihilation events. Such “pinning events” can also perturb the surface stress field and introduce undesirable surface morphology during subsequent growth (Fitzgerald and Samavedam, 1997; Samavedam and Fitzgerald, 1997). (ii) Thermal annealing: The threading defect mobility, and hence the probability of their meeting and annihilating, can be increased by thermal annealing during or after growth. These techniques have been shown to lead to significant defect reduction in the GaAs/Si system (e.g., Chand et al., 1986), but the same caveat regarding lower defect interaction probabilities at lower densities applies. (iii) Strained layer superlattice filtering: Threading defect interaction probabilities may be increased by providing a specific

501

vector for defect motion. This has been achieved by incorporating strained layer superlattices (SLSs) into the epitaxial system, as first suggested by Matthews and Blakeslee (1 974- 1976). The principle is that at the SLS interfaces threading dislocations become interfacial misfit dislocations and propagate along individual interfaces for relatively large distances. As they do so, they may meet other defects and annihilate or even propagate all the way to the edge of the wafer. The SLS has to be incorporated with sufficient strain to deflect existing threading dislocations, but not so much strain as to generate substantial densities of new defects. This can in principle be achieved if the threading defects can act as the necessary misfit dislocation “sources”. Several groups [e.g., Olsen et al. (1975), Dupuis et al. (1986); Fischer et al. (1985); Liliental-Weber et al. (1987)l have claimed substantial success at reducing threading defect densities by this technique. Nevertheless, the same limitation of reduced interaction probabilities at reduced densities still applies. As analyzed by Hull et al. (1989 b) for the Ge,Si,,/Si( 100) system, the final attainable defect densities will depend upon layer growth times and temperatures, and misfit dislocation velocities. For Ge,Si Si(100) SLS structures grown at 550°C,final attainable defect densities of the order of 106-107 cm-2 were predicted. In compound semiconductor systems where dislocation velocities are higher, this minimum attainable density should be somewhat lower. (iv) Graded composition structures: Continuous compositional grading in the buffer layer has yielded threading defect densities in the range 105-106 cmP2 for lattice mismatch strains as high as 0.03 [e.g., Fitzgeraldetal. (1991);Tuppenetal. (1991)l.The major advantage of this technique is that instead of the misfit dislocations being con-

502

8 Interfaces

fined to a single interface, there will be a distribution through the buffer layer to compensate for the continuously varying strain field. This provides an extra degree of freedom for misfit dislocations to propagate past each other, as they will be at different heights in the structure, thereby minimizing pinning events. The vertical distribution of misfit dislocations in the buffer layer can also adjust during specimen cooling from the growth temperature, thereby accommodating the effects of differential thermal expansion coefficients. One challenge of this geometry is that it was found that dislocation pile ups can cause significant surface morphology (Fitzgerald and Samavedam, 1997; Samavedam and Fitzgerald, 1997) with ramifications for technological applications of these structures. All of the above techniques can be, and often are, used in conjunction. Threading defect densities can thereby be impressively reduced, but a “floor” of the order of 1o6 cmT2is generally experimentally encountered, and can be theoretically understood. Another technique that can be used to reduce densities of both interfacial and threading dislocation densities is “finite area” or “patterned” epitaxy. Here the growth is on finite substrate mesas or windows, or the epilayer is patterned after growth. The finite mesa approach has been explored in some detail by Fitzgerald et al. (1989). As illustrated in Fig. 8-37, patterned growth at relatively low strains in the InxGa,,As/ GaAs (100) system reveals significant reductions in both threading and misfit dislocation densities with decreasing mesa size. The interfacial misfit defect density is reduced due to the finite density of heterogeneous dislocation sources in the “low strain” regime. For heterogeneous source densities, Nhe, which are sufficiently low, the mesas will on average contain no dislocation sources, and therefore no misfit disloca-

Circle Diameter (microns)

-

f

l,OO\

500 ‘0

100 200 300 400 Circle diameter (microns)

500

Figure 8-37.Graphs of measured average linear misfit dislocation density vs. mesa size in the In,Ga,,As/ GaAs(100) (x=O.OS) system with a) 1 . 5 ~ 1 0 cm-2 ’ and b) lo4 cm-* pre-existing dislocations in the substrate (from Fitzgerald et al, 1989).

tions are expected. Threading dislocation densities will also be reduced, or even eliminated, for mesa areas substantially greater than this. This is because the misfit dislocations which do form may have sufficient velocities and time at temperature during growth to reach the mesa edge. This approach, however, is primarily beneficial in the “low” strain regime; in the “high strain” regime, homogeneous dislocation nucleation at the mesa surfaces (or edges) is likely to become significant. The finite epitaxy approach has also been applied to the GaAs/Si [e.g., Matyi et al. (1988)] and the


Ge,Si,,/Si systems [e.g., Noble et al. (1990); Hull et al. (1991b); Knall et al. (1994)], amongst others.

8.4.5 Electrical Properties of Misfit Dislocations The electronic structure of dislocations in semiconductors has been the subject of extensive studies, both by atomistic modeling of core structures and experimental probing of electrically active states. The primary experimental techniques employed are electron beam induced current (EBIC), cathodoluminescence (CL), photoluminescence (PL), deep level transient spectroscopy (DLTS), and electron paramagnetic resonance (EPR). Dislocations can be electrically active via a number of mechanisms. These include defect states associated with dangling bonds at the dislocation core, point defects stabilized by the dislocation strain field, and precipitation of impurities at the dislocation core. These defect states can be highly deleterious to electronic device performance, because they act as both carrier generation and recombination sites. Carrier generation can severely perturb carrier populations in minority carrier devices, and the recombination will quench optical activity in optoelectronic devices, amongst other undesirable side effects. Calculations of the 30" a/6 (2 11) and 90" a/6 (2 1 1) partial dislocation core structures in silicon [e.g., Jones (1979); Chelikowsky (1982); Jones et al. (1993)l suggest that there are essentially no deep states associated with them, because dangling bonds along the cores reconstruct. Core states on the straight dislocation would then require reconstruction defects, whose formation energy on the 90" a/6 (21 1) partial in silicon has been calculated as 1.2 eV (Heggie et al., 1993),which is much greater than k Tfor the

503

temperatures of interest. A more likely source of core states is at dislocation kinks, where ab initio calculations for the 30" a/6 (2 11) silicon partial (Huang et al., 1995)predict the existence of deep states. Experimentally, dislocations in silicon are generally observed to be electrically active. For example, EBIC and CL usually exhibit strong dislocation contrast, PL shows dislocation-related spectral features, and DLTS spectra reveal dislocation-related features. However, recent work demonstrates that such contrast or signal is generally associated with transition metal impurities within the dislocation strain field, rather than intrinsic core activity. Higgs et al. (1990,1992a) demonstrated that EBIC contrast and defect-related PL signals from partial dislocations in silicon disappeared at sufficiently low contamination levels (- 10" cmP3) or copper and nickel. This suggests that partial dislocation cores in silicon do not contain significant densities of deep level states in the absence of metallic impurities. Results from CL, PL, and EBIC studies show the electrical activity of dislocations in Ge,Si,, to be broadly consistent with those of silicon. For example, the PL spectrum of plastically deformed Ge,Sil, shows essentially the same broad spectral features as that of plastically deformed silicon (Higgs et al., 1992b). The dependence of electrical activity of misfit dislocations on transition metal contaminationin Ge,Si,, was also observed to follow similar qualitative trends to that of dislocations in silicon (Higgs and Kittler, 1993). The defect energy levels associated with dislocations in 111-V compound semiconductors are more complex, because separate sets of levels are associated with group I11 and group V terminated cores, as well as with the 30" and 90" partials. For further information, see Jones et al. (1981) and Sieber et al. (1993).

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8 Interfaces

The primary unwanted effects that misfit and threading dislocations will have upon device performance are as minority carrier generation and recombination centers, in reducing carrier mobility, and in acting as potential diffusion pipes. The electrical activity associated with misfit dislocations in Ge,Si based heterostructures has been directly measured by Ross et al. (1993) using in situ TEM measurements. In these experiments, the change in reverse bias leakage current in broad area (Si)/Ge,Si,,/Si (100) p-n junction structures was directly correlated with the interfacial dislocation density. From these experiments, an average generation current in the range lo9- lo4 A rn-’ of interfacial misfit dislocation length was determined. This current is much higher than predicted by classic Shockley -Hall-Read recombination statistics, and suggests that additional point defect states are generated by dislocation motion, as detected by EPR measurements of plastically deformed silicon (Weber and Alexander, 1977). Ismail (1996) has studied the effects of threading dislocation density upon electron mobility in modulation doped Ge,Si,,/Si heterostructures. It was observed that threading dislocation densities of the order of lo8 cmP2 were required to make a significant effect upon the measured electron mobility, while densities of the order of 10’ cmP2reduced the mobility by more than two orders of magnitude. 8.4.6 Summary

We have summarized those interfacial structural properties that are peculiar to lattice-mismatched interfaces. The elastic strain energy arising from lattice mismatch is relaxed by one of three mechanisms (or a combination thereof): interdiffusion, surface roughening, or misfit dislocations. Of

these mechanisms, interdiffusion is only significant at very high temperatures or in ultra-fine scale (i.e., a few atomic monolayers) structures. Roughening dominates at higher lattice mismatches and at higher growth or annealing temperatures. Misfit dislocation injection is the most prevalent mechanism at low and moderate lattice mismatches (less than about 2%). Relaxation of lattice mismatch strain by surface roughening has received a lot of attention in the past decade, and good mechanistic understanding of the fundamental mechanisms driving roughening, from the atomic to the micrometer scale, now exists. Relatively little attention has been focused, however, on the magnitude of strain relaxation generated by surface roughening. With regard to misfit dislocation injection, satisfactory equilibrium models for the critical thickness exist. These were first developed by Matthews-Blakeslee and van der Merwe more than two decades ago. Experimental studies have supported these equilibrium models in the limits of very high temperature and very sensitive measurement techniques. Kinetic barriers to misfit dislocation nucleation and propagation greatly limit interfacial relaxation rates. This is particularly true at lower strains where small numbers of dislocation sources exist, and in materials such as silicon and germanium, which have high activation barriers to dislocation glide. The Dodson-Tsao model provides a powerful framework for understanding and modeling these kinetically limited processes. This model assumes that dislocation velocities, and hence interfacial relaxation rates, are proportional to the Dodson-Tsao “excess stress”, and thermally activated over the Peierls barrier. Dislocation nucleation is assumed in this model to be by a combination of heterogeneous sources and multiplication mechanisms. Subsequent models by Hull et al., 1989a,

8.5 Interfaces Between Crystalline Systems Differing in Composition and Structure

Houghton, 1991, and Gosling et al., 1994 have extended this model to new microscopic dislocation mechanisms and to new structures and geometries. In situ and ex situ experimental studies have also begun to probe the kinetic properties of misfit dislocations, and have been at least partially successful in extracting those parameters necessary for the accurate applicationof kinetic modeling. Several techniques for controlling or even removing deleterious threading and interfacial misfit dislocations for strained layer thicknesses above the critical thickness have been developed. These include growing thicker layers, post-growththermal annealing, strained layer superlattice filtering, and compositional grading. At present, minimum threading dislocation densities are of the order of lo6 cm-* for super-critical layers with strains in the range 0.01 -0.04. Patterned epitaxy appears to offer the best prospects of reducing or eliminating misfit dislocations and/or threading defects in mesas or windows with dimensions of micrometers to tens of micrometers.

8.5 Interfaces Between Crystalline Systems Differing in Composition and Structure 8.5.1 Introduction

Up to this point, our discussion has been limited to epitaxial semiconductor systems involving materials with identical lattice structures, e.g., GeSi/Si, and AlAs/GaAs. The relief of strain due to lattice mismatch and the control of interface roughness are amongst the most important issues relevant to these interfaces. For some applications, it is desirable to fabricate epitaxial structures involving metals and insulators. This invariably involves the growth of materials with crystal structures that are different

505

from that of the substrate. The need to create a differently structured crystal on the host lattice leads to many complications not encountered in the epitaxial growth of isostructural interfaces. Some of the more prominent problems include: (1) The free energy of the interface is often non-negligible, thus promoting a nonuniform morphology of the epitaxial layer. (2) The difference in the crystal structures often allows pseudo-matching conditions for more than one interface orientation, so the overgrown layer may contain many competing epitaxial orientations. (3) A change in crystal symmetry across the heterointerface may demand the presence of specific interfacial defects (Pond and Cherns, 1985).

In this section, these issues and some of their solutions will be discussed, mainly using epitaxial metal-semiconductor (M-S) structures as examples. M-S structures are an essential part of virtually all electronic and optoelectronic devices. In recent years, much progress has been made in our understanding of the chemistry and metallurgy of these interfaces (e.g., Brillson, 1993). However, the electronic properties at these interfaces, on a microscopic scale, are still poorly understood. Most notably, the formation mechanism of the Schottky barrier height (SBH) at an M-S interface, despite much investigation and debate, remained, up to a few years ago, at the speculation stage (Tung, 1992). This lack of progress could be blamed, at least in part, on the complexity of atomic structures at ordinary polycrystalline M-S interfaces. There was little hope of deducing the atomic structures experimentally, nor was there any chance of calculating, from first principles, the electronic properties of these inter-

506

8 Interfaces

faces. SB theories were therefore limited to those that were based on bulk physical properties or were essentially phenomenological in nature. Neither of these two approaches was particularly successful. The missing link, obviously, was the relationship between the atomic structure and the electronic structure of the interface.With the arrival of epitaxial M-S interfaces a decade or so ago, new hope was injected to the SBH field. A few epitaxial M-S interfaces had simple enough atomic structures to enable experimental determination, and these were subsequently used to calculate SBH from first principles (Das et al., 1989; Fujitani and Asano, 1988, 1989). Epitaxial M-S structures have indeed stimulated significant advances in the SBH field and they will continue to serve as a conventient vehicle to pursue a possible solution to the long-standing SBH problem. In addition to offering opportunities for fundamental studies, epitaxial M -S structures also have numerous advantages over polycrystalline M- S structures in terms of performance in microelectronic devices (Tung and Inoue, 1997). These advantages include the possibility of monolithic vertical integration, high stability, and the possibility of hot-electron, highspeed devices. In this section, highlights of progress made in the field of epitaxial M-S systems, both on the scientific front and toward the applicationend, will be introduced. The majority of M-S structures are fabricated by the growth of a metallic thin film on a semiconductor substrate. Crystal structure and lattice parameter are importantconsiderations concerning possible epitaxial growth, and these salient features of common epitaxial metallic materials are collected in Table 8- 1 (p. 47 1). Because of favorable matching conditions in these M-S systems, it is usually not difficult for the overgrown metallic film to display preferred orientation. However, the quality of the M-S inter-

face depends critically on the precise way these films are prepared. So the main challenge in the fabrication of these epitaxial M-S interfaces is to increase the epitaxial perfection, e.g., to reduce the defect density, to achieve a unique epitaxial orientation, to maintain the uniformity of the overgrown layer, etc. To achieve these goals, care must be taken in all aspects of the epitaxial growth. When a metal layer is overgrown on a semiconductor, the original semiconductor surface usually becomes part of the eventual M-S interface. Any impurities or structural imperfections on the original surface of the semiconductor can greatly affect the M-S interface formation. Therefore, surface cleaning is extremely important for successful epitaxial growth. An example of surface imperfections which may affect the quality of the epitaxial growth is surface steps, as these may lead to interfacial dislocations (Pond and Cherns, 1985), as will be discussed. Careful surface preparation procedures such as the use of precisely oriented crystals (or deliberately offcut crystals), the removal of surface damage and contamination, the growth of a buffer layer, etc. usually pay big dividends. Since ultrahigh vacuum (UHV) techniques offer the most control over surface preparation, it is no accident that the highest quality epitaxial M-S interfaces which have been fabricated thus far have all been grown with UHV deposition techniques. However, the latest trend, obviously with practical applications in mind, has been to fabricate epitaxial M-S interfaces by more conventionaltechniques. As already mentioned, the growth of a metal layer on a semiconductorrequires nucleation of the metallic crystal and the creation of heterointerfaces, usually with nonnegligible interface energies. Precise control of the nucleation conditions at the initial stages of metal deposition is crucial to


achieving single epitaxial orientation and good layer morphology. Often the conditions for optimum nucleation of the initial metal differ considerably from the optimum conditions for metal (homo)epitaxial growth on the existing metal lattice. It is thus advantageous to use a two-step growth procedure whereby the initial metal, usually c5 nm thick, is deposited under conditions taylored for optimum nucleation. This thin metal layer is then used as a template for subsequent growth, which takes place under conditions optimized for high quality metal homoepitaxial growth. Such a two-step technique, known as the “template technique” (Tung et al., 1983a) has worked very well, not only for M-S structures such as epitaxial silicides, but also for epitaxial semiconductor and insulator systems such as GaAs/Si (Akiyama et al., 1986) and SiC/Si (Nishino et al., 1983). There are other ingenious approaches that have solved the nucleation problem of specific epitaxial M-S interfaces, such as by way of an interfacial layer or by the coalescence of epitaxial precipitates, as will be discussed next. 8.5.2 Fabrication of Epitaxial Silicide-Silicon Interfaces

Silicides are metal-silicon compounds with specific compositions and crystal structures. Most of them are electrically conductive, with a few displaying semiconducting properties. Highly oriented growth has been observed for many silicides on silicon. The two silicides, Nisi, and CoSi,, with their fluorite lattice structure and good lattice matches with silicon (see Table 8-l), are the most studied of all epitaxial silicides. Coincidentally, thin films of these two silicides have also shown the highest degree of crystalline perfection amongst all silicides. Since the silicon substrate is essentially an infinite source of silicon, silicide thin films

507

can be grown by providing only the metal, although at times it may be advantageous to provide both the metal and the silicon. Deposition of an elemental metal on silicon and annealing to suitable temperatures, known as solid-phase epitaxy (SPE), can lead to the growth of desired epitaxial silicide phases (Chiu et al., 1981; Saitoh et al., 1981). For thick layers (> 10 nm) of deposited metal, this reaction usually starts with the growth of metal-rich silicides and, progressively, different silicides may be grown, ending with silicon-rich silicides (Tung et al., 1982a). Co-deposition of metal and silicon, in a stoichiometric ratio on a heated silicon substrate, generally referred to as molecular beam epitaxy (MBE), may also be employed to grow epitaxial silicides (Bean and Poate, 1980).Thick (> 50 nm) silicide layers grown by SPE or MBE alone are frequently non-uniform and contain multiple orientations. As already alluded to, most of these problems may be solved by using the template technique (Tung et al., 1983a, b). The problem of epitaxial silicide growth is therefore often reduced to the growth of a high quality template layer. The exact method to grow an optimum template layer is obviously dependent on the particular system. It may require depositions of pure metal, layered metal and silicon, a co-deposited metal silicide of a particular stoichiometry, or a combination of the above; in short, whatever it takes. 8-5.2.1 Monolayers Reaction

Nisiz

Two epitaxial orientations are possible for CoSi, and Nisiz on Si (1 11). Type A oriented silicide has the same orientation as the silicon substrate, and Type B silicide shares the surface normal (1 1 1) axis with silicon, but is rotated 180”about this axis with

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8 Interfaces

respect to the silicon (Tung et a]., 1982a). High quality single crystals of Nisi, may be grown on Si (1 1 l), with either type A or type B orientation (Tung et al., 1983b), as illustrated in Fig. 8-38. When 16-20 A (1.62 nm) nickel is deposited at room temperature, subsequent annealing leads to the growth of type A Nisi, (Tung et al., 1983b; Hunt et al., 1986; von Kanel eta]., 1987). If a small amount (550 "C), the interface breaks up into inclined (1 11) facets. Indeed, interfacial faceting of this system is so complete that, in most well-annealed samples, the entire NiSi,/Si is made up of inclined (1 11) facets. d 4(1 11) type dislocations are required at the boundaries between two facets (Tung et al., 1985). It should be recognized that the reaction kinetics often play a role in determining silicide layer morphology. But the fact that not even a small portion of flat [ 1101NiSi,/Si interface has been

-

-

observed gives a clear indication that this interface may well be unstable.

CoSiz Type B is the dominant epitaxial orientation observed for CoSi, layers grown on Si(ll1) (Tung et al., 1982b, 1985; Arnaud D' Avitaya et al., 1985). CoSi, layers grown by the annealing of a few monolayers of deposited cobalt are often non-uniform in thickness and contain pinholes (Tung et al., 1986a). An important driving force for pinhole formation in epitaxial CoSi, films has been identified as a change in the surface energetics of the CoSi, (1 1 1) (Tung and Batstone, 1988a;HellmanandTung, 1988).Because of this knowledge, complete elimination of pinholes has been demonstrated either by silicon deposition or by co-deposition of CoSi, (Tung et al., 1986a; Hunt et al., 1987; Henz et al., 1987;Lin et al. 1988). However, layers grown by either of these techniques, even though pinhole-free, usually contain a high density of dislocations (Tung and Schrey, 1988). The avoidance of a high dislocation density in well-annealed CoSi, layers is difficult, and the only way it has been demonstrated involves beginning with the growth of a thin layer of epitaxial CoSi, at room temperature. Single crystal CoSi, can be grown at room temperature on Si( 111)by the deposition of 0.2 nm cobalt and the co-deposition of CoSi, (Tung and Schrey, 1989b). While it is not clear whether layers grown at room temperature have the fluorite structure or actually occupy a disordered simple cubic structure (Goncalves-Conto et al., 1996), the long range order and epitaxial perfection of these films are excellent. Dislocations found at these silicide interfaces are only those required by symmetry, due to the presence of steps on the original Si (111) surface. This one-toone correspondence of interface disloca-

-


tions to surface steps has even been utilized to monitor surface topographical changes due to various nonsilicide-related processes (Tung and Schrey, 1 9 8 9 ~ )For . example, a change of Si (1 11) surface topography due to silicon homoepitaxial growth is illustrated in Fig. 8-41 for this silicide “replica” method. The annealing of room-temperature-grown CoSi, layers to > 550°C usually leads to an increase in the dislocation density. Only in ultrathin CoSi, layers that were grown at room temperature by a very precisely controlled co-deposition method has the dislocation density been observed not to increase after such an anneal. Intriguing TEM contrasts have been observed on layers grown this way, as shown in Fig. 8-42 (Tung

Figure 8-41. Dark field TEM images of CoSi, layers grown at room temperature on an Si (1 1 1) surface: a) substrate surface, and b-d) surfaces after the growth of 5 nm of silicon at a rate of 0.05 nm s-’. The silicon deposition temperature was b) 750°C c) 650°C and c) 550°C.

51 1

and Schrey, 1988; Tung, 1989). Analyses suggested these contrasts to be associated with a novel stress-driven structural phase transformation at the interface, involving a few MLs of CoSi, (Eaglesham et al., 1990). It is known that this interfacial phase transformation is sensitive to preparation, that it takes place upon cooling, and that it can be removed by ion beam bombardment. But its exact nature is still not fully understood. Unlike Nisi, epitaxy on Si (loo), the issue for epitaxial CoSi, on Si (100) is not faceting, but multicrystallinity. There are two competing orientations for CoSi, epitaxy on Si(100) inaddition to theusualCoSi2(100)// Si ( loo), and they are CoSi, (1OO)//Si ( 100) and CoSi2(221)//Si(100) (Tunget al., 1988; Yalisove et al., 1989a; Jimenez et al., 1990), the latter being related to the (100) through twinning along inclined { 111} s. Most of the dislocations seen in (100)-oriented CoSi, areas are a/4 (1 11) in character. The previous discussion regarding steps of odd atomic height at an NiSi,/Si( 100) interface is also applicable here. Various deposition schedules have been studied in order to reduce the fraction of { 110) and { 221 } oriented grains in epitaxial CoSi, films. It is known that wafer roughness and surface cleanliness also have an effect on the observed areal fraction occupied by [ 1101 grains (Yalisove et al., 1989a). The best results thus far have been obtained by the deposition of -2 A (0.2 nm) cobalt followed by the co-deposition of a thin layer (6-14 A) of CoSi,. Shown in Fig. 8-43 is a single crystal CoSi, film grown on Si (100) using the template method. Co-deposition with a cobalt-rich composition, CoSi,, x - 1.6- 1.8, at an elevated temperature, 500 “C, has been shown to completely eliminate { 110) and { 221 } oriented grains (Jimenez et al., 1990), but this technique cannot be used to grow uniform layers less than 20 nm thick. There are other unusual methods to grow

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8 Interfaces

Figure 8-42. Dark field (220) TEM images of a 2.5 nm thick CoSi, layer on Si (1 11) which had been annealed to 600°C. This layer was originally grown at room temperature by cobalt predeposition and co-deposition of CoSi,. The approximate direction of the g vector is indicated on each micrograph. All pictures were taken in the weak beam, with (660) close to the Bragg condition. The reason for these domain-like contrasts is an interfacial phase transformation.

Figure 8-43. Plan view, (022) weak beam TEM image of a - 4 . 8 nm thick single crystal CoSi, layer, grown in two steps on Si( loo), with a final anneal at 600°C.

epitaxial CoSi, on Si(lOO), as will be discussed in later sections. CoSi, grows with a regular epitaxial orientationonSi(1 lO)(Yalisoveetal., 1989b). Again, in sharp contrast to Nisi, epitaxy

on this surface, faceting is not an issue for CoSi,. Uniform layers of CoSi, may be grown with cobalt deposition and CoSi, codeposition at room temperature, followed by annealing. There is no phase difference across a step at an otherwise planar (1 10) silicide/Si interface. However, most defects seen at the CoSi,/Si( 110) interfaces, e.g., see Fig. 8-44, are phase domain boundaries. The different phases arise from inequivalent lateral shifts at the silicide/Si interface, rather than from interfacial steps. As the CoSi, film thickness increases, additional dislocations are generated at the interface to relieve misfit stress. The kinetics of strain relief along the two orthogonal directions [I TO] and [OOl] are markedly different (Yalisove et al., 1989b). For a fixed growth and annealing schedule, the generation of dislocations occurs as if different critical

Figure 8-44. Weak beam TEM images of a 1.8 nm thick CoSi, layer grown on Si (1 10) at 500°C: a) (220) dark field and b) (3 3 1) dark field images show the correlation of the location of the two phases and the boundaries of these anti-phase domains.

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thicknesses were operative for these two directions; strain along [OOl] is relieved at a smaller film thickness than that along [ l TO] (Yalisove et al., 1989b). Epitaxial CoSi, has been grown on the less common Si(3 11) surface, where two epitaxial orientations are observed. These are the regular CoSi2(311)//Si(31 1) and a CoSi2(177)// Si ( 3 1l), which is due to a type B relationship with respect to the least-inclined [ 1111 (Yu et al., 1988). Other Silicides

Other silicides that have been grown epitaxially on silicon include Pd,Si (Saitoh et al., 1981; Freeouf et al., 1979), YSi, (Knap and Picraux, 1986; Gurvitch et al., 1987; Siegal et al., 1989), ErSi, (Arnaud d'Avitaya et al., 1989; Kaatz et al., 1990a), TbSi, (Kaatz et al., 1990a), ReSi,, PtSi (Ishiwara et al., 1979), and FeSi, (Cheng et al., 1984; von Kanel et al., 1994). Partially epitaxial or textured CrSi, (Shiau et al., 1984) and other platinum group (Chang et al., 1986) and refractory silicides (Chen et al., 1986) have also been grown. The crystal structures of some of these silicides can be found in Table 8-1. S i ( l l 1 ) is the most common substrate for the epitaxial growth of these silicides. Readers are referred to review articles on the epitaxial orientations of these semi-epitaxial films (Chen et al., 1986).

8.5.2.2 Interlayer Mediated Epitaxy Titanium-Interlayer Mediated Epitaxy

The titanium interlayer mediated epitaxy (TIME) technique (Dass et al., 1991) makes use of the observation that a thin titanium layer ("interlayer", < 10 nm thick), deposited on Si (100) prior to the deposition of cobalt (typically 12 - 15 nm), can promote the epitaxial growth of CoSi, in a subsequent

51 3

anneal. After the reaction, titanium is found near the surface in the forms of TiN and other titanium containing phases. Without the titanium interlayer, CoSi, is grown under otherwise similar conditions. It has been suggested that the titanium-interlayer serves as a diffusion barrier, which limits the Co-Si reaction until the temperature exceeds 500"C, allowing one (Co,Si) or both (Co,Si and CoSi) precursor phases in the ordinary Co-Si reaction sequence to be skipped (Hsia et al., 1991, 1992; Ogawa et al., 1993). Skipping the precursor silicide phase(s) is speculated to enhance the epitaxial growth of CoSi,. Epitaxial CoSi, layers grown by the original TIME process are often non-uniform in thickness. To improve on the lateral uniformity and the epitaxial quality of the TIME grown CoSi2 layers, a number of modifications have been found to be necessary. Firstly, the thickness of the titanium interlayer needs to be set at -4-7 nm instead of 2 nm as originally proposed, for cobalt layers - 12- 15 nm. When co-deposited TiSi, is used as the interlayer, the amount of titanium can be reduced (Tung and Schrey, 1996). A thin titanium cap, 1-3 nm thick, deposited over the cobalt layer to form a Ti/Co/Ti/Si starting configuration, was found to improve the degree of epitaxy and the homogeneity of the silicide reaction (Tung and Schrey, 1995). With a proper interlayer (and cap), the silicide reaction still needed to be managed carefully. Usually after an RTA at 650-800°C in N2, an essentially uniform, single crystal CoSi, layer is grown next to the silicon, while a Ti,Co,Si,/TiN bilayer is formed at the surface. 'Such a structure becomes unstable above 85OoC,as the surface Ti,Co,Si, decomposes and disrupts the CoSi, film. The removal of the surface Ti,Co,Si, layer (Hsia et al., 1991, 1992; Tung and Schrey, 1996) prior to high temperature annealing is thus essential to the success of TIME. The entire

-

514

8 Interfaces

TIME process is schematically shown in Fig. 8-45a. The TIME effect is an intriguing phenomenon, and CoSi, layers grown by TIME on lightly doped, blanket silicon wafers are of very high quality after a high temperature anneal (> 900 "C). There are indications that other refractory metals such as tantalum (Byun et al., 1993a, 1995) and zirconium (Byun et al., 1993b) can also be used as the interlayer. An obvious advantage of the TIME technique is its compatibility with standard silicon fabrication environments. However, the TIME process has some problems, the most serious of which being the formation of voids near the edges of CoSi, layers grown on silicon surfaces with an oxide pattern (Tung and Schrey, 1996; Byun et al., 1996). Because of this problem, the TIME process is presently not deemed a viable technique for the processing of ULSI devices.

Oxide Mediated Epitaxy The oxide mediated epitaxy (OME) technique (Tung, 1996a, b) uses a phenomenon similar to that responsible for the TIME effect, but is able to avoid most of TIME'S problems. A thin SiO, layer grown on silicon substrates in an aqueous bath containing H,O, is found to promote the epitaxial growth of CoSi,. When 1.5 -3 nm cobalt is deposited at room temperature on thin SiO, covered Si(100) and annealed at 600"C, a (100) oriented CoSi, layer is grown. Ultrathin CoSi,/Si (100) interfaces grown by OME are continuous and single crystalline, but they are characterized by microfaceting. Essentially the same OME procedures can be applied to grow continuous and singly oriented CoSi, layers on any silicon surface with an orientation far from the { 111 } (Tung, 1996b). Furthermore, OME growth is not significantly affected by sub-

-

-

Figure 8-45. Schematic diagrams of the a) TIME and b) OME processes.


strate doping, at least up to the levels commonly used for shallow junction formation (Tung, 1996b). After an epitaxial CoSi, layer is grown by OME, Auger electron spectroscopy indicates that the thin oxide layer originally residing on the silicon surface remains largely on the surface of the epitaxial CoSi, layer. This process is schematically shown in Fig. 8-45 b. OME grown, ultrathin CoSi, layers can be used as template layers for the growth of thicker CoSi, layers. Room temperature deposition of cobalt and annealing at 600-800°C can be used to increase the thickness of OME CoSi, layers. The degree of interfacial microfaceting is generally lessened when OME layers are made thicker by template growth. It is further reduced significantly after prolonged high temperature anneals. A planview TEM image of an 18 nm thick CoSi, layer grown by repeated deposition and annealing sequences on patterned silicon lines is shown in Fig. 8-46. The silicide morphology and/or thickness appear not to be affected by the presence of the oxide pattern.

-

515

OME grown CoSi, template layers have a significant fraction of type B orientated grains on Si(ll1) and Si(211) surfaces. However, as these layers are made thicker with subsequent deposition and annealing steps, the orientation of the layers changes to predominantly or entirely type A. OME is the only technique that is capable of generating type A CoSi, films on Si (1 1 1). Even though the OME technique is versatile and produces some very impressive results, a few important issues still need to be resolved before it can be applied to ULSI device fabrication. One problem concerns interfacial faceting of CoSi, layers on Si(100). Although the degree of faceting can be dramatically reduced by high temperature annealing (Tung, 1996b), the added thermal budget and the residual roughness are still serious concerns. In addition, the homogenization process during high temperature anneals is driven by the reduction of interface energy. Such a mechanism works well for blanket CoSi, layers, but need not work for narrow CoSi, lines. There are other issues dealing with manufacturing that are outside the scope of this discussion. 8.5.2.3 Growth of Silicon on Silicides

Figure 8-46. Planview TEM images: a) bright field and b) (200) dark field of a 12.6 nm thick epitaxial CoSi, layer grown by OME in narrow, arsenic-doped, source/drain areas [lighter in a)], separated by polysilicon [darker in a)].

It is possible to grow high quality epitaxial silicon on some surfaces of CoSi, and Nisi,. Thick double heterostructures (Si/silicide/Si, with thickness of silicide >50 nm) were demonstrated in some early works by both MBE and SPE (Tung et al., 1992a; Saitoh et al., 1980; Ishizaka and Shiraki, 1984). Double heterostructures involving thinner (c 10 nm) silicide layers are more interesting as there are potential applications as high speed devices (Rosencher et al., 1984; Tung et al., 1986a). The use of a silicon template is critical in ensuring uniform silicon overgrowth on silicides (Tung et al., 1986a; Henz et al., 1987, 1989; Lin

516

8 Interfaces

et al., 1988). Without it, the growth of silicon occurs three-dimensionally and the crystalline quality is poor. Epitaxial silicon may be grown in either type A or type B orientation on CoSi,( 111) using specially designed silicon templates based on the two surface structures of CoSi2(111) (Tung and Batstone, 1988b). If no special attention is paid to the surface structure of CoSi,, the overgrown silicon could contain both orientations (d’Anterroches and Arnaud d’Avitaya, 1986). Superlattices consisting of layers of epitaxial CoSi, and epitaxial silicon have also been fabricated, although the structural quality degrades rapidly with superlattice thickness (Hunt et a]., 1987; Henz et al., 1989). On NiSi2(lll), epitaxial silicon always occupies the type B orientation(Ishizakaand Shiraki, 1984;Tung et al., 1986b). Double heteroepitaxial structures fabricated on (1 11) are of rather high structural quality, as shown in Fig. 8-47. Perhaps due to unfavorable interface energetics, (100) is not the favored orientation for silicon grown by MBE on CoSi,( 100). Instead, finely textured films are often observed (Sullivan et al., 1992). This is rather unfortunate as it sets back possibly interesting research on metahemiconductor heterostructures and superlattices. The growth of high quality silicon on top of NiSi,/Si( 100) is difficult but not impossible.The silicon template technique described for the Nisi,/

Si (1 11) system was found to improve the uniformity of silicon layers grown on NiSi,/ Si(100) (Tung et al., 1986b; Itoh et al., 1989). However, the SioveJNiSi2interface appears to break up into inclined { 111} facets. At the initial stage of silicon growth on Nisi,, a novel morphology, that of an inverted Volmer-Weber, is observed (Tung et a]., 1993a). When the thickness of the Nisi, layer is small (< 10 nm), silicon overgrowth may lead to openings in the silicide layer (Tung et a]., 1986b) as a result of these pinholes. With thicker Nisi, layers, the amplitude of faceting also increases, but the structural defect in thick silicon overlayers eventually fades away toward the surface (Itoh et al., 1989; Tung et al., 1993a), as shown in Fig. 8-48a. High temperature annealing, described previously to be effective in removing facets at the Nisi, /Sisub interface, is also effective in removing the microfacets from the Si,,,, interface, as shown in Fig. 8-48b. Note, however, that post-growth annealing cannot lead to high quality Si/NiSi,/ Si(100) structures when the Nisi, layer is less than 10 nm thick, because the as-grown structures are already porous.

8.5.2.4 Conglomeration of Silicide Precipitates Mesotaxy and allotaxy are two techniques for producing epitaxial Si/silicide/Si

Figure 8-47. High resolution cross sectional TEM image of a Si/CoSi,/ Si (1 11) structure grown by the silicon template technique.


Figure 8-48. Cross sectional TEM images of 320 nm Si/50 nm NiSi,/Si(100) structures grown by MBE. The Nisi, layer was annealed at 800°C and the silicon overlayer was grown at 500°C with a 10 nm thick silicon template: a) as-grown structure, b) after postgrowth annealing at 960°C for 60 min in a vacuum furnace.

(a) MESOTAXY MeV Co Implantation

51 7

structures involving conglomeration of silicide precipitates. Mesotaxy (White et al., 1987) involves a high-energy, high-dose implantation of a silicide-forming metal (e.g., cobalt) into silicon, usually at an elevated temperature to minimize lattice damage, leading to the formation of epitaxial silicide crystallites throughout the depth of the implantation, as shown in Fig. 8-49 a. The size and density of silicide precipitates vary with depth, as they are constrained by the local composition (Bulle-Lieuwma et al., 1989a; Hull et al., 1990). If the peak metal compoexceeds a certain critisition, x in M,Si,,, cal composition, the silicide precipitates begin to coalesce and connect. A subsequent high temperature anneal leads to the formation of a continuous epitaxial silicide layer buried at some depth inside the silicon as shown in Fig. 8-49 b. For implanted cobalt, the critical composition is found to be around 16-19%, which is much smaller than the prediction of 27% if coalescence is assumed to take place when close-packed silicide spheres begin to overlap. This dis-

-

(b)ALLOTAXY Si-rich codeposition at

- 500%

Figure 8-49. Schematic diagrams of the a) mesotaxy and bj allotaxy techniques.

518

8 Interfaces

crepancy can be explained by the (precursor) conglomeration of silicide into islands with low aspect ratios. Indeed, the formation of a connected silicide layer is a required condition for the coalescence of the buried silicide layer (Hull et al., 1990). If the peak metal composition is below the critical composition, further annealing leads to coarsening of the silicide precipitates without the formation of a continuous layer. Mesotaxy generated high quality CoSi, and Nisi, layers buried in silicon with varied surface orientations. It was the first technique to generate single crystal Si/CoSi,/ Si (100) double heterostructures. However, because of the natural spread of the implantation process, a critical composition dictates a critical implantation dose, and therefore a minimum thickness of continuous buried silicide layer. For buried CoSi, layers in Si (100), the critical dose is close to 5 - 1 0 ~ 1 0 'Co ~ cm-, depending on the implantation energy, which means that continuous silicide layers cannot be grown by mesotaxy with a thickness of less than -20 nm (Maex et al., 1991). Buried epitaxial layers of Nisi,, YSi,,, and CrSi, have also been fabricated by mesotaxy (White et al., 1988). Inspired by the mesotaxy results, molecular beam allotaxy (MBA) attempts to generate a profile similar to that shown in Fig. 8-49a by using MBE with high SUCo flux ratios (Mantl and Bay, 1992). Trapezoidal shaped deposition profiles leave CoSi, islands buried in the silicon lattice, which are subsequently coalesced into a continuous epitaxial silicidelayer (Fig. 8-49b), as in the case of mesotaxy. The critical composition for coalescence in the allotaxy process is found to be similar to that for mesotaxy. The allotaxy technique is obviously more flexible than mesotaxy, as it allows important variables for the as-deposited depth profile, such as peak composition, deposition width,

and peak depth, to be independently adjusted (Dolle et al., 1994; Tung et al., 1993b). Flexibility notwithstanding, allotaxy still has a threshold thickness for continuous layer formation, because of the requirement for high quality silicon growth. Except for Si( 11I), the epitaxial growth of a silicon overlayer in allotaxy is achieved through the openings between silicide islands, which sets a limit on the maximum peak metal composition in the as-grown layer. The subsequent coalescence process is thus subject to the same kinetic constraints as in the mesotaxy case, including a minimum silicide layer thickness. On Si (loo), it is still difficult to grow buried CoSi, layers thinner than 20 nm by allotaxy. 8.5.3 Epitaxial Elemental Metals

The aluminum/silicon interface has many important applications in integrated circuits. The growth of epitaxial aluminum on silicon has largely been motivated by theimproved thermal stability (Missous et al., 1986; Yapsir et al., 1988a). Aluminum has a very large lattice mismatch with silicon -25%. If the matching condition of four aluminum lattice planes to three silicon lattice planes is considered then a small, - 0.56%, effective mismatch is found. Good epitaxy has been demonstrated for Al( 11 1) on Si (1 11). Aluminum is usually deposited at room temperature. As-deposited films contain both (111) and (100) oriented grains, which convert to pure (1 11) upon annealing to 400°C (LeGoues et al., 1986). The Al/Si interface is usually rough, probably as a result of poor vacuum conditions and the incomplete removal of oxide layer from the silicon surface (LeGoues et al., 1986). However, by using a partially ionized aluminum beam, flat interfaces between single crystal Al/Si have been fabricated (Yapsir et a]., 1988b; Lu et al., 1989). There is

8.5 interfaces Between Crystalline Systems Differing in Composition and Structure

evidence that under these conditions, the epitaxy maybe incommensurate in nature (Lu et al., 1989). Silver has a similar fourto-three type lattice matching condition with silicon. Thick layers of Ag( 1 11) have been grown on Si (1 11) under clean MBE conditions (Park et al., 1988, 1990). Elemental metals have also been grown on III-V compound semiconductors. The most notable of these are aluminum, silver, and iron. A large nominal lattice mismatch exists between GaAs and either aluminum of silver. With a45" azimuthal rotation, good lattice matching conditions may be established for these two metals on GaAs(100). This is indeed the most common epitaxial orientation for Al(100) grown on GaAs (100) (Cho and Dernier, 1978; Ludeke et al., 1980). However, (1 10) oriented aluminum has also been observed (Ludeke et al., 1973). It has been pointed out that reconstruction of the initial GaAs surface structure may influence the epitaxial orientation of the aluminum films (Donner et al., 1989). Silver grows with ( 1 00) orientation on GaAs (100) at elevated temperatures, and with pure (1 10) orientation at room temperature (Ludeke et al., 1982; Massies et al., 1982). Surprisingly, there is no azimuthal rotation for epitaxial Ag (100) on GaAs (100). The azimuthal orientation of the (110)oriented silver and aluminum appears to be related to the prevalent dangling bond direction on the GaAs (100) surface. Arsenic-stabilized and gallium-stabilized surfaces are known to have dangling bonds pointing in directions 90" apart, leading to Ag(ll0); this is also rotated by this angle (Massies et al., 1982). (1 10)-oriented aluminum has also been grown on GaAs(1 lo), with the expected 90" azimuthal rotation for better matching of the in-plane lattice parameters (Prinz et al., 1982). a-Fe (b.c.c.) has a lattice constant about one half of that of GaAs and ZnSe. This effective lattice matching

519

condition has led to the growth of single crystal iron on these two semiconductors (Prinz and Krebs, 1981, 1982; Krebs et al., 1987; Jonker et al., 1987). Iron grows with relative ease on GaAs (110) with regular epitaxial orientation (Prinz and Krebs, 1981, 1982), but growth has proved to be more difficult on GaAs(100) (Krebs et al., 1987). ZnSe( 100) appears to be a better substrate for epitaxial iron films (Jonker et al., 1987). High quality epitaxial Fe (100) films were also grown on a lattice-matched (twoto-one) InGaAs surface (Farrow et al., 1988). Interesting magnetic properties have been observed from epitaxial iron films. Other metals and superlattices have been grown on GaAs, e.g., metastable b.c.c. cobalt on GaAs (1 10) (Prinz, 1985) and metal superlattices on GaAs(100) (Baibich et a]., 1988; Lee et al., 1989). 8.5.4 Epitaxial Metallic Compounds on I11 -V Semiconductors

Except for refractory metals, most elemental metal/III-V compound semiconductor structures are thermodynamically unstable. Annealing, even at moderate temperatures, often leads to interdiffusion and the formation of other compound phases. Two groups of intermetallic compounds are found to have stable interfaces with III-V compound semiconductors with good lattice matching conditions (Sands, 1988). Hence these are good candidates for the formation of stable, single crystal M-S interfaces with GaAs. NiAl (Sands, 1988; Harbison et al., 1988), CoGa (Palmstrom et al., 1989a), NiGa(Guivarc'het al., 1987), CoAI, and related compounds form one group. They have the cubic CsCl crystal structure and lattice parameters 1-2% larger than one half the lattice parameter of GaAs (Sands, 1988). The exact lattice parameters of the gallides and aluminides may vary

-

520

8 Interfaces

slightly with the stoichiometry (Wunsch and Wachtel, 1982). The orientation of epitaxial films on GaAs or AlAs(100) is usually (100). However, (1 10) oriented growth has also been observed on (100)GaAs (Harbison et al., 1988; Palmstrom et al., 1989a; Guivarc’h et al., 1988). Careful control of the initial reaction on AlAs (100) has led to the successful growth of single crystal (100)CoAl andNiAl (Harbisonetal., 1988). The non-zero lattice mismatch results in a network of closely spaced misfit dislocations at the interface (Sands, 1988; Zhu et al., 1989). Overgrowth of GaAs or AlAs on these metals requires exposing the gallides or aluminides to As,, which can lead to instability and the formation of transition metal arsenides. This problem can be overcome by careful adjustment of the surface composition prior to the growth of GaAs or AlAs (Harbison et al., 1988; Sands et al., 1990). Buried thin (down to 1.5 nm) NiAl layers have been grown between AlAs cladding layers inside GaAs. However, the change of symmetry across the AlAs,,,,/NiAl interface leads to a phase difference at every step of the interface, which is an odd number of atomic planes in its height. [This situation is analogous to the antiphase domain boundaries in GaAs films grown on Si (100), due to surface steps. Also note that, at least in principle, silicon films may be grown without antiphase domain boundaries on a stepped GaAs surface.] This causes a high density of stacking faults to be present in the overgrown AlAs/GaAs. Rare earth (RE) monopnictides, mostly with the NaCl structure, form the other group of intermetallic compounds suitable for epitaxial growth on 111-V semiconductors. Here, an abundance of systems exist which are closely lattice-matched to GaAs (Palmstrom et al., 1990), ErAs (Palmstrom et al., 1988), YbAs (Richter et al., 1988), and LuAs (Palmstrom et al., 1989b); also,

alloyed (ternary) compounds, ErP,,As, (Le Corre et al., 1989) and Sc,-xErfis (Palmstrom et al., 1990), have been grown on GaAs (100). The usual (100) epitaxial orientation is found for these epitaxial systems. The alloyed compounds are investigated for the obvious reason of obtaining exact lattice matching. Growth on InP(100) has also been studied (Guivarc’h et al., 1989). RE metals are highly reactive, which leads to uniform growth of their arsenides. Similar to the epitaxial growth of GaAs, REAs may be grown in an arsenic overpressure, and the exact arsenic to RE ratio is not critical. RHEED intensity oscillations have been observed in the growth of Sco~,2Ero~,,As,indicating uniform layer-by-layer growth. Stability and lattice-match conditions seem also to be satisfied for a few RE chalcogenides/II-VI compound semiconductor systems (Palmstrom et al., 1990). These have yet to be tested. The overgrowth of 111-V compound semiconductors on RE monopnictide layers has been much more difficult (Palmstrom et al., 1988, 1990) than overgrowth on the aluminides (Harbison et al., 1988). GaAs grows with very rough surface morphology on REAs (Palmstrom et al., 1988). 8.5.5 Structure, Energetics, and Electronic Properties of M-S Interfaces 8.5.5.1 Epitaxial Silicide- Silicon Interfaces

Epitaxial CoSi,-Si and Nisi,-Si interfaces are the most perfect M-S interfaces available. Not surprisingly, they are also the best characterized M-S interfaces. Both type A and type B NiSiJSi (1 11) interfaces were found by high resolution electron microscopy (HREM) to agree with the sevenfold model (Cherns et al., 1982; Foll, 1982; Gibson et al., 1983), as shown in Fig. 8-50.


(a) TYPE A NiSiz/Si(lll)

(b) TYPE B NiSi2/Si(lll)

(c) TYPE B CoSi2/Si(lll)

(d) CoSi 2/Si(lOO)

(The terminology for the structure of a silicide interface, e.g., sevenfold, is based on the number of nearest silicon neighbor atoms to a metal atom at the interface. In a bulk disilicide lattice, each metal atom has a coordination number of eight.) These results are in agreement with those from Xray standing wave (XSW) and medium energy ion scattering (MEIS) studies (van Loenen et al., 1985b; Zegenhagen et al., 1987a; Robinson et al., 1988). For the type B CoSi,/Si( 111) interface, it is now clear that the eightfold structure is the one most frequently observed (Bulle-Lieuwma et al., 1989b). This structure was misidentified in earlier experiments as having fivefold coordination (Gibson et al., 1982; Fischer et al., 1987; Zegenhagen et al., 1987b). Two theoretical papers (van den Hoek et al., 1988;

521

Figure 8-50. Ball and stick models of epitaxial silicide interfaces: a) sevenfold type A NiSi,/Si ( 1 1 I), b) sevenfold type B NiSi,/Si (1 1 I), c) eightfold type B CoSi,/Si (1 1 l), and d) eightfold CoSi,/Si (100).

Hamann, 1988a) pointed to the high interfacial free energy for the fivefold model in comparison to the eightfold model. However, it is also known that the interfacial structure of type B CoSi,/Si (1 11) may vary according to the preparation - evidence for the sevenfold coordinated structure has been observed. Type A CoSi,/Si (1 11) is thought to be sevenfold coordinated (Bulle-Lieuwma et al., 1989b). High resolution images of the NiSi,/Si (100) interface have been interpreted to originate from the sixfold model (Cherns et al., 1984; d’Anterroches and Arnaud d’Avitaya, 1986), even though these images are also consistent with the eightfold model. Theoretical calculation (Fujitani and Asano, 1992) and the observation of interfacial reconstruction (Sullivan et al., 1992) both suggest the coordination number for

522

8 interfaces

the stable NiSi,/Si(100) interface to be higher than six. Full eightfold coordination is believed to be achieved at the CoSi,/ Si (100) interface. A 2 x 1 reconstruction (two domains) is often observed, and atomic models responsible for this interface reconstruction have been proposed (Loretto et al., 1989; Bulle-Liuewma et al., 1991). The occurrence of this reconstruction is dependent on the preparation of the silicide layer, it being most prominently seen in samples that have been annealed at higher temperatures. The interface between epitaxial CoSi, and Si (1 10) always shows a dechanneling peak in ion scattering experiments and domain contrasts in TEM. The experimental results are in agreement with the existence of a rigid shift between the CoSi, and the silicon, as seen in Fig. 8-44, with an in-plane component along the [ 1101 direction. It should be noted that, with the proposed rigid shift, interfacial cobalt atoms are situated on bridge sites over the silicon lattice, again achieving an eightfold coordination. Other silicide interfaces, notably the Pd,Si/Si (111), have also been studied by HREM (Krakow, 1982). However, the interface is rough and the structure non-uniform. An intriguing dependence of the SBH on the epitaxial orientation has been observed at the epitaxial silicide interfaces. Type A and type B Nisi, have distinctively different SBHs (Tung, 1984; Hauenstein et al., 1985) on Si( 11l), as shown in Table 8-2. A low SBH, - 0.65 eV, for type A Nisi, on ntype Si (1 11) is very consistently measured (Tung, 1984; Tung et al., 1986c; Ospelt et al., 1988). As for SBH of type B Nisi,, there is some data fluctuation, depending on the preparation, diode processing, and the method of SBH measurements (Hauenstein et al., 1985; Ospelt et al., 1988). Uniform NiSi,/Si(100) interfaces show an SBH that is much lower on n-type silicon than either of the two NiSi,/Si (111) interfaces. Since

the NiSi,/Si (100) interface has an entirely different atomic structure from either of the two NiSi,/Si (1 11) interfaces, it is perhaps not surprising that the SBH is also different. It should be noted that the low SBH of 0.4 eV on n-type Si(100) (>0.7 eV on ptype silicon) measured from uniform Nisi, layers is also very different from the value of 0.6-0.7 eV usually observed for all phases of polycrystalline nickel silicides on silicon. As shown in Fig. 8-40, the facet bar density at an NiSi,/Si (100) interface can be controlled by processing. The presence of a few facet bars at NiSi,/Si (100) interfaces, which are otherwise flat, has little effect on the n-type SBH, but has a strong influence on the measured SBH of p-type silicon. The I- V deduced p-type SBH decreases rapidly as the density of facet bars increases, while a slower but noticeable decrease of the C- V SBH is concurrently observed. As a result, the C-V measured SBH for any specific diode significantlyexceeds that deduced from I- V. Mixed-morphology p-type diodes are “leaky”, having poor ideality factors (n 2 1.08 forN,> 10l6 ~ m - anddisplaying ~) reverse currents that do not saturate. There is also a clear dependence of the electron transport on the substrate doping level. All of these observations are consistent with the behavior of an inhomogeneous Schottky barrier, as explained in detail in an analytic theory on SB inhomogeneity (Tung, 1991; Sullivan et al., 1991). If it is assumed that the faceted regions have a local SBH of 0.47 eV, characteristic of the sevenfold type A (1 11) interface, while the planar background has a SBH of 0.72 eV, characteristic of the Nisi,( 100) interface, then the experimental results can even be explained semiquantitatively. The epitaxial system of NiSiz/Si (100) presents a very rare opportunity in the study of the SB formation mechanism, because it is the only demonstration of SBH inhomogeneity, on a length scale


smaller than the depletion width, which is artificially fabricated and studied. Results from this interface provided strong support from the transport theory of inhomogeneous SBs (Tung, 1991). The dependence of the SBH on interface orientation, with three different SBHs for three differently structured interfaces between the same two materials, has not been observed for nonepitaxial M-S systems and appears to be in disagreement with many existing SBH theories. Theoretical calculations have shed some light on the origin of the observed difference in A and B type SBHs. Very large supercell sizes were used and were found to be necessary to observe the difference in interface electronic properties due to the subtle difference in the interface atomic structures (Hamann, 1988b; Das et al., 1989; Fujitani and Asano, 1989). The experimentally observed difference in A and B type SBH is qualitatively reproduced in these first-principle calculations. Quantitative agreement also seems reasonable with the most sophisticated calculations. At this stage, it seems appropriate to attribute the mechanism for SBH formation, at least for these near perfect M-S interfaces, to intrinsic properties associated with the particular interfacial atomic structure. The SBH at the type B CoSi,/Si( 111 ) interface is also expected to depend on the interface atomic structure (Rees and Matthai, 1988). Films grown by room temperature deposition of - 1-5 nm thick cobalt and annealing to >600°Cusually show an SBH in the range 0.65-0.70 eV on n-type silicon (Rosencher et al., 1985). These interfaces have the eightfold structure. However, recent experiments on the growth of CoSi, layers at lower temperatures and with lower dislocation densities have produced interfaces that show considerable variation in SBH (Sullivan et al., 1993). A low SBH, -=0.3 eV, for some type B CoSi, layers on n-

523

type Si( 111) has been observed, which has tentatively been attributed to cobalt-rich portions of the interface. With the expected variation of atomic structure and the existence of a phase transformation at this M-S interface (both discussed earlier), the situation is expected to be quite complicated. The SBHs of single crystal CoSi, layers on Si(1 lO)andSi(100)aresimilar,both-0.7 eV on an n-type substrate. 8.5.5.2 Epitaxial Elemental Metals

The epitaxial interfaces Al/Si (1 11) and Ag/Si (1 11) have been studied by HREM (LeGoues et al., 1986,1987). The high density of interface steps and defects has so far prevented a conclusive understanding of the interface structures. AVSi(111) interfaces formed by a partially ionized beam appear to be flatter, but incommensurate (Lu et al., 1989). Depending on the growth conditions, an A1-Ga exchange reaction takes place at the AI/GaAs interface (Landgren and Ludeke, 1981). There is also a noted reaction at the interface of Fe/GaAs (Krebs et al., 1987). The interfaces between epitaxial aluminum and GaAs ( 100) have been studied by a number of techniques (Marra et al., 1979; Kiely and Cherns, 1988). An MBE prepared GaAs ( 1 00) surface may have a variety of reconstructions which are associated with different surface stoichiometries. The periodicities of some of these superstructures are found to be preserved at the Al/GaAs interface (Mizuki et al., 1988). It has been discovered that the Schottky barrier height between epitaxial aluminum of silver layers and GaAs is a function of the original GaAs surface reconstructiodstoichiometry (Cho and Dernier, 1978; Ludeke et al., 1982; Wang, 1983). However, different conclusions have been drawn in other studies (Barret and Massies, 1983; Svensson et al., 1983; Missous et al., 1986).

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8 Interfaces

8.5.5.3 Intermetallic Compounds on 111-V Semiconductors The interfaces between GaAs (AIAs) and a number of epitaxial intermetallic compounds have been examined by HREM (Harbison et al., 1988; Palmstrom et al., 1989a, b; Sands et al., 1990; Tabatabeie et al., 1988; Zhu et al., 1989). However, the atomic structures of these interfaces have not been properly modeled. Evidence for a reconstruction has been observed at the interface between NiAl and overgrown GaAs (Sands et al., 1990). Negative differential resistance has been observed at a discrete bias in electrical transport perpendicular to the interfaces of a GaAs/AIAs/NiAl/ AlAs/GaAs structure (Tabatabaie et al., 1988). This is thought to indicate quantization of states in the thin NiAl layer (Tabatabaie et al., 1988).

8.5.6 Conclusions We have briefly reviewed important developments in the field of epitaxial metalsemiconductor structures. Obviously, much has been accomplished in the fabrication

and characterization of these structures. But the need still exists for better structures and better electrical properties. Further studies should prove to be beneficial both to our understanding of the SBH mechanisms and, perhaps, to next generation devices.

8.6 Interfaces Between Crystalline and Amorphous Materials: Dielectrics on Silicon 8.6.1 The Si/Si02 System The Si/Si02 interface, which forms the heart of the gate structure in a metal-oxide- semiconductor field effect transistor (MOSFET), is arguably the most economically and technologically important interface in the world. The MOSFET, depicted in Fig. 8-51, has enabled the microelectronics revolution, and unique attributes of the Si/Si02 interface, such as ease of fabrication and low interface state density, have made this possible. The dimensions of MOSFETs and other devices have continuously shrunk since the advent of integrated circuits about forty years ago, according to

Figure 8-51. Schematic diagram of a simple n-channel MOSFET.

8.6 Interfaces Between Crystalline and Amorphous Materials: Dielectrics on Silicon

525

Table 8-3. Technology roadmap characteristics in the area of thermaythin films. First year of production DRAM generation Minimum feature size (nm) Equivalent oxide thickness (nm)

1997

1999

2001

2003

2006

2009

2012

256M 250 4-5

1G 180 3-4

1G 150 2-3

4G 130 2-3

16G

64G 70 8) dielectric constant, (b) thermodynamic stability with respect to the formation of SiO,, silicides, or oxides of other stoichiometry (i.e., they should not react with the underlying silicon), (c) a low concentration of interface states, (d) resistance to dopant and other impurity diffusion, (e) low leakage current, and (f) a large band gap (> 4 eV) and a large conduction band offset relative to silicon.

8.7 Conclusion In this chapter, we have attempted to outline the major structural characteristics of four generic classes of interface systems. For lattice-matched systems, high resolution electron microscopy techniques have been developed to probe the chemical structure across heterojunctions on the atomic scale. Recent electron holography results have demonstrated the potential to characterize and understand field distributions at interfaces defined by different dopants. Future evolutions of these techniques will enable greater understanding of the correlation between structural and electronic and optical properties of these systems. For latticemismatched isostructural systems, detailed mechanistic understanding of the primary relaxation modes, roughening, and misfit

dislocation injection, is evolving. Further, ever-increasing capabilities in atomistic simulations of defects, coupled with experiment, are enabling the understanding of the electronic and optical properties of interfacial dislocations to be refined. An enduring challenge, however, is the ability to control dislocation densities in high mismatch heterostructures. For these systems, a “floor” density of the order of lo6 cm-2 of threading defects is observed. For heterostructures consisting of dissimilar crystalline materials, such as epitaxial metal silicides on silicon, a major issue is the difficulties associated with wetting in many systems with high interfacial energy. Understanding and control of systems with multiple epitaxial relationships is also a major challenge. The structural quality attainable in some systems, such as NiSi,/Si and CoSi2/Si,however, has enabled significant advantages in the understanding of the fundamental mechanisms of Schottky barrier formation. Finally, the archetypal interface between crystalline and amorphous materials is the Si02/Si interface, which is of critical importance to the entire microelectronics industry. Although this is undoubtedly one of the most extensively studied materials systems in existence, much needs to be learnt about this interface and the fundamental mechanisms of silicon oxidation. The need to maintain ultrahigh perfection of electronic and dielectric properties as gate oxides in transistors become ever thinner is driving the industry to explore and apply new gate dielectric materials such as silicon oxynitrides.

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General Reading Thin Films: Heteroepitaxial Systems. Liu W. K., Santos M. B. (Ed.). (World Scientific Press, Singapore 1999). Materials Fundamentals of Molecular Beam Epitaxy. Tsao, J. Y. (Academic Press, Boston 1993). Germanium Silicon: Physics and Materials. Kull R., Bean J. C. (Ed.) (Academic Press, San Diego, 1999).


9 Material Properties of Hydrogenated Amorphous Silicon

..

.

R A Street and K Winer Xerox Palo Alto Research Center. Palo Alto. CA. U.S.A.

543 List of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 9.1.1 Plasma-Enhanced Chemical Vapor Deposition Growth of Hydrogenated Amorphous Silicon . . . . . . . . . . . . . . . . . . . . 546 9.1.2 Molecular Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549 9.1.3 Chemical Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 9.1.4 Localization of Electronic States . . . . . . . . . . . . . . . . . . . . . . . 552 9.2 Electronic Structure and Localized States . . . . . . . . . . . . . . . . . 553 9.2.1 Band Tail States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553 9.2.2 Doping and Dopant States . . . . . . . . . . . . . . . . . . . . . . . . . . 554 9.2.2.1 The Doping Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 9.2.2.2 Dopant States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556 9.2.3 Native Defects and Defect States . . . . . . . . . . . . . . . . . . . . . . 558 9.2.3.1 Microscopic Character of Defects . . . . . . . . . . . . . . . . . . . . . . 558 9.2.3.2 Dependence of the Defect Concentration on Doping . . . . . . . . . . . . 558 9.2.3.3 Distribution of Defect States . . . . . . . . . . . . . . . . . . . . . . . . . 559 9.2.3.4 Dependence of the Defect Concentration on Growth Conditions . . . . . . 561 9.2.4 Surfaces and Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 9.2.4.1 Surface States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 561 9.2.4.2 Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 9.2.4.3 Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 9.2.5 Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 9.3 Electronic Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564 Conductivity, Thermopower and Hall Effect . . . . . . . . . . . . . . . . . 564 9.3.1 566 9.3.2 The Drift Mobility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Defect Equilibrium and Metastability . . . . . . . . . . . . . . . . . . . 568 9.4.1 The Hydrogen Glass Model . . . . . . . . . . . . . . . . . . . . . . . . . 568 9.4.2 Thermal Equilibration of Electronic States . . . . . . . . . . . . . . . . . 570 The Defect Compensation Model of Doping . . . . . . . . . . . . . . . . . 571 9.4.3 573 9.4.4 The Weak Bond Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Distribution of Gap States . . . . . . . . . . . . . . . . . . . . . . . . 575 9.4.4.1 576 9.4.5 Defect Reaction Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . 576 9.4.5.1 Stretched Exponential Decay . . . . . . . . . . . . . . . . . . . . . . . . . 577 9.4.5.2 Hydrogen Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.6 Metastability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578 9.4.6.1 Defect Creation by Illumination . . . . . . . . . . . . . . . . . . . . . . . 580

542 9.4.6.2 9.5 9.5.1 9.5.2 9.5.2.1 9.5.3 9.6 9.7


Defect Creation by Bias and Current . . . . . . . . . . . . . . . . . . . . . Devices and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . Thin Film Transistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . P-i-n Photodiodes and Solar Cells . . . . . . . . . . . . . . . . . . . . . . The Photodiode Electrical Characteristics . . . . . . . . . . . . . . . . Matrix Addressed Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

582 583 583 584 . 585 589 592 593


List of Symbols and Abbreviations average recombination constant distance between sites creation probability of defects sample thickness characteristic distribution coefficient negatively charged defect states prefactor of diffusion coefficient hydrogen diffusion coefficient phosphorus distribution coefficient electron charge energy from the mobility edge energy activation energy of conductivity activation energy barrier of a thermal defect creation process mobility edge energy of conduction band slope of conduction band tail slope of valence band tail gap state energy associated with UDo demarcation energy Fermi energy energy to release hydrogen from a Si-H bond gap state energy associated with donor trap depth below conduction band mobility edge energy of valence band gap state energy of the valence band tail state energy provided by recombinations conductivity activation energy shift of defect band shift in Fermi energy change of energy of the ion core interaction with and without a defect Fermi function electric field LandC-g-factor illumination intensity hyperfine splitting nuclear spin crystal momentum Boltzmann constant time dependent rate constant reaction constant charge carrier density carrier density prefactor number of valence electrons

543

544


density of states distribution function distribution of conduction band energies distribution of trap energies concentration of the 4-fold silicon sites distribution function of the formation energy density of excess electrons in band edge states effective conduction band density of states defect concentration time dependent defect density decrease of excess electron density neutral defect density negatively charged defect density equilibrium defect density neutral defect density for unshifted Fermi energy dopant concentration hydrogen concentration trap concentration band tail density-of-states prefactor hole concentration Si - Si bond length cooling rate time temperature effective temperature of trap distribution slope of the exponential conduction band tail freezing temperature glass transition temperature parameter describing the Meyer-Neldel rule slope of the exponential valence band tail defect correlation energy formation energy of the defect formation energy of the neutral defects formation energy of the donor formation energy of the neutral dopant volume disorder potential glass volume lattice relaxation energy r.f. plasma power gas phase mole fraction mole fraction of impurity I mole fraction of P coordination number, number of neighbors in amorphous material


dispersion parameter, T/To deposition rate per unit r.f. plasma power pyrolytic rate constant stretched exponential parameter, TIT, temperature coefficient of Fermi energy bond angle between neighboring Si-atoms doping efficiency, [P,]/[P] dihedral angle charge carrier mobility free mobility of charge carriers effective drift mobility of charge carriers mobility prefactor width of gaussian distribution of defect states conductivity conductivity prefactor minimum metallic conductivity conductivity constant decay time free carrier lifetime lifetime of carrier in traps relaxation time rate prefactor, attempt-to-escape frequency C(T,T,, NH) entropy factor a-Ge :H a-Si a-Si :H a-Sic :H a-SiGe :H a-SiO,: H a-SiN,: H c-Si d.c. ESR MBE PECVD RDF r.f. r.m.s.

TIT U.V.

VPPm

hydrogenated amorphous germanium amorphous silicon hydrogenated amorphous silicon amorphous silicon carbide amorphous silicon-germanium alloy amorphous silicon oxide amorphous silicon nitride crystalline silicon direct current electron spin resonance molecular beam epitaxy plasma-enhanced chemical vapor deposition radial distribution function radio frequency root mean square thin film transistors ultra violet parts per million of volume

545

546


9.1 Introduction Hydrogenated amorphous silicon (a-Si:H) has been actively studied for about 30 years. The unhydrogenated material (a-Si) has such a large defect density that it is unusable for electronic devices, although there is continuing interest in its atomic structure. The beneficial effects of hydrogen were discovered at least in part by accident, when the material was deposited from silane (SiH4)gas in a plasma discharge. This method of growth results in a reduction of the defect density by about four orders of magnitude compared to unhydrogenated a-Si, giving material which is of device quality. It is now recognized that hydrogen removes defects by bonding to unterminated silicon atoms. The first demonstration of substitutional doping, made possible by the low defect density, was reported in 1975 and opened the way to many device applications (Spear and LeComber, 1975). Since that time the research effort has greatly expanded so that this material now dominates studies of amorphous semiconductors, and many technology applications have developed. The first photovoltaic solar cells made from a-Si :H were described by Carlson and Wronski (1976), and the conversion efficiency has steadily improved to its present value of 13-1496. In 1979 the plasma deposition of silicon nitride was used in conjunction with a-Si :H to produce field effect transistors (LeComber et al., 1979). Large area arrays of these thin film transistors (TFT) are now important in liquid crystal displays (Miki et al., 1987) and monolithic circuits for printing and input scanning applications (Thompson and Tuan, 1986). The combination of doping and transistor action means that essentially all of the circuit elements used in crystalline silicon electronics can be reproduced in a-Si: H,

giving it a broad versatility in electronic circuit design. The principal advantage of using a-Si :H is that it can be deposited over large areas on low cost substrates such as glass.

9.1.1 Plasma-Enhanced Chemical Vapor Deposition Growth of Hydrogenated Amorphous Silicon The usual method of depositing a-Si :H is by plasma decomposition of silane gas, SiH4, with other gases, such as PH,, B2H6, GeH, etc., added for doping and alloying. Silane decomposes thermally above about 450°C and amorphous films can be grown in this way at temperatures less than about 550°C. However, these films are of limited utility because the temperature is too high to retain the hydrogen. The deposition of hydrogenated films at lower temperatures requires a source of energy to dissociate the SiH4, which is the role of the plasma. The first plasma deposition system for amorphous silicon was a radio frequency (r.f.) inductive system developed by Chittick et al. (1969). Most subsequent reactors are in a diode configuration in which the plasma is confined between two parallel electrodes. This type of reactor is illustrated in Fig. 9-1, and consists of a gas inlet arrangeHeater

Gas inlet

-Pump

rf power Flow controllers source Figure 9-1. Schematic diagram of the main components of a typical r.f. diode plasma reactor for depositing a-Si :H and its alloys.

547

9.1 Introduction

ment, the deposition chamber which holds the heated substrate, a pumping system, and the source of power for the discharge. The deposition process is usually referred to as plasma-enhanced chemical vapour deposition (PECVD). There are numerous variations on this basic deposition process, but the resulting material is largely independent of the choice of technique. The structural and electronic properties of the film depend on the conditions of growth, particularly substrate temperature, r.f. power and gas composition. Figure 9-2 summarizes some typical measurements of PECVD a-Si :H films (Knights and Lucovsky, 1980). The hydrogen content varies between 8 and 40 at.% and decreases slowly as the substrate temperature is raised. In addition, the hydrogen content depends on the r.f. power in the plasma and on the composition of the gas; Fig. 9-2b shows the

variation when SiH, is diluted to 5% concentration in argon. The defect density also depends on the substrate temperature and power with variations of more than a factor 1000. The minimum defect densities of 10*5-10'6 cmP3usually occur between 200 and 300°C and at low r.f. power densities (;

Q.,

0

C

.-01 0 .c

'?,

01

Ol

.-C0

2

10-2

10-3 10-6

10-~ 10" Gas-phase mole fraction of As

ation rates of phosphine and silane, p is the pyrolytic rate constant, and a is the deposition rate per unit r.f. plasma power Wrp This relation describes the competition between impurity incorporation via pyrolysis (= /3 Xfl") and via plasma-enhanced decomposition (= a W). When the latter dominates (at high r.f. plasma power and large X,), the distribution coefficient is essentially constant between 5 and 10. When thermal decomposition of the impurity gas (i.e., BzH6, ASH,, PH,, etc.) dominates impurity incorporation (low r.f. plasma power and small X), the distribution coefficient can attain values near 30 for P (Bsmall) and near 300 for As (p large). Finally, active dopant incorporation can be described by the chemical reaction

(9-6) so that by the law of mass action at equilibrium and [P,'] = [e-] one obtains [P,'] = Xf1I2 as observed experimentally (Street, 1982). We can now express r] completely in

lo5

terms of X , to obtain

"

aW

The same competition between plasma-enhanced decomposition and pyrolysis determines the doping efficiency in a-Si :H. Under conditions where plasma decomposition dominates such a high growth rates or small p's (i.e. B or P doping) the doping efficiency is simply proportional to x-'". Under conditions where thermal decomposition is significant such as low growth rates and large p's (i.e. As doping), r] is constant and very small, as observed in Fig. 9-10.

9.2.2.2 Dopant States Four-fold coordinated dopants such as B4 and P, form effective mass donors and acceptors with localized dopant states near the band edges, as in c-Si. The variations in

9.2 Electronic Structure and Localized States

disorder potential broaden the dopant levels, similar to the band tailing of the silicon states. Donor states have been observed through their electron spin resonance (ESR) hyperfine interaction with the spin of donor electrons (Stutzmann and Street, 1985). Donor electrons in a-Si:H are more localized than in c-Si and the hyperfine interaction is correspondingly stronger. The donor band is deeper in the gap and broader than the shallow, well-defined donor levels in c-Si. Because the valence band is much broader than the conduction band tail in a-Si :H, hyperfine measurements have not been able to detect the corresponding B, donor states in B-doped a-Si:H. The probable distributions of P4, As, and B, dopant states in highly-doped a-Si :H are shown in Fig. 9-1 1. The arsenic donor is deeper than the phosphorus donor because of differences in size, electronegativity and bond strength. The P! ESR hyperfine signal in a-Si :H exhibits two lines split by AH = 24.5 mT with a peak-to-peak line width of about 6 mT for each line (Stutzmann and Street, 1985). The two hyperfine lines are due to

EV 0.1 0.2 0.3 0.L 0.5 Energy in eV

-0.3 -0.2 -0.1

EC

Figure 9-11. Distributions of shallow donors states in doped a-Si :H. Such states are broadened relative to their crystalline silicon counterparts by the network disorder. Dashed lines represent the band tails (Street, 1987).

557

the interaction of the spins of electrons localized at P, sites with the spin I = 1/2 of the 31Pnucleus. The 31Phyperfine signal increases with the gas-phase P mole fraction X,, but the concentration of neutral donors is much smaller than that of ionized donors, because of compensational defects. The distribution of electrons which occupy the conduction band tail states can be measured by photoemission yield spectroscopy (Wineret al., 1988). In undoped slightly P-doped a-Si : H, the expected Boltzmann fall-off in the density of occupied states above the Fermi energy is observed. However, as the gas-phase P mole-fraction increases beyond the Fermi tail broadens considerably. Dividing the measured occupied density of states by the FermiDirac occupation function reveal an exponentially increasing total density of states above the Fermi energy consistent with the leading edge of the P, donor band of states. The density and location of donor states observed by this method agrees with those inferred from the ESR hyperfine measurements. The carriers near the band edge include those occupying dopant states as well as the intrinsic band tail states, and in n-type a-Si :H there are roughly equal concentrations of each, because the band tail overlaps the donor band. The density of shallow carriers is quite low because of the low doping efficiency and the compensation by defects. The doping effect in a-Si :H is consequently rather weak. For example, at a gas phase doping level of 1%, less than 1% of the phosphorus is in the form of 4-fold donor states, and of these donors, about 90% are compensated by deep defects. Of the remaining 10% of the donor electrons at the band edge, most occupy band tail states, so that the free electron concentration is only 1 O4 of the impurity concentration. The low mobility of free carriers in a-Si :H compared to c-Si, results

558


in the conductivity of n-type a-Si :H being more than five orders of magnitude below that of c-Si.

9.2.3 Native Defects and Defect States Unsatisfied or “dangling” bonds are the dominant native defect in a-Si :H; the amphoteric nature of this defect gives rise to either unoccupied (positively-charged), singly-occupied (neutral), or doubly-occupied (negatively-charged)electronic states. These localized states lie near the middle of the mobility gap and greatly affect the movement of the Fermi energy and transport and recombination processes. An understandingof the character and distribution of defect states and their dependence on growth conditions and doping level is essential for the successful application of a-Si :H and its alloys. Not surprisingly, a multitude of experimental methods have been developed and intensive effort has been expended in the pursuit of this understanding.

9.2.3.1 Microscopic Character of Defects Defect states are generally the most localized of all electronic states in a-Si :H, lying deep in the mobility gap at low densities. Most of our knowledge concerning the microscopic character of defects is derived from electron spin resonance (ESR) measurements. ESR measures both the concentration and the local environment of the neutral paramagnetic defects in a-Si:H. The concentration of charged defects can also be determined by ESR by illuminating the material with band gap light during the measurement to depopulate charged defects and make them spin active (Street and Biegelsen, 1982). The dominant defect in undoped a-Si :H has a nearly symmetric spin signal at a g-value of 2.0055 and a peak-to-

peak width of ~ 0 . 7 5mT. These characteristics are similar to those of the ESR signal from unterminated bonds at the c-Si/Si02 interface, which has led to the identification of the g=2.0055 signal in a-Si:H as due to undercoordinated or “dangling” bonds. It has also been proposed that native defects are better described by overcoordinated or “floating” bonds (Pantelides, 1986). Such floating bonds have many of the same properties as dangling bond except that they are predicted to be very mobile whereas dangling bonds should be essentially immobile. Recent calculations and defect diffusion measurements have all but ruled out the floating bond hypothesis (Fedders and Carlssen, 1989; Jackson et al., 1990); the dangling bond remains the only defect model that can consistently account for the properties of native a-Si :H defects.

9.2.3.2 Dependence of the Defect Concentration on Doping The incorporation of substitutional impurities during growth leads to an increased charge carrier concentration in both c-Si and a-Si :H. In a-Si :H, the majority of extrinsic charge carriers are taken up to form compensating charged defects. This process can be described schematically in the case of P doping by the following chemical reactions P,

% P4++e-

Si4 + e-

% Si;

(9-8) (9-9)

where the subscripts refers to the coordination. The reactions are independent but they are linked by their dependence on the carrier concentration. The required coordination changes are accomplishedvia hydrogen bond diffusion, and the kinetics of this and similar reactions is determined by the kinetics of dispersive hydrogen diffusion. Applying the law of mass action to reactions (9-8)


559

pendences on growth conditions and doping determined by different laboratories usually agree. However, the number of different methods for measuring defect state distributions is nearly as large as the number of different laboratories interested in this problem! The defect distributions extracted or inferred from these many methods do not always agree and at least two distinct schools have developed whose disagreement in the placement of defect state energies in the gap amounts to several tenths of 1051 ' ' ' I, i d lo-' lo-' 10-510-5 10-i an electron volt (Lang et al., 1982, Okushi B2H6 PH3,ASH, et al., 1982). The results of three typical Dopant gas concentration in cm" experimental methods which provide a more or less consistent picture of the defect Figure 9-12. Defect concentrations as a function of gas phase mole fraction of boron, phosphorus, and arstate distribution in a-Si:H are shown in senic (Stutzmann et al., 1987). Fig. 9-13. The luminescence transition observed in P-doped a-Si:H at 0.8-0.9 eV (Fig. 9-13) and (9-9) leads to the square-root depenhas been interpreted as a band-tail-to-defect dence of the defect [Si;] and active dopant transition (Street, 1982). The 0.9 eV ener[Pi] concentrations on the solid-phase P gy, therefore, is a measure of the separation concentration [PI, which is proportional to between the charged defect band peak and, the gas-phase phosphorus mole fraction most probably, the conduction band tail. The under most deposition conditions. This shape and the 0.3 eV width of the luminessquare-root dependence of [Si;] on X, is cence band should be characteristic of the observed for all substitutional dopants, as shape of the defect band. The defect distribution inferred from deep-level transient shown in Fig. 9-12. However, the high spectroscopy (Lang et a]., 1982) and optical intrinsic defect density in a-Ge :H masks the absorption measurements is consistent with doping dependence in this material. the luminescence measurements: negatively-charged D- defect states lie in a broad 9.2.3.3 Distribution of Defect States band 0.8-1 eV below the conduction band mobility edge in P-doped a-Si :H. The optiThe defect concentration in undoped cal absorption data indicate a defect level at a-Si :H determined by ESR or optical ababout the same energy. Similar measuresorption typically lies between lOI5 and ments on p-type material find a defect lev1OI6 cm-3 for optimized deposition condiel which is well separated from the valence tions. In heavily-doped a-Si : H, the defect concentrations can increase to 10" ~ m - ~ . band edge (Kocka et al., 1987). In summary, the majority of doping-induced states and The detection of such small defect concenthe Fermi energy lie opposite each other in trations by ESR and optical absorption the gap; the Fermi energy of doped a-Si: H measurements (Jackson and Amer, 1982) is lies in a relative minimum in the gap state relatively simple and has become so standistribution. This picture has been condardized that the defect concentration dec _

-

9 Material Properties of Hydrogenated Amorphous Silicon I

I

I

I

I

I

I

l

l

CAPACITANCE

OPTICAL ABSORPTION

P.?.? EXPERIMENT -CALCULATION

I

)I

I

,

I

I

I

I

I

TRANSIENT CAPACITANCE

-

E,-W

\LUMINESCENCE

I

. 0.6

0.8 1.0

I

1.2 1.4 1.6 ENERGY eV

I

1.8

I

2.0

Figure 9-13. Typical data from which a consistent distribution of gap states has been inferred; obtained from luminescence, deep level transient spectroscopy, and optical absorption experiments (Street et al., 1985). E, is the defect level measured from Ec and W is the contribution to the optical transition energies from lattice relaxation. The calculated absorption is a convolution of the conduction band and the defect level distribution.

F P-tYPe

Ec

-------- --

undoped

firmed by several other types of capacitance and absorption measurements, as well as by photoemission spectroscopy measurements (Winer et al., 1988). A schematic description of the distribution of gap states in ptype, n-type, and intrinsic a-Si :H is shown in Fig. 9-14. The 0.1-0.3 eV difference between the negatively-charged (doubly-occupied) and neutral (singly-occupied) defect state energies determined from optical absorption data is a measure of the defect correlation energy, U,, defined as the energy cost to plase a second electron on a singly-occupied, localized defect level (Jackson, 1982). Electron spin resonance and optical absorption measurements are also consistent with a small, positive value of U , (Street and Biegelsen, 1982; Dersch et al., 1980; Jackson, 1982). The doubly occupied defect gap state energy level lies above the singly occupied level by an energy U,, as depicted in Fig. 9-14. This view of the distribution of defect states in intrinsic a-Si :H is generally accepted. However, the defect energy levels observed in doped a-Si :H are not consistent with these observations in undoped material, and suggest instead a defect correlation energy that is negative. The apparently conflicting requirements of a small, positive correlationenergy in intrinsic a-Si :H and the reversal of the defect energy order-

n-type

Figure 9-14. Schematic distribution of defect state in the gap for n-type, intrinsic and p-type a-Si :H. The two levels of the dagling bond are separated by the correlation energy Uc. The shift, AE, of the defect levels with doping given by Eq. (10-48) and dicussed in the text.


ing in a doped a-Si: H can be resolved by invoking a broadly-distributed pool of virtual defect states within a chemical equilibrium framework of defect formation from which the system can choose to form defects in order to minimize the system free energy (Winer, 1989). This defect formation framework is discussed in detail in Sec. 9.4.

9.2.3.4 Dependence of the Defect Concentration on Growth Conditions Thin films of a-Si :H are typically deposited onto heated (250" C ) glass substrates by the r.f. plasma decomposition of silane at gas pressures near 100 mTorr. Under these conditions, growth rates of about 1 A per second are typically achieved. Ion bombardment, U.V. exposure, and strong electric fields accompany such plasma-enhanced chemical vapor deposition, which can enhance defect formation while complicating the analysis of growth processes. The dominant growth parameter under normal deposition conditions, however, is the substrate temperature, whose effect on the defect concentration is shown schematically in Fig. 9-2a. The minimum defect concentration near 3 ~ 1 0 cm-3 ' ~ is obtained for substrate temperatures between about 200 and 300°C. Growth in this temperature range results in reasonably homogeneous, highly photoconductive, high resistivity a-Si :H films suitable for photovoltaic and photoelectronic applications. On either side of this optimal growth temperature range, the material properties degrade for reasons that depend on the details of the growthprocesses, which are not yet completely understood. In simple terms, the defect concentration increases as the growth temperature is reduced because strain-relieving chemical processes that depend on surface diffusion are kinetically limited. As the growth temperature

561

increases beyond the optimal range, increased desorption at strain-relieving species like hydrogen again lead to an increased defect concentration. More detailed models which attempt to account for the behavior of Fig. 9-2a as discussed elsewhere (Tanaka and Matsuda 1987; Winer, 1990).

9.2.4 Surfaces and Interfaces The electronic states specific to semiconductor surfaces and interfaces can affect device performance when the active layer are very thin. Although adsorption of water, oxygen, and other gases has been shown to lead to large changes in the measured conductivity of a-Si :H under certain conditions (Tanielian, 1982), the effects of surface or interface states on a-Si:H device performance are usually negligible. This is due, in part, to two factors. Firstly, there is little distinction between localized bulk and localized surface or interface states in terms of their distribution in the gap which might otherwise affect electronic transport and recombination processes. Secondly, the concentration of intrinsic surface states in a-Si :H is quite low: typically 5 x 10" cm-' compared to 5 x 1014 cmP2 on c-Si. This is due to the effective passivation of the surface by hydrogen at growth termination which makes the a-Si :H surface relatively stable against oxidation in air compared to c-Si (Ley et al., 1981).

9.2.4.1 Surface States The concentration of intrinsic surface states has been determined by a variety of methods, usually by measuring the defect volume concentration as a function of film thickness and extrapolating to zero thickness (Jackson et al., 1983). The distribution of surface states has been measured by photoemission spectroscopy (Winer and Ley,

562


1987). Most methods find an intrinsic surface defect concentration between 1 and 10x 10" cm-* in optimally-grown intrinsic a-Si :H which increase upon n-type doping and initial oxidation. Though small by c-Si standards, this surface defect concentration is equivalent to quite a high volume defect concentration when the layer of a-Si: H is thin. This excess density of gap states at the surface relative to the bulk can be removed by slight boron doping. In fact, the lowest conductivity a-Si:H films are usually obtained by 10 vppm gas-phase boron doping which might be related to the removal of surface or interface states. The reduction in occupied surface gap states allows the valence band tail to be directly observed over a wide energy range by surface-sensitive photoemission spectroscopy. The exponential nature of the tail is maintained over several orders of magnitude in the density of states, and the slope of the tail agrees with values inferred from bulk transport and optical absorption measurements. In general, the distributions of localized surface and bulk states in the band gap are essentially the same. The surface properties of a-SiGe :H alloys are similar to those of a-Si: H (Aljishi et al., 1990), while little is known concerning the surface properties of a-Sic : H or other quaternary alloys systems.

9.2.4.2 Oxidation In the initial stages of oxidation (01 monolayers), surface defect states are induced by activated oxygen adsorption which have been attributed to chemisorbed 3-fold coordinated surface oxygen atoms (Winer amd Ley, 1987). The distribution of these oxygen-induced states is similar to that of defects induced by n-type doping by overcoordinated phosphorus atoms incorporated from the plasma into the a-Si :H film

during growth. This suggests that the overcoordinated chemisorbed oxygen is likewise a surface donor, contrary to the normally strongly electronegative character of adsorbed oxygen. Upon further oxidation (for example, air exposure for long times) a true oxide layer forms with a change to slightly upward band bending and a correspondingly wider band gap than a-Si :H (Berner et a]., 1987; Ley et al., 1981). In clean undoped a-Si :H, the free surface is under electron accumulation corresponding to an 0.5 eV downward band bending. Upon either n- or p-type doping, this downward band bending is removed. Activated oxygen adsorption pins the surface Fermi level just above midgap which results in an 0.25 eV downward band bending. On fully oxidized surfaces, however, the bands appear to be bent in the upward direction, as expected for the strongly electronegative surface oxide (Street et al., 1985b; Berner et al., 1987).

9.2.4.3 Interfaces Interfaces are an integral part of all a-Si :H-based devices and their properties can greatly affect device performance. For example, the gate field that extends from the silicon nitride layer into the undoped a-Si :H active layer in an a-Si :H thin film transistor not only enhances the channel conductivity but can lead to defect creation near the a-SiN,: Wa-Si :H interface, which changes the transistor off voltage. Interface properties become even more important in multilayer structures. A multitude of phenomena initially observed in crystals have been observed in a-Si :H multilayer systems as well and generally result from the same physical origins. Examples are sub-band optical absorption (Hattori et al., 1988), resonant tunneling (Miyazaki et al., 1987), acoustic phonon


zone-folding (Santos et al., 1986), and persistent photoconductivity (Kakalios and Fritzsche, 1984). Multilayers of alternating n- and p-type a-Si:H layers (so-called “nipi” doping superlattices) and alternating alloy heterostructures (i.e. a-Si :H/ a-Ge :H .. .) have been grown and studied for many years. Such structures display a wide variety of phenomena similar to the crystalline analogs. After some initial uncertainties, there is now good evidence for carrier quantization in ultrathin a-Si :H heterostructures (Hattori et a]., 1988; Miyazaki et al., 1987). Interface abruptness is a key problem for substantiating claims of quantized behavior in and exploitation of a-Si :H heterostructure multilayers. The low growth rates typical for a-Si:H (0.5-1.0 A/s, comparable to MBE growth rates) allow ultrathin multilayer growth with near atomic resolution (Yang et al., 1987). 9.2.5 Alloys

A major application of a-Si:H is for large-area solar cell arrays. In this application, the ability to lower the band gap of a-Si :H by alloying with Ge in order to more effectively match the solar spectrum has led to more efficient multijunction devices. On the other hand, alloying a-Si :H with carbon has led to efficient electroluminescent pin diodes with emission in the red, yellow, and green (Kruangam et al., 1987). In addition, amorphous silicon nitrides (a-Si :N,: H) and oxides (a-Si :0,:H) are used as gate dielectrics for TFTs, and for passivation and interlayer dielectrics in active matrix arrays. A-Si :H alloys are usually grown in the plasma-enhanced mode as pure a-Si :H but with the addition of methane, germane, ammonia, etc. as appropriate. The study of alloy properties has proceeded in parallel with that of a-Si :H. Our discussion is limited to weak alloys with the Group IV elements C

563

and Ge, since the properties of these are the most extensively studied. As might be expected these alloy properties deviate little from those of a-Si :Hat low alloy levels with a few interesting exceptions. Dilution of silane with methane for C incorporation generally slows the growth rate with a particularly steep drop occurring near 90% gas-phase methane mole fraction. This is due to the small incorporation probability of C for the PECVD growth mode at 250°C; the distribution coefficient for C under these conditions is typically less than 0.1. There is a large incorporation probability of Ge into a-SiGe:H films. However, growth of good quality a-SiGe :H is usually made at reduced growth rates, but this is due to the high hydrogen dilution which has been found to be necessary in order to reduce the otherwise large defect concentrations in undiluted a-SiGe :H films. Significant changes in the band gap of a-Si:H occur for C or Ge concentrations above about 10%. Infrared absorption spectra of such alloys show a Si-H stretching mode near 2100 cm-’ in addition to the stretching mode at 2000 cm-’ normally observed in pure, optimally-grown a-Si:H. The 2100 cm-’ mode increases in strength with increased C or Ge incorporation, similar to the increase observed with decreasing growth temperature in unalloyed a-Si:H. This behavior is believed to be due to increased hydrogen incorporation, perhaps in the form of clusters, which results from growth far from optimal conditions. The neutral defect (spin) concentration and Urbach edge (valence band tail) slope in undoped a-Si:H alloys also increase with increasing C or Ge incorporation. Post-deposition annealing near the deposition temperature can reduce the defect concentration by up to an order of magnitude with a concomitant decrease in the Urbach edge slope.

564


However, the infrared absorption spectra of a-SiGe :H and a-Sic :H alloys are unaffected by such thermal annealing. Alloy defect concentrations are always higher than that of unalloyed a-Si :H, usually by between 10 and 100 times. This is probably due to the inadequate knowledge of optimal growth conditions of a-Si :H alloys. Electron spin resonance data show that the dominant spinactive (g = 2.0055) defect in a-Si: H and its alloys are the same for moderate alloy compositions (Stutzmann et al., 1989). The spin centers range to g = 2.0037 for C concentrations above about 40%, which probably is due to the emergence of C-C bonds as the dominant structural unit near this concentration. In a-Si:Ge:H alloys the Ge dangling bond dominates when the Ge concentration is above 20-30 at%.

9.3 Electronic Transport 9.3.1 Electrical Conductivity, Thermopower and Hall Effect The conductivity, a, is the product of the carrier density, n, and the carrier mobility, p, and the electron charge, e.

This equation is usually written as r

L

J

where

a(E)= N (J9 e PLO k T

(9-14)

o(T)= ami,exp [-(E,-E,)IkT]

(9-15)

a ( E ) is the conductivity that would be observed when EF = E. The conductivity is determined by the density-of-states, the carrier mobility and the Boltzmann factor. When there is a sufficiently high defect density at the Fermi energy, as in unhydrogenated amorphous silicon, conduction takes place by variable range hopping, with a temperature dependence exp [-AIT”4] (Mott, 1968). The low defect density in a-Si :H prevents this mechanism from contributing significantly, and instead conduction takes place by electrons or holes at the band edges where both the density of states and the mobility increase rapidly with energy. For the particular case in which a (E) increases abruptly from zero to a finite value a ~atnthe mobility edge energy, E,, evaluation of Eq. (9-12) gives

is referred to as the minimum metallic (9-10) omin conductivity and is given by The total conductivity is an integral over the a,,, = N (E,) e k T (9-16) density-of-states, N (E) a=nep,

a = N (El e y ( E )f (E, T ) dE

(9-1 1)

where f ( E , T ) is the Fermi function. The integral contains contributions from electron transport above the Fermi energy EF and hole transport below EP When conductivity takes place far from EFby a single type of carrier, non-degenerate statistics can be applied and so (9-12)

where & is the free carrier mobility at Ec. There is considerable doubt about the sharpness or even the existence of a mobility edge (Abrahams et al., 1979; Mott and Kaveh, 1985). Nevertheless, virtually all the conductivity experiments are analyzed in terms of Eq. (9-15) which is areasonable approximation even if p ( E ) does not change abruptly, provided that it increases rapidly over a limited energy range. The conductivity of a-Si:H is usually thermally activated, at least over a limited

9.3 Electronic Transport

temperature range, and is described by, a ( T ) = ooexp [-E,/kT]

(9- 17)

Comparison of Eqs. (9-15) and (9-17) suggests that a measurement of CJ ( T ) immediately gives the location of the mobility edge (Ec-EF), and that the prefactor gives the conductivity at the mobility edge. In actual fact there is a huge variation in the values of a, which is shown by the results in Fig. 9-15 for undoped and doped a-Si:H. The correlation between a, and the activation energy, E,, is referred to as the Meyer-Neldel rule (after its first observation in polycrystalline materials by Meyer and Neldel (1937)), and is described by In oo= In aoo+ E,/kT,

(9-1 8)

where aoois a constant with a value of about 0.1 Q-' cm-' and k T, is - 50 meV. A substantial part of the variation in the conductivity prefactor is due to the tempera-

7

1

Chicogo

-

0

A

A 0

0 0

J 3

0

0.5 Activation

I.o

E n e r g y Ea (ev)

Figure 9-15. Measured values of the conductivity prefactor uoversus the conductivity activation energy, showing the Meyer-Neldel rule (Tanielian, 1982).

565

ture dependence of the Fermi energy (Beyer and Overhof, 1984) (E,

- EF)

= (Ec - EF)O - y T

(9-19)

from which it follows that a ( T ) = a. eylkexp [-(EC-EF),/kT] (9-20) Various experiments show that a, is 100-200 Q-' cm-', and that ycan vary in the range &5x104 eV/K, due to the shape of the density of states distribution and the temperature dependence of the band gap energy. The free mobility according to Eq. (9-16) is ,q,= ao/N(Ec)e kT=10-15 cm2/Vs (9-21)

The thermopower measures the average energy of the transport with respect to the Fermi energy. The sign of the thermopower determines whether there is electron or hole transport, and confirms that n-type and p-type doping occurs in a-Si :H. This observation is important because the Hall effect, which is the more common measure of the doping type in crystalline semiconductors, has an anomalous sign in amorphous semiconductors as described shortly. The thermopower is expected to exhibit the same activation energy as the conductivity when conduction occurs above a well defined mobility edge (Cutler and Mott, 1969). Figure 9-16 shows examples of the temperature dependence of the thermopower in both ntype and p-type a-Si :H. The thermopower energy does decrease with doping, as expected from the shift of the Fermi energy by doping, but is always smaller than the conductivity energy by about 0.1 eV. This shows that the simple conduction model of an abrupt mobility edge is not exact, although the reason for the difference in energy of conductivity and thermopower is not resolved. Possible mechanisms include long range potential fluctuations of the band edges due to charged localized states, a

566


Figure 9-16. Temperature dependence of the thermopower of n-type (left) and p-type (right) a-Si :H (see Fig. 10-9). The doping levels range from to 2x10-* (Beyer and Overhof, 1984).

u 1 2 3 4 5

0

gradual rather than abrupt increase in the mobility near E,, or polaron conduction. The charged defects and dopants in doped material make the potential fluctuations the most probable mechanism, but this model may not apply to undoped a-Si :H which has many fewer charged defects. A curious aspect of carrier transport in a-Si :H is the anomalous sign reversal in the Hall mobility coefficient. In doped a-Si :H the magnitude of the Hall mobility usually lies between 0.01 and 0.1 cm2Ns (LeComber et al., 1977) much lower than typical values (= 100-1000 cm2/Vs) observed in c-Si, and also lower than the drift mobility of a-Si:H. However, the sign of the Hall coefficient is opposite to the sign of the thermopower (i.e. positive in n-type and negative in p-type a-Si :H). Upon crystallization of a-Si:H, the Hall coefficients revert to their proper sign. The origin of this anomalous sign reversal is not completely understood, but is presumed to be related to the very short scattering lengths (Friedman, 1971; Emin, 1977).

9.3.2 The Drift Mobility Conduction of electron and holes occurs by frequent trapping in the tail states fol-

lowed by excitation to the higher energy conducting states. The drift mobility, b,is the free carrier mobility reduced by the fraction of time that the carrier spends in the traps (9-22) When there is a single trapping level, with density NT, at energy ET below Ec, b = PO N , / [ N , exp (ETlk T ) + Nc] = & (NcINT) exp (-ET/k T )

(9-23)

where N , is the effective conduction band density of states, and the approximate expression applies when b 4 PO. The drift mobility is thermally activated with the energy of the traps. A distribution of trap energies, N(E,), arising from the band tail of localized states, gives a drift mobility which reflects the average release time of the carriers. When the band tail distribution is sufficiently broad, the drift mobility becomes dispersive and is time dependent, following the relation (Scher and Montroll, 1975), 0

b = P D t

a1

-

(9-24)

where

cx = TIT, ,

(9-25)

567

9.3 Electronic Transport

is the dispersion parameter. The unusual time-dependence occurs because the probability that a carrier is trapped in a very deep trap increases with time. Of the many theoretical studies of dispersive transport by multiple trapping, the analysis of Tiedje and Rose (1980) and similarly Orenstein and Kastner (1981), is particularly instructive because the physical mechanism is easy to understand. The approach in this model is to consider an exponential band tail of traps with density proportional to exp (-ElkTo), where E is the energy from the mobility edge. A demarcation energy, E D , which varies with the time, t, after the start of the experiment is defined by ED

= k T In (mot)

(9-26)

EDis the energy at which the average release time of the carrier from the trap is just equal to the time t. Provided the temperature is less than To, electrons in traps which are shallower than EDwill have been excited to the mobility edge and trapped many times, but electrons in states deeper than E D have a very low probability of release within the time t. Thus the states deeper than E D are occupied in proportion to the density of states, but the states above ED have had time to equilibrate and follow a Boltzmann distribution for which the electron density decreases at smaller trap energies. The electron distribution therefore has a peak at ED,and from the definition of ED,this peak moves to larger trapping energies as time progresses. The approximation is made that all the electrons reside at ED, so that the problem can be treated as trapping at a single level, with the added property that the trap energy is time dependent. Substituting EDfrom Eq. (9-26) into Eq. (9-23), with the assumed exponential density of states gives b ( t ) = h a (1-a) (mot)"'

(9-27)

3

~

5

6

7

8

9

Inverse temperature I O O O / T in K-'

2.2

2.6

3.0

3.4

3.8

Inverse temperature 1 0 0 0 / T in K-'

Figure 9-17. Temperature dependence of the (a) electron and (b) hole drift mobility at different applied fields ranging from 5x 10' V/cm to 5x lo4 Vkm. The field dependence of pD is caused by the dispersion (Marshall et al., 1986; Nebel et al., 1989).

568


which has a power law time dependence in agreement with the measurements. In the time-of-flight experiment, the drift mobility is deduced from the time taken for a carrier to cross the sample. It is easily shown that the measured drift mobility is

[

pEp=oo

]

--1

O0

2poU - a)

a

[$I"'

1

(9-28)

where d is the sample thickness and F is the applied electric field. Thus the dispersive mobility is time, thickness and field dependent, and its magnitude is given in terms of the slope of the exponential band tail. Figure 9-17 shows the field dependence of the electron and hole drift mobilities at different temperatures (Marshall et al., 1986, Nebel et al., 1989). The electron mobility is thermally activated, as expected for a trap limited process and at room temperature there is no field dependence and no dispersion because ToS 300 K. However, in the low temperature dispersive regime, there is a large field dependence of and a time-dependent dispersion parameter a described by TIT,. The data for holes is qualitatively similar; the only difference is that the temperature scale is changed, so that the hole transport is dispersive up to 400500 K. The difference occurs because the valence band tail is wider than the conduction band tail. The mobility measurements find a dispersion parameter T,=T, of 250300 K for electrons and To=Tv of 400450 K for holes (Tiedje et al., 1981).

9.4 Defect Equilibrium

and Metastability

Chemical bonding rearrangements are an important influence on the electronic properties of a-Si :H. Defect and dopant states

are created and annihilated either thermally or by external excitations such as illumination, leading to metastable structures. The thermal changes are described by thermodynamic equilibria with defect and dopant concentrations determined by minimization of the free energy. It is perhaps surprising to be able to apply equilibrium concepts to a-Si:H, because the amorphous phase of a solid is not the lowest free energy phase. However, subsets of network constituents may be in equilibrium with each other even if the network structure as a whole is not in its lowest energy state. The collective motion of many atoms is required to achieve long-range order, and there are strong topological constraints which usually prevent such ordering. However, chemical bonding transformations of defects of dopants require the cooperation of only a small number of atoms. Therefore, the small concentrations of defects or impurities in a-Si:H may be expected to participate in local thermodynamic equilibrium which takes place within the more or less rigid Si random network. Evidence that such equilibration is mediated by hydrogen motion is presented and discussed in Sec. 9.4.5.2.

9.4.1 The Hydrogen Glass Model The properties needed to describe the chemical bonding changes in a-Si :H are the equilibrium state and the kinetics of the process. Equilibrium is calculated from the formation energies of the various species, by minimizing the free energy, or equivalently, by applying the law of mass action to the chemical reactions describing the changes. For example, the reaction may correspond to a change in atomic coordination which causes the creation and annihilation of defect or dopant states Si4*Si3

or P,*P4

(9-29)

569

9.4 Defect Equilibrium and Metastability

The kinetics of the reaction are described by , required for the struca relaxation time, z ture to overcome the bonding constraints which inhibit the reaction. tR is associated with an energy barrier, EB, which arises from the bonding energies and is illustrated in Fig. 9-1 8 by a configurational coordinate diagram. The energy difference between the two potential minima is the defect formation energy, UD, and determines the equilibrium concentrations of the two species. The equilibration time is related to the barrier height by ZR = O&'

exp (-EB/k T)

(9-30)

where o, is a rate prefactor of order lOI3 sec-'. A larger energy barrier obviously requires a higher temperature to achieve equilibrium in a fixed time. The formation energy UD and the barrier energy EB are often of very different magnitudes. There is a close similarity between the defect or dopant equilibration of a-Si :H and the behavior of glasses near the glass transition, which is useful to keep in mind in the analysis of the a-Si: H results. Configurations with an energy barrier of the type illustrated in Fig. 9-18 exhibit a high temperature equilibrium and a low temperature frozen state when the thermal energy is in-

sufficient to overcome the barrier. The temperature, T E , at which freezing occurs is calculated from Eq. (9-30) by equating the cooling rate, R,, with dT/dz,, TE In (aok Ti/R,E,) = E B / k

(9-31)

The approximate solution to Eq. (9-31) for a freezing temperature in the vicinity of 500 K is

k TE = EB/(30-In R,)

(9-32)

from which it is readily found that an energy barrier of 1-1.5 eV is needed for TE= 500 K for a normal cooling rate of 10100 K/s. An order of magnitude increase in cooling rate raises the freezing temperature by about 40°C.Below TE, the equilibration time is observed as a slow relaxation of the structure towards the equilibrium state. Figure 9- 19 illustrates the properties of a normal glass by showing the temperature dependence of the volume, V,. There is a change of the slope of Vo(T) as the glass cools from the liquid state, which denotes the glass transition temperature TG. The

FROZEN IN STATE (SLOWLY RELAXING) ~

,THERMAL EQUILIBRIUM

Barrier

*..*

Configuration Figure 9-18. Configurational coordinate diagram of the equilibration between two states separated by a potential energy barrier.

+'"*.

EOUlLlBRlUM

TEMPERATURE

Figure 9-19. Illustration of the properties of a normal glass near the glass transition. The low temperature frozen state is kinetically determined and depends on the cooling rate.

570


glass is in a liquid-like equilibrium above TG, but the structural equilibration time increases rapidly as it is cooled. The glass transition occurs when the equilibration time becomes longer than the measurement time, so that the equilibrium can no longer be maintained so that the structure is frozen. The transition temperature is higher when the glass is cooled faster, and the properties of the frozen state depend on the thermal history. Slow structural relaxation is observed at temperatures just below TG. The glass-like characteristics are exhibited by the electronic properties of a-Si :H. However, a-Si:H is not a normal glass; it cannot be quenched from the melt. In a glass, all network constituents that contribute to the electronic structure participate in the structural equilibration. In a-Si :H, the disordered Si network is more or less rigid and the majority of Si atoms are fixed in a non-equilibrium configuration which persists up to the crystallization temperature (600°C). As is discussed in later sections, the kinetics of the equilibration of defects and dopants are governed by the motion of hydrogen, which mediates the coordination changes necessary in the approach to dopant or defect equilibrium. Virtually all hydrogen incorporated into the a-Si:H network participates in defect formation and dopant activation reactions, which are in turn governed by a hydrogen chemical potential. It is the kinetics of hydrogen motion which determines the kinetics of defect formation and dopant activation reactions in a-Si :H. The analogy between dopant activation kinetics in a-Si :H and the kinetics of structural relaxation in glasses can be interpreted in terms of the glassy behavior of the hydrogen subnetwork in a-Si :H, which has been termed the hydrogen glass model (Street et al., 1987a).

9.4.2 Thermal Equilibration of Electronic States Figure 9-20 shows the temperature dependence of the d.c. conductivity of n-type a-Si :H for different thermal treatments, and the features of the data are obviously similar to those of glasses in Fig. 9-19. There is a change of slope at about TE= 130“C which distinguishes the high and low temperature regimes. Fast quenching from high temperature results in a higher conductivity than slow cooling, at a given temperature below 100°C. Above T,, the conductivity has a different activation energy and is independent of the thermal history. This is the equilibrium regime in which the defect and dopant densities are temperature dependent according to free energy minimization. The structure is frozen at lower temperature and has the metastable structure characteristic of a glass below the glass transition tempera-

ENCH TEMPERATURE

x

EQUILIBRIUM

0

Ta 250°C Ta = 122O C

0

2

3 4 INVERSE TEMPERATURE l O O O / l IN K - 7

5

Figure 9-20. The temperature dependence of the d.c. conductivity of n-type a-Si :H, after annealing and cooling from different temperatures, and in a steady state equilibrium. The measurements are made during warming (Street et al., 1988b).


ture. If the temperature is not too low, then there is slow relaxation of the structure which is described in Sec. 9.4.5. Metastable defects are also created thermally in undoped a-Si :H. Figure 9-2 1 shows the temperature dependence of the defect density between 200 "C and400"C for material deposited under different plasma conditions. The defect density increases with temperature with an activation energy of about 0.2 eV. Although the defect density is reversible, a high metastable density is maintained by rapid quenching from the anneal temperature. Prolonged annealing at a lower temperature reduces the defect density back to its original value. Thus both doped and undoped a-Si:H have the glass-like property of a high tem-

Y 3x10"

571

perature equilibrium and a low temperature frozen state. The equilibration temperature of undoped a-Si: H is higher than that of n-type material, indicating a slower relaxation process, arising from a higher barrier energy. The relaxation of p-type material is faster, yielding a lower equilibration temperature. Metastable defect creation is a related phenomenon. Here defects are created by an external stress such as illumination or bias. The defects are metastable provided that the temperature is well below the equilibration temperature, but are removed by annealing (see Sec. 9.4.6.).

9.4.3 The Defect Compensation Model of Doping The reversible changes in the conductivity of doped a-Si :H arise because the equilibration of defects and dopants alters the electrical conductivity. The charged defects act as compensating centers for the dopants, so that the density, nBT, of excess electrons occupying band edge states is (9-33)

-*5

where Ndonand ND are the dopant and defect concentrations. The conductivity is

A

9

c

10'6

(T

z u) w

0 2

ii

u)

K

3 3~10'~

1015

1.4 1.6 1.0 2.0 2.2 2.4 INVERSE QUENCH TEMPERATURE lOW& IN K'

Figure 9-21. The temperature dependence of the equilibrium neutral defect density in undoped a-Si : H deposited with different deposition conditions (Street and Winer, 1989).

= nBTe

(9-34)

is the effective drift mobility. where Thus, changes in the density of donor and defect states are reflected in the conductivity. Equilibration occurs between the different bonding states of the silicon and dopant atoms, which can both have atomic coordination 3 or 4. The lowest energy states are S i i and P;, as indicated by the 8 -N rule (see Sec. 9.1.3). The formation energies of P, and Si, are large enough that neither would normally be expected to have a large concentration. However, when both states are formed, the electron liberated from the donor is trapped by the dangling bond, lib-

572


erating a substantial energy and promoting their formation. The compensation of phosphorus donors by defects is described by the chemical reaction P!

+ Si," % P: + Si,

(9-35)

The equilibrium state of doped a-Si:H is calculated by applying the law of mass action Np4 = Nsi3 = K No Np3 ; K = exp [ - ( u p + u D ) / k TI

(9-36)

where the different N's denote the concentrations of the different species, No is the concentration of 4-fold silicon sites, and K is the reaction constant. Up and U D are the formation energies of donor and defect. Single values of the formation energies are assumed for simplicity; the next section includes a distribution of formation energies, which is more appropriate for a disordered material. When the doping efficiency is sufficiently low that Np4Q Np3,and Np4 is equated to Nsi, as required by charge neutrality, then Eq. (9-36) becomes Np4 = Nsi, = (9-37) = (NoNp)"* eXp [-(up+uD)/2 k T ]

This equation predicts the square root law for defect creation which is observed in the data of Fig. 9-12. The thermodynamics also predicts that the doping efficiency is temperature dependent and explains the high metastable d.c. conductivity which is frozen in by quenching (Street et al., 1988a). Defect equilibration also occurs in undoped a-Si :H. In the absence of dopants, the model predicts that the temperature dependence of the defect density is NDO = No exp (-UDdk T )

(9-38)

The defect density does increase with temperature as is seen in the data of Fig. 9-21.

However, the temperature dependence has an activation energy of only about 0.2 eV and a small No, whereas the model for doping just described indicates a considerably larger value of the formation energy (Street et al., 1988a). The difference originates from the distribution of formation energies, which must be included to get the correct defect density. This is discussed in the next section. This type of defect reaction provides a general explanation of all the other metastable phenomena described in Sec. 9.4.6. The formation energies of charged defects and dopants depend on the position of the Fermi energy, EF defect:

UD

= UDo - (EF- ED)

dopant: Up = Up,

-(Ep-

EF)

(9-39) (9-40)

UDoand Urn are the formation energies of the neutral states and ED and E p are the associated gap state energies. The second terms in Eqs. (9-39) and (9-40) are the contributions to the formation energy from the transfer of an electron from the Fermi energy to the defect or from the donor to EF.The negatively charged defect density is given by a Boltzmann expression (Shockley and Moll, 1960) ND- = No exp [-uDo/k TI *

exp [(EF-&)/k T ] =

= NDOeXp [(EF-ED)/k T ]

(9-41)

and there are similar expressions for positive defects and donors. Equation (9-41) assumes that the defects have the same formation energy and gap state levels in doped and undoped a-Si :H. The defect density is, therefore, a function of the position of the Fermi energy, and Eq. (9-41) expresses the interaction between the electronic properties and the bonding structure. The equilibrium defect density in Eq. (9-41) increases

573


exponentially as EF moves from the dangling bond gap state energy. Thus, doping increases the defect density, as does any other process which moves the Fermi energy from mid-gap, such as illumination or voltage bias. The doping efficiency is suppressed by doping, but enhanced by compensation. All of these effects are observed in a-Si :H. 9.4.4 The Weak Bond Model

(a)

Ec

Conduction band

2 \

'\

. e

EV

LT-'Ew

/

#

0

Dangling

'\, bond 0

0

e

ED

Valence band

(b) Weak bond

Figure 9-22. (a) Energy level diagram showing the conversion of a weak Si-Si bond into a dangling bond: (b) Illustration of the hydrogen-mediated weak bond model in which a hydrogen atom moves from a Si-H bond and breaks a weak bond, leaving two defects (DHand Dw) (Street and Winer, 1989).

trons, before and after the bond is broken and the sum represents the change in energy of all the valence band states other than from the broken weak bond. AE,,, is the change in energy of the ion core interaction for the structure with and without the defect. The weak bond model assumes that the terms in the square bracket in Eq. (9-43) are small, so that UDO

ED and EWBare the gap energies of the defect electron and of the valence band tail state associated with the weak bond. E , and EG are energies of the valence band elec-

.

Weak bond

The random network of an amorphous material such as a-Si :H implies that the formation energy varies from site to site. A full evaluation of the equilibrium must include this distribution and also the disorder broadening of the defect energy levels. The generalized form of Eq. (9-38) is

where No ( U D )is the distribution function of the formation energy. Calculations of the distribution of formation energies have been addressed by the weak bond model (Stutzmann, 1987; Smith and Wagner, 1987). Figure 9-22a shows a schematic model of a weak Si-Si bond, and a pair of dangling bonds. When the weak bond is converted into a neutral dangling bond, the electron energy increases from that of a bonding state in the valence band to that of a non-bonding state in the gap. The formation energy of a neutral defect is

\

2:

ED-

EWB

(9-44)

The distribution of defect formation energies is therefore described by the density of valence band tail states. Most states have a high formation energy, but an exponentially decreasing number have lower formation energies. In equilibrium, virtually all the band tail states which are further from the

574


valence band than ED convert into defects, while only a small temperature dependent fraction of the states between ED and the mobility edge convert. The weak bond model is useful because the distribution of formation energies can be evaluated from the known valence band and defect density of states distributions. A calculation of the defect density requires a specific physical model for defect creation. Dangling bond defects form by the breaking of silicon bonds, and several specific models have been proposed (Smith and Wagner, 1987; Street and Winer, 1989; Zafar and Schiff, 1989). We analyze a model in which the bonds are broken by the motion of hydrogen. Figure 9-22 b shows hydrogen released from an Si-H bond, breaking a Si-Si bond to give two separate defects. Experimental evidence for the involvement of hydrogen in the equilibration is described in a later section. The hydrogen-mediated weak bond model of Fig. 9-22 b is described by the defect reaction Si-H

+ (weak bond) * D, + Dw

(9-45)

The two defects may be electrically identical but make different contributions to the entropy. The law of mass action solution for the defect density, including the distribution of formation energies, is (Street and Winer, 1989) ND = 2NH Nvo eXp (-ED / k T v ) .

.I NHexp+ ND expl k(2Tv)UDO/ k T ) (D 'o

dUDo

(9-46)

where Tv is the slope of the exponential valence band tail. Nvo is the band tail density of states at the assumed zero of the energy scale for ED. Numerical integration of Eq. (9-46) gives an excellent fit to the data of Fig. 9-2 1, for band tail and defect parameters which are consistent with the known electrical properties. The weak temperature

dependence of ND follows directly from the distribution of formation energies (Street and Winer, 1989). The weak bond model also explains the variation of the defect density with the growth conditions in the plasma reactor. In material with more disorder, the valence band tail is broader (i.e. larger Tv) and ND increases according to Eq. (9-46). The defect density is conveniently expressed as ND = E (T, Tv, NH) Nvo k Tv * exp [-EDlk Tv]

*

(9-47)

where 5- (T, Tv, NH)represents the entropy factor which differs for each specific defect creation model, but which is a slowly varying function. The equilibrium defect density is primarily sensitive to Tv and ED,through the exponential factor. For example, raising Tv from 500 K to 1000 K increases the defect density by a factor of about 100. The sensitivity of the defect density to the band tail slope accounts for the large change in defect density with deposition conditions and annealing. Figure 9-23 shows the correlation between the valence band tail slope and the defect density for undoped a-Si :H deposited by different methods and under different deposition conditions. The data show that a high defect density is correlated with a wide band tail slope, and is explained by the equilibrium model. The band tails are much broader at low deposition temperatures, so that Eq. (9-47) predicts the higher defect density which is observed. The defect density is reduced when the low deposition temperature material is annealed, and the band tail slope is correspondingly reduced. Similarly, the slope of the Urbach tail and the defect density both increase at deposition temperatures well above 300 "C,and are associated with a lower hydrogen concentration in the film. Both EDand Tv may change in alloys of a-Si :H and this is perhaps the origin of the differ-


-

B 10' C

U

a C

n

-

CJl

%lo" c

D

I

0

la

I

50 100 Band tail slope E,," in meV

I

150

Figure9-23. Dependence of the defect density on the slope of the Urbach absorption edge for undoped a-Si : H deposited under a variety of conditions (Stutzmann, 1989).

ent defect densities in these materials. There is a larger defect density in low band gap a-SiGe :H alloys, which is predicted from the reduced value of ED accompanying the shrinking of the band gap. In the larger gap alloys, such as a-Sic :H, the predicted reduction in N D due to the larger ED seems to be more than offset by a larger T,, so that the defect density is again greater than in a-Si :H. There is, however, no complete explanation of why a-Si :H has the lowest defect density of all the alloys which have been studied.

9.4.4.1 The Distribution of Gap States The theory described above only considers defects with a single energy in the gap. Neutral defects in undoped a-Si:H are known to be distributed in an approximate-

575

ly Gaussian band -0.1 eV wide. Bar-Yam and Joannopoulos et a]. (1986) first pointed out that the minimization of the free energy of the broadened defect band causes a shift of the defect gap state energy level. The reason is that the gap state energy is contained within Eq. (9-44) for the defect formation energy. Thus, states that are at a lower energy in the band gap will have a lower formation energy and, therefore, a higher equilibrium density. This is the basis of the defect pool concept, in which there is a distribution of available states where defects can be formed, which are selected on the basis of energy minimization. The interesting feature of this dependence on gap state energy is that it leads to different defect state distributions depending on the charge state of the defect. The formation energy of positively charged defects is not influenced by the energy of the gap state, because the defect is unoccupied. On the other hand, negative defects contain two electrons and the gap state energy enters twice. For a Gaussian distribution of possible defect state energies, there is a shift of the defect band to low energy by (Street and Winer, 1989) (T2

AE=k TV

(9-48)

for each electron in the defect, where a i s the width of the Gaussian distribution. Measured values of the defect band width are imprecise but lie in the range 0.20.3 eV, corresponding to (T = 0.1 eV. The predicted shift of the peak is therefore about 0.2 eV, when k T, = 45 meV. This shift of the defect energy with doping explains some of the differences in the measured defect energies. The equilibration process has the effect of removing gap states from near the Fermi energy. Either unoccupied states above EF, or occupied states below E , are

576


energetically preferred to partially occupied states at EF.The shift of the defect levels with doping is illustrated in Fig. 9-14.

9.4.5 Defect Reaction Kinetics

I

I

I

The relaxation kinetics follow a stretched exponential relation AnBT

There is a temperature dependent equilibration time associated with the chemical bonding changes. The very long time constant at room temperature is responsible for the metastability phenomena, because the structure is frozen. An example of the slow relaxation towards equilibrium in n-type a-Si:H is shown in Fig. 9-24 by the time dependence of the electrons occupying shallow states, nBT, following a rapid quench from 210°C. nBT decays slowly to a steady state equilibrium, with the decay taking more than a year at room temperature, but only a few minutes at 125 "C. The temperature dependence of the relaxation time, T,is plotted in Fig. 9-25, and has an activation energy of about 1 eV, which measures the energy barrier for bonding rearrangement. The relaxation is faster in p-type than in n-type a-Si :H and has a slightly lower activation energy. A similar relaxation occurs in undoped a-Si :H, with a larger activation energy and a longer relaxation time (Street and Winer, 1989). Equations (9-30) and (9-31) relate the relaxation time to the equilibration temperature.

I

9.4.5.1 Stretched Exponential Decay

1

= no eXp [-(t/@]

with O re,,,insert the parameters obtained for y h = 1 [given as ( ) in columns 1 and 21 into Eq. (10-4), which gives xMand x$tk, taking x G , , from ~ the phase diagram; x h is obtained via x h = 1-xii from the liquidus line, which for an ideal solution is determined by the fusion parameters of silicon (taken by Weber as Tii= 1685 K, AHii=0.525 eV, ASii=3.62 kB) (Weber, 1983). Actually, the liquidus lines of liquid Si-M are nonideal. For the silicon-rich side of the phase diagram, the deviations of the activity coefficient [ yki=~$d)'/x\i]from one are described by relative partial enthalpies and excess kB entropies, which are proportional to and are given by AH& =0.52 (x',)~ eV and AeS&=3.62k , (xL)~ for copper in silicon, by m & = 0 . 9 4 ( x ' , ) ~ eV and A.,S&=5.12kB ( X A ) for ~ ~palladium, ~ and by AH,&= 1.41 (x',)~ eV, AeS&=8.68kB kB for the 3d elements from titanium to nickel. Assuming that these relations are valid at all temperatures and compositions, using the Gibbs-Duhem equation for x h the same quantities AHgi and AeS& with xLi replacing x h on the right sides are obtained. This leads to y h =exp (AH&/kB T-h,S&/kB); fit obtained by Schroter and Seibt (1999a); expenmental data (eight values for T > T,,,) obtained by Young (1982); experimental data and analysis by Dorward and Kirkaldy (1968); experimental data published by Frank (1991); experimental data after Hauber (1986) and Hauber et al. (1989); experimental data of Lisiak and Milnes (1975); experimental data of Collins et al. (1957) Trumbore (1960), Sprokel and Fairfield (1965), Dorward and Kirkaldy (1968), and Stolwijk et al. (1984). a

(xL)~

10.2 Transition Elements in Intrinsic Silicon

icon T$! (Weber, 1983), such that its value has to be taken as a free parameter in the analysis of data with unknown error of T registration, (2) the formation enthalpies of metal silicides are not known with sufficient precision (Schlesinger, 1990).

10.2.2 Diffusion Compilations of diffusion data (Weber, 1983; Graff, 1986; Weber and Gilles, 1990; Schroter and Seibt, 1999a) show that 3d transition elements and the 4d element Pd are among the fastest diffusing impurities in intrinsic silicon with diffusion coefficients as high as to lo4 cm2/s (Co, Ni, and Cu at 1000°C, see Table 10-4). This explains why these impurities are harmful during device processing. For instance, for a wafer with a thickness of typically 500 ym, penetration might take less than 10 s for metal impurities. High diffusion coefficients along with low migration enthalpies are characteristics of simple interstitial diffusion, in which case no diffusion vehicle is needed and the formation of covalent bonds with silicon neighbors does not take place. For a simple interstitial diffusion mechanism, an Arrhenius-type behavior of the diffusion coefficient is expected

[T I

D=L&exp --

(1 0-6)

where Do is the pre-exponential factor, and AHgim’) the migration barrier. Electron paramagnetic resonance measurements have confirmed that Cr, Mn and Fe, which can be quenched to room temperature, predominantly occupy the tetrahedral interstitial site (Ludwig and Woodbury, 1962). In addition, the electronic structure of the dominant defect, as measured by deep-level transient spectroscopy [for review, see Graff (1986) and Schroter and Seibt (1999b)], is in agreement with total

609

energy calculations of the interstitial metal atom [Beeler et al. (1985), Zunger (1986), see Chap. 4 of this Volume]. There have been reports about a substitutional component of Ni (Kitagawa and Nakashima, 1987, 1989), but it should be emphasized that its concentration is several orders of magnitude smaller than the total Ni solubility. For Mn and Cr, a substitutional component has been found after co-diffusion with Cu (Ludwig and Woodbury, 1962). The mechanism of M, formation upon Cu precipitation is not yet understood. As can be seen from Fig. 10-3, there is a clear distinction between the diffusivities of impurities that occupy substitutional sites (e.g., shallow dopants) and those on interstitial sites. However, there is also a considerable variation in the diffusivities within the 3d row. From Ti to Ni the diffusivity at 1000°C increases by about six orders of magnitude and the migration enthalpy decreases by a factor of four. Surprisingly, a rather simple hard sphere model, which takes into account the variation of atomic size within the 3d row, satisfactorily explains these trends, which have been discussed as a “diffusion puzzle” for a long time (Zunger, 1986). In this model, Utzig (1989) calculates the elastic energy required to move Mi from one tetrahedral interstitial site (T site) to the next via the hexagonal interstitial site (H site) as the saddle point (see Fig. 10-4). The pre-exponential factor is calculated as the migration entropy A S P ) using an approach by Zener (1952). The T site is in the center of the tetrahedron formed by four Si atoms [ ~ ‘ ~ ’ = 4The ]. distance between the center of the tetrahedron and its comers is the same as that between two neighboring silicon lattice sites, do. The hard sphere radius of the T site is then R(T)= do- rsi, rsi = d0/2 being the atomic radius of silicon, so that R(T)= 0.5 do= 1.17 P\ (0.117 nm). The H site is in the center of a

61 0

10 High-Temperature Properties of Transition Elements in Silicon

T in OC

.-C0 sUa: u)

1043

1,

,

,

,

,

,

,

,

,

,]

0.6 0.7 0.8 0.9 1 .O 1.1 1.2 1.3 1.4 1.5

1OOOR in K-1

Figure 10-3. High temperature diffusion coefficients of the 3d elements and Pd in silicon. There is a clear distinction between the diffusivities of impurities that occupy substitutional sites and those of the metal impurities that occupy tetrahedral interstitial sites. There is also a considerable variation of D within the 3d row, which has been explained by a simple hard-sphere model (see text); references are for Ti: Hocine and Mathiot (1988) (solid line), Nakashima and Hashimoto (1992) (dashed line); V Nakashima and Hashimoto (1992); Cr: Bendik et al. (1970) (solid line), Zhu et al. (1989) (dashed line); Mn: Gilles et al. (1986); Fe: Struthers (1956) (solid line), Isobe et al. (1989) (dashed line); Co: Utzig and Gilles (1989); Ni: Bakhadyrkhanov et al. (1980); Cu: Hall and Racette (1964); Pd: Frank (1991). The values for Cu have been measured in highly boron doped silicon (see text).

hexagonal ring formed by six Si atoms [ z ( ~ ) =61 and has a hard sphere radius 0.95 do -rsi=0.45 do= 1.05 A (0.105 nm). Inserting an atom of radius rM into the interstitial site requires an elastic energy given by

Figure 10-4. The tetrahedral (T-site: 0 ) and the hexagonal interstitial site (H-site: +) in the diamond lattice. 3d-e1ements occupy the T-site and diffuse presumably the ~ -as the~ i point, ~ ~

where a is the central force constant per next ) Si-neighbor for the T site and z ( ~ for the H size] : a =3.02 eV/A (Keating, 1966). The difference A U,,= U:r) (rM)- U::) ( r M ) is a contribution to A H P ) . The atomic radii of the 3d elements, taken as the distance of closest approach in the metal (see Table 10-3: Hall, 1967), have been corrected following an empirical rule detected by Goldschmidt (1928). Depending on the coordination number L , the interatomic distance was found to be about 3% less if z is 8 instead of 12, 4% less if it is 6 (H site), and 12% less if it is 4 (T site). In Table 10-3 calculated values of AU,, are compared with measured values of A H g i ) for 3d elements. The agreement is quite satisfactory. The sharp drop of A H L ~ ) from Ti to Cr, and the subsequent slow decrease, are quite well reproduced by this simple model. Note that the estimation of

61 1


AUe, for copper is for Culo), while the experimental data are for Cu?). Under the condition that the diffusion barrier is primarily due to elastic strain, which appears to be fulfilled for the 3d elements, Zener (1 952) has given an approximate formula to calculate the migration entropy

(1 0-7)

where K is the elastic modulus and T;:) the melting point of silicon. Taking Do= 1/6 d i f e x p [AShmi)],wherefis the Debye frequency, measured values of the pre-exponential factor of diffusion Do can also be compared with the prediction of the simple hard sphere model (see Table 10-3), again showing remarkable agreement.

Table 10-3. Comparison of experimental migration barriers A H r ) with calculated elastic contributions AUe1’. rMb

(nm) 0.1467 0.1338 0.1357 0.1267 Mn 0.1306 0.1261 Fe 0.1260 Co 0.1252 Ni 0.1244 Cuc 0.1276

Ti V Cr

AUel A H F ’ Do(AU,I) (cm2/s) (eV) ( e v ) 2.15 0.99 1.15 0.50 0.75 0.46 0.46 0.42 0.38 0.55

1.79 1.55 0.81 0.70 0.68 0.37 0.47 0.18

DO (cm2/s)

0 . 5 2 ~ 1 0 - ~1.45~10-’ 2 . l O ~ l O - ~9 . 0 ~ 1 0 - ~ 0 . 2 3 ~ 1 0 - ~1.0X10-2 0.14~10-~ 1 . 7 0 ~ 1 0 - 0~ . 6 9 ~ 1 0 - ~ 1.34~10-~ 1 . 3 4 ~ 1 0 - ~1 . 3 ~ 1 0 - ~ 1 . 3 0 ~ 1 0 - 0~ . 9 0 ~ 1 0 - ~ 1 . 2 5 ~ 1 0 - ~2.0x10-3 1 4 . 5 ~ 1 0 - ~0 . 3 ~ 1 0 - ~

Diffusion coefficients D , estimated from the time necessary to saturate Si samples with a 3d element M (Weber, 1983) showed that care must be taken if D, is evaluated from a concentration profile. One type of experiment to measure the diffusion coefficient D M is usually performed with either a finite source or an infinite source of M at the surface of the silicon. Finite source experiments avoiding silicide formation have been found to suffer from silicon surface reactions which are difficult to control. The alternative boundary condition is a constant surface concentration, realized by the deposition of a metal film onto the silicon surface and by inducing the formation of the silicide phase. There is an easy check of the basic requirement in this experiment. For a well-defined boundary condition, the surface concentration, extrapolated from the diffusion profile, must coincide with the solubility data at the diffusion temperature. Let us consider as an example the diffusion of Mn in Si. In the temperature range between 900 “C and 1200“C symmetric diffusion profiles were obtained after in-diffusion from opposite surfaces of Si samples (Fig. 10-5a; Gilles et al., 1986). Surface concentrations were found to be in good agreement with the solubility data (Fig. 10-5b), which means that boundary conditions independent of time have been achieved. Such checks are indispensible to accurately determine migration enthalpies below 1 eV. Note that this agreement does not imply that the equilibrium phase has formed, as discussed in Sec. 10.2.1. An independent method for measuring D, below 150°C is the result of a study of the pairing reaction MI+’+A‘,-’ (M, A?), where A, is a shallow acceptor. The kinetics of pair formation is determined by the diffusion of M,’+’.According to Reiss et al. (1956) the diffusing species Mi+’is captured by A\-) via electrostatic attraction as soon as +

Utzig (1989); the references from which Utzig has taken experimental values can be found in Table 10-4 [compare m?)];rM is the atomic radius of the respective metal atom (Darken and Guroy, 1953); ‘copper is known to diffuse as Cur’in silicon, while atomic radii are for neutral atoms (see text). a

612


10’6

loi5 1

6

c ._ c

E.

1oi4

-1.0

(a)

- 0.5

0

0.5

1.o

Xia

0.8

0.7

(b)

in 1 0 . ~K”

Figure 10-5. Solubility and diffusion coefficient of Mn in silicon (after Gilles et al., 1986). (a) Concentration profiles determined by the tracer method after diffusion from both surfaces into specimens of thickness 2a for different temperatures: 1200°C (o),1080°C (D),990°C (o), 920°C (A). (b) Temperature dependence of diffusion coefficients, D,calculated from diffusion profiles of the total Mn-concentration (tracer method, solid square, cp. (a)) or those of interstitial Mn (DLTS, open squares). The surface concentration of those profiles (tracer method, solid circles) agree well with the saturation concentrations.

the electrostatic energy exceeds the thermal energy, k,T, of the ion. The identity of these two energy terms defines the capture radius, R, such that from the relaxation time constant, tp,the diffusivity, DY), of MI+) can be calculated

where E = 11.7 is the static dielectric constant of silicon, E~ the permittivity of free space and, e the unity of electric charge. In order to determine the relaxation time, isolated Mi has to be quenched to a temperature below which the ratio [Mf+’A‘,-)]/ [My)]> 1, and at which the relaxation time is experimentally accessible. While for

Cr, Fe, and Mn both conditions can be fulfilled below 100“C, for Co, relaxation is already complete during or immediately after quenching (Bergholz, 1983). The 1/T range is significantly larger for the low T(< 2 x 1 OT3 K-’) than for the high Texperiment ( 5 - 9 ~ 1 0K-’), ~ and the prefactor Do and the migration enthalpy A H L ~ ) should have smaller limits of error when derived from the low T data. Both sets of data are available for Cri, Mni, Fei, and Cui, but a common fit to them (see Table 10-4) would only be meaningful if the charge state of Mi is either the same in both T ranges, which is the case for Cu, or has a weak influence on D. The high T diffusion data for Mn, Fe, and Co have been shown to refer to the neutral


61 3

Table 10-4. Diffusion coefficients of interstitially dissolved transition metals in silicon. ImpurDo (lo-’ cm2/s) ity Ti

V Cr

1.45 12

AH^' (ev)

T range (“C)

Reference

Remarks, material

1.79 2.05

950- 1200 Hocine and Mathiot (1988) (2)a (a)’, FZ, Cz 600- 1500 (a)’, (a)‘ Nakashima and Hashimoto (1992) 1.55 0.9 600- 1200 Nakashima and (a)’, (a)‘ Hashimoto (1992) 1.o 1.0k0.3 900- 1250 Bendik et al. (1970) cz 3.0 1.120.3 850- 1050 Zhu et al. (1989) ( I ) a (a)’, Cz 0.85 1.3 20- 1 0 0 Zhu and Barbier (I 990) (a) (8)‘, Cz 0.26 0.81+0.02 30- 1050 (1) Zhu and Barbier (1990) 0.069+0.022 0.6320.03 900- 1200 Gilles et al. (1986) (a)’, (b)’, FZ 0.72 0.24 14-90 Nakashima and (a)’ (P)‘, FZ Hashimoto (1991) 0.70 0.13 14- 1200 Nakashima and Hashimoto (1991) 0.87 1000-1250 0.62 (b)’ Struthers (1956) 800- 1070 Isobe et al. (1989) 0.65 0.095 (1)” (a)’, FZ 0.77 30-85 2.3 Shepherd and (C)’ WC Turner (1962) 0- 1070 Nakashima and (1II)d 0.66 0.11 Hashimoto (1991) 0.68 0.13 30- 1250 Weber (1983) (IVd 0.37 900- 1100 Utzig (1989) 0.097 (3)a (b) Fz 0.47 800- 1300 0.2 Bakhadyrkhanov (b) et al. (1980) (b)’ FZ 0.5 400-700 0.40 Hall and Racette (1964) *d Keller et al. (1 990) 0.3 0.15 0.39 0.45 -95-700 Mesh and Heiser (1996) (V) Istratov et al. (1998 a) - 8- 900 0.03+0.003 0.1820.01 (Y)‘ ( W d Graff et al. (1985) 950- 1150 0.89 8 (a) Graff (1995) 700- I300 Frank ( 199I ) 0.22 0.03 (d)

’

Mn

Charge D ( 1000°C) state (cm’/s) (Ti!”)

6.6~10-~ (Cr!”)

(Cry’) Mn!” Mnr-’

(md

Fe

co Ni

cu

Pd

’

’

’

~.~xIO-~ 9.2~

1.1~10“ 1.3 x 10“ 5.6~10-~~ 1.6~10“ 2.2 x 10” 3.4 x lo4

2.2 x 10“ Felo’ Fey’

2.2 x 10” 2.5~10~ 2.1~10-~~ 2.7 x 10“

Cora' (Niy)) Cu:

Pd,

2.6 x 10“ 3.3 x 10-5 2.8 x 1.3~10~’ 7 . 6 I~O4 1.3 x 104’ 5.8X10-5t 2.4xIO-’ 4 . 0 lo-’ ~

a Boundary conditions: (1) [MI,,= [MI,, (1) [M],,=[M], between 900 and 1200°C, (3) surface phase identified as equilibrium phase; concentration determined by: (a) DLTS, (b) radioactive tracer, (c) resistivity; (d) neutron activation analysis; ‘techniques other than in-diffusion: ( a )out-diffusion from supersaturated solution between 600 and 800°C, (p) pairing kinetics, ( y ) ion drift; analysis (I)-(VI) common fit to data from references: (I) Zhu and Barbier (1990), Zhu et al. (1989), (11) Gilles et al. (1986), Nakashima and Hashimoto (1991), (111) Isobe et al. (1989), Nakashima and Hashimoto (1992), (IV) Struthers (1956), Shepherd and Turner (1962), (V) Mesli and Heiser (1996), Hall and Racette (1964), (VI) ion-drift data (-8- 107°C) from Istratov et at. (1998a), one value at 900°C from Struthers (1956), * reanalysis of data from Hall and Racette (1964), extrapolated value.

’

’

interstitial species M!O)(Gilles eta]., 1990a) (see Sec. 10.3), and those of Cu to Cuf+’ (Hall and Racette, 1964), while those of Ti and Cr have been proposed to refer to Ti,!” and Cr,!”, respectively, and those of nickel

to Ni,!+’ (Weber, 1983). The low T data refer to Crf+),Mni++),Fet+),Fe:’), and Cut+’. The effect of the charge state of Mi on D M has been studied recently for Fei by means of its pairing reaction with B under a Schott-

614


Diffusion parameters for CuI+) at lower temperatures have been derived from the kinetics of the pairing reaction, either studied by C - V or by transient ion drift measurements for temperatures between 220 and (1) D (Fe,!')) 280 K or 300 and 400 K, respectively (Mes= 10-2xexp (-0.84 eV/k, T ) cm2/s li and Heiser, 1994). Since these investigaD (Fe,!") tions started from step-like concentration = 1 . 4 ~ exp (-0.69/kB T ) cm2/s profiles of (CuiA,)-pairs, the influence of (Heiser and Mesli, 1992) internal electric fields have to be included into the analysis as well as a [O{') Cu:"] (2) AHg)(Felo))= 0.56 eV pairing reaction below 300 K. With these AHg)(Fe{+))= 0.92 eV corrections, Mesli and Heiser derived the (Koveshnikov and Rozgonyi, 1995) consistent relation D,, ( T )for intrinsic silicon; the corresponding parameters are listTakahashi et al. (1 992) studied the precipitaed in Table 10-4. Recently, Istratov et al. tion kinetics of Fei in n-type Si and the kinet(1998 a) performed ion drift experiments for ics of its pair formation with B in p-type Si CuI+)in Si. Making use of computer simuand obtained AHF)(Felo))= (0.80 k 0.01) lations by Heiser and Weber ( 1 998), the aueV and AHg"(Fe?)) = (0.68 f 0.01) eV, rethors found pair dissociation to be rate-conspectively. As long as the discrepancy retrolling in Ga-doped material, while in Bmains unsettled, parameters derived from doped silicon a temperature region (> 255 K) common fits to high T and low T diffusion exists, where the copper diffusion coeffidata have to be considered as preliminary. cient can be determined. The values of Do The parameters for Cup), given in Table and A H F ) have been obtained from a com10-4 with reference to Hall and Racette mon fit to their values measured between (1964), have not been directly derived from 265 K and 380 K and a single value at 1173 their experimental data. The authors used silicon highly doped with 5 x lo2' B / c ~ - ~ , K measured by Struthers (1956). The low activation energies of Cu diffuso their results, obtained for temperatures between 400 and 700°C, refer to CuI+) in sion given by Keller et al. (1990) and by Istratov et al. (1998a) imply D,, values at room extrinsic silicon (see Sec. 10.3). Direct analysis of their data yielded D(H7R)=4.7 temperature that are at least three orders of x exp (-0.43 eV/kBT) Cm2 S-'. magnitude larger than those of any other 3d element. By chemomechanical polishing at Keller et al. (1990) considered the effect room temperature, Cu is able to penetrate a of (A,Cui)-pairing on the copper diffusivity Si wafer within a couple of hours (Schnegg and corrected D(H,R)for the fraction of paired Cu!+) using the model of Reiss et al. et a]., 1988; Prescha et al., 1989; Keller et (1956) and pure Coulomb interaction beal., 1990). Taking an extrapolation of the tween the ions. Their procedure yields diffusion data of Keller et al. (1990) and D'K)=3x10-3 ex p (-0 . 1 5 / k g T ) cm2/s. Istratov's data (Istratov et al., 1998a) yields Considering in addition screening of the diffusion coefficients at room temperature Coulomb interaction by free holes, Mesli and of 8 x lop6cm2 s-' and 2.4 x cm2 s-', Heiser again using the model of Reiss et al. respectively. Using the relation t,, = d2/Dfor a rough estimate with d=300 pm for the waobtained D(M,H)= 5x exp (-0.40/kB T ) fer thickness, about 2 min and 1 h were obcm2/s, which is very close to D(H,R).

ky contact. There is agreement that the effect exists and is significant, but two different results have been obtained and are still under discussion (Heiser and Mesli, 1996):

10.3 Solubility and Diffusion in Extrinsic Silicon

tained, respectively, for the time t, which Cu needs to penetrate the wafer. Apparently, the recent results on Cu-diffusivity would easily account for the time scale of the chemomechanical effect. However, since the solubility of Cu extrapolated to room temperature is found to be far less than 1 atom/cm3, the current of Cu in intrinsic Si would be much too small to accumulate any measurable amount of Cu in the wafer within a couple of hours. From the increase in resistivity, it has been concluded that the formation of CUBcomplexes plays a major role in the solubility enhancement. To generate these immobile pairs, a dramatic solubility enhancement of Cui is needed at least near the interface to the polishing chemical. Part of this enhancement could result from electronic contributions to the solubility (Fermi level effect), if the Fermi level would be lowered in relation to the valence band by interfacial charges. Since the donor level of Cui is expected to be high in the band gap or even inside the conduction band, the enhancement would be strong at room temperature, but by far insufficient to explain the effect of chemomechanical polishing. This is a puzzle that has yet to be solved. In summary, diffusion data of 3d transition elements in intrinsic Si have been improved to such an extent that even these small migration enthalpies are quite reliable. Unlike the solubility data, which show an abrupt increase on going from Co to Ni, such an abrupt increase in the diffusion coefficients occurs between Fe and Co. The latter helps in understanding why Co, Ni, and Cu cannot be quenched on interstitial sites: the lower migration barrier of those impurities favors precipitation or out-diffusion during or after quenching since their diffusivities near room temperature are several orders of magnitude higher than those of Fe, Mn, and Cr.

615

10.3 Solubility and Diffusion in Extrinsic Silicon 10.3.1 Introduction A semiconductor is termed extrinsic if the dopant concentration (B, P) exceeds the thermal equilibrium concentration of the intrinsic carriers, ni. In Chap. 5 of this Volume the temperature dependence of ni is shown for Si, Ge and GaAs. At room temperature Si is normally extrinsic due to doping or residual impurities (ni= 10'' ~ m - ~ ) , whereas at temperatures above 700°C a minimum dopant concentration of 10l8 atoms/cm3 is required to affect the position of the Fermi level. As will be shown below, by shifting the Fermi level, the concentration of charged impurity species can be enhanced to dominate the solubility, such as Mi+' by doping with B, or h4;) by doping with P. Hence information about charge states at high temperatures can be obtained from solubility data, but no detailed information can be obtained about the defect species. We are now dealing with a ternary system, and the solubility of 3d elements is composed of additional terms, e.g., pairs of substitutional or interstitial impurities with dopant atoms. In this situation, apartial classification of impurity species involved in the solubility enhancement can be derived from an analysis of diffusion profiles. Unlike gold diffusion in intrinsic silicon (see Chap. 5 of this Volume), transport of 3d metal atoms in extrinsic Si was found not to be limited by the diffusion of intrinsic defects (vacancies or Si self interstitials), but by diffusion of the interstitial metal impurity. The effective diffusion coefficient of the impurity, Deff, is determined by the ratio of the average times that an atom stays on interstitial and substitutional sites or in complexes. The solubility enhance-

61 6


ment of charged impurities by Fermi level shift and the simultaneous variation of D,, are experimentally accessible quantities and can be combined to separate electronic properties of interstitial species and of immobile, i.e., substitutional, species and complexes. A more refined classification of immobile species is provided by Mossbauer spectroscopy of Co and by Rutherford backscattering combined with channeling of Cu. Mossbauer spectroscopy discriminates between different Co species according to their s electron densities at the nucleus site (isomer shift) and the electric field gradient produced by distortions of the cubic environment (quadrupole splitting). In the following sections an analysis of solubility and diffusion data is presented. It gives clear evidence that above 600 "C interstitial metal impurities are deep donors with a level related to that calculated from first principles at zero temperature (Beeler et al., 1985). It further indicates a rather abrupt change of the electronic configuration of these impurities around 900°C.

Consider, e.g., an impurity ionization level C('/+)in the band gap of Si above the Fermi level. E C- C('/+)( E , being the conduction band edge) is the change in the standard chemical potential for the reaction to form a positively charged donor and a free electron in the conduction band (Van Vechten and Thurmond, 1976). The variation of [M'@] as predicted by Eq. (10-9) is depicted schematically in Fig. 10-6. The solubility is the sum over all impurity species and their charge states, i.e. [Mleq = C [My'leq + C [MY)],, U

(10-10)

0

It is obvious from Fig. 10-6 that charge states of impurity species can be derived directly from the slope of In [MI,, with Fermi energy if one species and one charge state are dominant. In order to vary the Fermi energy in the temperature regime of interest (700- 1200"C), the dopant concentration must exceed the intrinsic carrier density, ni (see Chap. 5 of this Volume). At 700°C a minimum dopant concentration

10.3.2 Solubility The dependence of the solubility on the position of the Fermi level results from an electronic contribution to the partial enthalpy of solution AHE') for the charged species (see Sec. 10.2.1). Shockley and Moll (1960) argued that this contribution is the electron transfer energy from the defect doto the Fermi level E F ,or from nor level c('/+) EF to the defect acceptor level C(-'O). Since the solubility of the neutral species is independent of E,, the concentration ratio of two species that differ in their charge states by + 1 or - 1 is given by

EV

( E F -Ev) in eV

EC

Figure 10-6. Solubility at 900 K of the charged species M(+), M(-), and M'*-' relative to that of the uncharged species M(') for a point defect M as a function of the Fermi energy.

10.3 Solubility and Diffusion in Extrinsic Silicon

of 10" atoms/cm3 is necessary to affect the position of the Fermi level; at 1200°C it is 2 x 1019atoms/cm3. Figure 10-7 shows an example of how the solubility of Mn in Si is affected by doping with B or P at three different temperatures. The Fermi energy was calculated using Ehrenberg's approximation (Ehrenberg, 1950). All dopants were assumed to be ionized at the diffusion temperature. As can be seen in Fig. 10-7, at 1040°C there is hardly any variation in the solubility with Fermi energy. As the interstitial species of manganese, Mni, is the dominant one in intrinsic Si (see Sec. 10.2), it is neutral at that temperature ([MnIeq=[Mnfo'],,), because of the lack of electronic contributions to the solubility by doping. At lower diffusion temperatures, solubility variations with Fermi energy become more pronounced. At 850 "C and by doping

61 7

with B up to lo2' atoms/cm3, the solubility of Mn is increased tenfold compared to its value in intrinsic silicon, while at 700°C the solubility is enhanced by two orders of magnitude. By doping with P up to 1O2' atoms/ cm3, there is an even stronger solubility enhancement of up to four orders of magnitude. Similar effects were also observed for Co and Fe (Gilles et al, 1990a; McHugo et a]., 1998). These interstitial impurities are neutral in intrinsic Si above 800°C and show a pronounced solubility enhancement in Band P-doped Si at 700°C. The electronic contributions to the partial enthalpy of solution AH$i) are quite similar for Cu (data from Hall and Racette 1964), Co, Fe and Mn. As illustrated in Fig. 10-8 these 3d elements show a solubility en-

m 1040°C 850°C

0 700°C

( E F -Ev) in eV I

I

I

0

02

04

(€,-€,)

I

I

06

08

10

in eV

Figure 10-7. Solubility of manganese [Mn],, versus Fermi energy for three different temperatures: 1040°C (m), 850°C (a), and 700°C (0).Data are from Gilles et al. (1990a). The Fermi energy was calculated using Ehrenberg's approximation (Ehrenberg, 1950).

Figure 10-8. Solubility of Cu, Mn, Fe, and Co versus Fermi energy at 700"C, demonstrating the electronic contribution to the partial enthalpy of solution MEi).The slopes expected for a single positively charged species (1+) and a threefold negatively charged species (3-) are indicated (data for Cu: after Hall and Racette, 1964; and for Mn, Fe, Co: after Gilles et al., 1990a).

618


10.3.3 Diffusion

hancement in B-doped Si which is mainly caused by a single positively charged species. In P-doped Si multiple negative charge states are involved. It is interesting to note that the Cu solubility drops initially on doping with P before the solubility enhancement sets in. This clearly shows that Cu is positively charged in intrinsic Si at 700 "C and 600 "C (Hall and Racette, 1964). Therefore, part of the enthalpy Qcu (see Sec. 10.2.1) of the Cu solubility is indeed of electronic origin. For 4d and 5d transition elements, measurements of the solubility in extrinsic Si are available for Au at a temperature of 1000 "C or above. The data show a solubility enhancement by doping with P and As of up to one order of magnitude at 1000°C, and a factor of three in highly B-doped Si. On going to a higher temperature, the solubility enhancement is less pronounced (see Table 10-5).

Although the solubility data of Fig. 10-8 clearly show that charged species are the dominant defects in extrinsic silicon at 700"C, they do not allow the determination of the lattice site occupied by the respective impurity. A distinction between MY) and M r ) or M!2-', M:2-), and M,P is not possible. However, it is generally accepted that interstitial species of 3d elements are much more mobile than substitutional species and pairs with shallow dopants. The transport of transition metal impurities is determined by diffusion via interstitial sites. Hence measurements of the influence of doping on the diffusion coefficient of transition elements can supply valuable information about the identity of the lattice site predominantly occupied by the impurity. Hall and Racette (1964) reported fast diffusion of Cu in intrinsic and B-doped Si, but a strong retardation in P- and As-doped Si.

Table 10-5. Solubility of gold in extrinsic silicona3b. ~~

Doping (~m-~)

1000°C

[B]=9x10'9 3.1~10'~ [B]=3x10'9C 1.5x1Ol6 [B]=1.5~10'~ -

1050°C -

-

1100°C

1200°C

1300°C

Reference

7.3 ~ 1 0 '1.3 ~ x 1017 1.7 ~ 1 0 ' ~ Brown et al. (1975) 4.4x1Ol6 Rodriguez Schachtrup et al. (1997) 3.2~10'~ Cagnina (1969)

Intrinsic

1 . 0 ~ 1 0 ' ~1 . 9 ~ 1 0 ' ~ 3 . 2 ~ 1 0 ' 7~ . 2 ~ 1 0 ' ~1 . 1 ~ 1 0 ' ~ Table 10-2 3.1x10'6 2.0x101-5 Cagnina ( 1 969) [P]=lx10'8 1.2~10'~ [PI = 4 x 10'8 Cagnina (1 969) O'Shaughnessy et al. (1974) [ P ] = 4 ~ 1 0 ' ~ 3 . 2 ~ 1 0 ' ~3 . 8 ~ 1 0 ' ~5 . 3 ~ 1 0 ' ~8 . 8 ~ 1 0 ' ~ 1.8x10'7 Cagnina (1969) [P]=6~10'~ 6.7~10'~ 1.3~10'~ [PI =7 x 10'9 Cagnina (1969) 1.ox 1017 Cagnina (1969) [PI = 8 x 1019 Cagnina (1969) [ A ~ ] = 4 x 1 0 ' ~1 . 9 ~ 1 0 ' ~ Cagnina (1969) [ A s ] = 6 ~ 1 0 ' ~3 . 5 ~ 1 0 ' ~ 8.2~10'~ [As]=7~10'~ Cagnina (1969)

a Atoms/cm3; data obtained from saturation experiments unless otherwise indicated; data obtained by extrapolating concentration profiles to the surface; the solubility data for intrinsic silicon reported by O'Shaughnessy et al. (1974) are below those calculated from Table 10-2 by about 20% indicating a systematic deviation.

61 9

10.3 Solubility a n d Diffusion in Extrinsic Silicon

A more detailed analysis was possible for Co in Si. In Fig. 10-9 the influence of doping on the solubility (taken as the surface concentration) and diffusion of Co at 700 "C are shown. Note that samples of intrinsic Si would have been saturated with Co at a concentration of 2 x 10" atoms/cm3 for either diffusion time. In intrinsic and B-doped Si an annealing time of 9 min was sufficient to nearly saturate the Si specimens (diffusion from both sides of the specimen), but seven days were necessary to obtain a com-

0

05

parable depth in the P-doped sample (diffusion from one side of the specimen only). Diffusion coefficients for Co and other 3d elements are summarized in Table 10-6. For all 3d elements investigated so far (Cu, Co, Mn, and Fe) the trends are the same: (1) solubility enhancement in P-doped Si coupled with a strong retardation of the effective diffusion coefficient, and (2) solubility enhancement in B-doped Si which does not affect the diffusion coefficient significantly. (3) For Co, Mn, and Fe those electronic contributions to the solubility and diffusivity disappear towards higher temperatures. Only a little information is available on the diffusion of 4d and 5d transition elements in extrinsic Si. For Au in Si it has been found that doping with B leads to an increased effective diffusion coefficient. The result is interpreted analogous to the findings for 3d transition elements, i.e., a positive charge state of the interstitial species, the concentration of which amounts to only a fraction of the total solubility.

10

15

X in mrn

Figure 10-9. Concentration profiles of Co in silicon showing the influence of dopants on the solubility (taken as the surface concentration) and diffusion of co at 700°C: 8x10" B-atoms/cm3, tdiff=9min (01, 1 x10" P-atoms/cm3. tdiff=7d (0).Note that the solubility of Co in intrinsic silicon is 2 x 10" Co-atoms/ cm3 at 700°C (after Gilles et al., 1990a).

10.3.4 High Temperature Electronic Structure In order to identify charge states and impurity species, it is necessary to go further into the classification of immobile species by applying appropriate experimental tech-

Table 10-6. Comparison of the effective diffusion coefficients D,, of 3d transition elements in extrinsic and intrinsic silicon at 700°C.

D,, (cm2/s)

Doping concentration (~m-~) P: 1 x 10'0 P: s x 1014 B: s x l o L 9

Mn

Fe

[PI,, , probably caused by a new mode of injection gettering, its role for Pt in PDG with [P](~"'QI [PI,, is not clear at present. The action of the kick-out mechanism on M, drives injection gettering. Its direct action on 3d elements with a predominant interstitial component in intrinsic silicon is expected to be rather small. However, PDG experimerits at 920°C for 54 min { [CO](~' ' ~~~~' )4 x 1 0 ' ~~ m - [~C ,O ] , , = ~ . ~ X ~ ~Om ' "- ~ , s p e c -

Depth

[rml

Figure 10-33. Simulation (Kveder et al., 2000) and experimental data (Sveinbjornsson et al., 1993) of PDG for Au in Si. The initial gold concentration was uniform at 3 x I O ' ~cm-3 and below the solubility of Au at 980°C which is 8.6 x loi5 atoms/cm3. The points show the experimental SIMS profiles for P and Au after PDG. A) PDG at 980°C for 30 min followed by slow cooling down to 900°C with a rate of 5 Wmin, then fast cooling; B) additional annealing of the same sample at 1150°C, for 15 min without P exposition and quenching. The phosphorus glass was removed from the surface before the second annealing.

654


imen quenched with arate of about 1000 WS after PDG} have clearly shown, that concentrations of Co in the highly P-doped layer are of the same order as those found for AU { [ ~ o ] ( ~ ~ r fx) = 3 cmp3, [CO](~"'~)= 1013~ m - (Kuhnapfel, ~] 1987). This puzzle has not really been solved yet, but independent experimental findings have indicated possible solutions. Studying solubility and diffusion of Mn, Fe, and Co in P-doped silicon and including literature data on Cu in their analysis, Gilles et al. (1990a) found that the ratio r = [Mileq/ [M,],, for these elements drastically decreases from the value in intrinsic silicon (r%l)to r=l and further to r Q 1, when the P-concentration becomes larger than the intrinsic electron concentration (see Sec. 10.3). These results establish the prerequisite for the injection-gettering mode to operate in the limited region of high P-doping, but they also imply the possibility of a stronger segregation-gettering by the multiple acceptor action of Co,. Since the model developed for Au in Si and described above comprises both mechanisms, numerical simulations and comparison with available experimental results for Co in Si are expected to extend the validity range of the model to 3d elements. Figure 10-34. (a) Lattice image of PSG/Si interface Segregation and Injection Gettering (Precipitation Mode) For [PI,, experimental results, especially from TEM, indicate a new mode of injection gettering which is driven by local gradients of [I]/[I],, and is associated with the incorporation of inactive P into the silicon wafer occurring simultaneously with P-in-diffusion. We propose to call it the precipitation mode of injection gettering. It has been detected by the fact that silicide precipitates grow from the PSG/Si interface near to Sip needles. In this section, we brief-

in the neighborhood of a Sip particle growing into the silicon. Note the protrusion of the Sip particle and of thePSG/Si interface near the particle. The undisturbed interface is indicated by the dotted line. (b) Brightfield TEM image of the PSG/Si interface showing a Sip particle and a precipitate identified as Nisi, (according to Ourmazd and Schroter, 1985).

ly outline the main feature of the precipitation mode and silicide formation. For [PI,,, SIP precipitates have been observed to grow from the Si/PSG interface (PSG: phosphorus silicate glass) into the silicon bulk (Bourret and Schroter, 1984). For every Si-atom, that becomes in-

10.6 Summary and Outlook

corporated into the SIP particle, 1 .S silicon interstitials have to be injected into the silicon to adjust the difference of the silicon specific volumes. As a result, a current of silicon interstitials is generated at the progressing SiP/Si interface. Since epitaxial growth of silicon has been observed at PSG/Si interfaces near to the Sip precipitates (see Fig. 10-34a), it has been argued that some part of this I current is directed towards this region of the interface. In the presence of substitutional metallic impurities, the local silicon interstitial current is expected to induce a local impurity current towards the PSG/Si interface. This local configuration might be considered as a small pump of injection gettering. It is local in the sense that its operation is limited to the region of high P-doping. Consequently, it should act on all impurities where r s 1, i.e., also on 3d elements. Indeed, after PDG of Nidoped wafers, Nisi, precipitates have been observed at the SiP/PSG and the surrounding Si/PSG interface by TEM (Ourmazd and Schroter, 1984) as is shown in Fig. 10-34b. Recently, Pt has also been found after PDG with Sip growth as the orthorhombic PtSi precipitate at Sip (Correia et al., 1996). Modeling and numerical simulation of the local precipitation mode of injection gettering associated with Sip growth and silicide formation are open problems at present.

10.6 Summary and Outlook In this chapter we have outlined the high temperature characteristics of those transition elements in silicon, that have been studied in some detail. These are the 3d elements from Ti to Cu, the 4d element Pd, and the 5d elements Au and Pt. The solubility and diffusivity of 3d elements and Au have been investigated in intrinsic and extrinsic silicon. In intrinsic silicon, all 3d elements

655

and Pd dissolve predominantly on tetrahedral interstitial sites, which means that [Mileq> [Msleq,while Au and Pt mainly dissolve substitutionally, so that for them [Mileqc [M,],, . For Mn,, Fe, , Co,, and Cu,, the charge state of the dominant species has been determined to be MIo'. For temperatures below 1100 K, the interstitial species of Mn, Fe, Co, and Cu have been shown to be donors, the substitutional ones to be multiple acceptors. Consequently, in extrinsic silicon [M,],, > [Mileq in this temperature range. For Mn,, Fe, , and Co,, a strong shift of the donor level towards the valence band above 1100 K indicates a transition from a low temperature to a high temperature atomic configuration. Compared to the usual solubilities in metallic systems, partial solution enthalpies found for the transition elements in silicon are very large (1.5 -2.1 eV). Coi, Ni,, Pd,, and Cui are among the fastest diffusing impurities in silicon with migration enthalpies below 0.5 eV. For the lighter 3d elements, the diffusivities decrease and AH&"')increases to about 1.8 eV for Tii. The systematics and for the heavier 3d elements also the absolute values of these interstitial diffusivities have been explained by a simple hard sphere model. If the concept of atomic radius is transferred to these metallic impurities in silicon, the difference of the elastic energy between the tetrahedral and the hexagonal site has been found to be a major contribution to the migration enthalpy of diffusion. Concerning the precipitation behavior of the fast diffusing transition elements cobalt, nickel, copper, and palladium, there is now some detailed knowledge as to which precipitate structure and composition forms under various experimental conditions. We have seen that precipitation of these impurities is closely related to the more general question of how systems with large driving forces relax toward thermal equilibrium.

656


Apparently, kinetically selected structures are initially formed. They transform into energetically more favorable configurations during Ostwald ripening or internal ripening, a process closely related to the metastability of the initially formed structures. A still open question is the nucleation of these structures which usually involves extremely large nucleation barriers and indicates the existence of precursor states not observed so far. Heterogeneous precipitation at extended defects has been summarized for iron, nickel, and copper impurities in silicon and related to the heterogeneous nucleation of precipitate structures that realize large growthrates. The challenging problem of relating the atomic and electronic structures of silicide precipitates has been tackled and has led to initial results concerning the introduction of bandlike and localized states. Theoretical calculations of the electronic structure of silicide precipitates are clearly needed to advance this exciting field. The fundamental knowledge of thermodynamic and transport properties of transition elements was applied to the problem of gettering, i.e., the question of how these impurities can be located away from the device-active area to improve the device properties. Gettering techniques were classified into relaxation, segregation, and injection gettering, according to the different mechanism by which they are governed. For interstitially dissolved 3d transition elements, relaxation gettering is dominant for internal as well as for various types of external gettering techniques. Other types of gettering mechanism have been identified for phosphorus diffusion gettering. A quantitative model of PDG, comprising segregation and injection gettering, has been developed recently for Au in Si and has yielded excellent agreement with experimental data. We consider a phenomenological classification as a prerequisite for microscopic models.

The development of such models will allow the gettering efficiency to be evaluated especially with respect to processing temperature and time. A challenge for the future will be the treatment of the simultaneous action of internal and external gettering in silicon materials for solar cells.

Acknowledgements The authors would like to thank Prof. P. Haasen, Dr. H. Hedemann, Dr. K. Graff, Dr. A. Koch, and Dr. F. Riedel for their critical comments on this chapter, Profs. G . Borchardt and H. Feichtinger for helpful remarks concerning Sec. 10.2 and K. Heisig for preparing part of the drawings. Financial support by the Sonderforschungsbereich 345 and the German Ministry for Education and Research is gratefully acknowledged.

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Seibt, M., Griess, M., Istratov, A. A., Hedemann, H., Sattler, A., Schroter, W. (1998a), Phys. Status Solidi ( a ) 166, 171. Seibt, M., Apel, M., Doller, A., Ewe, H., Spiecker, E., Schroter,W., Zozime, A. (1998b), in: Semiconductor Silicon 1998: Huff, H. R., Gosele, U. M., Tsuya, H. (Eds.). Pennington, NJ: Electrochem. Soc., p. 1064. Seibt, M., Hedemann, H., Istratov, A. A,, Riedel, F., Sattler, A., Schroter, W. (1999), Phys. Status Solidi ( a ) 171, 301. Shaikh, A. A., Schroter, W., Bergholz, W. (1983, J. Appl. Phys. 58, 2519. Shen, B., Sekiguchi, T., Jablonski, J., Sumino, K. (1994), J. Appl. Phys. 76, 4540. Shen, B., Sekiguchi, T., Sumino, K. (1995), in: Materials Science Forum, Vols. 196-201: Ferenczi, G. (Ed.). Aerdermannsdorf, Switzerland: Trans Tech, p. 1207. Shen, B., Sekiguchi, T., Zhang, R., Shi, Y., Shi, H., Yang, K., Zheng, Y., Sumino, K. (1996),Jpn. J. Appl. Phys. 35, 3301. Shen, B., Zhang, X. Y., Yang, K., Chen, P., Zhang, R., Shi, Y., Zheng, Y. D., Sekiguchi, T. Sumino, K. (1997), Appl. Phys. Lett. 70, 1876. Shepherd, W. H., Turner, J. A. (1962), J. Phys. Chem. Solids 23, 1697. Shimura, F., (1988), Semiconductor Silicon Crystal Technology. San Diego, CA: Academic. Shockley, W.,Moll, J.L. (1960), Phys. Rev. 119,1480. Silcock, J. M., Tunstall, W. J. (1964), Phil. Mag. 10, 361. Solberg, J. K. (1978), Acta Cryst. A34, 684. Solberg, J. K.,Nes,E. (1978a),J. MaterSci. 13,2233. Solberg, J. K., Nes, E. (1978b), Phil. Mag. A37, 465. Spiecker,E., Seibt,M.,Schroter, W. (1997), Phys. Rev. B 55,9577. Sprokel, G. J., Fairfield, J. M. (1965),J. Electrochem. SOC. I 12, 200, Stacy, W. T., Allison, D. F., Wu, T. C. (1981), in: Serniconductor Silicon 1981: Huff, H. R., Kriegler, R. J., Takeishi, Y. (Eds.). Pennington, NJ: The Electrochem. SOC.,p. 354. Stolwijk, N. A., Schuster, B., Holzl, J. (1984), Appl. Phys. A33, 133. Struthers, J. D. (1956), J. Appl. Phys. 27, 1560. Sveinbjomsson, E. O.,Engstrom, O., Sodervall, U. (1993), J. Appl. Phys. 73, 731 1. Takahashi,H., Suezawa,M., Sumino,K. (1992),Phys. Rev. B46, 1882. Tan, T. Y., Gardner, E. E., Tice, W. K. (1977), Appl. Phys. Lett. 30, 175. Tan, T. Y., Gafiteanu, R., Joshi, J. M., Gosele, U. M. (1998), in: Semiconductor Silicon 1998: Huff, H. R., Gosele, U. M., Tsuya, H. (Eds.). Pennington, NJ: The Electrochem. SOC.,p. 1050. Tice, W. K., Tan, T. Y. (1976), J. Appl. Phys. 28, 564. Trumbore, F. A. (1960), Bell Syst. Tech. J. 39, 205. Tung, R. T., Gibson, J. M., Poate, J. M. (1983), Phys. Rev. Lett. 50, 429.

Utzig, J. (1988), J. Appl. Phys. 64, 3629. Utzig, J. (1989), J. Appl. Phys. 65, 3868. Utzig, J., Gilles, D. (1989), Materials Science Forum, Vols. 38-41: Ferenczi, G. (Ed.). Aedermannsdorf, Switzerland: Trans Tech, p. 729. Van Vechten, J. A., Thurmond, C. D. (1976), Phys. Rev. B14, 3539. Verhoef, L. A., Michiels, P. P., Roorda, S., Sinke, W. C. (1990), Muter. Sci. Eng. B7, 49. Wagner, R., Kampmann, R. (1991), in: Materials Science and Technology Vol. 5: Cahn, R. W., Haasen, P., Kramer, E. J. (Eds.). Weinheim: VCH, Chap. 4. Weber, E. R. (1983), Appl. Phys. A30, 1. Weber, E. R., Gilles, D. (1990), in: SerniconductorSilicon 1990: Huff, H. R., Barraclough, K. G., Chikawa, Y. I. (Eds.). Pennington, NJ: The Electrochem. SOC.,p. 387. Wendt, H., Cerva, H., Lehmann, V., Palmer, W. (1989), J. Appl. Phys. 65, 2402. Wong, H., Cheung, N. W., Chu, P. K. (1988), Appl. Phys. Lett. 52, 889. Wong-Leung, J., Ascheron, C. E., Petravic, M., Elliman, R. G., Williams, J. S. (1995),Appl. Phys. Lett. 66, 1231. Wong-Leung, J., Eaglesham, D. J., Sapjeta, J., Jacobson, D. C., Poate, J. M., Williams, J. S. (1998), J. Appl. Phys. 83, 580. Wosinski, T. (1990), in: Defect Control in Semiconductors: Sumino, K. (Ed.). Amsterdam: North-Holland, p. 1465. Yoshida, M., Furusho, K. (1964), Jpn. J. Appl. Phys. 3, 521. Yang, T. F. (l982), Diploma Thesis, Gottingen. Zener, C. (1952), in: Imperfections of Nearly Perfect Crystals: Shockley, W. (Ed.). New York: Wiley, p. 289. Zhu, J., Barbier,D. (1990),Mater.Res. SOC.Proc. 163, 567. Zhu, J., Diz, J., Barbier, D., Langner, A. (1989), Mater. Sci. Eng. B4, 185. Zunger, A. (1986), Solid State Phys. 39, 275.

General Reading Benedek, G., Cavallini, A., Schroter, W. (Eds.) (1989), Point and Extended Defects in Semiconductors, NATO AS1 Series B 202, New York: Plenum Press. Frank, W. Gosele, U., Mehrer, H., Seeger, A. (1984), “Diffusion in Silicon and Germanium“, in: Diffusion in Crystalline Solids: Murch, G. E., Nowick, A. S. (Eds.), Orlando: Academic Press, pp. 64-142. Graff, K. (2000), Metal Impurities in Silicon Device Fabrication, 2nd Edition, Heidelberg: Springer Verlag. Shimura, F. (1988), Semiconductor Silicon Crystal Technology. San Diego: Academic Press. Weber, E. R. (1983), “Transition Metals in Silicon”, Appl. Phys. A 30,l.


11 Fundamental Aspects of S i c

.

.

Wolfgang J Choyke and Robert P Devaty Department of Physics and Astronomy. University of Pittsburgh. Pittsburgh. U.S.A.

List of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . 663 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 11.2 Polytypism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 I 1.2.1 Crystallography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 11.2.2 Inequivalent Sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666 11.2.3 Some Properties of Simple Polytypes . . . . . . . . . . . . . . . . . . . 667 11.2.4 Origin of Polytypism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668 11.3 Band Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670 11.3.1 The General Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670 11.3.2 The Conduction Band Edges . . . . . . . . . . . . . . . . . . . . . . . . 672 11.3.3 The Valence Band Edges . . . . . . . . . . . . . . . . . . . . . . . . . . 677 11.4 Phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679 11.4.1 Calculations of Phonon Dispersion Relations . . . . . . . . . . . . . . . 679 11.4.2 Infrared Transmission and Reflection . . . . . . . . . . . . . . . . . . . 679 Phonon Frequencies Measured by Low Temperature Photoluminescence 11.4.3 (LTPL) and the k-space Locations of Conduction Band Minima . . . . . . 681 1 1.4.4 First and Second Order Raman Scattering . . . . . . . . . . . . . . . . . 682 Raman Scattering from Free Carriers . . . . . . . . . . . . . . . . . . . . 683 11.4.5 11.5 Intrinsic Excitons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686 11.6 Shallow Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687 11.6.1 Shallow Donors: Nitrogen and Phosphorus . . . . . . . . . . . . . . . . 688 11.6.1.1 Nitrogen 11.6.1.2 Phosphorus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691 11.6.2 Acceptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692 Deep Centers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.7 694 11.7.1 Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694 11.7.1.1 Titanium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.7.1.2 Vanadium 696 697 11.7.1.3 Chromium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.7.1.4 Molybdenum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698 11.7.1.5 Scandium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 698 11.7.1.6 Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 11.7.2 Rare Earths: Erbium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 11.7.3 Intrinsic Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 11.7.3.1 Deep Level Transient Spectroscopy (DLTS) . . . . . . . . . . . . . . . . 700 11.7.3.2 Electron Spin Resonance and Positron Annihilation . . . . . . . . . . . . 701

662

11.7.3.3 11.8 11.8.1 11.8.2 11.8.3 11.8.4 11.9 11.10

11 Fundamental Aspects of SIC

Low Temperature Photoluminescence . . . . . . . . . . . . . . . . . Transport Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . Carrier Effective Masses . . . . . . . . . . . . . . . . . . . . . . . . . . Mobilities and Mobility Anisotropy . . . . . . . . . . . . . . . . . . . . Hall Scattering Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . Time-Resolved Measurements and Lifetimes . . . . . . . . . . . . . Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . 702

.

704 704 704 705 . 706 708 708


List of Symbols and Abbreviations a aH

B C

Cn CN

D (E) E e ED

EGX

Ex

Fvib

9 h

i

4 j

Jn

k k33 m

m

N n nC 4

RH rH

S T t

V

Vr

X

a Y3 ACF ES

e

PD

Y"

lattice constant Bohr radius magnetic flux density Capacitance-Voltage (C-V) stacking sequence lattice constant density of state energy fundamental charge ionization energy indirect exciton energy gap exciton binding energy vibrational contribution to the free energy g-factor Planck constant divided by 2 n index current of ballistic electrons electric current density coefficient wavevector Boltzmann constant mass mass tensor number of atomic layers number: carrier density Mott criterion wave vector Hall coefficient Hall scattering factor spin temperature time Capacitance-Voltage (C-V) tunnel voltage position absorption coefficient coefficient for nonradiative Auger recombination crystal field splitting static dielectric constant propagation angle drift mobility mobility

663

664


effective “spin” photon frequency ANNNI BEEM CB CVD DAP DDLTS DFT DLTS ENDOR ESR FB f.c.c. FTIR h.c.p. HPT LA LO LTPL MCDA OCDR ODMR PAS STM TA TO

uv

VB

axial (or anisotropic) next nearest neighbor ballistic electron emission microscopy conduction band chemical vapor deposition donor-acceptor pair double-correlated deep level transient spectroscopy density functional theory deep level transient spectroscopy electron nuclear double resonance electron spin resonance free-to-bound face centered cubic Fourier transform infrared hexagonal close packed hybrid pseudo potential Longitudinal acoustic Longitudinal optic low temperature photoluminescence magnetic circular dichroism absorption optically detected cyclotron resonance optically detected magnetic resonance positron annihilation spectroscopy scanning tunneling microscopy transverse acoustic transverse optic ultraviolet valence band

1 1.2 Polytypism

11.1 Introduction The fact that S i c is a newcomer to Vol. 4 of this Series is somewhat surprising considering that its history goes back to before the creation of the solar system. Grains of S i c from outside the solar system have managed to survive and reach the Earth. Astrophysicists now believe (Bernatowicz and Walker, 1997) that this Sic, which is more than 4.6 billion years old (the age of the solar system), originated primarily around stars on the asymptotic giant branch and that a small fraction comes from ejecta of supernova. The concept of a bond between carbon and silicon was suggested as early as 1824 by Berzelius. In 1891, Acheson published the results of his industrial process for making Sic, and in an appendix to Acheson’s paper Frazier gave evidence for the polytypism to be found in the crystals grown by Acheson. Electroluminescence was first seen in S i c in 1907 (Round, 1907). Careful X-ray structural analysis was done by Burdeck and Owen as early as 1918. Rectifying properties and n- and p-type doping of S i c were all established in the 1950s. Its excellent high temperature semiconducting characteristics were also recognized in the 1950s (O’Connor and Smiltens, 1960). So why has it taken until the end of the twentieth century to hit the mainstream of the semiconductor literature? It is only now that relatively large b o d e crystals [4 in (100 mm) diameter] of a single polytype have become a reality. Uniform epitaxial growth on such a 3 in wafer cut from such a boule has very recently been demonstrated. Doped n- and p-type 2 in (50 mm) wafers are now (1999) commercially available. The dynamic doping range of epitaxial films grown on wafers can range from a high of 1019cmP3to a low of I O l 3 ~ m - With ~ . such S i c available in the 4H and 6H polytype forms, a large number of exciting power and

665

high frequency device structures are possible, and many have been demonstrated. The giant semiconductor market is awakening to these possibilities and consequently the move of S i c into the mainstream. However, S i c cannot be viewed as a simple extension of the well known column IV semiconductors germanium, silicon, or an average of diamond and silicon. Hence the unusual fundamental aspects of SIC are the subjects of this chapter.

11.2 Polytypism 11.2.1 Crystallography As already mentioned, Frazier in 1893 deduced by optical goniometry that crystals of S i c grown by Acheson had numerous crystallographic structures called polytypes. Crystallographers have had a field day with Sic, and have discovered over 170 polytypes to date. Polytypism radically influences the properties of Sic, and thus we will now describe it in some detail. Let us consider a number of possible ways of arranging hard spheres in close packing as shown in Fig. 11 - 1. For our purposes, let us designate a Si-C atom pair in an A plane double layer as Aa, in a B plane as Bb, and in a C plane as Cc. It is now possible to generate a series of double layer stacking sequences along the principal crystal axis (the z-axis, which is orthogonal to the x- and y-axes shown in Fig. 11-1). For a stacking AaBbCcAaBbCc ... we generate the cubic polytype of 3C S i c or the zincblende form of S i c . If we stack the double layers as AaBbAaBb ..., we generate the hexagonal polytype 2H S i c or the wurtzite form of Sic. Other common polytypes of S i c may be generated by the following stacking sequences of the bi-layers along the z-axis: 4H S i c (AaBbAaCcAaBbAaCc ...),

666

11 Fundamental Aspects of Sic

11.2.2 Inequivalent Sites

Figure 11-1. Close-packed planes perpendicular to the c-axis [OOOI] (the principal axis) in hexagonal and rhombohedra1 lattices or the [l 1 I] direction in zincblende lattices. The z axis mentioned in the text is perpendicular to the x - y plane.

6H S i c (AaBbCcAaCcBbAaBbCcAaCcBb ...), and 15R S i c (AaBbCcAaCcBbCcAaBbAaCcAaBbCcBbAaBbCcAaCcBbCcAaBbAaCcAaBbCcBb ...). The notation, called Ramsdell notation, is straightforward: C for cubic, H for hexagonal, and R for rhombohedra]. For simplicity in Sic, A, B, C stands for Aa, Bb, Cc. As can be seen, the unit cell repeat distances along the zaxis can get to be very long. In fact one polytype has been identified with a repeat distance along the principal c-axis (z-axis of Fig. 11-1) of 1200A (120nm). The question of polytype stability is still a puzzle and is being studied by a number of theoretical groups.

One reason that the long slender unit cells of the various polytypes of S i c are more than a crystallographic curiosity is that these different unit cells have different numbers of inequivalent silicon or carbon sublattice sites upon which to substitute dopants, or about which point defects may form. This feature and the variation of band gap with polytype (to be discussed later) have a profound effect on the properties of the different polytypes and create a family of semiconductors out of Sic. Consider the number of inequivalent sites in five of the simplest S i c polytypes: Zincblende, 3C Sic, and wurtzite 2H have just one site, but 4H S i c has two, 6H S i c has three, and 15R S i c has five inequivalent sites. What does this mean? Nitrogen acts as a shallow donor in S i c when it substitutes on the carbon sublattice, and similarly aluminum acts as an acceptor when it substitutes on the silicon sublattice. Then, in 4H S i c there are two donors/acceptors, in 6H S i c there are three donors/acceptors, and in 15R S i c there are five donors and acceptors, respectively, all due to the substitution of a single chemical dopant. The reason for this can be seen more clearly in Fig. 11-2, where we show a schematic representation of the atomic arrangements of the silicon and carbon atoms in the (1 120) plane of the 6H S i c hexagonal pyramid. Generally, if the stacking of the atomic bi-layers of any S i c polytype is represented in the (1 120) plane, then the complicated stacking sequences can be expressed in terms of simple “zig-zags”. In Fig. 11-2, it can be seen that for 6H S i c there is a “zig” of three lattice positions ABCA to the right and a “zag” of three lattice positions to the left ACBA. As shorthand notation, we write (33) for 6H, (22) for 4H, and (232323) for 15R, etc. Again on Fig. 11-2, we depict car-

11.2 Polytypism

6H Sic Inequivalent Sites

4

1

Iyl

Site

$h

Carbon Planes “like”

12

0

12

8 8 16 16

667

Figure 11-2. Schematic diagram to illustrate the inequivalent sites in 6H Sic. N,, N,, and N, are nitrogen atoms substituting on three inequivalent carbon sites in the S i c lattice. N, is substituting on a hexagonal site h and N2 and N, are substituting on two quasi-cubic sites k, and k,. The inequivalence of the sites is illustrated, in the table, by the distance of each of the substitutional nitrogen atoms to carbon “like” and silicon ‘‘like’’ planes. The listed distances are measured in units specified by the scale given on the left. The length of the unit cell of 6H S i c is 15.1 A (1.51 nm), as indicated on the left of the figure.

C A B C A B

bon atoms in the bi-layers with small black circles and silicon atoms with larger shaded circles. A bi-layer designated h is one in which the carbon and silicon atoms find themselves in a quasi-hexagonal stacking environment with respect to the neighboring bi-layers. In the same spirit, k, and k2 are bi-layers where the carbon and silicon atoms find themselves in a quasi-cubic stacking environment with respect to their neighboring bi-layers. Let us now substitute nitrogen atoms at the h, k,, and k2 carbon sites and call them N,, N2, and N3, respectively. On the right in Fig. 11-2 is a table which illustrates that distances in the same crystallographic column (A, B, or C) of N,, N,, and N, atoms from carbon and silicon

“like” planes are the same for nearest neighbors but different for second and third neighbors. The nitrogen atoms substituting on the k, and k2 sites sense different environments than a nitrogen atom substituting at an h site. This leads to the unusual situation of three distinct nitrogen donors in 6H Sic.

11.2.3 Some Properties of Simple Polytypes The stacking sequences and selected physical properties of 3C Sic, 15R Sic, 6H Sic, 4H S i c , and 2H S i c , the polytypes of greatest interest in current research and development, are given on Fig. 11-3. The lattice constant in the zincblende 3C S i c

668


Figure 11-3. A summary of some of the physical properties of 3C, 15R,6H, 4H, and 2H Sic. If these polytypes are represented in the (1 120) plane of a hexagonal pyramid, then the repeat distance along the c-axis would be C,.

modification and the width of the pyramid faces and the lengths of the unit cells parallel to the principal or c-axis (z-axis of Fig. 11- 1) are obtained from X-ray measurements. Recently, Bauer et al.’s (1998) very precise X-ray measurements yielded highprecision determinations of atomic positions in 4H S i c and 6H Sic. These measurements were also compared to results from calculations based on density functional theory (DFT) within the local-density approximation. The unit cell geometries of the polytypes dictate the atoms per unit cell and the number of inequivalent sites contained in a particular unit cell. The space groups for the various polytypes are a consequence of the placement of the carbon and silicon atoms in each polytype. The indirect exci-

ton energy gap EGx (eV) , measured at 2 K, is obtained from optical measurements and given at the bottom of Fig. 11-3. The band structure and energy gaps in S i c will be discussed in some detail in Sec. 11.3.

11.2.4 Origin of Polytypism The underlying causes of the multitudinous stacking arrangements exhibited by S i c polytypes are not well understood. Explanations based on both high temperature thermodynamic equilibrium states and details of the kinetics during growth have been proposed. One of the earliest proposed growth mechanisms is Frank’s model (195 1) of spiral growth around screw dislocations. In the last decade, powerful computational

11.2 Polytypism

669

techniques have been applied to the calculation of bulk cohesive energies of the important SIC polytypes, beginning with the work of Heine et al. (1992a, b). These calculations are challenging because the differences in cohesive energy are only a few millielectronvolts per atom, so that high accuracy is required. Not surprisingly, the results obtained by various groups differ due to differences in their assumptions and procedures. The recent paper by Limpijumnong and Lambrecht (1998) provides a comparison of results and numerous references to the literature. According to calculations, 4H,6H, and 15R S i c have the lowest total energies of the important polytypes, but which polytype has the lowest energy differs among the calculations. The total energy for 3C S i c is larger, and the value for 2H S i c is the highest. The results of these sophisticated electronic structure calculations are frequently interpreted and compared using the axial (or anisotropic) next nearest neighbor Ising (ANNNI) model, which was originally developed to explain the appearance of many complex phases, somewhat analogous to polytypes, in certain magnetic materials. For application to Sic, each double layer in the stacking sequence is assigned a value of o,=+l or -1 for its ‘spin’, depending on its relationship to the preceding bi-layer in the sequence. Parallel (anti-parallel) ‘spins’ correspond to cubic (hexagonal) stacking. Coefficients J,, in the expression for the energy

same stacking configuration for the nth nearest double layers. Typically, the interactions are cut off at n = 3, although higher values of n as well as terms describing interactions among four double layers are sometimes included. At zero temperature, the phase diagram for this model is easily worked out, and there is a point at which an infinite number of phases (polytypes) can coexist ( J 1 = - 2 J2, J,=O with J,>O). According to the calculations of Cheng et a]. (1988), S i c lies very close to this point, suggesting a favorable situation for polytypism. Results calculated by other groups (Limpijumnong and Lambrecht, 1998; Bechstedt et al., 1997), are not so close to this point. Limpijumnong and Lambrecht (1998) use the ANNNI model as a parameterization scheme, using calculated results for enough polytypes to uniquely set the coefficients, then attempt to predict the free energies of additional polytypes. The origin of the interactions between double layers separated by quite considerable distances is not understood. Heine et al. ( 1 992 a) discuss an analogy with Friedel oscillations in metals. Recently, Bauer et al. (1998) have carefully reexamined the locations of atoms within the unit cells of S i c polytypes, which may provide clues regarding the relationship between relaxation of atomic positions and stability. There may also be a connection between stoichiometry and polytypism (Tairov and Tsvetkov, 1984). Because the calculated total energies of polytypes are so close, additional small effects may be important. The vibrational contribution to the free energy,

describe the interactions between adjacent double layers ( n = l), next nearest double layers ( n = 2 ) , etc. The index i is summed over the total number of bilayers N . A positive value for a coefficient J,, favors the

Fvib=

Z j,k

{w+ 2

+ kB T In

[

,I])?[

1-exp

670


called the phonon free energy, will differ for each polytype due to small differences in the phonon dispersion relations. Bechstedt et al. (1997) calculated differences about a factor of ten larger than Cheng et al. (1990). There is also qualitative disagreement: Cheng and co-workers find that the phonon free energy tends to stabilize 6H S i c with respect to 4H S i c with increasing temperature, while Bechstedt and co-workers find the opposite. Some papers have attempted to relate results of bulk calculations to the mechanism of growth. For example, the parameters of the ANNNI model can be used to describe the addition of a layer (Heine et al., 1992b), but it is highly questionable whether the values of these parameters obtained from bulk calculation apply, even if the ANNNI model is valid. Perhaps a more promising avenue for progress in the near future is the detailed study of growth mechanisms using modern methods of surface science.

11.3 Band Structure 11.3.1 The General Picture A fairly thorough review of theoretical topics relating to fundamental properties of S i c up to early 1997 is given by Choyke et al. (1997). Most of the theoretical discussions are related to the band structures of S i c polytypes, and the progress that has been made on band theory since the current upsurge of industrial interest in S i c in this decade is impressive. During this period, much improved size, polytype, and dopant control of bulk crystals of S i c has been obtained, making possible excellent epitaxial growth on wafers cut from such bulk crystals. This in turn has made possible experimental verification of the theory, and points to areas that require much further study. To give a general overview of the band struc-

ture of 2H, 4H, 6H, and 3C S i c we show in Fig. 11-4 a slightly simplified version of the electronic band structures E (k)calculated by Chen and Srichaikul (1997). The positions of the valence band maxima and the conduction band minima are indicated for these four polytypes. From this, it follows that these S i c polytypes are large band-gap indirect semiconductors. All S i c polytypes measured to date are indirect semiconductors and we expect all S i c polytypes to follow this pattern. To the right of each of the four calculated polytype band structures in Fig. 11-4 we give the experimentally obtained values of the exciton band gaps EGx. These authors use a hybrid pseudo-potential (HPT) and tight binding approach to obtain the band structures in Fig. 11-4. We chose these calculations to illustrate the band structures of 2H, 4H, 6H, and 3C Sic, because the band-gaps are fitted to the given experimental values. A number of excellent first principles calculations have also become available recently (Choyke et al., 1997; Persson and Lindefelt, 1997), and there is good agreement among these calculations. In Fig. 11-4 we have arranged the polytypes with the 2H wurtzite structure at the top and the 3C zincblende structure at the bottom. This ordering in terms of “hexagonality” shows a number of interesting trends. As we go from 2H S i c to 3C Si c the forbidden gap becomes progressively smaller. Lambrecht et al. ( 1 997) have shown how this comes to pass from their band theoretical considerations. It is important to devise experimental tests for the determination of the qualitative reliability of the new band structure calculations. Optical reflectivity measurements on various polytypes in the middle ultraviolet region (4-1 1 eV) on large “as-grown’’ optical surfaces are now possible due to improved substrate wafers and epitaxial growth. Such reflectometer measurements combined

11.3 Band Structure

S

t

5 V

w

2H S i c

EGX(2K) = 3.330 e~

O

m~

r

m~

A

671

Figure 11-4. The bandstructure of 2H, 4H,6H, and 3C S i c near the valence band maximum (VBmax)and the conduction band minimum (CBmin); E,, (2 K) is the exciton band gap in electronvolts measured at 2 K.

H K

S

t

4H Sic

s

so

EGX(2K) = 3.265 eV

w

k~

r

M L

A

HK

5

t

5

6H Sic

v

w

EG,

o

r

ML

A

(2K) = 3.023 eV

HK

3C S i c

E G X (2K) = 2.390 eV

with a strong theoretical effort (Lambrecht et al., 1993,1994; Suttrop et al., 1993) have given a detailed interpretation of the measured spectra and provide a strong test of the theory. Room temperature spectra were reported for 4H, 15R, 6H, and 3C S i c , while

the reflectivity was calculated for 2H, 4H, 6H, and 3C S i c . This allowed a consideration of trends among polytypes. While many features in the measured reflectivity may be interpreted using calculated critical point transitions at symmetry points in the Bril-

672

11 Fundamental Aspects of Sic

louin zone, an important result of this work is that the major peaks in the reflectivity are associated with rather extended regions of k-space, over which the energy difference between two bands is nearly constant. Calculations of the UV optical properties were extended to 25 eV by Lambrecht et al. (1997).

ent approaches, have obtained the effective mass tensor components for the bottoms of the conduction bands of these polytypes. Experiment has met with major obstacles in accurately confirming the theoretical effective mass tensor values, except in 3C S i c and 4H Sic. In Fig. 11-5 we have adapted a table from an article by Wellenhofer and Rossler ( 1 997 a) to summarize the current theoretical and experimental findings at the conduction band minima for 2H, 4H, 6H, 15R, and 3C Sic. To simplify the figure we have left out references to the various calculations and measurements, but these may be found in the paper of Wellenhofer and Rossler (1997 a). Lambrecht et al. (1997) gave a theoretical interpretation, based on the band struc-

11.3.2 The Conduction Band Edges Of particular value for the modeling of S i c devices is the guide that band theory gives us in locating the positions of the conduction band minima in the 3C S i c zincblende Brillouin zone, the 2H, 4H, and 6H S i c hexagonal Brillouin zones, and the 15R S i c rhombohedra1 Brillouin zone. Various theoretical groups, applying slightly differm(mJ

THEORY

EXPERIMENT ~

3C Sic mll

mi

minimum at X 0.70 0.23

2H Sic ml mil

mM-K mM-L

0.40 0.26

S

mM-K

mM-L

k,

0.66 0.3 1 0.30

mX.K

mx.u

0.68 0.23

0.60 0.29

0.667 0.247

0.67 0.25

0.67 0.22

0.45 0.26

0.45 0.27

0.43 0.26

0.57 0.32 0.32

0.58 0.28 0.31

0.57 0.28 0.31

0.58 0.3 1 0.33

mL: 0.18

0.30

mil: 0.22

0.48

minimum along M-L 0.78 0.23 1.2-2.0

15R Sic mx-r

0.63 0.23

minimum at M

6H Sic mM-r

0.67 0.25

minimum at K

4H Sic mM-r

~~

0.67 0.22 0.41

0.75 0.27 1.95

0.77 0.24 1.24

0.75 0.24 1.83

m l : 0.35

0.24

0.25 0.42

mil: 1.4

0.34

1.7

m l : 0.28

0.24

mil: 0.53

0.38

2.0

minimum at X

Figure 11-5. Theoretical and experimental values for the effective electron masses in 3C, 2H, 4H,6H, and 15R Sic. The columns compare theoretical as well as experimental values obtained in a variety of ways.

11.3 Band Structure

673

partially occupied and participate in the optical absorption. We shall now illustrate details of this interband absorption for polytypes 4H and 6H. For 4H Sic, it appears adequate to consider transitions in the Brillouin zone at the conduction band minimum, which has been located to be at point M. In the case of 6H Sic, however, we must take into account the entire M-U-L axis, due to the fact that the lowest conduction band is extremely flat in this direction. In Figs. 1 1-6 and 11-7 we show the theoretical band structure interpretation of the optical absorption for 4H and 6H Sic, as well as the experimental optical absorption data. The figures are based on Fig. 11-1 inLambrechtet al.’s paper(1997). In contrast to the valence to conduction band indirect transitions where phonons play such a vital role, we show only direct transitions in Fig. 11-6 for the inter-conduction

tures of undoped S i c polytypes, of the optical absorption attributed to the first few inter-conduction band transitions in heavily n-type doped Sic. This optical absorption has been evident in heavily n-type doped platelets since Acheson’s time, leading to a variety of colorful platelets for different polytypes. Measurements on such platelets were first reported in 1965 by Biedermann on 4H, 6H, 15R, and 8H Sic, and on 3C S i c by Patrick and Choyke in 1969. At the time, it was supposed that the observed absorption bands were due to transitions from the lowest conduction band to higher conduction bands. Our current understanding requires a generalization in that the modern band structure calculations indicate that in polytypes such as 4H S i c there is a second conduction band very close to the lowest conduction band (1 30 meV), and hence under heavy doping the second band may be

4H SiC:N THEORY

EXPERIMENT 3.0

2.5

~

----- r---

2.0

~

~

150

1

100

1.5

50

c--a (crn-I) Absorption Coefficient

Energy Levels at M point for CB Minima

Figure 11-6. Comparison of experiment and theory for inter-conduction-band optical transitions in heavily doped n-type 4H SIC.

674

1 1 Fundamental Aspects of SIC

Figure 11-7. Comparison of experiment and theory for inter-conduction-band optical transitions in heavily. doped n-type 6H Sic. . ..

6H SiC:N EXPERIMENT

THEORY 3.0

CB6 CB5

2.5

2.0

1.5

1 .o

x

9

0.5

w8

0.0

+---(r (crn-l) Absorption Coefficient

Wavevector

band transitions in 4H S i c near the M point. Symmetry arguments are used to assert that the inter-conduction band optical transitions are allowed between bands of the same symmetry for E (1 c and allowed for bands of different symmetry for E Ic . Agreement between experiment and theory is very satisfactory. In the case of 6H S i c (Fig. 11-7), transitions from CB, to bands up to CB, are considered. In 6H Sic, the whole M-U-L axis is believed to be important in explaining these transitions. Again the selection rules and the calculated band structures reproduce the observed absorption peaks reasonably well, except for the separation of the peaks labeled A and B. Lambrecht et al. (1997) believe that the A-B fine structure can be explained in terms of the double minimum (Camel's Back) structure of the lowest 6H S i c conduction band. Recently, ballistic-electron emission microscopy (BEEM) has been used to get

k ---D

quantitative values of the energy separations of several of the lowest conduction bands near the minimum. Im et al. (1998a, b, c) and Kaczer et al. (1998) have reported BEEM measurements on platinum and palladium Schottky contacts in 4H and 6H Sic, as well as palladium Schottky contacts in 15R Sic. In the BEEM technique, the dependence of the current of ballistic electrons (Ic) from the scanning tunneling microscope (STM) tip into the S i c sample as a function of tunnel voltage (V,) at constant tunnel current, can be measured. In this way, the conduction band structure of S i c may be probed. Figure 1 1-8 gives BEEM data for 6H and 4H S i c for both palladium and platinum contact films, but for 15R Sic, only data for palladium contact films is shown. We show in Fig. 1 1-8 plots of I, (PA) as a function of V,. Each set of curves represents an average of more than one hundred individual Ic-VT data sets. In the cases where

11.3 Band Structure

5 4

2a

3

w 2 M u

I

0 1.o

4

1.s

2.0

1.5

2.0

VT (v)

2.5

3

a

2

2

W

0

n

1

0 1.o

.."

5

0.5

VT (v)

2.5

675

both the palladium and the platinum curves are shown, the platinum data is offset by a constant factor from the palladium curve for the sake of clarity. Bell and Kaiser (1988) have given a theoretical model for the BEEM spectrum, which has been used to fit the data near the threshold, giving rise to the solid curves. BEEM can also detect higher lying conduction band minima when the STM tip voltage (V,) reaches a value such that the hot ballistic electrons have enough energy to reach a higher conduction band minimum. An onset of additional BEEM current (I,) is then expected, which can best be observed by taking a derivative of the BEEM (Zc- V,) curve. Such derivative curves are shown as insets on the three data plots of Fig. 11-8. The single threshold in 6H S i c and the first and second thresholds in 4H and 15R SIC are indicated by arrows pointing to the changes in slopes of the derivative curves in the insets. The arrows on the integral curves indicate the threshold voltages determined from the fits to the Bell-Kaiser model. In the case of 6H Sic, Schottky barrier heights of 1.27 2 0.02 eV for palladium and 1.3420.02 eV for platinum are obtained. For 4H Sic, the palladium threshold is 1.5420.03 eV and the platinum threshold is 1.5820.03 eV. Note that the difference of the Schottky barrier energies between 4H and 6H S i c is 0.24 eV, which is just about the difference between the measured exciton band gaps for these two polytypes. In the case of 15R S i c , the threshold for the

v

u

Y

0.0

Figure 11-8. Averaged BEEM ( I , versus V,) data taken from metal (palladiudplatinum) 6H, 4H, and 15R S i c contacts. The platinum curve is vertically offset for clarity. Solid curves are fits to the data using the Bell-Kaiser model with arrows indicating thresholds extracted from the fits. Insets are the derivative spectra dI,ldV, as a function of V, for palladium contacts, where the changes in slopes are indicated by arrows.

676


palladium contacts is about 1.22 eV. The difference between the exciton energy gaps of 6H S i c and 15R S i c is 37 meV, whereas the difference in the Schottky barriers is about 50 meV. The difference of 13 meV is well within the error of the measurements. As already mentioned, for 6H S i c we see no additional onset of tunnel current. However, for both 4H and 15R S i c we see second thresholds in the derivative curves. For 4H Sic, a measured energy difference of approximately 140 meV is obtained between the minima of the two lowest conduction bands, CB, and CB,. For 15R Sic, the derivative curve also shows two clear onsets separating CB, and CB, by about 500 meV. A comparison of these BEEM results with band calculations is shown in Fig. 11-9. The top row displays the lowest lying conduction bands in 6H, 4H, and 15R S i c as obtained from theory. In 6H S i c we see no second conduction band minimum within 0.6 eV of the minimum of CB, . In 4H S i c there is a second higher minimum at the

4

15R SIC

4H Sic

6H S i c

p

M point approximately 130 meV above the first minimum. For 15R S i c theory predicts two minima, one at point X of CB, and the second at the point L of CB, in the rhombohedral Brillouin zone of 15R Sic, approximately 500 meV above the minimum at X. The derivative BEEM spectra shown in Fig. 11-8 do not directly map the density of states of the Si c polytype, but it might be expected that each higher lying conduction band minimum will introduce an abrupt increase in the density of states. Consequently, in the second row of Fig. 11-9 we show the theoretically calculated curves for the density of states of 6H, 4H, and 15R S i c as a function of energy above the zero of energy at the minima of the lowest lying conduction bands. The arrows on the density of states curves indicate the onset of an increase in the density of states. For 6H S i c no additional increase in the density of states is seen, but for 4H S i c we see one at about 120 meV and for 15R S i c there is one indicated at roughly 500 meV.

0.4 0.2

. . . .

0.4

0.2

0.0

M U L

M

M

0.0

M

L

A

L

X

A

I

00

02

0.4

06

E (e V) --a

08

0.0

0.2

04

E (cV) --+

0.6

08

00

02

04

06

E (eV) --+

08

Figure 11-9. Calculated conduction bands and density of states for 6H, 4H, and 15R S i c near the conduction band edges (Im et al., 1998; Kaczer et al., 1998).

677

11.3 Band Structure

11.3.3 The Valence Band Edges Considerably less is known about the valence band edges of S i c than about the conduction band edges. However, it is generally agreed that the maximum of the valence bands in all polytypes is at or very near the r p o i n t in the Brillouin zone. In zincblende or 3C S i c the top of the valence band is sixfold degenerate, including spin but neglecting the spin-orbit interaction. The spinorbit splitting for 3C S i c has been experimentally determined to be about 10 meV (Humphreys et al., 1981). If we include the spin-orbit interaction, we have fourfold and twofold degenerate bands at the rpoint. For the hexagonal and rhombohedra1 polytypes, we must also take into account the effect of the crystal field. In 6H, 15R, 4H, and 2H S i c the crystal field splitting is expected to be considerably larger than the spin-orbit splitting. If we include the crystal field splitting for these polytypes, we obtain three twofold degenerate valence bands at the r p o i n t . A number of theory groups (Persson and Lindefelt, 1996, 1997; Lambrecht et al., 1997; Wellenhofer and Rossler, 1997 a) have recently made calculations of the details of the valence band structure near the rpoint and have given estimates of the hole effective masses for the three highest lying valence bands. In Fig. 11-10 we show the valence band edge of 6H SIC (Wellenhofer and Rossler, 1997a). The spin-orbit splitting has been adjusted to agree with the measured spinorbit splittings reported by Humphreys et al. (1981). The crystal-field splitting is also in good agreement with experimental findings, and is discussed later. Lambrecht et al. (1997) among others have given a theoretical treatment i n which they show that the crystal-field splitting (the region ACF 1 x 102 c m z 0 Grain size = 5 x 103 cmz @

1011

Grainsize< l x lO-3cm2 FeB Pair in Fz - silicon

1013 1014 1015 Fe - concentration rcrn-31

1012

1016

Figure 12-13. Measured bulk minority carrier lifetime versus iron-doping level for float-zoned multicrystalline silicon ingots with various grain sizes. For comparison, the lifetime in boron doped Fzsingle crystals is shown as a function of the FeB pair.

12.3 Monocrystalline and Polycrystalline Silicon

cause the precipitates have to be dissolved first, which is a slow rate-limiting step. This is the reason, for instance, why dislocation tangles in as-grown mc-silicon remain recombination active after the normal gettering step during cell processing.

Oxygen and Carbon Besides the doping elements, carbon and oxygen are the impurities with the highest concentrations in mc-silicon. Similar to Czsilicon, both elements show a typical distribution in the ingot: the oxygen decreases from the bottom to the top, while carbon shows the opposite behavior. The concentrations are in the range of about 2 - 12 x 10'' cm-3 for oxygen and 0.05-5x l O I 7 cmW3for carbon. Close to the bottom, the oxygen concentration can reach above 1OI8 cmW3.The concentrations of dissolved oxygen and carbon are usually determined by FTIR spectroscopy. Interstitial oxygen and substitutional carbon are associated with optical absorption lines at 1107 cm-' and 605 cm-], respectively, in silicon. In addition, a broader line at 1224 cm-' can occur in the spectrum. This line has been associated with oxygen precipitates (Shimura et al., 1980; Hu, 1980) and explained by excitation of the LO-mode (longitudinal optical phonon) of SO,. The LO-mode is normally infrared inactive for bulk SiO,, but can become active for particles that are small enough to become electrically polarized. Calculations of the polarization show that the 1224 cm-' band arises if the particles are smallerthan A/2n n,, where Ais the wavelength of the incident radiation and n , the refractive index of the embedding matrix, and have a plate-like shape (Hu, 1980). The FTIR investigations actually confirm that oxygen can precipitate in as-grown and processed silicon wafers, as can be seen in Fig. 12-14. The amount of precipitated

1.4

=

i

.-2 s

1.2

735

Interstitial oxygen

/

1107m-'

1.0

K

e 0.8

0

8 u

6

0.6

Sio2 - precipitates 1224 ~ m - 1

0.4 0.2

lo00 1050 1100 1150 1200 1250 1300 Wavenumber [m-11

Figure 12-14. FTIR spectrum of dissolved oxygen at various positions in an mc-silicon ingot. The broad absorption band at 1224 cm-' is due to precipitated SiO,.

oxygen depends on the growth conditions, which vary for commercial material. The size, density, and morphology of precipitated SiO, and S i c have been studied and confirmed by TEM and HREM (Fig. 12-15). Basically, two types of SiO, precipitate can be observed in as-grown mc-silicon: plate-like precipitates on { 1 1 1 } planes and spherical, amorphous SiO, particles. The sizes vary between 5 and 100 nm depending on the annealing conditions. The plate-like defects have a lateral extension up to 100 nm and a thickness of one or two atomic layers. These precipitates have not been clearly identified, but may be stacking faults decorated with some smaller SiO, precipitates of below 1 nm in size. The typical SiO, platelets lying on { l o o } planes which are observed in Cz-silicon after long annealing times are not observed here. Both types of defect can occur with densities up to 10" cmP3 depending on the initial oxygen concentration and the thermal conditions during crystal growth.

736

12 New Materials: Semiconductors for Solar Cells

Figure 12-15. HREM image a) of an amorphous, spherical, and plate-like SiO, precipitate and b) in as-grown mc-silicon. The plates lie on (1 11) planes.

S i c precipitates rarely occur in me-silicon. The precipitates have a facetted shape and the sizes vary between 5 and 20 nm. Oxygen and carbon Precipitates are not uniformly distributed but occur in regions of higher dislocation densities, which indicates that dislocations are preferential sites for segregation and precipitation. In view of the observed inhomogeneous distribution of transition metals, it has been suggested that the oxygendecorated dislocations are preferential sites for metal precipitation and thus enhance the enrichment in the areas of low lifetime.

An important aspect for applications is that specimens with precipitated oxygen have lower carrier lifetimes compared to specimens with interstitial oxygen only. This is shown in Fig. 12-16 where the carrier lifetime, as measured by the y-PCD method, is depicted as a function of the peak height of the 1224 cm-' band. Independent of whether oxygen and carbon are partly precipitated, the as-grown material is supersaturated with these impurities. Any high temperature annealing step will lead to further precipitation, as will be discussed in de-


FTIR - absorption at 1224 cm-1

737

melt during growth or is incorporated in the final ribbon. The techpiques can be distinguished basically by considering the directions of the sheet growth and of the proceeding solidification front. In the first class, the solid-liquid interface proceeds parallel to the sheet pulling direction; in the second class they are perpendicular to each other and mainly decoupled, which allows higher growth speeds.

12.3.3.1 Technological Development I

0.01

I

I

I

I

0.02 0.03 0.04 0.05 FTIR - peak height [au.]

Figure 12-16. The carrier lifetime of mc-silicon as a function of the FTIR peak height of the 1224 cm-' band, whichcorrelates linearly with the amount ofprecipitated SO,.

tail in Sec. 12.3.4.1. Since annealing treatments are an integral part of solar cell processing, oxygen precipitation and its impact on the lifetime of the material and the solar cell performance are very important aspects of multicrystalline silicon.

12.3.3 Ribbon Growth Technologies Many research efforts have been directed towards the development of growth processes where the material is directly grown in the form of sheets or ribbons (Goetzberger and Rauber, 1989; Zst Znt. Con5 on Shaped Crystal Growth, 1987). In the meantime, the first products have reached the commercial market or are close to industrial production. Mainly, two developments can be distinguished, and the technological and material aspects of some of these new materials shall be presented here. Sheet growth techniques require some guiding system to shape the solidifying melt. The shaping system is either in contact with the

The technology that is most advanced is based on the edge-defined film fed growth (EFG) process and belongs to the first class. The velocity of the melt interface is equal to the growth velocity and determined by the thermal gradients. In the technical process, the die is shaped as a closed octagon and hollow tubes of several meters length are grown. The technique allows continuous operation, since the crucible can be replenished. The sides of the octagonal pipe are 10 cm wide and are separated by a laser. The resulting ribbons are cut into wafers of standard dimensions, but other shapes are also possible. In the continuous growth process, capillary forces supply the melt through grooves or channels inside the die. The melt meniscus is anchored at the outer edges of the shaped die and adjusts its position with respect to the pulling speed as long as enough melt can be supplied by the capillary action. One of the problems is to achieve continuous, stable growth, which requires good temperature control. The growth rates are around 1 cm min-', while the temperature gradients at the ribbon edge can become quite high, up to 250 OC cm-'. This can cause internal stresses and high dislocation densities. It is evident that in the EFG technique the die material is of great importance. High

738


density graphite is the usual die material, therefore interaction with the silicon melt mainly introduces carbon and metal impurities into the silicon. To reduce contact with the shaping die several other techniques have been developed, which differ by the degree of wetting between the die and the melt. Processes with little contact between melt and shaping elements are the dendritic web growth (D-WEB) and the string ribbon growth method. In both techniques, contact with the shaping system is limited to the edges of the sheet. The ribbon is stabilized either by dendrites, which grow simultaneously with the ribbon (D-WEB), or by high temperature filaments which are fed through the melt to the crystallization front (string ribbon). A problem with these growth techniques is that they are difficult to control because temperature variations of only +_1 OC in the D-WEB process and +5 OC in the string ribbon technique can be tolerated. Both techniques are now being commercialized on a small scale. The direction of development is to grow thinner ribbons of about 100 pm thickness. The major technological challenge is in controlling the cooling profile so that the ribbon is grown at a commercially useful speed, but is still not too stressed or buckled. The temperature gradient in the growth direction at the liquid-solid interface dictates the maximum growth speed. Typical gradients for a growth speed of 20 mm min-' are about

5OO0C cm-'. These large gradients cannot be maintained along the length of the growing ribbon and have to be reduced in a controlled way to avoid large thermal stresses. Otherwise plastic flow occurs and buckled, nonflat ribbons result. In the second class of techniques, higher ribbon growth velocities are obtained because the sheet velocity and the solidification velocity are mainly perpendicular to the sheet growth direction. Currently, the most promising approach is the ribbon growth on substrate (RGS) technology (Lange and Schwirtlich, 1990).The melt is cast on a horizontally moving substrate through a die, which shapes the ribbon and determines the width (Fig. 12-17). The technique allows continuous operation if the substrate rotates like a conveyer belt. The requirements for the substrate material are similar to those for other techniques: a high degree of inertness against the silicon melt and no adhesion at lower temperatures, so that ribbon and substrate can be separated. Graphite materials with an appropriate surface coating are used here. The contact between solidifying melt and substrate is a crucial problem in these techniques, since it to a large extent determines the resulting microstructure of the ribbon and the contamination with impurities. Another problem is the smoothness of the opposite surface of the ribbon, since the material expands upon freezing and forms hillocks. Smooth surfaces can only be obtained if melt that solidifies outside the die

Figure 12-17. Schematic representation of the ribbon growth on substrate (RGS) process. Solidification proceeds perpendicular to the moving substrate.


is covered by a thin capping layer. This can be achieved, for instance, by exposing the surface to an oxygen gas flow. The problem in this case is, however, that the oxygen concentration in the ribbons becomes high, so that it is difficult to maintain a high material quality. The advantage of the RGS or similar methods is that the solid-liquid interface proceeds almost perpendicular to the sheet pulling direction, and the solidification rate becomes independent of the sheet growth velocity. In practice, however, there are other constraints that usually limit the growth rate. For instance, for the RGS technique it is necessary to mainly solidify the melt inside the die, therefore the sheet velocity is to some extent determined by the geometry of the die and the solidification rate, which depends on the temperature difference between melt and substrate temperature. Typical sheet velocities for a ribbon thickness of about 300 pm are between 0.5 and 3 m min-', which is about a factor 100400 times faster than the EFG technique. From the perspective of a high output of wafer area with time, only the RGS technique shows a substantial improvement compared to all other methods.

12.3.3.2 Microstructure and Electronic Properties The sheet growth methods also result in rather different microstructures and solar cell properties. The most thoroughly investigated materials are currently EFG and RGS ribbons and some of the characteristic features shall be discussed next.

Edge-Defined Film Fed Growth (EFG) Ribbons EFG, D-WEB, string ribbon growth, or related techniques in general produce high

739

quality material. The ribbons are characterized by a very low density of grain boundaries, most of them being coherent twin boundaries. For instance, in EFG ribbons the twins are arranged in thin lamellae which run parallel to the growth direction. The other main crystallographic defects in this material are stacking faults, S i c precipitates, and dislocations with average densities of about lo4 cm2 and local densities up to lo6 cmP2.All of these defects are electrically active to some extent, which is partly due to contamination with impurities. LBIC topograms of EFG solar cells show that highly dislocated grains are mainly responsible for the efficiency losses (Fig. 12-18). A reduction of the recombination activity by hydrogen passivation is possible and is in fact required to yield acceptable efficiency levels. Because of the generally high quality of the ribbons grown by these methods, the solar cell efficiency ranges between about 14 and 17%.

Ribbon Growth on Substrate (RGS)Ribbons The interaction between melt and substrate determines the microstructure of the RGS ribbons. At high temperatures the melt must wet the entire substrate so that a complete ribbon without holes can be obtained. On the other hand the ribbon must not stick to the substrate so that they can be separated at lower temperatures. A balance can be achieved by controlling the size of the contact area between the melt and the substrate. The contact areas are also the nucleation sites for the solidifying melt, and mostly a rather high density of nucleating grains results. Since the solidification is completed rapidly, selective growth and the development of larger grains is rather limited. A typical feature of the technique is therefore a small grain size between 100 and 1000 pm. The microstructure depends to some extent

740

12

New Materials: Semiconductors for Solar Cells Figure 12-18. High resolution LBIC topogram of an EFG solar cell. (The measured short circuit current is color-coded and increases from blue to red.) The enhanced recombination in some grains (low current) is due to a high dislocation density, which is shown on the left side. Selective etching of the surface at the same position reveals the dislocations by etch pits. (The contact finger is indicated by a pink color.)

on the temperature profile between the substrate and the ribbon, but can only be varied within certain limits. The RGS process is also characterized by high thermal stresses, because of the necessary sticking of the ribbon to the substrate at higher temperatures. Therefore the ribbons also contain higher dislocation densities ranging between lo5 and lo7 cmp2, with a local density of up to lo* cmp2. Optimization of the temperature profile and post-annealing treatments may reduce the dislocation densities to lower levels in the future. The LBIC topogram in Fig. 12-19 depicts the recombination properties of the defects in an RGS solar cell. A high recombination activity is observed in dislocated areas and for many grain boundaries. Calibrated LBIC and EBIC measurements show, however, that the bulk lifetimes are comparable to those for mc-silicon. Solar cells made from

this material therefore have quite good short circuit currents, whereas the open circuit voltages are low. Local current voltage measurements show that leakage currents at the p-n junction are responsible for the lower voltage in comparison with mc-silicon. The main features of the electrical behavior can be related to the high concentrations of carbon and oxygen (= 10” cmp3) in this material. During cooling of the ribbons or the following high temperature cell psocesses, oxygen and carbon precipitate rapidly at dislocations and grain boundaries (Fig. 12-20). The high density of precipitates along the extended defects is believed to cause the formation of a high density of trapping states due to the formation of new donors and the gettering of metal impurities. If such a heavily decorated defect penetrates the p-n junction, leakage currents may occur along the defect. Currently, it is assumed that these defects are responsible for the low


74 1

this case. Nonetheless, the material needs hydrogen passivation to yield acceptable efficiency levels. Efficiencies of almost 12% have been obtained so far.

12.3.4 Properties of Efficiency Limiting Defects

Figure 12-19. High resolution LBIC topogram of a RGS solar cell. (The measured short circuit current is color-coded and increases from blue to red.) The enhanced recombination (low current) is due to some heavily decorated grain boundaries, which are marked by yellow lines in the optical micrograph of the corresponding etched surface (see Fig. 12-20).

Figure 12-20. TEM image of a heavily decorated grain boundary in RGS silicon. The precipitates consist of amorphous S O 2 particles.

open circuit voltage of RGS ribbons. The recombination activity of some of the defects can be reduced by hydrogen passivation, but since the efficiency losses are partly due to these shunts passivation is less effective in

The recombination of electrons and holes at lattice defects is a major source of efficiency losses in a semiconductor solar cell. The main impurities that have been identified to enhance the recombination in the bulk and of extended lattice defects are oxygen, carbon, and some transition metals. The impurities are either introduced during preparation of the starting material or later during the various steps of the solar cell processing. The general structural and physical properties of these defects as far as they are important for solar cell materials will be discussed in the following sections.

12.3.4.1 Oxygen and Carbon Related Defects Monocrystalline Silicon Some of the basic properties, such as solubility and diffusivity, are summarized in Chap. 5 of this Volume or in many review articles (Moller, 1993; Mikkelsen, 1986; Newman, 1988;Weinberg, 1990; Kimerling, 1986; Bourret, 1987; Leroueille, 198l), and shall not be repeated here. Oxygen is interstitially dissolved in silicon and occupies a position between two silicon atoms in a slightly off-center position. No electrical activity has been observed for an oxygen atom in the interstitial position itself, but oxygen can give rise to a number of electrically active defects in supersaturated crystals upon annealing. Depending on the annealing temperature and times, different stages of oxygen precipitation have been observed

742


for oxygen rich Cz-silicon. An important aspect of oxygen precipitation is that the formation is associated with a volume change. As soon as the volume increase of the growing precipitate can no longer be elastically adapted, the surrounding matrix is either plastically deformed or self-interstitials are emitted (about one silicon atom for two oxygen atoms). Alternatively, the absorption of vacancies is also feasible. The self-interstitial emission or vacancy absorption can lead to the formation of a variety of interstitialtype stacking faults and dislocation loops. Considering only shorter annealing times which are typical for solar silicon processes (less than 100 h) mainly three different stages of defect formation in Cz-silicon can be distinguished.

Primary OxygenAgglomeration Between 400 "C and 550 "C The first stage occurs at temperatures around 450 "C. The diffusivity is so low that only the agglomeration of a few oxygen atoms can occur. The defect, which forms after annealing times of several hours, introduces two shallow donor levels in the band gap which are considered as two different charge states (O/+ and +/++) of the same defect. Several trap levels between E, 70 meV and E, - 150 meV are observed successively, which suggests that the so called thermal donor in fact consists of a family of similar defects (named TD1-16). After annealing above 550 "C, the thermal donors disappear. At 450 "C, the concentrations increase up to values of about 3 x 10l6 cm-3 with annealing time. Since the oxygen concentration in the bulk decreases at the same time, it has been assumed that the thermal donors are different stages of small oxygen agglomerates, which develop into each other by the addition of more oxygen atoms. To explain the kinetics of the process quantita-

tively, it has to be assumed that the oxygen diffusion at low temperatures is about 2-3 orders faster than the extrapolation for the normal oxygen diffusion at high temperatures (Ourmazd et al., 1984). A possible explanation is that diffusion occurs via a faster diffusing species, for instance, an oxygen dimer, which can only form at lower temperatures because of a low binding energy.

Oxygen Precipitation Between 550" and 700 "C In this temperature range, an appreciable loss of oxygen occurs already after 1020 h due to precipitation. Several defect morphologies can be observed: (1) Ribbon-like defects aligned along (1 10) directions with a cross section of a few nanometers, which lie on { 113) planes or, if they grow thicker, on { 100) planes. High resolution TEM revealed a crystalline structure, which was at first identified as a high pressure SiO, phase (coesite). Later measurements indicated a rather low oxygen concentration and the features were re-interpreted as hexagonal silicon (Bourret, 1987). The exact nature of these very small crystalline precipitates thus remains controversial. (2) Plate-like amorphous oxygen precipitates on { 100) planes with diameters up to 50 nm. The precipitates are often accompanied by prismatic dislocation loops. (3) Stacking fault loop defects on { 111 ) planes with a diameter up to 100 nm. They are probably formed by the agglomeration of silicon self-interstitials.

Oxygen Precipitation Above 700 "C In this temperature range, the ribbon defects are no longer stable. Below 900 O C , only the amorphous plate-like precipitates oc-


cur with edges along the (1 10) d'irections. As before, the emitted self-interstitials condense into loop defects on ( 1 11 ] planes. They are very often attached to the precipitates. Above 900 "C, the precipitates get more compact and take the shape of a regular or truncated octahedron. The growth of these amorphous precipitates is often accompanied by the punching-out of prismatic dislocation loops to relieve the strain. At temperatures above I I00 "C, the precipitates become polyhedral or nearly spherical and very large stacking faults with extensions up to 200 pm occur. Precipitate densities vary between lo3 and 10" cm-3 in Cz-silicon. The main features of the precipitation of spherical precipitates can be explained on the basis of conventional nucleation growth theories, and are noncontroversial (Ham, 1958). It has been found that precipitates formed between 600" and 950 "C are electrically active and associated with donor states (Leroueille, 1981). They are commonly termed "new donors" in order to distinguish them from the thermal donors formed at low temperatures. It is assumed that these donor states are related to the Si02/Si interface states and probably result from incomplete oxidation (excess silicon) in the Si02 precipitate near the interface. These donor states are destroyed by a high temperature heat treatment when the complete composition at the interface is restored (Holzlein et a]., 1986). Carbon Precipitation and Interaction with Oxygen

The main aspects of the oxygen behavior described so far are valid for Cz-crystals with low carbon concentrations. Experimental results frequently show that carbon can have a significant influence on the precipitation behavior at all stages. Since car-

743

bon is frequently present in comparable concentrations, especially in solar cell silicon, these interaction processes are very important. In contrast to oxygen, a carbon atom occupies a substitutional position. Because it is a smaller atom compared to silicon, it leads to a lattice contraction of about one atomic volume for each carbon atom. This is in contrast to the lattice expansion of oxygen; therefore it can be expected that an attractive interaction between oxygen and carbon atoms can occur, which may help to reduce the strain. If both carbon and oxygen are present in high concentrations, the carbon solubility is enhanced. In fact, dissolved carbon concentrations of up to 2 x 1O'* cm-3 have been measured, exceeding the maximum solubility by an order of magnitude (Bean and Newman, 1971; Newman and Wakefield, 1961; Kalejs et al., 1984; Benton et al., 1988; Foll et al., 1981). In carbon rich (>5 x 10l6 ~ m - Cz-crys~ ) tals, silicon carbide precipitates are rarely observed (Kolbesen and Muhlbauer, 1982). This is partly due to fact that carbon has a diffusion coefficient that is about an order of magnitude lower compared to oxygen, so that for typical cooling conditions diffusion becomes too slow for precipitation of the S i c particles. Another reason may be the lack of suitable nuclei for heterogeneous nucleation. The situation is different in polycrystalline ingots and ribbon materials. S i c precipitation can be observed particularly for carbon concentrations near or above the maximum solubility limit. Carbon on a substitutional site is an isoelectronic element to silicon and electrically inactive. The electrical properties of SIC precipitates, if they occur, are likely to be determined by their semiconducting bulk properties. It can be expected that the electrical conductance is strongly affected by the contamination of impurities (doping)

744


from the surrounding silicon matrix. Contaminated Sic precipitates in the micrometer range will be rather conductive and thus detrimental for the performance of a p-n junction if they lie in the depletion region, for instance. The main effect of carbon is, however, its impact on oxygen precipitation if the carbon concentration is above about 3 x 10l6 ~ m - Due ~ . to the interaction of carbon and oxygen atoms, the formation of oxygen nuclei is made easier. The result is a higher oxygen precipitate density and an enhanced precipitation rate. Multiclystalline Silicon In mc- or ribbon silicon, the carbon concentration is usually so high that the precipitation behavior of oxygen can be expected to be different from that for Cz-silicon. In order to compare the precipitation behavior in multicrystalline silicon with that in monocrystalline material, systematic investigations of the oxygen precipitation in preannealed mc-silicon with low carbon concentration have been carried out (Moller et al., 1995, 1999). The main result is that preannealed Cz-silicon shows essentially the same precipitation behavior. For oxygen concentrations above about 3 x l O I 7 cmP3, the concentration decreases between 750 and 1050 "C due to Si02 precipitation (Fig. 12-21). Below 2x lo" ~ m - precipitation ~, no longer occurs. This indicates that the presence of dislocations and grain boundaries in mc-silicon has no influence on the amount of precipitated oxygen. The distribution of precipitates and their morphology, as described in Sec. 12.3.1.2 are, however, different. Differences also occur for mc-silicon with higher carbon concentrations and no pre-annealing (at 1260 "C for 1 h). The precipitation rate is enhanced then, which suggests that the presence of carbon

0

1 h 2 h 4 h A 8 h A 16h 0 24h @ 24 h,Cz-

0

200

400

600 800 Temperature [OC]

loo0

1; x)

Figure 12-21. Interstitially dissolved oxygen in mcsilicon as a function of the annealing temperature and for different annealing times. The results are compared with those for Cz-silicon. All specimens have been pre-annealed at 1260°C for 1 h to dissolve all previously formed oxygen nuclei.

and a previous low temperature annealing treatment, for instance, during crystallization, increase the number of nucleation sites for precipitation. The final amount of precipitated oxygen after a sufficiently long annealing time is less affected; however, the density and size of precipitates are different in these cases. Compared to Cz-silicon, higher precipitate densities up to 10l2cm-3 can be observed in mc-silicon. Numerical Simulation of the Oxygen Precipitation The experimental results demonstrate that the distribution of SiO, precipitates depends considerably on the previous processing conditions. Smaller oxygen clusters that have formed earlier act as nucleation centers for the following processing steps. It is therefore necessary to understand the modifications of oxygen that occur for a given


sequence of thermal annealing steps. A theoretical model that is suitable to describe multi-step annealing processes has to take into account nucleation, growth, and particularly the dissolution of precipitates. In recent years, it has been shown that a theoretical description based on chemical rate equations can be used to simulate the oxygen precipitation in Cz-silicon numerically (Schrems et al., 1989; Schrems, 1994; Lifshitz and Slozov, 1959; Hatzell et al., 1985). The fundamental quantity in the model is a size-distribution functionf(n, t), which depends on the number n of oxygen atoms in the precipitate and the time t. The growth or shrinkage of a precipitate occurs by the absorption or emission of a single oxygen atom, which is described by a rate equation. For each particle of size n, one equation is required. Since this problem is numerically not tractable for precipitates up to a size of about 100 nm, the equations for larger n have to be approximated by a Foker-Planck type equation with a continuous variable n [for a complete description of the model, see Schrems (1994) and Lifshitz and Slozov (1959)l. The model has been shown to yield very good agreement for oxygen precipitation in Cz-silicon, and recently it has also been applied successfully to the precipitation behavior in mc-silicon (Moller et al., 1999). The development of the precipitation process as described by this model will be discussed for two situations. In the first case, oxygen precipitation is simulated for a single annealing step. The calculated size distribution at different annealing temperatures for 1 h annealing is shown in Fig. 12-22. An important feature is that at first a continuous distribution of cluster sizes occurs. With increasing temperature, a peak develops in the size distribution for a cluster size of about 1O6 atoms. These large clusters grow with increasing annealing time, while small-

/

745

8cQ=

/- 9oo= 103 7M) 102

100

101

J1-=

oc 102 103

104

IW

106

107 108 109

Number of oxygen atoms

Figure 12-22. The size distributionf(n) as a function of the particle size n for different annealing temperatures and 1 h annealing time. The initial concentration of interstitial oxygen for the simulation is 1 x 10'' ( 3 ~ ~ .

er clusters below about lo4 atoms shrink. This can be interpreted as the formation of a precipitate in the usual sense, because the distribution of the large clusters separates from the small-cluster distribution. For constant annealing time and temperature, the number of precipitates per unit volume decreases with the initial oxygen concentration, while the size remains more or less the same. Below an oxygen concentration of ~, no precipitates about 4 x 10" ~ m - almost can be observed anymore, which is in agreement with the experiments. The results further show that even after a short annealing time a certain number of larger clusters is formed. If a second annealing step follows, re-distribution of the cluster sizes must occur and the question arises how the initial distribution affects the final size distribution. Numerical results for two step annealing processes, in which the annealing conditions of the first step are varied, show that much higher densities or cluster sizes can occur

746


compared to in a single annealing step. The results can be interpreted in the following way: For a given annealing temperature, a critical cluster size exists above which clusters grow and smaller ones shrink. If the previous annealing treatment has produced more clusters above the critical value, the final distribution will have a higher density of larger clusters. The size distribution above the critical value determines the development of the larger clusters in the following annealing step. This result also explains why the annealing conditions during crystal growth are important. They determine the cluster size distribution of asgrown crystals which are used for the following wafer processing. The simulation is accurate enough now to yield guidelines for optimization of the crystallization and device processes, which is important in view of the detrimental effect of oxygen precipitates. In multicrystalline and ribbon silicon, it has to be considered, however, that other factors that can enhance the nuclei formation also have to be taken into account, for instance, if the carbon concentration is high.

12.3.4.2 Gettering of Transition Metals The gettering of transition metals is described in detail in Chap. 10 of this Volume. In standard solar cell fabrication, several processing steps are accompanied by gettering: the formation of the p-n junction by the diffusion of phosphorus, the formation of the back-surface field by the diffusion of aluminum, and internal gettering by oxygen precipitates. The first two processes are in many cases important and necessary steps to remove transition metals from the bulk to the surface regions and to improve the device performance. Internal gettering does not remove impurities from the bulk region. In general, it is supposed that internal get-

tering is unfavorable; however, there are not enough experimental data available to confirm or reject the hypothesis. Gettering procedures, which are very effective in Fz- and Cz-silicon, are found to work less effectively on polycrystalline silicon. An example is shown in Fig. 12-23 for the EFG material, but similar results have been observed for other low cost, solar cell materials (Weber et al., 1996). The reason is that the transition metals are mainly trapped at extended defects, such as dislocations, grain boundaries, or precipitates, and cannot be removed easily by gettering. One of the factors hindering effective gettering is the difficulty to dissolve the precipitates within a reasonable amount of time at normal gettering temperatures. A further disadvantage is that the recombination activity of dislocations and grain boundaries is enhanced by contamination with transition metals, such a copper, iron, or nickel (Stemmer et al., 1993; Ihlal and Nouet, 1994). This is due to additional energy states in the band gap, which are introduced by the impurities. Theoretical calcu-

250 I

0 As gown materis

After Fe diffusion After geaering

Figure 12-23. Dependence of the minority camer diffusion length in as-grown samples, after iron diffusion, and after phosphorus diffusion gettering for three types of material: float-zone, Cz-grown and EFG-silicon for solar cells (from left to right).


lations and experimental results indeed show that clean and reconstructed grain boundaries or dislocations do not have energy states in the band gap (Poullain et al., 1987). The impurities are either dissolved at the extended defects, occupying energetically favorable sites, or form metal silicide precipitates, but in most cases the relationship between the atomic structure of the defects and the electronic states is unclear. There are indications, however, that the recombination activity of metal silicide precipitates is either comparable or significantly higher than that of interstitial metals. For instance, in EFG silicon it has been found that the decrease in the diffusion length due to the contamination of extended defects was found to be at least 4-5 times higher than it would be if just due to the presence of metals in the dissolved, interstitial state (Pizzini et al., 1986). Although it is of crucial importance to understand the conditions for the precipitation of metal impurities, the morphology of the defects, and the corresponding electrical activity, still many details are unknown for solar silicon. Some details of the trapping process have been studied in the case of iron (Weber et al., 1996; Bailey et al., 1996), which is the most dangerous impurity in p-doped bulk silicon due to the strong recombination activity of interstitial iron and the FeB pairs. It was found that the precipitation rate of interstitial iron (measured by ESR) turned out to be inversely proportional to the square of the diffusion length. In other words, in a material with low initial diffusion length, iron precipitated faster, indicating that materials with a low lifetime also contained more nucleation sites. If the density of nucleation sites is only higher in certain parts of the wafers, for instance, in dislocation tangles as described in Sec. 12.3.2.2, these areas remain particular detrimental, since they show a lower life-

747

time and can hardly be improved by gettering. Currently, it must be admitted that certain limitations exist to improve a low-cost material where the density of extended defects is higher.

12.3.4.3 Hydrogen Passivation Hydrogen passivation is also an important step in device processing. As explained in the previous section, in a low cost material certain trapping centers cannot be removed by the standard gettering techniques and passivation may be the only possible way to improve the efficiency. A problem with hydrogen passivation is the observation that improvement of the performance varies considerably with the material. For instance, mc-silicon which already has a rather high efficiency (around 14%) shows only a marginal increase (0.1-OS%, depending on the material), which in many cases does not justify the increased processing costs. On the other hand, EFG cells can only reach acceptable efficiency levels after passivation. Several passivation techniques are mainly used in standard device technology: ion implantation with a Kaufmann source, microwave induced remote plasma deposition of H, gas (Sivothaman et al., 1993; Spiegel et al., 1995; Vinckier and De Jaegere, 1989), or plasma-enhanced deposition of silicon nitride films (PECVD - SiN,) using silane and ammonia gas. SiN, layers are especially attractive, because they also passivate surface states very efficiently. In most cases, it is quite unclear how passivation occurs, which is due to the complexity of the hydrogen behavior in silicon. While the hydrogen passivation of shallow level impurities is quite well understood, much less is known about the passivation of deep level impurities defects. Some details about the passivation of the most troublesome transi-

748


tion metals are discussed in Chap. 4 of this Volume. The mechanism by which hydrogen passivates deep levels is also fairly clear in cases where the origins are dangling bonds, for instance, at grain boundaries, interfaces, or dislocations. Binding of the hydrogen atom to the dangling bond forms bonding and anti-bonding states which are pushed into the valence and conduction bands, respectively. The incorporation of hydrogen into silicon is a necessary prerequisite for passivation, but very complicated. The complex diffusion mechanism is responsible for this behavior, and involves the existence of three different charge states for atomic hydrogen, Hf, Ho, H-, trapping at defects, and the formation of the rather immobile H2 molecule. Furthermore, in a polycrystalline material the penetration is probably enhanced because of the accelerated diffusion along grain boundaries, so that the distribution of hydrogen in the bulk is difficult to predict. It is quite possible that in some cases only near surface recombination centers are passivated and most of the defects in a 300-400 pm thick solar cell are not affected. The behavior of hydrogen in semiconductors has been the object of intense experimental and theoretical investigations over the last decade (Corbett et al., 1986; Van Wieringen and Warmholtz, 1956; Ichimiya and Furuichi, 1968; Pearton, 1985; Mogro-Camper0 et al., 1985; Johnson and Herring, 1992; Zundel and Weber, 1992; Seager et al., 1990). The picture of the state of hydrogen in the silicon lattice which has evolved during recent years can only be briefly summarized here. The three forms of hydrogen are in equilibrium among themselves, and the bound and molecular forms dominate at low temperatures, which explains why hydrogen is rather immobile then. At higher temperatures, the bound

configurations break up and the atomic form dominates, and therefore the effective diffusivity becomes high. The understanding and interpretation of the diffusion behavior of hydrogen in semiconductors is complicated by the fact that trapping at impurities and lattice defects, and molecule formation, can occur. The earliest high temperature measurements in silicon determined the diffusion coefficient (Van Wieringen and Warmholtz, 1956) as

& = 9.4 x

exp

(- T)

0.48 eV (cm2 s-I)

(12-4) which is thought to describe the migration of atomic hydrogen H+. Theoretical studies of the diffusion are also in reasonable agreement with these values. The situation for Ho and H- is less clear. There are results that indicate a slightly slower diffusion for H(Johnson and Herring, 1992). Extrapolation to low temperatures (500 pm), and the epitaxial deposition of the absorber layer. In particular, dislocations and impurities can be introduced during the high temperature steps from the interaction with the substrate or the S i c layer.

12.4.3.2 Amorphous Solar Cells In hydrogenated amorphous silicon, the concentration of charge carriers, their mobility, and lifetime depend in a complex way on the doping level and the temperature, as described in Chap. 9 of this Volume. While the shallow tail states essentially limit the mobility of charge carriers, the mid-gap states dominate the recombination. This requires a special design for a solar cell, which differs from the conventional p-n diode structure. Since both the mobility and lifetime of minority carriers in a doped film decrease significantly with the doping level, the collection efficiency in doped regions will be very poor. Sufficient mobility and lifetime values are only obtained in intrinsic material. Therefore amorphous silicon solar cells require a p-i-n structure where the intrinsic layer is the main absorber region (thickness about 0.4-0.8 pm) and then- and p-regions are kept very thin, usually below 10 nm. In undoped a-Si:H, the mobility is about 0.1 cm2 V-' s-l and the lifetimes vary between 3 and 30 ps. The main problem for amorphous silicon is the creation of electrically active defects under illumination. After an hour of illumination, dangling bond states with mid-gap levels are created due to a bonding rearrangement. Their density increases first and then saturates. Although the defects are met-

755

astable and can be removed by annealing above 15OoC, this is very undesirable for photovoltaic applications. The degradation phenomenon, known as the Staebler-Wronski effect, is an intrinsic problem of the amorphous structure and has important consequences for the operation and design of solar cells (Wronski, 1984). In general, most of the degradation of an a-Si:H solar cell occurs within the first one hundred hours and is accompanied by a drop in the efficiency by 10-30%. This effect seriously limits the performance of a solar cell to efficiencies below 10%. Since the dangling bond states introduce mid-gap levels, they are particularly effective recombination centers in the intrinsic layer of a p-i-n solar cell. Evidently, a reduction of the thickness of the layer increases the stability, but also reduces the efficiency, because more light is absorbed in the doped regions. The general approach to the problem is to fabricate tandem cells where two or more solar cells with different thicknesses or even band gaps are stacked one upon the other. The band gap can be narrowed or widened by alloying with germanium or carbon, respectively. In this case, the intrinsic layers in each cell can be kept smaller without sacrificing efficiency. With double layer junctions, solar cells with an efficiency above 10% have been obtained on small areas (Privato et al., 1997). In commercial a-Si :H solar cells, however, large areas have to be covered with a film of uniform thickness and quality. This is difficult to achieve, and one of the most important electrical losses in amorphous modules is a low shunt resistance due to the occurrence of pinholes in the thin layer. Considering the technical feasibility of large-scale production, this is another important problem for any thin film technology.

756


12.5 Polycrystalline Thin Film Compound Semiconductors Crystalline and amorphous silicon is still the leading material for photovoltaic applications. Up to now, only two additional semiconductors have shown definite potential for replacing silicon in the future, i.e., CdTe and Cu(In,Ga)Se,. Other materials including GaAs, InP, CdSe, ZnP, Cu,S, Cu,O, and selenium have been investigated, but are no longer considered for mass production due to high costs or other reasons.

12.5.1 Cadmium-Telluride Considering the basic photovoltaic properties of 11-VI compounds, CdTe is the optimum material for use in thin film solar cells. It is a direct semiconductor with a band gap of 1.45 eV and thus very well suited to the solar spectrum (see Fig. 12-3 and Table 12-1). 90% of the light can be absorbed in a layer of a few micrometers. CdTe is a semiconductor with a strong ionicity in the bonding, which explains the high chemical and thermal stability. It crystallizes in Table 12-1. Structural and electronic properties of some monocrystalline 11-VI compounds. The conductivity type is given for as-grown, unintentionally doped crystals. Compound

Lattice constant a, c

(4a

Band gap energy (eV)

Conductivity type

ZnS CdS ZnSe CdSe HgSe ZnTe CdTe HgTe

5.47 5.88 5.67 4.30,7.02 6.08 6.01 6.48 6.46

3.7 2.3 2.7 1.8 -0.15 2.26 1.45 -0.14

n n, P n n P P n, P

a

1 A = 1.000 x lo-'' m.

the cubic zincblende structure, but the energetic difference to form a hexagonal structure appears to be small since the hexagonal phase can easily occur during thin film deposition. Above 400 "C, the stoichiometric compound is the stable solid phase. The vapor pressures of cadmium and in equilibrium with CdTe differ only slightly, so that tellurium stable vapor pressure conditions can be generated and crystals with a homogeneous stoichiometry can be obtained rather easily. As-grown films show only a slight cadmium deficiency, which leads to native p-doping of a thin film. This property is due to a shallow acceptor level at 0.05 eV above the valence band edge and has been related to the cadmium vacancy. Intrinsically pdoped films are well suited for further solar cell processes, since additional doping is not necessary. The congruent deposition of cadmium and tellurium on a substrate leads to selfstabilizing stoichiometric condensation as long as the temperature is kept above 400 "C. In many cases, deposition occurs at lower temperatures with larger deviations from the stoichiometric ratio, but annealing the films above this temperature can easily restore the stoichiometric ratio. This allows numerous deposition techniques to be applied. Oxygen, which is often unintentionally introduced, is not a critical impurity, and may even enhancep-doping (Bonnet, 1997). External doping is possible, for instance, with indium for n-type and silver for p-type CdTe. It is difficult, however, to manufacture p-n junctions in a thin-film form because the doping elements are rather mobile, particularly along grain boundaries, and can easily degrade the junction properties. Furthermore, surface recombination plays an important role in thin films and would severely reduce the photocurrent without appropriate surface passivation. Heterojunction structures are therefore the most ade-

12.5 Polycrystalline Thin Film Compound Semiconductors

quate device configurations. Nowadays, most of the research is focused on the CdS/ CdTe heterojunction. Since CdS has the same strong tendency to form stable compounds, but is natively n-type by a slight nonstoichiometry, it is ideally suited for a heterojunction device (Fig. 12-5 a).

12.5.1.1 Processing Techniques and Related Material Problems CdS has a rather large band gap of 2.3 eV but absorbs some light in the visible spectrum (1.6-3.2 eV). Most of the light passes through and is absorbed in the CdTe layer. If the CdS layer thickness is reduced, more light is absorbed in the CdTe layer, which is favorable. Since the open circuit voltage and the fill factor start to decrease, however, because of shunts or pinholes (small holes penetrating the layer), there appears to be an optimum thickness of about 50-80 nm. The CdS layer should be highly doped and as thin as feasible for a pinhole free continuous film. The highest quality films are obtained with closed spaced sublimation (CSS), a modified evaporation process where substrates and sources are very close together with a relatively small temperature difference, so that the films grow under close to equilibrium conditions. Sublimation processes are very fast (> 10 pm m i d ) , and the material yield is high since substrate and source are close together. Another depositionprocess which is used for production is chemical spraying. On a small commercial scale for consumer applications, CdTe films are at present deposited by screen-printing. There are some doubts on the feasibility of this process for large-scale production. The alternatives are to deposit the CdTe layer by the same techniques as the CdS layer. In addition, electrodeposition is a viable option. Although slow, it can be applied to a large

757

number of substrates in parallel. The deposition occurs either at temperatures above 500 "C or the films are annealed later. Contacting the p-type CdTe layer on the back side is a difficult task. Basically, there are two general principles for making ohmic contacts to p-type semiconductors: 1) Deposition of a metal that has a work function higher than the electron affinity of the semiconductor in order to align the upper valence band edge to the Fermi level of the metal. 2) Formation of a highly doped surface layer thin enough for holes to tunnel through to a metal contact. In both cases there are problems for CdTe. Low cost metals with appropriate work functions > 5 eV are not available. P-doping by diffusion from the surface has the drawback that dopants generally diffuse preferentially along grain boundaries, leading to shunting before a sufficient doping level can be achieved. Using thicker than necessary films can alleviate the latter problem, but in practice another approach is pursued. The CdTe film is combined with another semiconductor, which is easier to dope and then contacted with an appropriate metal. The highest efficiency cells have been obtained with copper-doped graphite. Another possibility is copper-doped ZnTe. In both cases, the danger exists that upon annealing copper can rapidly diffuse into the CdTe film and reduce the performance. Two other p-type semiconductors have been considered, namely HgTe and tellurium, but in all cases the modifications of the surface remain a delicate process, which depends on the material and its microstructure.

12.5.1.2 Electronic Properties The performance of the solar cell depends very much on the quality of the interface re-

758


gion between CdS and CdTe. The CdS has a significant lattice mismatch to CdTe, which causes a high density of interface defects and states. The problem is however less severe, since it has been observed that a mixed CdS,Te,-, phase is formed at the interface. The performance of the solar cell, in particular the open circuit voltage, depends on the formation of an appropriate interface phase: best intermediate layers achieve 850 meV, whereas for “insufficient” mixing the voltage stays below 800 meV. It is assumed that formation of the intermediate phase is responsible for the reduction of structural defects at the interface and thereby of recombination centers (Jensen et al., 1996; Al-Ani et al., 1993). The mixing is promoted by three factors: (1) a smaller grain size of the CdS film, (2) a higher deposition temperature of the substrate, and (3) in-diffusion of C1 ions. The formation of smaller grains in the CdS film requires a low temperature deposition process, such as chemical bath deposition at 70 “C, whereas closed spaced sublimation at 400-500 “C is less favorable. In practice, only relatively thin CdS,Tel, layers can be formed, which limits the performance. In the thin film technology, particularly of compound semiconductors, maximum performance can often only be achieved by special treatments after deposition. These procedures can be heat treatments, annealing in a certain gas atmosphere, or the indiffusion of certain elements, such as hydrogen. Although in many cases the physical processes are not completely understood, it can in general be assumed that both microstructural changes and/or the removal of electrically active defect states occur. For the CdTe/CdS device, it has become common practice to diffuse C1 ions into the film from a CdC1, source which has been deposited on the surface. In other cases, such as screen printing or electrodeposition, the C1

ions are supplied during the growth process of the CdTe layer. Detailed investigations show that mainly the density of CdTe/CdS interface states is reduced by the activation process. Unfortunately, at the same time new defect centers are formed in the space charge region, which limits the possible improvement (Bonnet, 1997; Rohatgi, 1992). On small cells using fabrication processes and materials close to production conditions, efficiencies of 14.3% have been obtained, and for laboratory cells 16%. Recent industrial production results for modules are somewhat lower at around 9-10%. The advantage of the technology is the reduced cost compared to that of silicon cells. There are, however, concerns about environmental and health problems with the widespread use and deployment of cadmium. Although incineration studies have shown that the emission of toxic cadmium during the exposure of modules to fire is negligible, doubts remain as to whether large scale cadmium technology is acceptable.

12.5.2 Chalcopyrite Semiconductors 12.5.2.1 General Properties of CuInSe, and Related Compounds Ternary chalcopyrite semiconductors with the composition A’ B’” XT’ have attracted interest because of their diverse optical, electrical, and structural properties (Gibart et al., 1980; Kuriyama and Nakamura, 1987). Details of the compounds that have been most thoroughly investigated so far are summarized in Table 12-2. Some have band-gap energies in the range 1-2 eV and are attractive candidates for photovoltaic applications. The research focused mainly on the compound CuInSe, and the related quaternary compound Cu(In,Ga)Se,, but CuGaSe, and CuInS, with even more suitable band-gap energies also open prospects for future thin film devices.


Table 12-2. Structural and electronic properties of some copper-based ternary compounds with chalcopyrite structure. Compound CuGaS, CuInS, CuGaSe, CuInSe, CuAITe, CuGaTe, CuInTe,

aa

5.35 5.52 5.596 5.782 5.964 5.994 6.197

c/aa.b Eg (ev)"

1.959 2.016 1.966 2.0097 1.975 1.987 2.00

Ty6(°C)d 975 810 672

2.43 1.43 1.68 1.04 2.06 1.23 1.04 ~~

a lattice constant; c long axis of the unit cell; E, band gap energy; TYbtransition temperature between ordered and disordered phase. a

The chalcopyrite lattice can be developed from the sphalerite structure by duplicating the unit cell and arranging the cations A and B on the cation sublattice (Fig. 12-29). The unit cell is characterized by a tetragonal dis-

Figure 12-29. Tetragonal unit cell of the chalcopyrite lattice for an ABX,compound. The unit cell is characterized by a tetragonal distortion along the c-axis. Because of the different bond strengths, the anion X usually adopts an equilibrium position that is closer to one pair of cations than to the other. In addition, the structure of a vacancy-antisite defect pair (2 VB+BA) is shown, which has been proposed for CuInSe,.

759

tortion along the c-axis (Jaffe and Zunger, 1984; Romeo, 1980). It appears to be a common feature of many copper-ternaries that a phase transition from the chalcopyrite to the cubic sphalerite structure occurs at elevated temperatures due to a random distribution of A and B atoms in the cation sublattice. It is also a characteristic feature of the chalcopyrites that the structure can be maintained over a rather wide range of compositions, in some cases several percent. It is assumed that this is achieved by the incorporation of intrinsic point defects such as vacancies, interstitial atoms, and antisite defects. Absorption measurements for single- and polycrystalline CuInSe, show an enormously high absorption for this material in comparison with other semiconductors, and confirm the behavior as a direct semiconductor (Kazmerski and Wagner, 1985; Shah and Wernick, 1975; Kazmerski, 1977). Specimens prepared by different techniques and subjected to various annealing treatments show, however, that the empirical band gaps vary between 0.92 and 1.04 eV. It has been suggested and experimentally verified that tail states and a band gap narrowing occur due to high concentrations of intrinsic shallow doping defects (Neumann, 1986), which can be related to the composition and microstructure. The high density of intrinsic point defects determines not only the optical absorption to some extent, but also the conductivity and other electrical properties. For instance, CuInSe, and CuInS, can be made n- or ptype by changing the stoichiometry. Typical values for the carrier concentrations in nand p-type single crystal CuInSe, are in the range I 0l6- 10'' cmP3.Measurements of the Hall mobilities show, however, that the concentrations of ionized defects can be as high as 1019 ~ m -which ~ , is considerably higher compared to the free-carrier concentration.

760


This indicates a high degree of compensation of acceptor and donor-like defects, and seems to be characteristic for copper-ternary semiconductors. Systematic investigations of the relationship between the conductivity and stoichiometry of single crystals are depicted in Fig. 12-30 for CuInSe, (Neumann and Tomlinson, 1990;Noufi eta]., 1984). It is now generally accepted that the results can be explained on the basis of a point defect model, which assumes that intrinsic point defects compensate for the deviation from ideal stoichiometry and introduce shallow acceptor and donor levels in the band gap. The intrinsic point defects, which have to be considered in general, are vacancies, interstitials, and antisite defects. In a compound with the general formula ABX,, twelve different native defects have to be considered,

Figure 12-30. Experimental results for the n- and ptype conductivity as a function of the stoichiometry for CuInSe, single crystals and comparison with a numerical calculation using the theoretical formation energies given in Fig. 12-31. The experimentally determined energy levels of the intrinsic defects, which have been used in the calculation, are summarized in Table 12-3. In polycrystalline thin films, the p-type region is enlarged (light area) due to influence of the grain boundaries on the band-gap states.

three vacancies: VA, V,, V,, three interstitials: Ai, B i , Xi, and six antisite defects: A,, BA, A,, B,, X,, X,. In addition, the formation of complexes is feasible because the concentrations can become very high. Chalcopyrite semiconductors are mainly covalently bonded compounds but with a high degree of ionicity. Identification of the dominant doping defects for each composition has therefore been based on the assumption that the ternary chalcopyrites can be analyzed in a similar way to ionic crystals. In the Kroger model, the defect chemistry of ionic crystals is determined by certain equilibria between intrinsic defects, which can be described by a mass law of action (Kroger, 1983; Groenink and Janse, 1978). In thermodynamical equilibrium, the defect concentrations are not independent of each other but related by these internal equilibria. The concentrations depend on the stoichiometry of the crystal. For a given composition and temperature, the concentrations of all defects are completely determined by these internal equilibria and can be calculated, provided that their formation enthalpies are known. For CuInSe, the formation energies AHf of some defects have been determined recently by a first-principle, self-consistent, electronic structure calculation (Zhang et al., 1997). An important new aspect is that the formation energies are not fixed constants but vary considerably with the Fermi level and the chemical potential of the atomic species (Fig. 12-31). This means that the formation energies also depend on the composition of the crystal. Since the formation energies of the anion-cation antisites and the selenium and indium interstitial appear to be too high, only six native defects have to be considered. The defect with the lowest energy is the copper vacancy, while some of the other defects, such as the indium vacancy and the antisites CuIn and Inc,, have


761

Figure 12-31. The formation energies of the main intrinsic defects in CuInSe, as a function of the atomic chemical potential of copper (kc,) and indium (pin). Neutral and charged defects are considered. Intermediate values of the chemical potentials are obtained by linear extrapolation between the values at ,ku=pIn=-2(Zhang et al., 1997).

-2.0 -1.5 Cu-poor

-1.0

pa

-0.5

0

-0.5

-1.0 ph

-2.0 In-poor

-1.5

Chemical potential [eV]

comparably low, even negative, energies in some composition regimes. Another important result is that the interaction of the copper vacancy and the indium-copper antisite can lead to a complex 2Vc, + Inc,, with a lower formation energy compared to the copper vacancy Vcu. The atomic structure of the defect is shown in Fig. 12-29. It is dominant for copper-poor crystals, and because of the donor character should be responsible for the n-type behavior in this regime. Based on these results and experimental information about the electronic levels in the band gap (Table 12-3), the concentrations of all defects, electrons, and holes have been calculated as a function of the composition (Klais et al., 1998). The results for the conductivity behavior are included in Fig. 12-30 and show rather good experimental

agreement for most of the compositions. A characteristic feature is that in a narrow range of compositions the carrier concentration drops by several orders of magnitude and the conductivity changes from n- to p-type behavior, or vice versa. The results also confirm that a high concentration of compensating acceptor and donor defects occurs. The electronic properties of a polycrystalline compound film, and possibly the defect chemistry as well, may differ considerably from the monocrystalline behavior, because of the additional grain boundary states, as discussed in Sec. 12.4.3. This general behavior is also observed for copperternaries, where the correlation between conductivity and composition for selenium deficient polycrystalline films differs significantly from the single crystal behavior

762


Table 12-3. Calculated energy levels ET of the main intrinsic defectsa and comparison with experimental results (in parentheses).

Vg))

vp;-

EV -k ET

30 (30-45)

170 (120-200)

- ET

100 (55-90)

250 (200-232)

Acceptors

EC

v:,-'3-

cu:;-

410 (400)

670

290 (220-320)

340 (350-370)

200 (120-232)

v-12In

cu-/2In

580 (570)

200

a Zhang et al. (1997); the theoretical values have been used for the calculation of the defect chemistry and conductivity shown in Fig. 12-30.

(Noufi et al., 1984). It is also verified that the grain size has a significant influence on the lifetime of charge carriers (Bacher et al., 1996). If the composition of the films is near the ideal stoichiometry, the material is always p-type, whereas a large deficiency of copper converts the conductivity into n-type behavior (Fig. 12-30). The band gap of CuInSe, below the optimal value of 1.5 eV for photovoltaic applications, limits the utilization of this material for single-junction devices. Since the band gap increases from CuInSe, (1.04 eV) to CuGaSe, (1.68 eV), the formation of a quaternary compound CuIn,Ga,,Se, offers the possibility to adjust the band-gap energy by changing the In/Ga ratio. The highest efficiencies of about 15-17% for laboratory cells are actually based on the compound CuIn,Gal-,Se2 (CIGS). The development of a CuInSe,-,S, cell is still hampered by the fact that with increasing sulfur content, the p-type conductivity decreases. It has been shown, however, that small additions of sulfur can increase the efficiency of CIGS cells, which demonstrates the beneficial effect of sulfur. The typical CIS device structure is based on the heterostructure concept with borondoped ZnO as a window material (wide band

gap) on top (Fig. 12-5b). In practice, a thin intermediate layer of CdS is required, although the role of the buffer is not well understood. In the future it would be desirable to replace the heavy metal in the buffer layer by an alternative compound. Some possible candidates are ZnSe, In& (Karg et al., 1997), and indium or tin hydroxy compounds (Hariskos et al., 1996), but these are less effective so far compared to CdS. The films are deposited on soda lime float glass, which yields the highest efficiencies. This is due to the release of sodium into the semiconductor film, which appears to have a beneficial effect on the device's performance.

12.5.2.2 Deposition Techniques For large scale production, two deposition techniques for the CIS absorber layer are mainly considered: (1) Selenization of metal precursor layers and subsequent annealing. For example, for the CIS fabrication, lnSe and copper precursors are deposited on the substrate. Selenization occurs by annealing in H,S or selenium vapor or from a selenium precursor layer. Relatively large


grains ( > 1 pm) develop under these conditions. In this process, the composition of the absorber is limited to indium-rich material. The incorporation of gallium is also difficult and limited to small amounts. (2) The best films are obtained by co-evaporation of all elements. The process gives full flexibility in device optimization, but is more difficult to incorporate in a large scale fabrication process. In general, CIS films grown under copper-rich conditions show better crystalline quality than those grown under indium-rich conditions. For high copper :indium ratios the compensation reduces significantly, but the hole concentration increases above cmP3. In practice, indium-rich p-type films are therefore grown, which have a more suitable resistance. Sodium can be incorporated either from the glass substrate or directly during the deposition process. The n-type CdS layer is deposited by a chemical bath process, and is subsequently dried. The transparent conductive ZnO window layer is mostly deposited by sputtering with a bi-layer structure made of an inner undoped layer and outer aluminum- or boron-doped layer. ZnO has a band gap around 3.3 eV and thus has high transmission in the visible range. The main purpose of the window layer is to reduce recombination at the front surface, which is important for a thin film device.

12.5.2.3 Electronic Properties The device’s properties are mainly determined by the electrical properties of the bulk absorber (CIS or CIGS), the buffer material (CdS, etc.), and the interface. Experimental results confirm that a good microscopic crystal quality is an essential basis for a good solar cell. Because of the complex defect chemistry of ternary chalcopyrites in

763

combination with the presence of a high density of grain boundaries in the polycrystalline films, the interpretation of experimental results is, however, a very difficult task. In addition, the role of sodium and oxygen has to be considered, mainly in the CdS layer. It is therefore not surprising that many of the observed phenomena are not fully understood, despite a wealth of information. Since in chalcopyrites large deviations from stoichiometry can occur, the density of intrinsic defects with shallow donor and acceptor character and the compensation may be high. Indeed, it has been observed that the analysis of electrical and optical results has to take into account a high density of donor and acceptor defects. Any inhomogeneous distribution in the crystal can lead to potential fluctuations, which influence the optical and electrical properties. For instance, experimental results on the optical transitions between impurity tail-states near the band edges have been explained by potential fluctuations (Karg et al., 1997). For the ZnO/CdS/CulnSe, system, a considerable increase in efficiency was achieved by the use of soda lime glass as a substrate material. During deposition of the CuInSe, absorber film, sodium diffuses from the substrate and disperses into the film. It could be shown that sodium affects not only the grain growth and conductivity properties of the film but also the CdS interface formation and properties. There is evidence that it gives rise to a shallow acceptor state that increases the effective carrier concentration of the absorber (Probst et al., 1996). Sodium also reacts with SeO,, which mainly occurs at the surface, and leads to an enrichment of selenium there. It has been verified that the lifetime of the charge carriers in the absorber is significantly influenced by the grain size. Therefore the grain boundary states are important for nonradiative recombination processes.

764


However, the origin of the defect states has not been clearly identified and the role of extrinsic defects, such as sodium, trapped at the grain boundaries cannot be ruled out yet. Whether the observed improvement of the efficiency after sodium diffusion is due to the impact on the grain size and structure or to the impurity levels themselves is unclear. An important electrical property of a heterostructure interface is the change in the energy gap and the alignment of the band edges (band-offset). Investigations of CdS layers deposited on cleaved CuInSe, in UHV have shown that there is an offset of the valence band edge by 0.8 eV and of the conduction band by 0.65 eV (Loher et al., 1995; Schmid et al., 1993). These are values that cannot be operative in a real cell solar, since for the achieved performance a band offset close to zero is expected. This indicates that under normal processing conditions the interface composition and structure must be changed. Although it could be shown that sodium contributes to the band alignment, this effect alone could not explain the beneficial effect of sodium on the efficiency. For technological applications, the longterm stability of the devices and modules is a crucial aspect. Considering the main thin film materials today, each one has its own stability problems. For amorphous silicon it is the light induced defect formation and corresponding degradation of the device, for cadmium telluride it is the ohmic contact to the CdTe, and for CIS or CIGS it is the sensitivity to humidity. Water vapor is known to reduce the power output of a CIS solar cell. Since sodium enriches in the bulk and at the surface when CIS layers are deposited on sodium lime glass, interactions between sodium and water can lead to chemical reactions. It has been suggested that these affect the electrical transport proper-

ties, but the detailed nature of these effects and the role of water vapor are not yet resolved.

12.6 Special Solar Cell Concepts 12.6.1 High Efficiency Solar Cell Materials GaAs and InP are direct semiconductors with an optimum band gap between 1.4 and 1.6 eV (see Fig. 12-3) and a high absorption coefficient. Only thin layers of about a few micrometers are required for a solar cell. Since these materials have also received considerable attention for high speed and opto-electronic applications, a number of deposition techniques are available, such as MOCVD or LPE. The epitaxial growth of layers with a low density of defects requires a monocrystalline substrate of the same material or at least a semiconductor with similar properties. The important parameters are the lattice constants and the band gap energy, which are summarized for some semiconductor compounds in Fig. 12-32. The systems that have to be considered here are InGaP and AlGaAs in combination with GaAs and germanium. However, even for a system with a good lattice match, the defect density of the epitaxial layer is to a large extent determined by the defect density of the substrate material. Experimental results show that, for instance, dislocations from the substrate grow into the epilayer or give rise to the nucleation of other defects. Therefore for high efficiencies it is necessary to start from a substrate crystal with a high material quality, which in most cases is a requirement that at present can only be fulfilled by a few semiconductors, such as GaAs or germanium. Silicon is less suitable because of the difference in lattice constant. The lattice match to GaAs can, however, be

12.6 Special Solar Cell Concepts

Figure 12-32. Energy band gap and lattice constant for some semiconductor elements and compounds. Solid lines connect binary compounds, which are used to form ternary compounds. For ternary compounds with a noncubic chalcopyrite structure, the smaller lattice constant is taken.

4.0 3.6 3.2 2.8 Y

w"

2.4

0

2.0

F 5 A

-0

B

m

GaP

0

0 CdS

AlAs

CdSe

0

765

ZnTe

AlSb

1.6

0

CdTe

1.2 0.8

CuInTe2

0Ge

0.4

5.4 5.5

PbTe

5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5

Latticeconstant a [A]

improved by inserting a strained SiGe buffer layer: Si/Si,Ge,-JGaAs. Epitaxial techniques are therefore in general rather expensive at present and only useful for high efficiency solar cells or if cost considerations are less important, for instance, for application in spacecraft. An advantage of the epitaxial thin film techniques is that they allow fabrication of complex device structures with cells of different band gaps stacked upon each other (tandem cells), which can utilize the spectrum of the light more efficiently. Efficiencies around 30% have been achieved for a number of monolithic tandem structures based on AIGaAs/Si (Umeno et al., 1994), AlGaAs/GaAs (Chung et al., 1989), and InGaP/GaAs (Andreev et a]., 1997).

12.6.2 Dye Sensitized TiOz A new kind of solar cell has been developed by Gratzel and co-workers (O'Regan and Gratzel, 1991; Nazeeruddin et al.,

1993). It is based on a dye-sensitized nanocrystalline, wide band gap semiconductor, usually titanium dioxide. The principal solar cell structure is explained in Fig. 12-33. The photoelectrode consists of a nanoporous film (thickness about 10 pm) of dyecovered TiO, particles, which is deposited on a transparent conducting oxide Sn0,:F on glass. The counter electrode also consists of glass with a conducting oxide on which a catalytic amount of platinum is present. In a complete ceII, photo- and counterelectrode are clamped together and the space between the electrodes and the porous TiOz nanoparticles is filled with an electrolyte consisting of an organic liquid containing a redox couple, usually iodide/triiodide (I-/I;). The working principle of the cell is as follows: The light is absorbed by a monolayer of a suitable ruthenium dye, which covers the TiO, surface. Since a dye monolayer on a flat surface absorbs less than 1% of the incoming light, the surface area has to be enlarged by a factor of 1000. This is achieved

766


Figure 12-33. Schematic diagram of a nanocrystalline TiO, dye-sensitized solar cell. Enlarged region shows the working principle and charge carrier transport when the cell is illuminated.

by using TiO, nanoparticles with a diameter of approximately 20 nm. The incoming photons excite electrons in the dye, which are immediately injected into the TiO, conduction band leaving an oxidized dye molecule. Electrons percolate through the TiO, and are fed into the external circuit. At the counterelectrode triiodide is reduced to iodide by platinum by the uptake of electrons from the external circuit. Iodide is transported through the electrolyte towards the photoelectrode where it reduces the oxidized dye, which is ready again for excitation. Since the basic principle here differs completely from that of semiconductor solar cells, new approaches are required to determine, for instance, the loss mechanisms and how to eliminate them. The most important parameters turned out to be: the mobility and relaxation rate constant of electrons in the TiO,, the electrolyte diffusion constant, the dye content of the cell, and the series resistance of the transparent conductive oxide layers. Efficiencies between 4and 8%have been reported, but further improvements can certainly be expected (McEvoy and Gratzel, 1994). An advantage of the cell is that it can easily be fabricated and incorporated into a glass structure, for instance, glass windows. Technical difficulties lie in the permanent encapsulation of the electrolyte between the two glass plates.

12.7 References Abe, T. (1997), in: Proc. 7th Workshop on the Role of Impurities and Defects in Silicon Device Processing: NREL Report CP-520-233386, p. 7. Al-Ani, S., Makadsi, M., Al-Shakarchi, I., Hogarth, C. (1 993), J. Mater. Sci. 28, 25 1. Andreev, V., Khvostikov, V., Rumyantsev, V., Paleeva, E., Shvarts, M. (1997), in: 14th European Photovoltaic Solar Energy Conference: Bedford, U.K.: Stephens & Associates, p. 1369. Aratani, F., Fukai, M., Sakaguchi, Y., Yuge, N., Baba, H., Suhara, S., Habu, Y. (1989), in: ZOth European Photovoltaic Solar Energy Conference: Bedford, U.K.: Stephens & Associates, p. 462. Bacher, G., Braun, W., Ohnesorge, B., Forchel, A,, Karg, F., Riedl, W. (1996), Cryst. Res. Technol. 31, 737. Bailey, J., McHugo, S., Hieslmair, H., Weber, E. (1996), J. Electron. Mater. 25, 1417. Ballhorn, G., Weber, K., Armand, S., Stocks, M., Blakers, A. (1997), in: 14th European Photovoltaic Solar Energy Conference: Bedford, U.K.: Stephens & Associates, p. 1011. Bauer, G. H., Bruggemann, R. (1997), in: 14th European Photovoltaic Solar Energy Conference: Bedford, U.K.: Stephens & Associates, p. 558. Bean, A. R., Newman, R. C. (1971), J. Phys. Chem. Solids32, 1211. Beaucarne, G., Poortmanns J., Caymax, M., Nijs, J., Mertens, R. (1997), in: 14th European Photovoltaic Solar Energy Conference: Bedford, U.K.: Stephens & Associates, p. 1007. Benton, J.,Asom, M., Sauer, R., Kimerling, L. (1988), MRS Symp. Proc. 104, 85. Binns, M., McQuaid, S., Newman R., Lightowlers, E. (1994), Mater. Sci. Forum 143, 861. Blakers, A. W. (1990), Adv. Solid State Phys. 30,403. Blakers, A. W., Wang, A., Milne, A. M., Zhao, J., Green, M. A. (1996), Appl. Phys. Lett. 55, 1363. Bonnet, D. (1997), in: 14th European Photovoltaic Solar Energy Conference: Bedford, U.K.: Stephens & Associates, p. 2688. Bourret, A. (1987), Microsc. Semicond. MateK, Inst. Phys. Con$ Ser. 87, 197.

12.7 References

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New Materials: Semiconductors for Solar Cells

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General Reading 14th EurOpeQn Photovoltaic Solar Energy Conference: Bedford, U.K.: Stephens & Associates (1997). 25th IEEE Photovoltaic Specialists Conference: New York: IEEE (1996). 1st Int. Con$ on Shaped Crystal Growth, J. Cryst. Growth (1987), 87.


13 New Materials: Gallium Nitride

.

Eicke R Weber and Joachim Kriiger Department of Materials Science and Engineering. University of California. Berkeley. CA. U.S.A. and Materials Science Division. Lawrence Berkeley National Laboratory. Berkeley. CA. U.S.A.

Christian Kisielowski National Center for Electron Microscopy. Lawrence Berkeley National Laboratory. Berkeley. CA. U.S.A.

772 List of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774 13.1 13.1.1 Applications of GaN and Related Alloys . . . . . . . . . . . . . . . . . 774 13.1.2 Specific Materials Problems of III-Nitrides . . . . . . . . . . . . . . . . 775 Growth of GaN and Related Alloys . . . . . . . . . . . . . . . . . . . 777 13.2 13.2.1 Bulk Growth from Solution . . . . . . . . . . . . . . . . . . . . . . . . 777 Hydride Vapor Phase Epitaxy (HVPE) of III-Nitrides . . . . . . . . . . . 778 13.2.2 Metal-Organic Vapor Phase Epitaxy (MOVPE) of III-Nitrides . . . . . . 778 13.2.3 Molecular Beam Epitaxy (MBE) of III-Nitrides . . . . . . . . . . . . . . 780 13.2.4 Epitaxial Lateral Overgrowth (ELOG) of III-Nitrides . . . . . . . . . . . 781 13.2.5 13.2.6 Laser Lift-off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782 Defects in III-Nitrides . . . . . . . . . . . . . . . . . . . . . . . . . . 783 13.3 783 13.3.1 Extended Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787 Point Defects and Doping Issues . . . . . . . . . . . . . . . . . . . . . . 13.3.2 Optical Properties of III-Nitrides . . . . . . . . . . . . . . . . . . . . 789 13.4 789 13.4.1 Bandedge-Related Transitions . . . . . . . . . . . . . . . . . . . . . . . 794 Donor- Acceptor Pairs . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.2 13.4.3 Yellow Luminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . 795 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13.4.4 Cubic GaN 796 Electrical Properties of III-Nitrides . . . . . . . . . . . . . . . . . . . 797 13.5 13.6 Devices Based on III-Nitrides . . . . . . . . . . . . . . . . . . . . . . 800 Optical Devices: Light Emitting Diodes (LEDS) and Lasers . . . . . . . 801 13.6.1 Electronic Devices: Field Effect Transistors (FETs) . . . . . . . . . . . . 803 13.6.2 13.7 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803 13.8 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804 13.9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804

772


List of Symbols and Abbreviations a b C

d e Ea E (A)

f

h J

WLO

kB

m

me

m (h) n Ndisl

P R T

a

lattice parameter Burgers vector lattice parameter distance between acceptor states along dislocation line electron charge activation energy acceptor ionization energy occupation fraction of acceptor states longitudinal optical phonon energy total spin momentum Boltzmann constant carrier effective mass free electron mass hole effective mass electron concentration dislocation density vapor pressure distance between donor and acceptor temperature

r

parameter in Varshni equation, Hayne’s rule parameter in Varshni equation, Hayne’s rule exciton-phonon coupling strength axial crystal field splitting spin-orbit splitting dielectric constant Debye screening length electron mobility frequency linewidth

AX BDT BE CBED 2D 3D DAP dc DVD-RAM DX eA ECR

acceptor-bound exciton brittle to ductile transition temperature bound exciton convergent beam electron diffraction two-dimensional three-dimensional donor-acceptor pair direct current digital video disk random access memory donor with large lattice relaxation, donor-bound exciton conduction-band-acceptor electron cyclotron resonance

P YPh

ACR

As0 & Ad

iJ Y


EELS ELOG FE FET FWHM

FX HEMT HVPE LD LED LEO LO LT MBE MD-SLS M-I-n MOCVD MOSFET MOVPE MQW ODMR PL RF RT SEM TEM TM VPE w-GaN

electron energy loss spectroscopy epitaxial lateral overgrowth free exciton field effect transistor full width half maximum free exciton high electron mobility transistor hydride vapor phase epitaxy laser diode light emitting diode lateral epitaxial overgrowth longitudinal optical low-temperature molecular beam epitaxy modulation-doped strained layer superlattice metal-insulator-n-semiconductor metal-organic chemical vapor deposition metal-oxide-semiconductor field effect transistor metal-organic vapor phase epitaxy multi quantum well optically detected magnetic resonance photoluminescence radio frequency room temperature scanning electron microscope transmission electron microscope trimethyl vapor phase epitaxy wurtzite-GaN

773

774


13.1 Introduction The recent surge of interest in GaN and the related group 111-N alloy system (III=gallium, indium, or aluminum) is rapidly establishing this materials system as the third most important semiconductor after silicon and the conventional 111-V semiconductor compounds related to GaAs. This development was triggered by reports on the p-type doping of this wide band gap material by Amano et al. (1989), which was rapidly followed by the fabrication of p/n junctions, light emitting diodes, and laser structures with emission wavelengths ranging from the visible spectrum to the ultraviolet (Nakamura and Fasol, 1997). Since then, any commercially viable 111--nitride technology develops within unprecedented short periods of time. This chapter attempts to provide a concise introduction into this rapidly developing field of research and device development. More detailed discussions can be found in several recent reviews, e.g., Pankove and Moustakas (1998, 1999), Edgar (1994), Edgar et al. (1999), Pearton et al. (1999), Nakamura and Fasol (1997), Orton and Foxon (1998), Monemar (1999), Liu and Lau (1998), and Ambacher (1998).

13.1.1 Applications of GaN and Related Alloys The unique combination of a direct band gap, which can range from the red for InN to the deep UV for AIN, with bonding strength resistant against recombinationenhanced defect formation and motion, allows efficient light emitting diodes (LEDs) and lasers (LDs) to be realised in the whole visible range (Nakamura and Fasol, 1997). Applications for these solid state emitters range from displays such as brilliant large TV screens on the street or decorative illu-

mination, e.g., in Pachinko gambling machines in Japan, to traffic lights and lasers in high density compact disk drives for optical information storage. For instance, it is expected that the capacity of re-writable DVD-RAM disks will increase from the current 4.7 GB to 15 GB by switching to a blue laser. This gain in information storage capacity will allow 6 h of continuous video storage and is bound to turn over the current market structure for home-video applications. The blue or ultraviolet photons can even stimulate suitable phosphors for the creation of white light, and are expected to soon revolutionize room illumination. The rapid advancements of GaN-based opto-electronic technologies witnessed over the last 10 years can be best demonstrated by a chronological plot of the evolution of the energy conversion efficiency of LEDs in comparison with GaAs-based LEDs (Fig. 13-1). Gallium nitride is also a rare exception in the history of semiconductors with commercial applications way ahead of scientific understanding. Unlike with many other semiconductor systems, GaN-based devices are already available in electronic shops even though comparatively little fundamental insight has been gained into their functioning mechanisms. For example, blue LEDs were already commercialized in 1992, but seven years later the basic nature of the radiative recombination mechanisms in these devices is still the topic of controversial scientific discussions. In addition to optical applications, 111-N heterostructures are very promising candidates for demanding transistor applications. In this field, currently the most intensely developed devices are high power, high frequency microwave amplifiers based on AlGaN/GaN high electron mobility (HEMT) structures (Nguyen et al., 1998; Sullivan et al., 1998; Wu et al., 1998).

13.1 Introduction

AllnGaPlGaP (red, orange, yellow)

n

3

k

to E

- f Unfilteredincandescent 101

-!ia

8

f Yellow filferedincandescenf

AAnGaPlGaP

k-1

775

-

DH AIGaAs,AIGaAs

f Red filtered incandescent

Y

E B 5 n

1:

1965

Thomas Edison's (red, Yellow) first lighf bulb GaP:N (green)

1970

1975

1980

1985

1990

1995

2000

Time [years] Figure 13-1. Chronological breakdown of the development of the performance of GaN- and GaAs-based LEDs (Ponce and Bour, 1997).

Further applications are currently under consideration in R&D labs, such as visible-transparent ("solar blind") detectors and radiation-hard electronics. Although it is not yet clear in which of these fields IIInitrides will finally prevail, it is already safe to state that this materials system will take a substantial share of the nonsilicon semiconductor market and thus warrants intense research efforts to improve the materials quality and optimize it for specific applications.

13.1.2 Specific Materials Problems of III-Nitrides The unusual combination of electronic properties and mechanical stability of IIInitrides has to be paid for by the need to deal with extraordinary materials problems which to date prevent the fabrication of devices with a low density of crystal defects. Commercial

LEDs are known to contain densities of threading dislocations in excess of 1 O8 cmP2, sometimes even reaching 10" cmP2(Lester et al., 1995). At the core of this problem is the fact that the high bond strength of GaN results in a melting point near 2800°C. In this temperature range the equilibrium nitrogen partial pressure is extrapolated to be above 45 kbar (4.5GN m-*) (Nakamura and Fasol, 1997; Grzegory and Porowski, 1999), which hitherto prevented any direct experimental determination of the melting point and any single crystal growth from the melt. Therefore device structures can only be obtained by heteroepitaxial deposition on substrates such as sapphire or Sic. Connected with the high melting point is a high brittle-ductile transition temperature so that most thin film deposition has to be performed in the brittle regime, i.e., essentially depositing a ceramic material (see Fig. 13-2).

776

-

,-g


1 .o

1 .o

0.8

0.8

0.6

0.6

c;

\

c;

I-

-c;E ,-

\

0.4

0.4

0.2

0.2

0.0

0.0

I-

6 rn

Figure 13-2. Brittle to ductile transition temperature TBDTand temperature of onset of dislocation motion Tplast in selected materials systems. Values are given as fractions of the melting point temperature. Typical growth temperatures of GaN [TMOCVD(GaN)= 1050°C and TMBE(GaN)= 725"CI and of GaAs (TGaAs= 600°C and TLT.,,,,=200 "C) are indicated. For further details see text.

The current rapid progress in the development of GaN-based devices is based on experience with thin film growth which is commonly gained in trial and error processes. Consequently, many of the physical processes which control the performance of GaN thin films and heterostructures are "handled" in some manner, but are not yet fully understood. Stress and strain in GaN thin films is one of these issues. It was recognized early on that large stresses originate from growth on lattice mismatched substrates, sapphire, or Sic, with thermal expansion coefficients that differ from that of GaN (Table 13-1). Film cracking was reported and investigated (Hiramatsu et al., 1993). It could be avoided if the film thickness was kept below 4 pm. Amano et al. (1986) introduced the growth of AIN buffer layers in order to improve the structural quality of the GaN main layers. Dislocation annihilation in the buf-

fer layer region was stimulated by this growth process. Similar results were obtained by growing a GaN buffer layer at temperatures around 700 K (Nakamura, 1991). However, it was not until recently that the

Table 13-1. Comparison of the two most popular substrate materials for hetero-epitaxial growth of GaN." Material

Lattice parameter a

Lattice mismatch to w-GaN

(.Qb

w-GaN A1203

6H-SIC

3.189 4.758 3.08

- 14% +4%

Thermal expansion coefficient (at 300 K) ( 10-6 K-')

5.59 7.5 4.2

a Note that the GaN hexagon when grown on sapphire is rotated by 30" with respect to the sapphire hexagon. The real lattice mismatch is therefore only - 14%; 1 A=o.I nm.

13.2 Growth of G a N and Related Alloys

large impact of buffer layer growth on the stress in the films was discovered (Rieger et al., 1996; Kisielowski et al., 1996b). Moreover, it was pointed out that the growth of buffer layers contributes with a biaxial strain to the overall stress in the thin films which can also be altered by the growth of main layers of different lattice constants (Kisielowski et al., 1996b). Lattice parameters are usually changed by a variation of the native defect concentrations or by the incorporation of dopants and impurities. Such point defects introduce hydrostatic strain components. Thus hydrostatic and biaxial strain components coexist in the films, and are physically of different origin. The biaxial strain comes from the growth on lattice-mismatched substrates with different thermal expansion coefficients. The hydrostatic strain, however, originates from the incorporation of point defects. It was shown that a balance of these strains can be exploited to strain engineer desired film properties (Kisielowski et al., 1996b; Klockenbrink et al., 1997; Fujii et al., 1997; Kisielowski, 1999a). In contrast to all other IIIN semiconductors in practical use, III-nitrides crystallize preferentially in the hexagonal form with a wurtzite lattice. Therefore the usual thin film growth plane is the densely packed polar (0001) plane which corresponds to the (1 11) plane of cubic semiconductors. Thus the polarity of the layers has to be taken into account and antiphase domains with inverted polarity can frequently be observed. Very recently, it was realized that lateral current transport at heteroepitaxial interfaces such as AIGaN/GaN cannot be understood without taking into account the large pyro- and piezoelectric effects caused by the built-in charge polarization at the (0001) interface and its modification by the stress state of the structures (Yu et al., 1997). Besides these problems with structural defects and residual strain, there are very

777

challenging problems with p-type doping, which will be discussed in Sec. 13.3.2, and technological problems such as obtaining good ohmic contacts with p-GaN, which are outside the scope of this chapter. A good summary concerning these problems can be found in recent reviews, e.g., Nakamura and Fasol (1997), Pankove and Moustakas (1998, 1999), Edgar et al. (1999), and Liu and Lau (1998).

13.2 Growth of GaN and Related Alloys The key factor that has to be considered in the growth of GaN compared with other III/V semiconductors is the high melting point combined with the high nitrogen vapor pressure at elevated temperatures. This property has prevented, up to now, single crystal growth from the melt and results in thin film deposition being a dynamic equilibrium between deposition and decornposition (Newman 1998), as given by the nitrogen desorption rate measured in 1965 by Munir and Searcy (Fig. 13-3). This limits the substrate temperature of all deposition techniques working in a vacuum or with low nitrogen flow rates to lower values compared to deposition techniques working at ambient or enhanced pressure or at high nitrogen flow rates.

13.2.1 Bulk Growth from Solution In the sec. 13.1.2 it was pointed out that the high melting point of GaN combined with the high nitrogen partial pressure at the melting point hitherto prevented any melt growth of single crystal GaN. Nevertheless, the group at the UNIPRESS institute (Warsaw, Poland) succeeded in the solution growth of unseeded GaN single crystal platelets of the order of 1 cm2 in size (Grzegory and Porowski, 1999). Although these

778


Y 0

0 @O

lo-'

1

6.5

a,

0

111""

7.0

T

T ('K)

,

I

7.5 x

lo4

8.0 ( 0

lz;

+

Iccentricity

.-0c + u L W

..o

a i 0 c

(a)

+

I (b)

Figure 1-7. Floating zone growth configurations. (a) Keck, small diameter; (b) Needle-eye, large diameter.

18

1 Silicon Processing

than the machined rod, so that as the zone was established and passed up through the polysilicon rod, with the coil now just inside the rod diameter, the smaller molten zone volume involved could then be successfully moved through the length of the rod without prematurely falling out. Establishing this as a reliable production procedure took much effort, and the design of highly specialized zoners. By this crucible-free technique standard crystal product, zero dislocation density silicon up to 150 mm diameter, is made at a purity close to that of the input polysilicon. Resistivities are available up to 5000 C2 cm, and in limited amounts even higher, well beyond that attainable by Czochralski growth. The control of doping to specific resistivity bands in float zoned (FZ) silicon is approached in three ways. Firstly, by gas phase doping during crystal growth, adding diluted phosphine, PH,, or diborane, B2H6, to the argon gas flow through the zoner, a wide range of both n- and p-type specifications can be made. The higher resistivities are more difficult to meet, and the tolerances quoted get wider. The equilibrium segregation coefficients for boron and phosphorus in silicon are 0.8 and 0.35, respectively, and so doping uniformity, both axially and radially, is somewhat easier to achieve with boron. The second doping method used is only available to the polysilicon producers. The thin rods used to construct the inverted “U” structures, for the reactors in which the silicon deposition occurs, are made by fast pulling from a pure silicon melt. By adding phosphorus or boron to the melt, doped thin rods can be made to various specifications and stocked, to be used later when the deposition rods are planned for float zoning. Then as the molten zone is passed through the polysilicon rod the dopant in the core is released. Very precise resistivity control

can be achieved by this method, with high run-to-run reproducibility. The third method, only possible for phosphorus, n-type, material, is neutron transmutation doping (NTD) which has become very important for power applications.

1.4.2 Neutron Transmutation Doped Silicon By float zoning undoped material under very clean conditions crystal can be produced in which the resistivity is of the order of 5000 C2 cm or greater, and with a very low residual phosphorus and boron. If this ingot is placed into a nuclear reactor, transmutation doping generates phosphorus in an extremely uniform distribution, avoiding the growth striation phenomena common to both the float zone and Czochralski growth methods, to be discussed later. This method is particularly suitable for making the high resistivity silicon required for power device applications, where the other doping techniques cannot match NTD material in its ability to meet very close tolerances. Normal elemental silicon consists of three stable isotopes with abundancies as: 28Si 29~i ,Osi

92.21% 4.70% 3.09%

The possibility of doping silicon by transmuting the 30Si isotope into 31Pwas first recognized by Lark-Horowitz (195 1). Later, Tanenbaum and Mills (1961) made detailed experiments to verify that the scheme was potentially useful, but this work was dormant until when Herrmann and Mucke (1973) published their power device study. Since then the major developments have taken place, leading to a series of international conferences and many papers on this sole topic.

1.4 Single Crystal Silicon

The principal nuclear reaction upon which the whole process depends is

The stable 30Si isotope captures a thermal neutron to form 31Si with the emission of yrays. For this isotope of natural abundance 3.09%,the capture cross-section for ~ or a thermal neutron is 0.1 I X I O - ~cm2, 0.11 barn. In its turn 31Siis unstable and decays with a half life of 2.62 h to the stable phosphorus isotope 31Pwith the emission of an electron of energy 1.47 MeV. During neutron irradiation other nuclear reactions occur, some of which must be taken into account: 28Si(nt, fi

+2 9 ~ i

(15)

and 2 9 ~(nt, i fi

+3 0 ~ i

The thermal neutron capture cross-sections for these are 0.08 and 0.28 barn, respectively, and the only real effect on the process arises from ingot heating by the emitted yrays. However, two other reactions occur, which are much more important: loB (q,a) + 'Li

(17)

In this reaction a total energy release of 2.5 MeV is associated with the a and lithium particles, which leads to considerable short range lattice damage. Boron has a very high thermal neutron capture cross-section of >755 barn, but, provided the boron concentration in the silicon is kept low, the effect is small. The most serious side reaction in the process is 31

p (nt, y ) +32 p

f,,,=14.3d

' 32s+(18)

Since the capture cross-section here is only 0.2 barn the amount of sulfur produced is minute in doping terms, but the long half

19

life for the decay of 32Pcan impose restrictions on the handling of low resistivity NTD silicon. All the reactions so far have referred to thermal neutrons, that is, neutrons which have already been scattered by sufficient collisions within the pile that their energy has reached thermal equilibrium with the medium before intersecting the silicon. Such neutrons, at room temperature, have an average energy of only 0.025 eV and a velocity of 2200 d s . However, fast neutrons in the pile, with energies in excess of I MeV, also reach the silicon. These give rise to much of the lattice damage generated during transmutation doping, and are also responsible for reactions of the type 28Si (nf, a) + 25Mg

(19)

producing a high energy a-particle. Even without reaction, the head-on collision of a 1 MeV neutron with a silicon atom will knock out about 200 silicon atoms from their lattice sites. Thus the slow-to-fast neutron ratio in the nuclear reactor is critical, and it is for this reason that heavy water reactors, with slow-to-fast ratios around 1000: 1 (a much higher ratio than available in light water and other reactors), have proved to successful for NTD processing. The subject of neutron irradiation damage has proved to be a matter of great complexity, beyond the scope of this chapter. Much lattice disarray is introduced, immediately after irradiation high resistivity values are found, and at this point most of the phosphorus formed is interstitial. Therefore the post-irradiation annealing process is crucial and has been studied in depth. The resistivity values, expected from the total reactor neutron flux, are fully realized after about 1 h at 600 "C; however, defect studies indicate the need for a higher temperature, and poor minority carrier lifetime has been a problem (Meese, 1978). The producer's

20


postanneal processes, which at the introduction of NTD products were at moderate temperature, sometimes relying on the high temperature semiconductor fabrication to complete the anneal, subsequently moved to higher temperatures and more complex time- temperature scheduIes.

-Q, + c W

-

300 3

P

100

W

m

(31

200

10

L

:1.0 a

c

Y m W

100 h

m m

For many years it was thought that any residual carbon in silicon was of little importance; it is an isoelectronic group 4 element, it occupies substitutional sites in the lattice, and silicon carbide is an insulator. The first indication of device linked effects came when Akiyama et al. (1973) reported a correlation between high carbon concentrations, reduced breakdown voltage, and increased reverse current leakage in rectifier diodes. Because this work used silicon with a very high carbon level (between 1 and 2x1017 atoms/cm3) close to the solid solubility limit, and only appeared as a short communication, its significance was generally overlooked at the time. Carbon was not listed in most purchasing specifications. The common requirement of trichlorosilane for organosilicon and semiconductor use has already been noted in Sec. 1.2, and many of the world's polysilicon plants are cosited with, or close to a silicones plant. Thus, when in mid 1975, accidentally and undetected, a quantity of high-carbon float zone silicon reached device lines, serious yield problems were met in rectifier, thyristor, and power transistor manufacture. Subsequent research showed that, while not affecting the breakdown voltage, lower levels of carbon still degrade the reverse leakage, as is shown in the plot of Fig. 1-8. Recognizing a severe problem, polysilicon producers made major plant overhauls to remove carbonaceous sources from pumps,

:

U

Y m W

1.4.3 Carbon and Nitrogen in Float-Zoned Silicon

-+

.

0.1

loy5

W

v) L

W

W >

I

I

L

10'6 loy7 Carbon concentration (atoms/cm3)

0 "

Figure 1-8. Rectifier diode failure as a function of carbon concentration: 0 breakdown voltage; x reverse leakage current. Note that, even when the breakdown voltage has been restored, leakage effects persist to much lower carbon levels. The dashed vertical line marks C,,, the carbon solid solubility saturation value.

valves, glands, etc., set new low carbon operating standards, and instituted strict test procedures - in single crystal the substitutional carbon has an infrared absorption at 16.6 pm (605 cm-') measured by differential (double-beam) spectrophotometry, ASTM Standard F123. Today carbon levels are rigorously controlled by all silane, TCS, and polysilicon producers, to ensure final silicon levels below around 2 x 10l6 atoms/ cm3 . The role of nitrogen in silicon is quite different. Unlike other group 5 elements, such as P, or As, nitrogen does not behave as a donor impurity. An electronic center deep in the band gap has been reported by Tokumaru et al. (1982), but in general nitrogen does not appear to be electrically active in melt doped silicon. Another distinguishing feature is its low solid solubility: 3 ~ 1 0 ' ~ atoms/cm3 at the melting point of silicon (Yatsurugi et al., 1973). This is much lower than for other light elements, such as carbon, N = 3 . 5 ~ 1 0 cmP3, ' ~ or oxygen, 1 . 7 ~ 10" atoms/cm3. In float zoned silicon the


equilibrium solid solubility is often exceeded, the excess concentration being proportional to the zone velocity, where typically the values met may be up to 5 x 1015atoms/ cm3 (Yatsurugi et al., 1973). The low electrical activity of nitrogen in silicon is useful because it has a major attribute, in that nitrogen doping at low concentrations, limited by its solid solubility, effectively inhibits dislocation generation and propagation, as first reported by Abe et al. (1981). Second-phase hardening is a well known metallurgical phenomenon, but usually occurs at higher concentrations. Low levels of nitrogen in silicon, in the 1015 atoms/cm3 range, impart resistance to the thermally induced warp of wafers met during device fabrication. Wafers sliced from Czochralski grown silicon contain oxygen on the order of 10l8 at./cm3. The interstitial oxygen has the function of strengthening the silicon crystal lattice, by raising the yield limit for onset of slip dislocations. This function is weakened if a significant fraction of interstitial oxygen is turned into oxide precipitates via precipitation process. Normal float zoned silicon slices, with an

120

Slices all 380um thick Load 5 0 9 Span 6 3 m m

21

oxygen content less then 1 ~ 1 0atoms/cm3, '~ and also low in carbon, distort readily under thermal stress, but with nitrogen doping outperform high oxygen Czochralski material. A simple demonstration to compare the normal FZ and CZ material is as follows. Standard, polished, (100) orientation single crystal slices, 76 mm diameter, 380 pm thick mounted on a three support point silica jig span 63 mm, and loaded by a 50 g weight are heated at 1150°C for 1 h, ramping the temperature up and down from 850°C in 30 min measuring the change in warp, and, by Secco etching, the amount of crystallographic slip caused by the controlled thermal stress. The results in Figure 1-9 clearly demonstrates that nitrogen doping strengthens FZ wafers. The NFZ is not currently used in commercial products. 1.4.4 Periodic Crystal Growth

Temperature oscillations during crystal growth have been recognized for a long time, and their effects described (Carruthers, 1967; Hurle, 1967; Chedzey and Hurle, 1966). At first sight this may appear an odd

IlOOl orientation

___

Change in TIR (warp) LH axis Extent of slip RH axis

70

60

-

50 .p ul

40 % 30 I I I I

20

L

0

lo

I N-doped

standard

m

.-g -0

0-doped

Figure 1-9. A comparison of warp and slip after loading slices ( 1 h at 1150°C) (LH: left hand, RH: right hand). [Note that curvature in a silicon slice is hardly ever a simple saucer shape; it is more like a potato chip (potato crisp). Modern metrology equipment scans the whole surface to arrive at a single value, the total indicator reading (TIR), and also provides plots of the surfaces.]

22


concept, but the underlying principle is simple and can easily be demonstrated (Hurle et al., 1974). A small channel containing gallium (a metal which, conveniently, is molten at temperatures above 30°C) with a number of thermocouples inserted equispaced along its length is well wrapped in thermal insulation to prevent heat loss. One end of the channel is clamped to a flowing water cooler, and so held at around 3540°C. The other end is attached to a heater, whose temperature is gradually increased. At first, simple heat flow along the channel creates a thermal gradient, recorded by the thermocouples. However, as this temperature gradient is increased, a point is reached when the thermocouple signals suddenly change into regular sinusoidal oscillation. The system behaves analogously to an electrical AC driven oscillator, whose frequency is determined by the inductancecapacitance product. Here the thermal diffusivity, kinematic viscosity, and channel dimensions, replace their electrical counterparts in an equivalent thermal-mechanical resonator. Thermal oscillations have been seen widely in many crystal growth systems, not only in semiconductors - Si, Ge, GaAs, InSb, etc. -but also in LiNbO,, garnets, and most oxides and fluorides (Cockayne and Gates, 1967). Superposition of oscillations on the temperature near the solid-liquid interface between a crystal and its melt causes large regular fluctuations in the growth conditions. The driving force, which determines the overall rate of growth, is provided by supercooling - setting the melt temperature close to the interface a little below the melting point. Since most crystal growth rates are relatively slow, this value is normally smaller than the magnitude of the thermal oscillations, and so the growth becomes highly dynamic, and even, at the peak of each cycle, includes momen-

tary meltback. This periodic nature of crystal growth controls the incorporation of dopants and impurities into the crystal, whose concentrations may vary markedly, the changes exactly replicating the periodicity. The regularity of these growth striations can be seen by etching, and by spreading resistance (microresistivity) measurements, made on a cut vertical section of a crystal, as shown in Fig. 1-10. Since the crystal growth interface across a diameter is always curved, cut slices intersect several striae, and subsequent delineation reveals a spiral radial impurity distribution pattern in the slice, as shown in the X-ray topograph of the carbon distribution in a float-zoned slice

Figure 1-10. Periodic crystal growth (1). Spreading resistance plot (above), with points taken at 10 pm intervals along the growth axis. Etched surface micrograph (below), showing the structure variations within a single striation.


Figure 1-11. Periodic crystal growth (2). X-ray topograph of the carbon distribution across a cut slice. C, = 4 x 1 0 ' ~ atoms/cm3.

in Fig. 1-11. (Note: the X-ray topography technique is covered in Sec. 1.6.1). If growth periodicity did not include a meltback within the cycle its effect on impurity distribution would be far less severe. This has been demonstrated by the float zone growth of small diameter rods, when the latent heat of solidification generated at the interface can escape more easily than at larger diameters, permitting higher growth rates. As the rate is increased, a point is reached when the supercooling gradient overcomes the thermal oscillations, and at a growth rate above 3 m d m i n the striae disappear. This research, while interesting, is not a production option. In the case of Czochralski growth, as will be discussed later, the melt is normally positioned in the heat field to keep thermal convection low, the axial pitch of striations is closely linked to the growth parameters. The etched vertical section shown in Fig. 1-10 was taken from an 80 mm diameter, (100) orientation, crystal pulled at 1.5 mm/ min, with a rotation rate of 15 rpm hence the

23

thickness of the silicon layer grown per revolution was 100 pm, which, as the measurements show, is also the striation pitch. On the other hand if the crystal is grown under high thermal convection, then the striae are closely spaced, discontinuous, and aperiodic (Carruthers et al., 1977). Spreading resistance measurements taken on the slices cut from such crystals reveal an extremely wide scatter of values. The effects of normal striated silicon in device manufacture are quite variable. In some cases it does not seem to matter, but in other cases striae can cause serious losses. Again because of the greater difficulties in zoner operation, float zone silicon tends to have more problems. For example, in the manufacture of UHF transistors, for applications at around 500 MHz, the cut-off frequency, ft, is a function of the collector-base current, Zcbrwhich is very susceptible to small, local, microresistivity variations. In a direct comparative trial, the percentage standard deviations about the mean offt,ft, at the operating Zcbcurrent, has been measured using three materials sources (see Table 1-3). In the third material an epitaxial layer of the same type, and resistivity as the underlaying substrate, deposited from the vapor phase, and so free of the melt-growth striae, provides an extended bulk material within which the transistors are fabricated. As the table shows neither CZ nor FZ can match extended bulk epitaxy, EBE, while the FZ Table 1-3. The effect of resistivity striations on device performance. 6:standard deviation, f t : mean value of the cut-off frequency. Type of material

oU;)in %

Float zone Czochralski Epitaxially extended bulk

24 10 3

24


material is the worst in this application. EBE material is used in large scale production of these devices, its additional cost for outweighed by the yield improvement. Epitaxy therefore is one way to overcome the bulk striation problem. Another is the neutron transmutation doping method already described, and whose importance in the high voltage and power fields will now be more fully appreciated. Again the costs are obviously somewhat higher than for the conventionally doped materials, but the fabrication and device performance are far superior. Herzer (1977, 1980) and Herrmann and Herzer (1975) have examined the interaction of striations in NTD doping. Using material with a starting resistivity of 10 times the final value shows no background striations, at 5 times slight striations are seen, while an initial resistivity 2 times final, gave +lo% variations. A third, and the most widely used way to overcome striation effects, which introduces no added costs, is that employed in MOS integrated circuit fabrication. Taking n-MOS as the example, the substrate is p-type, boron doped at around 20-30 Q cm resistivity. The MOS devices are made entirely by ion implantation, with n+ source and drain channels, and an n- gate implant equivalent to a resistivity of somewhere around 1-5 SZ cm. These implant concentrations are at least 10 times higher than the substrate boron level, and striation effects are reduced to insignificance; that is, similar to the NTD situation. Today integrated circuit manufacture consumes more than 90% of the world’s semiconductor silicon as Czochralski crystal, our next topic.

1.5 Czochralski Silicon The increasing size of crystals pulled by the Czochralski (1917) technique, and

the technological developments associated with the growth of dislocation-free material, in which there is close control over not only the dopants, but all impurities, represents one of the outstanding achievements in semiconductor processing. The silicon pullers used initially were quite simple (Teal and Buehler, 1952). The charge, consisting of small lumps of broken polysilicon, was melted together with a small precise amount of dopant, from a silicon alloy made with P, As, or Sb (n-type), or B (ptype), at just above the melting point, 1412°C in a pure silica crucible, retained in a graphite holder to prevent it sagging, held under an argon atmosphere; either resistance or RF induction heating was used. A thin, single crystal, seed rod mounted in a rotating shaft or a stainless steel cable was lowered into contact with the melt surface, and a little melted off in order to establish a clean solid-liquid interface. Then, as the temperature was lowered, silicon started to solidify on the seed, which was withdrawn at a controlled rate to pull a crystal of the desired resistivity, ultimately almost emptying the crucible. This apparently simple description is deceptive, there were many hidden subtleties needing to be understood. It was soon realized that, to be able to pull a crystal at all, without spurious growth at the crucible wall, it was essential to have a centrosymmetric heat field - the introduction of crucible rotation followed, which also minimized random convection in the melt. As charge sizes increased, RF heating was abandoned, and the tapering of graphite resistance heaters was used to shape the best vertical heat field profile. However, having established this in the melt - crystal interface region, it could only be maintained as melt was used by introducing a crucible lift mechanism. The furnace configuration which resulted, as shown in

Silicon

27

Increasing growth I

I

'

I

I

,

:

I

Facetted

I

I

Convex

,

I

Inversion

Peripheral ring facet

Concave

Figure 1-13. The changes in interface shape of a (1 11) orientation silicon crystal as the growh rate is increased. As the growth rate increases latent heat of solidification at the interface plays the most significant role in determining its shape (LHT, latent heat temperature profile; MHT, main heater temperature profile; hatching indicates the solid crystal). (1, A) Low speed, small central facet, convex. (2, B) Somewhat faster pull, larger central facet, still convex. (3, C) Even faster pull, latent heat generation now compensates for heat losses across the whole interface, which becomes a ( 11 1 ] mirror surface; the point of inversion. (4, D) Speed of growth greater than fof inversion, producing a wide ring facet and a small relatively shallow central concavity. (4, E) Speed faster still. The central cavity is deeper and wider so there is a narrower ring. (5, F) The pull rate is now very fast and any MHT/LHT compensation is outside the pheriphery of the crystal. Very deep concavity, no ring facet.

drawn from the residual melt, which can lead to stress-generated dislocations running back up into the solid, so causing yield losses, the final part of the crystal is grown tapered in a cone to a point. Mastery of the zero dislocation growth mode, for both CZ and FZ techniques, at the end of the 1960s, preceded the later machine development which led to the crystals weighing 200 kg or more with diameter of up to 300/400 mm in the current development. Many thousand

tons of dislocation-free silicon have been produced annually.

1.5.2 Constitutional Supercooling For epitaxial substrates, large amounts of very highly doped, n+ and p+, zero dislocation crystal are needed, which involves the particular problem of constitutional supercooling, as described for metals by Rutter and Chalmers (1953). At the crystal-melt,

28


solid-liquid interface of a growing crystal impurity segregation occurs, its coefficient, different for each dopant, defined by keff =

c,

concentration in solid = (1-2) concentration in bulk liquid C1

For a rejected impurity ke, is less than 1.0, but as a result of the rejection, a boundary layer builds up in the liquid at the interface, at a higher concentration than in the bulk, from which the crystal grows. Therefore the effective k,, for a finite growth rate is higher than the equilibrium value, k,, and rises with increasing growth rate. The thickness of the boundary layer, 6, within which fluid motion is laminar, relatively slow, and hence nonmixing, so that diffusion is the predominant transport mechanism, is determined by the crystal rotation stirring, and as the rotation rate increases the boundary layer gets thinner. This relationship is given by the Burton, Prim, and Schlichter (Burton et al., 1953) equation

where vg is the growth velocity, and D the impurity diffusion coefficient in the liquid, of the order of 5x1OP5cm s. This formula shows that keff varies continuously from k,, at very low growth rates, to 1.O, at very high rates. The higher impurity level in the boundary layer results in a silicon-dopant composition of lower freezing point, as seen in Fig. 1-14. The temperature gradient from the solid into the melt, necessary to allow growth at the chosen rate, is also shown in Fig. 1-14. At the higher rates needed to obtain the desired interface shape for dislocation free growth, and when the dopant levels are also high, a region is formed in the liquid, ahead of the crystal, which is supercooled by virtue of its local constitution,

I

Temperature gradient into melt L W

a + L m

Liquidus for the Wdopant

01

5

a

Position of maximum supercooling due to local composition

I-

TCG

1

Distance into melt

Figure 1-14. Constitutional supercooling during crystal growth. k,= C,IC,, keff= C,/C,, 6= 1.6 D113v 1 I 3 w-1/2 , TcG: crystal growth temperature. As vg and 6 + 0 , k,, + k 0 ; and as vg and 6 become large, keff 4 1 .o.

and in which nucleation and random crystallization can happen. As the advancing interface approaches this point, the single crystal rapidly becomes polycrystalline. The greatest risk of this occurring is in the later stages of n+, or p+ crystal growth, when segregation by normal freezing, as defined by Eq. (1-l), further increases the already high initial dopant concentration. Studies of the onset of constitutional supercooling in these crystals (Wilkes and Perkins, 1971-72), using striation etching to reveal the details, has shown that the initital perturbations, and formation of cellular structure, in (1 11) orientation silicon, originate on the inner edge of the ring facet, as shown in Fig. 1-15. Achieving high production yield and reproducibility for this material demands precise control of the pulling parameters.

1.5 Czochralski Silicon

29

Figure 1-15. The onset of constitutional supercooling at the inner edge of the ring facet during the growth of dislocation free, (1 1 1) orientation, n+ Sb doped, silicon. Note: In the enlargements the arrow t points outwards radially. At a later stage of growth, the whole interface breaks up into a hexagonal cellular structure, prior to the transition from single crystal to polycrystal.

1.5.3 The Incorporation of Carbon and Oxygen Most of the components in the hot zone of a puller are made of some form of carbon - graphite heaters and crucible holder, and carbon felts in the baffle assembly - but careful housekeeping can virtually eliminate these as a source of contamination. Maintaining the pullers leak-tight, using ultrapure argon as the purge gas, and employing rigorous purging schedules after loading the charge, remove air or moisture, which could otherwise react with the carbon parts to form CO, to dissolve into molten silicon; and as we have seen, polysilicon itself is very low in carbon - yet carbon can be a problem.

During the first step of meltdown of the polysilicon into the pure silica-glass crucible the system is at its hottest, up to around 150O-155O0C, to achieve meltdown in a short time. Under these conditions reaction between the graphite crucible holder and the outer surface of the silica crucible releases carbon monoxide [see Equation (l)]. This is the prime source of the carbon impurity. After the meltdown is complete and the temperature is lowered, to around 1420-1430°C for the start of pulling, the reaction only continues at a much lower rate (Barraclough and Wilkes, 1986). In an atmospheric pressure puller, where the argon purge rate is commonly around 60 L/min, the initial carbon content in the crys'~ but, if the tal is around 2 ~ 1 0atoms/cm3;

30


start is deliberately delayed, this steadily rises as more carbon is slowly dissolved. Operating the puller at a reduced pressure, of about 20 torr ( ~ 2 6 0 0Pa), with an argon input of 10 L/min at normal temperature and pressure, the effective gas displacement rate sweeping out the chamber is increased six-fold, and the silicon crystal produced contains far less carbon - by at least an order of magnitude. Under carefully regulated conditions, a large proportion of the crystal can be grown with carbon below its infrared absorption detection limit of 5 x lOI5 atoms/ cm3. In this case when meltdown is complete, and during crystal growth, further carbon transfer is insignificant. Today all large silicon Czochralski production pullers are operated at reduced pressure. While risk of carbon incorporation is essentially limited to the meltdown period, another reaction continues throughout the whole process - that between the silicon and the inner surface of the crucible, dissolving oxygen into the melt: Si + SiO,

+ 2 SiO

(20)

which, at the same time, allows any other electrically active impurities present in the silica into the melt. Crucible quality depends on the quality of natural sources of silica. The superior crucible quality can be obtained by the use of fused synthetic SiO, made from semiconductor grade materials. CZ silicon growing using ultrapure polysilicon and synthetic quartz crucibles can result in resistivity greater than 200 Ohm-cm. Today, the use of commercial grade quartz crucible and polysilicon can produce CZ silicon with resistivity up to 50 Ohm-cm, nor p-type. Returning to the oxygen dissolution, as can be seen in Fig. 1-12b, this occurs primarily along the hotter inner wall of the crucible, and to a lesser degree across its base; and, while thermal convection transports

the SiO up to the free melt surface where it can evaporate, a small fraction of dissolved oxygen becomes incorporated into the growing crystal. This is a highly dynamic equilibrium, altering continuously as silicon is withdrawn from the crucible, and the ratio of melt volume to crucible surface contact area changes. In a normal CZ crystal, the oxygen concentration is highest at the seed end, and gradually decreased along its length. To a first approximation, the oxygen concentration incorporated is proportional to the total crucible area contacted by the melt. In the Czochralski system, melt fluid dynamics clearly play a vital role in the growth, and in the incoporation of all impurities, into the crystal; the prime contributors being the thermal convection and the mechanical drive provided by the crystal and crucible rotations - usually in opposite sense. The convective drive is influenced by several factors. In fluid flow adjacent to a hot vertical wall, the velocity is a function of the temperature gradient, height up the wall, h, and Prandtl number, P r (Schlichting, 1968): v K

f (AT). fi.Pr-'

( 1-41

where the dimensionless Prandtl number, the ratio of the kinematic viscosity to the thermal diffusivity, is a measure of the relative ease of movement and heat transport in a fluid element. The value of Pr (Si, liq.) is 0.015, a lower value than that of mercury, 0.023. [In comparison Pr (H,O, room temperature) is 7, and Pr of glycerol is 300.1 Because liquid silicon has such a low Pr value, as heat flows through the wall into silicon it readily convects. (A stability analysis for convection links this low P r to the rotationally coupled thermal oscillations, described in Sec. 1.4.4 above.) Therefore thermal convection is less in a relatively wide flat melt, as is normal in CZ

31


silicon, and decreases as the liquid diminishes. (Note: in the CZ growth of oxides, with Pr around 30, taller narrower crucibles are common.) Positioning the crucible lower in the heat field, with a greater power transfer into the upper part of the melt, also promotes a reduction in the convective drive. Again, the baffle configuration surrounding the heater - crucible assembly reduces the temperature gradients in the system, and can be arranged to keep the crucible wall cooler, so reducing its dissolution rate (Moody, 1986). For a given CZ growing system, i.e., fixed starting melt geometry and hot zone thermal distribution, etc., the parameters that can significantly alter the oxygen incorporation are crucible and crystal rotations and growth rate variations. The effect of crystal/crucible rotation on the fluid flow patterns were studied in the past by simulation using fluid of similar viscosity as that of silicon melt at room temperature (Carruthers and Nassau, 1968). In the real crystal growth, however, the flow patterns can be significantly altered by the presence of thermal convection. The results of the simulations provide very useful information on the effect of rotational parameters. Kakimot0 et al. observed thermal and forced convection flows of silicon melt directly during Czochralski growth using X-ray radiography with solid tracers, for various crystal and crucible rotation speeds. The effect of non-axial symmetrical temperature distributions on the thermal convection flows was clearly observed. The suppression of thermal convection by crystal rotation-induced forced convection was also evidenced. One way to gain information on the flow properties of a growing system is to analyze grown crystals following parametric growing experiments. One finds that forced convection is effective in controlled oxygen incorporation.

Crucible rotation develops radial pressure gradients which enhance the thermal convection flow arising from non-vertical temperature gradient. Therefore, fast crucible rotation helps the transport of oxygen from near the crucible wall to the growing crystal and enhances incorporation. Fig. 116 shows the effect of crucible rotation on the incorporation level. Fast melt flow also results in a thinner melt-crucible boundary diffusion layer, a condition that will enhance crucible dissolution. Crystal rotation rate determines the magnitude of the upward melt flow. This flow can serve as oxygen transport from crucible bottom to the growing interface. The net effect on the overall flow pattern and oxygen incorporation depends on its magnitude and rotational direction relative to the crucible rotation. Fig. 1-17 (Lin & Benson) shows several axial oxygen concentration profiles of silicon grown with several combinations of crystal/crucible rotation rates, under both

1.I 5

0

CRYSTAL ROTATION 28 RPM

0.2

0.4 0.6 FRACTIONSOLIDIFIED

0.8

5

Figure 1-16. Oxygen profiles at various crucible rotation rates, with crystal rotation rate held at 28 rpm (From Moody, 1986).

32

c

a

I a


21

v

z 19

11

~~~

cI

0.2

0.1

0.3 0.4 0.5 0.6 FRACTION SOLIDIFIED

07

0.8

Figure 1-17. Axial oxygen profiles of silicon crystal grown with several combinations of crystal and Crucible rotation rates (From Lin & Benson, 1987).

counter- and iso-rotation conditions in the same grower and a reduced pressure. These results show that the forced convection induced by crystalkrucible rotations has very significant effects on the melt flow pattern, even in the presence of thermal convection. The bulk of the incorporation behavior is

consistent with, and can be interpreted from, the simulated flow patterns (Carruthers and Nassau, 1968). From previous discussions, it is seen that forced convection is an effective tool for controlling oxygen incorporation. In order to achieve a desired oxygen level with axial uniformity in a silicon crystal, the following procedure may be carried out. Experimentally, for a given crystal growing system, one can establish oxygen incorporation profiles as a function of crystalkrucible rotation rates via studies such as shown in Figures 1-16 & 1-17. Using selected rotational parameters at different stages of crystal growth, one can develop and tailor the growth processes to grow crystals of desired oxygen concentration with substantial axial and radial uniformity. Figure 1-18 (Lin & Benson) shows an example of using variable crucible rotation rates to change the oxygen incorporation levels during the growth, while the crystal rotation rate is maintained constant. It shows that the crucible ramping to a higher rotation rate effectively raises the oxygen

22

t

z 9 a I-

I-

0

a

$ 81 0

1

0.1

I 0.2

I I I I 0.3 0.4 0.5 0.6 FRACTION SOLIDIFIED

I

I

0.7

0.8

2" 0.9

Figure. 1-18. Axial oxygen profile of a silicon crystal showing the effect of crucible rotation rate on oxygen incorporation level (From Lin & Benson, 1987).


level and changes the oxygen concentration profile. The incorporation level can be further enhanced when alternate ramping-up and -down of crucible rotation at medium and high rates are employed, as shown in the Figure 1-18. This process works well for the production of medium to high oxygen content material but good yields at lower oxygen concentration are difficult to achieve. This problem is now addressed in the next section.

1.5.4 Magnetic Czochralski Silicon Electromagnetic stirring and other effects in molten metals have been recognized for many years, and, in the intense radiofrequency fields within the heater coil of a float zoner, magnetic levitation in part supports the molten silicon. Some large Czochralski pullers have used a three-legged graphite picket heater, driven from a threephase AC mains supply at 50-60 Hz, the heavy heater current inducing rotational forces in the melt, where flow rates as high as 20 rpm have been observed. The latest puller designs have returned to using twolegged picket heaters and DC drive to avoid this effect. Today it is the application of static magnetic fields to dampen out the convection flows in Czochralski systems that is important. The early work by Chedzey and Hurle (1966) was initially directed towards the suppression of growth-striae in FZ, and then in CZ crystals (Hurle, 1967). Czochralski growth in a transverse magnetic field was reported by Witt et al. (1970), but it is the work, initiated by Hoshi et al. (1980), who applied very large electromagnets to commercial silicon pullers, that stimulated worldwide interest, and major developments. The results of Hoshi et al. show that products with a wide range of oxygen con-

33

tent can be made by Czochralski growth in a strong magnetic field; the technique offers the control of resistivity up to 5000 SZ cm, and also higher than normal growth rates. Both electromagnets and superconducting cryomagnets have been used to provide fields in the general range of 1000-5000 G (0.1-0.5 T). Hoshi et al. (1980) and Suzuki et al. (198 1) first used a transverse magnetic field, with the lines of force parallel to the melt surface; axial fields have also been applied (Hoshikawa, 1982; Hoshikawa et al., 1984; Cartwright et al., 1985). As the strength of the magnetic field is increased, fluid motion perpendicular to the lines of force is progressively dampened out until, in a high field, it is suppressed altogether. Thus in an axial, vertical, field the radial fluid flow across the surface is reduced; whereas in a transverse, horizontal, field it is the axial (upwards at the crucible wall, and downwards beneath the crystal) and azimuthal motions (rotational shear around the crucible wall) which are reduced but then not the radial flow. Clearly, in either mode there is a strong effect on thermal convection. Hoshi and Suzuki showed that a horizontal field of 0.15 T was sufficient to suppress the convection in a melt contained in a 25 cm diameter crucible. Again, the balance between field strength and the crucible and crystal rotations, both in their rates and relative senses, is apparent in the effects on impurity distribution. In a vertical field a wide range of oxygen concentrations is possible, but, because the radial flow is reduced, it is difficult to achieve acceptable radial uniformity, compared with the results possible in the absence of a field, whereas very good radial impurity distribution is possible using a transverse horizontal field. The two magnetic field modes are distinguished principally by the large differences in their temperature distributions, and gra-

34


dients, which to a considerable degree determine the alternative product properties. Using the vertical-field conditions the increased radial temperature gradients are larger than if no field were present, whereas in the same puller under horizontal field conditions the temperature gradients are reduced, and can be much smaller than with no field. As we have previously seen, the oxygen dissolution rate is set by the wall temperature, and experience now suggests that horizontal-mode growth is more suitable for the production of controlled lowoxygen silicon. While both modes sharply reduce the growth striae, produced by thermal fluctuations in the melt close to the interface, which are a feature common to all zero field growth, again it is the low-temperature gradient beneath the crystal, available under transverse fields of around 0.25-0.3 T which permits growth rates some 50% higher than with no field, yet maintaining the correct interface shape required for dislocation-free growth. A more flexible use of magnetic field which minimizes the undesirable characteristics of the vertical magnetic field is the use of “cusp” magnetic field. A CZ system with cusp magnetic field (Hirata & Hoshikawa, 1989) uses two sets of coils (often superconducting) co-axially with the crystal, which are energized in opposing directions. In this arrangement, the symmetry plane between the two coils can be placed at the melt-crystal interface throughout the growth process. The resulting cusp field effect is such that there is orthogonal component on the crucible wall which damps the erosion effect (to dissolve oxygen) by the melt flow, while there is no orthogonal magnetic component exerted on the melt surface (free-surface evaporation is not retarded). The net effect is a decreased oxygen level. On the other hand, when the melt surface is located away from the symmetry plane of

the cusp magnetic field, the melt surface will be subjected to the effect of orthogonal magnetic components, resulting in reduced oxygen evaporation and increased oxygen level (Series, 1989). In summary, Czochralski silicon technology is indeed very complex. A large number of highly interactive, adjustable parameters are available in the thermal design of the core furnace, its heater and baffles, and in the aspect ratio of the melt; in the mechanical movements to position, lift and rotate the crucible and crystal; and now in the magnetic conditions, in mode choice, and field strength and position. It is, however, precisely this flexibility in design variables and growth control, not available to the same degree in float zoning, that gives the Czochralski technique its power to address the product requirements.

1.5.5 Evolution in Czochralski Crystal Diameter As semiconductor technology continues to advance, the IC design rule is approaching 0.1 ym by 2006, if not earlier. In parallel with the design rule decrease, the increased circuit design complexity results in increased chip size. This has been the major driving force for increased wafer diameter for the last twenty five years, that is, to increase the required number of IC’s per wafer in order to reduce IC manufacturing cost. In 1960, wafer diameter used was 1” when the IC was in its infancy. Today, 200 mm is the main stream, which was initiated in the late 1980s. In 1995, the development of 300 mm wafer was initiated, targeting for IC manufacture in 0.18 ym design rule generation. Concurrently, Japan has launched a project for development of the 400/450 mm wafer era technology. In the up-scaling of the wafer diameter, in the 300 mm-450 mm diameter range, the most significant techni-


cal challenges are in the crystal growth. The growing process is far more complex than in the past. Unlike small diameter crystals, the dislocation-free as-grown yield will dominate the cost of the manufacturing of 300/450 mm diameter wafers. To economically produce large diameter silicon crystals, one needs to employ large charge size for growing a long crystal. A charge greater than 200 kg for 300 mm diameter crystal growth or 400 kg for a 400/450 mm crystal is necessary At this melt size, thermal convection is severe. The temperature fluctuations associated with the thermal convection will make initial thin neck growth more difficult. The thermal convection would also result in higher oxygen incorporation in the crystal. It is common to apply an external magnetic field, such as a cusp magnetic field, to the large melt to reduce the thermal convection effect and to reduce the melt-crucible interaction. When growing a CZ crystal weighing 150 kg or more employing a thin neck growth to achieve the initial dislocationfree seed, one must consider the risk of fracturing of the thin neck due to the crystal weight exceeding the fracture strength of silicon. An estimate based strictly on fracture strength in tensile mode (Kim & Smetana, 1990) predicts that the crystal weight limit is about 200 kg when the smallest neck is - 4 mm in diameter (a targeted neck diameter commonly used for necking). However, for 400-450 mm diameter growth, the crystal weight needs to be in the range of 400-500 kg to be comparable with the 200 mm crystals in production economics. At this weight level and to avoid neck fracture, the “Dash Neck” diameter needs to be larger than 6 mm, a diameter that is difficult to achieve dislocation free structure in the necking process. One of the solutions is to devise a “crystal suspending system” to help support the crystal weight through a

35

“subsidiary cone” grown following the dislocation-free neck is established (Yamagishi et al.). Another crystal weight related problem is the “creep” phenomenon at the high stress concentration region at the “plastic temperature”, >900 “C. The intersection of the crystal neck and “crown” is such a region (Chiou et al., 1997). When the stress from the crystal weight (plus the meniscus column and surface tension in the melt) exceeds the critical resolved shear stress for slip, slip dislocations will be generated and propagate down the crystal, along the slip systems, (llO)/(lll). Two possible consequences may result. If the slip exits the crystal, the dislocation-free growing process will not be interrupted, but the crystal length above this point will not be useful. If the dislocation reaches the growing solid-liquid interface, the continued growth will not be dislocation-free. The latter case occurs when the crystal length, L, is less than L = R . Tan 54.74”, where R is the radius of the growing crystal. Besides weight related problems, the large diameter silicon requires growth rate reduction as well. As the crystal diameter is increased, dissipation of the massive latent heat of solidification from the freezing interface becomes more difficult, since the heat transfer paths are longer. This can be understood from the heat balance shown in Figure 1-12. In silicon crystal growth, a sufficiently high growth rate is essential to maintain a steady crystal growth in order to maintain the dislocation-free structure. One can enhance the growth rate by enhancing the heat transfer rate via increased crystal surface cooling. Radiation shields have been used to reduce the radiation effect from the melt and from the heater (von Ammon et al., 1995). However, by doing so, the thermal gradient is increased resulting in more curved isotherms and interface shapes, enhancing the condition for higher

36


thermal stress. The stress induced slip can occur causing structure loss. In the severe case, the high thermal stress can cause crystal cracking. Eventually, the growth rate issue may be a limiting factor in determining the maximum diameter for CZ silicon. The increase in diameter has a profound effect on the crystal’s cooling rate and, therefore, the microdefect formation. The formation and density of grow-in microdefects, the so called D-defects (family of defects by vacancy clusters) and A-defects (interstitial clusters) are functions of growth rate and post-solidification annealing temperatures. (Umeno et al., 1997, Voronkov et al., 1997) Analyses show that an increase in diameter increases the dwell time of crystal in 900-1 100°C range (von Ammon, 1996). Slow cooling reduces D-defect density. Therefore, the diameter increase causes the reduction in D defect density. The D-defects on wafer surface cause oxide thinning and its density is directly correlated with the defect density in the GO1 (Gate Oxide Integrity) test. Therefore, it appears that the diameter increase certainly has a positive effect on the microdefect density. It appears that large diameter crystals grown today and in the foreseeable future will contain either vacancy or self-interstitial type microdefects, or both. A crystal growth process for growing defect-free materials is not yet available. In the CMOS processing employing thin gate oxides, < 5 nm, and shallow junctions, clusters of vacancy-type or interstitial-type defects are undesirable. Therefore, IC makers may resort to epitaxial wafers or hydrogen annealed wafers (Kubota et al., 1994). The epitaxial silicon layer has higher quality than the melt grown bulk silicon. The layer is essential free of interstitial oxygen, carbon and microdefects, and lower in surface particle and metal contamination than the bulk wafer. The DRAM manufacturing

group has been the largest user of the polished wafers. The microdefect problem associated with the bulk wafer may drive a significant fraction of the DRAM manufacturers to switch to epitaxial wafers. Two possible epi structures exist: plp’ andp-lp-. The former has also been popular with the microprocessor and ASIC manufacturers, the advantages including improved gate oxide quality, internal gettering, latch-up immunity, etc. The p-lp- approach is useful to “mask” the microdefect problems in the polished p- wafers. The microdefects, neither dislocation loops or voids are not found to extend into the epitaxial layer during the epitaxial growth (Shimizu et al., 1997).

1.6 Wafer Preparation Silicon semiconductor devices are mostly fabricated on polished wafers or epitaxial wafers. Thus, the first step in device fabrication is the preparation of mirror polished, clean and damage-free silicon surfaces in accordance with the specifications. As the design rule of device fabrication advances into the deep sub-micron region, the device processing and performance are more sensitive to starting material’s characteristics. The requirements of the geometrical tolerance of the polished wafers as well as their bulk characteristics are becoming more stringent. The polished wafers are prepared through the complex sequence of shaping, polishing and cleaning steps after a single crystal ingot is grown. Although the detailed shaping processes vary depending on the manufacturer. The processes described below are generic in nature. Newly introduced processing technologies will be discussed where appropriate. Figure 1-19 is a flow chart showing a generic wafer shaping process.

1.6 Wafer Preparation

37

Figure 1-19. Flow chart describing generic steps involved in wafer preparation employing modern technologies.

Wafer Shaping Process Crystal Growth Ingot Surface Grinding, Orientation Flattening or Notching Wafer Slicing by ID or Multiple Wire Saw Edge I Notch

Donor Anneal (P- only)

4

v

H

Final Cleaning and Packaging

v

I

The single crystal ingot is first evaluated for crystal perfection and resistivity before it is surface ground to a cylindrical shape of a precise diameter. Flat(s) or a notch with preferred crystallographic orientations are ground on the ingot surface parallel to the crystal axis. The primary flat or notch, for example, is positioned perpendicular to a (1 10) direction on a (100) wafer, is used for alignment of the wafer in the device processing with automated handling equipment. The primary flat, or notch, also serves as an orientation reference for chip layout, since devices fabricated on wafers are crystallographically oriented. The existence of secondary flat on the wafer, shorter than the

primary, is used to identify the wafer surface orientation and conductivity type (SEMI International Standards).

1.6.1 Slicing The slicing operation produces silicon slices from the ground ingot. Slicing defines the critical mechanical aspects of a wafer, such as thickness, taper, warp, etc. The slicing is commonly carried out by an inner diameter (ID) circular saw, Figure 119a, after the ingot is rigidly mounted to maintain an accurate crystallographic orientation as previously determined by X-ray diffraction. The ID saw uses a thin stainless

38


steel blade bonded with diamond particles on the inner edge of the blade. Recently, the development of multiple-wire saws has enabled the silicon slicing to result in high throughput and superior mechanical properties such as significantly reduced bow and wrap. Figure 1-19b shows a schematic of a multiple-wire saw. In this arrangement, parallel, equally spaced and properly tensioned stainless steel wires spun across two pulleys are part of a single stainless steel wire winding through a complex set of pulleys. Cutting of multiple slices results when the ingot is pressed against the traveling wires under injection of slurry. Although the cutting rate is much slower than the ordinary ID saw (ordinary ID saw is 80-100 times higher rate), as many as 300 slices can be produced simultaneously. Besides higher throughput, the multiple-wire saw has other major advantages over the ID saw. Slicing by the multi-wire is actually the result of low speed grinding/lapping action by the slurry. Improved bow, warp, TTV, and taper are much easily obtained than with the ID saw. In addition, the slow lapping action by the moving wire results in small kerf loss which affords more slices per inch of ingot. It is shown that the kerf size loss is very close to the diameter of the wire used. The multiple-wire saw offers material savings (reduces kerf loss by 30% compared to the ID saw), increased productivity and improved wafer mechanical properties. It has

Silicon Ingot

Crystal Ingot

been used for slicing 200 mm and 300 mm diameter wafers and is expected to be used for the future “diameter generations”.

1.6.2 Edge Rounding The square edge of sliced silicon wafers is rounded by an edge grinder. The roundededge wafers greatly reduce mechanical defects, such as edge chips and cracks induced by wafer handling. Edge chips and cracks can serve as stress raisers which facilitate the onset of wafer breakage or plastic deformation and slip dislocations during thermal processing. In addition, the rounded edge eliminates occurrence of epitaxial crown (thicker epitaxial layer at the wafer edge) in the epitaxial deposition process and pile-up of the photoresist at the wafer edge. The shape of the rounded edge usually follows an industrial standard (i.e. SEMI standard) in which the edge profile fits within the boundary of a standard template. However, variations from the “standard” exist. In some applications, the rounded edge is modified to be more “blunt” in order to facilitate the chemical mechanical polishing (CMP) operation for inter-level dielectric planerization. In this case, the “blunt” edge supposedly prevents the wafer from slipping out of the template during polishing. Other applications require more “rounded” edge shapes for increased strength. Often, a compromise on the edge profile is required.

f’x ire

ID Saw

Multiple Wire Saw

Figure 1-20. Schematics showing the traditional ID saw and recently developed multiple-wire saw for silicon wafer slicing.


1.6.3 LappinglGrinding The lapping of the silicon slice surface takes place when the slice is ground between two counter rotating cast iron plates in the presence of an abrasive slurry, usually a mixture of submicron-sized alumina or silicon carbide particles suspended in a solution. The purpose of lapping operation is to remove the non-uniform damage left by slicing, and to attain a high degree of parallelism and flatness, both global and local. In fact, post-lapping slices possess the best mechanical characteristics in the entire shaping process flow. The subsequent mirror-polishing operation generally degrades the flatness characteristics attained by the lapping operation. However, lapping with slurry also introduces fresh damage to the silicon surface which requires subsequent chemical etching and chemical-mechanical polishing for removal. Chemical etching and CMP of the silicon surface degrades the wafer flatness. To circumvent this situation, surface grinder (with a precision grinder bonded with diamond particles) on both sides of the wafer is employed to achieve surface flatness with reduced surface damage. With reduced surface damage, the need for chemical etching and CMP is also reduced and good mechanical properties may be retained.

1.6.4 Chemical Etching Chemical etching of the slices is done to remove mechanical damage induced during the previous shaping steps - ingot surface grinding and slicing . The etching can be carried out by either an acidic solution or a caustic etchant. The acidic system is mostly based on HN0,-HF system (or with modifiers such as acetic acid (Robbins & Schwartz, 1960). The surface material removal is the result of two-step reactions.

39

The Si surface is first oxidized by HNO, to form S O 2 , followed by its removal by HF. The acid etch produces a smooth and shiny surface. However, since the reaction is exothermic, temperature control is critical in order to maintain uniform etching. Caustic etching uses a alkaline solution (Moreland, 1985), such as KOH, with certain stabilizers. The KOH etch offers a uniform etching rate, but produces a rougher surface than the acid etch, since KOH etching rate is crystallographic orientation dependent. Chemical etching of the slice may be repeated after subsequent mechanical operations such as edge rounding and lapping/surface grinding to remove mechanical damage.

1.6.5 Polishing Polishing is accomplished by a chemicalmechanical polishing process involving a polishing pad and a slurry. The polishing slurry is usually an alkaline colloidal solution containing sub-micron-sized silica particles. While CMP is used to remove surface damage and to produce a mirror-finished surface, it also degrades the wafer flatness achieved by lapping/grounding. Therefore, it is essential to optimize operational parameters so as to minimize the polishing time and flatness degradation. Double-side polishing (CMP on both front and back surfaces simultaneously) has been found to result in superior flatness than the single side polishing arrangements. The combination of surface grinding (on both sides of the wafer) and double-side CMP has shown to result in superior total indicator reading (TIR), total thickness variation (TTV) and local flatness. Such an approach is becoming a standard manufacturing process for large diameter wafers (2300 mm) preparation. The wafer preparation via mechanical methods (i.e., grinding, CMP etc.) has its

40


limits in the degree of flatness that it can achieve. To supplement and to fine tune the local topography for further improvement in local flatness, tools such as plasma assisted chemical etching (PACE) (Bollinger & Zarowin, 1988) have been developed. Such a tool employs a spatially confined plasma with a scanning mechanism to allow material removal to be controlled as desired over the wafer surface. The PACE utilizes low energy neutral ions (i.e. W

0 3 L

c

2 Depth (prn)

5

d

Figure 1-22. X-ray topography of a sawn and step-etched slice. Reflection: [ 2201, Mo K, radiation.


43

Initial, as sawn, values 80 - 120 s

u L m

P 20 a

E

57

0

0

5

10

15

20

Depth o f etch per side (prn)

25

30

Figure 1-23. The dept of damage beneath a sawn surface measured by the etch/X-ray rocking curve technique (AW = W , - Wc).

30 min, examined by interference contrast microscopy in Fig. 1-24a, reveals the { 1 1 1 } slip lines, while the topograph in Fig. 1-24b shows the stress relief by plastic flow, creating an array of long dislocation loops on slip planes on either side of the scratch. Thus, in the presence of differential damage between two surfaces a slice bows - hollow on the least damaged side. If the bow, B, measured as the maximum depth of the hollowed side of the slice, diameter d, is taken to have a uniform radius of curvature, r = d2/(8B), then the relation between bow and strain (Tamura and Sunami, 1972), is given by &=--

16 tsi B 3 d2

At temperatures below around 500 "C elastic deformation leads to brittle fracture as &>5x103, at a stress in the silicon > lo9 N m-2. At higher temperatures, the elastic bending gives way to plastic deformation as the stress is applied, shown in the plot of Fig. 1-25.

Figure 1-24. Surface damage in silicon. Annealing of an abraison scratch in a [ 111 ] orientation polished slice (1 100°C for 30 min]. (a) Interference contrast microscopy revealing slip relief along { 11 1 ] planes. (b) X-ray topograph showing the stress relief by plastic flow, creating a network of long dislocation loops on ( 11 1 ] slip planes on either side of the original scratch.

Since both silicon and germanium are hard brittle elements of the diamond cubic lattice structure, from the outset of the semiconductor industry diamond sawing has remained the prime route to slicing ingot material. Initially the sawblades were steel discs, slotted around the periphery, into which diamond grit particles were pressed. Such saw discs when rotated at high speed around 1500-2000rpm, with water as a coolant, cut both germanium and silicon

44


'""r

Elastic deformation

lo7

\'

10' Yield stress ( N ~ I - ~ )

well. However, to cut thin slices accurately such blades have to be thicker than the wanted slices, and this is obviously very wasteful of the crystal material. As a result, these peripheral blades were rapidly superseded by internal diameter blades. Thin high tensile rolled steel sheet is punched out into large discs with a central hole around which a band of diamond of closely controlled particle size is electroplated. This blade is clamped into a mounting frame which is stretched over an outer ring in high tension, sufficient to enlarge the central diamond saw hole towards its elastic limit, so providing a thin but extremely rigid blade, capable of very precise slicing with minimum kerf loss of material. Very considerable effort has gone into the development of the internal diameter sawing machines and blades to meet the continuing scaling up of slice diameters. When an internal diameter diamond blade, stretched in tension over an outer ring and rotating at high speed, is driven forward into silicon to saw a slice, the tension is slightly relaxed and the blade vibrates (wobbles) slightly. The ingot on one side of the kerf slot is rigid, whereas the partially cut slice on the other side of the sawblade can relax a little. As the blade edge vibrates, the diamond on its sides impacts

E\% n.

Figure 1-25. Deformation and fracture of silicon resulting from mechanical stress. Note: For silicon Y/(l - P ) = 1.8 x 10" (N m-'), and so, approximately, the stresdstrain ratio is 2 x 10" ( Y :Young's modulus, P : Poisson's ratio). Hence for example at a stress of lo8 N m-' the corresponding strain is 5 x

\

1O'O

against the ingot and slice, causing differential damage, where, on the next cut, the newly exposed ingot surface becomes the other side of the next slice. Such slices may be cut perfectly uniform in thickness but bowed, until they are etched to remove the damage before polishing, when they relax to a very low bow value. On the other hand, if a blade is mounted and run incorrectly, so that it deflects during slicing, no amount of subsequent etching can correct the ensuing permanent bow. The forces which are generated at the blade edge during sawing can be followed by mounting the ingot on a dynamometer attached to an x - y - z - t chart recorder. The forces F,, F,, and F,, measured simultaneously as the blade traverses the full diameter of the ingot, are related to the operating conditions. Typical results, looking at variable cutting rates, are shown in Fig. 1-26. Here F , is the direct loading force between the advancing ingot and blade, F , is the tangential, dragging, force along the blade periphery, and F , is the smaller, but very important, vibrational force perpendicular to the blade. At a low feed rate the saw is only in gentle contact with the silicon and free to vibrate; then, as the feed rate is increased towards its optimum, the blade is held more firmly and vibration decreases ... and on the


0.8 -

45

- 160

“ W L 0

0.6 -

- 120

-

5

-80

-

%

0

.cn

- 40

-

0.2

n 0

0.4 -

E

-E, 3

’c

L

-

“t

.g - 4

0

1

n I

2

I

3

4

I

5 Saw feed rate (crn rnin-’1

0

(a1

cn

-5-

-3

-2

-1

0

1

2

Saw blade deflection (pml

3

(b)

Figure 1-26. Damage during silicon slicing. In (a) the force measurements and bow were recorded using distilled water as the cutting fluid ( 0 Fx, x Fy, + Fz, 0 bow). The effect of replacing this by a 1% solution of polyethylene glycol (6000 mol wt.) is seen in a force F, (A) of 0.04 N, and a bow ( 0 ) of under 10 pm. Subsequently in (b) it is necessary to etch the sawn slices to reveal the true distortion associated with blade deflection. + marks the zero bow, zero saw blade deflection intersection of the two axes.

slices sawn so does the bow. Finally, as the feed rate is set too high, the pressure between the ingot and the blade begins to relax the blade tension, F, starts to rise again and the bow becomes severe. Taken further, beyond its stress limit, the blade ruptures. The role of the cutting fluid, “lubricant”, can also be studied. As an example: at such high rotation rates, around 2000 rpm, centripetal forces rapidly remove the cutting fluid from the blade edge, and the liquid film whose thickness should provide a cushion against F , is very thin. The long chain molecule polyethylene glycol both improves the streamline flow of high speed liquids and increases their viscosity, so maintaining a thicker film. Applied to silicon slicing under otherwise optimum feed conditions, the F, is halved, and the bow reduced even more. It is recognized that the slicing quality has key influence on the yield on the subse-

quent polished wafer manufacturing steps, and has major impact on the overall production cost. For ULSI fabrication, the mechanical specifications for wafers are stringent and tolerances are tight on parameters such as local flatness, TTV, thickness distribution. To improve these parameters for large diameter wafers (>200 mm) the ID saw is being replaced with multiple-wire saws as previously discussed in the section on sawing. During later device processing the slice meets several high-temperature stages in which, if residual peripheral damage is still present, the heating and cooling gradients will lead to slip, and yield losses. This is shown in Fig. 1-27. Here the transistor printout marking of rejects on-slice at Test1, matches the slip, revealed by etching the back of a slice, which had been inadequately etched after grinding. Lapping is a very different issue. While it is used after slicing to provide slices of

46


la)

(b)

Figure 1-27. Device failures from slice fabrication. The Test-1 printout on-slice of UHF transistor rejects in (a) is linked directly to the process induced crystallographic defects revealed by selectively etching the reverse back face, seen in (b). Note the high incidence of failures initiated from the periphery, particularly near to the reference flat, contributed to by insufficient ingot etching after grinding.

the close thickness uniformity necessary to proceed on to etching and polishing, to remove any saw marks, and to improve the planarity and parallelism, fundamentelly it is a retrograde process. The abrasive pressure is directed into the silicon surface. Under very low load, in hand lapping, the depth of damage generated is proportional to, but somewhat greater than the abrasive particle size (Buck and McKim, 1956). When the pressure is increased, as is necessary to achieve useful stock removal rates from commercial lapping machines, both the depth of damage, and the site density, rise steeply - under normal operating conditions to at least 3-4 times particle size. For example using a 20 pm, close particle size distribution, water classified alumina, WCA, at a load of 30 g/cm2, the damage extends to a depth of around 90 pm - worse than in the original sawn slice. Where lapping is part of the slice machining, deep etching is needed subsequently to remove the subsurface structural damage it has caused. The issue of residual mechanical damage and flatness requirements in the large slices,

of diameter 200 mm and above, required for the latest ULSI microprocessor and memory chip applications has focused attention on the lapping process and possible alternatives. The new standards of flatness in the final polished wafers are measured in hundredth of a micrometer (pm). This is needed because, in the fabrication of ULSI circuits, the lithography uses submicrometer dimensions with minimum feature sizes currently around 0.290.18 pm but decreasing and expected to be down to 0.1 ym by the year 2006. Associated with these dimensions, the thickness of gate oxides is now below 50 A, and with close tolerances of 5 a few angstroms, and is decreasing. Thus the underlying substrate surface has to be polished to display required surface micro roughness in additional to the local flatness. The requirements of the wafer characteristics for ULSI processing for the current and future design rule generations is mapped out in the National Technology Roadmap of Semiconductors (SIA, 1997). Overall, mechanical damage and its elimination play an important role in determining the wafer manufacturing process and final mechanical properties of the polished wafers.

1.7 Oxygen in Czochralski Silicon 1.7.1 The Behavior of Oxygen in Silicon The oxygen incorporation behavior in a CZ growth system is the result of dynamic balance between crucible dissolution, melt surface evaporation, thermal convection and forced convection induced by crucible and crystal rotations. Since “oxygen in silicon melt” is a dynamic system, the oxygen concentration profile along a grown CZ

1.7 Oxygen in Czochralski Silicon

crystal depends on the growing process. Although one can obtain an “effective” segregation coefficient from such an oxygen profile assuming normal freezing behavior, however, the coefficient so obtained has no relationship with the “equilibrium segregation coefficient”, k,. The k, is a physical constant related to the binary phase equilibrium of silicon and oxygen. In general, a segregation coefficient less than unity implies an eutectic phase diagram. The melting temperature of silicon containing oxygen is lower than pure silicon. On the other hand, if k,> 1, the solidus would terminate with a peritectic reaction. The k, = 1 would indicate a situation where liquidus and solidus merge, a condition not consistent with the phase rule. The k, for oxygen in silicon has been widely studied for the last 25 years. The reported values range from greater to less than unity, including unity. Ekhalt and Carlberg (1989), in their study of oxygen solubility, proposed a phase diagram in which the slope of the liquidus near Si is consistent with k, 1300 “C, disperses the precipitates and restores the absorption. However, if the temperature is held at around 450 “C, any unprecipitated interstitial oxygen present forms “thermal donors”, which cause major resistivity changes in the crystal. This thermal behavior pattern was first established by Kaiser et al. (1956) and then expanded (Kaiser, 1957; Kaiser et al., 1958). Long Czochralski crystals, which are grown over a period of many hours, slowly withdrawing into a cooler chamber, experience a different thermal history between the seed and tail ends, depicted in Fig. 1.28. The thermal history of the grown CZ silicon has profound effects on the precipitation kinetics of interstitial oxygen during the subsequent heat treatments. The oxygen precipitate gettering has been related to the reduction of leakage current yield losses of DRAM and other devices (for example, Steinbeck, 1980a, b; Lin and Moerschel, 1986). Other studies have shown device failures associated with crystal defects, either present at the start of the fabrication process or formed during it, and also linked to the oxygen status. From defect etching studies, many observers noted that where a high density of surface defect features (e.g., oxidation induced stacking faults, seen after the first furnace step) was found on one side

48


Heat losses :

formation

600 OC 7oooc

Carbon via

1

8oooc]

Heterogeneous and homogeneous nucleation

Precipitate growth Oxide precipitation condensing interstitials

L(

lzoooc~

1420OC

fault defects 0, C, in solution; high Si interstitial concentration Melt stirring and convection

f

Conduction along crystal and convective transfer from surface t o gas

/ /

High temperature radiation

-

Figure 1-28. The variable thermal history of an as-grown Czochralski silicon crystal.

of a slice, the opposite face had a very low density. In one direction, this was soon linked to residual damage remaining after slice polishing. Similar work demonstrated the relation between oxidation-induced stacking faults, the slice heat treatment temperature, and oxygen precipitation (Matsushita, 1982). Much device engineering research was explored the generation and suppression of oxidation-induced stacking faults during fabrication (Stimmel, 1986), but to use bulk silicon it is necessary to understand the basic precipitation mechanism.

1.7.2 The Precipitation of Oxygen in Sqicon In normal CZ growth processes, the interstitial oxygen incorporated during solidification is on the order of 10'8/~m3. This oxygen concentration is above its solid solubility limits at the subsequent thermal processing temperatures, i.e., the oxygen is supersaturated. The kinetics of the precipitation varies depends on the thermal history, the oxygen concentration and degree of oxygen supersaturation and heat treatment temperatures. Research into bulk crystallization from liquids, to produce, for example, fertilizers and salts, has contributed much to nucleation concepts, and in particular the particle


of critical radius rc. In a supersaturated liquid, or solid, at the outset tiny atomic clusters form and redisperse in a highly dynamic situation, but some merge and grow, until, reaching a certain critical radius, they become stable, and from then on will not redissolve. In such a process there is an initial incubation period during which sufficient nuclei reach rc, then faster precipitation, which dies away as the equilibrium solubility is approached. Many systems exhibit this behavior, including the solid state precipitation of oxygen in silicon, where at 750 "C, the process has still not reached equilibrium after over 1000 h - solid state reactions are very slow. In this approach it should be expected that the nuclei formed by other impurities present will affect the initial nucleation induction step. Thus in the silicon case, the distribution of oxide precipitates across a slice after heat treatment closely maps the grown in carbon distribution shown in Fig. 1-11 (Wilkes, 1983), and also influences the actual precipitation kinetics (Kishino et al., 1979; Craven, 1981; Shimura et al., 1985; Barraclough and Wilkes, 1986). After nucleation, the main precipitation process reduces the bound interstitial oxygen concentration, developing different numbers and sizes of particles according to the temperature employed. A simple model can be used to predict the qualitative behavior correctly, and provides a basis for understanding the theoretical approach. Suppose two similar, adjacent, samples of the same impurity content, and with the same high background nucleation site density, are annealed for a long time, but at different temperatures in the supersaturation range. (1) In the sample heated at the high temperature the supersaturation driving force for precipitation is low, whereas the

49

diffusion rate of oxygen through the silicon is high. Once a few particles exceed the critical radius, rapid precipitation reduces the oxygen concentration, leading to the formation of a low density of large particles, making use of only a few of the available nucleation sites. (2) Conversely, in the sample heated at a low temperature, by the same reasoning, the supersaturation is high, but now the diffusion is low. The second phase must precipitate, but, since the oxygen only moves slowly and through a short range, a high density of small particles is predicted, making use of many of the available sites. (3) Since the native oxide film on the surface of the silicon sample is effectively a particle of infinite radius, present at time zero, and needing no incubation period, the supersaturation-diffusion model provides a simple and obvious explanation for the existence, close to the surface, of denuded zones, free of any precipitation. From the start of the heating process, oxygen close to the surface can diffuse out into the native oxide layer, so reducing its concentration and inhibiting precipitate formation in this region. The depth of this denuded zone is expected to be of a similar magnitude to the distance between particles in the bulk - deeper when formed at a higher temperature, but very shallow from a low temperature anneal. Again this is as observed in practice. In a quantitative approach, the mathematics of diffusion-limited precipitation (Ham, 1958) have been applied to the case of oxygen in silicon. The starting concentration of bound interstitial oxygen, C,,is assumed to be uniform. After a short induction period

50


small precipitates are formed, whose density, N , remains constant throughout the remainder of the process. The particles are assumed to grow by diffusion with a spherical shape, and a common radius, ro(t),small compared to the interparticle distance, and taken to be a constant corresponding to the final value r,, at t + 00. The particle are a form of silica containing oxygen at a concentration Cp,while that in the matrix close to the particle is C,,,the equilibrium solid solubility at the temperature chosen. The Wigner-Seitz approximation replaces the cubic cells around each particle, accounting for the total volume, by equivalent spheres of radius R, defined by (4/3) n R3 N = 1. The oxygen concentration profile as a function of position, and time, C ( r , t ) can be represented by a Fourier series:

n=O

. exp

(-5)

In this result An has the dimensions of inverse length, and can take an infinite number of discrete positive values, which are the required solutions. Expanding this in a power series for small values of the argument gives

a; D

1

(1-1 1)

R3 3 D ro

(1-12)

2, =-

and 2, =-

If a particle does not nucleate, r, = 0; there is no oxygen diffusion, and the supersaturation is maintained indefinitely. Normally, after an initial transient, the first term of the Fourier series in Eq. (1-7) dominates when

r

(1-13)

satisfying the boundary conditions C = C,, at r = r,, and where zn is the relaxation time constant. Fick’s diffusion equation in spherical coordinates may be written

while the requirement that there be no net oxygen flux across the outer sphere boundary is defined by

The constant A, ;30 has the dimensions of concentration and a value somewhat less than Co- C,,. The oxygen distribution so described is essentially uniform, with a value slightly less than C,, throughout the diffusion volume, except in a small region of radius about 5 ro, around the particle, in what may be described as a random-walk - well model, as shown in Fig. 1-29. Further manipulation of the equations leads to two important expressions: 113

(1-14) and

Differentiating Eq. (1-7) with respect to r and t and substituting into Eq. (1-8) leads to the core expression given by Ham: tan [&(r-r,,)] =

anr ,

r =R

(1-10)

If it is reasonably assumed that the oxide is close to Si02 in its composition, then a

51


(SANS) to validate the theoretical model (Livingston et al., 1984), as shown in Fig. 1-30.

lo4

I

I

I

/'

!

I

'\

I

I

Temperature IOCI 1100 1000 900 800 700

/'11°"

I

1

Figure 1-29. The random-walk - well model of diffusion limited precipitation.

loe 107

Only within a region of about 5 x the particle radius does a diffusing oxygen atom become trapped to a particular site and the number of particles formed is strictly defined.

value can be assigned to Cp. The values of C,, C,,, and the relaxation time constant, ,z, are obtained from the infrared absorption measurements used to follow the precipitation process (Binns et al.; Newman et al., 1983a; Wilkes, 1983). Hence, values for the particle density, N, and its radius, Y, can be obtained at various annealing temperatures, based solely on kinetic data. This can then be compared with direct measurements obtained from integrational etch pit counts, and scattering. By near infrared transmission the optical scattering from the large particles formed by high temperature anneals can be used to calculate Nand r. Similarly, the very small particles, with radii less than 100 A, can be measured by small angle neutron scattering

104/T 1 K - l )

Figure 1-30. Oxygen precipitation in silicon. The particle radii and their corresponding number densities, based on the four methods shown, all assume spherical geometry. However, in the random walkwell theory the particle shape does not significantly affect the overall data given. The symbols are: 0 radius derived from kinetics, n radius from etch pit measurements, x radius from neutron scattering, + radius from optical scattering.

Figure 1-31. Direct lattice image of a platelike oxide precipitate in silicon. Finlike features extend above, and probably below, the main (100) habit plane. Sample annealed at 750°C for 431 h.

52


The analysis of SANS results also provides information about the shape of the particles, which has recently been allied to high resolution transmission electron microscopy, to reveal platelet precipitates, shown in Fig. 1-31 (Bergholtz et al., 1989). The total assembly of particle radii from these various techniques, plotted against reciprocal temperature in Fig. 1-30, shows a remarkable coherence of results, in spite of the different nature of the experimental methods and approximations involved, and the diffusion-limited precipitation theory underpins the qualitative model set out earlier.

1.7.3 Thermal Donors and Enhanced Diffusion The problems surrounding the understanding of thermal donors, their formation, and behavior, are aggravated by the lower temperatures involved, 350-500 "C, in any kinetic study, and by the complexity of their structure, where work suggests that four interstitial oxygen atoms are involved in a TD center (Newman and Claybourn, 1988). Following the oxygen precipitation kinetics at low temperatures requires a more sensitive method than infrared absorption; this is provided by the technique of the relaxation of stress induced dichroism (Corbett and Watkins, 1961), which has been applied to the silicon-oxygen system (Benton et al., 1983; Newman et al., 1983b). In this procedure, a small silicon rod sample, cut with a [ 1111 axis, is heated at a temperature of 450-5OO0C, under a high pressure applied along the axis; subsequently the sample is cooled while still under stress. As a result of diffusion while stressed, the number of bound interstitial oxygen atoms, IZ,, linking matrix silicon sites in the [l 111 axial bonds becomes less than the number, n2,in each of the bonds in the [Ill], [Till, and [lIi], directions. If now

linearly polarized 9 pm infrared light is used to measure the oxygen absorption coefficient, in directions parallel and perpendicular to the stressed [ 1111 axis in the samples, the following relations apply: (1-16) from which

(a,- all)= const . (n2- n l )

(1-17)

When such a prepared test sample is then annealed at some chosen temperature but under no load, further diffusion allows the oxygen to return towards a random distribution, relaxing the induced stress dichroism, by a first order kinetic process, with a relaxation time constant z*.Using a normalized dimensionless parameter (a,- ali)la, the constant z* is given by the slope d [log (a,-all)/a,]/dt, and is equal to z/8 where l/zis the fundamental frequency of a single diffusion jump at the temperature concerned. The diffusion coefficient then follows from the simple relationship that D = @(8 z),where a. = 5.42 A, the lattice constant of silicon. An early problem in the understanding of thermal donors arose from their speed of formation, requiring only a short heating time to reach an equilibrium resistivity. The role of lattice defects in this process is now recognized to be a major contributor. In their stress dichroism study, Benton et al. (1983) observed that, if the silicon was given a 900 "C/2 h heat treatment followed by quick cooling to eliminate donors (but thereby freezing in excess silicon self-interstitials) before going into the stress dichroism procedure as described above, the value of the diffusion coefficient, D , was enhanced by nearly two orders of magnitude. Another way to alter the intrinsic defect balance in silicon is by irradiation. Newman et al. (1983 b) used 2 MeV electrons onto a

1.8 Gettering Engineering

stressed silicon sample target held on a water-cooled block at well below 60°C. After irradiation the 9 pm signal was lowered, while the generation of oxygen- vacancy ( 0 -V ) A-centers was measured by their infrared absorption at 830 cm-’. On subsequent relaxation, the induced dichroism now decayed exponentially - with D several orders higher. Oxygen can also trap mobile silicon self-interstitials, to form an (0-1) center, with absorption at 935 cm-’. Tin is an efficient trap for vacancies in silicon; as-grown Sn-doped crystals have similar (0-I) center concentrations to undoped silicon, but substantially lower (0-V) A-center levels, and in this material the relaxation of stress dichroism is retarded by a factor of approximately 6. Involvement of both vacancies and interstitials in this diffusion was proposed by Gosele and Tan (1983). A simplistic view of a single jump could be that either oxygen traps a vacancy to form an Acenter, which then intersects a self-interstitial, or, alternatively, an (0-1) center is formed, which then traps a vacancy. The reality is more complex than this. Enhanced diffusion is seen after metallic contamination by copper or iron. Carbon enters into a number of low temperature centers with oxygen and silicon, and as nucleation sites for self-interstitials (Davies, 1989). Free electron effects have been used to provide an explanation for dopant concentration-dependent thermal donor kinetics (Wada, 1984; Wada and Inoue, 1986); while in the precipitation of oxygen in heavily doped, n+ and p+, silicon, Bains et al. (1990) have observed both enhanced (p’) and retarded (n+) precipitation, which they also link to the free electron model. Finally the thermal donor formation in p-type, 0.3 S2 cm, material at 450°C is accompanied by the simultaneous loss of substitutional boron (Newman and Claybourn, 1988). Overall, while the diffusion-limited

53

precipitation model provides a sound basis for understanding the behavior of oxygen in dislocation-free silicon, which is applied in the “crystal engineering” discussed next, there is still much to be learned about the detailed mechanism of enhanced diffusion and thermal donors.

1.8 Gettering Engineering In the preceding sections of this chapter, reference has been made at various points to the ability of defects to act as gettering sites, sinks, for fast diffusing impurities. Also the serious deleterious effects of such defects, where they intersect device structures, has been emphasized, In addition the very slow nature of solid-state oxygen precipitation, seen above, has to be overcome if any use is to be made of such bulk precipitates. The controlled application of external surface mechanical damage (extrinsic gettering), and internal bulk oxide particles (intrinsic gettering) is now addressed.

1.8.1 Extrinsic Gettering in Silicon Mechanical damage in a silicon surface has to be quantified in both density and depth, where as seen in Figs. 1-22 and 1-23, only a few damage sites extend to any great depth. Since etch rates are a function of the intensity of damage, they fall rapidly during the initial stages of etching, so it is very difficult to leave a well-controlled residual damage level on the back side and achieve the required slice thickness tolerances by trying to limit the etching. This also leaves more to be polished off the front surface. What is required is to create intentionally a high density of relatively shallow lattice disorder, whose associated stress relaxes into stacking faults and dislocation loops early on the device thermal processing, to

54


provide a high gettering capacity. The lattice distortion around the dislocations sets up strained regions, the actual gettering sites, which, in accommodating the diffusing impurities, relax further into stable lower energy atomic configurations. There are several controlled backside damage options available from polished slice suppliers, aimed to match the individual device processes: MOS, bipolar, etc. The damage is reinserted starting from well-etched slices. One method, widely used, employs a high adjustable-pressure water jet system, commonly used at around 1000 psi (=70 bar), which contains fine ground silica of well-defined particle size (about 1 pm). The grades of damage generated by the impingement of this jet on slices traversed beneath are achieved by varying the pressure, number of jets, and the traverse speed. Afterwards the front surface is polished in the normal way. Typical site densities obtained by this treatment range between 5x103 cmP2 to 5x107 cm-2. An example of a higher damage level slice, before and after treatment, is shown in Fig. 1-32, while the rocking

Figure 1-32. Extrinsic gettering by silica-high pressure water jet treatment. Note the well-etched surface to remove uncontrolled damage prior to treatment, and the uniformity of mechanical damage sites generated (SEM photograph).

curve broadening from this process is low to moderate: AW = 10” to 30”. (Note other values: deep-etched slice 0” to 4/8”, sawn slice 80” to loo”, lapped slice AW> 120”.) Lighter damage is most suitable for MOS device processes when, during the first oxidation at around 1000-1 100°C, stacking fault gettering sites are formed on the treated back surface at a density of around lo5 cmP2, which has a negligible effect on the subsequent mechanical behavior, warp, etc. However, as device feature sizes continue to shrink, there is strong emphasis on reducing both the maximum temperatures, and the total thermal inventory, used in fabrication. At temperatures below 1000°C the stacking fault generation is more complex and influenced by the oxidation ambient (Claeys et al., 1981). Again, if the damage is too light, instead of forming getter sites on heating, a large proportion may be annealed out. This is seen when first stage polished surfaces, with some submicrometer damage, are compared by etching to reveal defects before and after an 1100°C thermal cycle, when most of the damage sites disappear, and too low a stacking fault density results. The gettering performance, extrinsic or intrinsic, is monitored by etching the front polished surface, in which the device structures are fabricated, to reveal point defect sites: S-pits - shallow saucer etch pits, or haze, which are known to be related to the presence of heavy metal impurities, to low carrier lifetimes, and to emitter-collector leakage, which are all detrimental to yields. Again where the device process involves a number of high temperature stages, the extrinsic gettering performance gradually falls, and a higher initial damage level is necessary to counter this. For bipolar applications the same rules stand, but now the process employs higher temperatures, up to 1200 “C, where shallow


damage sites are more easily annealed out, and gettering performance falls more rapidly through the successive high-temperature stages. While damage depths around 1-1.5 pm may be adequate in an MOS process, bipolar conditions can demand 24 pm, and even then the efficiency may be lower. Alternative approaches for inserting the mechanical back-surface damage, also widely used, are brush damage, or abrasive polishing, of the deep-etched slice, an example of which is seen in Fig. 1-33. By choice of materials and operating conditions (soft or hard brush, abrasive size, pressure, etc.) well-controlled products result, suitable for both MOS and bipolar applications. Finally, in a further development of extrinsic gettering, it has been recognized that fine grain polycrystalline silicon is an excellent, high temperature resistant, gettering material. Using low pressure chemical vapor deposition (LPCVD) and a silane source, in a process closely similar to that employed during the fabrication of polysilicon interconnects, a thin, 1-2 pm, layer is deposited on the deep-etched slices, at a temperature of 600-650 "C,prior to the polishing stage, which becomes the extrinsic gettering backside of the slice. Known as enhanced gettering (EG) this additional step is obviously rather more expensive to manufacture than the other routes described for providing extrinsic gettering, but its performance, particularly in the multistage higher temperature applications, such as in bipolar circuits, is superior, maintaining very low S-pit densities, and high lifetimes, as shown in Fig. 1-34. Achieving the best results in this field involves very close liaison between the slice manufacturer and the consumer device in Order to match the incoming to the specific fabrication process.

55

Figure 1-33. Extrinsic gettering by abrasive (brush) treatment: (a) and (b) show lower and higher damage, respectively. Note the well-etched underlying substrates.

56


Number o f ,oxidation cycles

Figure 1-34. Enhanced gettering by deposited polysilicon. Comparison between EG and mechanical backside damage (MBD) treatments. Material: Medium oxygen content, p-type, (100) orientation. Test: bipolar oxidation cycle - 1 100°C, steam, 2 h. S-pits: x; lifetime: orientation: 0 .

1.8.2 Intrinsic Gettering in Silicon The beneficial effects of oxygen precipitates in the bulk of a device structure, and also in the substrate of an epitaxial slice, were reported by Tan et al. (1977) and Yang et al. (1978). Now there are many papers on this topic, which, since it directly interfaces to device processing, has attracted much attention. The single stage heat treatments described in Sec. 1.7.2 are obviously far too slow to provide crystal-engineered slices tailored to meet device specifications. However, this is not the only constraint. Any useful process must make consistent intrinsically gettered slices using input silicon slices containing the varying amounts of oxygen typical of normal Czochralski growth. Earlier work concentrated on two-step processes, with a first high temperature heat treatment, followed by a second at a lower temperature, the so-called HI-LO, treatment. Typical times and temperatures used

are: 16 h at 1150°C and 6 4 h at 650°C (Yamamoto et al., 1980). While other variants of two-step treatments have been proposed, this HI-LO process shows the principles, using the models developed in Sec. 1.7.2 above. In the first step, the high temperature, 1 150 "C, anneal is in a range where the supersaturation of bound interstitial oxygen is relatively low but diffusion high; any preexisting microprecipitates near the surface tend to dissolve. Oxygen readily diffuses to the surface oxide, so developing a concentration gradient near the surface, while deeper in the bulk, precipitates start to form. In addition to conventional analysis methods, for example, by a SIMS profile on a cut section through the slice, the concentration gradient from the out-diffusion can also be measured by reheating the sample at 450 "C, to generate thermal donors from the remaining interstitial oxygen, and then making a microresistivity scan on a beveled section, to calculate the gradient profile. The results from material with a bulk value [Oil around 8 x 1017cmP3 show the surface concentration falling to around 5 x 1017 after 6 h, with a precipitate denuded zone 20 pm deep, while after 16 h the values are around 3-4x 1017 with a denuded zone up to 50 pm deep. While the interstitial oxygen content is lowered at step 1, in the following low temperature step 2 at 650 "C the supersaturation is still high and precipitate growth continues at the sites formed at step 1 but there is little added fresh bulk nucleation. The desired intrinsic gettering structure, bulk precipitates and a surface denuded zone, is achieved - but there are problems. The amount of bound interstitial oxygen precipitated by this process, and whether or not a denuded zone is formed, are a direct function of the original oxygen content, as shown in Fig. 1-35. In addition, in this plot


No denuded

E

+

2

Denuded zone I

I"

7.0

8.0

9.0

10.0

initial oxygen concentration [oil (10'~%

1

Figure 1-35. Two-stage oxygen precipitation in silicon. Thermal cycles: 1150°C, 16 h; 650°C, 64 h. Other two-stage processes exhibit similar behavior, with no denuded zone formation below an initial oxygen concentration of around 8x l O I 7 atoms/cm3.

the wider scatter of results from material of lower initial oxygen content reflects the effects of other contributory factors. For example, in the influence of carbon on nucleation, where using material of normal high oxygen content but ultralow in carbon, I), that is, less soluble in the liquid, are moved to the start end of the ingot. Provided the distribution coefficients k , are not close to 1 - a condition satisfied by Ge - this very simple process can after very few zone passes produce semiconductor purity in an ingot. A remarkable result. One can appreciate the effectiveness of zone refining from the graphs in Fig. 2-1, where the theoretical ultimate distributions for impurities having different distribution coefficients are given. Orders of magnitude improvement in purification are indicated. However, these dramatic results must only be taken as a guide since solid-state diffusion and vapor transport can reduce the effectiveness of impurity removal. 2.3.3 Problems with Specific Compounds Processing by conventional zone refining or chemical purification methods is often insufficient on its own as a means of achieving semiconductor purity in compounds. Inevitably there is some problem or problems, some difficult-to-remove residual impurity or some quirk of contamination that needs to be dealt with in an unconventional manner if the ultimate goal of semiconductor purity is to be achieved. The equilibrium distribution coefficient k , of a solute (dopant, impurity or excess component) is the ratio of the concentration of the solute in the solid, C,, to the concentration of the solute in the liquid, C,, if the phases are kept in contact for a sufficiently long period for them to come to equilibrium.

2.3 Purification

Initial concentration

-20v / k =

0.01

I

-24 "V

Length solidified

Figure 2-1. Theoretical ultimate distributions for dopants having different distribution coefficients (k) after multiple zone refining passes in an ingot where the zone length is 10% of the ingot length. It is assumed that there is no back reflection of dopant from the freezing of the last zone length. The results highlight the potential of zone refining (see Pfann, 1966).

In this section problems or aspects of purification will be considered which have proved to be important in the achievement of semiconductor purity of the more important compound semiconductors. It should be stressed that achieving semiconductor purity in compounds is a very demanding and generally costly process and one that is frequently underestimated. The processes of purification and the avoidance of contamination represent a continuous battle if the ultimate in semiconductor performance is to be achieved. In the case of many of the 11-VI compounds for example the presence of impurities could still be the principal problem preventing their effective development.

2.3.3.1 InSb and GaSb Indium antimonide (Hulme and Mullin, 1962) has attracted much more research and development (R&D) over the years than GaSb. Major factors in this interest are of course the device applications of the material. InSb, for example, is an impor-

75

tant infrared detector material suitable for detectors working in the 3-5 pm region of the spectrum. The low melting point of InSb, 525"C, combined with the negligible vapor pressure of Sb over its melt make InSb an ideal candidate for conventional zone refining procedures. However, the straightforward process is of limited value because of troublesome impurities, particularly Zn and Te. Not only do they exhibit anisotropic segregation (Mullin, 1962), but in the case of Te the value of its effective distribution coefficient, keff (see Sec. 2.7.5) can range from -0.5 for growth in an non[lll]direction to -4.0 for growth on a (111) facet. Thus Te would be distributed in polycrystalline material as though the effective k were some weighted mean of these values, that is, close to one. Zinc has a value of keffranging from -2.3 to 3.0. But more troublesome is its volatility at the melting point of InSb. Vapor transport of Zn above the ingot can reduce the efficiency of zone refining. This problem has been overcome by using the volatility of Zn to advantage in a two-stage evaporation and zone-refining procedure (Hulme, 1959). Zone-refined Sb in excess of that required to form stoichiometric InSb is added to high-purity In in a boat in a modified zone-refining apparatus and melted under vacuum. Both Zn and Sb evaporate from the molten charge and condense on the cooled upper surface of the outer containing tube. The excess Sb traps in the very small quantity of the more volatile Zn. After a timed period when the excess Sb has evaporated the ingot is cooled and frozen. It is then zone refined under an atmosphere of H,, a condition where the Sb has negligible volatility. The purification process is highly reproducible, resulting in the production of very high

-

76

2 Compound Semiconductor Processing

purity InSb with some 60% of the ingot having a carrier concentration less than 1 x loi4 ~ m - ~ . GaSb has not been developed in this way but it can be zone refined. The incentive to purify the material further, however, is limited by the belief that the residual carrier level, -2 x 1016 p-type carriers per cm3,is determined by fundamental aspects of the band structure of the compound. 2.3.3.2 InAs and GaAs InAs and GaAs present additional handling problems because at their melting points the As dissociation pressures are respectively 0.3 and 1.O atm. Nevertheless, considerable R&D effort has been carried out on GaAs using conventional hot wall technologies. However, a major problem encountered on zone refining GaAs has been the failure to achieve purities with carrier levels below 10I6 to lo1’ n-type carriers per cm3. This has been shown by Hicks and Greene (1971) to be due to the reaction between Ga in the liquid Ga, As melts and the silica containing vessel, which introduces a fairly constant level of Si into the ingots at about one part per million: (2-1) 4Ga(L) + SiO,(S) = 2Ga,O(v) + Si(so1n)

-

-

The problem can be overcome by using BN or graphite boats. However, the zonerefining process has generally been superseded and simplified by in situ compounding of very high purity Ga and As which are now available as a result of improvements in chemical purification methods (see Sec. 2.6.2). 2.3.3.3 InP and GaP The very high vapor pressures generated by these compounds at their melting points, some 27 atm and 32 atm for InP

and GaP respectively, makes zone refining a difficult and potentially hazardous process. The compounds can nevertheless be prepared in horizontal systems by distilling the P, into the molten group I11 element contained in a silica or BN boat. By limiting the amount of group V distilled so that the group I11 element is in excess of stoichiometry the working vapor pressures are reduced. Crystallization under these conditions has an additional advantage; there is a very much greater purification effect for impurities from group I11 rich liquids than from stoichiometric melts. The disadvantage of course is that crystallization occurs under conditions of constitutional supercooling, which can result in trapping of the impurity-rich group I11 element in the solid. With the availability of purer starting elements, formation of the compounds from stoichiometric melts is now more usual. Nevertheless, further purification is generally required, and is now often achieved by pre-pulling charges using the liquid encapsulation technique. InP having 1015 carriers/cm3 can be produced in this way. A similar purification procedure for GaP can be used. The current commercial demands on GaP are somewhat less than on InP since it is either used as doped material or as a substrate on which active layers are grown. There is clearly scope for the development of further purification procedures for both these compounds. 2.3.3.4 11-VI Compounds The state of development of the 11-VI compounds is significantly behind that of the 111-V compounds even though they have a much longer history. Many of the 11-VI compounds, especially the higher energy gap oxides, sulfides and selenides, are not accessible by melt growth tech-

2.4 Technical Constraints to Melt Growth Techniques

niques and as a consequence there is a much greater emphasis in the use of vapor growth techniques to grow these difficult compounds. Our knowledge of the use of vapor growth as a purification technology is primitive. There is no equivalent to zone refining. Hence there is a more general tendency to rely on the use of elements that have been purified chemically or by zone refining. The elements Hg, Cd and Te, components of the exceptionally well developed infrared detector material Hg, -,Cd,Te, are now available as very high purity elements as a result of multiple zone refining technologies (Cd and Te) and distillation techniques (Hg). Hence compounds of these elements are prepared in situ by direct reaction. Most of the other elements Zn, Se and S although currently available in conventional high purity form are generally not as pure as the detector materials and do not form very pure semiconducting compounds. Zone refining of the 11-VI compounds is not efficacious because of the volatility of both the group I1 and group VI elements as well as the compounds themselves. Hence there has been little development of conventional zone-refining technology for the compounds. However, a related zone-refining technology called the traveling heater method (THM) or sometimes the traveling solvent method has attracted much interest and development for the 11-VI compounds. In the traveling heater method a molten zone is moved through the ingot as in zone refining, but in THM the zone comprises a solvent of Te or Se. Thus the compound dissolves at the leading edge of the zone and crystallizes out at the trailing edge. This has two advantages. Firstly, it reduces the temperature of crystallization significantly below the melting point of the

77

compound, thus markedly reducing the vapor pressure of the components of the compound, effectively eliminating evaporation. Secondly, it provides a group VI rich solution in which impurities are exceptionally soluble, a condition which results in the crystallization of a very pure compound. Because of the reduced growth temperature it is also possible to eliminate sub-grain boundaries. The technique, however, has not yet been developed to grow large completely single crystals. The process has been exploited particularly by Triboulet (1994) and the CRNS Bellevue group for the preparation and purification of Hg, - ,Cd,Te, Hg, - ,Zn,Te, CdTe, HgTe and ZnTe, as well as CdMnTe. It clearly has scope for the preparation and purification of ZnSe and various alloys of the compounds. The potential disadvantage of the technique is that the crystallization occurs under conditions of constitutional supercooling and solvent trapping can occur and give rise to group VI rich precipitates tokether with impurities. Nevertheless it would appear that by optimizing the temperature gradients and the gradient of constitutional supercooling (see Sec. 2.7.4) the worst effects of solvent trapping can be avoided.

2.4 Technical Constraints to Melt Growth Techniques The processing of compound semiconductors by melt growth techniques both for purification and crystal growth is generally much more difficult than the processing of Ge because of constraints imposed by the properties of the materials. Some of the significant properties which lead to constraints in the use of melt growth and related processing are listed in

78


Table 2-1. Material properties of main semiconductors.

Compound

Melting point ("C)

Vapor pressure at M.Pt.(atm)

InSb GaSb InAs GaAs InP GaP HgSe HgTe CdSe CdTe

525 712 943 1238 1062 1465 799 670 1239 1092

4 x 10-8 1 x 10-6 0.33 1.o 27.5 32

ZnSe ZnTe Ge Si

1526 1300 960 1420

0.5 0.6

12.5 0.3 0.65

CRSS at M.Pt (MPa)

0.7 0.36

0.2

0.70 1.85

Table 2-1. Consideration of a wider range of properties, chemical reactivity, melting point, vapor pressure, critical resolved shear stress and ionicity are important in understanding the suitability, or more often, the unsuitability of a particular technology.

2.4.1 Chemical Reactivity Although not specifically listed in Table 2-1, chemical reactivity is an important constraint in all processing. The main problems arise from the reactivity of the molten semiconductor with the container or the gaseous environment. In this respect container materials have proved to be the dominant source of contamination for compound semiconductor melts. Vitreous silica is widely used as a crucible or boat material and is essentially stable against attack from the lower melting point materials like Ge (937"C), InSb (525°C) and GaSb (712°C). But, for higher melting point materials there is gen-

References

Muller and Jacob (1984) Muller and Jacob (1984) Van der Boomgaard and Schol(l957) Arthur (1967); Thomas et al. (1990) Bachmann and Biihler (1974); Thomas et al. (1990) Nygren et al. (1971) Mayer (1984) Harman (1967); Strauss (1971) Bassam et al. (1994); Lorenz (1967) Isshiki (1992); Strauss (1971); Balasubramanian and Wilcox (1992) Isshiki (1992); Lorenz (1967) Isshiki (1992); Lorenz (1967) Thomas et al. (1990) Thomas et al. (1990)

erally contamination with silicon due to the reduction of the SiO, by the melt, in the case of GaAs (1238°C) it is typically above the part per million (ppm) level in the crystallized material. Pyrolytic boron nitride PBN can be used to overcome this problem and is well suited to the growth of 111-V compounds since it is a 111-V also and does not appear to give rise to electrically contaminating impurities. It is however expensive. Graphite is also used since it is stable in an inert atmosphere and does not appear to directly cause electrically active doping by contaminating melts. Graphite will react with silica at high temperature, but at lower temperatures ( < 900 "C) it is a very useful material and is used as a slider boat material in liquid phase epitaxy (LPE) and as a boat material for 11-VI compounds. But, carbon can be electrically active as an acceptor in GaAs for example. It can be introduced on an As vacancy site via CO under Ga-rich growth conditions, hence the importance of removing 0, and H,O.

2.5 Crystal Growth

Another potential source of impurity contamination are the impurities such as S etc. in the graphite. These can generally be removed by vacuum heat treatment at very high temperatures ( > 1500"C). Graphite is a very useful material but since it varies in quality must be used with care. The gaseous environment is also a major cause for concern. Processing in vacuum is possible, but the volatility of the group V, I1 or VI components needs to be taken into account. This is discussed later. All the melts and compounds oxidize readily and it is vital to remove all sources of oxygen such as 0, and H,O from the source materials and the environmental gases. Pure H, or forming gas are very effective reducing agents and will remove oxides readily at temperature. Hydrogen does however react to form unpleasant poisionous 'hydrides and extreme precautions need to be taken to avoid leaks not only with pure H, but also with forming gas (N2/H2 mixture). Pure inert gases such as N, ,A or He are safer and consequentally are more frequentally used. 2.4.2 Melting Point The melting point affects the choice of crucible material, and with it the extent of chemical reaction. Also, above about 1000°C radiation fields tend to dominate thermal distribution, creating design problems and the need for radiation baffles. Also, above 1100-1200°C silica starts to soften, which generally means it needs to be supported by another material such as graphite. 2.4.3 Vapor Pressure Vapor pressure is probably the most crucial parameter affecting melt growth technologies. The long delay in the development of GaAs, InP and GaP is attributable

79

in part to the problems posed by the vapor pressure of the group V component generated on melting these compounds. Thus a melt of these materials will rapidly lose its group V component unless there is a pressure of the group V component above the melt at least equal to the equilibrium vapor pressure over the melt. Two types of technology have emerged to deal with this problem: hot wall technology and liquid encapsulation (see Sec. 2.5).

2.5 Crystal Growth The main techniques for growing crystals of compound semiconductors can conveniently be grouped into four categories: horizontal growth, vertical growth, crystal pulling and liquid encapsulated Czochralski (LEC) pulling. Although this classification differentiates the techniques by the physical disposition of the different growth processes it is very important to appreciate that each technology gives rise to different crystallization conditions which affect the quality and efficiency of production for different III-V compounds. Factors such as the ease of seeding for crystal growth, crystal shape, twinning, the effect of growth in a constrained volume, temperature gradients, visibility and the economics of production and ease of automation are critical factors in the choice of a particular technology. The suitability of these techniques for particular compounds, which are listed in Table 2-2, have evolved with time and experience. They have all been refined for particular applications and are still undergoing both research and commercial development. Their application to the growth of particular compounds will be discussed in later sections.

80


Table 2-2. General applicability of growth techniques. Technique: Compound InSb GaSb InAs GaAs InP GaP HgSe HgTe CdSe CdTe ZnSe ZnTe HgS ZnS CdS

Zone melting horizontal Bridgman

VGF vertical Bridgman

*** *** *** *** * *

P P P c*** : L*** c * :L** c * : L**

* ***

** *** ** *** ** **

Conventional vertical pulling

*** ***

Liquid encapsulation pulling

***

***

*** ***

Vapor growth P P P P P P P P

*** *** *** *** ***

*** ***

The more stars, currently the more appropriate the technique. P potentially applicable;C: conventional VGF; L: LEC VGF.

a

2.5.1 Horizontal Growth

Horizontal growth (HG) is used here to cover all the horizontal crystallization techniques. They represent a subset of the zone-melting technologies described by Pfann (1966). A typical horizontal growth arrangement is shown schematically in Fig. 2-2 and discussed more fully in relationship to the growth of GaAs in Sec. 2.6.2.The growth of a single crystal can be carried out by controlled freezing of an ingot of molten semiconductor in a boat. The singularity of the ingot is achieved either by relying on self-seeding or through the use of a single-crystal seed which initially contacts the melt. The technique is often referred to as the horizontal Bridgman technique when the ingot is withdrawn from a furnace. The furnace can of course be moved relative to the ingot and this can be beneficial in that there may be less mechanical disturbance to the ingot and the crystallization process.

In the case of compound semiconductors the main problems generally concern the need to accurately control the thermal profiles, hence the movement of large furnaces tends to be undesirable and a combination of power control and the movement of small independent heaters is generally preferred in order to carry out the crystallization process. These benefits can also be achieved by using furnaces with independently controllable windings so arranged that the thermal profile can be moved. The attraction of HG stems from its relative simplicity and ease of automation. The method can be applied readily to compounds that can be processed in vitreous silica, that is, for compounds melting at temperatures less than about 1250 "C having vapor pressures at the melting point not significantly in excess of one atmosphere. An advantage of the HG is that it can be used to prepare the compound from the elements as an ingot which can then be subsequently zone refined in the same ap-

2.5 Crystal Growth

81

T JTM,,.

/

X

Figure 2-2. Schematic of a conventional horizontal growth apparatus used for the preparation and zoning of 111-V compounds. The ingot in the boat B is contained in a sealed tube A. C is the boat used to hold the volatile component prior to its distillation into the group I11 element in A in order to form the compound. D is an anticonvection baffle and E the tube support for the thermocouples H and their support tube. F is a multiple section furnace. G is the traveling heater for the zone formation and movement.

paratus. Such an ingot can also be grown as a single crystal and even zone refined as a single crystal without taking it from the same apparatus. In situ compounding of the elements can also be used in vertical pressure pulling systems (Sec. 2.6.2), but the ability to zone refine in a horizontal system is a distinct advantage when superpure elements are not available. An important advantage of the HG technique is that its design readily lends itself to the establishment of low temperature gradients at the solid-liquid interface without creating a control problem. This contrasts with the situation in the pulling process where relatively high temperature gradients are needed to maintain control of the shape of the crystal. Low temperature gradients are extremely important in minimizing stress induced slip on crystallization and hence in minimizing dislocation formation. In the case of the HG growth of GaAs it is possible to grow low dislocation density material, typically

-

around lo2 dislocations/cm2, a factor of 100 less than currently found in routinely grown LEC vertically pulled crystals. This is very important for laser diodes based on GaAs, where even a single dislocation can readily bring about device failure. There are, however, disadvantages to the horizontal techniques. These can be of a scientific fundamental nature, such as constitutional supercooling or stress, or they can be preparation-related and involve, for example, growth orientation, contamination, or shape. One of the fundamental problems which is not widely recognised is constitutional supercooling, which can occur as a result of a nonstoichiometric melt due to inaccurate vapor pressure control. This can be especially troublesome with low temperature gradients as is analyzed later in Sec. 2.7.4. The most troublesome problems occur as a result of the contact of the melt and the grown crystal with the boat. The long

82


period of contact can be a source of impurities by reaction with the boat. Silicon as noted previously is a major problem with GaAs, but also the diffusion of impurities through the silica with the higher melting point compounds can also result in crystal contamination. Misnucleation from the walls of the container can give rise to twinning, grain boundaries and more often polycrystallinity. Also crystallization in a confined shape with materials like 111-V compounds which expand on freezing, especially if combined with localized sticking, will inevitably lead to stress, slip and dislocation formation. However, provided nonwetting surfaces are used for the containing boats and a nonconfining boat shape is used, this problem can be minimized. Most of the disadvantages are qualitative rather than absolute. They detract from the versatility and universality of the technique. In certain cases they may not be significant, such as in the case of the growth of low resistivity GaAs, for example, for especially for material which is subsequently sliced and diced for the fabrication of small discrete devices such as laser diodes. However, for integrated circuit applications where large area uniformity is crucially important HG is unattractive. Indeed the D-shape of HG ingots alone appears to have ruled them out for integrated circuit applications. Also the growth of very large cross section ingots as single crystals is fraught with difficulty. 2.5.2 Vertical Growth

Crystallization of ingots in a vertical container by the Stockbarger or vertical Bridgman techniques used to be associated with the growth of high-quality singlecrystal optical materials like CaF, . But, in the last few years the technology has been

refined and developed as a vertical gradient freeze technique for the growth of GaAs, InP and GaP (Gault et al., 1986; Clemens et al., 1986; Bourret, 1990). The relatively recent application of the VGF technique to the growth of GaAs occurred in response to the need to find a cost effective solution to the production of uniform GaAs wafers compatible with integrated circuit technology. Here there is a requirement for circular wafers having precise dimensions and very good electrical uniformity. “Conventional” wisdom would consider that crystallization in a vertical rigid container would give rise to unacceptable stress due to the expansion of the liquid GaAs on freezing. In the event this has not apparently been a problem. The growth process is fairly straightforward and is illustrated in Figs. 2-3 a and b. In the study by Gault et al. (1986), which was a development of earlier studies (see review by Bourret, 1990), the VGF growth of large diamater Gap, InP and GaAs was reported. No B20, encapsulant was used. The type of apparatus is illustrated in Fig. 2-3 a. However, it appears that for the reproducible growth of GaAs it is necessary to use a B203 encapsulant in a BN crucible (Bourret, 1990) such as that illustrated in Fig. 2-3b. The B203, which is now more generally used for InP, is not only a more effective encapsulant, making for a safer and simpler system, but the nonwetting characteristics of the GaAs melt with respect to the container wall reduce the twinning probability. The vertical gradient freeze technique involves the controlled freezing from the bottom up of a molten charge of material held in a tube-shaped vertical container. The freezing is best brought about not by the movement of the furnace relative to the tube, but by the use of a furnace comprising separate independently controlled

2.5 Crystal Growth

--A

--A

1

--

B

-B

-C

--C

--D

-D - LE

--E

--

83

F

-E

-F

--

G

.-

H

-G -H

-L --

I

-M

--J .-

.-

.-

K L

M

Figure 2-3. Schematic diagrams of crucibles used in the vertical gradient freeze technique, (a) “Conventional” VGF showing compound F, melt E and separate holder J containing group V component K at a controlled temperature in order to maintain sufficient pressure of V to avoid the dissociation of the compound. Plug B allows pressure equilibration between the crucible and the outer chamber. Loss of group V into the outer chamber is inevitable even when PG > pd and is one of the drawbacks of the technique. A, furnace; C, BN crucible; D, main containing vessel; G, seed: H, crucible support; I, gap for group V transport; J, crucible for holding V; K, source of group V; L, base support; M, holder. (b) Liquid encapsulation VGF with PG> pd; symbols have same meaning as above. B,O, encapsulant LE covers the melt and prevents the loss of the volatile component.

84


heating elements. Adjustment of the heating elements controls the position of the thermal profiles so that the movement of the liquid-solid interface can be raised smoothly to bring about the crystallization of an ingot. The technique provides two important growth conditions. It naturally lends itself to low temperature gradients, which in turn favor low dislocation densities. And, secondly, it provides an ingot of ideal shape of the required diameter. Provided the interface shape is flat or at least the growth surface is slightly convex the expansion problem on freezing does not appear to be serious and any stress can be annealed out. The main problems appear to be those involving design difficulties of the thermal furnaces, the choice of boat material, BN is generally used, and the choice of conditions which allow seeding and the growth of [IOO] crystals without twinning. The ingots are usually encapsulated with B,O, . Whether the technique will supersede the LEC technique for the growth of GaAs is an open question. This can only be effectiveiy assessed when commercially sensitive information on single-crystal growth yield comes available. 2.5.3 Crystal Pulling

The Teal and Little crystal pulling technique which was developed successfully for Ge was naturally tried for the 111-V compounds, but the problem of the volatility of the group V elements and their rapid loss from melts in the case of the arsenides and phosphides presented insuperable problems. The antimonides which have low dissociation pressures at their melting points can, however, be grown by any of the Ge-type semiconductor technologies. The crystal growth of the aluminum com-

pounds by either the horizontal or the vertical pulling techniques has never been developed because of the extreme reactivity of the A1 with traces of oxygen or water and with the silica boats. Any bulk material simply oxidizes in the atmosphere. The VP technique is illustrated in Fig. 2-4. The main factors affecting the design concern the type of heating, the crucible and the outer jacket. Heating can be by resistance heating or, for more versatility, induction-coupled R F power to a conducting crucible, generally graphite or a graphite support to a silica or PBN crucible. The outer jacket is usually silica and for strength reasons can only be used with internal gas pressures not in excess of about 2 atm. The growth of a single crystal involves lowering a seed mounted in a seed holder or chuck on the pull rod into a melt of the compound just above the melting point. After melting back a small amount of the seed, the seed-on process, the power to the melt is controlled so as to allow crystallization of the melt on the seed as it is gradually rotated and withdrawn from the melt. The shape of the crystal is controlled by the shape of the meniscus under the seed (Sec. 2.7.2). The whole process requires considerable operator skill and judgment. The growth can be automated by using a sensor to monitor the crystal diameter and provide feed back to the power control (Sec. 2.7.2). Constant diameter crystals are needed for producing standard sized wafers for device fabrication. This basic process can only be applied to the growth of compounds that have virtually no vapor pressure at the melting point. This is a very restrictive condition for the growth of compounds which generally dissociate near the melting point to some extent. In the case of the 111-V compounds and the 11-VI compounds the technology

2.5 Crystal Growth

is only really suitable for the growth of InSb and GaSb. As a consequence, considerable effort has been devoted to developing alternative technologies for the growth of compounds. Two types of technology aim to overcome the vapor pressure problem and loss of group V component. These are hot wall technology and liquid encapsulation technology. In hot wall technology the walls of the containing vessel surrounding the 111-V compounds are kept sufficiently hot to prevent condensation of arsenic or phosphorus on the walls. This requires temperatures of 600 "C or 700 "C, respectively, for the two elements. This condition is possible to apply in the case of horizontal crystal growth involving the use of a sealed silica tube but it creates serious technical problems in the case of a thermally complex vertical pulling apparatus since it requires the seals, pull rod and bearings, etc., to be heated and inert to the hot reactive component elements. Nevertheless, the problems of hot wall technology have been tackled by a variety of pulling methods with varying degrees of success. They are the syringe pulling and magnetic pulling methods, which have been reviewed by Gremmelmaier (1962) and Fischer (1970), and the pressure balancing technique, which has been proposed by Mullin and coworkers (1972). The principal problem is that of devising a pulling mechanism which prevents the volatile group V elements from being lost or from condensing of the on the walls of the system. Syringe pullers use a pull rod, generally ceramic, which is a close tolerance fit in a long bearing. Although such a seal is not perfect the loss of volatile elements can be minimized. The magnetic puller is a tour de force in which the whole ceramic pulling system contained in the pulling chamber is

-

1 0 0 0 0

-0

Figure 24. Vertical pulling apparatus for low pressure liquid encapsulation. The silica outer vessel N with viewing port J is held between end plates 0 and P. The induction heating coils couple into the graphite surround F mounted on Q. The seed A is fixed in the chuck on the pull rod K which rotates and moves through the bearing and seal L. The crystal C grows from the seed through a necking process at B and on withdrawal pulls out a layer of B,O, over its surface. Loss of the volatile group V component from the seed, crystal and melt is prevented if PG>pd.

85

-

86


kept above the condensation temperature of the volatile component. Translation and rotation are achieved by magnetic coupling to suitably sited and protected magnetic material on the pull rod. Neither syringe pullers nor magnetic pullers have achieved any significant following. They are expensive, technically difficult and not entirely satisfactory technologies. An alternative technology proposed and demonstrated by the author has been referred to as the pressure balancing technology (Mullin et al., 1972). This method overcomes loss of the volatile component up the pull rod by arranging for a liquid seal at the top of the bearing housing through which the pull rod is pulled. The inside of the BN bearing has a screw thread so that rotation of the BN pull rod causes the B,O, liquid sealant to be “wound up” the shaft and kept in the upper reservoir. The inert gas pressure in the system is kept above the dissociation pressure and through the use of a u-tube gauge internal and external pressures can be kept the same. Of course the whole of the apparatus has to be kept above the condensation temperature of the volatile components. The pressure balancing technology works surprisingly well but was not developed and exploited because of the success of liquid encapsulation technology, which has transformed the whole of 111-V pulling technology for the arsenides and phosphides. 2.5.4 Liquid Encapsulated Czochralski (LEC) Pulling

Liquid encapsulation often referred to as the liquid encapsulation Czochralski (LEC) technique is illustrated in Fig. 2-4. The liquid encapsulation technique (Mullin et al., 1965, 1968; Mullin, 1989) avoids the need for hot walls and permits the use of

conventional pull rods. It is elegantly simple. It involves the use of an inert layer of transparent liquid, usually B,O, , which floats on the surface of the melt, acts as a liquid seal and prevents the loss of the dissociating volatile component provided the pressure of external gas P, is greater than that of the dissociation vapor pressure P, of the volatile component. The encapsulant should possess additional properties. It should be immiscible with the melt and be unreactive towards it. But, most importantly, the encapsulant should wet the crystal and the crucible. Further, its viscosity and the temperature dependence of its viscosity should be such as to allow it to be drawn up with an encase the emerging crystal as a thin film of encapsulant. The latter property is desirable in order to prevent the decomposition of the hot crystal throughout the course of the crystal growing process after it has pulled clear from the layer of the encapsulant. Although many glass-like encapsulants have been tried only B,O, and related mixtures fulfill sufficiently well these characteristics. 2.5.4.1 The Low Pressure LEC Technique

For compounds that have dissociation pressures not in excess of about two atmospheres it is possible to apply the liquid encapsulation techniques using Ge-type crystal pulling chambers. For this low pressure liquid encapsulation technology it is possible to use an outer jacket of the growth chamber made of silica such as that illustrated in Fig. 2-4. Such a system would be suitable for the growth of InAs or GaAs (Sec. 2.6.2). 2.5.4.2 The High Pressure LEC Technique

Silica growth chambers are not strong enough for compounds having high dissociation pressures ( > 2 atm) and steel or

2.6 Crystal Growth of Specific Compounds

metal pressure vessels are used. Pressure vessels have been designed for working upto 200 atm. The use of such steel pressure vessels has enabled the development of a unique technology which has been applied to the crystal pulling of InP and Gap, compounds which have dissociation pressures at their melting points of -27.5 atm and -32 atm respectively. The technology effectively simplifies the growth of these compounds so that the growth process is very similar to that of Ge except that an encapsulant is used and the pulling is carried out under a high pressure of inert gas in a steel pressure vessel. The process can be viewed directly via an optical window using a video camera. An example of a research system is shown in Fig. 2-5. The technical success of the LEC high pressure technology lies in the confinement of the chemically reactive elements such as arsenic and phosphorus to the region of the melt under the liquid encapsulant and out of contact with the chamber wall, the pull rod assembly, bearings seals, etc. Indeed the pressure chamber walls and the pull rod seals need only be capable of withstanding the inert gas pressure at relatively low temperatures, thus avoiding difficult design problems. Of course, the inert gas pressure must such that P, is greater than P, in order to avoid vapor loss. The overall effect of this technology has been to revolutionize the growth of these compounds, enabling them to be grown commercially.

2.6 Crystal Growth of Specific Compounds In discussing the crystal growth of specific compounds emphasis will be given to what is considered to be the most effective technique for general application. The main considerations under discussion will

87

Figure 2-5. 200 atm high pressure LEC crystal puller developed at RSRE showing water cooled steel pressure vessel and two optical ports for viewing, one fitted with a video camera. Below the steel pressure vessel is a large chamber containing the weighing cell for diameter control.

relate to the problem areas of diameter control, dislocations, grain boundaries, twinning and purity. A factor which can be important in the growth of compound semiconductors is the anisotropy introduced by the presence of two dissimilar atoms in the zinc blende lattice (Sec. 2.7.1). Thus the [I 1 I] direction where the surface terminates with group V atoms [some authors confusingly use the reverse designation: see discussion in Hulme and Mullin (1962)l differs in properties and behavior from the [TTT]which terminates in group I11 atoms. The designation [I 11]A or [I 11]B, where A and B represent the group I11 and group V atoms respectively, avoids ambiguity. The anistropy al-

t

tt

( F , ) directions. This anistropy is impor-

tant for all compounds but is particularly important in the case of the growth of the In compounds and is directly relevant to the problem of twinning. 2.6.1 InSb

Both the HG and the VP techniques are used for the preparation of single crystals of InSb. The former method is attractive for obtaining a controlled shape and the highest purity compound whereas the VP technique is more versatile and offers scope for growth in specific orientations. The compound can be formed by heating the elements together since molten In will dissolve Sb. Hence the horizontal technique is not required for preparing the compound. However, the technique does offer scope for the growth of single crystals which can be zone refined in order to obtain very high purity uniform crystals. It is particularly important with InSb to avoid growth in the 11111 direction since (111) facet formation gives rise to the facet effect and can cause very nonuniform crystals. The HG technique also enables single crystal zone refining in growth directions, which minimizes facet formation on the growth surface at the solid-liquid interface, such as the [211]Sb or [311]Sb orientations. The technique has been used successfully for the growth of high purity p-type single crystals for detectors but requires considerable care in control of the growth conditions in order to avoid twin formation. Crystal pulling using a Ge-type puller is a more versatile technique and is probably now used more frequently but it does suffer from the same twinning problems as already discussed. The (111)Sb facet is more stable, requiring a greater supercool-

ing for nucleation and growth on its surface than the (TTT)In facet. As a result, twinning tends to be more probable on the (11l)Sb facet when it is present at the edge of crystals, where it is subject to liquid motion, exposure to the gas environment and greater temperature fluctations than when it is at the center of a pulled crystal. Thus growth in the [111]Sb direction is least likely to cause twinning even though there is a central (11l)Sb facet whereas growth in the reverse [TTTIIn direction has the greatest likelihood of twinning since there is then the possibility of the formation of three (111)Sb-type edge facets. Although growth in the [111]Sb direction offers the greatest opportunity to avoid twinning and the preparation of completely single crystals it is not to be recommended for undoped crystals or for doped crystals with dopants which exhibit a marked facet effect since the usual capricious size behavior of the central or principal (111)Sb fact can give rise to very nonuniform crystals. Growth in the [211]Sb or [311]Sb direction is usually recommended. Twinning and trapezoidal shape problems for the crystals may ensue, but by careful control of temperature gradient and temperature stability these effects can be minimized. 2.6.2 InAs and GaAs

The growth characteristics of both of these compounds are similar and both can be grown by the horizontal technique and by liquid encapsulation. However, the R&D carried out on GaAs vastly exceeds that on InAs. All the early work on these compounds involved their preparation in an HG apparatus (Sec. 2.5.1) in which As was distilled into the liquid group I11 element contained in a boat. The temperature of the liquid alloy was raised to the melting


point of the compound as the composition of the liquid approached stoichiometry. Finally the melt was progressively crystallized to form an ingot. A fairly high yield of self-seeded single crystal ingots could be obtained in this way. As an alternative a single-crystal seed at one end of the boat could be used to give controlled nucleation, but this is not a simple process and requires considerable development. Although crystals can be grown in low temperature gradients, resulting in low dislocation densities, scaling up the process to cut circular sections is not an efficient or very successful process. It is understandable then that the advantages of the VP technique using the liquid encapsulation technique has resulted in LEC becoming the industry standard for the growth of GaAs and InAs. The role of liquid encapsulation was considerably enhanced by two significant developments: in situ compounding and the production of semi-insulating (SI) GaAs without recourse to Cr doping. In situ compounding of the elements Ga and As was made possible by the introduction of steel pressure vessels. Liquid As at the melting point of GaAs 1238°C has pressure of -80 atm. Thus progressively raising the temperature of a crucible containing a charge of elemental Ga and As under a layer of B,O, in a pressure vessel containing inert gas at 100 atm to a little in excess of 1238"C is a convenient way of of forming a GaAs melt whilst avoiding significant loss of As. This in situ compounding has eliminated the need for compounding using a horizontal apparatus, a significant simplification. An additional important development was the use of BN crucibles. This had two effects, it avoided contamination by Si, which is endemic with the use of SiO, crucibles, thus giving a convenient very

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rapid processing route to the formation of very high purity GaAs charges for LEC growth. Also, and somewhat inadvertently, it provided a route to the production of SI GaAs. Swiggard and coworkers (1979) reported that GaAs prepared in BN crucibles generally had very high resistivity and furthermore the electrical properties of the product were relatively stable to the type of heat treatments needed to anneal out ion implantation damage. This was a very important result in connection with the use of GaAs for integrated circuits since SI material provided an excellent insulator on which integrated circuits could be fabricated using ion implantation. A complete explanation of the reasons for the formation of SI GaAs and for its semi-insulating character is the subject of continuing scientific debate which is beyond the scope of this article. However, the materials science of the processing of SI GaAs is important. It is evident that the SI properties are fundamentally connected with the EL 2 center, which is a complex defect involving an As antisite, that is, As on a Ga site. EL 2 is a well characterized electron trap 0.75 eV below the conduction band. In detailed studies it has been shown that the acceptor carbon combines with the EL 2 donor to control the resistivity of the GaAs. From a processing point of view a critical preparation parameter was shown to be the melt stoichiometry (Holmes et al., 1982). Thus the As atom fraction in the melt needed to be greater than 0.475 in order for the resulting crystal to be semi-insulating. This result is qualitatively consistent with the concept of an As antisite being responsible for the SI properties. The LEC technique is now a well established industrial process for the production of 2 inch and 3 inch diameter GaAs either as doped n-type material for use as sub-

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strates in the fabrication of devices such as light emitting diodes or as SI material for ion implantation and the fabrication of integrated circuits. However, in the last few years the VGF technique has assumed increasing importance as a means of preparing SI and doped GaAs crystals. As noted earlier the VGF technique involves the progressive crystallization of a molten charge in a vertical crucible by continuous adjustment or programming of the thermal profiles. It is a simple concept but its practical implementation is particularly demanding because of the lack of visibility and inability to follow exactly what is happening in the growth process and identify the onset of defect formation. This is a consequence of the use of nontransparent BN crucibles. Pressure vessels, often used for safety reasons, can also be a hindrance to visibility. Nevertheless, the quality of VGF crystals can be as good if not better than LEC crystals, indeed their dislocation densities are generally lower and more importantly uniformly distributed, a consequence, as with the horizontal technique, of the design resulting in low temperature gradients. The major unknown factors in both techniques are the average reproducible yields of single crystals that can be obtained. Yield is an overriding consideration in any growth process in the assessment of its commercial viability. One of the major factors which affects yield is twinning. The precise cause or causes of twinning in any growth run is difficult to identify, and whilst the general process is understood, what exactly brings about a twin misnucleation, be it an impurity, temperature fluctuation, foreign body or facet size, is rarely identifiable as a cause and effect relationship. As a result, trial and error development effort is normally expended in finding suitable twin-free growth conditions.

Twinning can be a serious problem in the VGF process not least because of the need to use [loo] seeds in order to meet industrial demand for (100) wafers. Here there is the additional problem of seedingon blind. The lack of visibility is a big handicap in VGF. Thus unlike the situation in the LEC process it is not possible to identify, for example, the causes of poor crystal quality and or twinning except by inference after growth. With LEC, twins are generally visible and crystals can often be regrown to eliminate them. Nevertheless, VGF is now a commercial process for GaAs and one must assume that sufficiently twin-free conditions can be developed in the growth process. General crystal growth experience would suggest that B,O, quality, boat material, interface shape and thermal stability would need to be carefully controlled. Indium arsenide has similar processing problems to GaAs, although here the melting point is lower and the vapor pressure at the melting point is 0.3 atm. But there is very much less commercial interest in InAs and only the horizontal growth and LEC techniques appear to be used. Twinning is possibly an even more troublesome problem with InAs than with GaAs. The problem is multiple laminar twinning. Again its origin is uncertain, although it is possible to develop twin-free growth conditions.

-

2.6.3 InP The application of the concept of liquid encapsulation to the growth of III-V compounds was initially reported for the growth of InAs and GaAs by Mullin and his colleagues (1965). The use of B,O, is well known metallurgically and has a long history in protecting molten metals from oxidation and vapor loss. In the case of the IV-VI semiconductors Metz et al. (1962)


used B,O, in the crystal growth of volatile compounds of PbTe and PbSe. However, the most significant advance in the III-V compounds came with the application of liquid encapsulation to the concept of high pressure pulling in steel pressure vessels. Liquid encapsulation high pressure pulling was initially applied to the growth of InP and GaP (Mullin et al., 1968) and represented a breakthrough in the growth of these materials as high-quality single crystals. There is now considerable commercial interest in InP due in part to the InP-based structures used in the fabrication of very high quality lasers. It is becoming the laser material par excellence. The principal method of preparation of the raw material uses a pressurized horizontal technique involving distillation of P4 into a boat of molten In as discussed earlier. Crystal growth using the LEC technique is often carried out using a pre-pulled charge of InP. The LEC growth of InP has analogous problems to those of GaAs with respect to temperature gradients and the loss of the group V component. However, in addition, twinning of the crystals during growth is more of a problem. The effect of evaporation from the surface of the hot crystal after it has emerged from the B 2 0 3 is more troublesome than it is with GaAs even though the absolute temperatures are less. The loss of P, from the crystal as it merges from the B,O, is connected, firstly, with the very high gas velocities near the crystal surface, and secondly with the temperature of the crystal surface, which is controlled by the temperature gradients. The high gas velocities are caused by Rayleigh convection driven by the high pressure, large temperature differences and relatively large dimensions of the Bknard cells in the growth chamber. Convec-

91

tion that can occur in pressure pulling systems correlates with the magnitude of the Rayleigh number R,, which is given by (Chesswas et al., 1971)

ATgd3P2

(2-2) TKO vo where AT is the temperature difference of the depth of volume of convecting gas (the temperature difference between surfaces driving the BCnard cell), and T is an average gas temperature, d is the depth of volume of convecting gas, KO is the thermal diffusivity, vo is the kinematic viscosity and P is the gas pressure. Note that R, depends on the square of the gas pressure, the cube of d and the temperature difference between surfaces driving the convective Benard cell. It is important therefore in the pulling systems to avoid large free volumes with large temperature differences between the hot and cold surfaces. The temperature gradient effects are basically similar to those encountered in the LEC pulling of GaAs. Attempts to reduce the temperature gradients in order to reduce the dislocation density cause a slower rate of fall off in surface temperature of the crystal surface above the layer of B 2 0 3 with consequent loss of the B,O, encapsulating film. The very high dissociation pressure of the InP also exacerbates the problem of P, loss. The loss of P, results in the deterioration of the surface quality of the InP involving the formation of In droplets which can move into the bulk InP under the applied temperature gradient by temperature gradient zone melting (TGZM) towards the solid-liquid interface. The need for low dislocation density is very important for device applications and there is an imperative need to reduce them well below the norm of lo4 to lo5 cm-’ generally found in undoped and lightly R,

=

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doped material to lo3 or nearer 10’ cm-’ for many device applications. Attempts to reduce the temperature gradients and the dislocation desities have been reported by Hirano et al. (1992). They used a system of double heat shields or baffles in order to reduce the temperature gradients. This was done in a way that minimized P4 loss presumably by minimizing gaseous convection.

2.6.4 II-VI Compounds: General The status and development of II-VI crystal growth is very different to that of the III-V compounds. Most strikingly there is no successful pulling technology and it is only in the last few years that large-area CdTe and Cd,Zn, - ,Te singlecrystal material has become available. The reasons for this are partly historical and partly materials property related. A significant R&D effort was deployed on the IIVI compounds in the 1950s and 1960s, but following the lack of any significant commercial device promise the major research companies stopped work on the II-VI compounds. The enthusiasts continued, but the problems were formidable and progress was slow. In this phase of development, bulk vapor growth of the II-VI compounds was the most successful crystal growth technology. However, in the early 1980s there was a resurgence of interest in the II-VI compounds partly at least following the availability of the newer low temperature epitaxial technologies which were developed in the 1970s and 1980s for the III-V compounds. The constraints to the melt growth of the II-VI compounds are fundamentally similar to those of the III-V compounds but practically very much more difficult to overcome. All the II-VI compounds exert significant vapor pressures of their compo-

nents at the their melting points. ZnS and CdS have inaccessibly high melting points for melt growth. The more ionic nature of the compounds compared with the III-V compounds gives rise to low critical resolved shear stresses and ease of deformation of the compounds. The high point defect concentrations of the compounds near the melting points conspire with the high diffusion rates in the II-VI compounds, they are orders of magnitude greater than in the III-V compounds, to allow polygonization of dislocations and the formation of grain boundaries and especially subgrain boundaries. The latter are virtually unknown in III-V compounds. Liquid encapsulated pulling cannot be used to overcome the volatility of the compounds since B,O, is partially miscible with II-VI melts. Even if LEC could be used, the ease of deformation would probably limit the value of the technology. The emergence of II-VI epitaxial device structures stimulated new developments in the crystal growth of the II-VI compounds. One can readily identify requirements which were and still are responsible for creating the need for this work: bulk Hg,-,Cd,Te for 3-5 pm and 8-14 ym detectors, CdTe and Cd, -,Zn,Te substrates for epitaxial Hg, -,Cd,Te and ZnSe for blue light emitting diodes and lasers.

2.6.4.1 Bulk Hg, -,Cd,Te Research on mercury cadmium telluride (MCT) has never waned since its discovery and it is still an active topic of materials R&D. Three main bulk techniques have been developed, the vertical Bridgman technique, the American quench anneal technique, an equivalent UK technology called the cast recrystallize anneal (CRA) technique and a traveling heater technology.


The vertical Bridgman technique involves sealing the pure elements in a thickwalled (3 mm) silica tube, a requirement needed to handle the Hg pressure, which can exceed 20 atm for melts used in the preparation of Hgo,,Cdo.2Te.After melting and mixing in a rocking furnace, the charge is frozen as an ingot and transferred to a VB apparatus where it is again completely melted and then slowly crystallized by withdrawal from the furnace. The resulting ingot has a composition gradient which varies from an x of 0.3 to less than -0.18 depending on the start composition. Much effort has been devoted on devising controlled mixing schemes to maximize the yield of x=O.2 and 0.3 detector material. These attempts have included work on the accelerated crucible rotation technique (ACRT), which involves increasing the rotation of the crucible in one direction from rest, slowing it down, and then repeating the operation. This can then be carried out in the opposite direction, but this is not essential. A great deal of study has been carried out by Capper and his colleagues (1994) at Mullard/Philips Research Laboratories (now GEC-Marconi) on this technology with very good results. The melt mixing conditions have attracted much study and whilst a great deal has been discovered the interactions between the complex transient Couette flow the spiral shearing and the Eckman flows across the solid-liquid interface are still not understood. The need to prepare very uniform MCT has resulted in the development of a unique technology, that of quench anneal (QA) or CRA. The method involves rapidly casting a melt of the appropriate MCT compositions in order to produce a macro uniform solid. On a micro scale, however, the material is extremely nonuniform a consequence of the dendritic growth as

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well as the effects of constitutional supercooling. Advantage is then taken of the very high interdiffusion in these compounds and the material is recrystallized in a temperature gradient. This gives uniform MCT but also a high acceptor concentration, which equates to the high Hg vacancy concentration. This is eliminated by a final Hg anneal at low temperature. This is an astonishingly well developed technology, a consequence of support from a military infrared detector programme. The third bulk technology is the travelling heater method (Triboulet, 1994), which was described in connection with the purification and preparation of MCT in Sec. 2.3.3.4. This technique is also used for the growth of Zn, - ,Cd,Te an alternative to MCT as a detector material. Material with very uniform x can be grown but the extent of material development is confidential and not available. Although bulk grown MCT is still used it is rapidly being superseded by liquid phase epitaxy (LPE) and by metal organic vapor phase epitaxy (MOVPE) and the less developed molecular beam epitaxy (MBE). These epitaxial technologies require highquality substrates which is the main reason for the extensive development of CdTe and Cd - ,Zn,Te.

2.6.4.2 CdTe and Cd, -,Zn,Te The most developed technology for these materials is the vertical Bridgman technique, where 2 inch and 3 inch diameter crystals, principally of Cd, -,Zn,Te, for use as substrates for MCTZ are under development. Again the technique involves the withdrawal of a molten charge of material from a furnace. The growth of both CdTe (Rudolph, 1995) and Cd,-,Zn,Te (Sen and Stannard, 1995) have recently been reviewed. The major

94


problems affecting the production of highquality single crystals are the avoidance of twins and both large and small angle boundaries. Tellurium precipitates cannot be avoided during growth but can be eliminated by a post-growth anneal in Cd vapor. The unequivocal correlation of the causes of the defects with the growth conditions is difficult to establish but it would appear that the main requirements for good growth are a flat to convex growth surface (relative to the solid) together with low axial and radial temperature gradients. The use of too low an axial temperature gradient can cause a condition of constitutional supercooling and hence a compromise value needs to be selected. Naturally a stoichiometric melt is needed which strictly requires a controlled separate Cd vapor source. However, since the effective distribution coefficient of Zn is 1.3 its segregation can also result in a condition of constitutional supercooling and hence it is important to grow ingots slowly to give time for rejected solute to diffuse into the melt and not build up as a solute boundary layer. The horizontal growth technique has also been developed over the last few years to grow high quality CdTe and Cd, -,Zn,Te. Crystals allowing the selection of single crystal sections greater than 2.5 inch in dimension have been grown from 4 kg ingots (Liao et al., 1992). Larger systems are under development. Seeds are mounted in a raised section at the top of the boat. Seeded growth propagates freely across the top of the surface of the liquid, resulting in the formation of large singlecrystal areas. There is very little detailed information available on the reasons for the good growth other than it is important to avoid propagation from the multiple grains which can be initiated by growth

nucleated on the bottom silica surface of the boat. 2.6.4.3 ZnSe The very high melting point of ZnSe, 1526"C, makes the vertical Bridgman technique very difficult and most studies have been carried out using vertical gradient freeze technology. But neither of these melt growth techniques give really good quality crystals. Significantly, using a bulk seeded physical vapor transport technique better ZnSe crystals have been obtained by Cantwell et al. (1992). This method is now used by Eagle Picher as a production method. The technique uses 2 inch diameter seeds at either end of a quartz tube. A charge is situated half way between the seeds and is transported to the seeds using an appropriate temperature gradient. The growth of up to 2 inches of crystal has been reported. Very good quality ZnSe having etch pit densities of 5 x lo4 cmP2 has been grown. It is evident that growth at temperatures below the melting point are very important for ZnSe. Indeed bulk vapor growth could be the technology of the future for the II-VI compounds.

-

2.6.4.4 ZnS and CdS The very high melting points of ZnS and CdS mean that melt growth is not possible. As a consequence considerable effort has been devoted to the development of vapor growth techniques for these compounds. A variety of physical vapor transport arrangements have been attempted. Probably the most successful has been the PiperPolich technique (Piper and Polich, 1961). This is illustrated in Fig. 2-6a. It uses a tube having a coned tip. The charge can first be transported by an appropriate temperature gradient away from the tip. Growth is achieved by physically moving

2.7 Fundamental Aspects of Crystal Growth

G

r

B

A

A

the tube so that the tip sees a progressively lower temperature than the charge. A single crystal can be grown from the tip. An important factor in the growth of most 11-VI and other compounds is the necessity to maintain similar vapor pressures of both components during growth. This requirement can be fulfilled by using a separate source of the more volatile component. Its vapor pressure can then be independently controlled and adjusted to that of the other component. The concept is illustrated in Fig. 2-6 b. A major problem with this and all the other earlier vapor growth technologies is that the crystal grows against the silica tube, often sticking to it. On cooling, differential contraction between the crystal and the tube causes strain and stress, resulting in the introduction of dislocations. Attempts have been made to develop freegrowing systems for CdTe and other 11-VI

F

95

I

Figure 2-6. Schematic illustrations of vapor growth techniques. (a) Pipe-Polich technique showing the growth crucible A supported by an outer jacket B mounted inside the furnace F. Movement of A relative to the heater (thermal profile) causes vapor transport of the charge G and its crystallization in the cone of the crucible. (b) Controlled vapor pressure method; growth crucible A has a long side tube D containing the elemental source E which controls the vapor pressure of the more volatile component; note seed crystal C and charge G and thermal profile.

compounds in which the crystal grows out of contact with the tube but it is not an easy technology and very carefully designed thermal systems are required.

2.7 Fundamental Aspects of Crystal Growth The purpose of this section is to provide a brief insight into the origin and mechanism of those dominant phenomena which are of practical importance in the processing of compound semiconductors and which can affect crystal quality and perfection. Only the significant aspects of structure, vapor pressure, temperature distribution, diameter control, facet effect, anisotropic segregation, twinning, solute distribution, constitutional supercooling, dislocations and grain boundaries will be considered.

96


2.7.1 Structure Germanium and Si have a simple diamond cubic structure, which is centrosymmetric, and as a consequence there are no significant growth anisotropies. However, in the case of the compounds the different atoms have different electron affinities and as a result on finds a polarization of properties. In the case of the III-V and II-VI compounds the crystal is either zinc blende or wurtzite. This conveys a polar nature to the structure, and as result for the zinc blende, for example, growth in the [hkl] direction is different to growth in the [6@ direction. The crystal structure shown in Fig. 2-7 highlights this difference. The bond directions are (1 11) or (TIT) where the (TIT) direction terminates in a singly bonded group I11 atom and the opposite (1 11) terminates in a triply bonded group V atom. The (111) planes therefore have different polarities from the (TIT} planes and hence different stabilities. Thus each will require a different supercooling in order to initiate nucleation and growth. One of the most significant phenomena associated with structure is the development of (1 111 or (TIT} type facets on growth surfaces. These can give rise to the facet effect and correlate with twin formation (see Sec. 2.7.5). 2.7.2 Temperature Distribution, Crystal Shape and Diameter Control One of the more difficult problems in growing crystals from the melt is the problem of arranging for the most suitable temperature distribution and temperature gradients in the growth chamber. Thermal modeling should ultimately provide a quantitative scientific background to the process but in practice it is still an operation requiring considerable skill and know-how.

Modeling horizontal growth is of course very much simpler than modeling vertical pulling. From the practical viewpoint it is important to appreciate that the relatively low temperature gradients normally used in the growth of compounds means that very small practical changes in the growth chamber, such as a small movement of a heat shield can often have a dramatic effect on crystal growth. It also is evident that many thermal models do not take full account of practical thermal arrangements. A major problem in HG and in VGF is the control of interface shape. It is generally recognised that the growth surface should be flat or slightly convex. Concave growth surfaces frequently result in crystal growth defects such as grain boundaries or trapped-in solute. Unfortunately, many heater designs involving a simple extra heater zone used to form a liquid zone are naturally prone to form concave growth surfaces. The use of modeling and the introduction of better thermal design concepts is beginning to overcome this problem. Vertical pulling apparatus, in contrast, is very difficult to model thermally, especially in the critical region of the solid-liquid interface. Unlike HG, where shape is controlled by the shape of the boat and is not an experimental problem, in VP shape or diameter control is a major problem, and one on which a vast amount of R&D effort is expended. The critical parameters controlling interface shape are the thermal heat balance at the solid-liquid interface and the surface tension forces operating between the solid, liquid and gaseous surfaces. The simplest approximation of the heat balance at the solid-liquid interface is given by


97

Figure 2-7. Zinc blende lattice showing (1 11) and (TTT) bond directions and the nature of the lattice polarity.

98


where G is the temperature gradient, CJ is the thermal conductivity, e, is the density of the crystal and Hf is the latent heat of fusion. The temperature gradient G,(Z= S, L) refers to the gradient normal to the solid-liquid interface. In crystal pulling a net loss or gain of heat normal to the crystal axis at the solidliquid interface will cause the growth surface to become convex or concave. The crystal diameter, however, is determined by the shape of the meniscus above the melt. Figure 2-8 shows the steady-state position of the crystal being pulled from the melt and the shape of the meniscus. To a first approximation a meniscus which increases in diameter from the crystal causes the growing solid to increase in diameter. A meniscus which decreases in diameter or waists in from the crystal causes a growing crystal to decrease in diameter. However, this model is only an approximation since shape is also controlled by surface tension forces. Crystals appear to fall into two categories depending on whether their melts completely wet their solids or not. Melts of diamond cubic or zinc blende do not completely wet their own solids i.e.,

Figure 2-8. Diagrammatic illustration of the meniscus contact between a melt and its crystal at an angle 0, (0; for a crystal growing at constant diameter)to the vertical where the edge of the crystal is at an angle 0, and at a height h above the melt surface.

+

&G < & , 4 L G , where 41J refers to the interfacial free energies of the respective pairs of the three phases solid, liquid and gas. Thus under equilibrium conditions where the crystal is growing as a right cylinder the meniscus will contact the solid at a specific angle 0, , but at a general angle 0 when growing in or out (see Fig. 2-8). Thus if @0,the crystal will grow out. It is important to note that 0, is not zero but has a positive value for semiconductors, being 11" for Si and 13" for Ge. Thus the actual pull of crystallizing atoms when the liquid meets the solid at a positive angle 0, gives rise to a right cylinder. Device technology - certainly that related to intergrated circuits - requires wafers having a tight specification on diameter, hence there is a need for diameter control in crystal pulling in order to grow constant-diameter crystals. Since the seeding process uses small-diameter single crystals for use as seeds, the pulling system needs to be able to be programmed to achieve a carefully controlled variation in crystal diameter both at the beginning and end of growth. A number of technologies (Hurle, 1993) have been proposed to monitor and control crystal diameter but the most versatile technique (Hurle, 1977) involves continuously monitoring the weight of the crystal (in practice the crystal plus pull rod), or the weight of the melt (in practice the melt plus crucible) and from a knowledge of the pull rate or, strictly, normal growth rate one can monitor continuously the crystal diameter. Diameter control involves either comparing the weight (weight mode) or the rate of weight change (differential weight mode) to the desired weight or desired rate of weight change and using the difference


or error signal in order to control and vary the power to the melt. An example of a commercially produced weighing cell attached to a RSRE research crystal puller is shown in Fig. 2-5. The weight mode has the advantage of the ability to correct errors generated in the previous stage of growth. The signal-to-noise ratio is good and the system can be used down to low growth rates, but corrected errors can give rise to a damped oscillation in the shape which propagates down the crystal. The differential weight mode seeks to keep the diameter at its present value, ignoring previous history. The signal-tonoise is less good because of the signal differentiation. This mode tends to be a more stable servoloop, which is less sensitive to the thermal lags in the system. One of the problems of growing 111-V compounds using either of the weighing methods is that the immediate response of the error signal to a requested change in diameter is opposite to the intended change. That is, a request for an increase in diameter gives an error signal that causes a decrease in diameter. This so-called weighing anomaly arises from two effects. Firstly, 111-V compounds expand on freezing and, secondly the apparent weight of the crystal contains contributions arising from surface tension forces. A practical solution has been found in that the predicted anomalous error signal is subtracted from the total error signal to give a corrected error signal. This technology has enabled the controlled diameter growth of GaAs, InP, Gap, Ge, Si and many other crystals.

2.7.3 Solute Distribution Dopants and impurities are the main solutes of interest in crystal growth studies of Si and Ge. In the case of the compounds, however, there is an additional source of

99

interest and study, which is the solute effect of excess of one of the components. Such an excess is a very common problem in growth of compounds and readily leads to conditions of constitutional supercooling and heavily defected growth. Solute distribution during crystallization can be conveniently described in terms of distribution coefficients as illustrated in Fig. 2-9. As a result of crystallization, since the solute is less soluble in the solid in the example chosen, rejected solute increases in concentration at the solid-liquid interface and assumes a steady-state concentration as a result of diffusion and convective mixing away from the interface. It is convenient to define in this situation an interface distribution coefficient k* (k* = CJC,) and an effective distribution

SOLUTE CONCENTRATION

1II

SUPERCOOL1NG

*-

SI L INTERFACE

DISTANCE

Figure 2-9. (a) Solute (k, < 1) distribution during crystal growth showing interface and bulk concentrations C, and C , and the “mathematical” boundary layer 6. b) Liquidus distribution corresponding to the solute distribution above showing three different real temperature distributions PI, the stable situation, Pz, the critical situation and P,, the unstable situation due to the zone of constitutional supercooling.

100


coefficient keff (k,,,= C,/C,). The latter is the parameter measured experimentally since both the concentration in the bulk melt and the crystal are accessible to measurement. However, k* is not immediately accessible; it is simply the equilibrium distribution Coefficient k, modulated by the growth process. If incorporation were an equilibrium process, for example involving growth under ideally slow conditions, then k* would equal k, . In practice, k* is often a function of orientation, growth rate and solute concentration. Most of our knowledge of transport in the melt and its effects, particularly on crystallization, have been obtained on pulled crystals, where the effects of stirring can be modeled. The relationship between k*, keff and the stirring conditions was derived by Burton, Prim and Slichter (BPS) (1953) in a classic paper in which they introduced a parameter 6, which was related to but was not the diffusion layer thickness. The mathematical convenience of 6 is that it can be used to model the height of the boundary layer at the growth surface under different stirring conditions. In the BPS model the relationship between keffand k* is given by

kerf

=

[k* + (1

k* - k*)e-’]

(2-4)

where A = v 6 / D and 6 = 1.6 D1/3v:l6 w-1/2, where v is the growth velocity, D is the diffusion coefficient of the solute in the liquid, v, is the kinematic viscosity and w is the angular rotation rate. The model makes use of an earlier analysis by Cochran (1934), who analyzed the flow velocity normal to a disc rotating in a semiinfinite fluid. From Eq. (2-4) the effect of growth rate and rotation rate on the incorporation of impurities and dopants can be predicted. Under good stirring conditions 6 + 0,

and hence kefftends to the value of k*,but where stirring conditions are poor 6 + 00 and kerf tends to 1. The model has been used in predicting the onset of constitutional supercooling in the growth of heavily doped melts (Hurle, 1961; Bardsley et al., 1962), but here its significance in the growth of compounds growing under nonstoichiometric conditions will be considered.

2.7.4 Constitutional Supercooling Consider the segregation situation illustrated in Fig. 2-9. In (a) the rejected solute forms a boundary layer where the concentration of solute rejected decreases with distance away from the interface. This concentration distribution is represented in (b) by the liquidus temperature, or freezing temperature distribution. Superimposed on this is the actual physical temperature distribution. If the slope PI is greater than the slope of the liquidus distribution at the solid-liquid interface, then the temperature of the melt will always be greater than the liquidus temperatures in the melt ahead of the interface, giving a stable situation. However, if the actual temperature distribution is, as shown by P,, less than the slope of the liquidus at the interface then in the shaded region there will exist as shown in the diagram a region of the melt where the actual temperature is less than the liquidus temperatures, resulting in an unstable situation. The melt will be supercooled. Under these conditions a perturbation on the growth surface will experience greater supercooling, resulting in accelerating growth into the bulk melt. The critical condition for the onset of supercooling was taken by Hurle (1961) to be the condition when the gradient of constitutional supercooling became equal to or greater than zero. The gradient of con-

101


stitutional supercooling was defined as the difference between the gradient of the liquidus and the actual temperature gradient at the interface. Using the BPS model the gradient of constitutional supercooling (dS/dx),,, is given by

UrnC,(l - k*) - GL D [ k * (1 - k*)e-A]

+

(2-5)

where m is the gradient of the liquidus, C, the solute concentration and the other parameters are as defined in Eq. (2-4). Putting (dS/dx),,, = 0 one can obtain the critical growth velocity for the onset of constitutional supercooling. ucrit given by ucrit

=

+

DGL[k* (1 - k*)e-A] rnC,(l - k*)

(2-6)

Thus the critical (maximum) growth velocity for good stirring conditions (6 -,0) is DGL/(mCL) and for bad conditions (6 -+ co),[DG,/m C,)] x k*. If from Eq. (2-3) asGsis very much larger than u e S H f ,we can substitute (as/oL) G, for G,. In the case of GaAs, if G, is 50°C c111-l and as/ 0,=0.54, and m=3"C (at.%)-', C L = l at.% and D=10-4cm2 s-' for ideally good stirring conditions, the critical growth cm velocity ucritwould be equal to 9 x s-' (3.2 cm h-l). Under poor stirring conditions ucrit is modulated by a factor of k*. Thus constitutional supercooling is very sensitive to small distribution coefficients. This is a very important aspect of the growth of compounds where it is often very difficult to control the stoichiometry of the melt of dissociable compounds. In the case of the arsenides and phosphides of the 111-V compounds, the excess component in nonstoichiometric melts behaves as a solute with negligible solubility in the solid, that is with a k* of - l o p 6 . The significance therefore is that it is extremely difficult to avoid constitutional supercool-

ing in the growth of compounds unless the melts are very close to stoichiometry. In the case of horizontal growth one has the additional hazard of low temperature gradients . The effect of growth under conditions of constitutional supercooling (Bardsley et al., 1962; Hurle et al. 1961) is illustrated in Fig. 2-10. A planar growth surface initially breaks up into a sinusoidal or rumpled surface. Where the solid-liquid interface becomes parallel to { l l l} planes the growth surface develops a ridge or roof-type structure delineated by (111) facets. The regions between the rooftops are valleys where the rejected solute gets trapped. The regions of the crystals grown behind the rooftops between adjacent valleys are the so-called cells; the growth gives rise to a cellular structure. The cells grow more or less independently of one another. Examples of cellular structure on the surface of a crystal can be seen in Fig. 2-11. The effect of progressive constitutional supercooling is to cause the crystal to de-

Uniform Crystal

1. Planar

Rejected S$I~

2. Rumpled

IllllType Facets

3. Facet Development

Trapped Solute

4. Full Cellular Structure Cell Boundaries

Figure 2-10. Effect of constitutional supercooling on a planar growth front 1. Rejected solute causes the growth surface to rumple 2 and then develop a faceted structure 3. The full cellular structure traps in solute as illustrated.

102

2 Compound Semiconductor Processii

slowly with good stirring and with as large a temperature gradient at the interface as possible.

2.7.5 Facet Effect, Anisotropic Segregation and Twinning

Figure 2-11. Crystal end showing the development of cell structure which is evident from the faceted grooves on its surface.

velop polycrystallinity. The trapping of excess solute initially represents a separate liquid phase for the case of a group I11 element. The trapped droplets move under the influence of the temperature gradient (TGZM) towards the solid-liquid interface. The droplets ultimately get frozen in since the crystal growth rate is greater than the diffusion-controlled transport rate of the droplets. The resulting two-phase regions create strain and dislocations and marked nonuniformity. Additionally the facets on the ridge structure exhibit the facet effect giving rise to additional nonuniform dopant and impurity incorporation. Great care is therefore required in the melt growth of compound semiconductors if constitutional supercooling effects are to be avoided. The basic need is to maintain stoichiometric melts and to grow crystals

Facets or atomically flat planes, which are generally of low index, so-called singular planes, are a feature of compound semiconductor growth; they can adversely affect both the yield and quality of crystal growth. The most troublesome facets are of the (111) or {'TTT) type. Four of each type can occur over a closed volume. Facets develop when the (111) planes become tangential to the solid-liquid interface as illustrated in Fig. 2-12. The majority of the crystal surface, which comprises growth steps which are easy sites for nucleation, requires negligible supercooling for growth and thus follows the melt isotherm. However, where the isotherm becomes tangential to the (111) the facet plane truncates the growth surface, there are no growth steps on the (111) plane, and there

n '(111)

FACET

Figure 2-12. Diagrammatic representation of the formation of a (111) facet on a growing crystal showing the equilibrium melting point isotherm TM.The T'-AT isotherm illustrates the potential for the development of a maximum supercooling A T


is a difficulty of nucleation. The facet lags in growth behind the rest of the surface defined by the melt isotherm. The facet grows in size sufficiently in order to develop sufficient supercooling AT in the melt above its surface to initiate nucleation and subsequent growth. Hulme and Mullin (1959) discovered that many impurities are preferentially adsorbed on [l 1I] planes. The effect known as the facet effect is dramatically large for the case of Te in InSb, where the distribution coefficient for growth on a { 11l} type facet was 4 whereas just off a { 11l} type facet it was 0.5, giving a facet ratio k[on (111) facet)]/k[off (111) facet] of -8, which can result in very marked dopant nonuniformities. The diagrams at the bottom of each montage in Fig. 2-13 illustrate the relationship of the { 11I} planes for growth in the [IIIIIn and [loo] growth directions. For growth in the [TTT]In direction there will be three (111) directions of the opposite type at 70.5" to the [TTTIIn direction. For the [loo] direction there will be two ( i i i ) I n and two (111)Sb directions at 55" to the [IOO]. Differences in facet behavior can be seen in Fig. 2-13, which is a montage of autoradiographs of slices cut from InSb crystals that were grown using radioactive 127Teas a dopant. The brighter regions are 127Terich. The diagrams at the bottom of Fig. 2-13 illustrate the "spraying out" effect of the 127Teradiation onto the autoradiography film. Slices were taken from different positions down crystals grown in the [TTT] and [loo] directions. The [iiT]In crystal shows the central or principal facet together with the three edge facets which are of the { 111)Sb type. The disappearance of one of the { 111)Sb facets in the last slice is indicative of a recently formed twin. The [IOO] crystal shows two opposite {TTT}In

--

103

facets and two opposite { 111)Sb facets, the differences in size clearly indicating that the (111)Sb facets are larger than the {iiT)In and require more supercooling for growth. Note the evidence of a small (100) principal facet. Figure 2-14 is a longitudinal section of a '27Te-doped (1 11) crystal which shows the coring effect of the (111) principal facet and also the rotational striations which have a periodicity of one per revolution. The autoradiographs clearly indicate that facet development is an important and critical phenomenon in crystal growth and can bring about very significant dopant and impurity nonuniformities. Twinning can be a particular problem in the growth of 111-V compounds and can strongly affect yield in any growth process. The growth twins occur on (111) planes, which is the twin composition plane and can be described as a rotation of 60" about the (1 11) direction. First nearest neighbor atoms are not affected by the rotation, only second nearest neighbors. The interaction energy associated with the marked increase in distance of the second nearest neighbors is thus quite small, a factor which enhances the twinning probability. The exact mechanism of twinning is not understood as a cause and effect phenomenon. Thermodynamic conditions for twinning on edge facets have been proposed by Hurle (1995) in a recent model. Differences in material behavior appear to be predicted, but to what extent kinetic effects are involved is still an open question. Thus anything that could allow an atom to go down on a (111) surface misoriented in rotation by 60"could be implicated. Impurity atoms, temperature fluctuations and stoichiometry have all been invoked but unequivocal proof as opposed to strong evidence, e.g. stoichiometry, has not been established.

104


Figure 2-13. Montage of autoradiographs of slices cut from (a) [ill] In and (b) [loo] InSb crystals that had been grown from a ‘”Te-doped melt. The bright regions of Te-rich growth illustrate the development of facets: (a) the central or principal (TTT) In facet and the large edge (111) Sb facets - the disappearance of one facet effect in the last slice‘shows the momentary effect of twinning; (b) note the development of the opposite (1 11) Sb edge facets and the smaller (111) In facets as well as evidence of a (10) facet. The diagram at the bottom of each montage illustrates the crystallographic directions and the “spraying out” effect of the lZ7Teradiation into the autoradiographic film.

Twinning continues to be one of the more frustrating and annoying yield-limiting phenomena in crystal growth. Facet formation appears to be a necessary but not unique requirement for twinning. One correlation that is associated with twinning is that the avoidance of facet forma-

tion can reduce or eliminate twinning. However, any surface which is tangenital is prone to develop a facet. Unto a { 11I} der equivalent growth conditions the lower the temperature gradients, the bigger the facet, since a fixed supercooling is required for growth on a facet. Since low tempera-


105

Figure 2-14. Facet-effect nonuniformities illustrated with an autoradiograph of a longitudinal cross-section of an InSb crystal grown from a lZ7Te-dopedmelt. The principal (1 11) facet causes very marked nonuniformity. Note the oneper-revolution striations.

ture gradients are a basic requirement to minimize dislocation formation, it is often difficult to avoid facet formation and twinning in crystal pulling.

2.7.6 Dislocations and Grain Boundaries Dislocations and grain boundaries.are a major impediment to the quality of 111-V (Jordan et al., 1980) and 11-VI compounds (Williams and Vere, 1987) grown from the melt. In the case of 111-V compounds and possibly in the case of the 11-VI compounds one of the main causes of dislocation formation during growth or under post-growth conditions are adverse temperature distributions that give rise to strain and resulting stress. Vertical pulling provides a classic example of this phenomenon. Steep temperature gradients can result in the inner region of the crystal being at a different temperature to the outer. This can give rise to a hoop stress which acts on the inclined (111) planes to produce slip and dislocation formation. Considerable effort has been

devoted to theoretically analyzing (Jordan et al., 1980; Volkl and Miiller, 1989) this problem and to practically analyzing means of avoiding or minimizing the problem. Most research has been carried out on the LEC growth of GaAs although other useful information has been obtained from the growth of other 111-V compounds such as InSb, InP and Gap. There is now general agreement that steep temperature gradients which are conductive to good diameter control and pulling conditions are detrimental in LEC growth and lead to relatively high dislocation densities, around 5 x lo4 for GaAs and InP in the pulled crystals. These densities can be reduced typically by a factor of ten or more by using reduced temperature gradients but these lead to poor diameter control loss of B,O, from the surface of the pulled crystal with consequent deterioration in crystal quality. One of the critical regions requiring good thermal control is at the solid-liquid interface itself and the region around the surface of the B 2 0 , . Thus Jordan and

106


coworkers (1980) have shown that the heat loss from the crystal to the B 2 0 3 is 50 times as great as the heat loss from the crystal to the ambient gas. In effect the gas acts as a thermal insulator in comparison to the B 2 0 3 . This situation favors hoop stresses. It also leads to considerable difficulty in crystal diameter control, thus the well-known phenomenon of the rapid decrease in crystal diameter as it emerges from the surface of the B 2 0 3 due to the reduction in temperature gradient due to reduced thermal loss from the top surface of the crystal. Jacob (1982) has advocated the growth of GaAs completely submerged under B 2 0 3 but the technique does not appear to have a large following. An alternative way of reducing dislocation densities is to harden the lattice by doping (Jacob et al., 1983). Dopants make dislocation motion difficult either by a pinning effect or by simply reducing dislocation velocities. However, rather high doping densities are required, typically above 10f*atoms/cm3 and the technique has only very limited scope for heavily doped material for special applications. The current state of development is one where LEC is a commercially viable technique with versatile doping and growth orientation abilities, but where the ultimate is not low dislocation density, say lo3 readily achievable. In contrast, VGF can achieve these low dislocation densities but it is not a versatile technique and is more suited to dedicated product applications. The melt growth of 11-VI compounds, unlike that of the 111-V compounds, gives rise to the formation of grain boundaries. The reason for the formation of grain boundaries is probably associated with the more ionic character of the 11-VI lattice and the considerably enhanced diffusion in 11-VI compounds compared with 111-V compounds.

The grain boundaries may be loosely classified as small angle, around degree, and large angle, around a degree. Small-angle boundaries are very difficult to remove and indeed are quite stable. Large-angle boundaries can usually be seen visually by lightly grinding a surface. The minority carrier lifetime can be severely affected by grain boundaries, hence the development of methods aimed at eliminating grain boundaries is a priority in 11VI compounds.

2.8 Wafering and Slice Preparation The conversion of a bulk crystal into a form suitable for device fabrication is a vital and crucially important stage in processing. It is not a topic that attracts much published literature (Tada et al., 1990) if only because wafer processing is commercially sensitive, since wafer quality correlates directly with saleability. Most device fabrication procedures involve some form of planar technology. The machinery used for cutting and wafering of compounds is usually the same as that developed for the Si integrated circuit market, where the requirement is for accurately dimensioned circular wafers. In the case of the compounds the diameters are currently much less than the standard 6 inch Si. Two inch GaAs and InP is now being replaced by 3 inch material as the norm. The need for circular wafers is one of the main driving forces for the development of the LEC and VGF processes. The H G technique is supported only where it can achieve characteristics not readily achievable as effectively in other techniques, such low-cost production of very low dislocation density GaAs for laser diodes.

2.9 References

As-grown crystals are not ideally circular and after growth they are normally ground into a right cylinder having the correct diameter. The cylindrical boules are then sliced into wafers. In the Si industry this process is carried out using a high speed diamond slitting wheel. The compound semiconductors are structurally much weaker than Si and early attempts at using this technology often resulted in failure and broken wafers. In the research area slow speed cutting was developed. In an attempt to overcome wheel wobble, cutting wheels were used which were clamped and mounted and driven from their periphery. The narrower diameter internal edge of the wheel was used for cutting. The wheels were stressed to create stiffness. All cutting is a highly skilled process which requires exceptionally high quality machines in which vibration is totally eliminated. The boule is mounted on an adjustable table which fits both the X-ray orientation equipment and the cutting machine. In this way precisely oriented boules are sliced often to 0.1" or less. Commercial pressures and the need to reduce cutting times have resulted in improvements and developments in high-speed saws which can now be used successfully for cutting GaAs and InP and the 111-V compounds. All cutting gives rise to surface damage, which may be < 10 pm for Si, and up to 50 pm for GaAs and even more for 11-VI compounds. This damage must be removed. It can be achieved by a lapping process, but now that surfaces can be cut sufficiently flat it is usually sufficient to chemically polish the surfaces directly removing up to three times the depth of cutting damage at least. Often up to 100300 pm is needed to remove all trace damage and prepare the highest quality polished surface for wafers. The quality of epitaxial growth is crucially dependent on

107

the quality of surface finish on wafers. It is a major concern in the purchase of such wafers. The finishing treatment for wafers involves the use of final etches for two reasons. Firstly, even a chemical polish introduces minor damage due to the loading of the specimen, and secondly, there is a need to prevent electropositive elements like Cu plating back onto the highly polished surface since such contamination could be detrimental to subsequent device structures fabricated on the wafers. The technology and know-how of these processes, however, are generally commercially confidental.

2.9 References Al-Bassam, A. A. I., Al-Juffali, A. A., Al-Dhafiri, A. M. (1994), J. Cryst. Growth 135, 476. Arthur, J. R. (1967), J. Phys. Chem. Solids 28, 2257. Bachmann, K. J., Biihler, E. (1974), J. Electrochem. SOC.121, 835. Balasubramanian, R., Wilcox, W. R. (1993), in: Proc. E-MRS Conf. (Symp. F) CdTe and Related Cd Rich Alloys, Strasbourg, June 1992. Mater. Sci. Eng. B 16, 1. Bardeen, J., Brattain, W. H. (1948), Phys. Rev. 74, 203. Bardsley, W., Boulton, J. S., Hurle, D. T. J. (1962), Solid-state Electron. 5, 395. Bourret, E. D. (1990), Am. Assoc. Cryst. Growth Newslett. 20 (3), 8. Burton, J. A., Prim, R. C., Slichter, W. P. (1953), J. Chem. Phys. 21, 1987. Cantell, G., Harsch, W. C., Cotal, H. L., Markey, B. G., MacKeever, S. W. S., Thomas, J. E. (1992), J. Appl. Phys. 7f,2931. Capper, P. (1994), Prog. Cryst. Growth Charact. Mater. 28, 1. Chesswas, M., Cockayne, B., Hurle, D. T. J., Jakeman, E., Mullin, J. B. (1971), J Cryst. Growth if, 225. Clemens, J. E., Gault, W. A., Monberg, E. M. (1986), AT&T Tech. J. 65, 86. Cochran, W. G. (1934), Proc. Camb. Phil. SOC.30, 365. Czochralski, J. (1917), Z . Phys. Chem. (Leipzig) 92, 219. Fischer, A. G. (1970), J. Electrochem. SOC.117,41C. Gault, W. A,, Monberg, E. M., Clemens, J. E. (1986), J. Cryst. Growth 74, 491.

108


Gremmelmaier, R. (1962), “Czochralski Technique”, in: Compound Semiconductors,Vol. I: Preparation of 111- V Compounds: Willardson, R. K., Goering, H. L. (Eds.). New York: Reinhold, p. 254. Harman, T. C. (1967), “Properties of Mercury Chalcogenides”, in: Physics and Chemistry of IIVI Compounds:Aven, M., Prener, J. S. (Eds.). Amsterdam: North-Holland, p. 767. Hicks, H. G. B., Greene, P. D. (1971), Proc. 3rd Int. Symp. on GaAs and Related Compounds, Aachen, 1970, Inst. Phys. Conf. Ser. 9. Bristol: Institute of Physics, p. 92. Hirano, R., Kanazawa, T., Nakamura, M. (1992), 4th Int. Con$ on InP and Related Materials, Newport, 1992. Piscataway, NJ: IEEE, p. 546. Holmes, D. E., Chen, R. T., Elliott, K. R., Kirkpatrick, C. G. (1982), Appl. Phys. Lett. 40, 46. Hukin, D. A. (1989), in: Proc. 4th Int. Photovoltaic Science and Engineering Con$ Edge Cliff, NSW, Australia: International Radio and Electrical Engineers of Australia, p. 719. Hulme, K. F. (1959), J. Electron. Control 6, 397. Hulme, K. F., Mullin, J. B. (1959), Phil. Mag. 4, 1286. Hulme, K. F., Mullin, J. B. (1962), Solid-state Electron. 5, 211. Hurle, D. T. J. (1961), Solid-State Electron. 3, 37. Hurle, D. T. J. (1977), J. Cryst. Growth 42, 473. Hurle, D. T. J. (1993), J. Cryst. Growth 128, 15. Hurle, D. T. J. (1995), J. Cryst. Growth 147, 239. Hurle, D. T. J., Jones, O., Mullin, J. B. (1961), SolidState Electron. 3, 317. Isshiki, M. (1992), “Bulk Growth of Widegap 11-VI Single Crystals”, in: Widegap11- V ICompoundsfor Opto-Electronic Applications: Ruda, H. E. (Ed.). London: Chapman and Hall, p. 3. Jacob, G. (1982), J. Cryst. Growth 58, 455. Jacob, G., Duseaux, M., Farges, J. P., Van Den Boom, M. M., Roksnoer, P. J. (1983), J. Cryst. Growth 61, 417. Jordan, A. S., Caruso, R., Von Neida, A. R. (1980), Bell Syst. Tech. J. 59, 593. Liao, P. K., Chen, M. C., Castro, C. A. (1992), in: 10th Int. Conf. on Crystal Growth, Sun Diego, C A 1992. Oral Presentation Abstracts. Thousand Oaks, CA: American Association for Crystal Growth, p. 161. Lorenz, M. R. (1967), “Crystal Growth of 11-VI Compounds”, in: Proc. Int. Conf. on 11-VI Semiconducting Compounds,Providence, RI. New York: W. A. Benjamin, p. 215. Maier, H. (1984), in: Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, new series, Vol. 17: Technology of Semiconductors. Berlin: Springer, p. 5. Metz, E. P. A., Miller, R. C., Mazelsky, R. (1962), J. Appl. Phys. 33, 2016. Muller, G., Jacob, H. (1984), in: Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology,New Series, Vol.17: Technology of Semiconductors. Berlin: Springer, p. 12.

Mullin, J. B. (1962), Segregation in InSb, in: Compound Semiconductors,Vol. 1: Preparation of III- V Compounds: Willardson, R.K., Goering, H. L. (Eds.). New York: Reinhold, p. 365. Mullin, J. B. (1975a), “Crystal Growth from the Melt: I. General”, in: Crystal Growth and Characterization, Proc. ISSCG2 Spring School, Lake Kawaguchi, Japan, 1974 Ueda, R., Mullin, J. B. (Eds.). Amsterdam: North-Holland, p. 61. Mullin, J. B. (1975b), “Crystal Growth from the Melt: 11. Dissociable Compounds”, in: Crystal Growth and Characterization, Proc. ISSCG2 Spring School, Lake Kawaguchi. Japan, 1974: Ueda, R., Mullin, J. B. (Eds.). Amsterdam: North-Holand, p. 75. Mullin, J. B. (1989), “Melt Growth of 111-V Compounds by the Liquid Encapsulation and Horizontal Growth Techniques”, in: ZII- V Semiconducting Materials and Devices: Malik, R. J. (Ed.). Amsterdam: Elsevier, Chap. 1, p. 1. Mullin, J. B., Straughan, B. W., Brickell, W. S. (1965), J. Cryst. Growth 26, 782. Mullin, J. B., Heritage, R. J., Holliday, C. H., Straughan, B. W. (1968), J. Cryst. Growth 3/4, 281. Mullin, J. B., MacEwan, W. R., Holliday, C. H., Webb, A. E. V. (1972), J. Cryst. Growth 13/14,

640.

Nygren, S. F., Ringel, C. M., Verleur, H. W. (1971), J. Electrochem. SOC.118, 306. Pfann, W. G. (1966), Zone Melting, 2nd ed. New York Wiley. Piper, W. W., Polich, S. J. (1961), J. Appl. Phys. 32, 1278. Rudolph, P. (1995), Prog. Cryst. Growth Charact. Muter., to be published. Rudolph, P., Umetsu, K., Koh, H. J., Fukada, T. (1994), J. Cryst. Growth 143, 359. Sen, S., Stannard, J. E. (1995), Prog. Cryst. Growth Charact. Muter., to be published. Shockley, W. (1949), Bell Syst. Tech. J. 28, 435. Strauss, A. J. (1971), in: Proc. Int. Symp. Cadmium Telluride, Strmbourg. June 1971: Siffert, P., Comet, A. (Eds.). Strasbourg: Centre de Recherches Nuclkaires, p. l l . Swiggard, E. M., Lee, S. H., von Batchelder, F.W. (1979), Proc. 7th Int. Symp. on Gallium Arsenide and Related Compounds,St. Louis 1978. Inst. Phys. Con$ Ser. 45b. Bristol: Institute of Physics, p. 125. Tada, K., Tatsumi, M., Morioka, M., Araki, T., Kawase, T. (1990), Semiconductorsand Semimetals, Vol.31, Indium Phosphide: Crystal Growth and Characterization: Willardson, R. K., Beer, A. C. (Eds.), New York: Academic, p. 175; see especially pp. 222ff. Teal, G. K. (1958), Transistor Technology, Vol. 1: Bridgers, H. E., Scaff, J. H., Shive, J. N. (Eds.).. New York: Van Nostrand, Chap. 4. Thomas, R. N., Hobgood, H. M., Ravishankar, P. S., Braggins, T. T. (1990), J. Cryst. Growth 99, 643.

2.9 References

Thomas, R. N., Hobgood, H. M., Ravishankar, P. S., Braggins, T. T. (1993), Prog. Cryst. Growth Charact Muter. 26, 219. Triboulet, R. (1994), Prog. Cryst Growth Charact. Muter. 28, 85. Van Karman, T. (1921), Z. Angew. Math. Mech. 1, 233. Van der Boomgaard, J., Schol, K. (1957), Philips Res. Rep. 12, 127. Volkl, J., Muller, G. (1989), .ICryst. Growth 97, 136. Welker, H. (1952), Z. Naturforsch. 7a, 744. Welker, H. (1953), Z. Naturforsch. 8a, 248. Willardson, R. K., Goering, H. L. (Eds.) (1962), Compound Semiconductors, Vol. 1: Preparation of IZI- V Compounds. New York: Reinhold. Williams, D. J., Vere, A. W. (1987), .ICryst. Growth 83. 341.

General Reading Bardsley, W, Hurle, D. T. J., Mullin, J. B. (Eds.) (1979), Crystal Growth: A Tutorial Approach. Amsterdam: North-Holland. Brice, J. C. (1965), Growth of Crystals from the Melt. Amsterdam: North-Holland.

109

Hurle, D. T. J. (Ed.) (1993, 1994, 1995), Handbook of Crystal Growth: Vol. 1, Fundamentals; Vol.2, Bulk Crystal Growth; Vol.3, Thin Films and Epitaxy. Amsterdam: Elsevier Science. Malik, R. J. (Ed.) (1989), ZII- VSemiconductor Materials and Devices. Amsterdam: Elsevier Science. Includes chapter on “Melt Growth of 111-V Compounds by the Liquid Encapsulation and Horizontal Growth Techniques” by J. B. Mullin, p. 1. Miller, L. S., Mullin, J. B. (Eds.) (1991), EZectronic Materials: From Silicon to Organics. New York: Plenum. Pfann, W. G. (1963), Zone Melting. New York: Wiley. Thomas, R. N., Hobgood, H. M., Ravishankar, P. S., Braggins, T. T. (1993), “Meeting Device Needs Through Melt Growth of Large-Diameter Elemental and Compound Semiconductors”. Prog. Cryst. Growth Charact. Muter. 26, 219. Ueda, R., Mullin, J. B. (Eds.) (1975), Crystal Growth and Characterisation. Amsterdam: North-Holland. Willardson, R. K., Goering, H. L. (Eds.) (1962), Compound Semiconductors: Vol.1, Preparation of IIZ- V Compounds. New York: Reinhold. Includes a chapter on “Segregation in InSb” by J. B. Mullin, p. 365. Proceedings of the International Conferences on Crystal Growth. 1965, Oxford: Pergamon. 1968, 1971, 1974, 1977, 1980, 1983, 1986, 1989, 1992, Amsterdam: Elsevier.

Handbook of Semiconductor Technology

Kenneth A. Jackson, Wolfaana Schroter Copyright 0WILEY-VCH Verlag GmbH, 2000

3 Epitaxial Growth

.

Thomas F Kuech

Department of Chemical Engineering. University of Wisconsin. Madison. WI. U.S.A. Michael A. Tischler

Advanced Technology Materials. Inc., Danbury. CT. U.S.A.

List of 3.1 3.2 3.2.1 3.2.2 3.2.3 3.3 3.3.1 3.3.1.1 3.3.1.2 3.3.2 3.4 3.4.1 3.5 3.6 3.6.1 3.6.1.1 3.6.1.2 3.6.1.3 3.6.1.4 3.6.2 3.6.3 3.6.4 3.7 3.8

Symbols and Abbreviations ........................................ 112 Introduction ...................................................... 114 The Epitaxial Process: General Features .............................. 118 119 Surface Thermodynamics and Surface Structure ....................... 124 Surface Transport and Incorporation ................................ 126 Growth Behaviors ................................................ Chemical Vapor Deposition: Technology and Issues ..................... 130 132 Reactors: Mass, Fluid, and Thermal Transport ........................ Fluid Behavior and Reactor Design ................................. 132 135 Mass and Thermal Transport ....................................... 136 Gas Phase and Surface Chemistry ................................... Liquid Phase Epitaxy (LPE) Technology .............................. 140 143 LPE Growth Procedures ........................................... Molecular Beam Epitaxy (MBE) Technology .......................... 146 Specific Epitaxial Systems: Materials and Growth Issues . . . . . . . . . . . . . . . . 152 152 Silicon Chemical Vapor Deposition .................................. Silicon Chemical Vapor Deposition: Surface and Reactor Considerations . 152 Silicon Chemical Vapor Deposition: Growth Chemistry . . . . . . . . . . . . . . . . 156 Heterojunction Formation ......................................... 159 Impurity Incorporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 161 GaAS MBE ...................................................... 166 Growth of AlGaAs by LPE ........................................ InP Metal Organic Vapor Phase Epitaxy (MOVPE) . . . . . . . . . . . . . . . . . . . 170 Acknowledgement ................................................. 175 References ....................................................... 175

112

3 Epitaxial Growth

List of Symbols and Abbreviations A C

cis

CS d D

DO Ds E G

Gform Grnigr

H J k

kB

K Kn 1 L m M n N

4

P

e Q

QWap

R S

S t

T Vms

W X

Xi a a0

Y

Ysalse

surface area; aperture area concentration concentration of solute (As) in the solid local concentration of diffusing species diameter of gas molecule; thickness of epitaxial layer diffusivity; gas phase diffusion coefficient diffusion coeficient surface diffusion coefficient energy free energy free energy of formation free energy of migration enthalpy flux rate constant Boltzmann constant equilibrium constant Knudsen number distance a reactor dimension slope of liquidus curve molecular weight number density of gas Avogadro’s number weight fraction of component i pressure partial pressure of component i activation energy heat of vaporization cooling rate; gas constant height of steps entropy time temperature mean stream velocity of gas work distance mole fraction of component i rate constant rate constant pre-exponential surface tension interfacial energy between solids A and B


energy of solid and vapor interface thickness of diffusional boundary layer energy per unit area of terrace ledge energy per unit length energy per kink site angle fraction of available adsorption sites terrace width; mean free path of gas molecule kinematic viscosity of gas kink density

2DEG AFM APCVD BEP CVD DEZ DFB DH FET FWHM GR LPCVD LPE MBE MOMBE MOSFET MOVPE PBN PL RHEED RTP SBH SI STM TBP TEI TLK TLV TMI UHV

two-dimensional electron gas atomic force microscope or micrograph atmospheric pressure chemical vapor deposition beam equivalent pressure chemical vapor deposition diethyl zinc distributed feedback double heterostructure field effect transistor full width at half maximum growth rate low pressure chemical vapor deposition liquid phase epitaxy molecular beam epitaxy metal-organic molecular beam epitaxy metal oxide semiconductor field effect transistor metal-organic vapor phase epitaxy pyrolytic boron nitride photoluminescence reflection high energy electron diffraction rapid thermal processing Schottky barrier height semi-insulating scanning tunneling microscope tertiary butylphosphine triethyl indium terraces, ledges, kinks threshold limit value trimethyl indium ultra-high vacuum

113

114

3 Epitaxial Growth

3.1 Introduction The development of modern semiconductor devices and circuits has required the integration of a large number of different materials. The formation of these devices requires the controlled deposition and processing of several types of materials: metals, semiconductors and insulators. Metals primarily form the interconnections between different semiconductor regions, while insulators serve to electrically isolate the metal wires from the semiconductor. The deposition of SiO, and other materials may also serve to form the active region of the device structure, as in the case of the Si-based metal oxide semiconductor field effect transistor (MOSFET). Materials deposition and surface modification of the semiconductors are required in order to form the individual elements in devices and circuits. Thus, resistors, pn junctions, transistors and a wide variety of other devices are formed by an assortment of materials processes. These processes, encompassing metals, semiconductors, and insulators, are produced in thin layer form on the surface of the substrate wafer or through modification of the near surface region of the wafer. A typical cross-section of a Si device structure is shown in Fig. 3-1. Many different types of processing steps and materials modification techniques have to be applied to develop such a structure and finally pro-

duce a working device. The formation of conducting regions in the semiconductor wafer, for example, in silicon, has traditionally been performed through the invention and application of processes which can modify the near surface regions of the wafer. The carrier concentration and conductivity type are modified through the processes of ion-implantation and solidstate diffusion. Silicon dioxide is grown through the thermal oxidation of Si or it is deposited, and serves as a local insulator. Deposition techniques, such as sputtering, thermal evaporation and chemical vapor deposition, have all been used to form semiconducting, insulating and metal or metallic conductive regions on the wafer surface. These important processes are discussed in other chapters within this volume. The processing and growth or deposition techniques will determine the final device structure, and hence device characteristics, as discussed in this chapter. The device characteristics depend crucially on the chemical, physical and structural properties of these deposited or fabricated layers, as well as on the interfaces between them. The local properties of these interfaces between dissimilar materials can be complex. The presence of a high concentration of structural defects or chemical impurities at the junction between n- and p-type semiconducting regions can drastically alter the electrical properties of a pn

Interconnect metallurgy I Figure 3-1. The cross-sec-

Fie,d Oxide Ohmic ‘Ontact Diffusion Barrier Gate Oxide Source-Drain Ion Implant

tion of a typical Si-based electronic structure. The device consists of many regions which have a difference in electrical properties. The technology used to generate these regions is indicated in this figure.

3.1 Introduction

junction. Similarly, structural imperfections or impurities at the interface between Si and SiO, can destroy the important passivation properties of the interface as well as degrading the electrical properties of the Si-SiO, junction in a MOSFET. Lastly, the interface between a metal and a semiconductor can yield rectifying or ohmic behavior depending on the electronic structure of the two materials and the physical characteristics of their interface. A major difficulty with many of these interfaces is the stochastic nature of the defects which control the interfacial properties. The rectifying Schottky barrier formed at most metal-semiconductor interfaces can, for example, be controlled only to f 10 meV out of a typical barrier height of 800meV. This variation in the Schottky barrier height (SBH) of 21-2% is due to minor differences in the interfacial structure between the two structurally different materials and the level and distribution of chemical impurities at these interfaces. The growth or deposition of polycrystalline layers on an existing single crystal substrate always leads to micro-structural variations along the interface. As the lateral device dimensions are reduced through improvements in the primary patterning technique, photolithography, these lateral property variations are averaged over smaller areas. Device characteristics and their thermal stability will thus exhibit larger variations as device dimensions shrink. In circuit applications, such variability between adjacent devices could render the circuit inoperable. The trend toward smaller lateral dimensions has been accompanied by a similar decrease in the vertical dimension of device structures. The existing processing techniques have been refined and pushed to produce smaller and thinner structures. Many of the techniques which rely on the

115

modification of the near surface region of a wafer, such as ion implantation and diffusion, are reaching their limits in producing thinner and thinner regions of controlled properties. Both thermal diffusion and ion-implantation are limited by the stochastic nature of the process itself. The impurity distribution in the near surface region of the wafer, produced by both of these processes, typically results in a Gaussian impurity depth profile reflecting the underlying random nature of atomic motion of the process. In addition, these techniques require elevated temperatures for impurity activation, as in the case of ion implantation and impurity redistribution. These thermal treatments can result in non-equilibrium concentrations of native defects which can affect subsequent processing steps and materials properties. The development of smaller, thinner and higher performance devices will require tighter constraints on the thermal and physical extremes during the fabrication process. Each generation of devices has, therefore, spurred innovation in new processing techniques. The resulting processing trends for semiconductor device fabrication are towards low thermal budget (both temperature and time) processing and deposition techniques. Low thermal budget processing offers many advantages in these applications, resulting in a smaller concentration of defects in the material as well as a reduction in the extent of impurity redistribution within the device structure. While control of impurities is important in the development of electronic devices, the physical structure, and in particular, the interfaces between materials are becoming increasingly important as device dimensions shrink. Control over the structural details of the crucial interfaces has been more difficult to achieve over a broad spectrum of processing conditions.

116

3 Epitaxial Growth

Again the trends have been to lower thermal budget processes, where interdiffusion of and reaction between materials is minimized. In this chapter, we will discuss the nature and application of a set of processing techniques collectively called epitaxial growth techniques. In particular, these techniques have been applied to the formation of thin layer semiconductor structures which comprise the active device regions. In most cases, the semiconductor will be deposited, or grown, in a crystalline form. Under special growth conditions, the growing layer can assume or replicate the physical structure of the underlying substrate. This replication of the crystalline arrangement of the substrate is known as epitaxy. Epitaxial growth leads to a structurally perfect film in many cases and is critically important in the formation of most modern device structures. There are many deposition techniques which may be used for semiconductor epitaxial growth. The choice of the specific technique is dependent on several issues. The structure of the growing film, the electrical properties and the interface between the deposited layer and the underlying materials are the principal considerations. The approach taken to control these depends on the specific device application. Amorphous films also have applications in device fabrication and can also be produced by many of the growth techniques described in this chapter. The deposited atoms in the epitaxial growth process arrange themselves on the growing surface, bonding to the underlying atoms of the substrate. The atomic arrangement of the substrate atoms determines the subsequent arrangement of atoms in the growing film, the resulting film being a direct continuation of the atomic structure of the single crystal sub-

strate. In principle, since the film is replicating the substrate, an epitaxial film could be as structurally perfect and free from defects as the substrate itself. Since the type of the deposited atoms can be varied during the deposition process, the composition of the growing film can be controlled in the growth direction, during the deposition. Many deposition techniques can now produce multi-layered epitaxial structures in which the individual layers are less than a nanometer thick and the interfaces between layers are essentially atomically abrupt. The formation of such highly perfect interfaces requires the use of low-temperature epitaxial growth processes. The most widely encountered epitaxial growth process is the formation of Si layers on an existing Si wafer or substrate. This controlled growth of a material on a substrate of the same overall chemical composition, as in, for example, the growth of Si on Si, is referred to as homoepitaxial growth. The homoepitaxial deposition of Si on the Si substrate is often used to form very thin layers of Si in which the electrical properties of the growing layer can differ substantially from these underlying layers. The controlled addition of electrically active impurities, or dopants, during epitaxial growth then allows for the formation of electrical as well as compositional interfaces. For example, a pn junction is formed by the addition of first p-type and then n-type impurities to the growing layer. This transition from p-to-n type material can often occur over only a few atomic layers. Just as the doping of the film can be altered over a few atomic layers, the composition of the film can be changed over similar dimensions. The process of growing materials of different composition, as in the alloy Si,Ge, - x on Si, is referred to as heteroepitaxial growth. The growth of Si,Ge, - x on

3.1 Introduction

117

Table 3-1. Examples of CVD reactants used in the epitaxial growth of semiconductors. Semiconductor

Reactants

Pressure regime

General term for this form of CVD

Si1icon

SiCI,H,, SiC1, SiH,, Si,H,

APCVD LPCVD and UHV-CVD

Germanium

GeH,

Sic GaAs

SiH, and C,H, Ga and AsCl, (CH,),Ga and ASH,

near atmospheric CVD near atmospheric CVD and LPCVD near atmospheric CVD and LPCVD near atmospheric CVD near atmospheric CVD near atmospheric CVD

APCVD, LPCVD, and UHV-CVD

InP A1,Ga -,As

near atmospheric CVD near atmospheric CVD

APCVD VPE MOVPE, MOCVD, OMVPE, or OMCVD MOVPE, etc. MOVPE, etc.

HgxCd, -xTe

near atmospheric CVD

MOVPE, etc.

near atmospheric CVD

MOVPE, etc.

Si substrates allows for a change in the electronic structure of the film. Such changes in local electronic structure form the basis of many of the new electronic devices. The heteroepitaxial growth of compound semiconductors, such as GaAs/ A1,Ga - ,As and InP/In,Ga - ,As,P, - y , is one of the most developed heteroepitaxial growth techniques. Quantum well lasers, high performance heterojunction transistors, and multilayer photodetectors are all products based on heteroepitaxial growth. There are several primary techniques used in the formation of epitaxial layers. The choice of the specific growth technique depends strongly on the required materials and the desired material structure. Physical deposition has been used for the growth of many films. In particular, molecular beam epitaxy or MBE has been used with great success in the fabrication of very thin layer device structures. In this technique, a heated substrate is exposed to

a flux of growth nutrients, usually elemental sources, within an ultra-high vacuum (UHV) environment. Materials growth from the gas phase at higher pressures is far more common and is referred to as chemical vapor deposition, or CVD. CVD techniques utilize high-vapor-pressurecompounds of the elements comprising the film. A variety of CVD techniques are summarized in Table 3-1. The volatile source compounds, such as SiH, in the growth of Si, are transported to the growth front, at which point they react, and are incorporated into the growing layer. In all cases, the deposition of the film and the formation of the epitaxial structure proceeds through a series of elementary steps or processes: i) transport of the growth nutrients to the growth front, ii) their decomposition at the growth surface, iii) surface migration of the deposited species and iv) the subsequent bonding into the growth front. The slowest of these elementary processes becomes the rate-limiting step in de-

3 Epitaxial Growth

118

termining the growth rate of the film. This chapter will deal with these elementary processes as they apply to CVD-based epitaxial growth and how they affect the formation of the epitaxial structure in the deposited layer. There are many issues associated with CVD of thin films. Since we are limiting our scope in this chapter to epitaxial films, the structure of the deposited layer or layers will have a definite relationship to the substrate. While this term describes the overall physical nature of the film, the details of the physical structure or perfection of the epitaxial layers is also important. In order to be useful, the deposited film must also possess other properties which bear directly on their utility within the overall device formation process. The deposited film must be uniform in thickness, composition, chemical, electrical and, perhaps, optical properties. Variations in the film properties correspond to changes in the resulting device properties over the wafer and from wafer-to-wafer. In general, the

S

Ll

surface must also be very smooth in order to allow photolithographic patterning. Surface defects will reduce the usable area of the deposited film and therefore decrease the yield of devices and circuits generated from the material. There are also defects within the film itself which must be controlled. Defects in the film, in the form of missing atoms (vacancies), rows of atoms (dislocations), or extra or missing planes of atoms (stacking faults), schematically shown Fig. 3-2, must be controlled or eliminated. These structural defects can be electrically active and interact with the electronic or optical devices formed from the epitaxial layers.

3.2 The Epitaxial Process: General Features The growth of an epitaxial film takes place on a crystal surface. This surface could consist of the same material, as in the epitaxial growth of Si on a Si substrate,

-

ii

z

edge or misfit dislocation

intrinsic stacking fault

extrinsic stacking fault

Figure 3-2. There are many defects which can typically form in thin film structures, ranging from missing atoms (vacancies), missing rows of atoms (dislocations) to extra or missing partial planes of atoms (stacking faults). T is the shear stress and S and P define the plane of the dislocation.

3.2 The Epitaxial Process: General Features

or on a surface of a different material, such as Al,Ga, -,As on GaAs. In all cases, the nature of the surface composition, chemistry and structure will play a major role in determining the essential features of the epitaxial growth process. The growth rate, electronic properties, and film structure are determined by the chemical and physical reactions occurring at this growth front. This section will focus on the physical nature of the growth surface and elementary processes occurring there. These processes are important for all forms of epitaxial growth: physical deposition, as in MBE, CVD and liquid phase epitaxy (LPE). The thermodynamic description of the growth surface is the starting point for this discussion. A growing surface, by definition, is not at equilibrium. The rate of materials deposition is very slow, under many growth conditions, compared to those transport and chemical reactions which must take place in order to approach and reach equilibrium. The actual growth of materials can often be assumed to be a small perturbation to the equilibrium structure and composition of the growth front. There are, of course, many occasions when these chemical and physical reactions are very slow and non-equilibrium structures appear on the surface and in the growing film. In any event, a thermodynamic description of the surface serves as a good starting place for the discussion of epitaxial growth processes.

3.2.1 Surface Thermodynamics and Surface Structure Thermodynamics is typically used to describe the relationship between bulk phases. This description, in general, does not recognize that the bulk phases have surfaces and that these surfaces can and do have properties which are different from the bulk

119

phases. The neglect of the surface in thermodynamic calculations is well justified in most cases. Most solid materials have an atomic density of about atoms/cm3. Consider a one cubic centimeter block of metal, the number of atoms on the surface of such a cube can be estimated from this bulk atomic density to be about 1 O I 5 atoms or of the total number. Since for typical materials this is a very small fraction, the surface can be ignored in the calculations. The deposition of a thin epitaxial film on an existing substrate, however, is quite a different case. A thin film of 0.1 pm in thickness has an areal density of about l O I 7 atoms/cm2.The atoms making up the interface or top surface then comprise 1% of the total number of atoms. In many cases, this 1 % of the total number of atoms could possibly be neglected in our considerations. However, in the early stages of growth all the atoms are on or near a surface. The surface energetics can then dominate the film growth over the bulk phase effects. In addition, for structures in which interfaces play a major role, such as MOSFET devices, the interface is composed of the near surface regions of two different materials. The surface regions of these devices often dominate their physical and electronic properties. The atoms in a surface layer are in a completely different environment than the atoms in the bulk of the solid. They have fewer nearest neighbors, the distribution of neighbors is anisotropic and the properties on an atomic scale are different (i.e., chemical bonding, positions, and so on). Since these detailed atomistic characteristics determine the thermodynamics of the macroscopic system, it is useful to talk about the surface as a distinct phase from the bulk. Internal surfaces or interfaces can be similarly considered as a distinct phase since the composition changes repid-

120

3 Epitaxial Growth

ly over a few atomic distances. The thermodynamic properties of the system can be considered to be the sum of the bulk and surface contributions, or in the latter case, an interfacial contribution. The most familiar of the characteristic energies associated with a surface is the surface tension. Surface tension, y , is defined as the reversible work involved in the formation of a unit area of new surface at a constant temperature, volume and number of atoms (Adamson, 1990): as A + O ,

posed of the bulk contributions and the surface contribution (Adamson, 1990) :

G=GB+GS

(3-2)

The surface contribution G S is defined in the same terms as the bulk free energy G B ~

i

=

~

i

T$ +

(3-3)

where H i and S i are the enthalpy and entropy of the particular phase and T is the temperature. The surface tension can be expressed as

(3-1)

(3-4)

where d W is the amount of work associated with the increment in area dA. In order to increase the area of the interface or surface, work must be done on the system, hence the sign of this energy term. The work done in forming a new surface is associated with the breaking of bonds, increasing or decreasing the distance between neighbors, and/or rearranging atoms. While the concept of surface tension is usually associated with a liquid, it has a similar physical definition in the case of a solid. The surface tension is used to describe both the work done in creating a new surface, such as cleaving a crystal or nucleating a new solid phase, or increasing the surface area, as in the formation of new internal surfaces or a reconstruction or rearrangement of the surface atoms. A grain boundary is an example of an internal boundary which may be formed by cold working of a material. The surface tension is related to the more familiar energies encountered in thermodynamics. The Helmholtz free energy, entropy, enthalpy and Gibbs free energy can all generally be defined in terms of the surface tension. For example, the total Gibbs free energy of a system can be com-

The other relationships of bulk thermodynamics can be used in the definition of other surface-related quantities. In particular, the surface entropy can be given as (3-5) or

(3-6) The surface energy, ES, and enthalpy, H S , are often very close in value, E S s H S ,allowing the surface energy to be expressed as E S g H S =G S + T S s

(3-7)

or (3-8) This concept of surface tension and surface energy of a solid will be useful in determining the underlying causes for surface rearrangement and the nucleation and growth behavior in epitaxial growth. The surface energy is almost always positive, indicating that surfaces are not energetically favored entities. A solid is al-


ways reluctant to form a new surface since it costs energy. Solids at high temperatures in equilibrium with their vapor or liquid phase will form a surface shape which minimizes this energy expenditure. Solids will therefore minimize their surface energy by altering their shape. The surface energy will be a function, in a crystalline solid, of the orientation of the solid. The surface energy can be estimated by looking at the number of broken bonds which had to be created when the surface was formed. The crystallographicplanes of a crystal can and do possess different numbers of bonds. The surfaces with greater number of bonds broken in the formation of the surface will generally result in the higher surface energy. Such high energy surfaces are energetically unfavorable to form and expand. A crystallite at thermodynamic equilibrium will develop well-defined crystallographic facets or planar surface features. The wellknown shape of naturally occurring crystals often reflect these thermodynamic influences. The tendency to form facets on the surfaces is not only manifested at a macroscopic scale but also at the microscopic or atomic scale. The more stable crystallographic faces will be formed at the expense of surfaces with higher free energy. For example, thermal faceting will take place in the case of the (100) surface of Ag at high temperatures. Near the melting point of Ag, the (100) crystal surface will decompose into microscopic facets with a (111) orientatios. Most epitaxial growth takes place on a single crystal substrate which has a well defined, overall orientation. Most wafers are oriented to a specific low-index crystallographic direction, e.g., (100) or (Ill), within a certain accuracy. If a wafer has a surface which is exactly a crystallographic plane, it is referred to as a singular surface. The wafer surface can have additional

121

structure aside from the above mentioned faceting. The detailed surface structure is characterized by three separate but related features: terraces, kinks and ledges. Often, the wafer will be specified to have a polished (100) surface which is intentionally misoriented at an angle towards another major crystal direction, as schematically shown in Fig. 3-3. Such surfaces are often referred to as vicinal surfaces. This intentional or unintentional off-orientation of the wafer increases the structure on the wafer surface. The terraces, ledges and kinks (TLK) on a such a surface are schematically shown in Fig. 3-3. The TLK description can be used to attempt to calculate the surface energy of a crystal by separately considering the contributions to the energies associated with the particular defects which make up the surface. In this context, the surface can be thought of as being made up of singular or atomically flat surfaces (terraces), plus steps (ledges) from one terrace to another, and kinks in those steps. This view extends the bond breaking model used in describing the surface energy. The formation of ledges and kinks are a consequence of entropic effects at temperatures greater than

Figure3-3. The surface of a substrate which is not perfectly oriented to coincide with an exact crystallographic plane consists of surface structures such as ledges, terraces and kinks in the terrace edges. These basis surface structures can influence the growth of the film.

122

3 Epitaxial Growth

a temperature of absolute zero. At 0 K, a wafer surface which has an orientation close to a major crystal axis, will consist only of terraces and ledges as shown in Fig. 3-4a. A surface which has a general orientation, i.e., not a singular or vicinal surface, will also have ledges consisting of sections interrupted by a jog or kink, i.e., a step in the line as shown in Fig. 3-4 b. A vicinal surface is the most commonly used surface in epitaxial growth. The surface energy of a vicinal surface can be described through the aid of Fig. 3-5 which illustrates a wafer surface of a (010) orientation miscut by an angle 8 towards the [IOO] direction. We will assume that 8 is small, i.e. 814". The surface, shown in Fig. 3-5, will consist of monatomic steps of height s, with a density tan (I 8 I)/s. The terrace will have an average width 1,where

(3-9) At 0 K, the surface energy can be written as &(I)

E s ( 8 ) = E s = ( 0 ) cos(8)+ - sin(8) S

(3-10)

Figure 3-5. A simple semiconductor surface will consist of terraces separated by monatomic steps (s). Under certain conditions, multi-step ledges are formed.

where E s ( 0 )is the energy per unit area of a singular terrace, dl) is the ledge energy per unit length of a ledge and Es(6') is the energy of the actual vicinal surface. It should be noted that the total terrace area is less than the total surface area, cos (8)=(terrace area)/(surface area), where the 'total surface area' would be the area of a plane at the vicinal angle 8. As 6' increases, the amount of singular surface, relative to the total surface area, decreases. The last term in the expression is the ledge energy contribution to the surface energy. This is simply the ledge energy per unit length, &(I),times the ledge density, S

Figure 3-4. a) At both 0 K and thermodynamic equilibrium, a substrate miscut towards a principal crystallographic plane will have only terraces terminated in ledges. b) A substrate of arbitrary miscut will possess kinks in addition to terraces and ledges.

(3-11)

S

The inclusion of kinks into the calculation of the surface energy involves the addition of a term consisting of the energy per kink site, d2),and the kink density, e. The kink density will depend, at 0 K, on the specific orientation of the surface. The surface energy then becomes (3-12) p) ES(B)=ES(0) cos(8)+ -sin(B)+e d2) S


Based on the number of possible broken bonds, an atom on a terrace will have the least number of broken bonds and will have the higher number of bonds to adjacent surface atoms. Atoms on ledges will have a higher number of broken bonds than the terrace while the kink sites have the fewest bonds to the surface. The surface energy of a particular feature will increase with the number of broken bonds. The kink sites will have the highest per atom energy followed by the ledge sites and finally the terrace sites. The surface structure, at equilibrium, will be determined by the minimum of this surface energy, at 0 K. It should be noted that the number of kinks, ledges and the terrace width are not independent variables but are constrained by the geometry of the surface, substrate orientation and vicinality. At higher temperatures, such as those used in the growth or deposition of epitaxial materials, the surface will have a more complex structure since entropy can play a role. As indicated in Eq. (3-3), the surface free energy contains both the surface energy (enthalpy) and the surface entropy. The increase in temperature allows the entropy term to gain in significance. Part of the surface energy will be associated with the configuration of atoms on the surface. As the temperature is increased, there is a driving force to increase the amount of disorder on the surface through the generation of atom vacancies, surface ledges and kinks. The addition of the these high energy structures increases surface energy but this increase is offset by the increase in the surface entropy. These energy considerations can lead to complicated surface structures. Such surface structures can be seen using surface sensitive techniques, such as the scanning tunneling microscope (STM) or electron diffraction. A STM micrograph of a Si surface is shown in Fig. 3-6.

123

Figure 3-6. A scanning tunneling micrograph (STM) of a clean (100) Si surface reveals the TLK structure characteristics of most surfaces.

The presence of such surface structures are readily seen in this picture, the flat terrace being bounded by alternating rough and smoother ledges. The alternating structure is attributed to the last aspect of surface structure important to the epitaxial growth of materials, surface reconstruction. So far, we have discussed the surface structure in terms of features residing on the surface of a truncated crystal. A truncated crystal is conceptualized as a surface formed by cleaving the crystal along a specific crystallographic plane. The bonds broken in this process are left ‘dangling’ from the surface. These dangling bonds are very energetic sites on the surface, readily forming new bonds with adatoms. The truncated crystal does provide an idealized view of the surface structure on an atomic scale. The very energetic dangling bonds left on the surface, in this construction, would however prefer to be part of a covalent bond if possible. This covalent bond could be formed through an interaction within an adsorbed species. In

124

3 Epitaxial Growth

the absence of adsorbed reactive species, the dangling bonds on the surface will often reform, bonding to adjacent atoms on the surface. This reformation process results in a new surface arrangement of atoms. This rearrangement away from the truncated crystal arrangement is referred to as surface reconstruction. Surface reconstruction on a semiconductor surface possesses both a short range and long range structure. The nature of the structure will depend on the temperature and surface chemical composition, as in the case of compound semiconductors. The reconstruction of a surface allows the surface energy to be decreased through the reformation of the broken bonds. Since the bonds are not at the angles and length found in the bulk, the energy expended in the creation of the surface is not fully recovered through the reconstruction process and hence the energy of the surface is still positive. The reconstructed surface of semiconductors will possess an altered chemical reactivity and therefore affects the process of epitaxial growth. The best studied surfaces, which are also used in epitaxial growth, are the (100)surfaces of Si and GaAs. In both of these cases the atomic level structure is dominated by the pairing of adjacent surface atoms, forming surface dimers. The dimers themselves can be arranged in a variety of configurations. The surface reconstruction of an epitaxial surface is most readily examined by electron diffraction techniques that can be easily incorporated into high vacuum growth apparatus, and by STM or AFM. The electron diffraction techniques average the surface structure over large dimensions while the STM images the atomic arrangement over a relatively small area. Both techniques can yield information on the details of the surface structure. The Si (100) surface is often characterized by

Figure 3-7. An atomic resolution image of the Si surface reveals that the terrace is composed of Si-dimer rows which alter their orientation with each successive layer.

rows of Si dimers running along the surface, as shown schematically in Fig. 3-7. The diamond structure of Si leads to an alteration of the Si dimer direction on successive planes of the Si crystal. This leads to dimer rows which rotate by 90" on each successive atom plane. This geometrical constraint has many implications for the transport of atoms on the surface and the attachment of new atoms to the growing surface. As seen in the STM micrograph of Fig. 3-7, the dimer rows end at step or ledge edges. If the ledge is parallel to the dimer row direction, a smooth ledge edge results. Ledges consisting of ends of dimer rows tend to be jagged and rough. The structure of these ledge edges is related to the detailed transport phenomena on the surface.

3.2.2 Surface Transport and Incorporation Film growth is the result of interaction between surface transport, structure and chemistry. The adsorbed species on the


growth front is often mobile and moves in order to find a favorable site for further decomposition, if necessary, and incorporation. The favorable sites on the surface are often the ledge edges and kinks described above which present a more reactive site. The initial deposition of an adatomcontaining species is typically thought of as occurring randomly over the surface. This picture is most correct for the physical deposition techniques which take place under ultra-high vacuum (UHV) conditions using elemental sources. The arrival of material to the growth front during CVD is quite different. In this case, adatom-bearing molecules can interact many times with the surface before final attachment to the surface. During these many interactions, the molecules can sample many different types of surface sites, i.e., kinks, vacancies, ledge edges, and so on. The final site of incorporation will have the appropriate geometry and chemistry allowing for the chemisorption of material on the surface. The reconstruction and the larger scale surface features therefore play a central role at the atomistic level in the epitaxial growth process. The growth species, once adsorbed on the surface, can often move over the surface through the process of thermal surface diffusion. Surface diffusion will occur at any temperature above absolute zero. Since surface diffusion is a kinetic process, it will be extremely sluggish at very low temperatures and increase exponentially with temperature. Like any other diffusional processes, surface diffusion follows Fick’s laws. The flux of a species across the surface will be proportional to its gradient in chemical potential.or, for dilute systems, its concentration grradient (Borg and Dienes, 1990) (3-13)

125

where J is the flux across a surface, D, is the surface diffusion coefficient, and C, is the local concentration of the diffusing species. The diffusion coefficient is determined by the same factor used in describing an atomistic picture of bulk diffusion. Temperature is the dominant factor in the diffusion coefficient which depends on an activation energy, Q: D, =Do

e-Ql(k~T)

(3-14)

If the activation energy is low, large diffusion rates can be observed. In general, activation energies for surface diffusion are smaller than that of the bulk. If diffusion entails the local breaking of bonds, a surface bonded atom most likely has fewer bonds to the substrate than a bulk atom has to neighboring bulk atoms. Hence, surface diffusion processes are typically more rapid. The diffusion coefficient also depends on a variety of factors which can influence both the pre-exponential term, D o , and the activation energy. The activation energy is comprised of the energy required for the atom to migrate from one low energy site, breaking its local bonds, to another low energy site. This contribution is referred to as the free energy of migration, Gmigr. The second contribution is related to the density of available sites for the atom to move into during the diffusion process. In many cases, the number of available sites is a strong function of temperature. The number of surface vacancies, ledges and kinks can all be a function of temperature through an activated process, characterized by an energy of formation, Gform.The concentration of vacancies, for example, typically follows an activated behavior. The activation energy is then the sum of both contributions, Q=Gmigr + Gform.The pre-exponential term of the diffusion Coefficient contains the frequency of jump attempts and geometrical configu-

126

3 Epitaxial Growth

ration (Borg and Dienes, 1990; Skewmon, 1989). The diffusion coefficient, along with the surface and interfacial energies, will determine the structure of the growing surface on an atomic and microscopic level.

3.2.3 Growth Behaviors The growth behavior in epitaxial systems is determined by the surface transport and the surface energetics of the materials system of interest. The above discussion focused on the surface transport required once the atoms are deposited. The atomic level motion and the energetics of the growth front will dictate the physical arrangement of these deposited atoms. The simple models of epitaxial growth predict different growth structures, derived from the chemical nature of the deposited atom, as well as the substrate serving as the template for the atomic arrangement of these species. In this case, there are generally two classes of epitaxial behavior based on whether the deposited atoms build a layer of the same structure and chemical composition as the substrate (homoepitaxial growth) or the growing layer is different in chemical composition, and perhaps physical structure, from the substrate (heteroepitaxial growth). Since epitaxial growth of a semiconductor requires that the deposited atoms assume an orientation which is directly related to the underlying substrate, there will, in both cases, be a known geometric relationship between the deposited layer and the underlying crystalline substrate. There are two dominant forms of growth behavior seen in homoepitaxial growth. These growth modes are related to the transport and incorporation kinetics of the adsorbed atom on the growth surface. Since there is no difference in the physical and chemical properties during homoepi-

taxy, this growth can proceed in a wellcontrolled manner. The growth or addition of atoms to the surface can proceed in two different growth modes or behavior: step-flow growth or layer-by-layer growth. These two-dimensional growth modes are often collectively referred to as Frank-Van der Merwe growth. (Three-dimensional growth can also occur, which results in a rough, uncontrolled interface.) In the stepflow mode, atoms deposited on the growth front diffuse to naturally occurring step edges. Since these step edges and step kinks, shown in Fig. 3-3, provide several atoms for the migrating atom to attach to, diffusing atoms will naturally bind there and be incorporated into the growing film. At high growth temperatures, the atoms have sufficient mobility to migrate across the surface before encountering other adatoms. The epitaxial growth then proceeds with the step-flowing across the growth front, leaving a very smooth atomically flat surface with a terrace-like structure. The characteristic terrace structure of step-flow growth, interrupted by monatomic steps, is seen in Fig. 3-7 for Si atoms on a Si surface. A similar terrace structure is found on GaAs during epitaxial growth by chemical vapor deposition as shown in Fig. 3-8 (Nayak and Kuech). This figure was obtained using an atomic force microscope. This particular epitaxial layer was grown at a high temperature, 650 "C, and a modest growth rate of 0.05 pm/min. At this growth rate, there is about one monolayer being grown every second. In this case, the steps are spaced about 0.1 pm apart. The miscut of this GaAs surface is 2" towards the (1 10) direction. This vicinal surface should have a terrace width of z 7 nm if the steps are monatomic in height. The large terrace width indicates that the steps observed in Fig. 3-8 consist of more than a


Figure 3-8. A GaAs growth surface, formed by metalorganic vapor phase epitaxy (MOVPE), is also composed of the TLK structure. The GaAs surface presented here in an atomic force micrograph (AFM) has multi-atomic steps which are 3 to 4 atoms in height (Nayak and Kuech).

single atomic step. This phenomenon is referred to as step-bunching and is often seen in many epitaxial systems. The origin of the step-bunching phenomenon is complex and can be affected by the detailed chemistry of the attachment of atoms to the step edge, the diffusional process on the surface and any impurities on the growth surface. In step-flow growth, the transport of the atoms across the surface is rapid compared to the rate at which adsorbed adatoms would meet, bond together and nucleate a new layer of the growth surface. Since all the atoms are reaching a step, an estimate of the lower limit on the diffusion coefficient on the surface from the terrace spacing, I , can be made through A.

- % 2 f i 2

(3-15)

where D , is the surface diffusion coefficient, t is the time for one monolayer growth, and

127

1/2 is the average distance an atomic would have to move on the surface before reaching a step edge. For the GaAs image shown in Fig. 3-8, this simple formula leads m2/s. to a value of about D , x 6 x The self-diffusioncoefficient for Ga self-diffusion in GaAs at similar temperatures is m2/s much lower, values of Dbulk% being reported. Such a large difference between the surface and bulk diffusion coefficients is typical of values found in the semiconductor materials systems and reflects the lower number of bonds and the higher number of diffusion sites available to the adsorbed atoms on a surface. The step-flow growth described above does not always occur under the epitaxial growth conditions encountered in many growth techniques. The step-flow mode of growth only occurs when the diffusing atoms have sufficient time and mobility to reach a step edge and be incorporated into the crystal before encountering a sufficient number of other adatoms that can lead to the nucleation of a new atomic layer on an existing terrace. Both a high flux of atoms to the growth front and a low growth temperature, leading to a slow surface diffusiion of adatoms across the growing crystal, can lead to the shift from a step-flow growth behavior to the other dominant growth behavior referred to as layer-bylayer growth. In layer-by-layer growth, adatoms will encounter other adatoms on the growth front. Some of these atoms will bind together and result in the formation of a new layer of the crystal. The surface structure present in layer-by-layer growth can often have growth occurring over several layers at once as depicted in Fig. 3-9c, b. This multilayer growth can lead to a rough surface with many atomic levels. This rough growth can become part of the internal structure of the epitaxial materials. Homoepitaxial growth is often

128

3 Epitaxial Growth

Figure 3-9. There are three principal growth modes commonly identified in thin film formation: a) Frankvan der Merwe or layer-by-layer growth, b) StranskiKrastanov growth (finite layer plus island growth) and c) Volmer-Weber or island growth.

used to create very sharp transitions in doping and hence electrical characteristics within the material. A smooth growth surface results in very sharp and planar internal interfaces. The use of conditions which result in a layer-by-layer growth mode will result, however, in a ragged transition region between two carrier types. Most epitaxial growth therefore is performed under growth conditions which yield step-flow growth behavior. The growth of a smooth internal interface becomes a more important issue when both the chemical composition and electrical characteristics change at the growth front as in the more complicated and yet more interesting case of heteroepitaxial growth. In this case, the deposited atoms

are different in chemical composition from the substrate. The best known heteroepitaxial semiconductor systems are Al,Ga, -,As grown on GaAs and Si,Ge,-, on Si. Heteroepitaxial growth has several distinct advantages over homoepitaxy as well as several complicating features. The major advantage is the use of bandgap engineering - the construction of layers with different bandgaps to achieve specific optical or electronic properties. There are several considerations which complicate the development of a heteroepitaxial growth technique. The primary considerations are the thermal expansion coeflicients and lattice parameters of the two materials and the strength of the chemical bonding across the heterointerface. These three issues are not independent variables but they all contribute to the formation of the thin film structures. The chemical bonding between the growing overlayer and the underlying substrate can determine the growth behavior leading to large scale morphological features. Three fundamental growth behaviors have been identified in heteroepitaxy associated with initial nucleation and growth of the film. They are characterized by the surface energies associated with the interfaces between the epitaxial materials and the substrate. These three modes, Frank-van der Merwe, Stranski-Krastanov, and VolmerWeber growth, can be observed in several growth systems. Frank-van der Merwe growth is the single-layer growth mode discussed in reference to homoepitaxial growth. In terms of surface energies, the heteroepitaxial layer is considered to ‘wet’ the substrate leading to good uniform surface coverage. The formation of the heterointerface results in the destruction of the solid-vapor interfaces which would have been present had the materials chosen to not interact. A simple criterion for the ‘wet-


ting’ of the substrate is then YSA/SB

YSA/V

+

YSA/V

(3-16)

where ySAISB is the interfacial energy between solid A and solid B and ysiIv is the surface energy of the solid vapor interface. The two solid-vapor interfaces were destroyed in the formation of the heterointerface. The formation of the interface is favored over the two separate interfaces. This type of behavior is found in systems which are chemically similar, e.g., GaAsAl,Ga, -,As, with similar lattice parameters. The ‘non-wetting’ of two materials hinders the formation of an initially single-layer growth mode. The epitaxial material does not bond to the substrate surface due to a difference in crystal structure, chemical reactivity or a very large difference in lattice parameter. Energetically, the inequality given in Eq. (3-16) does not hold and the two materials would prefer to form their own solid-vapor interfaces in preference to the solid-solid heterointerface: YSA/SB

’

YsA/V

+

YSA/V

(3-17)

The resulting initial growth behavior is a Volmer-Weber growth mode in which islands of the heteroepitaxial materials form on the surface of the substrate as shown schematically in Fig. 3-9. The material develops large growth islands whose density and shape are determined by the supersaturation of the growth ambient and the surface energetics of the growing islands. There are intermediate cases between these two growth mode extremes. The last major growth mode develops as a result of the interplay between the mechanical stresses which may develop in the thin film and the forces promoting adhesion between the epitaxial layer and the substrate. Lattice-matched heteroepitaxial semiconductor growth can proceed in a manner

129

quite similar to the homoepitaxial case, as described above, exhibiting a Frank-van der Merwe growth mode. Layer-by-layer and step-flow growth is observed in many systems in which the chemical bonding and lattice parameters are similar between the two materials. However there are many heteroepitaxial systems which have different bond strengths and lattice parameters with respect to the substrate. If the interfacial energy of the epitaxial layer and substrate favors a strong bonding or adhesion to the substrate, the initial stages of growth will generally be characterized by the deposition of thin planar films of epitaxial materials. The difference in lattice parameter will then lead to the development of internal stresses in the film due to the lattice mismatch between epitaxial layer and substrate. As the thin film strives to maintain perfect registry with the atoms in the substrate, the atomic positions in the epitaxial layer are shifted from their normal bulk values to conform to those of the atoms in the substrate. This shift in atomic position leads to a tetragonal distortion of the unit cell within the epitaxial layer and the development of an internal stress. Thin, highly perfect layers can therefore be grown in which the atoms in the thin layer are locked in perfect registry with the plane of the substrate surface despite the lattice mismatch. This process is referred to pseudomorphic growth. It is therefore possible to grow highly mismatched materials, without extended defects, to a limited or ‘critical’ thickness (Fitzgerald, 1991). The exact maximum thickness prior to the formation of extended defects which relieve the built-in stress, commonly referred to as the critical thickness, is specific to the particular materials combination. Many interesting materials structures can be invented and have been developed based on the use of pseudomorphic materials integrated in-

130

3 Epitaxial Growth

to a multilayer structure. The internal stress in the films can modify the electronic band structure which leads to the controlled formation of new optical and electrical properties which cannot be obtained in the nonstressed semiconductors. As the epitaxial layer grows, this internal stress continues to develop until the elastic energy stored in the film is sufficient to be released in the formation of defects. These defects occur typically in the form of dislocations. These dislocation can further multiply and propagate through the extent of the film releasing the internal stress and relaxing the atomic positions in the epitaxial layer to their bulk positions. Once the strain in the deposited film becomes too large, the film relaxes and three-dimensional islands form on the surface. The formation of the strain relieved structure, beyond the critical thickness, often leaves a structure in which there is a thin pseudomorphic layer remaining next to the substrate with the three-dimensional island growth of the defected and strained relieved materials residing above this layer. This growth mode, schematically shown in Fig. 3-9 b, is referred to as a Stranski-Krastanov growth mode. There are several common epitaxial growth modes which have been observed, as described above. The appearance of a particular growth mode has been rationalized in terms of the interfacial energies associated with the epitaxial layer-substrate interface and the stresses induced by the lattic mismatch. Other considerations can often dominate the appearance of a particular growth mode. The temperature and rate of growth, as well as other kinetic factors, can often give rise to growth behavior which would not be expected on the basis of purely energetic considerations. Lastly, the final microstructure and morphology of the epitaxial films will also be affected by

the initial perfection of the substrate and the difference in thermal expansion coefficients of the two materials. Defects in the substrate can propagate into the epitaxial layer. A dislocation intersecting the growth front will continue into the epitaxial layer since this structural information forms part of the epitaxial seed that is replicated into the growing film. Almost all epitaxial films are grown at temperatures which are substantially higher than room temperature. The difference in thermal expansion coefficients may also generate a great deal of strain in the film upon cooling from the growth temperature. This strain may also be released through the formation of dislocations and other extended defects.

3.3 Chemical Vapor Deposition: Technology and Issues Chemical vapor deposition or CVD is the deposition of thin films from the gas phase onto a substrate. As such, this process encompasses a wide variety of concerns which are not seen in other forms of crystal growth, such as those based on physical evaporation. Gas phase and surface chemistry, along with the thermal fluid environment from which the crystal is growing, must be controlled to a high degree in order to produce a high quality crystal that will become the device structure of interest. The basic CVD system consists of a flowing gas phase ambient which passes over a heated substrate. The mechanical aspects of the CVD system are conceptually divided into two separate components: the gas panel and the reactor. The gas panel mixes and schedules the gas phase reactants or nutrients into the reactor. The gas panel construction is designed so that accurately synthesized mixtures of reactants are injected at precisely the cor-

-

3.3 Chemical Vapor Deposition: Technology and Issues

Induction Coil \

Silicon Wafers / &mm,mm

m

131

Gas Inlet

,Radiant

Heaters

Gas Inlet

mmmmm

Horizontal CVD Reactor

,Exhaust Barrel CVD Reactor

. Inlet

control @

Gas

xhaust

Horizontal LPCVD Reactor

Vertical CVD Reactor

Figure 3-10. Schematic of several reactor configurations commonly employed in chemical vapor deposition technology.

rect time to yield the desired structure. The valves and meters used in its construction are designed to exclude unintentional contaminants which would lead to unwanted impurities in the films. While the gas panel is of a common design in most CVD systems, the CVD reactors are quite varied depending on the growth chemistry and desired product. The reactor design is therefore materials specific. Examples of various reactors used in the epitaxial growth of semiconductors are shown in Fig. 3-10. The features important in most of these reactors centers on the uniform flow of nutrients over the growth surface of the wafer and the removal of the reaction by-products. The CVD growth of semiconductors is often conceptualized as consisting of several

steps, as schematically shown in Fig. 3-11 for the case of Si growth. Generally, the slowest of these steps will limit the observed growth rate. There are several principal factors which influence each of these primary conceptual steps in the CVD epitaxial process. Energy is directed into the reactor in order for the desired chemical reactions to occur. This energy comes typically in the form of heat through the placement of the reactor in a furnace or through the use of a locally heated substrate holder. In the latter case, the walls of the reactor and the gas stream can remain cool relative to the hot substrate. This latter configuration suppresses the gas phase decomposition of the nutrients prior to their arrival at the growth front. In all cases, there are common features to the CVD process

132

3 Epitaxial Growth

3.3.1 Reactors: Mass, Fluid, and Thermal Transport

3.3.1.1 Fluid Behavior and Reactor Design

= RT

Transport to surface:

Jgas

Surface Reaction:

Jsurfaco

gas-

ps"rllcl

6

= K , PsUrbCe

Figure 3-11. Si growth, like most semiconductor growth systems, can be conceptualized as consisting of several steps as shown here, involving gas phase and surface chemistry as well as surface transport leading to the incorporation of the deposited atom into the growing structure.

which bear on the growth of most epitaxial films. The specific nature of these elementary steps can influence the film composition, its electrical and optical properties, the uniformity of the thickness of the film and properties across the substrate and between substrates, the structure and abruptness of electrical and compositional interfaces, and finally the presence of defects in the film. The issues of uniformity and defects bear directly on the utility of the epitaxial films in later device processing. Defects, particularly morphological defects on the growth surface, make subsequent processing difficult, particularly the process of photolithography. The discussion of the epitaxial growth of semiconductors by CVD will therefore center on the principal influences of each of these primary steps in the microscopic model of the film growth.

The CVD reactor is typically a reaction chamber through which the reactant gases flow and in which the heated wafers are placed. There are several principal reactor geometries which are,used in the growth of compound and elemental semiconductors. The choice of a specific reactor depends on the growth chemistry and pressure regime used in the growth process. These operating conditions are in turn determined by the growth chemistry. The four reactors shown in Fig. 3-10 are those most commonly found in the manufacturing of epitaxial semiconductors. The horizontal, barrel and rotating disk reactors are all forms of 'cold-wall' reactors. These reactors operate at relatively high pressures, between 1 Torr and atmospheric pressure (760 Torr). The fourth reactor pictured in this figure is a low pressure 'hot-wall' reactor referred to as an LPCVD system. This reactor operates at pressures as low as 0.001 Torr or about atm. The mass and fluid transport in these systems can be quite different. The first three systems operate in the viscous fluid regime where the continuum mechanics description of the fluid behavior can be used. The LPCVD can be operated in the molecular flow regime. The specific flow regime of the CVD environment is characterized by the Knudsen number which is based on the ratio of the mean free path of the gas molecule, l , to the typical physical dimension of the reactor, L : K n = l / L . The mean free path of a gas molecule of diameter d, at a gas pressure of P , is given by (3-18)


The Knudsen number is one of the many dimensionless numbers which can be used to describe general features of the fluid, thermal and mass transport. The mean free path of a gas molecule at room temperature is approximately given by 1 (cm)=O.OOS/P, where P is the pressure in Torr. At atmospheric pressure, ( 760 Torr) the mean free path is about 70 nm while at a low pressure of Torr the mean free path is 5 cm. The major flow regimes are then classified by the magnitude of the Knudsen number:

-

viscous flow transition flow molecular flow

--

*

\ TURBULENT

LAMINAR

133

----A VELOCITY

-

Kn < 1 Kn E 1 Kn 9 1

The viscous regime is characterized by low temperatures and high pressure. Most CVD systems which operate at moderate or near atmospheric pressures are therefore in the viscous flow regime. In this pressure regime, the fluid transport is described by the traditional fluid transport models which provide the equations governing the thermal, momentum and mass transport in the reactor. While the complete solution of the transport equations is generally difficult, several simplifications have arisen which provide a heuristic model of the growth environment. The design of CVD systems within this pressure regime typically focuses on the development of a laminar flow profile within the reactor. Laminar flow is characterized by the gas flowing smoothly across the surface, without turbulence, as shown in Fig. 3-12 for the case of a horizontal growth system. In the rotating disk reactor, a spinning disk is the substrate holder which acts as a centrifugal pump, resulting in a radial flow of gas across the surface. In the absence of laminar flow, turbulence or irregular mixing leads to a high degree of non-uniformity in the film growth since the gas flow and hence the flux of nutrients to the surface is

Figure 3-12. Laminar flow profiles can be developed in the reactor chamber leading to a controlled and regular flow of gas over the growing substrate surface.

changing with time. Laminar flow is readily established in most systems within a short entrance length of the reactor. The full fluid mechanical treatment can be subsequently carried out for most of these reactors. Such modeling efforts, requiring the numerical solution of the coupled heat, mass, and momentum transport equations, can be solved with considerable effort. The results of these calculations provide a detailed picture of the transport of nutrients within the CVD reactor. The calculated flow patterns resulting from such a calculation for a horizontal system is presented in Fig. 3-13 (Vossen and Kern, 1991). A complex fluid flow behavior within the reactor can be seen in this figure. The complexity of these flow fields, which add to the nonuniformity of the growth, can often be suppressed by an appropriate choice of growth conditions. In particular, the reduction in the reactor pressure at a constant mass flow can eliminate many of these recirculation effects and lead to a laminar flow profile in the reactor. Once laminar flow is established, the resulting gas phase fluid transport across the growth front is often characterized by the use of boundary layer

134

3 Epitaxial Growth

Figure 3-13. Numerical solution of the basic equations governing the mass, fluid and heat transport in the reactor can be used to predict many of the complex flow patterns and phenomena in a CVD reactor. This figure illustrates the results of such a calculation for a horizontal reactor. (a) The predicted flow pattern from a symmetric and asymmetric inlet geometry. The latter leads to a complex fluid flow. (b) Recirculations in the flow field can result from geometric differences in the reactor shape [Vossen and Kern, 19911.

theory. Boundary layer theory is a simplified description of fluid flow based on specific assumptions. A boundary layer is a hypothetical gas phase region near the growth surface over which the gas velocity is zero. This stagnant region of gas allows for the easy solution of the diffusion equation for mass flow across this boundary layer. The extent of the boundary layer is dependent on the gas velocity and viscosity. It arises from the ‘no-slip’ condition at the reactor walls where the gas velocity is zero. In practice, the assumptions of the boundary layer theory are not strictly met for most reactors, yet this simplification can predict some of the general features of the growth process. The flux to the surface is found by postulating a growth reaction at the surface in series with the gas phase transport to the growth front as seen in Fig. 3-11. The diffusion of growth nutrients

across this boundary layer provide the growth front with the reactants for the film to develop and grow. At steady state, the flux through the gas phase and the reaction rate at the surface are equal. Several reviews and discussions of the modeling methods and considerations used in describing these reactors can be found in the references to this chapter (Hess and Jensen, 1989; Middleman and Yeckel, 1986; Ouazzani and Rosenberger 1990; Vossen and Kern, 1991). LPCVD reactors, as shown in Fig. 3-10, typically have a large number of wafers that are stacked close together within the heated region of the furnace. Models of these reactors consider the gas flow around the wafers as well as between the wafers. The calculation of the fluid flow in such systems is divided into two separate regimes where the gas flow in the annular region around the wafers is often treated as a viscous fluid flow and the mass transport radially between the wafers is considered to be diffusionally based. This model provides an accurate picture of the fluid and mass transport until the characteristic distances, such as the wafer spacing, become less than the mean free path in the gas. Reactors operating in the molecular flow regime, K n 4 1, are often used when the growth rate is limited by the surface reaction rate of a growth species. In this case, the simple models based on continuum fluid mechanics and diffusion are no longer accurate. The detailed motion of individual gas molecules, as they enter, transverse, react and leave the reactor must be considered. This detailed molecular description is addressed through numerical techniques which have been developed to build a macroscopic description of the growth process from the trajectories of individual molecules. These calculational methods, referred to as Monte Carlo techniques, are


based on the statistical nature of molecular flow. Such numerical models require timeconsuming calculations, but can yield an accurate description of mass transport in the reactor. 3.3.1.2 Mass and Thermal Transport

The fluid behavior within the reactor provides a description of the overall mass motion in the system. In LPCVD growth there is a high mole fraction of the reactants in the gas phase, while, in the case of higher pressure growth processes, the reactants are diluted in a carrier gas. A carrier gas is typically an inert dilutent, such as He, N, , or H, , which is used to control the partial pressure of the reactants while maintaining an overall reactor pressure or flow. In the case of LPCVD systems, the mass transport is largely given by the fluid flow. The high pressure reactors possess a reactant mass transport due to both convection, through entrainment in the carrier gas flow and diffusion through the boundary layer. The gas phase diffusion coefficient for thermal and mass transport are similar in magnitude and their transport in these types of reactor are described by similar theoretical formalisms. The uniform growth of an epitaxial film requires that the flux of the reactants to the growth front be uniform over the wafer surface as well as among all the wafers in the reactor. This uniformity requirement places constraints on the mass transport in the reactor. The mass transport must be designed to provide this constant flux to the surface despite changes gas phase conditions in the reactor. The mass transport in high pressure reactors is complicated by the consumption of the nutrients as the gas flows over the heated growth surface. The growth rate, GR, of the film, measured in thickness per unit time, is equal to the flux of nutrients at

135

the growth surface (3-19) where D is the gas phase diffusion coefficient and c is the concentration of reactants in the gas phase at the growth front and no is the number density of atoms in the film. The gas phase diffusion of reactants near the surface is modified by the overall fluid flow and the gas phase concentration of reactants. The gas phase reactant concentration will vary over the surface of the wafer because of depletion of the reactants from the gas stream resulting from upstream deposition of the thin film. The design of the reactor can substantially reduce these depletion effects. Early modeling efforts treated this depletion of the gas phase of reactants through the formation of a diffusional boundary layer of thickness ddiff,in analogy to the boundary layer formed as the laminar flow profile is generated in the fluid flow. This diffusional boundary layer will grow as the gas flows over the heated substrate and the gas phase near the growing wafer becomes depleted of nutrients (3-20) where v is the kinematic viscosity of the gas, V,, is the mean stream velocity of the gas, and x is the distance along the gas flow. The flux to the surface or GR can then be approximated by

c being the gas phase concentration of the reactants in the bulk of the gas at a given position along the reactor. Since 6diff is a function of position in the reactor, the growth rate will, in principle, vary along

136

3 Epitaxial Growth

the length of the reactor. In order to achieve uniform growth over large substrate areas in a horizontal reactor, the cross-sectional area of the reactor is often reduced in order to locally increase the V,, in the reactor. This increase in the gas velocity along the reactor can offset the drop in the growth rate due to gas phase depletion. Other approaches to increasing the uniformity have been the use of other alternative carrier gases to H, , which alter the gas phase viscosity, as well as the use of very high reactor flow velocities. The latter approach can lead to the growth of uniform films at the expense of low utilization of the growth reactants.

3.3.2 Gas Phase and Surface Chemistry The description of most chemical systems begins with an equilibrium thermodynamic analysis of the overall process. The term equilibrium implies that the system is unchanging in time which is clearly not the case for the process of crystal growth. The process of crystal growth is inherently not an equilibrium thermodynamic process since it entails a net deposition of material. As described above, the growth rate of a material can be affected by a variety of macroscopic transport phenomena. No matter what the transport limitations are in the system, there must be a thermodynamic driving force for the deposition of material. This driving force or supersaturation can be calculated by the application of conventional concepts of the law of mass action to the chemical reactions of importance for film growth. This driving force arises from the free energy change of the overall chemical reaction responsible for the net deposition of material. The application of thermodynamics can provide some useful and important information on this driving force. Thermodynamics can indi-

cate whether a reaction is energetically possible and, if it is possible, the expected maximum extent of that reaction. While thermodynamics can indicate the feasibility of a reaction, the actual occurrence and rate of the reaction will depend on the temperature and the specific species involved. Not all reactions will occur under the desired thermal conditions supplied in the reactor. In those cases, non-thermal energy sources are often used. External energy sources, such as ultra-violet (UV) radiation or an applied plasma, can provide sufficient energy to initiate the growth reaction through the breakdown of the growth precursor. In most cases, the simplicity of implementation and uniformity of growth afforded by the simple heating of the substrate is favored over these other energy sources. The growth chemistry occurring within the reactor is generally divided between that occurring in the gas phase and on the surface. There has been a wide assortment of gas phase compounds used in the growth of semiconductors. Some of the more common reactants for silicon deposition are listed in Table 3-2. Many of these compounds will decompose or react in the gas phase at relatively low temperatures. Disilane, Si,H,, will rapidly decompose in the gas phase at temperatures of 700°C. The reaction products will further react in the gas phase producing other species which eventually reach the surface. The gas phase decomposition of Si,H, eventually leads to a mixture of SiH,, Si,H,, and SiH, reaching the surface, as shown below. Disilane decomposition (unimolecular decomposition) Si,H, * SiH,+SiH, Silane formation (gas phase reaction) SiH,+H, * SiH,


137

Table 3-2. Thermodynamic and physical properties of Si-based growth sources. State at room temperature

Vapor pressure at 22°C (Torr)

Free energy of formation (kcal/mol)

SiCl, SiHC1,

liquid liquid

- 148.16

SiH,Cl, SiH,Cl SiH, Si,H,

gas gas gas gas

208 533 1200 (23 psig) 47 990 (928 psig)

Compound

Disilane reformation (gas phase reaction) (3) SiH,+SiH, * Si,H, In this case, the use of disilane leads primarily to the arrival of SiH, and Si,H, to the growth front since reactions (2) and (3) occur very rapidly in the gas phase at elevated temperatures in a H, carrier gas. Such a rapid reaction leads to a very low steady state concentration of SiH, in the gas phase. If the gas phase decomposition of Si,H, goes to completion, i.e., the formation of SiH,, disilane-based growth of Si would then result in a factor of two in growth rate over that found with SiH,. In this case, gas phase reactions result in the in situ generation of a growth precursor, SiH,, which reaches the surface. Not all gas phase reactions lead to benign or useful reaction products. Many compound semiconductors are grown through the metal-organic vapor phase epitaxy (MOVPE) process. A feature of this process is the use of volatile metal compounds, such as (C,H,),Ga and (CH,),In, typically in conjunction with group V hydrides, such as ASH, and PH,. The metal organic compounds, while being stable at room temperature, do undergo gas phase decomposition at temperatures low compared to typical substrate temperatures. These compounds decompose and react in the hot gas phase regions of the

- 11 5.34 -43

+ 13.6 + 30.4

reactor, as well as at the growth surface, leading to depletion or elimination of the growth reactant prior to its arrival to the growth surface. The decomposition of the metal organic compounds leads to nonvolatile by-products, containing the metal species, which are deposited on the reactor interior walls. This gas phase pre-reaction results in a reduction of the growth rate and an increase in growth rate non-uniformities along the wafer. Other types of deleterious gas phase reactions lead to the formation of undesired gas phase chemical species which are subsequently transported to the growth surface and result in defect formation. This is particularly true for particle-forming reactions. The gas phase reactions described above all depend on temperature and reactor pressure. In the case of the metal-organic compounds, the use of a 'cold-wall' reactor allows the gas phase to remain cool prior to its arrival to the growth front. The gas phase reactions are therefore suppressed. Many reactions, such as the uni-molecular decomposition of Si,H, given in Eq. (l), rely on collisions with other gas phase molecules for their initial stages of decomposition. These gas phase decomposition reactions can be effectively suppressed through the use of low reactor pressures. The low reactor pressures reduces the probability of gas phase collisions and sub-

138

3 Epitaxial Growth

sequent decomposition. Low pressure reactors utilize this dependence on the reactor pressure to eliminate the gas phase decomposition of the growth reactants. In these cases, the gas phase chemistry no longer plays a great role in the growth chemistry. As a result, the direct reaction of the growth reactants with the growth front is the principal reaction in the overall growth chemistry. The thermodynamic and mass transport relationships can determine the necessary conditions for growth and the uniform arrival of the growth nutrients to the surface. Once at the surface, the decomposition and incorporation of the material will be dependent on the details of the surface structure and surface chemistry. The elementary steps in these surface processes start with the adsorption of a reactive species. The adsorption of these species depends on the availability of an adsorption site and the energy required or released upon adsorption for reactions. There are often many gas phase species competing for the same surface sites. The resulting surface composition, in terms of adsorbed species, will be the result of this competition, determined by the relative gas phase concentrations and the energetics of the adsorption process. The surface adsorption of reactive species can be described by several simple models. Most of these models are based on equilibrium thermodynamic considerations. In these models, the surface concentration of reacting species will result from a balance between the arriving species, Rgas,interacting with vacant surface sites, V, and those adsorbed species, R, , which may subsequently be available for desorption. adsorption:

Rga,+V

desorption: R , + V

R,

(4)

% R,,,+V

(5)

where k,, and k,, are the rate constants for the adsorption and desorption processes. The simplest of these models is the Langmuir adsorption isotherm. This model assumes thermodynamic equilibrium between the gas phase and surface adsorbed species. The constraints in the model include the restriction of only one type of surface site and a limit of one monolayer of adsorbed species. The fraction of available adsorption sites is given in terms of the reactant partial pressure in the gas phase. The fraction of available adsorption sites, 0,covered by given reactive species is given by

(3-22) where P is the partial pressure of the reactive species, Rgas,over the growth surface, and a is typically written in Arrhenius form as

(3-23) Qad being an activation energy associated with the adsorption process, and C I a~ constant (Adamson, 1990). This simple equation allows for a description of the temperature dependence and the partial pressure dependence of the surface concentration of reacting species and can often, despite its simplicity, describe the features of many adsorption processes. At low partial pressures, the surface coverage is simply proportional to the gas phase concentration: 0z CI P . Correspondingly, at high pressures, the surface coverage becomes unity. Temperature affects the surface coverage through favoring high coverages at low temperatures where the desorption of species would be suppressed. The Langmuir adsorption isotherm can be modified to account for more than a single adsorbed species. If several species


are competing for the same adsorption sites, the site coverage of each species will be affected by the presence of the other chemical entities on the surface. The site fraction of a particular adsorbed species is then given by

139

The growth rate expression, formed by combining these two expressions, will have a temperature dependence related to both the adsorption and decomposition processes, combined with the gas phase concentration of reactant at the growth front

(3-24)

where the sum is over all the species ( j ) available for adsorption. This is a common situation during growth. In the case of SiH,-based Si growth, SiH, , SiH,, and H all complete for the same sites on the surface. Adsorption is the first step leading to a surface reaction. Once adsorbed, the reactant undergoes further decomposition or reaction with an ultimate by-product being the incorporated atom. There are several simple types of surface reactions which may occur. In practice, these simple models may not adequately describe the detailed surface reaction kinetics, but they do serve to describe the overall phenomena. The reaction rate of adsorbed species will be dependent on its surface coverage, the concentration and nature of the nearest neighbors and the temperature. The gas. phase chemistry is coupled into the surface or heterogeneous reactions to complete the model of the growth chemistry. The simplest model of the surface growth reactions is the direct decomposition of the reactant on the adsorbed site. In this case, the growth rate will be proportional to the surface coverage of the adsorbed reactant GR cc 0 or GR=krX,O

(3-25)

where krxnis a rate constant for the decomposition of the surface species. This rate constant is also assumed to follow an Arrhenius rate expression (3-26)

This relationship can lead to a complicated behavior dependent on growth temperature and reactant concentration. For many systems, the partial pressures and resulting surface coverages of reactant are low, leading to the reduced expression GR M krxn,oa. P exp

(-";;"...'> (3-28)

This expression indicates that the growth rate will have a linear dependence on the gas phase reactant concentration and an exponential dependence on temperature. Such behavior is often seen in many CVD growth systems despite the actual presence of a more complicated growth chemistry than assumed in this simple model. More complicated surface reaction schemes have been proposed to describe the CVD growth behavior. Many surface species require the co-reaction of two adsorbed species on nearby sites for the completion of the growth reaction. In this case, the growth rate will be proportional to the surface coverage of both reacting species. Again, the surface coverage of each species could be described by the Langmuir model. The growth rate reaction will then be proportional to both reactant surface coverages. The constant of proportionality will be the reaction rate constant k,,, GR =

krxn a1 a2

e pz

(1+ a , PI +a, P2)2

(3-29)

140

3 Epitaxial Growth

This particular model is referred to as the Langmuir-Hinshelwood reaction law and has been used to describe the growth behavior of GaAs from (CH,),GA and ASH,. The temperature and pressure dependencies of this expression are quite complicated and have been used to explain the often observed complex behavior of the growth rate on reactor variables. The generalization to other growth situations can be derived through a combination of the adsorption law and the assumption of a specific chemical mechanism. Examples of the development of these rate relationships for common CVD epitaxial systems will be discussed later. The surface reactions involved in epitaxial growth are dependent on the detailed surface structure present at the growth temperature under the chosen growth conditions. These surface structures are, in turn, partly determined by the presence of adsorbed species. Steps, kinks, and terrace structures, as well as local reconstruction, can present a variety of different adsorption sites for the arriving chemical species. In particular, impurities can adsorb, in addition to the primary growth reactants, on the surface perturbing the growth chemistry and the growth morphology. The incorporation of impurities has been described using the same concepts as discussed for the growth reaction itself. The impurity source can undergo gas phase reactions, adsorb on the surface, and be incorporated into the growing film. Many impurity sources can only strongly adsorb at specific surface sites, e.g., steps on the surface. Small variations in substrate orientation, sometimes referred to as miscut, lead to large changes in the efficiency of impurity incorporation. Such detailed factors can complicate the growth behavior and final properties of the epitaxial film.

3.4 Liquid Phase Epitaxy (LPE) Technology Liquid phase epitaxy (LPE) was first demonstrated by Nelson (1963) and has been used to deposit a wide range of materials, including 111-V and 11-VI semiconductors, as well as magnetic garnet materials (Giess and Ghez, 1975).The flexible nature of LPE and the ability to produce high purity material has been used to produce the first demonstrations of many electronic and optical devices, including the first room temperature cw operation of a GaAs/Al,Ga, -,As double heterostructure laser. The advantages of LPE include relatively simple and inexpensive equipment, high utilization efficiency of precursor material and the ability to produce high purity and high optical efficiency material over a wide range of thicknesses. In addition, LPE is a near-equilibrium growth technique. The growth rate is strongly dependent on the substrate orientation, which leads to unique abilities to regrow and planarize patterned substrates. These advantages have made LPE a common deposition technique for a wide range of LEDs where low cost is a major issue as well as buried heterostructure and DFB lasers which take advantage of LPE's regrowth capability. The weakness of LPE comes from its inability to controllably grow very thin layers of a specific composition required in heterostructure electronic devices such as superlattice or quantum well devices. The growth rate in LPE is generally higher than in MOVPE or MBE, which limits LPE's ability to produce very thin layers. Absolute layer thickness control is also not as good as these other techniques, as a result of the manner by which the growth is initiated and terminated. Because LPE is a near-equilibrium technique, not all materi-

3.4 Liquid Phase Epitaxy (LPE) Technology

als can be grown by this technique. Miscibility gaps occur for some compositions of ternary and quaternary materials which prevent their deposition by LPE due to phase separation during growth. Finally, surface morphology is typically not as good as in MOVPE or MBE, which again precludes its use for the growth of certain device structures. Thus, for more sophisticated devices which include quantum wells, superlattices or etched gratings, MBE and MOVPE are most commonly the growth techniques of choice. LPE growth occurs by precipitation of the desired material out of a supersaturated solution onto a substrate. In contrast to MOVPE and MBE, LPE takes place very near to equilibrium in a column-111-rich environment. The solvent element is typically the column111 constituent of the compound to be deposited (Ga or In); in some cases other low melting point metals such as Sn, Bi or Pb are used as the solvent. The thermodynamic driving force for LPE growth is produced by cooling the system below the liquidus temperature. In the

0

Ga

0.5

x-b

1

As

Figure 3-14. The Ga-As phase diagram can be used in the development of the LPE growth process of GaAs.

141

phase diagram for GaAs, shown in Fig. 3-14 (Casey and Panish, 1978), only a liquid exists above the convex line. Melt growth (i.e., Czochralski) is performed at the melting point of the stoichiometric solid (1238°C for GaAs) while LPE is performed at much lower temperatures. LPE growth of GaAs takes place by cooling a solution of Ga, containing a small amount of As at a temperature, TI, to its liquidus temperature, T2,at that composition, for example point B in Fig. 3-14. Upon further cooling to temperature, T3, at point C, the solution becomes supersaturated and GaAs begins to precipitate or grow onto the substrate. When sufficient GaAs has precipitated out, such that the liquid is no longer supersaturated, growth stops at point D. During this period, the liquid composition changes from B to D. Since most of the 111-V binary compounds are line compounds (i.e., no measurable homogeneity range), only stoichiometric GaAs is deposited. In ternary and quaternary compounds, this is not necessarily true since the composition of the deposited film depends on the supersaturation and liquid composition. As a result, not all alloy compositions can be grown at an arbitrary temperature. Many ternary and quaternary alloys possess a miscibility gap. A miscibility gap in the phase diagram implies that two solid phases or two solid compositions will simultaneously grow out of the liquid solution depending, of course, on the specific temperature and liquid compositions. Three principal variants of the LPE technique have been reported in the literature: tipping, dipping and sliding. Only the latter variant slider-based LPE, has seen widespread use. Tipping was the technique first used for LPE. In the tipping technique, the melt and substrate are placed at opposite ends of a crucible. Growth begins

142

3 Epitaxial Growth

by tipping the crucible so that the melt flows over the substrate. Growth is terminated by returning the crucible to its original position, thus removing the melt from the substrate. This method is limited to the growth of a single layer. The dipping technique permits the growth of multiple epitaxial layers on the substrate. In the dipping technique, the substrate is dipped into the melt to initiate growth, and removed from the melt to terminate growth. The substrate is moved to an additional dipping station and the growth procedure is repeated, accomplishing the growth of an additional layer in a multilayer structure. This technique has been used for multiple layer growths and for some commercial devices, however, like the tipping technique, thickness uniformity is only moderate. Device requirements of multiple layer structures, with thin layers of different compositions, have led to the dominance of the sliding method. The slider method is the most widely used for LPE because it permits straight-

forward growth of multiple layer structures with acceptable thickness uniformity. A schematic view of the slider system is shown in Fig. 3-15 and consists of a tray which holds the substrate and a slider which has multiple bins for different melts (Kuphal, 1991). Each melt is associated with the growth of a different layer and therefore requires a different melt composition. For example, p-n junctions are made by having one melt contain a p-type dopant and the next melt an n-type dopant. Heterostructures can be produced by preparation and use of ternary or quaternary melts. The slider fits over the substrate holder tray and growth is initiated by sliding a bin containing the desired melt over the substrate. The components of the LPE system are made of graphite. The melts do not generally wet the graphite, which permits termination of growth by wiping the melt off from the substrate when the slider is moved. This assembly is housed in a quartz tube which is purged with high purity hydrogen. A movable multi-zone fur-

Solution Bins

Movable Furnace

I Slider Assembly

Figure 3-15. Schematic view of the commonly used horizontal slider-type LPE system.


nace typically surrounds the quartz tube. Often a heat pipe is placed within the furnace to promote flat temperature zones. The slider is positioned using a quartz rod; this can be done manually or through a stepper motor controlled by a computer. Graphite covers are typically placed on top of the melts to prevent evaporation and contamination of the liquid melt. The melts that make up the LPE system can either be single- or two-phase. A single-phase melt is a liquid that is supersaturated at a specific temperature. The supersaturation must be small enough to prevent spontaneous nucleation of the solid phase in the melt. A two phase solution consists of a melt which contains a solid source. The graphite cover may be replaced by a substrate of the type being grown, assuring uniform saturation of the melt. The major advantage of the twophase method is to simplify control over the growth process. For example, in LPE the growth rate is determined by the exposure time and the degree of super saturation. In the two-phase method, the floating substrate melt cap acts as a source or sink of material to ensure saturation of the melt during the initial heating state. In addition to ensuring saturation, the cover also prevents source evaporation and helps control the geometry of the melt. Since there are now two substrates, when the system is cooled, growth takes place on both substrates. Depending on the thickness of the melt, this can result in a desirable decrease in the growth rate on the intentional substrate. It should be noted that this technique is most advantageous for the growth of binary compounds since substrates with arbitrary ternary and quaternary compositions are not available. The slider technique has been developed through many years of research and development experience. Slider LPE production-scale systems

143

exist which are computer controlled and can handle multiple round substrates, up to 50 mm in diameter (Shea et al., 1993). There are a number of practical problems in the LPE-slider technique. For example, enhanced edge growth on the substrate is a potential problem for LPE. Enhanced edge growth occurs for several reasons, such as an orientation-dependent growth rate, thermal convection and nonone-dimensional diffusion of the solute in the melt. If the grown layer thickness at the edge of the substrates becomes larger than the space between the substrate holder and the melt slider, graphite and the grown material will be scrapped off by the slider and cause scratches and other defects on the growth surface. This space cannot, however, be made too large or some of the melt will be carried over and contaminate the adjacent melt. The substrate-slider spacing is typically between 20 and 100 pm, which puts limits on maximum layer thickness as well as tolerances on substrate thickness. Enhanced edge growth can be minimized by reducing thermal convection in the melt through the use of small cooling rates or isothermal (step) growth and through the use of thin melts with lids which reduce two-dimensional diffusion. It can also be eliminated by making the melt contact area smaller than the substrate. 3.4.1 LPE Growth Procedures

The growth procedures in the LPE-slider technology are centered on the preparation of the melts and the time-temperature program of the subsequent growth sequence. Figure 3-16 illustrates a representative temperature cycle for LPE growth (Kuphal, 1991). The system is first heated to a temperature which is above the saturation temperature T,.This step produces a homogeneous melt. The temperature is

144

3 Epitaxial Growth

I

b

Time

Figure 3-16. Representative temperature cycle for LPE growth.

then lowered and the melt brought in contact with the substrate. Two common methods for lowering the temperature are shown, ‘equilibrium’ and step cooling. In ‘equilibrium’cooling, the system is slowly cooled during the growth step from to an end temperature, TE. In step cooling, the system is cooled to the supersaturation temperature TA prior to making contact with the substrate, and subsequent epitaxial growth proceeds at this at a fixed temperature. The substrate can also be heated to above the saturation temperature in contact with an undersaturated melt in order to perform an in situ etch of the substrate surface. This etching step can aid in removing saw or polishing damage as well as creating a more uniform density of nucleation sites. The disadvantage of this melt-back procedure is that can adversely affect surface morphology through nonuniform etching. As previously stated, LPE is a close-toequilibrium growth process. If growth went completely to equilibrium, the amount of material deposited would just equal the amount of solid precipitated from the supersaturated melt to re-establish the solid-melt equilibrium at that temperature. This situation does not normally occur because diffusion in the melt is not

rapid enough to achieve equilibrium conditions throughout the melt volume. The growth rate is typically limited by diffusion of the supersaturated species through the melt to the substrate surface. A simple diffusion model can be developed in which the melt is assumed to be semi-infinite in height and isothermal with no convection cells. Growth is assumed to proceed by deposition only on the substrate and the growth rate is determined by diffusion of the solute (the low concentration component of the melt). In the case of GaAs growth, this would be diffusion of As in the Ga melt to the GaAs substrate. The thickness of the epitaxial layer, d, that would be grown during time t is given for uniform cooling by

where R is the cooling rate, C i s is the concentration of the solute (As) in the solid, m is the slope of the liquidus curve which is assumed to be constant over the small temperature change associated with growth, D is the diffusivity and t is the growth time. For the step cooling case, the epitaxial layer thickness is given by (3-31) where AT is the temperature step (Casey and Panish, 1978). Growth rates for noninfinite melt heights as well as for ternary and quaternary materials have also been derived (Kuphal, 1991). Typical growth rates for LPE are around 1000&min. While a variety of techniques have been developed to lower the growth rate and provide short exposure times to the melt, LPE cannot compete with MOVPE or MBE in the formation of extremely thin layers.


145

Figure 3-17. Planarization of a 4 pm deep groove by LPE growth

of A1,Ga - Js/GaAs/Al,Ga layers [Kuphal, 19801.

One of the main characteristics of LPE is that it is a simple method to produce material with high purity and high optical efficiency. These positive material properties are derived directly from the growth method. LPE is performed under group 111-rich conditions, which results in a low density of group I11 vacancies. These vacancies have been attributed to non-radiative recombination centers which limit optical efficiency, carrier lifetime and diffusion length (Jordan et al., 1974; Ettenberg et al., 1976). High purity growth is aided by the fact that the melt tends to retain impurities by virtue of their small distribution coefficients. Pre-baking the Ga melt has also been shown to be very effective in reducing unintentional impurities and producing high purity GaAs (Amano et al., 1993). The impurity concentrations of S, Si and C in the melt have been reduced by Ga pre-baking. Oxygen is another deleterious impurity which forms a non-radiative deep level in a number of 111-V materials. If a small amount of A1 is incorporated in the melt, any oxygen present will preferentially form A1,0,, which will remain in the melt

-

,As

and prevent oxygen incorporation in the crystal (Stringfellow, 1981). The growth rate realized in LPE is orientation-dependent, which can lead to enhanced edge growth as discussed above. This orientation dependent growth rate can also be utilized to great advantage in regrowth on patterned substrates. The main use for this is to produce buried heterostructure and distributed feedback or DFB lasers. Figure 3-17 illustrates LPE growth over a 4 pm deep groove (Kuphal, 1991). The initially grooved surface has been fully planarized by the LPE growth of a series of AlGaAs/GaAs/AlGaAs layers. The large difference in growth rates on the (001) and (111) faces, especially between InP and the InGaAsP quaternary compounds, has even permitted the growth, in one step, of buried heterostructure lasers on pre-patterned substrates. It is almost impossible to produce these kinds of structures using any of the other common epitaxial growth techniques. The difficulty in achieving a smooth planar surface morphology over large areas is a major problem in LPE. As a near-equi-

146

3 Epitaxial Growth

librium process, the surface mobility is large and subsequently the lateral growth rates are high. The surface morphology becomes, therefore, very sensitive to the substrate orientation, the nature and number of defects on the substrate and the conditions used for initial nucleation of the growth. The most common LPE morphological feature is a terrace or facet. If the substrate misorientation is large, extended terraces will form which make device fabrication difficult. Small misorientations, 150) are required to maintain acceptable morphology. The photoluminescence (PL) response of high purity InP is dominated by two peaks, one exciton related and the other acceptor related. The exciton peak dominates the spectrum as the growth temperature is increased. The acceptor peak has been associated with both carbon and zinc; however in higher purity material it is most likely carbon whose source is from the metal-organic In source TMI. Typically, higher growth temperatures also yield higher PL efficiencies of the exciton related peak. For example, increasing the growth temperature from 600 to 650°C results in a decrease in the FWHM of the band edge PL peak as well as an almost total elimination of the PL peak attributed to carbon (Chen et al., 1986). Intentional impurity introduction can also be accomplished in MOVPE growth. A wide variety of dopants have been investigated for InP, to produce n- and p-type material as well as semi-insulating (SI) InP. Donor impurities include silicon, sulfur, selenium, tin (Veuhoff et al., 1992)and tellurium (Clawson et al., 1987), while cadmium (Blaauw et al., 1987), magnesium and zinc have been investigated as acceptors. Iron and chromium have been reported to form SI InP. N-type doping is typically performed using silicon or sulfur. Si and S have different advantages which must be evaluated with respect to the requirements of the final device. Si has a lower diffusion coefficient and is able to produce somewhat more abrupt doping interfaces. However, S is able to produce higher free carrier concentrations and the mobility for equivalent dopant concentrations is typically higher using S. Thus, in the growth of modulation doped heterostructure devices, where abrupt doping and compositional

174

3 Epitaxial Growth

interfaces are of prime importance, silicon is the donor of choice. Where high doping and conductivities are required (for example, in lasers) S is the dopant of choice. Both silane and disilane have been used as precursors for silicon doping. The doping behavior of silane in InP is very similar to that in GaAs. The incorporation is proportional to the mole fraction of silane in the reactor, the reactor pressure and the growth temperature and inversely proportional to the growth rate. Quite high carrier concentrations using SiH, (x2x lo1’ cmV3)have been achieved; lower temperatures are found to produce the best morphology at these high carrier concentrations (Clawson and Hanson, 1994). Disilane also acts similarly in InP doping as in GaAs. The main advantage of disilane over silane is the lower pyrolysis temperature and consequent insensitivity to growth temperature. Silicon incorporation from disilane also increases with increasing PH, mole fraction (Rose et al., 1989). H2Sis the precursor for S doping. Using H,S, the free carrier concentration is exponentially proportional to the mole fraction of H,S in the reactor. The incorporation of S decreases with decreasing reactor pressure (Moerman et al., 1991) and is also exponentially proportional to 1/T. P-type doping of InP has a more complicated growth behavior than n-type doping. The acceptor diffusion coefficients are typically concentration dependent, and dopant activation is affected by the reactor ambient during cool-down. The most common p-type dopants for InP are Zn and Mg. Zn doping is performed using diethyl zinc (DEZ). At atmospheric pressures, Zn incorporation from DEZ has a similar growth dependence to that of S using H2S. The Zn doping process is, however, much less efficient. Like H,S the incorporation of Zn is exponentially proportional to the

flow of H, through the DEZ bubbler and exponentially proportional to 1/T. At low pressures, the incorporation of Zn from DEZ is linear with the mole fraction of DEZ introduced into the reactor (Veuhoff et al., 1991). The temperature dependence of both of these elements is explained by their high vapor pressures. While a portion of the adsorbed Zn is incorporated into the growing crystal, a fraction of the surface adsorbed Zn evaporates and diffuses into the reactor ambient. This behavior leads to a dependence of dopant incorporation on growth rate. At high temperatures the dopant incorporation increases with growth rate. If the desorption of Zn is kinetically limited, the higher growth rates will trap more of the dopant into the growing layer. Similar to H2S, the incorporation of Zn decreases with decreasing reactor pressure. Lower reactor pressures lead to an enhanced mass transport of Zn from the growth front resulting in a reduced Zn incorporation rate. Mg, Cd and Be (Cole et al., 1991) have also been investigated as p-type dopants in InP. The incorporation of Mg, at low reactor pressures, is superlinear with mole fraction of bis-methyl cyclopentadienyl magnesium in the reactor and thus harder to control than DEZ. Maximum carrier concentrations achievable for both Zn and Mg are about 2 x lo1*cmP3. An interesting facet of acceptor doping in InP is the observation the acceptor activation is dependent on the gas ambient present in the reactor during cool-down. The acceptor impurities can become passivated with hydrogen during cool-down. The acceptors are still physically incorporated in the crystal, but they are not electrically active due to the co-introduction of hydrogen. Passivation is strongest for cooling in ambients which can produce atomic hydrogen at the growth front. Such hydrogen passivation arises from the surface-

3.8 References

catalyzed decomposition of the group V sources. Since ASH, is more readily decomposed than PH,, this passivation effect is strongest for cooling in ASH,, less for PH, and even less for cooling in H,. This effect is not observed for n-type InP. Semi-insulating InP has also been grown by MOVPE using iron (Franke et al., 1990) and chromium (Harlow et al., ! cm have been 1994). Resistivities of lo8 2 achieved through the incorporation of both of these elements. Both Fe and Cr by themselves act as deep acceptors allowing for the compensation of n-type materials (Wolf et al., 1993).

3.7 Acknowledgement The authors would like to acknowledge the help of Prof. Max Lagally, Department of Materials Science and Engineering, University of Wisconsin, Madison, in the preparation of this chapter. He also provided the scanning tunneling micrographs.

3.8 References Adamson, A. W. (1990), Physical Chemistry of Surfaces, 5th ed. New York: Wiley. Amano, T., Kond, S., Nagai, H., Maruyama, S. (1993), Jpn. J. Appl. Phys. 32, 3692. Blaauw, C., Emmerstorfer, B., Springthorpe, A. J. (1987), J. Cryst. Growth 84, 431. Bollen, L. J. M. (1978), Acta Electron. 21, 185. Borg, R. J., Dienes, G. J. (1990), Introduction to Solid State Diffusion. San Diego, CA: Academic Press. Briggs, A. T. R., Butler, B. R. (1987), J. Cryst. Growth 85, 535. Buchan, N. I., Larsen, C. A., Stringfellow, G. B. (1987), Appl. Phys. Lett. 51, 1024. Buchan, N. I., Larsen, C. A., Stringfellow, G. B. (1988), J. Cryst. Growth 92, 591. Casey, H. C., Jr., Panish, M. B. (1978), Heterostruclure Lasers, Part B. New York: Academic Press. Chen, C. H., Kitamura, M., Cohen, R. M., Stringfellow, G. B. (1986) Appl. Phys. Lett. 49, 963. Chen, J. A., Lee, J. H., Lee, S. C., Lin, H. H. (1989), J. Appl. Phys. 65, 4006.

175

Cho, A. Y. (1985 a), in: The Technology and Physics of Molecular Beam Epitaxy: Parker, E. H. (Ed.). New York: Plenum Press. Cho, A. Y. (1985 b), in: The Technology andphysics of Molecular Beam Epitaxy: Parker, E. H. (Ed.). New York: Plenum Press, p. 6. Cho, A. Y, Hayashi, I. (1971), J. Appl. Phys. 42,4422. Clawson, A. R., Hanson, C. M. (1994), in: Proc. 6th Int. Conf. on InP and Related Materials, March 27-31, Santa Barbara, CA. Piscataway, NJ: IEEE, p. 114. Clawson, A. R., Vu, T. T., Elder, D. I. (1987), J. Cryst. Growth 83, 211. Cole, S., Davis, L., Duncan, W. J., Marsh, E. M., Moss, R. H., Rothwell, W. J. M., Skevington, P. J., Spiller, G. D. T. (1991), J. Cryst. Growth 107, 254. Eguchi, K., Ohba, Y, Kushibe, M., Funamizu, M., Nakanishi, T. (1988), J. Cryst. Growth 93, 88. Ettenberg, M., Olsen, G. H., Nuese, C. H. (1976), Appl. Phys. Lett. 29, 141. Farrow, R. F. C. (1974), J. Electrochem. SOC.121,899. Fitzgerald, E. A. (1991), Muter. Sci. Rep. 7, 87. Franke, D., Harde, P., Wolfram, P., Grotet, N. (1990), J. Cryst. Growth 100, 309. Ghidini, G., Smith, F. W (1984), J. Electrochem. SOC. 131, 2924. Giess, E. A., Ghez, R. (1975), in: Epitaxial Growth, Part A: Matthews, J. W. (Ed.). New York: Academic Press. Harlow, M. J., Duncan, W J., Lealman, I. F., Spurdens, P. C. (1994), in: Proc. 6th Int. Con$ on ZnP and Rel. Muter., March 27-31, Santa Barbara, CA. Piscataway, NJ: IEEE, p. 64. Heckingbottom, R., Davies, G. J. (1980), J. Cryst. Growth 50, 644. Hess, D., Jensen, K. F. (1989), Microelectronics Processing, Adv. Chem., Vol. 221. Washington, DC: American Chemical Society. Jordan, A. S., von Neida, A. R., Caruso, R., Kim, C. (1974), J. Electrochem. SOC.121, 153. Knudsen, M. (1909), Ann. Phys. (Leipzig) 4, 999. Kuech, T. F., Wolford, D. J., Veuhoff, E., Deline, V., Mooney, P. M., Potemski, R., Bradley, J. A. (1987), J. Appl. Phys. 62, 632. Kunzel, H., Fischer, A., Ploog, K. (1980), Appl. Phys. 22, 23. Kuphal, E. (1980), Appl. Phys. A 52, 380. Lu, Y C., Bauser, E., Queisser, H. J. (1992), J. Cryst. Growth 121, 566. Meyerson, B. S., Uram, K. J., LeGoues, F. K. (1988), Appl. Phys. lett. 53, 2555. Middleman, S., Yeckel, A. J. (1986), J. Electrochem. SOC.133, 1951. Moerman, I., Coudenys, G., Demeester, P., Crawley, J. (1991), in: Proc. 3rd Int. Conf. on InP and Rel. Muter., April 8-11, Cardiff, U.K. Piscataway, NJ: IEEE, p. 472. Nayak, S., Kuech, T. F., unpublished. Neave, J. H., Blood, P., Joyce, B. A. (1980), Appl. Phys. Lett. 36, 311.

176

3 Epitaxial Growth

Neave, J. H., Joyce, B. A., Dobson, P. J., Norton, N. (1983), Appl. Phys. A 31, 1. Nelson, H. (1963), RCA Rev. 24, 603. Ouazzani, J., Rosenburger, F. (1990), 1 Cryst. Growth 100, 545. Pfeiffer, L., West, K. W., Stormer, H. L., Baldwin, K. W. (1989), Appl. Phys. Lett. 55, 1888. Rode, D. L., Wagner, R. W., Schumaker, N. E. (1977), Appl. Phys. Lett. 30, 75. Rose, B., Kazmierski, C., Robein, D., Gao, Y. (1989), J. Cryst. Growth 94, 162. Shea, J. B., You, B. T., Kao, J. Y., Deng, J. R., Chang, Y. S., Chen, T. P. (1993), 1 Cryst. Growth 128, 533. Shewmon, P. (1989), Diffusion in Solids, 2nd ed. Warrendale, PA: TMS. Stall, R. A., Wood, C. E. C., Kirchner, P. D., Eastman, L. F. (1980), Electron. Lett. 16, 171. Stringfellow, G. B. (1981), 1 Cryst. Growth 55, 42. Stringfellow, G. B. (1982), Rep. Prog. Phys. 45,469. Thrush, E. J., Cureton, C. G., Trigg, J. M., Stagg, J. P., Butler, B. R. (1987), Chemtronics 2, 62. Veuhoff, E., Baumeister, H., Reiger, J. Gorgel, M., Treichler, R. (1991), in: Proc. 3rdZnt. ConJ on InP and Rel. Muter., April 8-1 1, Cardiff, U.K. Piscataway, NJ: IEEE, p. 72. Veuhoff. E., Rieger, J., Baumeister, H., Treichler, R. (1992), in: 4th Int. Con$ on InP and Related Materials, April 21-24, Newport, CA, p. 44.

Vossen, J. L., Kern, W. (1991), Thin Film Processing ZI. San Diego, CA: Academic Press. Wolf, T., Zinke, T., Krost, A., Bimberg, D. (1993), in: 5th Znt. Con$ on InP and Related Materials, April 19-22, Paris, France, p. 707. Wu, M. C., Su, Y. K. (1989), J. Cryst. Growth 96, 52.

General Reading Grovenor, C. R. (1989), Microelectronic Materials. Bristol, U.K.: Adam Hilger. Hess, D., Jensen, K. F. (1989), Microelectronics Processing. Washington, DC: American Chemical Society. Hurle, D. T. J. (Ed.) (1995), Handbook of Crystal Growth, Vol. 3. Amsterdam: Elsevier. Lee, H. (1990), Fundamentals of Microelectronics Processing. New York: McGraw-Hill. Massel, L. I., Gland, R. (1970), Handbook of Thin Film Technology. New York: McGraw-Hill. Muraka, S. P., Peckerar, M. C. (1989), Electronic Materials: Science and Technology.San Diego, CA: Academic. Vossen, J. L., Kern, W. (1991), Thin Film Processes ZZ. San Diego, CA: Academic.

Handbook of Semiconductor Technology

Kenneth A. Jackson, Wolfaana Schroter Copyright 0WILEY-VCH Verlag GmbH, 2000

4 Photolithography Rainer Leuschner Infineon Technology. Memory Products. Erlangen. Germany

Georg Pawlowski Clariant Japan K . K., BU Electronic Materials. Shizuoka. Japan

List of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . 179 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 4.2 Exposure Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 184 4.2.1 Image Formation and Resolution . . . . . . . . . . . . . . . . . . . . . . . Contact and Proximity Printing . . . . . . . . . . . . . . . . . . . . . . . . 186 4.2.2 186 4.2.2.1 Optical Mask Aligner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2.2 X-Ray Stepper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 4.2.3 Projection Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 4.2.3.1 Near UV Projection Systems . . . . . . . . . . . . . . . . . . . . . . . . . 189 4.2.3.2 Deep UV Projection Systems . . . . . . . . . . . . . . . . . . . . . . . . . 190 4.2.3.3 Nonconventional UV Lithography . . . . . . . . . . . . . . . . . . . . . . 191 4.2.4 Post-Optical Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 4.3 Photoresist Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 4.3.1 Quality Control and Resist Deposition . . . . . . . . . . . . . . . . . . . . 195 4.3.1.1 Purity and Storage Stability . . . . . . . . . . . . . . . . . . . . . . . . . 195 4.3.1.2 Resist Coating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 4.3.2 Resist Exposure and Development . . . . . . . . . . . . . . . . . . . . . . 197 4.3.2.1 Characteristic Curve and Standing Wave Effects . . . . . . . . . . . . . . . 197 4.3.2.2 Process Latitudes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 4.3.2.3 Dissolution Rate and Development Methods . . . . . . . . . . . . . . . . . 199 4.3.3 Pattern Inspection and Resist Profile Simulation . . . . . . . . . . . . . . . 201 4.3.4 Etching, Resist Stripping and Planarization Concepts . . . . . . . . . . . . 201 4.4 Photoresists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 4.4.1 Principles of Photoresist Chemistry . . . . . . . . . . . . . . . . . . . . . 203 4.4.2 Negative-Tone Resists . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 4.4.2.1 Photocrosslinking via Azides . . . . . . . . . . . . . . . . . . . . . . . . . 204 4.4.2.2 Free-Radical-Initiated Polymerization . . . . . . . . . . . . . . . . . . . . 205 4.4.2.3 Acid-Catalyzed Crosslinking . . . . . . . . . . . . . . . . . . . . . . . . . 206 4.4.3 Positive-Tone Resists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 4.4.3.1 Dissolution Inhibition/Dissolution Promotion . . . . . . . . . . . . . . . . 214 4.4.3.2 Acid-Catalyzed Deblocking . . . . . . . . . . . . . . . . . . . . . . . . . 221 4.4.3.3 Polymer Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

178

4.4.4 4.5 4.5.1 4.5.1.1 4.5.1.2 4.5.2 4.5.2.1 4.5.2.2 4.5.3 4.5.3.1 4.5.3.2 4.5.4 4.5.4.1 4.5.4.2 4.6 4.7

4 Photolithography

Solvents for Photoresists and Main Resist Suppliers . . . . . . . . . . . . . Special Photoresist Techniques . . . . . . . . . . . . . . . . . . . . . . . Nonconventional Diazo Resist Processes . . . . . . . . . . . . . . . . . . . Resist Profile Modification and Image Reversal . . . . . . . . . . . . . . . Bilayer Systems for Contrast Enhancement . . . . . . . . . . . . . . . . . Suppression of Reflections and Standing Wave Effects . . . . . . . . . . . Dyed Resists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Antireflective Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon-Containing Multilayer Resists . . . . . . . . . . . . . . . . . . . . Negative-Tone Silicon Bilayer Resists . . . . . . . . . . . . . . . . . . . . Positive-Tone Silicon Bilayer Resists . . . . . . . . . . . . . . . . . . . . Top Surface Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gas Phase Silylation Systems . . . . . . . . . . . . . . . . . . . . . . . . Liquid Phase Silylation Systems . . . . . . . . . . . . . . . . . . . . . . . Trends in Photolithography . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

233 234 234 234 236 237 237 237 240 241 242 245 245 246 252 254


List of Symbols and Abbreviations CD DR DOF D,", D: Ea FT G k , , k2 n NA 0.N. r R S TG

a

critical dimension dissolution rate depth of focus dose to clear activation energy film thickness of resist proximity gap constants refractive index numerical aperture Ohnishi number ring parameter reflectivity swing ratio glass transition temperature

Y

resist absorptivity resist contrast extinction coefficient angle wavelength

AAS ABC AFM AHR ALC APSQ ARC ARCH ASIC BARC BCB BDMADS CA CAR CARL CEL CMP coo CQUEST DESIRE DNQ

atomic absorption spectroscopy (azidobenza1)cyclohexanones atomic force microscope acid-hardening resist acid labile compound acetylated phenylsilsesquioxane antireflective coating advanced resist chemical amplified application specific integrated circuit bottom antireflective coating benzoc yclobutane bis(dimethy1amino)dimethylsilane chemical amplification chemical amplified resist chemical amplification of resist lines contrast enhancement layer chemical-mechanical polishing cost of ownership Canon quadrupole efficient stepper technology diffusion enhanced silylating resist diazo-naphthoquinone

Y &

e

179

180

DPI DR DRAM DUV EBL ECR EVE excimer FFP FIB-CVD FLEX HAE HELIOS heptaMDS HMCTS HMDS HMMM HX IBL IC ICA ICP-MS ICP-OES IPL KTFR LAE LIGA LSI MAE MCM MEMS MIE MIF MLR MOSFET MSNR MTF NBSE NTRS NUV O,-RIE OPC OPTIMA OSPR PAC

4 Photolithography

diphenyl iodinium dissolution rates dynamic random access memory deep ultraviolet (300- 100 nm) electron beam lithography electron cyclotron resonance ethylvinylether excited dimer film-forming polymer focused ion beam chemical vapor deposition focus latitude enhancement exposure high activation energy high energy lithography illumination by Oxford’s synchroton heptamethy ldisilazane hexamethylc yclotrisilazane hexamethyldisilazane hexamethoxymethyl melamine hydrogen halogen ion beam lithography integrated circuit indene carboxylic acid inductively coupled plasma mass spectroscopy inductively coupled plasma optical emission spectroscopy ion projection lithography Kodak’s thin film resist low activation energy Lithographie, Galvanoumformung, Abformung large scale integration medium activation energy multichip modulus microelectronic mechanical system magneton enhanced ion etcher metal-ion-free multi-layer resist metal-oxide-silicon field effect transistor methacrylated silicon-based negative resist modulation transfer function nitrobenzyl sulfonate ester National Technology Roadmap for Semiconductors near-ultraviolet oxygen reactive ion etching optical proximity correction outline pattern transfer imaging organosilicon positive resist photoactive compound


PAG PBOCMOST PBOCST PBOST PCM PCVD PEB PHS PI PMGI PMIPK PMMA PROMOTE PSMT PTMS RBS RIE SABRE SAFE SAHR SCALPEL SEM SHRINC SIA SIMS SLR SNR SRAM SUCCESS TARC t-BOC TFT/LCD THP TMAH TMMGU TMSDEA TPS TSI ULSI

uv

VHSI XL XRL

photoacid generator poly-(t-butoxycarbonyl-methoxystyrene) poly-(t-butoxycarbonyl-oxystyrene) poly-(t-butoxystyrene) portable conformable mask plasma chemical vapor deposition post exposure bake pol yh ydrox y styrene photo initiator poly(methy1 glutarimide) poly(methy1 isoprophenyl ketone) poly(methylmethacry1ate) profile modification technique phase shifting mask technology pyrogallol trismethyl sulfonate Rutherford backscattering spectroscopy reactive ion etching silicon added bilayer resist scanning tunneling microscope aligned field emission silylated acid hardening resist scattering with angular limitation projection electron beam lithography scanning electron microscope super high resolution illuminating control Semiconductor Industry Association secondary ion mass spectrometry single layer resist silicon-based negative resist static random access memory sulfonium compound containing expellable sophisticated side groups top antireflective coating tertiary butyloxycarbonyl thin film transistor/liquid-crystal display tetrah ydropyran tetrameth y lammoniumh ydroxide tetramethoxy methyl glycoluril trimethylsilyldiethylamine triphenyl sulfonium top surface imaging ultra large scale integration ultraviolet very high speed integration crosslinker X-ray lithography

181

182

4 Photolithography

4.1 Introduction The definition of the numerous electrical functions assembled on integrated circuits (ICs) is usually accomplished with the aid of an illumination-based imaging technique called photolithography. Photolithography provides a method to transform a complex master image with radiation into thousands of three-dimensional replicas of a photoresist film coated onto a substrate with utmost accuracy, speed and cost efficiency. The real or digitized master image is provided by either a mask or a serial writing technique. Being stroked by the radiation, the exposed photoresist areas change their solubility or polarity properties. The material’s chemistry selection and its processing conditions determine the tonality of the relief image: If the reproduction corresponds to the original, it is termed a positive; if it is reversed, it is a negative reproduction. The discrimination between image and nonimage areas is accomplished by selective removal of either the exposed (positive) or unexposed (negative) resist through a development method (Fig. 4- I), resulting in the desired three-dimensional relief image. The remaining photoresist portions protect the underlying substrate from the attack of processing chemicals, e.g., etching agents, and allow the whole device to be subjected to the undifferentiated action of these. Photolithography has become an inevitable element in the manufacturing sequence of microelectronic circuits and other devices, such as multi-chip modules (MCMs) (La11 and Bhagath, 1993), micromechanical devices (Rogner et al., 1992), thin film recording heads for magnetic disks (Bond, 1993), color filters (Kudo et al., 1996a, b), or thin film transistor/liquid-crystal displays (TFT/LCD) (Howard, 1992; Bardsley, 1998). Many of these products are integral parts of the hardware platform mandatory

for an effective handling of the growing information density worldwide. The base material for the production of an integrated circuit consists of an intensively cleaned, highly polished disk, called a wafer, with a diameter up to 300 mm (Brunkhorst and Sloat, 1998; Bullis and O’Mara, 1993), which has been sliced from a large monocrystalline silicon rod of extreme purity. Each wafer provides hundreds of small separate chips, containing millions of electrical elements, such as capacitors, diodes, and transistors on a field size of 1 to 2 cm2. During its metamorphosis from a polished silicon plate to disk carrying ICs, the wafer is subjected to many different operations. Certain key steps are used repeatedly in IC fabrication, among which lithography plays a dominant role to delineate the patterns of conducting and insulating areas (Einspruch, 1985).

Figure 4-1. Formation of positive and negative tone pattern.

4.1 Introduction

Initially, the wafer is thermally oxidized at - 1000°C. During this step a thin layer of silicon dioxide grows on the silicon substrate. This Si0,-layer will protect selected areas of the substrate from penetration by dopant ions. The wafer is spin-coated with a solution of the photoresist, which solidifies to a uniform 0.5 to 2 mm thick film after the solvent is evaporated on a hot-plate at elevated temperature. The coated wafer is then imagewise irradiated and the soluble resist portions are removed by a development procedure. Next, the SO,-layer, which is imagewise protected by the resist, is etched away where it is uncovered to open the desired portions of the silicon surface. At this point, the resist is removed (stripped) to avoid device contamination with resist impurities. The wafer is now ready for a further key processing step: ion implantation, which gives the silicon its electrical properties. High-energy ions of dopant elements (boron, phosphorus) are fired at the wafer and penetrate the open areas of the silicon surface. The substrate surface is reoxidized,

-

Oxidation

source

drain

Mask 1

-

and the wafer is again coated with a photoresist to allow further processing, e.g. insulation, or metallization steps. In a final lithographic step, contacts and connections for pins used to plug the chip into a printed circuit board are defined. At present, up to 24 lithographic and more than 250 separate processing steps are employed for the manufacture of electronic devices, resulting in a production time of one month for a single chip (Bullis and O’Mara, 1993). A simplified IC manufacturing procedure is given in Fig. 4-2. An ongoing challenge in IC production is to further shrink the lateral device geometry, with the aim of building even more complex circuits, e.g. dynamic random access memory (DRAM) devices with higher storage capacity. This demand for higher resolution is the driving force for steady improvement of the photolithographic process (Gargini et al., 1998). Figure 4-3 illustrates the developments of storage capacity and required feature size for memory devices (left), and summarizes the applied or required technologies and photoresist characteristics to produce the devices (right).

silicoc ox de.

n -silicon

Doping

Definitionof source & drain

Oxidation

Mask 2 Definition of the gate

-

gate oxide

Oxidation

contact pads

Mask 3

;

Opening of contacts

183

Metallization

Mask 4 I Metal patterning

Figure 4-2. Planar technology: simplified production steps in MOSFET manufacture.

184

4 Photolithography

10.00 Technology:UV-broadband contad & proximity priiter Chemistry: Azido I isoprene resists Tonality: Negative,single layer Pros: High sensitivity, good adhesion, low cost Cons: Swelling, resdution > 2.0 pin I

Y

3.00 256 kBit DRAM

P)

.-N

Technology:g-line & i-line (436 & 365 nm) stepper Chemistry: DNQ I novolak resists Tonality: Positive, single layer Pros: High resdution. wide process laditudes Cons: Low sensitivity, invariable chromophore

u)

e! 3

+-

(0

2

5

:..

5

16 MBit DRAM

0.30

~

Technology: DUV (248 & 193 nm) excimer stepper 8, scanner (e-beam, x-ray systems. IPL ?) Chemistry: Chemically amplified resists Tonality: PositiveInegative, single (mug layer Pros: High resolution. high sensitivity, adjustment to any wavelength Cons: Process sensitivity, high investment costs

4 GBit DRAM 16 GBit DRAM

1970

1980

1990

2000

Availability for production [year]

2010

Figure 4-3. Development of storage capacity and minimum feature size of memory devices (left) and technologies usable for memory device production.

4.2 Exposure Tools 4.2.1 Image Formation and Resolution ICs are usually patterned with near UV radiation sources, e.g. mercurylrare gas discharge lamps. To achieve optimum resolution, the emitted light is filtered and corrected by filter and lens systems to yield narrow-banded radiation. Contact, proximity or projection exposure tools (Fig. 4-4)have found commercial use, each having certain advantages, and handicaps over the other (Soane and Martynenko, 1989). The history of the different lithographic exposure tools is outlined by Bruning (1997). In an optical lithographical system, light passes through the transparent areas of the mask. In the photoresist, the basic phenomenon to be seen is Fresnel diffraction. Figure 4-5 compares the aerial images of the above-described exposure methods. Con-

tact printing readily approaches a perfect pattern transfer. But, with growing distance between mask and wafer (proximity printing), interference patterns occur, ending in an aerial image with a smooth distribution of the light intensity with its peak in the centre of the slit and tails beyond the area defined by the mask. When adjacent slits are projected, the situation becomes more complex, as a series of undulating maxima and minima are observed, with maxima smaller than 100% and minima greater than 0% transmission. The minimal printable linewidth CD (critical dimension) is given by the wavelength 2, the proximity gap G and the resist film thickness FT [Thompson et al., 1983; Eq. (4-1)]:

CD = 312 d 2 (G + FTl2)

(4-1)

In projection printing the special frequencies of the diffraction pattern are collected

4.2 Exposure Tools

185

by the objective lens, which rebuilds the areal image of the mask in the wafer plane. For an ideal lens, the image quality is only restricted by the diffracted light that it does not pass through the lens due to the limited size of the numerical aperture (NA). The NA of a lens system in air is defined in Eq. (4-2), with 8 denoting the maximum angle of the diffracted light that can enter the lens (Mack, 1993a): NA = sin (8/2)

Figure 4-4. Mask/die arrangement in (a) contact, (b) proximity and (c) projection printing.

I

(4-2)

A rough estimation of the limits of projection printing can be given by the Rayleigh [Eq. (4-3)]. The resolution (=critical dimension, CD) is a function of the radiation wavelength A,theNA and an empirically determined constant k , which is governed by the type of photoresist, substrate, and the

-

3

Mask

Relative intensity

50

0

Figure 4-5. Comparison of aerial images obtained by contact, proximity and projection printing. (Reproduced after Soane, 1989.)

186

4 Photolithography

process environment (Lin, 1990).Under laboratory conditions, k , is assumed to be 20.5,whereas under production conditions, k , typically has a value of > 0.8 to > 1.2 depending on the reflectivity of the substrate.

CD=k, ’ U N A

7 - r -

----

(4-3)

Values for k2 are in the range of 0.4 to 0.9 under laboratory and production conditions. Studies by Dammel et al. (1990) and Boettiger et al. (1994) revealed that Eq. (4-4) is only roughly valid in the sub-half-micron range, and larger focus budgets than predicted may be observed in reality. From Eq. (4-3) it is obvious that a decrease of ilalso will result in improved resolution capability, which thus may be obtained by either using NUV radiation with a high NA system, or by deep UV radiation with a smaller N A . A shorter wavelength ilshould yield a better focus budget at a defined resolution but with shrinking feature size it cannot totally compensate the corresponding DOF reduction as shown in Fig. 4-6 (Arden, 1990).The DOF problem is a major physical limitation for single layer resists in optical submicron lithography, as a minimum resist thickness of >0.35 pm is necessary to ensure both coverage of the topography and sufficient etch resistance. The considerations mentioned above are based on the assumption that the light strikes the mask only from one direction (coherent illumination). In reality, it comes from a

\

400

385 nm

-

248 nm

‘

4

I-

0.2

1200

,”--

0.3

0.4

0.5

0.6

Numerical aperture

0.7

’---,

1000

g

, 7

(4-4)

436 nrn

c

At a fixed wavelength, a larger NA allows the reproduction of smaller patterns. As seen from inspection of Eq. (4-4), the penalty for obtaining higher resolution by increasing the NA is a smaller depth-of-focus (DOF). The empirical constant k2 in Eq. (4-4) also depends on the type of materials used.

DOF= k , * A/(NA)*

--

800

u

c

. I! 600 c 3 -

0

E

400 200

0 Depth of focus [ p m ]

Figure 4-6. The impact of resolution on depth of focus.

range of angles rather than just one (partial coherence). The impact on the resolution is expressed by the modulation transfer function (MTF), which describes the image contrast as a function of the spatial frequency (Thompson et al., 1983 and Mack, 1993 A).

4.2.2 Contact and Proximity Printing 4.2.2.1 Optical Mask Aligner

With respect to the equipment, 1:l contact printing is the simplest method. It is widely used for the production of devices with low resolution requirements (> 5 pm). A mask consisting of a glass or quartz substrate carrying an array of thin chrome pat-

4.2 Exposure Tools

terns as absorber, is brought into intimate contact with the resist. This allows the simultaneous formation of many dies within one exposure, is cheap, and offers optimal pattern reproduction. Repeated contacts between mask and film may give rise to severe scratches, or sticking of resist pieces on the mask. Damaged mask patterns are then reproduced in the resist, which require additional time for reworking and mask cleaning, and diminish the yield. In shadow proximity exposure, the mask is separated by a gap of about 40 pm from the wafer plane. This avoids contamination and damage problems, but causes degradation of resolution due to diffraction effects (compare Eq. (4-1)). Optical mask aligners are usually equipped with mercury/xenon discharge lamps providing high output around: 400 nm, 3 10 nm and 250 nm (Fig. 4-7). In contact printing, broad band illumination is preferred, because standing wave effects are less pronounced when polychromatic light is used. Contact printing can be advantageously used to pattern very thick resist layers (< 200 pm) with high aspect ratios

KrF

2

I

XeCl

ArF

193

f

200

308

A!f : !

300

436

365

Wavelength [nrn]

AO5A

400

5

I

Figure 4-7. Comparison of emission spectra and energies provided by a mercury lamp and excimer lasers. (Courtesy of W. Spiess. Reproduced with permission.)

187

because the resist thickness is not limited by the depth-of-focus of any optical projection system (Loechel et al., 1994). Specially designed mask aligners allow for front and rear alignment (Cromer, 1993), which is needed for micromechanical applications, where the silicon substrate is etched through. 4.2.2.2 X-Ray Stepper

The resolution limits of optical systems using short wavelength radiation and improved resists together with optical tricks (Chu et al., 1991) are expected to be around 0.10-0.13 pm mainly due to the inadequate depth-of-focus budgets. Surface imaging schemes may give rise to further reductions of the device geometry at the price of increased process complexity. Ultra large scale integration (ULSI) patterns smaller than 0.13 pm without any depth-of-focus problem may be achieved using X-ray radiation (Peters and Frankel, 1989). The basic concept of X-ray lithography (XRL) is proximity printing. The improvement of the aerial image using X-ray beams compared with 200 nm radiation is quite obvious with respect to Eq. (4-1). Laser-based plasma sources (Chaker et al., 1991) emit “soft” X-rays of a wavelength (0.8-2.2 nm), which is short enough to give images not deteriorated by diffraction (Guo and Cerrina, 1991). Their medium brilliance (c 10 mW/cm2) requires highly sensitive resists (c50 mJ/cm2), and their resolution capability (-0.2 pm) is controlled by the penumbral blur (Frackoviak et al., 1993). Such data are also achieved by deep ultra violet (DUV) lithography, and it is doubtful, whether this approach will see a breakthrough into large volume production. In contrast, bright (compact) synchrotron storage rings with a power of > 100 mW/cm2 are candidates to become production tools in the future for sub 0.2 pm

188

4 Photolithography

lithography (Yanof et al., 1992; Simon et al., 1998), due to their high resolution capability (>70 nm; Ogawa et al., 1993) combined with high throughput. Other unique and important advantages of XRL are its insensitivity to dust particles and substrate topography (Yoshioka, 1990), as neither reflection nor backscattering effects occur, resulting in excellent linewidth control over topography as demonstrated in Fig. 4-8. Although these features make XRL superior to any other irradiation technique presently known, several problems exist, which have hampered its introduction into high-end IC production for more than a decade. The large size of, and high capital investments for, synchrotron sources as well as their complex ancillary system are severe drawbacks in the competition with other technologies, but a cost per bit analysis demonstrates that synchrotron XRL might be the cheapest method of manufacturing ULSI-

devices (Roltsch, 1991). Various functional circuits (e.g., SRAM with critical dimensions of 0.35 pm) have been manufactured using XRL (Technology News, 1993). The suitability of XRL for the fabrication of three-dimensional microelements for integrated optics, sensors, and microgears by the LIGA process (German: Lithographie, Galvanoformung, Abformung) will only be mentioned here (Rogner et al., 1992; Ehrfeld et al., 1998).The first ‘commercialized’ compact synchrotron with superconducting magnets is the high energy lithography illumination by Oxford’s synchrotron (HELIOS) from Oxford Instruments (Kempson et al. 1991). Several state-of-the-art descriptions of synchrotron sources used in lithography have been given recently (Maldonado, 1991; Schmidtetal., 1991; Yoshihara, 1992; Cerrina, 1992; Smith, 1995). The usable wavelength range of X-rays (0.5-4 nm) is determined by the absorption properties of the mask and of the resist.

Figure 4-8. SEM photograph of AZR PN 114 (left: 0.4 mm lines & spaces; right 0.175 mm lines. Dose: 9 mJ/cm2, development: 60 sec. 0.135 N AZTM MIF 312) over metal topography exposed with X-ray radiation provided by a laser plasma source. (Courtesy of Hampshire Instruments, Ltd. Reproduced with permission.)

4.2 Exposure Tools

These photons are neither reflected nor refracted by any material known today and have to be used as they are produced by the source. As no optical system can be applied, neither projection nor reduction techniques, only 1 : 1 shadow printing with proximity gaps of -40 pm can be employed (Guo et al., 1991). High quality X-ray masks consist of a thin, X-ray transparent membrane (14 pm), which makes them very sensitive to distortions due to absorber stress (Acosta, 1991; Chaker et al., 1991). Their defect-free production and repair are difficult tasks (Koek et al., 1993). These problems have not been satisfactorily solved over the last ten years. Recently, progress has been reported (Wasiket al., 1998). High overlay accuracy (< 70 nm) has been demonstrated (Tsuyuzaki et al., 1994; Aoyama et al., 1997).

4.2.3 Projection Printing 4.2.3.1 Near UV Projection Systems

Current IC lithography is clearly dominated by projection printing methods. In the early 1980s, 1: 1 full-field scanning optical projection cameras were the workhorses of IC lithography (Thompson et al, 1983). These machines operate with a special, low numerical aperture (NA) ring-field mirror lens. Their benefits were high throughput, and the property to allow exposure over a range of wavelengths. But their resolution capability did not meet the aggravating IC design rules. The increase of the NA of the mirror lens gave way to cameras with higher resolving power at the penalty of smaller exposure fields, resulting in the step-and-scan camera concept. Although these new cameras allow the NA to be doubled (> 0.3), they could not compete with the step-and-repeat reduction cameras (stepper), which currently dominate advanced IC production.

189

Modern steppers use monochromatic radiation (e.g. 436 nm or 365 nm, g- or i-line of the mercury emission spectrum, respectively; Fig. 4-7), a complex system of lenses with an NA > 0.5 and allow diminution of the mask image by a factor of 5 x or lox. As the field dimensions of the imaging system are of limited size, only a small part of the wafer, i.e. a single chip, is exposed during one irradiation step (Fig. 4-9). This lowers the production throughput, but yields highly reproducible patterns, as the same mask is used for each distinct unit. Beside resolution and DOF (Yamanaka et al., 1993), the image field size is another important issue, as it decreases with increasing NA due to difficulties in manufacturing adequate optics of large size (Noelscher et al., 1990). Several IC companies switched from g- to i-line lithography to manufacture the 4 MBit DRAM chips with critical dimensions (CD) of 0.8 pm, and now use this technology for the production of 16 MBit DRAMS or other devices with 0.5 pm design rules (Greeneich and Katz, 1990).

Mirror Light source Filter

I +

x-y stage

Figure 4-9. Schematic drawing of a step and repeat camera.

190

4 Photolithography

These products require a DOF budget of 1.5 pm due to topography, limited wafer flatness and focus error of the stepper (Peters, 1991). The first version of the 64 MB DRAM with CDs of 0.4-0.35 mm has been produced with i-line, but the shrunk versions (0.35 to 0.3 pm) required a switch to DUV lithography for certain critical levels. 4.2.3.2 Deep UV Projection Systems

As the production of small feature sizes is one major challenge in ULSI lithography, it became inevitable to investigate DUV radiation for providing higher resolution together with an increased DOF budget (Mack, 1993 a). However, previously used lens glass has to be replaced by quartz with high DUV transmission. Mercury-xenon lamps have a high radiation output in the near UV range, but a very low one in the 200 to 300 nm region, which excludes the use of narrow band pass filters to avoid chromatic aberrations and demands mirror projection optics. Two commercial DUV mirror projection systems operate with servicefriendly and inexpensive high pressure mercury-xenon lamps. As their brilliance is poor, resists of high sensitivity ( < 5 mJ/cm2) are mandatory. However, antireflective coatings may be omitted in the case of broadband illumination (Kuyel et al., 1991). The Ultratech stepper operates at a wavelength of 249k 3 nm, while the SVG Micrascan machine (step-and-scan concept) provides exposure illumination over a 240 to 255 nm bandwidth (Buckley and Karatzas, 1989). A different approach to DUV illumination systems is based on excimer lasers (excited dimer), which are very powerful pulsed gas lasers, in which excited diatomic noble gadhalogen molecules formed by a high voltage electric discharge, e.g. XeCl (308 nm), and especially KrF (248.5 nm) or

ArF (193 nm), emit the laser radiation during their transition to the repulsive ground state (Fig. 4-7; Jain, 1990). By injection locking, their emission is extremely narrow banded ( 1.OOO in appropriate developers, with dissolution speeds of 3000 n d m i n in the exposed, and only a few n d m i n in the unexposed areas (dark erosion). The DR of a resist can be measured in-situ by reflectivity monitoring during development (Thomson, 1990). Commercially available in-situ dissolution rate monitors (DRMs) are important tools for resist manufacturers as they help to identify novel high performance resist materials. The DR measurement gives not only general information about the dissolution rate and contrast but also characterizes the resist dissolution at any film thickness at the same time. This allows the detection of minor dissolution gradients or film inhomogeneities, which usually cause formation of non-optimum profiles.

loo0

. v)

a,

10

C

0 ._ c

-03 v)

1

._ v)

n 0.1

Both the selection of developer type and development method contribute to the resolution, the image profile and the dark erosion. The use of solvent-based developers, typically xylene, or anisole, is declining as they may cause resist swelling, severe environmental pollution and waste disposal problems. Therefore metal-ion free (MIF) developers, containing buffered aqueous solutions of tetramethylammonium hydroxide (TMAH), or similar amines as bases, are recently greatly favored over solvent developers. An aqueous 2.38% TMAH solution (0.26 N) has become the worldwide developer standard, and novel resists should show compatibility and excellent performance with this standard to be globally accepted. However, a large number of formulations with different base-strength are available for specific processes. Beside TMAH they may contain surfactants and wetting agents, to improve the across-the-wafer development uniformity and to reduce development time and surface residues, called scum (Shimada et al., 1993). The shelf life of aqueous-alkaline developers is limited, as they are gradually neutralized by carbon dioxide absorbed from the air. Modern resists are characterized by their development latitude, which is the allow-

1

1

0

X

+

,

+---,---

.+

-+-...

, - - . . . ,

Exposed Unexposed

. T . .I

+---... +

10 20 PAC concentration [“h]

I

30

Figure 4-20. DRs of an unexposed and fully exposed DQNnovolak resist. The D R ratio is defined as: DR,,,l DRunexp. (Data taken from Meyerhofer, 1980.)

4.3 Photoresist Processing

able variation in development time at a defined linewidth loss. Spray, puddle and immersion development methods are currently in use. The first two methods give better process reproducibility and meet in-line process and automatization requirements. Normally, development is a time-controlled process. Better process latitudes can be obtained when end point detection methods are applied (Thomson, 1990). Developers are optimized for room temperature processing (23 "C), as pattern acuity decreases with increasing temperature.

4.3.3 Pattern Inspection and Resist Profile Simulation Prior to substrate etching, the lithographically generated patterns are normally inspected with respect to the remaining film thickness, linewidth, line profile and defect density. The resist thickness is measured either optically or mechanically with a profile meter. Patterns can be inspected without damage with conventional optical microscopes, digital laser microscopes (Worster and Politzer, 1993), scanning atomic force microscopes (AFM; Toledo-Crow et al., 1993; Nelson, 1998), or low voltage scanning electron microscopes (SEMs; Allen et al., 1993b; Yoshimura et al., 1998). Defects caused by particles are detectable by the measurement of electrical short circuits or line interrupts in special test patterns. Several computer programs which simulate the lithographic behaviour of photoresists have been developed. They are valuable tools for the design, characterization, property prediction, and optimization of photoresist processing, including off-axis or FLEX illumination, diazonaphtoquinone and chemical amplification resists or top surface imaging processes (Hartney, 1994). Simulators like Solid C/Sigma C GmbH, SAMPLE/University of California (Toh et

201

al., 1991b) and PROLITH/Finle Technologies, Inc., Austin, Texas, (Mack and Connors, 1992), as the most popular programs, have tremendous value to the lithographic community and allow comparison of experimental versus theoretical image characteristics (Trefonas and Mack, 1991). PROLITH calculations showed that for partially coherent exposure systems there is a fundamental difference between positive and negative resists with respect to process latitudes. The existence of tone dependency in lithographic imaging leads to an important conclusion: for any one pattern there is an optimum resist tone to print this pattern. It is now widely accepted for example, that contact holes have much greater depth of focus when imaged with a positive resist (Mack and Connors, 1992).The CARPS program is a simulator which makes it possible to optimize the resist composition (Ushirogouchi et al, 1990). The interested reader is referred to review articles (Neureuther and Oldham, 1985; Hartney, 1994).

4.3.4 Etching, Resist Stripping and Planarization Resist hardening procedures enhance the adhesion between film and substrate, and improve the thermal and the chemical resistance towards wet and dry etch processes. It is achieved through the application of a post bake (hard bake), where the shaped resist images are subjected to a forced heat treatment, which removes residual solvent and may crosslink the resist (White, 1986). The selection of the optimum temperature is critical, as resist flow and hardening are competing processes. Hardening is also achieved by DUV illumination combined with an increasing temperature gradient during exposure (deep UV curing; Vollmann and Pawlowski, 1988). Resist hardening crosslinks the resist surface while ther-

202

4 Photolithography

ma1 flow is negligible. It may severely impede the final stripping of the films. Etching: The main function of a resist is to protect underlying parts of the substrate from overall area chemical or physical processes (Thompson et al., 1983). These include wet etching of the substrate surface; i.e. a buffered hydrofluoric acid etch of a silicon dioxide surface. Other substrates require alternative wet etchants, e.g. hydrofluoric acid with nitric, acetic or phosphoric acid, ceric ammonium nitrate-nitric acid, or alkaline potassium permanganate solutions. Wet etching is isotropic in nature and may lead to undercut phenomena, especially if the resist shows insufficient adhesion (Fig. 4-21). Many etch chemicals attack and degrade the resist patterns. Wet etching processes are simple, cheap and provide high throughput (Murray, 1986). Dry etching methods, including reactive ion etching (RIE), sputter etching or ion milling (Thompson et al., 1983), find increasing attention for patterning and stripping purposes (Flamm, 1992). These processes can be performed anisotropically (Fig. 4-21), but they are very complex procedures and may give rise to high radiation flux and elevated temperatures. They require resists with high chemical resistance

and dimension stability. As a rule of thumb, the dry etch stability of organic resists increases with the amount of aromatic moieties. A major problem of today’s dry etch technologies are the formation of particles (Petrucci and Steinbruchel, 1990) or device contamination by metal ions from the reactor environment (Joubert et al., 1989). Details of the various dry etch techniques are given in the literature (Moreau, 1988 and Soane and Martynenko, 1989). Other high vacuum processes are additive processes, like ion implantation or sputter metallization. As ion implantation requires extremely high vacuum, the resist is subjected to DUV-hardening to avoid the emission of volatile products. Metallization is usually done by vacuum deposition methods, e.g. evaporation or sputtering, by which the whole device surface is metallized. Again, extreme vacuum is necessary and the resist has to withstand the metal deposition without drastic changes in its solvent solubility, which is important for its use in the metal lift-off technique (Fig. 4-22). Stripping: Only high-temperature stable photoresists, e.g., photosensitive polybenzoxazoles, will remain in the device as interlayer dielectric or buffer coat (Ahne et al., 1992). Standard resists are removed totally

Figure 4-21. Results of different etch processes: (left) wet etch (highly isotropic), (middle) dry etch (directional) and (right) dry etch (highly directional).

4.4 Photoresists

hv Mask

-111-

Exposure

Photoresist Substrate

U

Development

U

Metallization

n Metal layer

Lift off (Stripping)

Figure 4-22. Process flow of the lift-off process.

after the above-mentioned processes have been finished. To avoid any damaging of the processed substrate, mild chemical methods at low temperatures should by used. Stripping solvents which dissolve the remaining resist portions include e.g. glycol ethers, trichloromethane (Soane and Martynenko, 1989), ethanol amine, dimethylsulfoxide, or N-methyl-2-pyrrolidone. The application of ultrasound may enhance stripping performance. Difficult-to-remove, thermally crosslinked materials are chemically decomposed by oxidation using Caro’s acid. Some of the known stripping agents cannot be applied to alumina surfaces due to corrosion problems (Pai et al., 1991); in this case ozone or oxygen plasmas (ashing) are advantageously used. These plasmas are also successfully employed as stripping agents for resists on non-alumina substrates, but damage of the device surface is a problem still to be solved (Flamm, 1992). Planarization: Advanced photo lithography needs almost flat topography for the

203

subsequent photo layers, since reflections at edges and slopes can cause defects, and high topography steps may consume the tight DOF-budget. Multilayer resist systems have been proposed to planarize critical topography. Their use is restricted to local planarization, since the lateral flow range during the soft bake of the planarizing bottom resists is very limited. Other local planarization methods are based on liquid silicon oxide precursors, like spin-on glass or a mixture of silane and hydrogen peroxide condensed at low temperatures directly onto the wafer (flow-fill process). Especially for the metal layers, global planarization is possible by chemical-mechanical polishing (CMP) of the silicon oxide interlayer dielectric (Murarka et al., 1993). Recently, metal CMP is of rapidly increasing interest, because for the 0.18 pm device generation low-resistivity copper interconnects are essential and unfortunately, the patterning of copper is difficult since it cannot be etched in current plasma reactors (Li et al., 1994). The most viable patterning technique is the damascene process, where the dielectric is deposited and patterned first, then the copper is deposited on top. CMP then removes the surplus copper to leave just the in-laid interconnect pattern (Murarka and Hymes, 1995). One problem connected with global planarization by CMP for the exposure tool is to find the very low step height alignment marks with high accuracy and reliability. New alignment mark designs and sensors are under development (Rouchouze et al., 1997).

4.4 Photoresists 4.4.1 Principles of Photoresist Chemistry The use of positive and negative photoresists is a key element in the photolithographic process predominantly utilized in

204

4 Photolithography

the IC industry. While negative resists are used for circuits with relatively coarse structures, the production of high-end devices is dominated by positive resists. It was believed for a long time that negative resists are limited in their resolution capability. However, several new negative-tone materials print submicron patterns with similar accuracy to positive ones. A historical overview is given by Willson et al. (1997). Resist chemistry is classified by the principle of the radiation induced solubility change: crosslinking (photopolymerization), polarity change or polymer degradation. It is obvious that resist performance is strongly affected by the properties of the different components and their relative concentrations. While the film forming polymer affects the thermal stability and solubility properties of the resist, the sensitivity to the applied radiation is mainly determined by the quantum yield of the photoactive compound’s photochemical reaction. Two cases are distinguished: (1) single photon processes, where one photon changes the solubility property of only one chemical group and (2) chemical amplification processes, where one photon triggers many chemical reactions which change the solubility of the resist. In case (2) the resist sensitivity may be greatly enhanced compared with (1).

horse in semiconductor manufacturing to delineate structures with resolutions down to 2 pm (Thompson et al., 1983). Although such systems show big DR ratios, their resolution capability is limited by swelling during solvent-based development. When irradiated, the azido group eliminates molecular nitrogen to yield a highly reactive nitrene in both the singlet (Sl) and triplet (Tl) state, which may dimerize (azo dye formation (Tl, Sl)), add to double bonds (aziridine formation, Tl), form radicals (Tl), or insert into carbon-hydrogen bonds (secondary amine formation as main product, S1) (Fig. 4-23; Reiser, 1989). Nitrenes react with the ever-present atmospheric oxygen under formation of highlyabsorbing nitroso compounds, which deteriorate the image quality. Typically, difunctional azido compounds, namely 4-alkyl-2,5-bis(p-azidobenzal)cyclohexanones (ABC, sensitivity range 340 to 420 nm), or bis(p-azidocinnamy1idene)cyclohexanones (sensitivity range 365 to 480 nm), are employed (Thompson et al., 1983). Among the polymer binders suggested as matrix resins, poly-(cis-isoprene), became the most frequently used polymer

hv

R--N3

R-N.

+

4.4.2 Negative-Tone Resists 4.4.2.1 Photocrossslinking via Azides

Two-component crosslinking systems based on bifunctional azido derivatives as photoactive compound (PAC) and a reactive polymeric binder, have found widespread application in the printing plate and photoresist industries (Reiser, 1989). The first product for the electronic industry was Kodak’s Thin Film Resist (KTFR@),introduced in 1954, which became the work-

e)

2 R-N.

+

0 2

-

2 R-N=O

Figure 4-23. Photoreactions of azides.

N2

4.4 Photoresists

for large scale integration (LSI) microlithography (Reiser, 1989). The stripping of photocrosslinked isoprene resists may sometimes cause trouble and requires special strippers. Recently, Rutter et al. (1992) have used bifunctional azides to introduce photoreactivity into high-temperature stable benzocyclobutane (BCB) pre-polymers, which can be used as interlayer dielectric in multilayer interconnections due to their good thermal stability (>25OoC) and very low dielectric constant. Combinations of novolaks or polyhydroxystyrene (PHS) with new monofunctional azide sensitizers, e.g. 4-azidochalcone derivatives (Reiser, 1989), yield resists with high sensitivity towards i-line (365 nm, 13 yJ/cm2) or g-line (436 nm, 55 yJ/cm2) radiation. The alkaline developers allow delineation of structures in the submicron range without swelling (Bendig and Gruetzner, 1990). Their interesting lithographic performance has revived world-wide activities (Kawai et al., 1989; Nonogaki and Toriumi, 1990). 4.4.2.2 Free-Radical-Initiated Polymerization

Methacry late based photopolymerization is the basis for most dry-film photoresists and solder masks in printed circuit board manufacture and for high-temperature stable photoresists (e.g. photosensitive polyimides or their precursors) used as dielectric interlayers or buffer coats in the IC industry (Horie and Yamashita, 1995). Compositions useful for photolithography consist of a photoinitiator (PI), a matrix resin (e.g. polymers with methacrylate side groups) and optionally multifunctional monomers. Upon absorption of radiation, the PI is raised to an electronically excited state and generates radical fragments, which add to and initiate the polymerization of an unsat-

205

urated monomer (initiation). The resulting intermediate radical further adds to unreacted monomers, giving rise to molecular growth (propagation). The process is terminated by radical recombination, chain transfer or oxygen inhibition (termination). Oxygen is known to act as a quencher for the excited initiator and as a trap for free radicals by forming peroxy radicals of low reactivity. The chemistry and physics of the photopolymerization process (Fig. 4-24) are discussed in detail elsewhere (Rabek, 1987; Fouassier, 1989). Compared to many other photoimaging processes, systems based on photopolymerization have a remarkable high photospeed due to a chemically amplified mechanism. Although primary quantum yields (radicals produced per photon absorbed) are usually < I (Reiser, 1989), one absorbed photon may initiate polymerization of thousands of monomers. Shimizu (1988) reported an ultimate photopolymerization photoresist sensitivity of 13 yJ/cm2. The sensitivity and other resist parameters are strongly governed by the polymer morphology (Maerow, 1986). Like most negative working compositions based on an increase of molecular weight, the exposed, insoluble areas of the photopolymer film tend to swell, in particular during solvent development, making this chemistry definitively unsuitable for the fabrication of sub-ym microelectronic devices. The resolution requirements for hightemperature stable photoresists are less severe (>5 ym) and most of these materials on the market (Photoneece UR 5100@/ Toray, Pimel G-7610@/AsahiChemical, XB 7020@/OCG, Pyralin 2732@/Du Pont, and Ultradel 750 I @/Amoco) are based on special polyimide (pre) polymers with attached photopolymerisable methacrylate side groups. After exposure and development in organic solvents, these side groups

206

4 Photolithography

Formation of radicals:

Initiator (Initiator)*

+

RH

-

-

(Initiator)* Initiator - H

+

R

.

Initiation reaction:

Propagation reaction: R-C&-CH.

+ n C&=CH

I

I

R'

Termination reaction:

2

R'

R-C&-CH.

I

R'

Oxygen inhibition:

R-Ch-CH'

I

+

0 2

-

R--~?C&-CH-)FC&-CHI

R'

I

R'

R-Cb-CH-CH-Ct+-R I

I

R ' R '

R-Cli-CH-0-0. I

R'

R'

Figure 4-24. Simplified mechanism o f the photopolymerization process.

are released from the polymer in a subsequent curing step at temperatures above 300°C, and the final high-temperature stable (normally insoluble) polyimide is formed (Ahne et al., 1992; Horie and Yamashita, 1995). Most photoinitiators (PIS) are divided into two classes by their reaction mechanism: intramolecular bond cleavage to the radicals P* and I*, called photofragmentation, or intermolecular H-abstraction from a hydrogen donor RH, called a coinitiator, to form PIH* and R*. The former type of initiators is known as PI1, as radical formation occurs in an unimolecular process, the latter as PI2, since two molecules are involved. Examples of both types and their decomposition mechanisms have been reviewed indetail (Reiser, 1989; Rabek, 1987; Vesley, 1986; Timpe and Baumann, 1988). PI 1 compounds form free radicals mainly via the Norrish type I cleavage (Fig. 4-25). As an example, benzoin alkyl ethers, which exhibit a weak absorption band at 330 nm, decompose to benzoyl and benzylether radicals, which both participate in the initiation

reaction. The main side reactions of benzoin alkyl ethers are dimerization, H-abstraction and chain termination. Photoinitiators of the PI2 type include benzophenone, Michler's ketone, thioxanthones (QuantacureTM ITX, LucirinTM 85 13), benzil, quinone derivatives and 3ketocoumarines (Fig. 4-26; Reiser, 1989). These compounds abstract hydrogen from H-donors, typically tertiary amines with abstractable a - H atoms, such as triethyl amine, N-methyldiethanol amine, or 4-dimethylamino benzaldehyde. The intermediate exciplex decays to an a-amino radical, which acts as the initiator, while the ketyl radical does not contribute to this process. The oxygen sensitivity of PI2 systems is superior to that of the PI 1 type initiators, because the amine reacts with non-initiating peroxy radicals to reactive a-amino radicals. 4.4.2.3 Acid-Catalyzed Crosslinking

4.4.2.3.1 Cationic-Initiated Polymerization Besides radicals, cations and anions are capable of inducing photopolymerization

4.4 Photoresists

@-

207

Figure 4-25. The Norrish type I fragmentation of benzoin ether, ben-

&o

zil diketal and dialkoxy acetophenone derivatives.

Benzoinether

Benzildiketal

Dialkoxyacetophenone

0

Thioxanthone

mmR 0

R

0 0

Bis (ketocumarin)

Figure 4-26. Chemical structures of some Norrish type I1 photoinitiators.

reactions (Reiser, 1989). Photoinitiated cationic polymerization offers several advantages: (1) new monomers with unique properties can be polymerized, (2) recombination of the carbocations is excluded, giving rise to high polymerization degrees, and

(3) insensitivity to oxygen. Certain limitations have restricted its commercial breakthrough: (1) only few initiators are available, (2) sensitivity to termination reactions by nucleophilic impurities, e.g. bases and humidity, or ( 3 ) sensitivity to chain-transfer processes (Timpe and Baumann, 1988). The polymerization process, as exemplified with an epoxide in Fig. 4-27, is initiated by the photogenerated Lewis acid (BF3), which adds to the oxirane with ring opening and the formation of a carbocation. This reacts rapidly with a new epoxide molecule. The energy released during opening of the strained ring contributes to fast propagation of the addition. Several negative resists based on cationic polymerizable materials have been described by Crivello et al. (1988), Ito and Wilson (1984), and more recently by Hatzakis et al. (1991). They employed commercially available epoxy resins (e.g. Epi-Rez@ SU-8, Quatrex@ Epoxy Resins) together with triarylsulfonium salts for DUV and ebeam resists. An optimized material (EPTR) is capable of resolving 0.1 pm features in a 0.8 mm thick resist at an e-beam dose of

208

4 Photolithography

R' Ringopen

R

Monorner-

I

k Figure 4-27. Reaction mechanism of Lewis acid induced cationic photopolymerization.

5

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m/p = 10/0 S 4 = 14 - 15

4

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w

1

al

-

$

0.25

0

I

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5000

10000

15000

20000

25000

Moleculare weight

Figure 4-42. Effect of A: metdpara-cresol ratio, B: ortho/para link configuration ratio (S4), and C: molecular weight on contrast and exposure latitude. (Reproduced after Hanabata et al., 1986.)

4.4 Photoresists

to replace novolaks by new polymers to extend the applicability of DNQ resists. Due to their improved transparency in the DUV region and TGsup to 180 "C, poly(4-hydroxystyrene) (PHS) and copolymers thereof have received much attention (Pawlowski et al., 1990a). The film forming properties (Toriumi et al., 1991) and the unusual dissolution behaviour of PHS in aqueous-alkaline developers (Long and Rodriguez, 1991) have been investigated in detail. Its DR in standard MIF developers (2.38% of TMAH) is about 20 pm/min compared to 0.3 to 3 p d m i n for novolaks, which is far too much to delineate well defined relief images. PHS polymers have been modified with hydrophobic groups (Pawlowski et al., 1990a; McKean et al., 1990), which act as internal dissolution inhibitors to the attacking developer and make these materials promising for DUV resists. There are significant differences between, for example, DNQ-novolak and DNQ/PHS resists: while the former are inhibited by even small PAC-loadings, the latter are not. This experimental result suggests that there are links between the inhibitor and the polymer matrix. Depending on the secondary molecular structure, the hydrophilic groups may arrange themselves into more closed intramolecular, or more open intermolecular, hydrophilic assemblies. These assemblies may act as diffusion channels for the attack of the developer (Yeh et al., 1992; Dammel, 1993). The position of the hydroxy group in polyvinylphenols has a large effect on the dissolution rate. While the 2-hydroxy isomer is too slow and the 4-hydroxy isomer too fast for use in DNQ resists, the copolymerization of both allows one to choose any dissolution rate between the extremes (Dammel et al., 1994). The thermal flow resistance of such a 1:1copolymer resist was found to be improved over that of novolak resists.

221

DNQ resists based on aromatic poly-ortho-hydroxyamides with good lithographic performance have been introduced as photopatternable interlayer dielectric for multilayer electronic devices. These polyamides show comparable dissolution inhibition/ promotion characteristics in alkaline developers like novolaks, but by heating the developed resist pattern up to 350 "C the polymer converts into a high temperature stable polybenzoxazole with good dielectrical properties (Sezi et al., 1994; Sezi et al., 1999). 4.4.3.2 Acid-Catalyzed Deblocking

Conventional DNQ-resists exhibit only moderate photosensitivity and thus relatively poor production economics. With the present switch from NUV to DUV lithography required to print sub-quarter micrometer features, DNQ-based resists are no longer acceptable due to their high opacity below 300 nm. Furthermore, DUV irradiation tools provide only low photon densities due to their extreme spectral narrowing. This makes conventional resists far too slow to give meaningful device yields: resist sensitivity has become an increasingly important issue. New materials based on radiation-induced deprotection reactions and polarity changes of certain acid sensitive polymers meet these challenges (Fig. 4-43). The benefits of such systems for microlithography were first recognized by Ito, Willson, and Frechet (Ito et al., 1987), who introduced the concept of chemical amplification (CA) and called materials of that type chemically amplified resist (CAR). Positive CARS contain at least a photoacid generator (PAG) (compare Sec. 4.4.2.3), and a polymer with acid labile, hydrophobic protecting groups. Upon exposure, the photogenerated acid molecules induce a thermally catalyzed cleavage of the acid

4 Photolithography

222 Resist Substrate

Exposure

Acid generation

Post exposure bake Acid catalyzed deblocking Alkaline

4

Solvent

development

I

I

O \ ,O-C-CH3

$

0

OH

AH3

Figure 4-43. CAR concept: process flow of t-BOC protected positive resists.

labile groups. A sophisticated design concept allows for regeneration of the photoacid during the deblocking sequence, and thus one single molecule can induce a cataract of cleavage reactions, providing a gain mechanism to overcome the sensitivity limitations imposed by the quantum efficiency of the photochemical event. The usually more polar degradation/deprotection products cause the exposed resist to be soluble in an aqueous alkaline developer (Reichmanis et al., 1992). According to the number of active components in the resist, twoand three-component chemically amplified systems are distinguished. Two-Component Resists As implicated by the nomenclature, chemically amplified two component resists consist of two active resist components dissolved in a solvent, namely, a polymer masked with acid-sensitive protecting groups and a photoacid generator. According to the energy required for the deprotection reaction, three classes are distin-

guished: low activation energy (LAE) systems (E,< 25 kcal/mol), such as silylethers, ketals or acetals, medium (MAE) activation energy systems (Ea- 25-30 kcal/mol), such as carbonates, and high activation energy (HAE) systems (E,>30 kcal/mol), such as carboxylic acid esters, or ethers. The first commercially accepted chemically amplified resist material was developed by IBM (APEX series) and is based on the acid induced cleavage of PBOCST (Fig. 4-43), a poly-(4-hydroxystyrene) blocked with t-butyloxycarbonyl (t-BOC) groups (Willson et al., 1990). The photolytically produced acid molecules cleave the carbonate moieties (re)generating the alkali-soluble PHS resin as well as the volatile byproducts of carbon dioxide and isobutene upon application of a PEB at approx. 100°C (MAE system) (Sturtevant et al., 1992). The reaction does not require the presence of water and works equally well under the high vacuum conditions required during electron-beam exposure. The intermediately formed t-butyl cation stabilizes to isobutene, and liberates a new proton, which is

4.4 Photoresists

capable of inducing the next cleavage reaction. The early PBOCST materials were 100% protected. It turned out, however, that a protection degree of 15-35% is sufficient to render the PHS polymer insoluble in the standard MIF developers and additionally improve certain lithographic properties, such as contrast and image stability. While pure, fully t-BOC blocked PHS resins are thermally stable up to 190°C (Reiser, 1989), partially blocked materials decompose at lower temperatures due to an autocatalytic deprotection reaction caused by the presence of acidic phenol groups in the polymer. The catalytic chain length for the deprotection reaction of t-BOC based resists varies from 10 for methane sulfonic acid, through 200 for toluene sulfonic acid to 8.000 for trifluoromethane sulfonic acid (Houlihan et al., 1991), with an acid diffusion radius of less than 5 nm (McKean et al., 1989). These acid parameters have tremendous effects on the resist performance and need careful adjustment (Hashimoto et al., 1997). The selection of non-nucleophilic acids is mandatory for t-BOC chemistry, as nucleophilic acids, such as hydrochloric acid, fail to deblock the t-BOC groups via a catalytic mechanism. Ota et al. (1994) have reported that the intermediate t-butyl cations may alkylate the aromatic rings of the polymer in a competitive reaction to the desired isobutene formation and thus deteriorate the dissolution rate in the exposed areas. PBOCSTsystems behave as a dual tone resist (Fig. 4-43). The negative process with anisol as developer was employed to manufacture 1 Mbit DRAMS via DUV lithography (Maltabes et al., 1990), while the positive one has been investigated for 0.35 mm patterning (Brunsvold et al., 1993a). Several modifications of PBOCST resins have been reported, including t-BOC protected poly(hydroxypheny1 methacrylates)

223

(Przybilla et al., 1991), hydroxystyrene sulfone copolymers (Reichmanis et al., 1991), or the more recently developed hydroxystyrene vinyllactame copolymers (Kim et al., 1997). Although PBOCST materials have several limits in lithographic performance and even some severe shortcomings with respect to delay stability (Nalamasu et al., 1991), they are still used in state-of-the-art 0.25 pm production processes (Amblard et al., 1997). More recently developed t-BOC based resist formulations are less susceptible to these problems. A large number of alternative protecting groups has been proposed to block phenolic polymers. Among these, acetal protected PHS resists have received wide commercial interest due to their excellent resolution capabilities (Endo et al., 1991; Pawlowski, 1996). The acetal bond is formed by the reaction of PHS with vinylethers such as ethylvinylether (EVE-PHS, Fig. 4-44) or tetrahydropyran (THP, Fig. 4-44). The activation energy required for the acid-catalyzed acetal deprotection reaction is lower than that for t-BOC material and image formation may occur at room temperature (LAE system). However, completion of the reaction is usually achieved during a postexposure bake at 90°C. Acetal-based resists work well with less powerful acids, such as methane sulfonic acid generated from pyrogallol tris methane sulfonate (PTMS) as the photo acid generator (Ueno et al., 1991;Hattori et al., 1993), and require stoichiometric amounts of water for accurate image formation. The polymers exhibit excellent transparency at 248 nm ( ~ 0 . 1 5pm-'), but their T, is rather low. The diffusion ranges of two different acids (CH,SO,H; HPF,) in a THPblocked PHS CAR as a function of bake conditions were studied by Schlegel et al. (1991). High prebake temperatures reduce the diffusion range as the polymer matrix

224

4 Photolithography

solidifies. The mobility of CH,SO,H was found to be lower, resulting in superior images. Alternative THP-blocked polymers reported in the literature are hydroxy-polyimides (Omote et al., 1992) and polymethacrylates partially esterified with benzylalcohol (Taylor et al., 1991) or with the 193 nm-transparent tricyclodecanol (Nakano et al., 1994). Acetal-based two component resists have been steadily refined in recent years with respect to the polymer properties, such as molecular weight, polydispersity, protection group, and PAG selection (Houlihan et al., 1997a). Recent materials offer excellent imaging properties with respect to resolution and process stability (Spiess et al., 1998) and are considered major candidates for 0.18 pm DUV lithography. In addition, they provide excellent compatibility with electron- and ion-beam lithography (Novembre et al., 1996; Hudek et al., 1997). A solution to the TG issue of acetal-based resists is the incorporation of acid-labile crosslinks into the polymer (Taguchi et al., 1995; Schacht et al., 1997). An increase of the thermal flow stability by 30°C to approximately 150 "C while keeping the basic lithographic performance was demonstrated using this approach (Bantu et al., 1997). Schwalm and coworkers (1990) have used t-BOC blocked, phenolic sidegroups containing sulfonium salts acting simultaneously as photolytic acid generators and as acid-cleavable dissolution inhibitors in the highly transparent THP-PHS polymer matrix for their resist called SUCCESS (sulfonium compounds containing expellable sophisticated sidegroups). Although not fully compatible with standard processes, this resist series was considered a performance leader for a time of the best (Schwalm et al., 1994), and the SUCCESS concept is the basis for some of the best performing resist materials.

A class of protection groups requiring high activation energy (HAE system) is based on certain phenol ethers, such as allyl, benzyl, or t-butyl ethers (Ohnishi et al., 198 1). Although no commercial examples of pure ether protected PHS based resists are known today, some materials take advantage of mixed acetallt-butyl ether groups to improve certain lithographic properties. An important extension of PHS chemistry has been achieved with the introduction of novel co-monomers offering wider flexibility with respect to the protecting group selection. Particularly useful are (meth)acrylic acid esters obtained from t-butyl-, amyl-, or benzyl alcohol derivatives (Allen et al., 1993a). The image discrimination is based on the polarity change caused by the de-esterification of the carboxylic acid esters. The original ESCAP material (Fig. 4-44) developed by IBM contained approximately 70% 4-hydroxystyrene units to achieve compatibility with standard development processes and 30% acid sensitive t-butyl(meth)acrylate groups (It0 et al., 1994). As the relatively high contents of aliphatic units deteriorate the resist's etch stability, improved versions using terpolymers with reduced t-butylacrylate loading have been developed (Conley et al., 1997). The t-butylester group is thermally quite stable (HAE system) and allows prebake temperatures above the glass transition point of the resist. This densifies the polymer matrix and improves the insensitivity towards airborne base contaminants (annealing concept) (Breyta et al., 1994). Highly sensitive, dual tone materials have been designed based on t-butyl blocked poly(viny1 benzoic acid) (It0 et al., 1987). Due to transparency issues, their use is limited to i-line lithography. Similar systems based on poly-(4-hydroxystyrene) partially reacted with t-butyl bromoacetate (Fig. 4-44) exhibit better DUV compatibility (Onishi et al., 1996).

4.4 Photoresists

-

1.hv(H+)

-

AT(- 60 110°C) OH

OH CHsCHO + RICH

EVE-PHS ( M E system, R1 = C2H5, C3H7, etc.)

+n OH OH

OH

THP-PHS ( M E system)

OH

-

00

2.AT(-80-11OoC)

OH

CH3 + n H?c=(

+ nco2

R1

OH

PBOCST (APEX E. MAE system, R1= CH3, C2H5)

+n H & 4 c H 3

-

2. AT(- 110 150°C)

Rl OH

ESCAP (HAE system, R1= CH3, C2H5)

+ n H2C=(cH3

1 . 2 2. AT(- 90 - 130°C)

XZR, CH3

R1 H&' OAOH

PBOCMOST (HAE system, Rq = CH3, C2H5)

Figure 4-44. Acid catalyzed cleavage reactions useful in DUV lithography.

225

226

4 Photolithography

Even though industry standards with respect to DUV resist performance have not been settled yet, quite a few commercial and precommercial materials are available on the market. Commercially promoted positive tone resists include APEX and KrF-K materials (Shipley, Japan Synthetic Rubber) using t-BOC chemistry, AZ DX, PEK, TDUR, ARCH, and KrF-R materials (Clariant, Sumitomo, Tokyo Ohka, Olin Microelectronic Materials, Japan Synthetic Rubber) using acetal chemistry, and UV and KrF-M materials (Shipley, Japan Synthetic Rubber) using t-butylester chemistry. A detailed performance comparison study between t-BOC, acetal and t-butylester type resists has recently been published by Lai et al. (1997).

hyde produced upon acetal cleavage crosslinks with the polymer and deteriorates the image contrast (It0 et al., 1991). More recently, however, three-component systems have regained attention in the design of practical chemically amplified resists. Major changes from the first generation materials include the switch from inactive polymers to the acid-sensitive polymers described in the previous chapter and novel, more sophisticated dissolution inhibitors. Such combinations improve the resolution capability, usable depth-of-focus range, and pattern shape accuracy. In fact, several state-of-the-art resist materials use mixtures of these polymers with additional dissolution inhibitors as provided from Tokyo Ohka. ShinEtsu and Clariant.

Three-Component Systems

Issues in Chemically AmpliJied Resist Systems

Three-component systems consist of a film-forming polymer (FFP), a photoacid generator, and a monomolecular or oligomer acid sensitive dissolution inhibitor, which is cleaved to a dissolution promoter upon the action of acid. Due to separation of the functions, three-component materials principally offer a broader chemical flexibility compared with two-component systems. Early examples used inactive FFPs, such as alkylated poly-(4-hydroxystyrene) together with t-butyl carbonates of phenols (McKean et al., 1988; Aoai et al., 1994), t-butyl esters (Allen et al., 1993A), vinylethers (Taguchi et al., 1995), or silylethers (Schlegel et al., 1989) and a variety of acetal derivatives (Dammel et al., 1987; Roeschert et al., 1993b; Padmanaban et al., 1994). Acetal based three component materials gained attention in previous years but were finally discarded due to their inherent small PEB process window: when PEB temperatures above 70 "C are applied, the alde-

The acid amplification mechanism used in the earlier-described novel materials has resulted in considerable improvements with respect to photospeed, resolution capability, and other important performance properties. However, some inherent hurdles had to be overcome to allow their reliable use in a cost- and yield-orientated production environment. These problems are closely related to the photocatalytic mechanism, the relatively small amount of acid produced, and the acid diffusion properties in chemically amplified resist systems. Some of these problems include: storage stability, delay time stability, sensitivity to airborne contaminants, substrate sensitivity (He et al., 1997), linewidth stability, proximity effects, such as iso/dense bias or linewidth shortening (Ziegler et al., 1997), standing wave formation,

4.4 Photoresists

-

process temperature sensitivity, and outgassing of volatile resist components.

All chemically amplified positive resists are more or less sensitive to these effects; to a first approximation, selection of the polymer material and the type of generated acid may increase or decrease their perception. The resist vendors have developed additional proprietary methods to minimize these effects, usually via the selection of optimized process conditions and resist components, or special resist additives. In addition, the equipment manufacturers have provided sophisticated tools, such as temperature control or air filtration devices, and highly accurate hotplates, to ensure constant process conditions and environments at their extremes. A critical point is the image stability of chemically amplified materials during the various process steps (Fig. 4-45). Most at-

227

tention has been directed to the delay between exposure and post exposure bake, which significantly degrades the latent image, the photosensitivity, and the pattern linewidth. These effects intensify as the delay time is increased and may result in a loss of small lines or total failure of image formation. Schwartzkopf et al. (1991) have summarized the following causes for latent image instability in PBOCST onium salt resists: -

-

-

depletion of onium salt concentration at the resist surface during spin-coating, loss of generated photoacid at the top of the resist by volatilization or migration, contamination of the resist surface by ambient cleanroom air, resulting in neutralization of the photoacid, and migration of base insoluble photoproducts towards the resist surface.

Figure 4-45. Delay time effects in chemically amplified positive resists.

228

4 Photolithography

For the superacids produced by onium salts, virtually every compound is regarded as a base capable of neutralizing the acid. Amine concentrations in the ppb range were found to cause an insoluble skin at the top of the resist (Nalamasu et al., 1991), resulting in the T-shaped pattern profiles which can bring about complete bridging of the patterns after a few minutes (Fig. 4-46). Therefore PBOCST systems require an amine-free atmosphere for their proper function, which was achieved by filtering air through activated charcoal filters, yielding a stable manufacturing process (MacDonald et al., 1993). Another method to improve the latent image stability is the application of a protecting overcoat with the inherent disadvantage of a multi layer arrangement (Kumada et al., 1993; Oikawa et al., 1993), or the use of environmental lithographic chambers (Reichmanis et al., 1992; Holmes et al., 1993). Ito et al. (1993) observed that the meta isomer with a TGbelow the prebake temperature is much less sensitive to NMP contamination than para PBOCST leading to the general concept of resist annealing. Other countermeasures include the addition of bases or photosensitive base gener-

ating compounds (resist poisoning) to the resist formulation (Roeschert et al., 1993b ; Przybilla et al., 1993). Such additives also improve the contrast of the resist material. The use of extremely acid-labile protection groups, such as ketals, gives the resist environmental stability comparable to that of DNQ resists (Huang et al., 1994) as image formation proceeds during the exposure event. However, the ease of deprotection causes resist storage stability issues, which have not yet been solved. A tremendous amount of work has been dedicated towards the understanding of the mechanisms operative in chemically amplified resists by various academic and industrial working groups (Kamon et al., 1997; Itani et al., 1988). It is evident, however, that the complexity of these systems will prohibit the development of a universal description concept. It is worthwhile mentioning that additional issues have arisen from the rapid trend to print smaller features. While the industry’s CD average is clearly above 0.6 pm, the most advanced gate applications require CD control for design rules below 0.15 pm. In practice, such geometries are printed in the same production environment.

Figure 4-46. SEM picture of a resist with strong T-top formation.

4.4 Photoresists

This translates into mix-and-match lithography using different resist chemistries and thus requires strict cross contamination control and full compatibility with previously introduced standard processes and process chemicals. With the decreasing pattern sizes, CD control becomes an important issue, requiring extremely tight photospeed control and lot-to-lot consistency of resist materials. An increasing list of metal ion contaminants at concentrations below the 10 ppb range have to be consistently monitored, and the requirements for numbers and ultimate sizes of defects have already surpassed current detection capabilities. Resists for 193-nm Lithography According to the U. S. National Technology Roadmap for Semiconductors (NTRS) periodically provided by the Semiconductor Industry Association (SIA), ArF (193 nm) lithography is likely to be employed for the

229

delineation of features 0.15 pm and below (Brown, 1995). From the photoresists point of view, this technology change poses new, but “deja-vu” challenges to the materials: the development of a single layer resist with enhanced photospeed to minimize lens heating and destruction, improved etch resistance to allow the application of thin films, and adjusted thermal and hydrophilic properties to guarantee compatibility with established industry processes. Previously used polymers with etch-stability providing aromatic units, such as PHS, are ruled out due to their insufficient transparency at 193 nm (Fig. 4-30; Sec. 4.4.4.2). The first materials to meet at least part of these requirements were CARS, developed by IBM using aliphatic polyacrylates with acid cleavable t-butylacrylate units (Version 1.O & Version 2.0 resists) (Allen et al., 1991). While their lithographic performance was found adequate, both process compatibility and etch resistance of these materials did not meet the requirements (Fig. 4-47).

Figure 4-47. Correlation between the ring parameter r and empirical etch rates of several resists relative to standard DNQhovolak resists.

230

4 Photolithography

0.N. = Ntotal/ Nc - No

According to an empirical law discovered by Ohnishi, the RIE-etch resistance of a polymer is proportional to the Ohnishi Number O.N. which is defined as the quotient of the number of atoms in a polymer repeat unit and the difference between the number of carbon and oxygen atoms (Ohnishi et al., 1981; Eq. (4-8)).

More recently, Kunz et al. (1996) introduced the ring parameter r, given in Eq. (4-9), to describe the RIE etch resistance more accurately. I-

=mass of carbon in rings/ total mass of carbon

'CH, IBM Version 1.O resist: Poly-(methyl methacrylate-cmethacrylicacid-co-t-butyl methacrylate)

FujitsulClananffNippon Zeon: Poly-(2-methyladamantyl acrylate-co-mevalonic lactone acrylate)

LucenffOlin EM: Poly-(norbomene-alt-maleic anhydride-cmcrylic acid-co-1-butyl acrylate)

1%)

0

CH3

X C H 3

(4-8)

OH

+

H2qCH"

CH, UniversityAustin: Poly-(t-butoxycarbonylnorbomadiene-alt-maleicanhydride)

Figure 4-48. Chemical approaches to 193 nm polymers.

(4-9)

4.4 Photoresists

Researchers at Fujitsu included highly transparent alicyclic comonomers, such as isobornyl methacrylate, to increase the etch stability (Kaimoto et al., 1992), initiating the rapid evolution of alternative materials with improved overall performance (Fig. 4-48). An incomplete list of materials with the potential to find use in a production environment includes -

-

methacrylate based co- and terpolymers bearing alicyclic etch resistant menthyl (Shida et al., 1996), adamantyl (Takahashi et al., 1995), or tricyclodecyl units (Nakano et al., 1995), methacrylate based co- and terpolymers bearing etch resistant and solubility modifying tricyclodecyl, or tetracyclodecyl units with integrated partially protected carboxylic acid functions (Maeda et al., 1997),

-

-

-

-

231

methacrylate based co- and terpolymers with alicyclic etch resistant acid-cleavable 2-methyl adamantyl groups (Takechi et al., 1996), norbornene/maleic acid anhydride copolymers (Wallow et al., 1996), norbornene/maleic acid anhydride copolymers with cholate based dissolution inhibitors (Houlihan et al., 1997b), and nonacrylic copolymers (Allen et al., 1996; Okoroanyanwu et al., 1997)

Particularly interesting is the approach first used by Fujitsu, based on a copolymer of 2methyladamatyl methacrylate and mevalonic lactone methacrylate as polymer and an iodonium salt derived PAG. Both pendant groups are cleaved by the action of the acid. The material combines high photospeed (3 mJ/cm2), high resolution (0.12 pm) and excellent etch stability with industry standard 0.26 NTMAH developer compatibility (Fig. 4-49).

Formulation 1, Lot 10; 0.48 pm on 180 nm AZ BARLi II; SB 115 "C, 60 s; focus 0.0; 193 nm, 0.60 NA; PEB 110 "C, 60 s; LD26W developer, 20 s spray/puddle at 23 "C Figure 4-49. SEM pictures of an experimental ArF resist on basis poly-(2-methyladamatyl methacrylate-co-mevalonic lactone methacrylate).

232

4 Photolithography

Unfortunately, the mevalonic lactone acrylates are difficult to prepare driving the materials costs to unacceptable levels. 4.4.3.3 Polymer Degradation With a few exceptions, NUV radiation is not capable of cleaving thermally stable 0 bonds in organic molecules, because the average bond energy is about 350 kJ/mole, corresponding to photons of 340 nm wavelength. DUV radiation is able to break molecule bonds and photochemists have discovered several materials, which undergo lithographically useful scission reactions to provide positive-tone images. Poly(methy1 methacrylate) (PMMA) is a positive-tone chain scission resist with excellent resolution capability when irradiated with broadband DUV (240-260 nm), KrF excimer laser (248 nm), or ArF excimer laser (193 nm) radiation (Reiser, 1989; Sasago et al, 1991). Initially, a Norrish type I reaction occurs, which is followed by main chain scissions. Small molecule fragments, including carbon monoxide or dioxide as well as methyl or methoxy radicals, are formed, while the intermediates stabilizes under formation of unsaturated, low molecular weight fragments (Fig. 4-50; Reiser, 1989). The cleavage of PMMA proceeds only inefficiently: high doses (> 1000 mJ/cm2) are

CH3

CH3

CH3 Main chain scission

required to obtain adequate dissolution speed (Nakase, 1987). PMMA has several benefits as DUV resist (Wolf et al., 1987), including excellent resolution capability, ease of handling, good film forming properties, wide process latitude, and low price. In a 500 mm thick PMMA resist, patterns with nearly vertical sidewall profiles have been printed with XRL (Rogneret al., 1993). However, its low sensitivity is barely acceptable. The efficiency of the cleavage reaction is increased (- 80 mJ/cm2) when the DUV absorption is intensified by copolymerization with 3-oximino-2-butanone methacrylate or by addition of t-butyl benzoic acid as a photosensitizer (Reiser, 1989). Polymers of polybutene sulfone (Thompson et al., 1983) or poly(methy1 glutarimide) (PMGI) are also scissionable with DUV radiation. The photospeed of PMGI is comparable to PMMA, but, due to its imide groups, it is developable with aqueous bases, has better dry etch resistance, and a high glass transition point (> ISO°C), making PMGI useful as planarizing layer for multi-layer schemes (Reiser, 1989). In addition to PMMA, poly(methy1 isopropenyl ketone) (PMIPK) based resists, commercialized by Tokyo Ohka under the trade name ODUR 1010, are widely investigated as photoscissionable one-component resists (Hesp et al., 1990). All of these mainly aliphatic materials show poor dry etch resistance which limits their application. The principle of chemical amplification can also be applied to polymers which undergo main chain scission (Frechet et al., 1989). Polycarbonates derived from tertiary diols and certain diphenols are degraded in the presence of a PAG and by exposure to DUV (Fig. 4-5 1 ; Reiser, 1989). During development, advantage is taken of the higher DR of the degraded polymer fragments versus the intact polymer to

4.4 Photoresists

Figure 4-51. Photoreaction of main-chain degradable polycarbonates.

generate a positive image. The degradation concept has been extended to generate positive resists using polyacetals, polyazomethines, polyethers and polyesters with acid-cleavable bonds in their main chains (FrCchet et al., 1989, 1990; Ito and Schwalm, 1989).

4.4.4 Solvents for Photoresists and Main Resist Suppliers Photoresist materials for IC manufacture are usually sold as thoroughly filtered ( ~ 0 . 2pm) liquid solutions (liquid photoresists) in organic solvents, which have pronounced effects on certain photoresist properties, such as photospeed, coating uniformity and thermal flow behaviour (Salamy et al., 1990). The ideal solvent is non-toxic and non-hazardous (safer solvents; Boggs, 1989). Examples include 2-heptanone, cyclopentanone, cyclohexanone, 3-methoxybutyl acetate, propylene glycol monomethylether or its acetate, propylene glycol diacetate, ethyl lactate, ethylene carbonate, ethyl 3-ethoxypropionate and ethylpyruvate (Hurditch and Daraktchiev, 1994). The main resist suppliers are Tokyo Ohka, OEM ( O h Electronic Materials), Shipley (Rohm & Haas), Clariant, Sumitom0 Chemical, Nippon Zeon, Japan Synthetic Rubber, Mitsubishi Chemical, Shinetsu, and others (Gutmann et al., 1990a and

233

SST tabulation, 1993). The field of advanced g-, i-line and DUV resists is highly competitive and rapidly changing. In 1990 the authors believed that the resolution limits of DNQ-novolak resists had been reached with the performance obtained by the Tokyo Ohka g-line material TSMR-V3: 0.4 pm lines and spaces with vertical sidewall profiles were printed with a 0.54 NA stepper in a 1.26 ym thick resist (Satoh et al, 1989). This performance is now beyond standard for the last generation g-line resists. Today, i-line resists are available with an ultimate resolution ~ 0 . 2 pm 5 lines and spaces (Fig. 4-52), the capability to print 0.30 ym contact holes (e.g., Sumitomo Chemical PFI-66, Japan Synthetic Rubber PFR IX 1010, Hoechst AZ 7900, Fuji Hunt FHi-3900, OEM OiR 32, Mitsubishi Kasei MCPR i6600, Nagase NPR-L18SH5, Tokyo Ohka THMR-iP series, Hitachi Chemical RI-7300P), linearity better than 0.3 pm, and a focus budget >2.0 ym for 0.35 ym patterns.

Figure 4-52. SEM picture of 0.25 Frn lines and spaces printed in JSRRJCB new high-contrast i-line resist 1x500 using the ASM-L PAS 5000/50i-line stepper (NA =0.48)with a Levenson type phase-shifter design. Courtesy of IMEC, Leuven, Belgium. Reproduced with permission.

234

4 Photolithography

4.5 Special Photoresist Techniques 4.5.1 Nonconventional Diazo Resist Processes 4.5.1.1 Resist Profile Modification and Image Reversal

The perpetual drive to improve the performance of existent DNQ-novolak resists has stimulated research into advanced process schemes. Additional processing steps and modification of the basic chemistry have resulted in variants capable of producing positive and/or negative patterns. Their implementation in a production environment largely depends on the additional complexity they cause. The profile modification technique (PROMOTE) offers the capability of producing positive images with variable profile angles (Vollenbroek et al., 1991). The resist is irradiated (NUV) through a mask to yield the latent positive image. A DUV blanket exposure under anhydrous conditions (vacuum or elevated temperatures of approx. 100°C; Fukumoto et al., 1989) follows, leading to a selective crosslinking of the resist surface through PAC-resin ester linkages in the previously masked areas (Fig. 4-39 IV). Since the esterified top of the resist exhibits a low dissolution speed, overdevelopment yields negative sloped patterns suitable for lift-off processes. Positive or negative tone images are produced by the image reversal resist schemes. Originally, they were developed to improve the process latitude of DNQ resists, but the use of the same photoresist in either its positive or negative mode is of greater practical interest with respect to warehousing, reduction of printing defects by appropriate choice of best defect masking and control of sidewall angles. Several versions of image reversal resists have been described:

The indirect, amine-promoted image reversal process was developed by Moritz and Paal at IBM (Thompson et al., 1983). In their first experiments 1-hydroxyethyl-2-alkylimidazoline was added to the DNQ resist. After an imagewise NUV exposure the latent positive image can be developed (positive mode). When a bake step (image reversal bake) is inserted prior to development, the ICA decarboxylates via its ammonium salt to the parent indene derivative, which acts as an effective dissolution inhibitor (negative mode). A subsequent NUV flood exposure converts the unreacted DNQ into the corresponding ICA and enhances the developability. Useful modifications are based on diffusion of amine vapours (Alling and Stauffer, 1988), or a liquid ammonia soak (Ziger and Reighter, 1988), to provide the base catalysts. The ammonia soak process has been used for a lift-off process in fabrication of CMOS devices (Jones et al., 1988). The relevant chemistry of this base-catalyzed process is given in Fig. 4-53 (Reiser, 1989). The indirect image reversal process suffers either from low shelf life (the base is in the resist), or from an additional soaking step. An elegant approach to image reversal resists based on a 2,1-DNQ-4-sulfonate ester PAC and a small amount of hexamethoxymethylmelamine (HMMM) has been made available by Clariant (Spaket al., 1985), followed by similar materials from MacDermid and Shipley. This direct image reversal process proceeds according to the reaction sequence in Fig. 4-54: during the bake of the latent image, the ICA photoproduct forms the highly acidic indene, sulfonic acid, which induces the crosslinking reactions of HMMM (Buhr et al., 1989b). A subsequent NUV flood exposure solubilizes the yet unexposed regions; upon alkaline development a high quality negative image is obtained (compare: Figs. 4-16 and 4-54).

235

4.5 Special Photoresist Techniques

Resist

U

(@. hV

o=s=o

,

-N2 +W

OR

OR

kT

/

U

Post exposure bake

U

Flood exposure

R-NH2

+

1

Substrate

cq

o=s=o OR

Indirect (base induced) image reversa

n U

o=s=o I

OH

I

OH

Development

Direct (crosslinking) image reversal

Figure 4-53. Process flow and relevant chemistry of (left) the amine-promoted image reversal process and of (right) the direct image reversal (crosslinking) process (XL = unreacted crosslinker; NW = network).

Figure 4-54. Change of sidewall profile of a direct image reversal resist by variation of 1. and 2. exposure dose. (a) positive [ 1. expos.: 1 .5 s, 2. expos.: 2000 pJ/cm2], (b) vertical [ 1. expos.: 1.5 s, 2. expos.: 1000 pJ/cm2], and (c) undercut profiles [ 1. expos.: 0.5 s, 2. expos.: 1000 pJ/cm2].

This chemistry is the basis of the i-line sensitive AZ@ 5200 resist series. A related resist with equally good g- and i-line applicability is based on 7-methoxy substituted 2,l-DQN-4-sulfonate esters (Buhr et al., 1989b). This material resolves 0.40 pm lines and spaces with vertical sidewalls with an 0.54 NA g-line stepper (Seha and Perera, 1990). The lithographic properties of direct image reversal resists have been investigated by several groups (Gutmann et al,

1990b; Reuhman-Huisken et al., 1990), and compared with the indirect type (Grunwald et al., 1990). A key feature of image reversal resists is the potential to control the pattern profiles, e.g. vertical slopes for sub-pm etch applications, and undercut profiles for lift-off (Fig. 4-54). Another benefit is the excellent thermal stability of the patterns (> 200 "C) and the improved linewidth control over topography (Nicolau and Dusa, 1990).

236

4 Photolithography

4.5.1.2 Bilayer Systems for Contrast Enhancement

ized by General Electric under the tradename Altilith. The relevant chemistry of CELs is given in Fig. 4-55. The effects of CEL materials on critical dimensions and resist behaviour over highly reflecting topography have been studied intensively (Blanco et al., 1987). However, layer intermixing seems to be unavoidable, if CE-layers do not consist of water-soluble bleachable diazonium salts (Endo et al., 1989) and water soluble polymers, e.g. PVA (Halle, 1985), poly(viny1 phenol) (Sakurai et al., 1988), or poly(viny1 pyrrolidone) (Uchino et al., 1988). A system with two layers of different spectral sensitivity, introduced by Lin (IBM), consists of a thick planarization layer of DUV sensitive PMMA or PMGI and a thin NUV sensitive DNQ-novolak toplayer (Lyons and Moreau, 1988; Takenaka and Todokoro, 1989), which is opaque to light below 300 nm. The top material is patternwise exposed and developed, followed by a blanket exposure with DUV radiation and a second development with an organic solvent. The process was termed portable conformable mask (PCM), as the top resist

Contrast and quality of the latent resist image can be improved by the application of a contrast enhancement layer (CEL) on top of a conventional prebaked photoresist (White and Meyerhofer, 1986). A CEL is a thin photobleachable film with high initial absorbence of the applied radiation. During illumination, the CEL is bleached , and its non-linear transmission cuts off low intensity parts of the aerial image, allowing only the high-intensity parts to pass (Fig. 4-55). After illumination, the CEL is removed either prior to, or together with the development of the photoresist. Suitable photobleachable compounds for i- and g-line sensitive CE-layers were found among the substituted diary1 nitrones (West et al., 1988) which exhibit high extinction coefficients 5 and rearrange in the near UV ( ~ - 3 000) on exposure to nonabsorbing oxaziridines ( E < 5000) with quantum yields of 0.3. Unfortunately, they are somewhat unstable towards moisture (West et al., 1988). CELmaterials for g- and i-line are commercial-

CE-layer

'

UU-U tw

Resist Substrate

Q

Exposure

CEL

I CH= 0N+

0

hv

hv

Removal of CEL & resist development

4 2

+H20

Figure 4-55. Process flow and relevant chemistry of the CEL-technology.


acts as a zero-gap in-situ mask during DUV flood illumination, resulting in a nearly ideal image transfer to the bottom layer. Mid UV sensitive CARS based on blocked poly(viny1 benzoates) as toplayer in combination with PMGI as bottom layer have been described for use as PCM (It0 et al., 1987).

4.5.2 Suppression of Reflections and Standing Wave Effects 4.5.2.1 Dyed Resists

Accurate pattern transfer is heavily degraded when metallized, highly reflective topographic substrates are imaged. The degradation of critical dimensions is caused by both thin film interference effects due to non-uniform resist thicknesses over steps as well as by light scattering from underlying patterns, known as reflective notching (Bolsen et al., 1986). According to Eq. (4-7) (Sec. 4.3.2. l), these problems are alleviated by increasing resist absorption a through the addition of dyes absorbing in the actinic

1.20

I I

1.15 1.10

5 1.05

v

g

1.00 '3 Q) .E 0.95 J

0.90

k

0*85 0.80 1.30

1.40

1.50

1.60

Resist Thickness (pm)

1.70

Figure 4-56. Simulation of CD-variations of 1 pm lines and spaces with varying resist thickness on aluminium for undyed resist, dyed resist, and undyed resist with an ARC. (Reproduced from Noelscher et al., 1989 with permission.)

237

region (Fig. 4-56). The requirements with respect to absorbence, particle generation or solubility are met by only few dyes. These include, for example, coumarin and curcumin (Cernigliaro et al., 1989), or azodyes (Cagan et al., 1989). The main trade-offs for gaining added process latitudes on topography are losses in focus latitude and generation of non-vertical sidewall profiles (Fig. 4-57) due to the increase of the non-bleachable absorption (Cagan et al., 1989). Depending on the concentration and the chemical type of the selected dye, increasing dose requirements are often observed, which made the efficiency of this approach to a subject of intensive debate in the literature (Mack, 1988). 4.5.2.2 Antireflective Layers

The use of antireflective coatings (ARCS) is an alternative concept to minimize reflective notching and CD variations caused by interference effects (Brunner, 1991). The interest in this approach has emerged with the recent progress of DUV lithography, as it is believed that the inclusion of the ARC concepts is vital for DUV technology to become relevant to ULSI mass production (Barnes et al., 1991). The more common way is the deposition of thin sputtered inorganic films with light absorption properties on reflective substrates as bottom antireflective coatings (BARCs). A precise control of their thickness is very critical for maximum effect. Optionally, these films remain in the final device (integrated BARC). Their application introduces additional complexity and new sources of defects (Horn, 1991). Focus and exposure latitudes are significantly enhanced and become less sensitive to substrate reflectivity, resulting in a more robust process (Sethi et al., 1991; Fahey et al., 1994; Figs. 4-56 and 4-57). Anorganic

238

4 Photolithography

Figure 4-57. SEM pictures of positive resist patterns over silicide topography for (a) undyed resist, (b) dyed resist and (c) undyed resist on BARC. (Reproduced from Noelscher et al., 1989 with permission.)

BARC materials can be TiN, TaN, Si,N,, a-Si, a-C : H or other layers made by chemical vapor deposition. More recently, however, the use of organic BARCs has become popular (Krisa et al., 1996). These materials are simply spincoated at an optimized FTof 50 - 200 nm on the wafer and baked at high temperature to avoid intermixing with the subsequently coated photoresist. By selection of the BARC material, and depending on the need of the user, conformal or planar coating of the substrate is possible (Fig. 4-58).

Organic BARCs are less sensitive to FT variations, prevent potential contamination of sensitive devices, and bring about tremendous cost reductions as no additional deposition equipment is required. Pattern transfer to the substrate is achieved by an oxygen RIE step after photoresist development. State-of-the-art organic BARCs for NUV and DUV processes are provided by Tokyo Ohka, Brewer Science, Shipley and Clariant. Figure 4-59 demonstrates the elimination of reflective notching (hole burning) by the use of AZ BARLi.

Figure 4-58. Conformal and planar organic BARC arrangement on a topographic wafer.


239

Figure 4-59. Hole burning by accidental mirror elements. Top: without BARC, bottom: with BARC.

From inspection of Eq. (4-7) (Sec. 4.3.2.1),it is obvious that the reflectivity of the resistlair interface also contributes to thin film interference. Improvements of the CD control through the application of a top antireflective coating (TARC), which is spun on top of the resist to minimize the resistlair reflection, have been reported first by Tanaka et al. (1991 a), and later by Brunner (1991). This technique uses a thin (30-100 nm) organic film with a matched refractive index ?zTARC and an optimum thickness dTARCas defined by Eq. (4-lo), where ildenotes the radiation wavelength. ~ T A R C =A14 ~ T A R C

(4-10)

The optimum refractive index of the TARC of 1.28 is only met by Teflon, or certain perfluoroalkylpolyethers (Tanaka et al.,

199 1 a; Brunner, 199 l), which require special coating solvents and removers, and bring severe adhesion problems. Tanaka et al. (1991 a) have reported that on silicon substrates the CD control was improved by a factor of ten. A water-soluble TARC-material has been introduced by Clariant under the tradename AZ AQUATAR (Alexander et al., 1994). Although the optimum value of the refractive index is not matched by Aquatar (1.4), its water solubility allows easy processing and avoids intermixing with the photoresist. More advanced TARCs do not require extra bake, strip or etch steps, are nonabsorbing and therefore cause no exposure penalty or degradation of photoresist contrast. Recent work has demonstrated that TARC applications bring significant im-

240

4 Photolithography

provements, such as reduction of the swing ratio by a factor of 3, thus improving linewidth uniformity over topography, improved across-the-wafer uniformity, and a larger focus budget. However, TARCs do not eliminate reflective notching effects. Yoshino et al. (1994) compared the BARC and TARC concepts with respect to the simulated process windows in DUV lithography. The TARC has a smaller thickness latitude but it offers a wider process window for the resist. Arrangements with organic ARCS are superior to dyed resists with respect to resolution, latitudes, and linewidth control on topographic substrates, but introduce additional process complexity. Figure 4-56 compares the simulated CD variations as a function of resist thickness for a standard resist, a dyed resist, and an undyed resist with an ARC (Noelscheret al., 1989). Franzen et al. (1998) compared the costs of various lithography technologies (dyed resist, BARC and bilayer CARL resist) for a mass production target of 3000 wafer starts per week. They calculated that the Cost of Ownership value of a dyed resist is lower than for any other process in their comparison. The COOvalue for an integrated TiN-BARC process without removal of the antireflective layer is 42% less than that of a CARL bilayer resist process (compare4.5.4.2) and 53% less for an ex-situ TIN-BARC process. The a-Si-process with ex-situ etch and without integrated removal of the a-Si layer in the etch process is by far the most expensive process of all the processes described here. Thus the CARL process is an interesting possibility with high capability and comparable COO value.

4.5.3 Silicon-Containing Multilayer Resists The majority of the photoresists discussed in the previous chapters was devel-

oped for use as single layer resists (SLR). From the discussion it became evident that SLRs have certain limitations: restricted aspect (i.e. heighdwidth) ratios, limited focus budgets, sensitivity to topography and thin film interference effects, and lack of stability against aggressive etch chemicals. Together, these factors have been met only with very few high performance SLRs. A way to alleviate these obstacles is the use of multi layer resist (MLR) systems, which permit specialization of the separate layers, e.g. optimized sensitivity and resolution of the imaging layer, and adjusted dry etch resistance, optical density, and thermal stability of the bottom layer (Miller and Wallraff, 1994). With respect to e-beam lithography, problems arising from proximity, or electrostatic charging effects can be resolved by suitable MLR combinations (Moss et al., 1991). The main handicap of MLR systems is the increase of complexity involved with two or more layers, which translates into multiplying the probability of defects or unexpected aging phenomena. Moreover, MLR processing requires expensive dry etching equipment not commonly available in IC manufacture for oxygen plasmas. Single layer resists will therefore be used as long as they fulfil the respective requirements, and it is difficult to decide at what stage the incorporation of an MLR system is clearly favourable. On the other hand, new prototype devices and ASICs are often tested and manufactured using MLRs (Hatzakis et al. 1988). In reality, all techniques using an organic BARC or TARC are multilayer resist processes and, although they are often termed SLR, their complexity is comparable to MLR systems (Franzen et al., 1998). MLRs are composed of a 0.5 to 4 pm thick radiation-insensitive bottom resist, or planarizing coating, which has low resistance towards oxygen plasmas, submerges


the substrate topography and reduces interference effects by light absorption at the actinic wavelength (Thompson et al., 1983). Examples include hard-baked DNQ-novolak resists, polyimides or diamond-like carbon layers (Namattsu, 1988; Leuschner et al., 1993). In a MLR scheme, a second and normally much thinner top resist or imaging layer (0.2 to 1 .O pm) is coated on top of the planarizing coating. The top layer defines the feature dimensions and is thus sensitive towards radiation. Optionally, these two layers are separated by a third layer, an in general extremely thin (< 0.2 pm) but stable barrier layer with respect to an image transfer via dry etching (Hartney et al., 1989). It is most often selected from inorganic materials, e.g. silicon, silicon nitride and dioxide, titanium dioxide, polysilane, or spinon-glass (Hartney et al., 1989), and can be applied by either sputtering, plasma chemical vapour deposition (PCVD), or spincoating. The use of trilayer schemes has become quite unpopular, as the increasing complexity is not usually compensated by their benefits. Therefore, the following discussion will concentrate on silicon-containing top resists of bilayer schemes (Miller and Wallraff, 1994). A typical process flow is given in Fig. 4-60. The resistance of silicon-containing polymers towards oxygen reactive ion etching (0,-RIE) is controlled by their chemical structure, and the silicon content. During treatment with an oxygen plasma, the polymer surface is converted to a thin (5 to 20 nm) layer of silicon dioxide, which is highly resistant towards further plasma attack (Hartney et al., 1989). Oxygen etch resistance is not a linear function of the silicon content (Fig. 4-61): at silicon contents above 10 to 15% it remains constant (Jurgensen and Shaqfeh, 1989). A problem often encountered with the incorporation of

241

Spin coating of DNQ- novolak resist and hard bake (> 200 "C)

J/

\1

hv

.1

Exposure

Figure 4-60. Typical process flow of a silicon-based bilayer resist arrangement.

1

3 10 30 Percentage of silicon in the polymer

Figure 4-61. Effect of silicon content on the etching rate of organosilicon polymers in an oxygen plasma at 10 mTorr pressure and power=O.lS W/cm*. The etching rate is independant from the silicon position. (Reproduced from Hatzakis et al., 1988 with permission.)

242

4 Photolithography

silicon is the low glass transition temperature of these materials, which may lead to thermal flow and lack of resolution. Moreover, hydrophilicity is reduced as the silicon content increases, which may become an issue when aqueous-based development is desired. 4.5.3.1 Negative- Tone Silicon Bilayer Resists

The first examples of lithographically useful silicon-containing negative resists were based on poly(alky1 siloxane)s, which show an oxygen etch rate ratio of 1 : 50 compared to hardbaked novolak resist (Shaw et al., 1987). They exhibit low TG's (< 100°C) and tend to image-distorting thermal flow. Poly(silmethy1ene-) and poly(silpheny1ene si1oxane)s containing highly regular siliconcarbon and silicon-oxygen linkages in their

Q Q

-(--ki-O-)-(-Si-o-)I

0 I -(-Si-O-)-(-si-o-)-

I

SNR

-(-Si-O-)-(-Si-O-)I

0 I

-(-Si-O-)-(-Si-O-)-

I

0 I

I

CH, -(-.&i-o-)-(-Si-o-)I

0

I -(-Si-O-)-(-si-o-)I

CH3

ChCI

I

0 I

main chain are reported to have higher TG and e-beam sensitivities ranging from 25 yC/cm2 (Babich et al., 1989). More recently, a three-dimensional crosslinked poly(silpheny1ene siloxane) was prepared as negative-acting photoresist. It exhibits higher rigidity than conventional siloxanes, resulting in an improved contrast, minimized swelling upon development, and improved thermal stability. The addition of 2,2-dimethoxy-2-phenyl acetophenone as a photoinitiator enhanced the UV photospeed by a factor of 20 to about 20 mJ/cm2 without deterioration of the pattern profiles. 0.25 ym patterns could be delineated in a bilayer arrangement (Watanabe et al., 1991). Researchers from NTT obtained a high TGmaterial ( 1 50 " C ) with a partially chloromethylated poly(dipheny1 silsesquioxane) in which two chains are linked together by oxygen atoms (ladder type polysiloxanes).

I

P I CH C I 4

Vinyl-silsesquioxane

---Si-0-)I

(-Si-0-)-OH I

9 P -(-Si-0-)-(-Si-0-)-OH ,L

MSNR

APSQ

0

6

structure of silsesquioxane based negative working resists.


The material - called silicon based negative resist (SNR, Fig. 4-62) -is sensitive towards DUV and e-beam radiation ( 5 pC/cm2) and resolves 0.5 pm patterns on a hardbaked novolak (Tamamura and Tanaka, 1987). Adequate near UV sensitivity, resolution and oxygen etch resistance were achieved using the methacrylated silicon based negative resist (MSNR, Fig. 4-62), which utilized a methacrylated poly(pheny1 silsesquioxane) as polymer and a bisazide as PAC (Morita et al., 1986). The same group from NTT applied acetylated phenylsilsesquioxane oligomers (APSQ, Fig. 4-62) as the matrix polymer for both negative and positive bilayer resists (Ban and Tanaka, 1990). APSQ, together with azidopyrenes, gives a negative working DUV and e-beam sensitive resist with good resolution (Kawai et al., 1989). In combination with onium salts, the photoacid catalyzes the condensation reaction of the silanol groups in APSQ (Ban et al., 1990). This process is accelerated by a post-bake step, and 0.3 pm negative patterns have been obtained in a bilayer scheme (Tanaka et al., 1992). A silylated poly(viny1 silsesquioxane) gives an e-beam resist (7.6 pC/cm2) with an estimated etch rate ratio of 1 : 100 compared with a hardbaked positive resist (Saito et al., 1988). A three component material with improved DUV (25 mJ/cm2) and e-beam ( 5 pC/cm2) sensitivity has been formulated from poly(pheny1 silsesquioxane), a photoacid generator, and an additional crosslinker, e.g. hexamethoxymethylmelamine. Crosslinking probably occurs through etherbond formation. The material offers a tremendous etch latitude (Hiraoka and Yamaoka, 1991). 4.5.3.2 Positive- Tone Silicon Bilayer Resists

As reported by Miller and Michl (1989), polysilanes are attractive-positive acting

243

top resists for bilayer arrangements due to their bleaching ability and Si-Si bond scission reactions. These polymers with silicon in the main chain are glassy materials with high TG’s, exhibit good solubility in common organic solvents and form films of excellent quality. Their absorption maximum is centred around 320 nm, making them especially sensitive to mid- or deep UV radiation (Wallraff et al., 1991). Upon exposure, photodegradation occurs through cleavage of the Si-Si bonds into silyl radicals and silylenes, which stabilize via hydrogen abstraction to fragmented polysilanes (Fig. 4-63). As a side reaction, photooxidation to polysiloxanes with smaller molecular weights was detected. The fragmentation is accompanied by a pronounced bleaching effect. An extensive discussion of polysilane photochemistry has been given recently (Miller and Michl, 1989). Not surprisingly, the oxygen etch resistance of polysilanes is comparable to that of polysiloxanes. A large variety of aliphatic or aromatic polysilanes together with sensitizing additives have been studied as positive-acting top resists by Miller et al. (1991) and Wallraff et al. (1991). They have spun high molecular weight materials from toluene solu-

Figure 4-63. Change in molecular weight distribution of a 0.006% solution of poly(dodecylmethy1silane) upon irradiation with 0,2,4,and 8 pJ/cm2 at 3 13 nm. (Reproduced from Miller et al., 1989 with permission.)

244

4 Photolithography

tions on 1 ym thick hardbaked novolak films to yield a dry film thickness of 0.1 ym. Their investigations revealed that high DUV sensitivity (15 mJ/cm2), high resolution, and clean oxygen RIE pattern transfer are possible. As main problems remain the low yield polysilane synthesis utilizing difficult-to-handle metallic sodium or potassium (Reiser, 1989), the exclusion of metallic impurities in the resist and the contamination of the exposure tools upon self development. Synthesis problems may be overcome by plasma deposition of polysilanes and, combined with dry development, this allows an all-dry lithographic cycle (Kunz and Horn, 1991; Joubert et al., 1994). Polysilyne derivatives have been explored as photoresists for ArF (193 nm) excimer laser lithography (Kunz and Horn, 1991). These materials are photooxidized to polysiloxanes upon exposure to high energy radiation. Wet development using po-

CH3 Poly-(allyltrimethylsilane-sulfurdioxide)

I -(-CH2-CH-W-CH-)-

CH3-Si-Ck I

CH3

0

lar solvents yields a positive image with feature sizes smaller than 0.2 ym after oxygen RIE. Gozdz et al. (1986) prepared a bilayer resist by the copolymerization of sulfur dioxide, butene, and allyltrimethylsilane with 13% silicon content (Fig. 4-64), high ebeam sensitivity of 2 yC/cm2 and good resolution capability. Copolymers of 4-hydroxystyrene and vinyltrimethylsilane (Fig. 4-64) are excellent candidates for aqueous alkaline developable silicon-containing near and deep UV resists, as they show high transparency at 248 nm, no thermal flow up to 150°C and good oxygen RIE resistance (Sezi et al., 1989). Positive-acting DNQbased resists with a silicon content over 10% have been prepared by condensation of formaldehyde and a phenol with a siloxane group (Noguchi et al., 1990) (Fig. 4-64). Using a g-line stepper, 0.5 mm patterns were fabricated.

C k

94

Silicon containing novolak resin

OH

Vinyltrimethylsilane/hydroxystyrenecopolymer

?+

-(-Si-O-)-(-Si-O-)I

0 I

-(-Si-O-)-(-Si-O-)CHz

I

CHz I

(7 CHz

I

I

OH Poly-(hydroxybenzylsilsesquioxane)

Figure 4-64. Examples of silicon containing positive working resist materials.


By acetylation of phenylsilsesquioxane oligomers, a g-line sensitive alkali developable resist with a thermal stability up to 400°C and an ultimate resolution of 0.35 pm was obtained by Tanaka et al. (1989). The alkaline soluble phenolic groups containing poly(4-hydroxybenzylsilsesquioxane) resin of Hitachi's organosilicon positive resist OSPR-1334 (Fig. 4-64), acts in combination with DNQs as i-line, or g-line sensitive, positive top resist (Sugiyama et al., 1988). OSPR contains 18% silicon, has a TG of 107"C, an 0,-RIE rate ratio to hardbaked novolak of 28 and is strippable with alkaline developers after pattern transfer (Nate et al., 1991). A t-BOC blocked resin of this type has been evaluated by Brunsvold et al. (1993b) as DUV resist for 64 MBit DRAM production. The top layer materials for the MLR systems described so far contain silicon incorporated in their polymer structures. Another approach is to add a low molecular weight poly(pheny1 silsesquioxane) to a conventional g-line DNQ-resist. This mixture is commercialized by Hitachi under the tradename RG 8500P and has a submicron resolution capability (Toriumi et al., 1987). 4.5.4 Top Surface Imaging

Surface imaging in combination with dry development by means of an oxygen plasma has been suggested as a method of overcoming the inherent limitations present in conventional wet development photolithography. The strategy is to enhance the oxygen etch resistance of a metal-free resist through selective incorporation of silicon into the latent resist image by a suitable technique during or after the exposure (Roland, 1991; Taylor et al., 1990). The advantage of this top surface imaging (TSI) technique is obvious: the formation of the silicon-containing protective layer requires only a surface

245

modification. This should result in a reduction of exposure time, and an alleviation of both the depth-of-focus and thin film interference problems, as multilayer performance can be obtained with a single layer resist process. 4.5.4.1 Gas Phase Silylation Systems

The most prominent TSI scheme is the so-called DESIRE-process (diffusion enhanced silylating resist), which was developed in the mid 1980s by Roland at UCB Electronics, and Coopmans at IMEC. The pronounced interest arises from the fact that resists, based on dyed DNQ-novolak chemistry, with reproducible properties are commercially available (Plasmask) for g-line (150-G), i-line (200-g) and DUV (301-u) applications (Roland et al., 1990; Bauch et al., 1991). A scheme of the negative-tone DESIREprocess is outlined in Fig. 4-65. The resist is imagewise exposed, subjected to a socalled presilylation bake at approx. 160"C, and silylated in the gas phase at elevated temperature (140 to 170°C) to form a thin resist layer rich in silicon, which builds up the etch resistant SiO, layer during the oxygen etch (Laporte et al., 1991). The selectivity of the silylation has been determined by Rutherford backscattering spectroscopy: The thickness of the silylated layer is in the range of 150 to 200 nm in the exposed, and only 5 to 10 nm in the unexposed areas (Dijkstra, 1991). The silylation mechanism is critical and has been investigated in detail by Visser et al. (1987). It is a kinetically controlled simultaneous diffusionheaction process following Fick's diffusion law. Its diffusion coefficient depends on the PAC concentration. A thermally induced crosslinking reaction between the unphotolized PAC and the resin occurs in the unexposed areas during the

246

4 Photolithography

Resist Substrate

Dark area

U

Exposure

cb*

C W -

+

uuu hv /(

qy o=s=o I

OH

*?

,Novolak

kT

I

OR

OR

Bake & Silylation

0

Exposed area

+ y////////I////////1

Y (Cl%)3SI/N\SI(CH3)3

9

Si(CH3)3

Figure 4-65. Process flow of the DESIRE process.

presilylation bake. Therefore only the exposed areas can accommodate a large volume of the silylation agent. Due to finite contrasts of both the aerial image and the silylation, sloped silylated profiles are obtained (Reuhman-Huisken and Vollenbrock, 1991; Taira et al., 1991). Using the common silylation reagents, only the hydroxyl moieties of the resin are silylated in the exposed regions, while the carboxylic acid groups of the ICA are not. The Plasmask g-line material incorporates about 11% silicon, which is accompanied by a vertical and lateral resist swelling. While the vertical swelling does not affect the image accuracy, lateral swelling results in a kind of proximity effect, which may give rise to image distortions. The lateral swelling is influenced by the silylation agent and decreases in the following order (Dao et al., 1991): 1,1,3,3,5,5-hexamethylcyclotrisilazane (HMCTS) > heptamethyldisilazane (HeptaMDS) > hexamethyldisilazane (HMDS)>trimethylsilyl-diethylamine (TMSDEA) $- 1,1,3,3-tetramethyldisilazane (TMDS) (Fig. 4-66); it has been

reported that the latter suppresses any swelling and improves the processing latitudes (Goethals et al., 1991). Several research contributions denote specific advantages or drawbacks of DESIRE, when applied to practical design, imaging problems and proximity effects (Op de Beeck et al., 1990; Garza et al., 1991; Goethals et al., 1994). The main obstacles to the application of this technology are additional costs for a silylation machine and a plasma reactor, and low wafer throughput (approx. 5- 15 wafer/h). The major lithographic concerns are that of linewidth loss during etching, proximity effects, and stripping of the patterned silicon-containing resist. However, several advantages, such as the very impressive CD control over topography, offset some of these drawbacks (Fig. 4-67). The potential of DESIRE in production has been evaluated by Garza et al. (1991). The results from more than 1250 wafers indicate that it certainly extends the applicability of exposure equipment already in place. Linearity and process windows were found to be superior to standard resists. A study by Tak-


H3y l-!$-Si-N & i d

y2H5 L2H5

Trimethylsilyldiethylamine TMSDEA

Heptamethyldisilazane HeptaMDS

H3y

7

yH3

H-Si-N-Si-H

H3d

H3y

y

yH3

H$-Si-N-Si-C!+

LH3

Tetramethyldisilazane TMDS

/

H3C

247

Figure 4-66. Chemical structures of silylation agents.

LH3

Hexamethyldisilazane HMDS

1,1,3,3,5,5-Hexamethylcyclotrisilazane HMCTS

Figure 4-67. 0.25 mm lines and spaces of the Plasmask resist over aluminium topography (ASM-L PAS 5000/ 70 DUV stepper (NA=O.42)). Courtesy of IMEC, Leuven, Belgium. Reproduced with permission.

ehara et al. (1991) using the i-line material revealed that the resolution limit ( 10,' atom/cm3), which, upon annealing, diffuses into the underlying gate oxide and leads to performance degradation of metal oxide semiconductor (MOS) devices (Shioya et al., 1987a; Wright and Saraswat, 1988). In addition, the silane-produced films suffer from poor step coverage and adhesion problems, and tend to crack and peel off, especially over extreme topography (Ellwanger et al., 1991). These problems can be avoided by changing the reducing agent to SiH,CI, (dichlorosilane - DCS). The fabrication of DCS-WSi, films in a batch reactor (Shioya et al., 1987b; Selbrede, 1988; Hara et al., 1990) as well as in a plasma-enhanced single-wafer system (Wu et al., 1988) with lower F content, improved step coverage and adhesion, have recently been published. A specific problem with DCS-WSi, is related to in-depth compositional nonuniformity. DCS-WSi, films, especially those grown on poly-Si, show a reduction in x at the initial stages of the deposition

45 1

+

Figure9-22. Diffusion path of the dopants in the conventional dual polycide structure.

that is below the optimal regime of 2.2 to 2.6. Values smaller than 2, the stoichiometry of the stable tungsten silicide, have been observed (Hara et al., 1990). This is extremely unfavorable since the formation of a W-rich region at the WSi, /poly-Si interface can cause excessive interdiffusion of Si, localized stress, and adhesion problems following a high-temperature oxidation process. Sheet resistance nonuniformity across the wafer has also been a problem in DCS-WSi, in contrast to silane-based WSi, . Using single wafer reactor, highly uniform in composition (in depth and in lateral position) CVD WSi, films have been deposited on 200 mm Si wafers using SiH,CI,/WF, on SiOz or poly-Si (Telford et al., 1993). Annealing at 900°C in N, of such films deposited on P-doped poly-Si resulted in a uniform reduction of x to a value of 2.1 to 2.2 and resistivity values in the range of 80 to 100 pQ cm. The as-deposited films were predominantly in the hexagonal structure of WSi, , which transformed to the tetragonal structure upon annealing at temperatures above 600 "C. The films had a very good step coverage even at high aspect ratios and did not crack or peel off upon annealing. The films contained relatively little F : x 6 x lo1, to 2 x loi7 atoms/cm3.

452

9 Silicon Device Processing

For future scaled CMOS devices using thinner gate oxides, it is advantageous to work with a gate electrode material with a larger work function to obtain the desired threshold voltage. The larger work functions of Mo (4.7 V), W, or refractory silicides produce low and nearly symmetrical thresholds for p- and n-channel devices on moderately doped substrates (Kim et al., 1983). In addition, MOSFETs with refractory metal gates require much less channel doping than n polysilicon gate devices (Takeda et al., 1985) and reduced subthreshold leakage. However, they are rarely used directly on gate oxides as gate electrode materials due to incompatibilities with the underlying gate oxide, inability to form stable dielectrics, and poor contamination barrier characteristics. +

9.6.2 Contacts

After aluminum deposition, most processes need an annealing step at 400 “C anneal. This reduces defects and lowers contact resistance by dissolving any “native” silicon oxides between the aluminum and silicon. During this annealing - and other high-temperature processing steps - silicon tends to diffuse into the aluminum forming silicon pits and aluminum spikes. The silicon-into-aluminum diffusion can be suppressed by adding 0.5-2% silicon to a deposition source. When this alloy cools, however, the solubility of silicon in aluminum decreases, i.e., the aluminum becomes saturated with silicon and any excess silicon precipitates. The precipitated silicon causes an increase in contact resistance. The use a barrier layer between A1 and Si can reduce the diffusion of silicon into the aluminum during sintering and, at the same time, act as “etch-stops’’ to avoid aggressive etching of Si in the contact area due to a misalignment error.

The diffusion barrier can be chemically inert to the materials it separates, or it can be stuffed with small amounts of impurities to inhibit diffusion along fast diffusion paths such as grain boundaries or microcracks that the impurities seal. Diffusion barriers must satisfy a number of criteria. For example, they must be chemically and thermally stable, and they must adhere to both the silicon substrate and the metal film. In addition, they must have minimum intrinsic stress to avoid stress-induced-microcrack failures (Kohlhase et al., 1989). Titanium-tungsten (Ti-W) and titanium nitrides (TIN) are first choices for barrier layers for several reasons. They have very high thermodynamic stabilities and are relatively easy to process. Tungsten is the principal component of Ti-W ; it contains 3 -28 % titanium to improve adhesion, contact resistance, corrosion behavior and ease of etching. Although Ti-W alloys have shown excellent barrier properties, they have very high compressive film stress, resulting in film delamination from the sputtering chamber walls and the subsequent increase in particles. In addition, while TiW can be an excellent etch-stop with chlorine-based dry-etch compositions, it is also very prone to post-etch corrosion and undercut. Titanium nitride (TIN) is an excellent choice because of the following advantages : -

-

-

Extremely high thermal stability - TIN resists silicon interdiffusion at temperatures up to 600 “C for 20 h (Wittmer and Melchior, 1982); Low and stable contact resistance when used with a titanium silicide layer - contact resistivity for a Si/TiSi,/TiN/Al scheme remains stable when exposed to 550°C for 20 min (Wittmer, 1985); Low sheet resistance - can be used as a

9.6 Metallization

-

local interconnection in CMOS technology (Jeng et al., 1993); Low stress ( "N lo9 dyne cm- ') (Kohlhase et al., 1989); Excellent etch-stop capability (Brat et al., 1987).

Several methods have been proposed for TIN deposition, including sputtering, reactive evaporation, thermal nitridation of pure titanium and CVD. Recent results have shown that high quality TiN/TiSi, bilayer can be formed using Ti-rich TIN films deposited from a single TIN,,, alloy target followed by rapid thermal nitridation. Excellent contact resistance and junction thermal stability as well as tight control over the stoichiometry of the sputtered films have been demonstrated, as shown in Fig. 9-23 (Nakamura, 1993). Reactive sputtering of Ti in the presence of N, results in films with low stress and high adhesion (Circelli and Hems, 1988; Stimmell, 1986). The metallization scheme typically included a 10 to 30 nm thick layer of pure titanium, 80 nm and 120 nm thick layers of TIN and 800 nm of aluminum-I % silicon. TIN can also be formed by thermal nitridation of titanium in the presence of NH3

@O

4 8 12 16 Breakdown Voltage [ V ]

with furnace annealing or rapid thermal processing. The latter, in particular, forms a TiN/TiSi, structure during a two-step, self-aligned salicide process (Ku et al., 1987). However, there are limits to the quality of the resultant titanium nitride and its thickness. For high aspect ratio contact or via holes ( > 2 : l), film conformality is a critical issue. Collimated sputtering technology has been developed to deposit low resistance Ti and TIN films to improve the contact coverage. A collimator, whose aspect ratio is 1.O, is placed between the sputter target and the wafer so that the wafer can collect the fraction of Ti clusters with normal incidence angle to the surface of the wafer. The problems with collimated sputtering have been shown to consist of no deposition on the side of the contacts, low deposition rate, and particles generation from the collimator. CVD TIN becomes a viable alternative, since these films can be almost 100% conformal. It is also possible to completely fill sub-micrometer contact holes. Traditional CVD TiN processes involve the reaction TiCl, + N, + H, at 1000"C or TiC1, + NH, (6 TiC1, + 8 NH, + 6 TiN+24 HCl+N,) at lower

Figure 9-23. Breakdown voltage distributions of pure Ti and Ti(N,,J samples after (a) 450°C, (b) 525°C annealing.

2U

(Vb: >lObA)

453

Breakdown Voltage [ V ] ( V b : >106A)

454


temperatures (Price et al., 1986; Kurtz and Gordon, 1986). Since TiCl, and NH, react at room temperature to form a solid product, it is difficult to mix the gases and introduce them to the reactor without gas phase nucleation. It has been found (Price et al., 1986; Kurtz and Gordon, 1986) that these two gases neither react in the gas phase nor deposit any TIN film on surfaces in the temperature range of = 250-350 "C. Based on this fact, both a low-pressure, hot-tube system at 700°C and an atmospheric pressure, cold-wall tube reactor and deposited films at 500-650 "C were developed. More recently, a number of studies have demonstrated that the TiCl, + NH, reaction could be carried out in a low-pressure, cold-wall, single-wafer reactor at similar temperatures and high deposition rates (500-1000~/min)(Yokoyama et al., 1989; Sherman, 1990; Smith, 1989; Buitinget al., 1991). One group used a reactor with warm (rather than cold) walls ( =250- 350 "C) to prevent deposition on the walls (Smith, 1989). Although resistivity of these films is considerably higher than bulk TIN, it can be kept quite low when depositions are done at higher temperatures. Values from 100 to 300 pR cm are typical, with the lowest values observed at the highest temperatures. Excellent diffusion barrier properties have been demonstrated (Sherman, 1990; Reid et al., 1991; Travid et al., 1990) between silicon and aluminum. Contact resistance of = l o p 6R cm were obtained for TIN deposited onto titanium silicide (salicide) contacts and pf-Si (Sherman, 1990; Travid et al., 1990) with excellent leakage current. A number of studies have shown that conformality for TIN can be outstanding, even for sub-micrometer trenches (Yokoyama et al., 1989; Sherman, 1990; Smith, 1989; Buiting et al., 1991). Rather than using TiCl, as the Ti precursor in

CVD TiN, one could use an organometallic molecule, thereby avoiding chlorine contamination. Two choices are available. One possibility would be the use of tetrakis (dimethylamido) titanium, Ti(N[CH,],), and pyrolize it to yield TIN, since the molecule already contains nitrogen. It has been shown that a more successful approach involves reduction with NH, (Fix et al., 1989). In this case, deposition in an atmospheric-pressure, cold-wall tube reactor at 200-400 "C yielded reasonably pure stoichiometric films. Another approach would be to use biscyclopentadienyl titanium, (C,H,),Ti, again with NH, (Yokoyama et al., 1990). Here, reasonably pure films are reported at deposition temperatures of 450 "C in a low-pressure, coldwall reactor. If either film, when deposited at temperatures 400"C, can be shown to have properties similar to the higher temperature films deposited from TiCl, , they will be better choices than aluminum or silicon. Finally, the deposition temperature can be lowered using a glow discharge. Although a number of studies have shown that this is possible for TiCl,+ N, + H, or TiCl, + NH, , they all result in a large amount of chlorine incorporation. One exception has been reported where a TiCl,+NH, mixture was excited at 13.45 MHz, and the chlorine content of the film was found to be quite low at 400°C (Hilton et al., 1986). The performance of MOS ICs depends on several parameters, of which the RC time constant is probably the most important. As the size of MOSFET devices decreases, the RC time delay due to the wiring (metal and polysilicon layers) that is used to contact the device gate, source, and drain, does not scale with the shrinking of the physical dimensions of the device. Therefore, for downscaled MOSFETs, the RC speed enhancement can be leveled by

+

455

9.6 Metallization

the time delay due to the wiring. Selfaligned silicides (SALICIDEs) including PtSi, TiSi,, CoSi,, MoSi,, and WSi,, have been reported to simultaneously form silicide on source/drain and diffused interconnections with the gate. The conventional SALICIDE process flow for n-channel MOSFETs fabrication consists of the following steps. The sidewall oxide spacers are formed after polysilicon gate patterning, lightly-doped source/drain ion implantation, and activation. A thin metal film chosen to form metal silicide is then deposited to cover the entire surface area. Metal silicide is thermally formed at both polysilicon gate regions and source/drain diffusion regions. A selective etching process removes the unreacted metal from the silicon dioxide surfaces but does not attack the metal silicide. A layer of doped glass (BPSG or PSG) is then deposited, followed by flow, contact window opening, reflow, and A1 metallization. For noble and near noble metal silicides, the metal is the dominant moving species during the reaction. This reduces the probability of bridging between gate and source/drain because of less lateral silicide formation. One major disadvantage of no-

ble and near noble metal silicides is the high temperature limitation. This temperature limitation can be relaxed by the use of refractory metal silicides, due to their high temperature stability. The use of TiSi, and CoSi, in SALICIDE technology has received considerably more attention than other metal silicides because of low resistivity, good adhesion, and high temperature stability. A comparison between CoSi, and TiSi, is shown in Table 9-9. Using the conventional TiSi, SALICIDE process for CMOS applications causes several problems, including the formation of native oxide at the metal/% interface which slows down the reaction and results in a rough silicide surface, critical ambient control, lateral silicide growth, different amounts of Si consumption in p-channel and n-channel devices, and non-ohmic contacts due to significant dopant redistribution during silicide formation. The native oxides at the Ti/% interface cause the reaction to proceed in a non-uniform fashion, resulting in a rough silicide surface. In addition, a high concentration of As at the Ti/Si interface retards titanium silicide formation. Therefore, the growth rates of titanium silicides formed on n' (As doped)

Table 9-9. Comparison of the properties of CoSi, and TiSi,. Properties

CoSi,

TiSi,

Resistivity (pQ/cm) Metal-dopant compound formation Thermal stability on single crystal Si Thermal stability on polysilicon (undoped) Mechanical stress (dyneicm') Reaction temperature with SiO, ("C) Dominant diffusion species during silicide formation Sheet resistance control Resistivity to dry/wet etching Native oxide consumption Thermal stability in the Al/silicide/Si system Lattice match with Si

10-15 no good poor

13-16 Yes good poor (2-2.25) x 10" 700 "C Si poor poor good poor poor

(8-10) x 109 >1ooo"c

co good good poor poor good

456


and p + (B doped) regions are different, resulting in different amounts of silicon consumption in the diffusion regions of pand n-channel MOS devices. Furthermore, significant amounts of dopant redistribution in source and drain areas occurred during SALICIDE formation, which makes the ohmic contact resistance very difficult. The above mentioned problem is avoided in the source-drain extension structure (Taur et al., 1993), in which shallow p' (or n') source-drain extensions are used in conjunction with deeper p (or n') source/drain regions implanted after thick oxide spacer formation, as shown in Fig. 9-24. The shallow extension depth is decoupled from the deep junctions required for the SALICIDE process. A 600 A deep p + source-drain extension has been fabricated by Sb pre-amorphization and low energy BF, implantation (Taur et al., 1993). Another approach is to use selective silicon deposition to form raised sourcedrain structures (Mazure et al., 1992; Kotaki et al., 1993). Issues with SEG elevated S/D structures and technologies are: capacitance increase, effects of faceting. +

9.6.3 Interconnections The reduction in interconnection feature sizes has lead to reliability degradations

I

so08

DEEP EXTENSIONS

n -WELL

caused by electromigration and stress-induced migration. The increase in wiring resistance as a result of the increase in chip size has been solved by increasing the number of interconnection levels. To meet this requirement, the thicknesses of both conductors and inter-layer dielectrics have been kept constant to reduce parasitic resistances and capacitances, making contact- and via-hole aspect ratios greater than one. Therefore, new contact- and viahole filling technologies as well as highly reliable multilevel interconnection conductor systems will be required. An example of interconnection materials and technologies for 256 M DRAM is shown in Table 9-10 (Kikkawa, 1992). As traditional interconnection materials A1 as well as various alloys of A1 have been used. Aluminum has a number of ideal properties : (1) low resistivity = =2.8 pLR cm); (2) excellent adhesion to SiO,; and (3) excellent wire bonding properties. However, because of its very low melting point (660 "C), electromigration occurs at relatively low temperatures and low current densities. Electromigration of A1 atoms takes place at the grain boundaries within the metallization line. The electron stream creates a flow of these atoms because they are less tightly bound than those within grains where the atoms are bound in lattice positions. Because the atom flow

4008 DEE+

p - T Y P E SUBSTRATE

Figure 9-24. Schematic cross-section of 0.1 pm CMOS devices with source/drain extension structure for silicided junctions.

457

9.6 Metallization

Table 9-10. Interconnection materials and technologies for 256M DRAM (Kikkawa, 1992). Interconnection Word line Bit line Bit contact Capacitor contact Peripheral contact

Material

Process

Design rule

Aspect ratio

WSi,,poly-Si WSi, N + poly-Si N + poly-Si W/TiN/Ti

sputtering/LP-CVD sputtering doped LP-CVD doped LP-CVD blanket W-CVD collimated sputtering reflow sputtering (L. T.) collimated sputtering reflow sputtering (H. T.) collimated sputtering sputtering

0.25 0.25 0.25 0.25 0.3

1-1.4 0.5-1.0 2-4 3-6 3-4

0.3

3 -4

0.3 0.25

3-4 1-2

0.25 0.6

1-2 1-1.5

0.6

1-1.5

Al-Ge/TiN/Ti

Metal line

Via-hole

Al-Si-Cu/ TiN/Ti TiN/Al-Si-Cu/ TiN/Al-Si-Cu/TiN cu W/TiN/Ti Al-Ge/TiN/Ti

sputtering blanket W-CVD reactive sputtering reflow sputtering (L. T.) reactive sputtering

occurs along the grain boundary in the direction of electron flow, a grain boundary that extends completely across the metallization pattern (“bamboo” structure) should have greater electromigration resistance. However, this type of structure is not manufacturable. The practical method of reducing grain electromigration is to introduce impurities, such as Si and Cu, that passivate the grain boundaries. The additions of high percentages of Cu make alloys difficult to etch and prone to corrosion problems; therefore, large numbers of circuits are still being made with A1 (1 YOSi) or A1 (1 % Si) with a small percentage of Cu (10.5%). The addition of Si causes Si “nodule” formation due to Si precipitation within the line that can occur during cooling or during the operation of the device (Shen et al., 1985). As the nodule grows in size, the current density in the A1 around the nodule increases and the line can eventually crack because of the stress around the growing nodule. Nodule growth can also cause interlevel metal

shorts or time-dependent breakdowns. Another traditional problem with A1 metallization has been hillock formation. Hillocks are formed by solid-state diffusion of A1 to relieve the film stress during thermal cycling at temperatures below those where plastic flow can occur. Hillocks are also formed by electromigration. Ti (0.2-3 wt. %) has been substituted for Cu to add to an A1 (1% Si) alloy to reduce electromigration. These additions of Ti increase the resistivity. Thin multilayers of Ti and A1 (1 YOSi) have been proposed and demonstrated with a 10 to 100 times improvement in the mean time to failure compared to A1 (1 YOSi) films (Shen et a1.,1985; Jones et al., 1985; Gardner et al., 1985). It must be noted that it is especially important to create a good barrier between the contact to silicon if an Al-Si-Ti metallization is used because the solubility of Si in the AI,Ti intermetallic compound can be as high as 15% (Shen et al., 1985). A new interconnection structure using TiN/Al-1 %Si-0.5 %Cu/TiN/Al-

458


1 % S O . 5 OO/ Cu/TiN/Ti layered films has been developed for both electro- and stress-migration-resistant interconnections (Kikkawa et al., 1991). The multilayer interconnection shows larger Vickers hardness value, less tensile stress relaxation and longer electromigration lifetime in comparison with Al-Si-Cu single layer. These improvements are due to the rigid intermetallic compounds, Ti,Al, at the interface between TIN and Al-Si-Cu (Kikkawa et al., 1991). Contact holes with minimum geometries in the order of 0.25 pm and aspect ratio greater than one must be plugged with an interconnection material having good coverage, low resistivity, stability during thermal processing, and compatibility with existing processes. Aluminum alloy reflow sputtering is a promising low-cost technology for contact-hole filling. Aluminumgermanium (Al-Ge) alloy (Kikuta et al., 1991) can flow and fill in quarter-micrometer contact holes at 300 "C due to its lower eutectic temperature (424 "C) than other Al-alloys. A highly reliable sub-half-micrometer via and interconnection technology using high temperature sputter filling of Al-Si-Cu alloys has been developed by Nishimura et al. (1992). A thin Ti underlayer was employed to prevent Si from precipitating. The substrate temperature during the sputtering for a filled via was 500°C. Complete filling of a 0.15 pm diameter via with aspect ratio of 4.5 has been realized with four orders of magnitude improvement in electromigration resistance compared with conventional via formation sputtering. Silver is a potential candidate for ULSI interconnection because of its lowest resistivity compared with other interconnect materials. However, silver has numerous processing difficulties, which limited its wide use in the past (Table 9-11). The ma-

Table 9-11. Properties of Al, Cu, Ag and Au. Al Resistivity (pQ cm) 2.8 660 Melting point ( " C ) 1 EM endurance (normalized to Al) -400 Heat of formation of oxide (kcal/mol) Diffusion into S O , no no Agglomeration RIE easy

Cu

Ag

Au

1.7 1083 20

1.6 961 10

2.2 1063 20

-40

-7.3

-0.8

yes small difficult

yes no severe no diff- difficult cult

jor problems are the lack of reliable dry etching and the requirement of high temperature annealing needed to obtain low resistivity. A novel planarized silver interconnect technology with TiO, passivation has been developed by Ushiku et al. (1993). The process sequence is shown in Fig. 9-25. The first annealing at 400°C results in Ag planarization due to significant surface diffusion of Ag. After etching back or CMP process, the sample is then annealed at 600 "C. During annealing, Ti diffuses upwards through the Ag films to the surface and forms a TiO, layer. The TiO, layer protects the agglomeration in Ag films during annealing. Recently, a novel contact filling technique has been developed based on polysilicon plug and Ni silicidation with a TIN barrier layer (Iijima et al., 1992). The process details are shown in Fig. 9-26. This

(a) (b) (4 (d) Figure 9-25. Process sequence of Ag interconnection technique: (a) Ag deposition; (b) annealing at 400°C; (c) etch-back or polishing; and (d) annealing at 600°C.

9.6 Metallization

Poly-Si Plug

Poly-Si ,

/

\

,Ni

TiNlTi a) Ni Sputtering Si-Substrate Ni ,Si

b) Ni silicidation

-

1

Ni

Silicidation stop

c) Selective metal etch Si-Substrate

Figure 9-26. Schematic process sequence of the Ni,Si contact plug technology: (a) Ni sputtering; (b) Ni silicidation; and (c) selective metal etching.

process is self-aligned, selective, and is capable of filling both shallow and deep contacts simultaneously with the help of a TIN silicidation stop layer. During Ni silicidation, Ni diffuses into polysilicon plug, resulting in a flat plug surface. Excellent junction leakage and transistor characteristics have been obtained with these selective Ni,Si contact plug techniques. In order to achieve lower contact resistances in high aspect ratio contact-holes, metal plugging is necessary. CVD of metals, particularly selective deposition of interconnections, represents a fundamentally different capability for integrated circuit manufacture than has been available in the past. With its advent vertical wiring capabilities arise that will enhance the pace at which industry can implement multilevel metallization for three or more levels of interconnections. Especially in the deep submicrometer range, CVD metallization will reduce processing problems by provid-

459

ing an effective technique to achieve planarized wiring and by increasing reliability. For the past few years, A1 CVD has been investigated for its capability of achieving conformal step coverage (It0 et al., 1982b; Cooke et al., 1982; Lvey et al., 1984), selective growth onto the Si surface (Amazawa and Arita, 1991a ; Amazawa et al., 1988; Sasaoka et al., 1989; Masu et al., 1990; Shinzawa et al., 1989) and single crystal growth on Si wafer (Kobayashi et al., 1988). To provide full control over selective and nonselective deposition of high quality Al, Tsubouchi et a]. (1992), have developed a plasma excitation technique for A1 CVD deposition. Dimethylaluminum hydride [DMAH; (CH,),AlH] was chosen as the precursor due to its high vapor pressure ( z 2 Torr at 20 "C, ten times higher than that of triisobutyl aluminum). A1 is produced from DMAH and H, via the following reaction :

Using this process, single crystal (100) and (111) A1 are selectively deposited on (111) Si and (100) Si, respectively with resistivity close to the bulk resistivity. The selective growth mechanism is explained sequentially as follows : (1) the Si surface is hydrogen (H) terminated after cleaning by dilute HF, followed by a pure water rinse; (2) the terminated H atom (the terminator) reacts selectively with the CH, radical (the selective reacting radical) of adsorbed DMAH; and (3) after A1 deposition, the H atom of the DMAH molecule remains on the deposited surface as the new terminator. In the case of the nonselective deposition, the plasma supplies both electrons and H atoms to the SiO, surface. As a result, the reaction of C H , + H --t CH,

460


occurs on the SiO, surface, producing a thin A1 layer on SiO,. A 0.25 pm via plug process based on selective CVD aluminum for multilevel interconnect has been developed by Amazawa and Arita (1991b) using triisobutyl aluminum (TIBA), as shown in Fig. 9-27. Surface native oxides on Al, Ti, or W have prevented A1 growth. In situ RF cleaning was used in this study to remove native oxides prior to A1 deposition. In order to avoid A1 nucleation on dielectrics treated by RF etching, amorphous Si was deposited on dielectrics. 0.25 pm via holes with very low contact resistivity and excellent electromigration reliability have been demonstrated. In recent years CVD tungsten has received the most attention among CVD metals and is likely to replace aluminum alloys in the lower metallization levels because of better deposition uniformity than aluminum and excellent electromigration resistance. The higher resistivity of W relative to A1 can be tolerated because line lengths in the lower levels are relatively short. Tungsten originally attracted attention because of its potential for selective Via Hole First metal deposition & patterning Dielectric deposition Amorphous Si deposition Via opening

deposition. Tungsten deposition only occurs in the oxide or nitride windows that have been opened to the surface of the Si and not on the oxide and nitride surfaces. In applications such as via filling, barrier metal, and source/drain/gate shunts, selective deposition is attractive since it would allow the elimination of mask and etch steps, thereby reducing the complexity of the production process. Moreover, because deposition occurs only at the base of the feature, void-free feature filling is automatic and step coverage is not an issue. However, tungsten has poor adhesion to the underlying silicon (in the case of vias). The adhesion can be improved by performing a precleaning step to remove any residue or native oxide that may be present, followed by the deposition of an adhesion layer such as TiN. A novel doubleself-aligned TiSi,/TiN contact with selective CVD tungsten plug for submicrometer device and interconnection applications has been developed by Wang et al. (1991). As shown in Fig. 9-28, the reactively sputtered TIN layer on dielectric-1 layer provides a stable surface which prevents any tungsten nucleation during selective CVD ,AmorDhous Dielectric Titanium Aluminum ‘Silicon

-

in situ RF cleaning Selective Aluminum CVD

Si

Dioxide

CVD aluminum P W

Aluminum Titanium

Figure 9-27. Selective CVD aluminum via plug process.

9.6 Metallization

46 1

After Low temperature anneal, selective wet etch, and N 2

After dielectric 1 (Dl) deposition, TIN deposition, and contact patterning Ti FOX I

N-Well After: J Plasma CHF 3- 0 contact dry etch stop on TiSi 9OO'C NH 3 rapid thermal aneal to densify D1, and convert TiSi. to TiWiSi,- bilayer -

N-Well After selective CVD W deposition

,w Figure 9-28. Schematic process flow of SCVDW (selective CVD tungsten) plug process.

tungsten process. However, tungsten will nucleate on the TiN/TiSi, layer formed by RTA of TiSi, in presence of NH,. The selective nature of the tungsten deposition is initiated by the highly exothermic, rapid reaction of WF, with silicon to produce solid tungsten and gaseous silicon fluorides (2 WF, + 3 si + 2 w + 3 SiF,). Since the reaction involves Si consumption, the deposition is selective. The reaction is characterized by a fast growth rate, but the W thickness is self-limiting. After a thin layer of W is deposited, a barrier is created. This barrier prevents the WF, molecule from diffusing through the W film and reacting with the Si surface, or the Si is prevented from reaching the surface and reacting with WF,. The final W film thickness is dependent on substrate, deposition temperature, WF, partial pressure and

total pressure. Thicker W films can be deposited by adding a reducing agent such as H, to the reactor. Hydrogen dissociatively adsorbs on the growing tungsten film and reduces co-adsorbed WF, producing W and volatile H F (WF6+3 H, + W + 6 HF). Hydrogen does not readily adsorb dissociatively on silicon dioxide or nitride. It is this difference in adsorption behavior which, at least in principle should allow deposition to continue in a selective manner. Silicon reduction reaction which initiates selective deposition removes Si from under the edge of the oxide at the base of the contact hole and deposits W under the oxide. The haloing effect (encroachment of W at the Si/SiO, interface) as well as the wormholes (tunnel formation in the Si) (Broadbent and Stacy, 1985) can be mini-

462


mized by adding silane in the gas phase to reduce Si consumption at the W/Si interface (3 SiH, + WF, --* 2W + 3 SiF, + 6 H,). Silane reduction provided faster deposition rates, a lower deposition temperature and was a much cleaner process. However, the resulting W films contain Si and have larger resistivities than films deposited by hydrogen reduction (Kusumoto et al., 1988; Yu et al., 1989). Because of these interfacial problems, barrier layers such as TIN have been deposited between Si and W. Conformal composite layer metallization, such as tungsten selectively deposited onto patterned aluminum interconnection, has been demonstrated (Hey et al., 1986). Open circuit failures have been reduced dramatically because of improved step coverage and greater electromigration resistance from the uniform tungsten cladding layer that can be made to encapsulate the aluminum lines. Selectivity loss is the most serious concern with selective tungsten deposition. The selectivity loss on patterned silicon wafers has been related to the reaction intermediates or by-products such as silicon subfluorides and silicon oxyfluorides formed by etching of SiO, by WF, or H F ablation of SiO, (Foster et al., 1988; Hirase et al., 1988; Kwakman et al., 1988). Experimental results suggested that volatile tungsten subfluorides produced on tungsten surfaces adsorb on surrounding SO,, producing tungsten nuclei (Creighton, 1987). Process parameters which influence selectivity loss include the partial pressures of WF, and H, , total pressure, deposition temperature and time, and reactor configuration. In addition, dielectric surface properties also affect selectivity loss. For example, sputter-deposited SiO, exhibits a greater tendency towards selectivity loss than thermally grown SiO, (Sumiya et al., 1987). Because of these difficulties in selec-

tive tungsten CVD, blanket deposition with etch-back has been adopted in multilevel metallization schemes to achieve via fills. Copper is a potential candidate for interconnection because of its high conductivity and high reliability. Theoretically, copper exhibits significant advantages over aluminum as a high density interconnection material. The electrical resistivity of copper is 30-50% lower than that of aluminum alloys. Also, the electromigration performance of copper interconnections is expected to be more than two orders of magnitude better than for systems based on aluminum alloy due to copper’s considerably higher melting temperature. Thus, copper interconnections deposited with the same design rules as A1 alloys could increase the operating frequency of devices as well as allow higher current densities. Despite these advantages, however, there are several concerns with copper interconnection technology: (1) the lack of a suitable Cu dry-etch process; (2) copper is incompatible with silicon and acts as a “poison” to the active device area by forming deep acceptor level traps in the forbidden gap, reducing the minority carrier lifetime; (3) the lower heat of formation of copper oxide compared to Si/SiO, results in low thermal stability during annealing, planarization and etch-back processes; and (4) the high diffusion coefficient of copper in silicon dioxide. The fast diffusion of Cu through oxide and then into the Si substrate can be prevented by completely encapsulating Cu, as shown in Fig. 9-29 (Cho et al., 1991). Figure 9-29A involves the use of selective tungsten for encapsulation. Figure 9-29 B starts with the deposition of a seed layer (TiW) for tungsten into LTO trenches. The diffusion of Cu into the sides of trenches is protected by the use of nitride spacers.

9.6 Metallization

463

TiW Oxide Substrate

Substrate

Oxide Substrate

‘W Nitride Spacer

Oxide Substrate

Substrate

Oxide Substrate

(4

Substrate

Figure 9-29. Process sequence for (A) non-planar and (B) planar Cu interconnection with W cladding.

(8)

Selective CVD for metal surfaces has been the subject of a number of contradictory reports in recent literature, most probably because of the differences in surface pre-treatments, reactor systems and deposition conditions used by various groups (Jain et al., 1992a; Reynold et al., 1991;Norman et al., 1991; Baum and Larson, 1992). A number of groups have proposed that the interaction of organometallic precursors with the SiO, surface is a crucial aspect of the selective deposition of metals such as W and Cu in the presence of SiO, (Cheek et al., 1992; Creighton, 1991). The surface of SiO, consists partially of hydroxyl groups (Si-OH) and 0x0-groups (Si-0-Si) which are most likely to be the active sites available for absorption of the precursor molecule. Differences in selectivity have been attributed to the differences in the interaction of (hfac)CuL molecules with the hydroxyl groups in a series of model experiments on SiO, (Cab-0-Sil) surfaces (Hardcastle et al., 1991). Chemi-

cally passivating or removing the surface hydroxyl groups resulted in modified selectivity . (Jain et al., 1992b; Dubois and Zegarski, 1992). Copper CVD following the intentional modification of the SiO, surface hydroxyl groups on the silica surface using functionalized silanes with a variety of copper(1) precursors resulted in controlled selective deposition of copper on SiO, versus other metal surfaces.

9.6.4 Planarization for Multilevel Interconnections The trend toward modular VLSI design with computer aided routing of interconnections is pushing the technology toward multilevel metallization structures. Besides easing the routing problem, thus enhancing circuit performance, this results in smaller chip size connected with cost reduction because of the larger number of chips per wafer. Unfortunately, the topography created by the first-level metallization of-

464


ten makes continuous metal lines difficult in upper metal levels, seriously affecting die yield. To compensate for this topography, various planarizing and smoothening processes have been developed. In order to planarize the deposited dielectric layer over severe topography, the deposited dielectric layer must be thicker than the required final film thickness since a significant portion will be removed by the planarizing process. Furthermore, the thick deposited dielectric layer must be free from defects. The key film characteristics desirable for interlevel dielectrics are : Good step coverage on metal and dielectrics; Good gap filling for planarization; Low as-deposited stress and small hysteresis on heat treatment; No stress-voiding in metal lines either on heat treatment or long term storage; High dielectric breakdown strength; Stability with respect to ion migration; Low density of defects/particles. A common problem is the formation of voids or key holes in gaps with high aspect ratio. The CVD technology used to deposit a gap filling dielectric layer was originally based on the oxidation of silane. Silane oxide, however, does not give a very uniform coating over topography with aspect ratios of 0.5 or larger. The use of the CVD TEOS/oxygen process greatly improves the conformality of the deposited oxide. As a result, TEOS oxide has become the most popular film type for interlayer insulation in sub-pm devices. Reflow oxide films under A1 metallization are generally made with TEOS oxide films using normal pressure CVD. One technology attracting attention is the combination of TEOS and 0, normal pressure CVD. The step coverage is improved from TEOS+O, and voids in concave sections are eliminated.

The dielectric films deposited by thermal TEOS/ozone process tend to be rather porous and may absorb a significant amount of moisture (Nguyen et al., 1990). Therefore, it is common to use it in the dep/etch process so that the bulk thermal TEOS/ ozone film is etched away leaving only this film in the gap filling area (Pennington et al., 1989). The step coverage capability and the dielectric quality of the TEOS/ozone films can be improved by increasing the deposition pressure. The deposited TEOS/ozone films at atmospheric pressure (APCVD) or sub-atmospheric pressure (SACVD) using high ozone concentration tend to be thicker at the inside corners of a gap, thus giving a rounded or “reflowed” profile over a step (Nishimoto et al., 1989; Fujino et al., 1991; Kotani et al., 1989; Lee et al., 1990). This is opposite to the cusp formation over a step in standard CVD dielectric films. Furthermore, these AP-TEOS/ozone or SA-TEOS/ozone films tend to be denser and absorb less moisture than TEOS/ ozone films deposited at low pressure (KOtani et al., 1989; Lee et al., 1990). However, AP-TEOS/ozone film deposited with high ozone/TEOS ratio tend to be surface sensitive and pattern density sensitive. This would make the step coverage vary with different surfaces and pattern densities. Adding Ge to AP-TEOS/ozone films can significantly alter the mechanical properties of the film, dramatically reducing the reflow temperature and improving film stability (Baret et al., 1991). The capability of the AP-CVD TEOS/ozone deposition process to fill submicrometer high aspect ratio gaps or re-entrant profiles could provide significant simplifications to the planarization processes for future ULSI structures. The resist spin-on and etch-back procedures were developed to provide the low

9.6 Metallization

temperature planarization process (Adams and Capio, 1981). This process is based on the planarization capability of a photoresist which is coated in liquid form over the topography surface in question by spinning the wafer at high speed. This technique starts with the deposition of a 1-1.5 pm thick layer of CVD silicon dioxide. The exact thickness is determined by such parameters as polysilicon thickness, first metal layer thickness, and geometry pitch. After oxide deposition, the photoresist is spun onto the wafers and baked above the glass transition temperature to flow the resist and create a planar surface. Next, the nearly planar surface of the photoresist is transferred to the underlying dielectric film by using a dry-etching process that etches the photoresist and the dielectric layer at nearly equal rates (1 :1 selectivity). The etching process is continued until all the photoresist is removed so that the smooth photoresist surface contour is transferred into the dielectric film. Finally, a second deposition of silicon dioxide brings the interlayer metal dielectric to the desired thickness for the second level of metallization. This process has been widely used to planarize dielectric layers over A1 metallization. However, the degree of planarization depends not only on the resist coating thickness, but also on underlying geometries. Good planarity is obtained only for small closely spaced patterns. The planarity degrades rapidly when the pattern width or gap width exceeds several micrometers. Although this problem can be reduced by using an additional photolithography step (Sheldon et al., 1988), it increases the process complexity. The surface planarity of the spin-on layer can be greatly improved if thermally flowing polymer is used for the spin-on layer. Sufficient planarization can be achieved over geometries as large as several hundred micrometers (Ting et al., 1989).

465

While a very planar surface can be obtained by the photoresist etch-back technique, the planar surface results in oxides of varying thicknesses in areas where vias are to be cut to the first metal layer over diffusion areas, field areas, or polysilicon. Oxide thicknesses can vary by nearly 100% from area to area. For example, oxide thickness of nearly 1.8 pm can exist in areas where vias are over diffusions and are as thin as 0.9 pm of oxide over polysilicon. If a via fill or tungsten plug process is not available, a tapered via etching process produced by photoresist erosion etching is necessary to ensure adequate metal step coverage into the via. Tapering the developed vial profile in the thick resist layer has required post-exposure baking or carefully controlled post-develop baking of the thick resist. These processes are very temperature sensitive and often result in incomplete developing of the polysilicon vias. In addition, since the photoresist is lost during the via etch, it should be at least as thick as the thickest oxide. The via etching time must be long enough to etch the thickest oxides - those over diffusion areas. Consequently, the thinner oxides over polysilicon get nearly 100% over etching. This results in vias that are oversized with no taper. The resist spin-on etch-back process can be simplified if the spin-on material can be used either as a stand-alone dielectric layer or in conjunction with CVD dielectric films. Spin-on glass (SOG) films have received much attention for this application. There are many different types of SOG materials such as silicates, doped silicates and a variety of polysiloxanes. They can be coated from liquid to give a spin-on film with good surface planarity. SOG films can be cured at relatively low temperature to give a silicon dioxide-like film. However, the film properties depend on the

466


starting material and the curing conditions as well as subsequent processing conditions (Pai et al., 1987). In general, the density of SOG layer is lower than the thermal oxide and it cracks easily for thick layers. Therefore, it is usually used in conjunction with other CVD dielectric layers to form a CVD-SOG-CVD sandwich structure (Nguyen et al., 1990). A partial etch-back process is generally used to remove SOG from the via opening areas to avoid excessive moisture absorption in the SOG films. The silicate SOG film cured at low temperature is rather porous and can absorb a large amount of moisture. The porosity of the film can be reduced if the SOG is densified at high temperatures (i.e., 900”C), which is not acceptable for aluminum. Another way to reduce the porosity is by using siloxane materials, which have organic groups such as methyl or phenyl groups at the end of silicon-oxygen chain to relieve film stress and to reduce moisture absorption. With proper material choice, the moisture absorption of a siloxane film can be reduced to a negligible amount. In general, the wafers are soft baked after coating at 150-350°C to remove the solvent base. Then they are cured at 425 “C for 60 min. The resulting film is nearly 100% silicon dioxide with some organic substituents. This smoothing process fills in any voids created by the initial oxide deposition process. After curing, the process continues with a “blanket” etch-back. Then, the resulting substrate is capped with additional CVD oxide forming a CVD-SOG-CVD sandwich structure. Thick single coatings of SOG tent to crack. Topographies on the wafer can produce SOG as thin as a few hundred angstroms over high spots to as thick as 8000 8, between minimum spaced line pairs. To minimize the chance of cracking, the SOG is

spun on in two applications with soft baking after each coating application. The final cure plays an important role for the quality of the finished film. SOG cracks from thermal shock. If SOG remains in areas where vias are to be cut, out-gassing of retained or absorbed water can cause an “exploding” or “poisoning” of vias (Ting et al., 1987). This results in high contact resistance or open circuits. To prevent this, SOG should be etched back so there is none where vias were to be cut, leaving only fillets sandwiched between CVD oxide structures. The integrity of organic substituents containing siloxane films is destroyed by oxygen plasma, such as those commonly used for organic resist stripping. The siloxane film with organic groups partially removed by oxygen plasma is very porous, and it cracks easily and absorbs a large amount of water. Therefore, the oxygen plasma steps must be eliminated if the siloxane film is to remain on the wafer surface such as that used in the non-etch-back SOG planarization process. Otherwise, the siloxane film must be protected from the oxygen plasma by using a dense capping layer over the SOG film. A physical etching process has an incident-angle-dependent etching rate. It generally has a lower etching rate for flat surfaces than sloped surfaces. Therefore, physical etching processes can be used to remove sharp corners to give a smoother surface. Using repeated etching and deposition cycles, a planarized surface can be obtained over small dimensions. To reduce wafer handling for repeated dep/etch cycles, several equipment manufacturers have developed automated systems that combine etching and CVD deposition processes in a single system. By using different combinations of deposition and etching cycles one can obtain various degrees of

9.6 Metallization

planarization in the final dielectric layer surface. The well-known AMP-500 system uses plasma TEOS for the main dielectric layer. However, plasma TEOS does not have sufficient step coverage for tight geometries. Therefore, it is used in conjunction with thermal TEOS/O, to provide the needed step coverage. Unfortunately, thermal TEOS/O, has rather poor dielectric properties (i.e., a high water content as mentioned previously) so an etchback process is used to remove most of the film leaving only pockets of thermal TEOS/O, in the gaps to provide a planarized surface. Both SOG and resist etch-back planarize over a distance in the tens-of-micrometer range. For deep sub-half-micrometer devices, etch-back and SOG techniques are not sufficient for wafer planarization or topography smoothing. Chemical-mechanical polishing (CMP), which involves the use of mechanical padpolishing systems with fumed-silica as the slurry, offers one major advantage: global wafer planarity, as shown in Fig. 9-30. Planarity across the wafer is required for the following reasons: ~

-

-

Global planarity can compensate for shallow depth of focus (DOF) ( < 0.5 pm) with high numerical aperture lenses (i-line, 365 nm). This is essential for fine line lithography over a large stepper field size. With photoresist thickness variation over topography, CD control is very diffucult. Global planarity also improves metal step coverage and its associated reliability. Since metal is situated where the device topography is most severe, perfectly flat metals will improve device yield and reliability. Global planarity exerts an additive topography effect on the final metal layers.

467

-

Nonplanarization

I

Smoothing

I

1

I

I

n n

Local planarization

n n

Global planarization

Figure 9-30. Planarization capability.

Mechanistically, the removal rate, drldt, of a glass surface during polishing follows the Preston equation (Preston, 1927) dr/dt = K p (dsldt)

(9-1)

where p is the applied pressure, and ds/dt is the relative velocity between the glass surface and the pad. K , the proportionality constant, is termed the Preston coefficient. The units of K , area/force, relate it to the mechanical properties of the glass. At the fine polishing situations that are normally encountered in planarization, the Preston coefficient is related to the Young’s modulus and the hardness of the glass. It is only a weak function of the applied pressure and the relative velocity. During a brittle grinding situation, macroscopic chunks of material are removed from the glass surface, whereas polishing is characterized by near surface interactions and removal of molecular clusters of material. The key tooling elements of a CMP equipment are shown schematically in Fig. 9-31 (Thomas et al., 1991). Wafers are held by rotating wafer chucks or heads. The wafer surface is exposed to the opposing surface of a polishing pad which is also rotating. A controlled amount of pressure is applied during this process. A slurry fed

468


-YzzGF+ Figure 9-31. Key tooling elements of CMP equipment.

at a controlled rate wets the polishing pad and the wafer surface. The process of polishing is thought to occur according to the following sequence: (a) Formation of hydrogen bonding between the solvated oxide surface and the solvent in the slurry. The solvated oxide surface pertains to both the surface of the wafer and the surface of the slurry particles. (b) Formation of hydrogen bonding between the solvated surfaces on the wafer and on the slurry particles. (c) Formation of molecular bonding between the surfaces. (d) Removal of the bonded wafer surface as the slurry particle moves away. Polishing occurs when the depolymerization reaction proceeds faster than the polymerization reaction. The cleavage of the Si-0-Si below the wafer oxide surface is controlled by the diffusion of water through the oxide. The role of the slurry particle is to impart a chemical “tooth” to the polishing process. The strength of the bond between the slurry particle surface and the wafer surface determines the effective kinetic coefficient of friction between the two surfaces during polishing. Thus the chemical nature of the oxide dispersed in

the slurry is crucial to the final oxide removal rate. Cerium oxide shows in the highest removal rate, followed by Zr and Ti oxides. However, for the planarization process, the choice of the slurry components must be made not only based on the removal rate, but also on the planarity obtained, and the ability to distribute the particles effectively in a stable colloidal distribution. To achieve planarity with the polishing process is relatively simple. However, obtaining simultaneously stable, high removal rates and uniformity across the wafer is more challenging. The removal rate falls off with the age of the pad, causing process control problems. This dropoff with pad life is due to plastic deformation of the pad surface and the resultant glazing. Pad glazing appears to result in two phenomena : (1) the net area of contact between the pad and the wafer increases and hence the effective polishing pressure drops, and (2) the channels available for slurry transport to the interior of the wafer are blocked. It is hypothesized that the latter has the stronger effect. It has also been observed that an isolated small elevated feature on an otherwise flat topography polishes must faster than a dense array of elevated features. Large high areas polish the slowest. Hence differing densities of features within a die can result in degraded planarity due to different removal rates (Daubenspeck et al., 1991). Such a pattern sensitivity in polishing degrades within-die uniformity and if uncontrolled, might expose underlying layers in one portion of the wafer while leaving large under-polished regions in other parts. CMP can also be applied to form the aluminum contact and wiring plugs with different polishing liquids (Hayashi et al., 1992; Kikuta, 1993). Multilevel pla-

9.7 Cluster Tool Technology

narized-trench-aluminum interconnection using aluminum reflow sputtering and CMP has been demonstrated. Laser planarization is a viable technique for the fabrication of VLSI and ULSI interconnection layers (Magee et al., 1988; Wang and Ong, 1990). As shown in Fig. 9-32, via hole filling with a thin film of Au, Al, or Cu can be effectively planarized by briefly melting it with a pulsed XeCl (308 nm) excimer laser in a process vacuum chamber with substrate heating. Planarization is rapid because of the high surface tension and low viscosity of clean liquid metals. Micrometer and submicrometer diameter contacts and vias have been filled with A1 under proper conditions (Magee et al., 1988; Wang and Ong, 1990; Liu et al., 1989; Pramanik and Chen, 1989). Due to the high thermal diffusivity of A1 (1 cm2/s), the time required for heat transfer through a 1 pm thick film is only about 10 ns. A pulse tens of nanoseconds long is sufficient to melt the metal overlayer while minimizing metallurgical and thermal reactions between the film and its underlying barrier or dielectric layer. Dielectric films such as SiO, with thermal diffusivities one hundredth that of

Metal Cap Formation

1

a

After Laser Pulsing

lPlug

Formation

1

Figure 9-32. Laser planarization process.

469

molten A1 prevent heat transfer to the underlying substrate. The high surface tension, low viscosity, and excellent thermal diffusivity of A1 combined with the good thermal barrier of SiO, make it practical to planarize an A1 interconnection film without damaging underlying devices. The composite film stress changes from slightly compressive to slightly tensile after laser processing. Stress relief of the metal and out-diffusion of oxygen and other impurities occur during the laser process, similar to the zone-refining technique; this creates a high purity A1 alloy film which suppresses hillock growth. A general improvement in the distribution of contact resistance of the devices is observed on the laser planarized samples with no apparent shift in threshold or breakdown voltages. Pramanik et al. (1989) have shown a significant improvement in contact and via resistances of submicrometer contacts and vias with the laser planarization process with no observable junction degradation. The electromigration resistance of laser processed A1 wafers is significantly superior to the control devices (Boeck et al., 1990). Copper is also a good choice for the laser reflow process. Because Cu has lower reflectivity ( % 35%) than A1 (x90"/0), a lower incident laser fluence is required to reflow Cu, even though Cu melts at much higher temperature ( z1035 "C) than A1 (z660 "C).

9.7 Cluster Tool Technology Because of intense competition in manufacturing quality and cost, together with increasingly complex fabrication processes, future semiconductor manufacturing will require significant efforts toward defect reduction of any given process or tool. As shown in Fig. 9-33, for 4Mb DRAMS,

470


tion, wafers with 300 mm in ' C

O

L

0

L

5

I

I

I

--1

-?

-+-

10 20 30 40 50 60 70 SO 90 YIELD (%)

Figure 9-33. Relationship between defect density and yield for several DRAM generations.

1.6 defects/cm2 equals a 40% yield. That same defect density in the manufacturing of 16 Mb DRAMs will provide a yield of only 10YO,while the yield drops to zero for 64Mb DRAMs. By the year 2000, the number of discrete process steps in the manufacturing of advanced DRAM chips is expected to exceed 700, requiring an even more stringent control of both equipment and process induced defects. In addi-

diameter should become available by the year 2000. The increase in wafer diameter significantly increases the process equipment cost, primarily due to the increased tool complexity to meet the uniformity requirements across the larger wafers. Today, about 60-70% of the cost for an 8 inch wafer fab is spent on equipment. As shown in Fig. 9-34, it will require $ 2 billion fabs to manufacture 1GB DRAMs with feature sizes of 0.18 pm on wafers of 300-400 nm and five to six levels of interconnection (Chatterjee and Larrabee, 1993). Meanwhile, the typical life cycle of leading-edge ICs has dropped from five years to two or three years. When wafer fabrication areas change to new IC designs, they often need to dispose of still viable process equipment, rapidly escalating the manufacturing cost. As a result, the following trends in Si semiconductor industry could be observed over the past few years: -

Device/circuit scaling; Larger wafers; More dry processes;

Figure 9-34. Escalating costs of wafer fabrication factories (fabs).

9.7 Cluster Tool Technology -

-

-

More single wafer processes; New cleaning philosophy: minimizing the generation of particles rather than focusing on the removal of the particles once they are on the wafer; Increased automation of real-time process and factory control; Differentiated products; Fast (cycle time), economical (cost) manufacturing of a variety of products (flexibility) with first pass success (quality).

9.7.1 Advantages These requirements provide a significant opportunity for a new class of equipment for future IC manufacturing where largesize single wafers are processed and sequential process steps can be “clustered” into multichambered in situ processing modules or into linked cells of independent modules (Doering, 1992). The single wafer cluster tool technology offers significant advantages in IC manufacturing. The inherent cleanliness of process chambers and wafer transfer environments provide substantial improvements in both film and interface quality due to reduction in particle contamination and reactive impurities (H,O, 0,, etc.). This, together with the reduction of the number of times that a wafer must be “handled” moving between operations, results in lower defect densities/higher yields. In addition, fast processing of new devices moves a company quickly up the learning curve, allowing early product introduction. This in turn can result in higher prices for the product on the wafers as well as increased market share. Reduction of cycle times also accelerates process development and yield/defect learning, an extremely important factor for cost-effective manufacturing. Furthermore, as the wafer size increases,

47 1

the value of each wafer becomes greater, particularly for ASIC circuits, and the risk of committing a large number of wafers to a batch process becomes significant. In an era of increased attention to process monitoring and real-time control for improved tool reliability, single wafer processing also offers improved diagnostic access, especially in comparison to batch processes. Finally, since new processes can be developed in a “production” module, their transfer from R & D to production may well be shortened. The main functional units of a cluster tool are shown in Fig. 9-35. Main units include the following: -

-

-

Central handling platform: contains the transport mechanisms to move wafers from module to module; Cassette stations; Single process modules: provide single wafer processing environments for cleaning, CVD, PVD, RIE, RTP, and other processes. Some of the process modules may involve proprietary design and some may be stand-alone standard process modules; Batch modules: increase throughput of some slow process steps with batch or minibatch modules.

Figure 9-35. Main functional units of a cluster tool.

472


An important idea behind cluster tools is that a change in an IC fabrication process only requires a change in process modules. In this fashion, semiconductor manufacturers can accommodate a newly integrated process requiring a completely different set of process steps. They retain the cluster tool platform comprising the cluster controller and the transport and cassette modules with associated pumps, controls and power supplies. Only some of the peripheral process stations would then be needed to be upgraded, expanded, or replaced. The flexible, modular tools can be reconfigured to meet future process requirements developed on stand-alone R & D modules for rapid transfer to manufacturing, reducing retooling costs and extending the lifetime of installed equipment. Accordingly, capital expenditures are considerably reduced. One of the advantages of cluster tools is their capability to facilitate the performance of processes that would otherwise be very difficult or impossible. Most clustering activities are intended to reduce the costs of more sophisticated and advanced integrated processing tools by increasing performance and yield. In some cases, integrated clustering is intended to develop new materials, novel processes, and exotic structures.

9.7.2 Rapid Thermal Processing Rapid thermal processing (RTP) tools are strategically important for submicrometer manufacturing because of trends towards reduced thermal budget and tightened process control requirements on large diameter Si wafers. The desirable attributes of a RTP tool are rapid lamp heating, cold wall, the capability of rapidly changing the wafer temperature and processing environment for multiple in situ processing, and

single wafer processing. The capability of a rapid ramp rate allows short-time processing with enhanced temperature programmability and range. Since chemical reaction rates are thermally activated and thus usually increase significantly with temperature, much higher manufacturing throughput can be obtained in CVD processes using RTP. This overcomes the primary drawback to single wafer processing. The cold wall aspect is important for CVD applications where deposition takes place primarily on the wafer and not on the chamber wall. This minimizes contamination and particulate problems. The implementation of multiple in situ processing steps within the same equipment has the potential to reduce particulate contamination by improved control of the wafer environment, and increased throughput by reducing overall processing time. The single wafer processing feature is important for large wafer sizes to improve process control. In an era of increased attention to process monitoring and real-time control, single wafer processing also offers improved diagnostic access, especially in comparison to batch processing. Furthermore, each isolated single process module can be integrated or “clustered” to match processing needs in an “application specific” fashion. Various Si technology process modules are being developed in RTP for submicrometer device manufacturing. Formation of SALICIDE and TIN, junction formation, channel dopant profile control, thin gate dielectric formation, native oxide removal, glass reflow, and contact metallurgy sintering are some of these processes. By combining RTP with CVD (RT-CVD), the substrate temperature and the reactive gas flux are used as switches to turn a CVD reaction rapidly ON or OFF. The thermal exposure of the substrate is therefore minimized, allowing


ultrathin film deposition. In addition, precise control of layer thickness, and its composition and structure can be obtained. Furthermore, RT-CVD is capable of in situ multilayer processing for high purity interfaces, an extremely important characteristic of fabricating ultrathin high quality stacked dielectrics. The extremely fine control of layer thickness and composition, and the capability of in situ cleaning and processing by RT-CVD, lead to the possibility of multicycle processing within a single chamber, and have led to exciting breakthroughs in ULSI technologies. Because of its unique characteristics, RT-CVD is becoming the most important process module for integrated processing. In the following, some of the important clusterable processes that employ RTP and RT-CVD are discussed. 9.7.2.1 In Situ Dry Cleaning

The structural, chemical, and electrical properties of various interfaces between different layers (semiconductor/dielectric, semiconductor/semiconductor,and metal/ semiconductor) strongly influence the overall performance and reliability of the resulting devices. Approximately 40 YO of the processes used to fabricate today's ICs involve wafer cleaning steps. Wet cleaning processes for wafer surface cleaning are used exclusively to remove both particles and contaminants remaining on wafer surfaces after each process. As the devices become smaller and smaller, it will be more and more difficult for wet chemicals to clean abrupt contact holes and deep trenches. In addition, a much higher level of cleanliness is required for wafer surfaces of deep submicrometer devices. Furthermore, the large amount of chemical wastes generated by such processes are hazardous to the environment and their proper treat-

473

ment and disposal have become very expensive. Because of the equipment and process incompatibility, traditional wet cleaning processes have been prevented from being integrated into a cluster tool. For these reasons, significant advances must be made in cleaning technology. One promising possibility is to use vapor phase or gas phase dry cleaning technology, which requires only minute amounts of chemicals (Moslehi et al., 1992). Compared to liquid-based compositions, reactive gas species enjoy a greater access to the wafer surface because gas molecules don't have to diffuse through a thick water layer to reach the wafer. As a result, a gas phase system uses anhydrous H F from one 5 lb (-2.3 kg) H F bottle to process 90 000 wafers, compared to 2000 lb (- 900 kg) of 10% H F for a wet bench system. The typical method used for in situ cleaning in RT-CVD is the H, pre-bake ( 2 lOOO"C, 2 1 min). Limits may be placed on the contribution of the in situ cleaning to the total process thermal exposure in order to reduce autodoping and broadening of any existing doping profiles. As long as the partial pressures of 0, and H,O are kept below the critical values for a given temperature, the fast oxide etching rates reported by Ghidini and Smith (1994) and Smith and Ghidini (1982) should allow the pre-bake time to be reduced to the order of seconds. Recently, conditions have been established (not due to hydrogen passivation by H F treatment) by which Si and Ge,Si - epitaxies were achieved with 500-800°C H, pre-baking for 15-30 s (Jung et al., 1991a). Recently, in situ anhydrous H F (AHF) cleaning with H, in the range of 325-750°C has been demonstrated (Apte et al., 1991). The AHF cleaning process is simple and manufacturable, and it is selective in a way that it removes surface native oxides, but leaves thermal

474


oxides intact. The other potential low temperature gas phase RTP cleaning to remove native oxide layers and other surface contaminants is germane-assisted cleaning (Moslehi et al., 1992). The cleaning process composition consists of a mixture of GeH, and H, . The germane-to-hydrogen flow ratio is kept very low to prevent deposition or surface nucleation of germanium during the thermal cleaning process. The GeH,/ H, processes clean the Si substrate surface by direct reaction of GeH, with the native oxide layer, producing volatile germanium oxide species (GeO). Although this process works well on native oxides and CVD oxides, it does not easily remove thermally grown oxides. These RTP-based gas phase dry etching techniques can be easily integrated into various RTP-based thin-film growth and deposition process modules in a cluster tool environment. 9.7.2.2 Interface Engineering

Interface engineering is critical to high speed bipolar and Bi-CMOS processes. It consists of the steps of surface cleaning, controlled interfacial oxide or nitride growth, and polysilicon deposition (RTP cleaning, oxide/nitride growth by RTP, in situ doped poly-Si deposition by RTCVD). 9.7.2.3 Gate Stack of Oxide and Oxynitride

The gate stack process is a good example of a process which may potentially benefit from RTP cluster tool processing. It consists of RTP cleaning, gate dielectrics growth by RTP, and in situ poly-Si deposition by RT-CVD. Critical interfaces are kept free of contamination in a cluster tool to achieve excellent device performance and reliability. An excellent example is the fabrication of a simple MOS capacitor. The MOS capacitor can be fabricated com-

pletely within the same RT-CVD chamber, utilizing the processes of rapid thermal oxidation (RTO) and in situ doped poly-Si deposition. Additional processing can easily transform the MOS capacitor into a MOSFET. High quality MOS capacitors and MOSFETs have been demonstrated (Sturm et al., 1986). For a 290 A gate oxide and capacitor area of 4.5 x l o p 3 cm’, values of 5 x lo9 cm-, eV-’ for the midgap interface state density, ~ 1 0 1 0cm-’ for the fixed charges, and 10 MV/cm for the breakdown field were achieved. Oxynitride gate dielectrics grown by RTP of Si in presence of N,O are superior to conventional SiO, grown ones in 0, (N,O oxides have significantly less charge trapping and interface state generation under constant current stress, a tenfold increase in both charge-to breakdown and time-to-breakdown values, and much better dopant diffusion barrier properties) (Hwang et al., 1990). The lifetime of MOSFETs with N,O gate oxides is almost one order of magnitude longer than that of the control devices under identical channel hot-carrier stress conditions (Hwang et al., 1991). Stacked nitride/oxide (NO) films have received considerable attention due to their low defect density, low leakage current, diffusion barrier property, and excellent long-term reliability (Watanabe et al., 1984; Young et al., 1988; Weinberg et al., 1990). Charge trapping in the nitride or at the nitride/oxide interface has limited the application of these films to memory elements. It has been demonstrated that the charge trapping in NO layers can be considerably reduced by in situ multi-layer processing for high purity interfaces in a RT-CVD reactor. In the experiments, the bottom oxide of the NO structure is prepared by RTO in 0, at 1050°C followed by in situ nitride RT-CVD deposition us-


ing SiH, and NH, diluted in N, at 850°C. The nominal bottom oxide thickness was 40 8, and the nitride thickness was 30 A. The leakage current of the control oxide fabricated by RTO at 1050°C and NO devices are comparable at low fields. Capacitors with NO dielectrics exhibited V,, very close to that of the control oxide. Both control and NO devices exhibited Di, values of ~2 x 10'ocm-2 eV-', indicating excellent interfacial integrity. NO devices showed dramatic improvements in breakdown field distribution over the control oxides, although the control oxide and the bottom oxide of the NO layers were grown in the same RT-CVD reactor with the same recipe and in consecutive order. The high quality top nitride covered up or sealed the defects of the bottom oxide, thus significantly reducing the frequency of low-field breakdown events (Roy et al., 1988). Another possibility is that the in situ nitride deposition effectively protects the oxide from contamination before poly-Si deposition.

9.7.2.4 Deposition of DRAM Storage Dielectrics The application of RT-CVD technology to the formation of ultra-high density DRAM storage dielectrics is becoming increasingly important. The process could consist of RTP cleaning/surface passivation, storage dielectric deposition by RTCVD, in situ post-deposition RTP annealing, deposition of in situ doped polysilicon top electrode by RT-CVD. For oxide/nitride/oxide (ONO) DRAM storage dielectrics, the bottom SiO, over the bottom polysilicon electrode plays an important role in the film integrity. The reason is that the thin bottom SO,, usually a low-grade native SiO, , degrades the quality of O N 0 films. In addition, the bot-

475

tom SiO, prevents further scaling.of the effective dielectric thickness and thus limits the maximum attainable capacitance. Therefore, it is extremely critical for advanced DRAM manufacturing to eliminate the native oxides completely prior to dielectric deposition. It has been demonstrated that by using rapid thermal nitridation (RTN) in pure NH, of poly-Si surface prior to Si,N, deposition, (bottom native SiO, free) Si,N, dielectric (t,,, eff z 35 A) with enhanced reliability can be achieved (Lo et al., 1992). The defect-related dielectric breakdown caused by low-grade native SiO, is completely eliminated by the use of RTN. In addition, capacitors with RTN treatment have an improved lifetime (by factor M lo3) than the ones without RTN. The ultrathin stacked NO layer can also be fabricated by in situ multiprocessing (RTMP) (Ando et al., 1993). As shown in Fig. 9-36 a, the multiprocessing steps include in situ surface cleaning, RTN, rapid thermal CVD of the Si,N, films, and rapid thermal CVD of poly-Si. All these steps are carried out in sequence without lifting the vacuum. Elimination of interfacial oxides at the Si,N,/Si interface leads to high quality nitride films with low leakage current density and extremely high reliability. As shown in Fig. 9-36 b, the TDDB characteristics of Si,N, films prepared by in situ RTMP are improved about lo4 times over conventional LPCVD Si,N, films. This result clearly demonstrated the capability of in situ multiprocessing for the fabrication of high quality ultrathin films for ULSI applications.

9.7.2.5 Selective Deposition Processes Process complexity and number of mask levels steadily increases with each generation of IC technology. Projections of present trends indicate as many as 700 process

476


..

0

2

4 6 Time (mln)

8

10

7 In-rib RTMP

0

Stress time (sec)

Figure 9-36. (a) Schematic time-temperature profile of in situ RTMP processing for fabricating DRAM storage capacitors. (b) Comparison of TDDB characteristics of dielectrics fabricated by various techniques.

steps in IC technologies by the year 2000. The increased use of selective processes is one way to greatly reduce the number of process steps, since each selective process can eliminate many other process steps (usually mask levels, lithography and etching steps). Selective metal deposition (tungsten, copper, TIN) and selective silicide (TiSi,) processes are two of the better known and more mature of the various selective processes. Other possibilities include selective epitaxy processes for advanced CMOS isolation and for raised source/drain CMOS devices. Selective processes are emphasized here because they provide considerable leverage for cluster

tools. They eliminate the need for masking steps and facilitate more sequential processing steps within a single cluster tool before the wafer must be removed for lithography steps. Selective epitaxy growth has been applied to a novel transistor structure, the low-impurity-channel transistor (LICT), for advanced CMOS applications. By selectively growing a thin undoped Si epilayer on top of the heavily-doped wells, threshold voltages can be lowered and band bending made more gradual, thereby weakening the effective field for carriers and reducing surface-roughness scattering. In addition, carrier freeze-out is eliminated since no channel implantation is performed. The heavily-doped wells are for sharpening turn-offs and preventing punch-through. Fairly good transistor operation has been achieved for 0.1 pm CMOS devices implementing the LICT structure (Aoki et al., 1990). Critical to LICTs are steep impurity profiles which makes RT-CVD ideal for LICT fabrication since RT-CVD can provide minimal autodoping and out-diffusion of impurities (Gibbons et al., 1985; Lee at al., 1989; Jung et al., 1991b).

9.7.2.6 Ultra-Shallow Junction Formation Recently, a novel approach based on surface chemical adsorption of dissolvements from induced dopant gas molecules has been developed by Nishizawa et al. (1990b) and Inada et al. (1992) for very shallow, high quality p +-n junction formation. In this process boron atoms are incorporated into Si by diffusion in an oxygen-free atmosphere at a relatively low temperature. This process differs from the conventional diffusion process in which boron diffusion is performed in an oxygenrich environment. Kiyota et al. (1994) have developed a rapid thermal vapor-phase


doping technique to fabricate ultra-shallow boron-doped junctions with junction depth less than 30 nm and surface boron concentration of 5.8 x loi9 ~ m - ~ .

9.7.2.7 Integrated CMOS Processing Based on RTP A 0.25 ym CMOS technology has been developed and demonstrated with all-RTP thermal processing (Moslehi et al., 1993a). These RTPs cover a processing temperature range of 450" to 1100"C. The process features are listed in Table 9-12. Excellent CMOS transistors with considerable process simplification have been established. Improved RTP control over furnace was also demonstrated. These results show the effective use of RTP for IC manufacturing.

477

9.7.2.8 Ge,Si, -,/Si Heteroepitaxy by RT-CVD RT-CVD was the first non-UHV technique used to demonstrate high -performance Ge,Si I - ,/Si heterojunction bipolar transistors (HBTs). Early work showed higher current gains of 400 compared to Si devices and high unity gain cut off frequencies of 28 GHz (Kamins et al., 1989). Improved HBT performance has been obtained by controlling base dopant out-diffusion and using graded base layers (Sturm and Prinz, 1991). More recently, a double base HBT has been demonstrated which could find application as a single-transistor NAND gate (Prinz et al., 1992). Si, -,Ge,/Si heterostructure FETs have a potential for higher performance due to higher carrier mobilities in strained Si and

Table 9-12. List of the lamp-heated RTP-based CMOS fabrication processes (Moslehi et al., 1993a).

RTP-based processes

Applications

RTP parameter domain

Germane clean

split gate formation

Dry RTO

gate oxide, PBL oxide

Wet RTO Source/drain RTA and gate RTA

thick oxides ("0NED"-tank and sacrificial oxide) S/D activation, gate annealing

RTP tank formation

CMOS n & p well formation

LPCVD polysilicon

CMOS gate formation

LPCVD amorphous Si

CMOS gate formation

LPCVD tungsten

multilevel metal

TiN/TiSi, RTA reaction and annealing RTP sinter (FGA)

Salicide, silicided contacts

LPCVD nitride

PBL nitride deposition

LPCVD oxide

oxide spacers, undoped oxide

65O-75O0C, low pressure (75OoC/15torr) GeH,/H, 1000-1050°C, high pressure (1000°C/650 torr) 0, 950 - 1000"C, high pressure (1000 "C/650 torr) H,O/O, 950- 1O5O0C,high pressure (95OoC/650Torr) Ar or NH, 1050- 1lOO"C, high pressure (1 lOO0C/650 torr) NH, 650-750 "C, low pressure (650°C/1 5 torr) SiH,/Ar 50O-59O0C, low pressure (560°C/15 torr) SiH,/Ar 475-5OO0C, low pressure (475 T / 2 0 torr) SiH,/H,/WF,/Ar 65O-75O0C, low pressure (65O"/75O0C/1 torr) N,, Ar 450-475 "C, high pressure (475"C/650 torr) HJN, 80O-85O0C, low pressure (3 torr) SiH,/NH, 7O0-75O0C, low pressure (740°C/1 torr) TEOS/O,

forming gas annealing

478


Si, -,Ge, channels. Higher hole mobilities at room temperature have been achieved in GeSi/Si heterostructure FETs grown by RT-CVD with a buried SiGe channel compared to a silicon surface channel (Garone et al., 1992). Similarly, improvements in electron mobility have been reported in both surface and buried tensile strained Si channels on top of a relaxed Sio.,lGeo.29 layer (Welser et al., 1992). Peak effective mobilities were 2.2 times larger than those in devices fabricated in bulk silicon at room temperature. Si, -,Ge, alloys could provide low cost alternatives to compound semiconductors in the fabrication of long wavelength receivers and other optoelectronic integrated circuits due to the well-established Si VLSI technology. By adjusting the Ge content in the SiGe layers the operating wavelength can be tuned in the technologically important 1.3 to 1.55 pm range. RT-CVD has much to offer in growing epitaxial GeSi layers required for such devices. Low loss waveguides and directional couplers have been fabricated (Mayer et al., 1991). SiGe/ Si superlattice waveguide pin photodetectors with high internal quantum efficiency and low dark currents that can operate at 1.5 Gbit/s at 1.3 pm have been demonstrated (Jalali et al., 1992). Evidence of the fine control with which superlattice layers can be grown by RT-CVD is seen in the growth of a 50 period superlattice containing a 24 8, SiGe layer and a 23 8, Si layer (Sturm et al., 1991). The ability to rapidly switch the gases and growth temperature enables the optimization of growth temperature of individual layers, resulting in the realization of multiple quantum well (MQW) structures with minimum interdiffusion and high throughput. The SiGe layers are grown at low temperatures (550°-6500C) to avoid islanding growth and Si barrier layers are grown at some-

what higher temperatures (700" - 800 "C) in order to get adequate growth rates. The wide range of growth rates that RT-CVD can provide could be applied to the growth of thick waveguide layers and thin MQW layers to obtain integrated waveguidephotodetector structures. Further improvements in device performance can be expected utilizing the capability of RTCVD to grow selective epitaxial SiGe layers (Kamins et al., 1992) and SiGe on silicon-on-insulator (SOI) (Hsieh et al., 1991) structures. Commercial versions of RTP modules for CVD are not available with the uniformity and control required for the manufacturing environment. This is primarily due to the difficulties of measurement and control of wafer temperature and its uniformity across a large size wafer. The non-contact measurement and control of absolute temperature and of temperature uniformity across a wafer have proven to be major problems with single wafer RTP processing. Research is presently underway at many laboratories addressing these issues, and progress is being made (Moslehi et al., 1992; Peyton and Kwong, 1990). For example, the use of multi-zone heating techniques appear very promising for achieving process uniformity across a wafer. Several approaches are being explored for surface emissivity corrections to be used with non-contact temperature measurements in order to control the temperature magnitude as seen by a pyrometer looking at a wafer. All of these approaches appear promising but at present the single most important limitation is the lack of an RTP module design with acceptable process uniformity and control.


9.7.3 Single-Wafer Integrated Processing One factor is now driving clustered integrated processing toward a broader spectrum of applications in which sequential processes with very different character (temperature, chemistry, pressure) are linked in clusters; that is the significant benefits from exploiting the advantages of integrated processing by the possibility it offers to mix and match whichever process combinations will result in the highest quality materials and structures. To tailormake films with matching physical, structural, dielectric, mechanical, chemical, crystallographic, and electrical properties, the existing and future processes must be combined together. Some of the important clusterable processes are : Cleaning, CVD, PVD, and etching processes must be integrated to cope with topographical problems in the upper levels of metallization, including multilayered metallization. Self-aligned silicide process (cleaning, PVD, RTP, etching). Multilevel film etching or multistep etching. This is necessary for complex structures. Since it may require different chemistries and etching technologies for individual steps, cross contamination and particulates become important issues (cleaning, etching). Interface engineering. This is critical to bipolar and Bi-CMOS processes. It consists of the steps of surface cleaning, controlled interfacial oxide or nitride growth, and polysilicon growth (cleaning, RTP, CVD). Selective deposition/growth processes rely on well-defined, properly prepared surfaces which are highly amenable to integrated processing (cleaning, passivation, CVD). The increased use of selective processes is one way to greatly re-

-

-

-

-

479

duce the number of process steps, since each selective process can eliminate many other process steps (usually mask levels, lithography and etching steps). Selective processes are emphasized here because they provide considerable leverage for cluster tools. Gate stack of oxide (or oxynitride) and in situ doped polysilicon (cleaning, RTP, CVD). The gate stack process is a good example of a process which may potentially benefit from cluster tool processing (Apte et al., 1992). It consists of pre-gate cleaning, gate dielectric growth, and polysilicon electrode deposition and annealing. Critical interfaces are kept contamination-free in a cluster tool to achieve excellent device performance and reliability. DRAM storage dielectrics deposition (cleaning, CVD, RTP). Ultra shallow junction formation based on surface chemical adsorption of dissolvements from induced dopant gas molecules (cleaning, RTP) (Nishizawa et al., 1990b; Inada et al., 1992; Kiyota et al., 1994). BPSG flow (cleaning, CVD, high pressure RTP). To reduce the thermal budget for reflow, a single-wafer high-pressure RTP system has been used to reflow BPSG in steam or nitrogen at temperatures as low as 720°C. Oxide spacer/collar formation (etching, CVD, etching) (Matuszak et al., 1989).

Throughput has been an issue for cluster tools. For a single wafer process, 60 wafers per hour has been considered a reasonable figure. A substantial number of single wafer processes used or being considered in cluster tools achieve this value, including cleaning, stripping, RTP, and many etching processes. However, other etch processes and many CVD processes take

480


longer than 1 min. When these slower processes are integrated into the fabrication of cluster tools, typical throughputs are 10 to 25 wafers per hour. A cluster tool’s throughput is dictated by the slowest or “bottleneck” process and to a lesser extent by machine throughput (i.e., the speed of wafer handling including pumping and venting). Significant efforts are being made to reduce the process times for the potential bottleneck processes. For some of the longer-time processes, batch process modules may be required. However, one of the unique characteristics of single-wafer processing is the ability to manufacture small lots with a fast turnaround. This is extremely attractive for process development and for applications where short cycle times are significantly more valuable than the wafer cost. Simulation results have shown that for single wafer lots running through the cluster fabs, the theoretical cycle times can be as short as 5 days. This should be extremely valuable for small-volume ASIC runs. A performance comparison of conventional fabs and cluster-based fabs is made in (Wood et al., 1991), in which the cost per wafer is plotted against average cycle-time. As can be seen clearly, at high throughput, the wafer costs are comparable. However, for the low throughput time range, the wafer costs are much higher for conventional fabs. The total use of single-wafer processing for fast-cycle-time IC production has been demonstrated recently (Moslehi et al., 1993b). Complete 0.35 pm CMOS process integration and 3-day CMOS IC manufacturing cycle time have been established with all-RTP thermal processing. The future of cluster tools and the extent to which cluster tools will permeate and dominate IC manufacturing depends on the successful development of a broader

spectrum of single wafer processing technologies. In addition, to obtain fundamental mechanistic insight and to develop new levels of process control and material/ structure quality, the wafer surface and the process environment during the process must be studied in detail, using a variety of sophisticated techniques from surface science as well as mass and optical spectroscopy. If proposed benefits of improved process control, process configurability on a wafer-to-wafer basis and easy mixing of process technologies are to be realized, improved process sensors must be available and used in cluster tools. There is a great lack of adequate process sensors for key process variables including gas species and gas flows at the wafer, and thicknesses of films depositing or being etched on the wafer. Most sensors, if available, provide either indirect data or measure parameters at some point far off the wafer surface. It may be possible to use such remotely measured parameters with appropriate process and equipment models to infer values at the wafer. However, much research, development and process characterization work remains to be done.

9.8 References Note: IEDM stands for International Electron Device Meeting.

Abe, T., et al. (1992), ECS Softbound Proc. 92-7, p. 200. Adachi, H., Nishikawa, H., Komatsu, Y., Hourai, H., Sano, M., Shigamatsu, T. (1992), Muter. Res. SOC. Symp. Proc. 262, 815. Adams, A. C., Capio, C. P., (1981), .L Electrochem. SOC.128, 423. Ahn, J., Kwong, D. L. (1992), IEEE Electron. Device Lett. 13, 494. Ahn, J., Ting, W., Kwong, D. L. (1992a), IEEE Electron. Device Lett. 13, 117. Ahn, J., Ting, W., Kwong, D. L. (1992 b), IEEE Electron. Device Lett. 13, 186. Ajmera, A. C., Rozgonyi, G. A. (1986), Appl. Phys. Lett. 49, 1269.

9.8 References

Amazawa, T., Arita, Y. (1991 a), in: IEDM Tech. Digest. New York: IEEE, p. 265. Amazawa, T., Arita, Y. (1991 b), IEDM Tech. Digest. New York: IEEE, p. 625. Amazawa, T., Nakamura, H., Arita, Y (1988), IEDM Tech. Digest. New York: IEEE, p. 442. Ando, S., Horie, H., Imai, M., Oikawa, K., Kato, H., Ishiwari, H., Hijiya, S. (1990), VLSI Tech. Symp., 65. Ando, K., Yokozawa, A,, Ishitani, A. (1993), VLSI Tech. Symp., p. 47. Aoki. M., Ishii, T., Yoshimura, T., Kiyota, Y., Iijima, S., Yamanaka, T., Kure, T., Ohyu, K., Nishida, T., Okazaki, S., Seki, K., Shimohigashi, K. (1990), IEDM Tech. Digest. New York: IEEE, p. 939. Appels, J. A,, Kooi, E., Paffen, M. M., Schatorji, J. J. H., Verkuylen, W. H. C. G. (1970), Philips Res. Rep. 25, 119. Apte, P. P., Moslehi, M. M., Yeakley, R., Saraswat, K. C. (1991), in Extended Abstracts, PV 91-1, 573. Pennington, NJ: Electrochem. SOC. Apte, R., et al. (1992), VLSI Tech. Symp., Tech. Digest, p. 52. ASTM (1988), Annual Book of ASTM Standards, Vol. 10.05: Philadelphia, PA: ASTM. Baglee, D. A,, Smayling, M. C., Duane, M. P., Itoh, M. (1984), Jpn. J. Appl. Phys. 23, 884. Baglee, D. A,, et al. (1985), IEDM Tech. Digest. New York: IEEE, p. 384. Baker, F. K., Pfiester, J. R., Mele, T. C., Tseng, H. H., Tobin, P. J., Hayden, J. D., Bunderson, C. D., Parrillo, J. C. (1989), IEDM Tech. Digest. New York: IEEE, p. 443. Baret, G., Madar, R., Bernard, C. (1991), J. Electrochem. Soc. 138, 2830. Bassous, E., Yu, H. N., Maniscalco, V. (1976), J. Electrochem. SOC. 123, 1729. Baum, T. H., Larson, C. E. (1992), Chem. Muter. 4, 365. Bentini, G. G., Bianconi, M., Summonte, C. (1988), Appl. Phys. A45, 317. Boeck, B., et al. (1990), Proc 7th Int. IEEE V L S I Multilevel Interconnection Conf , Santa Clara, C A , p. 90. Borland, J. (1987), IEDM Tech. Digest. New York: IEEE, p. 13. Borland, J. (1989), Overview ofthe Latest in Intrinsic Gettering, Parts I & II. Semiconductor International. Borland, J., Deacon, T. (1984), Solid State Technol. 27, 123. Borland, J., Koelsch, R. (1993), Solid State Technol. 35, 28. Bousetta, A,, van den Berg, J. A,, Amour, D. G. (1991), Appl. Phys. Lett. 58, 1626. Brat, T., Parikh, N., Tsai, N. S., Sinha, A. K., Poole, J., Wickersham, Jr., C. (1987), J. Vac. Sci. Technol. B5, 1741. Broadbent, E. K., Stacy, W. T. (1985), Solid State Technol. 12, 51.

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Ruggles, G. A., Hong, S. N., Wortman, J. J., &tiirk, M., Myers, E. R., Hren, J. J., Fair, R. B. (1989), Muter. Res. SOC.Symp. Proc. 128, 611. Ruzyllo, J., Hoff, A. M., Frystak, D. C., Hossain, S. D. (1989), J. Electrochem. SOC.136, 1474. Ryuta, J., Morita, E., Tanaka, T., Shimanuki, Y (1990), Jpn. J. Appl. Phys. 29, L1947. Sai-Halasz, G. A., Harrison, H. B. (1986), IEEE Electron. Device Lett. 7, 534. Saito, M., et al. (1992), I E D k Tech. Digest. New York: IEEE, p. 897. Samato, S., Numano, M., Arnai, T., Matsushita, Y, Kobayashi, H., Yamamoto, A., Kawaguchi, T., Nadahar, S., Yamabe, K. (1993), Extended Abstracts Vol.93-2, Abst. No. 264, Electrochem. SOC. Fall Mtg.. New Orleans, L A , Oct. 10-15. 1993. Sameshima, T., Usui, S., Sekiya, M . (1987), J. Appl. Phys. 62, 71 1. Sanchez, J. J., Hsueh, K. K., DeMassa, T. A. (1989), IEEE Trans. Electron. Devices 36, 1125. Sanganeria, M., h i i r k , M. C., Harris, G., Maher, D. M., Batchelor, D., Wortman, J. J., Zhang, B., Zhong, Y L. (1991), Proc. 3rdInt. Symp. ULSISci. Tech., Electrochem. SOC.Spring Mtg. 1991, Washington, D. C., Saraswat, K. C., Brors, D. L., Fair, J. A,, Monning, K. A., Beyers, R. (1983), IEEE Trans. Electron Devices 30, 1497. Sasaoka, C., Nori, K., Kato, Y., Usui, A. (1989), Appl. Phys. Lett. 55, 741. Sedgwick, T. O., Michel, A. E., Deline, V. R. Cohen, S. A., Lasky, J. B. (1988), J Appl. Phys. 63, 1452. Seidel, T. (1975), J. Appl. Phys. 46, 600. Selbrede, S . C. (1988), Semicond. Int. 88, p. 254. Shahidi, G., et al. (1991), IEDM Tech. Digest. New York: IEEE, p. 663. Sheldon, D. J., et al. (1988), IEEE Trans. Semicond. Manuf. 1 . 140. Shen, B. W., et al. (1985), in: Proc. V L S IMultilevel Interconnection Con$ : New York: IEEE, p. 114. Sherman, A. (1990), J. Electrochem. SOC.137, 1892. Shibahara, K., Fujioto, Y, Hamada, M., Iwao, S., Tokashiki, K., Kunio, T. (1992). IEDM Tech. Digest. New York: IEEE, p. 275. Shibata, T., et al. (1983), IEDM Tech. Digest. New York: IEEE, p. 27. Shibata, T., Okita, A., Kato, Y ,Ohmi, T., Nitta, T. (1990), VLSI Tech. Symp.. p. 63. Shimizu, N., Naito, Y, Itoh, Y, Shibata, Y., Hashimoto, K., Nishio, M., Asai, A., Ohe, K., Umimoto, H., Hirofuji, Y (1992), IEDM Tech. Digest. New York: IEEE, p. 279. Shinzawa, T., Sugai, K., Kishida, S., Okabayashi, H. (1989), Workshop on Tungsten and Other CVD Metals f o r ULSl/VLSI Applications V l , Tokyo, Muter. Res. SOC.Symp. Proc., Vol. V. Tokyo: Materials Research Society, p. 377. Shioya, Y., Maeda, M. (1986), J Appl. Phys. 60, 327. Shioya, Y., Ikegami, K., Maeda, M., Yanagida, K. (1987a), J. Appl. Phys. 61, 561.

486


Shioya, Y., Kawamura, S., Kobayashi, I., Maeda, M., Yanagida, K. (1987b), J. Appl. Phys. 61, 5102. Smith, G. C. (1989), in: Workshop on Tungsten and Other Refractory Metals for VLSI Applications 1988: Blewer, R., McConica, C. (Eds.). Pittsburgh, PA: Materials Research Society, p. 275. Smith, F. W., Ghidini, G. (1982), J. Electrochem. SOC. 129, 1300. Stimmell, J. (1986), J. Vac. Sci. Technol. B 4 . 1377. Sturm, J. C., Prinz, E. J. (1991), IEEE Electron Device Lett. 12, 42. Stunn, J. C., Gronet, C. M., King, C. A., Wilson, S. D., Gibbons, J. F. (1986), IEEE Electron Device Lett. 7 , 577. Sturm, J. C., Schwartz, P. V., Prinz, E. J., Manoharan, H. (1991), J. Vac. Sci. Technol. B 9 , 204. Sumiya, T., Hirase, I., Rufin, D., Ukishima, S., Schack, M., Shishikura, M., Matsuura, M., Itoh, Proc. 10th Int. Con$ on Chemical on: Cullen, G. W. (Ed.). Pennington, NJ: Electrochem. Soc., p. 645. Sun, J. Y.-C., Wong, C. Y., Taur, Y., Hsu, C. C.-H. (1989), VLSI Tech. Symp., p. 17. Sung, J. M., Lu, C. Y., Chen, M. L., Hillenius, S. J., Lindenberger, W. S., Manchanda, L., Smith, T. E., Wang, S. J. (1989), IEDM Tech. Digest. New York: IEEE, p. 447. Sung, J. M., Lu, C. Y., Fritzinger, L. B., Sheng, T. T., Lee, K. H. (1990), IEEE Electron Device Lett. 11, 549. Takeda, E., et al. (1985), IEEE Trans. Electron Devices 32, 322. Takemura, H., Ohi, S., Sugiyama, M., Tashiro, T., Nakamae, M. (1987), IEDM Tech. Digest. New York: IEEE, p. 375. Tan, T. Y. (1977), Appl. Phys. Lett. 30, 175. Tanaka, A., Yamaji, T., Nishikawa, S . (1991), Jpn. J. Appl. Phys. Lett. 30, L775. Taur, Y., et al. (1993), IEDM Tech. Digest. New York: IEEE, p. 127. Tay, S. P., Ellul, J. P., White, J. J., King, M. I. H. (1987), J. Electrochem. SOC.134, 1484. Tay, S. P., Kalnitsky, A,, Kelly, G., Ellul, J. P., DeLalio, P., Irene, E. A. (1990), J. Electrochem. SOC. 137, 3579. Telford, S. G., Eizenberg, M., Change, M., Sinha, A. K., Gow, T. R. (1993), Appl. Phys. Lett. 62, 1766. Teng, C. W., Slawinski, C., Hunter, W. R. (1984), IEDM Tech. Digest. New York: IEEE, p. 586. Teng, C. W., et al. (1985), IEEE Trans. Electron Devices 32, 124. Thomas, M. E., etal. (1991), Tech. Proc. Semicond. Jpn. ( S E M I ) , p. 295. Ting, P. L., et al. (1987), Proc. IEEE VLSI Multilevel Interconnection Conf., p.61. Ting, C. H., et al. (1989), Proc. V-MIC Con$. p. 491. Travid, E. O., et al. (1990), IEDM Tech. Digest. New York: IEEE, p. 47. Tsai, M. Y., Streetman, B. G., Williams, P., Evans Jr., C. A. (1978), Appl. Phys. Lett. 32, 144.

Tseng, H. H., Tobin, P. J., Hayden, J. D., Chang, K. M. (1991), IEDM Tech. Digest. New York: IEEE, p. 75. Tseng, H. H., et al. (1993), IEDM Tech. Digest. New York: IEEE, p. 321. Tsuboushi, K., Masu, K. (1992), J. Vac. Sci. Technol. A 10, 856. Tsuya, H. (1991), The 9th Workshop of ULSI on Ultra Clean Tech., p. 5. Usami, A., Ando, M., Tsunekane, M., Wada, T. (1992), IEEE Trans. Electron Devices 39, 105. Ushiku, A., et al. (1993), VLSI Tech. Symp., p. 121. Vasquez, R. P., Madhukar, A. (1985), Appl. Phys. Lett. 47, 998. Vasquez, R. P., Madhukar, A. (1986), J. Appl. Phys. 60, 234. Verhaverbeke, S., Meuris, M., Mertens, P. W., Heyns, M. M., Philipossian, A,, Graf, D., Schnegg, R. (1991), IEDM Tech. Digest. New York: IEEE, p. 71. Verhaverbeke, S., et al. (1992), VLSI Tech. Symp., p. 22. Walters, M., Reisman, A. (1990), J. Electrochem. SOC. 137, 3596. Wang, S.-Q., Ong, E. (1990), Proc. 7th Int. IEEE VLSI Multilevel Interconnection Con$, Santa Clara, CA, p. 431. Wang, M., Bradbury, D., Hu, H. K., Chiu, K. Y. (1991), VLSI, 41. Watanabe, T., Ishikawa, M., Kumagai, J. (1984), IEDM Technical Digest. New York: IEEE, p. 173. Weber, E. R. (1988), Properties of Silicon. London: INSPEC, p. 236. Weber, E. R. (1990), in: Semiconductor Silicon, Vol. 90- 7 : Huff, H. R., Barraclough, K. G., Chikawa, J. I. (Eds). Pennington, NJ: Electrochem. SOC.,p. 585. Wei, C. Y., et al. (1992), IEEE Trans. Electron Devices 38, 2433. Weinberg, Z . A., Stein, K. J., Nguyen, T. N., Sun, J. Y. (1990), Appl. Phys. Lett. 57, 1248. Welser, J., Hoyt, J. L., Gibbons, J. F. (1992), IEDM Tech. Digest. New York: IEEE, 31, 7. Wen, D. S., et al. (1991), VLSI Tech. Symp., p. 83. Wittmer, M. (1985), J. Vac. Sci. Technol. A 3 , 1797. Wittmer, M., Melchior, M. (1982), Thin Solid Films 93, 397. Wong, C. Y., Lai, F. S . (1986), Appl. Phys. Lett. 48, 1658. Wong, C. Y., Sun, J. Y.-C., Taur, Y., Oh, C. S., Angelucci, R., Davari, B. (1988), IEDM Tech. Digest. New York: IEEE, p. 238. Wood, S., et al. (1991), Proc. Int. Semiconductor Manufacturing Sci. Symp., p. 208. Wright, P. J., Saraswat, K. C. (1988), IEEE Trans. Electron Devices 36, 1707. Wright, P. J., Saraswat, K. C. (1989), IEEE Trans. Electron Devices 36, 879. Wright, P. J., Kermani, A,, Saraswat, K. C. (1990), IEEE Trans. Electron Devices 37, 1836.

9.8 References

Wu, T. H. T., Bosler, R. S., Lamartine, B. C., Gregory, R. B., Tompkins, H. G. (1988), J. Vac. Sci. Technol. B6, 1707. Wu, C. P., McGinn, J. T., Hewitt, L. R. (1989a), J. Electron. Mater. 18, 721. Wu, I. W., Koyanagi, M., Holland, S., Huang, T. Y, Mikkelsen Jr., J. C., Bruce, R. H., Chiang, A. (1989b), J. ElectrochFm. SOC.136, 1638. Xu, X., Kuehn, R. T., Oztiirk, M. C., Wortman, J. J., Nemanich, R. J., Harris, G. S., Maher, D. M. (1993), J. Electron. Mater. 22, 335. Yamabe, K. (1990), in: Semiconductor Silicon, Vol. 90-7: Huff, H. R., Barraclough, K. G., Chikawa, J. I. (Eds). Pennington, NJ: Electrochem. SOC., p. 349. Yamabe, K., Imai, K. (1981), ZEEE Trans. Electron Devices 34, 1681. Yamabe, Y., Taniguchi, T., Matsushita, Y. (1983), Proc. Znt. Reliability Physics Symp. New York: IEEE, p. 184. Yamagishi, H., Fumegawa, I., Fujimake, N., Katayama, M. (1992), Semiconductor Sci. Technol. 7 , A135. Yang, W., Jayaraman, R., Sodini, C. G. (1988), ZEEE Trans. Electron Devices 35, 935. Yokoyama, N., Hinode, K., Homma, Y. (1989), J. Electrochem. SOC.136, 882.

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Yokoyama, N., Homma, Y., Hinode, K., Mukai, K. (1990), U. S. Patent 4 897 709. Yoon, G. W., Ahn, J., Lo, G. Q., Kwong, D. L. (1993a), Znt. Con$ SSDM, p. 145. Yoon, G. W., Joshi, A. B., Kim, J., Kwong, D. L. (1993 b), IEEE Electron Device Lett. 14, 179. Young, K. K., Hu, C., Oldham, W. (1988), ZEEE Electron Device Lett. 9, 616. Yu, M. L., Eldridge, B. N., Joshi, R. V. (1989), in: Tungsten and Other Refractory Metals for VLSZ Applications, Vol. IV: Blewer, A., McConica, C. M. (Eds.). Pittsburgh, PA: Materials Research Society, p. 221. Yu, C., Fazan, P. C., Mathews, V. K., Doan, T. T. (1992), Appl. Phys. Lett. 61, 1344. Zorinsky, E. J., et al. (1986), ZEDM Tech. Digest. New York: IEEE, p. 431.

General Reading Tungsten and Other Refractory Metals for VLSZ Applications, Vols. I, 11,111, IV, V, VI: Pittsburgh, PA: Materials Research Society.

Handbook of Semiconductor Technology Kenneth A. Jackson, Wolfaana Schroter

Copyright 0WILEY-VCH Verlag GmbH, 2000

10 Compound Semiconductor Device Processing

.

.

John M Parsey. Jr

Motorola. Semiconductor Products Sector. 111- V Device Development Laboratory. Tempe. AZ. U.S.A.

490 List of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493 10.1 10.2 Doping Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 10.2.1 Ion Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 10.2.2 Diffusion Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511 10.2.3 Epitaxial Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 10.3 Isolation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 10.3.1 Mesa Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 517 10.3.2 Ion Implantation Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.3 Sidegating and Backgating . . . . . . . . . . . . . . . . . . . . . . . . . 522 10.4 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 10.5 Etching Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 10.5.1 Wet Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 10.5.2 DryEtching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537 10.6 Ohmic Contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543 10.7 Schottky Barriers and Gates . . . . . . . . . . . . . . . . . . . . . . . 552 10.8 Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560 Dielectrics and Interlayer Isolation . . . . . . . . . . . . . . . . . . . . 567 10.9 10.10 Resistors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576 10.11 Metallization and Liftoff Processes . . . . . . . . . . . . . . . . . . . . 581 10.11.1 Metallization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 10.11.2 Liftoff Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 10.12 Backside Processing and Die Separation . . . . . . . . . . . . . . . . . 590 10.12.1 Backside Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592 10.12.2 Die Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597 10.13 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598

490


List of Symbols and Abbreviations A* Aa/ao C

D

DO Ea EC ED

EF Eg

Ev Fmax gm

Ids Isat 10

J

Jsat

k 1 L

m n 4 R RP M P

t

T V V.PP vbi vds vgs

Vi vsg

W

wc

x, Y

a ES

K

Richardson constant change in lattice parameter concentration; capacitance diffusivity diffusion coefficient activation energy conduction band energy donor energy level Fermi energy semiconductor energy gap valence band energy maximum oscillation frequency transconductance drain-source current (units are mA/mm) reverse bias saturation current thermionic current flux channel saturation current density Boltzmann constant; wave vector; segregation coefficient effective length length ion mass ideality factor charge resistance range scatter time; thickness temperature voltage applied voltage built-in potential drain-source voltage gate-source voltage impressed voltage sidegating voltage width effective contact width direction coordinates thermal expansion coefficient dielectric constant thermal conductivity


P

OB

Om X S

AC CBE C-HIGFET CMOS

cs

CVD DC ECR ECRE EOR erfc FA FIB FMA GSE GSMBE HBT HEMT HFET HIGFET HPA HV IC JFET LDD LEC LPE LTB MBE MESFET MIS MOCVD MODFET PCM PE PECVD pHEMT PR RF RIBE

resistivity Schottky barrier height metal work function electron affinity alternating current chemical beam epitaxy complementary heterostructure insulated-gate field-effect transistor complementary metal oxide silicon compound semiconductor chemical vapor deposition direct current electron-cyclotron resonance electron-cyclotron resonance etching end-of-range complementary error function furnace annealing focused ion beam failure mode analysis gas-source epitaxy gas-source molecular beam epitaxy heterostructure bipolar transistor high electron mobility transistor heterostructure field-effect transistor heterostructure insulated-gate field-effect transistor high power amplifier high vacuum integrated circuit junction field-effect transistor lightly-doped drain liquid encapsulated Czochralski liquid-phase epitaxy low-temperature buffer molecular beam epitaxy metal- semiconductor field-effect transistor metal -insulator- semiconductor metal-organic chemical vapor deposition modulation-doped field-effect transistor process control module plasma etching; piezo-electric plasma-enhanced chemical vapor deposition pseudomorphic high electron mobility transistor photoresist radio frequency reactive ion beam etching

49 1

492


RIE RTA SAGFET SAINT SARGIC SEM SPC TEM UHV

reactive ion etching rapid thermal annealing self-aligned gate field-effect transistor self-aligned implantation for n+ layer technology self-aligned refractory gate integrated circuit scanning electron microscope statistical process control transmission electron microscope ultra-high vacuum ultraviolet vertical cavity surface emitting laser vapor phase epitaxy

uv

VCSEL VPE

Companies AT - Assembly Technology, Kulicke and Soffa Industries, Inc., Willow Grove, PA. Disco Hi-Tec America, Inc., Tempe, AZ. Dynatex International, Santa Rosa, CA. Electrotech Corp., Santa Rosa, CA. Motorola, Inc., Schaumburg, IL. Nitto Denko Corp., Ltd., Tokyo. Plasmatherm, St. Petersburg, FL. TriQuint Semiconductor, Inc., Beaverton, OR. Vitesse Semiconductor Corp., Camarillo, CA.

10.1 Introduction

10.1 Introduction In the latter half of the 199Os, there has been a dramatic paradigm shift in the compound semiconductor field. Ion-implanted processes are being rapidly displaced by epitaxy-based approaches, as operating frequencies move well above - 1 GHz. The superior performance offered by epitaxial materials has become quite evident. Manufacturers are responding to these market demands with materials and processes to support high frequency communications and digital signal processing. Ion implanted metal-semiconductor field effect transistors (MESFET), and even high electron mobility transistor (HEMT) devices, are giving way to pseudomorphic high electron mobility transistors (pHEMT) and heterostructure bipolar transistors (HBT) (for further information on these devices, see Daembkes, 1991; or Ali et al., 1991). The compound semiconductor materials GaAs, InP, and related ternary compounds, such as InGaAs, AlGaAs, and InGaP, are used for the manufacture of ultrahigh speed analog, digital, and microwave devices, light-emitting devices such as lasers and light-emitting diodes, high speed electrical and photonic detectors, and solar cells. The last decade has seen exciting gains and improvements in device processing and process development. Wafer fabrication processes have stabilized, and device structures have begun to converge as “ideal” epitaxial structures have evolved, metallurgical interactions have been understood, and manufacturers incorporate the developments of the past decade into their standard process flows. Complex integrated circuits containing well in excess of 100000 gates have been fabricated for digital applications (Vitesse, 1990; Tsen et al., 1993). Using new technology, CGaAsTM (Motorola) digital devices

493

with more than 117 000 transistors have been manufactured (Brown, 1998). At the same time device dimensions continue to shrink: 0.7-0.5 ym gate lengths are commonplace (Gamand et al., 1988; Matsunaga et al., 1989; Saunier et al., 1988), devices with - 0.3 ym gates are in development (Thiede et al., 1998), and critical dimensions of less than 100 nm have been created in the laboratories (Bernstein and Ferry, 1988; Han et al., 1990; Studebaker, 1994; Pereiaslavets et al., 1996). Base thicknesses for HBTs are typically 60-80 nm in dimension for 75- 100 GHz operation (Low et al., 1998; Bayraktaroglu, 1993). Fabrication of compound semiconductor ICs integrates materials science, materials characterization and semiconductor process engineering. An implicit precept for the materials growth and device fabrication is that these processes must be manufacturable: controlled, reproducible, and supported by realistic fabrication and operating tolerances, especially for fine critical dimension geometries. In this sense, a process sequence for compound semiconductors should appear silicon-like. That is, carried out within Class 1 or Class 10 cleanroom facilities, it should have a well-defined, relatively planar process morphology supported by batch processing with automated equipment, and use automated step-and-repeat lithography for pattern generation. However, the utilization of “pure” silicon processing tools versus tools configured for compound semiconductor processing must be balanced against the material’s properties of GaAs, such as the cleavage properties, the piezoelectric nature of the compound semiconductor lattice, strongly differing thermal and electrical characteristics in the native state, vapor pressures, wafer mass, density, etc. During the late 1990s, GaAs substrates have grown to 150 pm (6 in.) in diameter, while InP can be routinely obtained with

494


75 pm diameter. The availability of large substrates has had a profound effect on the economics of GaAs device processing, reducing the cost of GaAs devices to roughly half that of silicon-based processes for equivalent functionality (Tomasetta, 1998). In contrast to silicon, gold and gold-based alloys are used in most of the present interconnect metallization schemes, and have been found to be suitable for circuit complexities in excess of 100000 gates. Some aluminum-based interconnection schemes (Vitesse, 1990, 1995) have been developed for high-density interconnection in digital applications, using alloy species such as copper to mitigate electromigration. However, for the preponderance of applications, NiGeAu compositions are used for ohmic contacts, and some form of gold-based metallurgy is used in gate structures to achieve low-resistance metal lines. The applications of multi-layer metallizations are growing rapidly: four-layer metal structures are readily available from “foundries” such as TriQuint and Vitesse. The successful process line must also be supported by statistical process control (SPC) and failure-mode analysis (FMA) methodology to ensure and maintain high quality and high yields from the process. The principal issues in processing are: 1) the selection of materials and design criteria to achieve a desired set of device characteristics and performance, and 2) the definition and control of the requisite processing steps. The starting materials can be created with ion implantation doping, by epitaxial crystal growth, or by a combination of these methods. A typical process sequence will involve doping (by diffusion, incorporation during epitaxial growth, or ion implantation), photoresist patterning, isolation, annealing, etching, various metallizations, dielectric depositions and die or wafer level testing, and chip handling, as

well as multiple passes through several of these steps. All of the process sequences must be successfully carried out at high yields to fabricate functional, cost-competitive devices. The workhorse of the compound semiconductor device fabrication activity has been the metal-semiconductor field effect transistor (MESFET), and related variants. These devices are relatively simple to fabricate, but necessitate extremely tight control of the gate formation process (particularly the surface preparation or the gate recess etching step) to achieve control over the device threshold voltage and uniformity. Very fine (submicrometer) gate dimensions are needed to realize high-frequency operating characteristics (e.g., > 10-20 GHz ft values) in MESFET devices. Since the early 1980s the heterostructure field effect transistor [HFET, HEMT, MODFET, HIGFET, etc., see Daembkes (1991)l has received extraordinary attention as a result of the higher frequency performance, better transfer characteristics, and relatively relaxed lithography requirements with respect to MESFETs, in order to realize a similar performance level. The base materials for these devices are created by molecular beam epitaxy (MBE) or by metal-organic chemical vapor deposition (MOCVD) methods. In HFET devices, the transfer characteristics are determined to a large extent by the multi-layered compound semiconductor heterostructure and the materials growth process. However, the fabrication process must be well characterized and controlled, as threshold voltages vary by 5- 15 mV per atomic layer, similar to those of MESFET devices. Thus even small errors in surface preparation, random material loss during photolithography steps, damage induced by ion implantation, or dry etching may result in large variations in device characteristics. The HFET device family, its his-

10.1 Introduction

tory, and performance characteristics are reviewed in depth by Daembkes (1991). In the last few years, there has been a gradual conversion from the HFET to the pseudomorphic HEMT, incorporating InGaAs layers to form the conducting channel, so displacing the GaAs channel structures (see Brech, et al., 1997 for example). These devices have substantially improved transfer characteristics relative to the GaAs channel devices, and thereby offer superior electrical performance without incurring any additional processing complexity. Heterostructure bipolar transistors (HBTs) are now receiving some attention as HFETs enter production. The HBT devices are fabricated on epitaxial materials, and are nearly totally dependent on the crystal growth process for their characteristics. Recently, there has been a shift in the starting material's structure, similar to that noted in the HEMT devices. In the case of the HBT, the structures were previously based on GaAs-AlGaAs hetero-barriers at the emitter-base junction (Ali et al., 1991). Presently, the trend is moving towards InGaPGaAs structures (Mochizuki et al., 1997; Lin et al. 1990; Ho et al., 1993; Ren et al., 1993), as devices fabricated with this materials system have shown phenomenally good reliability (Low et al., 1998; Pan et al., 1998). The HBT device characteristics were reviewed by Ali et al. (1991). The processing of HBTs is relatively straightforward, but requires a very high degree of process control, particularly over the base and collector etching and metallization steps. Dry etching of phosphorus-containing compounds is not compatible with all of the materials chemistries, so wet etching steps are required. However, the etching selectivity for some of these materials is in excess of thousands to 1, thus alleviating much of the concern for the wet etch processes (Ren et al., 1995). The transfer characteristics are

495

very sensitive to the distribution of the p- or n-type impurities in the collector-base (C-B) or emitter-base (E-B) junction regions, that is, the alignment of the metallurgical and electrical junctions. The materials quality and properties in the various layers are also crucial to the high frequency characteristics. It is notable that one major stumbling block in HBT devices has been the issue of reliability. This issue has been discussed at length at several venues (see GaAs IC, 1992, 1993a, b, 1994, 1998) without clear conclusion. The principal problem with these devices is that in the presence of high currents or elevated temperatures (i.e., stressful operating conditions), the dopant species may redistribute near the junctions, thereby altering the device characteristics. Commonly this is observed as a degradation of the device gain, and many groups have reported this behavior. This issue remains under intense debate and investigation (Yamada et al., 1994; Sugahara et al., 1993). However, very recent results in the InGaP-GaAs based materials have shown reliability to be extremely high (Low et al., 1998; Pan et al., 1998), approaching 10' hours at 150°C (Ueda et al., 1997). In the search for high-speed operation at extremely low power levels, a number of complementary devices have been fabricated. NPN and PNP devices such as junction field effect transistors (JFET) (Zuleeg et al., 1984, 1990; Wilson et al., 1989; Wada et al., 1989), and complementary heterostructure FETs (C-HIGFET) (Grider et al., 1991). The C-HIGFET circuit performance has been dramatically improved in recent years (Abrokwah et al., 1993), providing an ultra-low power GaAs-based circuit with much higher performance than similar silicon CMOS devices. More recently, HBTs (Ali et al., 1991; Slater et al., 1990; Kim et al., 1988), have yielded ultra-high performance devices and circuits. Enhancement-

496


depletion structures have also been developed for logic and mixed signal applications (Dautremont-Smith et al., 1990; Burton et al., 1983; Wada et al., 1997). Implicit in this discussion is the need to maintain very high yields through each step of the process sequence. As an example, consider a processing sequence for the fabrication of a GaAs device or integrated circuit (IC), as illustrated in Fig. 10-1. This

-

-

process sequence would produce a transistor or an IC with 2 , 3 , or more levels of interconnect, and resistors, capacitors, and inductors. Figure 10-1 also incorporates the steps needed for the fabrication of an HBT device, which entails a modified process sequence. Once the collector is defined and the emitter, base, and collector metallizations are complete, the subsequent processing steps are common to all fabrication flows.

r

Emitter Etch

1

I I

I I

I

A Base Etch

+ + 1

Dielectric Deposition Ohmic Contact

+ t +

Collector Etch Dielectric Deposition Ohmic Contact

IGate Metal Etch I

I Dielectric Deposition 1 + Dielectric Deposition l

rtl Isolation

First Level Interconnect

Figure 10-1. Schematic representation of a process flow for the fabrication of an FET or integrated circuit. Various steps may be incorporated or bypassed as appropriate. The process sequence will vary depending on the individual process flows, the device requirements, and the requisite thermal budget. Since the processing for a HBT device is markedly different from that for an FET, the HBT process sequence is described by the flow on the right side of the figure. At the “A”, the process flows merge to define the interconnect strategy, thinning, and back-surface metallurgy as required for the finished product.

10.1 Introduction

A “mask level” in this discussion incorporates numerous steps: cleaning, photoresist application, baking, exposing, developing, measurements, inspection, cleaning, a “layer” formation such as ion implantation, metallization, or dielectric deposition, additional inspection or measurements, and then returning to a cleaning step prior to a new mask level. The yields through each of these individual process sequence steps must be - 99% to realize just a 90% yield through a single mask level! If a 10 mask-level process were operating with a 90% yield at each mask level, only a 38% gross yield would be realized before the on-wafer electrical functionality evaluation. It is to the great credit of the wafer processing staff that very

high levels of process integrity and yield can be achieved and maintained. In addition to the plethora of process and materials related phenomena, such wellknown electrical phenomena as sidegating and backgating (discussed in Sec. 10.3.3) must be understood and controlled with respect to their impact on circuit performance (D’Avanzo, 1982; Makram-Ebeid andTuck, 1982a, Vuong et al., 1990; Finchem et al., 1988). These inter-device interactions can have a strongly destabilizing influence on device performance. While these latter problems are coming closer to mitigation (Smith et al., 1988a; Brown et al., 1989), complete elimination of the interaction between devices fabricated in compound semiconduc-

+ikq

Multilevel Metal Interconnect Metallization

I

Formation

I

Via Etch

‘ A I

I Resistor

I

t

1Via Seed Metal

t

- -fi I

Dieseparation

Lands

Scribe and Break

Metal Lines

I to Packaging I Figure 10-1. (continued).

497

I

498


tors has not yet been achieved. For example, DC sidegating performance has been observed to be extremely good in some cases (Smith et al., 1988b), but high-frequency performance may suffer from the vagaries of sidegating phenomena (Lin et al., 1990; Gray et al., 1990; Hitchens et al., 1989). Indiscrete devices, deep levels do not cause interactions, but rather give rise to dispersive effects and other time dependent behaviors. This chapter will deal with some of the general problems which have been faced and overcome in the processing of compound semiconductor materials for high speed device fabrication. It is not, nor can it be, exhaustive, as the topic is too vast. However, it will present a wide range of materials, device, and process issues illustrating the key concepts, features, and problems in the present state of the technology. Other chapters are devoted to detailed development of materials growth, device structures, and related characteristics, and will be referenced where necessary. The first sections will describe some of the issues involved in creating the desired electrical characteristics on or in the compound semiconductor substrate, and then the fabrication process steps and process sequences will be discussed. The generic process sequence described here could ultimately result in the fabrication of either an active or a passive device. However, it should be emphasized that this description does not represent any specific process flow, as such detailed information is considered highly proprietary.

10.2 Doping Processes GaAs and InP are the dominant materials in the compound semiconductor device arena, although research and small scale production activities span the gamut of III-

V and II-VI binary, ternary, and quaternary systems. This focus arises from the respective electronic and optical properties, and the demands of the market place. Electronic applications are present dominated by GaAs-based materials, especially for power amplification and high frequency (RF) devices in the range of - 1 GHz to - 75 GHz. For higher frequency requirements, InPbased HEMT devices can be used up to - 100 GHz. In both cases, very small gate lengths are required, with electron-beam definition needed to produce the fine features. Electro-optic devices are predominantly built from InP-based ternary and quaternary materials, with some GaAs-based device applications as well. In any of these applications, n-type, p-type, or mixed conductivity layers must be created to form the active device. The modified semiconductor conductivity allows for metal-semiconductor (Schottky barrier), p- n, p- i- n, or other forms of junction to be formed. The advantages of compound semiconductors over silicon lie predominantly in the large bandgaps and higher carrier mobilities. In general, these properties permit operation at higher temperatures and higher frequencies. An additional feature of compound semiconductors is the ability to “engineer the bandgap” (Capasso, 1987, 1990) through composition variation (i.e., the mixing of group I11 and V, or I1 and VI elements), i.e., binary, ternary, quaternary, or more complex compounds may be created. The group III-V (and the group II-VI) compound semiconductor elements may be mixed on either sublattice to tailor the bandgap and the optical and electronic properties. While there are some limitations imposed by thermodynamic and materials physics considerations, the electronic and optical properties may be readily optimized to the application, which makes the use of these materials so attractive for high-speed

10.2 Doping Processes

electronic and optoelectronic devices. The relationships of bandgap energy, directhdirect band transitions, lattice parameter, and chemical mixing are shown in Fig. 10-2. Diagrams such as this have provided the basis for understanding the entire 111-V compound semiconductor alloy system. To fabricate an active or passive device in a compound semiconductor material, conducting regions or layers must be created. These regions may be n- or p-type in character, but for most compound semiconductor device fabrication n-type (majority carrier) conductivity is utilized. This is due to the significantly reduced high-frequency performance of devices based upon hole transport (low carrier mobilities). As examples, the maximum drift mobility for electrons in n-type GaAs at room tem-

499

perature is in the range of 8000-8800 cm2 V-' s-l, versus 1200-1500 cm2 V-' s-l for n-type silicon (Sze, 1981, App. G, H; EMIS, 1990, Chap. 5). The maximum drift mobility for holes is 400-450 cm2 V-' s-' in GaAs, while being somewhat higher in Si at 450-500 cm2 V-' s-'. For InP these values are 4800 cm2 V-' s-' for electrons and 150 cm2 V-' s-l for holes, respectively (EMIS, 1991, Chaps. 2,4, 5). The high carrier mobilities in compound semiconductors arise from the polar nature of the lattice, and the concomitant differences in the band structure and the Fermi surface (Sze, 198 1, Chap. 1 ; EMIS, 1990, Chap. 7). It is the electron transport characteristics and the existence of a direct band gap that provide the large performance advantages over silicon devices. The direct band gap refers to the energy tran-

3.0

2.5

s v

P (II

=

0

2.0

1.5

C

8

1.o

0.5

0.0 5.2

5.6

6.0

6.4

6.8

Lattice Constant (A) Figure 10-2. The 111-V compound semiconductor multi-nary tree. Tie lines link the binary compounds along ternary compositions. Dark solid lines indicate a direct band gap transition, while a light line indicates an indirect band gap. Silicon-germanium is included for reference. The x-axis is the lattice parameter; the y-axis is the bandgap energy in electron volts. The inset (upper right) shows the nitride materials, silicon carbide, and diamond relationships relative to the 111-V materials. (Figure courtesy of Dr. J. Woodall and E. S . Harmon, MellWood Laboratories, Inc., West Lafayette, IN.)

500


sition when the valence band maxima coincide with the conduction band minimum at k = 0. This point is discussed by Sze (198 1, Chap. 1). Table 10-1 presents some of the critical physical properties of compound semiconductor materials. To create n-type behavior in compound semiconductors impurity species such as Si, Sn, Te, Se and S are suitable canditates. Acceptor impurities include Be, C, Zn, Cd, and Mn. Other transition metal species such as Cr, Ni, and Fe tend to produce midgap deep level states and high resistivity (“semi-insulating”) characteristics. Figure 10-3presents a summary of the energy levels for a number of impurity species in GaAs. Owing to

the differences in band structure and atomic configuration between the various compound semiconductors, group IV impurity species such as carbon or silicon may act as acceptors or donors in different 111-V alloys. The various dopant species may be introduced into a substrate or into epitaxial layers by the techniques of ion implantation or diffusion, or they can be grown-in during epitaxial layer growth. In the 111- V materials, the group V1 impurities generally yield higher electron densities than do the group IV species at same dose and energy (ion-implanted case) or the same atomic concentrations (epitaxial growth), due to autocompensation effects

Table 10-1. Selected properties of semiconductor materials at room temperature.

Melting point (“C) Lattice constant (nm) Density (g ~ m - ~ ) Thermal conductivity (W cm-’ K-I) Thermal expansion coefficient (x 10“ K-’) Heat capacity (J mol-l K-I) Band gap (eV) Electron mobility (cm V-’ s) Hole mobility (cm2 V-l s-’) a

Si a

GaAs”

1415 0.543 1 2.328 1 .5 2.6 19.6 1.12 1 500 450

1238 0.5653 5.32 0.46 6.86

1065 0.5869 4.79 -0.7 4.56 45.3 1.34 4800 150

50.7

1.424 8500 400

Sze (1981); EMIS (1991).

8

.mi8

Ge ,006

Te Se

.006.006

.& ,0059

0

Figure 10-3. Measured ionization energies for impurity atoms in GaAs. “D’ and “A” denote donor or acceptor behavior, respectively. Otherwise, levels above the “gap center” are donor-like, and those below the gap center are acceptor-like states. [Original figure from Sze (1981). Reprinted by permission of John Wiley & Sons, Inc.]


with the group IV species (amphoteric site selection by the dopant atoms). Carbon, a group IV element, is typically an effective acceptor in GaAs (as CAs) with relatively low autocompensation. In InP, carbon also acts mainly as an acceptor, although less readily incorporated. This behavior is advantageous for doping GaAs- or InP-based materials during epitaxial crystal growth by MOCVD or CBE methods. On the other hand, silicon (group IV) may exhibit strong autocompensation in GaAs and can produce dramatic reductions in desired electrical properties, particularly at high concentrations. The selection of ion implantation, diffusion, or epitaxial growth to create the conducting layers depends upon the requisite device’s electrical characteristics and the available fabrication process sequences. Diffusion-based methods for creating junctions have not been strongly pursued for compound materials in recent years, although several important applications exist in GaAs processing (Vogelsang et al., 1988; Wada et al., 1989; Harrington et al., 1988; Yuan et al., 1983). Control of the diffusedlayer depth and profile tends to be much more difficult than in ion-implanted or epitaxy-based processes, and therefore, interest in diffusion-based processes has waned. Ion implantation has been the choice of many process foundries for a broad range of applications (Rode et al., 1982; Shen et al., 1987; TriQuint, 1986; Vitesse, 1991). This is principally a result of the silicon-like nature of the process sequences, and the relatively low cost of device fabrication. Epitaxial layers, while somewhat more expensive than ion implanted substrates, have unleashed the power of compound semiconductors with the development of heterostructure device materials, and the near atomic level precision of doping and compositional variations. Due to the numer-

501

ous advantages of heterostructures (Daembkes, 1991; Ali and Gupta, 1991), these materials are rapidly displacing MESFET (metal-semiconductor field effect transistors) based on ion-implanted or epitaxial processes, especially for high-frequency and optoelectronic applications (Bayraktaroglu, 1993; Wada et al., 1997). Most of the n-type impurities are relatively stable in the compound semiconductor lattice. However, the diffusivities may vary strongly depending on the bandgap (binding energies), defect structure, concentration, and strain in the lattice structure. For example, the diffusivity of silicon in Al,,,Ga,.,As is roughly 10 times greater than that of silicon in GaAs (Schubert, 1990; Schubert et al., 1990). P-type impurities, such as Zn or Be, tend to be very rapid diffusers, and exhibit the combined effects of interstitial and substitutional diffusion. This behavior manifests itself as a “double diffusion front”, with interstitial species rapidly in-diffusing relative to the substitutional atoms (Tuck, 1988, Chap. 4; Gosele and Moorhead, 1981; Dobkin and Gibbons, 1984; van Ommen, 1983). Many of the ptype impurities (e.g., Mn, Zn, or Be) exhibit very large and anomalous diffusivities in compound semiconductor lattices (Jordan, 1982; Klein et al., 1980; Tuck, 1988, Chap. 5 ; Small et al., 1982). Control of the thermal budget (integrated time-temperature cycle) when annealing thus tends to be much more critical when dealing with acceptor species rather than donors. An example of the double diffusion behavior for Zn in GaAs is illustrated in Fig. 10-4. This phenomenon can give rise to an uncontrolled p-n junction position owing to the large difference between the diffusion rates of n-types and p-type impurities. Thus the final charge distribution is strongly dependent on the processing time-temperature sequences. Carbon atoms have been

502


. lSOCONCENTRATlON LEVEL

u

I 0

I

I

I

l

I

l

I I

100

DEPTH (pm)

1

I

200

Figure 10-4. Zinc diffusion behavior in GaAs. Isoconcentration (infinite source) diffusion has an erfc (complementary error function) profile. Concentration gradient diffusion reveals a concentration dependence of the diffusion constant and reflects the substitutional and interstitial diffusion behavior across regions I, 11, and 111. [After Gosele and Moorhead (1981), reprinted with permission of the authors.]

found to be very stable to thermal treatments in most compound semiconductors (Schubert, 1990). As aresult, carbon is rapidly becoming the acceptor of choice for p-type doping for numerous applications. However, in some compound semiconductor materials, such as InGaAIP, carbon is not always an effective dopant species, and Be, Mg, or Zn remain the dopants of choice. Another difficulty encountered with impurities such as chromium or magnesium is the propensity for out-diffusing and accumulating on the surface or at interfaces in the semiconductor material (Small et al., 1982; Tuck, 1988, Chap. 5 ) . This accumulation strongly alters the electronic properties in the surface region, and can lead to substantial inhomogeneities in the charge (resistivity) profile. It is this characteristic which led the industry away from the use of Cr-doped, semi-insulating GaAs substrates

to the “undoped” (native defect controlled) semi-insulating properties in the early 1980s. Rapid thermal annealing (RTA) or other short-duration, low-temperature processes may be used to minimize an undesirable impurity redistribution. Even for the donor impurities, with somewhat smaller diffusivities, it is generally desirable to minimize any atomic-level redistribution to maintain a “sharp” or “as-grown’’ impurity profile, or to prevent the movement of impurities into undesired regions of a device. For example, to maintain the gain of an HBT it is imperative to minimize diffusion between the collector-base and the emitter-base junction regions (Kim et al., 1991). In the case of an HEMT-type structure, the high mobility properties achieved by separating the donor species from the electron population are easily compromised if the donor atoms diffuse into the channel region. In the processing of epitaxial structures, thermal annealing may only be required for ohmic contact formation and device isolation (temperatures less than - 5OO0C), and thus little impurity redistribution occurs. However, in self-aligned processes [SAGFET - Mitsubishi (Noda et al., 1988), SARGIC - AT & T (Dautremont-Smith et al., 1990), SAINT - NTT (Yamasaki et al., 1988), and similar processes), or when implementing the lightly doped drain (LDD), ion implantation is necessary to reduce the channel resistance and to alter the impurity concentration in the source-gate and/or gate-drain regions. Herein, the redistribution effects during annealing are critical for the device characteristics and performance: lateral carrier spreading can alter the effective gate length; excess charge or image may create leakage paths of short circuits. It is critical that a minimal thermal cycle is utilized and that the implications of the charge distributions on the device implications of


the charge distributions on the device performance are well understood. Further information and a detailed treatment of various diffusion effects are provided in Secs. 10.4 and 10.8, and in Tuck (1988). One key issue in the use of ion implantation is the need for high-temperature annealing processes (see Sec. 10.8) to “activate” the implanted species, i.e., to place the impurities onto substitutional sites in the host lattice and restore the lattice disorder produced by the ion flux. This thermal treatment must be carried out prior to metallization steps, or to utilize contact metals that are stable at temperatures greater than 800-900°C. Diffusion doping processes also require relatively high temperatures with constraints similar to those in ion implantation-based processes. Epitaxial methods, on the other hand, have the impurity species incorporated during growth. However, the impurity distribution can be affected significantly by any process steps where temperatures exceed - 400-600 “C. High-dose ion implantation or highly doped epitaxial layers are used to make highly conducting “n+” or “p+” layers and permit the formation of very low resistivity ohmic contacts. “Good” values for contact resistances are typically in the range of sz cm-2 for n-type materials, and lop6- lop5 SZ cmp2for p-type materials [Sharma (1981), and references therein]. Ion implantation can also be used to selectively dope regions within devices. For example, creating resistor stripes or enhancing device operating characteristics with “buried P” layers (Makino et al., 1988; Noda et al., 1988), placing a p-type impurity below the n-type conducting channel to provide sharper pinch-off characteristics, or implementing the LDD (Kikaura et al., 1988) by selectively doping the gate-drain areas for improved gain linearity and breakdown properties.

-

503

The LDD process involves an additional donor concentration (n-type device), implanted selectively into the region between the drain and gate of an FET to reduce the drain-gate resistivity and create a graded electric field distribution. The LDD effectively decreases noise in HEMT devices, creates a lower source resistance, and mitigates short channel effects (Kikaura et al., 1988). In contrast to low-noise devices power FETs require highly doped source and drain regions to reduce the access and channel resistances, and reduce the heating problems associated with high operating currents. High-dose implants may be selectively added to increase the charge in these regions. In addition, all devices benefit from low contact resistances, which is a property well suited to selected area implantation. In other applications, such as low-noise amplifiers (LNA) or high-power, high-frequency power amplifiers (HPA), the critical issues are achieving a low source resistance, short, highly conductive gate structures, very high channel doping, and short (offset) gate-source spacing. For LNAs, a high concentration of charge must be localized very near to the surface of the semiconductor substrate in a selected area. Ion implantation is therefore carried out at very low energies (10-20 keV) to minimize the depth of the charge distribution. In power devices, the trade-offs become breakdown voltage, threshold voltage, ohmic-to-gate spacing, desired power, and maximum operating frequencies. Charge and distance must be carefully integrated to optimize the device performance. Epitaxial methods, which can precisely control the charge distribution in the surface regions, are now being applied to LNA and power device fabrication processes withgreat success (Ayaki et al., 1988; Danzilio et al. 1992; Pobanz et al., 1988; Tanaka et al., 1997; Goto et al., 1998; Takenaka et al., 1998).

504


As the understanding of compound semiconductor processing has improved, many processes have evolved to epitaxial materials structures. This is due primarily to the ability to better specify the charge spatial distribution, and to the introduction of homo- and heterostructure devices and fabrication processes that utilize the precision of the epitaxial growth processes to reproduce semiconductor layer structures to within a few atomic distances (see, for example, Daembkes, 1991; Ali et al., 1991). New device designs such as pHEMT and HBT, and new materials options incorporating InGaP layers, have taken advantage of the precision charge distributions and hetero-barriers provided by epitaxial materials. These devices realize superior electrical characteristics and high-speed performance without resorting to extremely fine gate geometries. However, by further exploiting the ability to create fine geometries (- 0.1 pm) using deep ultraviolet light, or direct writing (e-beam or X-ray) methods for heterostructure FETs (HFETs) (Aust et al., 1989; Suzuki et al., 1989), or in HBT devices (where the critical dimension is the base

thickness, predetermined by the epitaxial growth process) (Kim et al., 1988; Low et al., 1998), switching speeds have exceeded 185 GHz (Nubling et al., 1989), and maximum oscillation frequencies (FmaX)are in the range of 500 GHz (Yu, 1998).

10.2.1 Ion Implantation Ion implantation doping is the process of injecting a desired impurity species into a semiconductor material by ionizing the impurity atom, accelerating it through a high potential (a few kV to greater than MV levels), selecting the correct ion species via a transverse magnetic or electric field, and collimating and guiding the ion flux as a “beam” onto the semiconductor substrate. Figure 10-5 shows an ion implanter in schematic form. The ions, upon colliding at the surface of the host material, expend their energy in collisions with the lattice atoms, and after some distance cease motion inside the host material. A small fraction of the ions may be reflected (recoil) from the surface and not contribute to the doping of the semiconductor. This effect is enhanced at low

Figure 10-5. Schematic representation of a high-voltage, high-current ion implanter. The main components of the system are denoted. (Figure courtesy of Dr. L. Parachanian-Allen, Ibis Technology Corporation, Danvers, MA.)

505


ion energies or if the implanted species' mass is significantly less than that of the host material. The key issues in ion implantation are the control of the ion flux and purity, ion energy, and selection of the ion species (actually the m/q ratio, where m is the ion mass, and q is the charge state of the ion). This latter point requires that great care be taken to ensure that the selected m/q is predominantly the desired ion species, as many elements or complexes may have the requisite madcharge ratio. Long beam lines, while adding additional complexities, permit filtering of the ion beam to enhance selection of the desired species. Extreme cleanliness in the implanter system and ultra-high purity source materials are prerequisites to successful ion-implantation processes. The depth of the ion penetration is proportional to the ion energy, the ion mass, and the host material average atomic weight. Typically, energies between - 10 keV and 400 keV are utilized for implanting into compound semiconductors. Systems devel-

oping ion energies well above 1 MeV have been created for special applications. These energies will provide depths ranging from a few tens of nanometers to beyond a micrometer, depending on the ion species and the host material's properties, as shown in Table 10-2 (Gibbons et al., 1975).Ion doses range from - 10" ions cmP2 to greater than 1015 ions cm-2. Ion implanters are limited in their ion beam current (typically due to ion source limitations) and total power capabilities (beam current-accelerating voltage product). High dose implants require very extended times, which is hard on the ion sources and may cause the temperatures of the target wafer to rise substantially unless active cooling is provided. The latter point becomes more important as the dose-energy product increases. As the interactions with the lattice are statistical in nature, the impurities are distributed in essentially a Gaussian profile. The actual ion distribution is therefore described by the range, or peak concentration, R , , and the scatter, AR,, as shown in Fig. 10-6.

Table 10-2. Projected ion depths for 70 and 150 keV ion energiesasd. Sib

Ion

B

H

0

N F Si Se Ge C P As Zn S a

GaAs

InP b*c

70 keV

150 keV

70 keV

150 keV

70 keV

150 keV

2 19/60 7621109 164156 158147 187177

420183 1391I128 370198 344177 4601155

177190 6391162 106158 122167 94152 59133 27113 28114 144176 5513 1

3821146 12321205 2331100 26811 12 20719 1 129160 53125 56126 3 131126 120157 60128 112153

199110 1 7 181182 1 19165 137174 106158 66137 30115 31116 162185 -

4291164 13841230 26111 12 30 11126 2321102 145167 59128 63129 352196 -

34117 58133

67131 126159

-

-

42115 43116 155139 86134 84129 45117 80132

82128 87130 317160 188163 42115 92132 177160

-

30115 52129

-

All values in nanometers; data are presented as depthlstd. deviation; InP Values are scaled to GaAs results; Gibbons et al. (1975).

506


Figure 10-6. Generalized ion-implantation profile in a target material, R, represents the peak of the concentration profile from the surface. ARp is the standard deviation of the profile. End-of-range damage region refers to a zone of high displacement damage due to ions stopping and transferring their residual energy to the lattice.

These parameters adequately represent the bulk of the implanted ions, but additionally there is a tailing of the ion distribution into a depth significantly deeper than R,, known as “straggle”. This phenomenon is not well represented by existing theoretical models (Biersack et al., 1980). For the ion implantation of donor species into most compound semiconductors, electron concentrations typically saturate in the range of 3-8x 10l8 cmp3after a furnace anneal. Under rapid thermal annealing (RTA) conditions the maximum electron concentration can be raised to greater than lOI9 cm-3 (Liu et al., 1980). For high doses it has been observed that the activation efficiency increases when ion implantation is carried out at slightly elevated temperatures (Donelly, 1981, or with a “co-implanted” species such as fluorine (Pearton et al., 1990b). The former result was attributed to the in situ recovery of lattice displacements during the implantation cycle, while the latter effect is attributed to lattice recovery from the additional energy dissipated in the lattice. For ptype implants using Be, Cd, or Zn, hole con-

centrations saturate at about 5 - 8 x 10” cm-3 due to solid solubility effects. However, using Zn ions, acceptor concentrations above 3x 1019 cmp3 have been obtained (Kular et al., 1978). There are several advantages to the use of ion implantation: good control of the doping concentration and depth of the ion distribution peak; relatively good uniformity of the ion flux across the substrate (typically a few percent variation); directionality (relative to diffusion methods); and good waferto-wafer reproducibility in modern ion implanters. In addition, the ions may be selectively implanted or shadow-masked by using appropriate masking techniques. The ion energy is determined by the accelerating field and therefore easily quantified. The ion flux is readily measured as a “beam current” in the implanter apparatus. By integrating the current with time the total dose may be calculated and controlled (the assumption here is that the ion beam is composed predominantly of the desired ion species). Corrections can be applied for low energy implantation processes to account for


recoil losses. Ion ranging statistics are supported by a wealth of experimental and theoretical model information (Gibbons et al., 1975; Biersack et al., 1980; Zeigler et al., 1985), which has made the ion implantation process relatively straightforward to implement and control. The disadvantages to the ion implantation process are: substantially less than 100% efficiency in the activation process (ion species and host dependent); sensitivity of the activation to temperature; damage induced in the host material (defect introduction and electrical compensation); straggle and endof-range damage (deep random scattering and displacement events), as well as consideration of site selection and autocompensation. There is also a need to misorient the substrate with respect to the ion beam to avoid “channeling” which can, in turn, create shadowing effects at steps and edges of masked regions (Morgan, 1973; Kikaura et al., 1988). Some of these issues are addressed below. The efficiency of the activation process during annealing directly impacts the device characteristics, and is therefore used as a figure-of-merit for the implantation process. This figure-of-merit can be calculated from the ratio of the yielded charge in the lattice relative to the total measured ion dose. The effectiveness of the anneal cycle is affected by the amount of damage that is created by the ion flux, the site selection of the ion species (autocompensation), the annealing conditions (time and temperature), and the electrical compensation from the residual or native defects (see Sec. 10.8). Changes in the point defect concentration from the loss of volatile host atoms (e.g., As or P) may also alter the activation process. Defects arise from the displacement of atoms in the host lattice and the site selection of the implanted species. The defect family created by implantation consists of vacan-

507

cies, displacements, interstitials, complexes, substitutional atoms, antistructure, etc. Each of these defects carries a unique signature and provides electrical charge, compensation, and/or recombination centers in the lattice. At excessive doses there may be so many defects created that the lattice is nearly completely disarrayed or amorphized (Howes and Morgan, 1985, Chap. 5 ) . This phenomenon will occur at fluxes in excess of 1 0 ~ ~ - 1cm-* 0 ~ ~for heavy ions in most compound semiconductors; significantly larger flux densities are needed to amorphize when using light ions such as protons (Anderson and Park, 1978). It has been found that by implanting at temperatures above 150 “C- 200 “C, GaAs cannot be amorphized even at high doses, as the minor atomic displacements anneal during the implantation cycle (Anderson and Park, 1978). Straggle and channeling are the “random components” of the implantation process. These phenomena arise from the random redirection of the ions due to scattering events in the host material. The effects are observed as lateral or azimuthal spreading of the ions in the host. Straggle refers to ions that come to rest far beyond the predicted positions in the lattice. End-of-range (EOR) damage may arise when these ions transfer their energy to the lattice upon stopping deep in the crystal. Channeling is another component of straggle, observed as a non-Gaussian depth distribution (“tailing”), as illustrated in Fig. 10-6. Channeling occurs when the ions are scattered down the “open” directions (e.g., (1 1 1) in a compound semiconductor) in the host lattice, and travel significantly further into the surface than predicted by the theory (Gibbons et al., 1975; Morgan, 1973). This phenomenon is prevalent in open lattices such as GaAs, InP, and other 111-V materials with large lattice constants. Channeling behavior and electrical effects are discussed

508


1973). Rotating the substrate continuously during ion implantation may also be used to optimize the ion distribution. However, there is no known method for totally eliminating these effects. To counter the effects of straggle and channeling of donor impurities in FET-type devices, a p-type "back-doping'' or buried P implant may be added, deeper than the n-type implant, to sharpen the charge distribution at the bottom of the channel (Fig. 10-8). This step enhances the electron confinement and provides sharper Z- V characteristics at the expense of additional capacitance in the device. Great care must be taken to precisely position the p-dopant distribution and concentration to avoid compromising the device performance. Parasitic effects, isolation, and additional sidegating and backgating problems may arise from the presence of a p-type conducting layer (see Sec. 10.3.3).

in Kikaura et al. (1988), and Myers et al. (1979) for example. Ion channeling and straggle may negatively affect the device's performance. This effect is easily seen in Fig.10-7, where excessive sub-threshold leakage currents and a soft turn-on characteristic are evident. Interdevice interactions, such as sidegating, may also result from straggle due to the inability to adequately isolate adjacent devices. These manifestations are all related to the extended charge distribution in the depth of the channel below the gate. To ameliorate channeling the substrates are intentionally misaligned by 7- 13 degrees to the ion beam axis, and rotated about the normal to the wafer surface (Rosenblatt et al., 1988). In this manner the substrate presents a maximum apparent atomic density (amorphous-like) to the ion beam, which increases the likelihood of scattering events relative to the channeling probability (Morgan,

500

I

I

1

I

I

I

I

I

1

I

I

-3

-2

-1

0

+1

1

400 n

E

4E " Y

100

0

-4

+2

vgs(volts) Figure 10-7. Ids- Vgstransfer characteristics for an ion-implanted, and various epitaxial (MESFET and heterostructure) FETs. Note the lower on-resistance for the epitaxial-based structures relative to the ion-implanted case. The different device types are identified in the figure. The sharp turn-on characteristic and minimal sub-threshold leakage currents of the HEMT (high electron mobility transistor) devices are evident. Softer turn-on and higher sub-thresholds currents are characteristic of the ion-implanted and MESFET devices. (Figure courtesy of Dr. S . Wemple, Wemple Technologies, Wyomissing, PA.)


509

Figure 10-8. Representative ion-implantation profiles in an n+-n-buried-p device structure. R,, AR,, EOR, and channeled ion have the their usual meanings. The buried-p implant is placed to compensate the tail of the n-channel region implant, while being (ideally) fully depleted by the donor species. This buried-p layer creates a sharper substrate-side effective charge profile leading to a sharper I-V turn-on characteristic, and lower leakage currents in the transistor.

Implanting with a skewed alignment to the ion beam, while improving the ion distribution, can create other difficulties. If implantation is carried out after metal lines are defined, or with masking or dielectric layers present, as needed for device, LDD, buried-p, or isolation formation, self-alignment of the gate, etc. (e.g., gate metallizations, ohmic contacts), layers effectively screen the ion flux and shadow the areas adjacent to the metal runners as shown in Fig. 10-9. Shadowing can lead to nonsymmetric ion distributions, to nonuniform electric fields in the channel region, and create unexpected device asymmetries. To the designer, these effects may put significant constraints on the device layout (i.e., source and drain identity, or gate orientation) if predictable circuit characteristics are to be expected.

Several other issues are critical to the success of ion implantation processes. It is crucial to have “qualified”, controlled, semi-insulating (or conducting) substrate properties to achieve reproducible characteristics using ion implantation processes (Wilson et al., 1989, 1993). Prior to the mid 1980s, it was common to have Cr-doped or “Oxygen”-doped semi-insulating GaAs substrates (Makram-Ebeid and Tuck, 1982; Rees, 1980). In this time frame, the performance of ion implantation was strongly dependent on the raw materials, the crystal boule, the crystal grower, the crystal growth conditions, and even the position of the substrate in the boule. Chromium atoms rapidly out-diffuse from the bulk to the surface, rendering the active region partially compensated and highly resistive. This effect greatly complicates the use of high-temper-

510


Figure 10-9. Schematic representation of the effects of topology on ion-implantation profiles. The angle between the incoming ions and the substrate (typically 7" - 13" to the normal to the substrate surface, with a 45" rotation about the normal) is selected to minimize channeling. Ions are slowed near edges of photoresist features and may be deflected from metal trace corners, thereby perturbing the ion profiles in the host. The ion profile offset may be single-sided in systems with nonrotating and stations, while rotation of the substrate creates a more symmetric (two-sided) offset.

ature annealing processes required for activating the impurities, and has the undesirable compensation effect on the implanted species. Thus chromium-doped materials are rarely used for device manufacture. In the case of InP, iron atoms are used to create the semi-insulating properties with very similar considerations. As crystal growth methods and materials' purities have improved, these early approaches have rapidly given way to high purity semi-insulating GaAs substrate materials (no intentional additions of impurity species) with well-controlled properties. The semi-insulating conditions arises from the presence of native deep-level defects [e.g., EL2 (the native defect level at 0.8 eV below the conduction band edge) and other deep levels, balanced with the concentrations of residual donor and acceptor species (Makram-Ebeid et al., 1982; Martin et al., 1977; Lagowski et al., 1982; Milnes, 1973)l. InP crystals still require the addition of Fe to the crystal as there are no suitable native defects to produce undoped semi-insulating InP material (Cockayne et al., 1981; Parsey

-

et al., 1983). The present semi-insulating GaAs substrates are stable to extended thermal anneals at temperatures well above 900"C, and InP(Fe) substrates are stable at temperatures of 700 "C-800 "C. There are, however, sufficient variations in the substrate materials that many users still carry out "boule qualification" procedures to verify the performance of the material in their individual processes (Wilson et al., 1989). A boule qualification process will typically involve a representative implantation sequence followed by an annealing cycle, and then electrical measurements are carried out to test the implant activation efficiency and depth profiles. These qualification activities raise the expense associated with ion implantation processing, and may also affect design and processing conditions in order to compensate for the interaction of the substrate, ion implantation, and annealing processes. However, in the interests of maintaining high yields, such activity is presently use in some process facilities utilizing implantation techniques. Other highvolume GaAs foundries have achieved a

-


consistency of substrate supply, process stability and designs which accommodate most variations, and rarely require such qualification efforts [see Smith (1994)l.

10.2.2 Diffusion Methods Diffusion processes can be categorized as “closed tube” or “open tube”. The closed tube process typically involves sealing the impurity materials and the substrates in a vessel, evacuating or filling the vessel with an inert gas, and then subjecting the entire assembly to an annealing cycle to in-diffuse the impurity. This method is cumbersome expensive, difficult to control and reproduce, and unsuitable for production environments. The open tube approach to diffusion has been refined over several decades of silicon wafer processing. In compound semiconductors, the analogous technology is applied, with considerations to the vapor pressures and toxicity of the group V species and their respective chemical derivatives. Herein, the substrates are patterned as required, loaded into a containment vessel or “boat” and placed within a high-temperature furnace usually surrounded by an inert gas flow. The entire system is thermally equilibrated, and the dopant gases are introduced into the furnace atmosphere. In deference to the high vapor pressure of the group V species, overpressures of arsine, phosphine, or similar gases, may be employed to prevent dissociation of the substrate material during the process cycle. Similar methods may be employed for II-VI materials as well. These gases and the by-products of the dopant species (for example, silane, disilane, diethylzinc, dimethylmagnesium, carbon tetrachloride, etc.) are highly flammable or toxic, and must be handled in an environmentally safe manner. This requires extensive exhaust handling and safety equipment,

51 1

but does not impede the implementation and operation of these processes. The advantage of diffusion processes is that very shallow layers can be created in the surface region. These procedures are also supported by decades of experience from silicon processing, and thus are well established, “high-volume” manufacturing processes. Although the diffusivity of impurities in the compound semiconductors is relatively small at epitaxial growth temperatures, or at annealing or “drive-in” temperatures, diffusion can be significant particularly for most acceptor-type species (as noted above). The driving force is the impurity gradient, enhanced or retarded by strain, dislocations, and other sources of free energy. Defects can greately enhance the motion through the lattice by providing open sites for the impurities (Shewmon, 1973; Tuck, 1988). Therefore care must be taken in the diffusion doping process to ensure that the near-surface region is properly prepared and free of contaminants. Owing to the high vapor pressure of most of the groups V and VI elements, the surface may become nonstoichiometric during the process through the loss of arsenic or phosphorus, and create defects which enhance impurity migration. The overpressure of As, or P, is provided in the system to mitigate decomposition of the surface, as previously noted. Diffusion methods are principally used for p-type doping due to the rapid diffusivity of these species (Gosele and Moorhead, 1981; Wada et al., 1989; Tuck, 1988; Yuan et al., 1983); n-type impurities move relatively slowly. The diffusivities for various impurities in GaAs, InP, and other compound semiconductors are provided in Sze (1981, p. 68) and EMIS (1990, 1991). One other feature of most of the acceptor species mentioned above is their propensity for behaving as both an interstitial and a substitu-

51 2


tional diffuser. This creates the double diffusion front shown in Fig. 10-10, due to the more rapid diffusion of interstitial species relative to substitutional behavior (Gosele and Moorhead, 1981; Tuck, 1988, Chap. 4). As a result the electrical depth of the junction is difficult to control in diffusion processing. Three significant drawbacks to the use of diffusion doping in compound semiconductors are: 1) the lack of a stable native passivating oxide, unlike Si02 on Si, 2) the melting points of the compounds are, in general, much lower than that of silicon, and 3) the vapor pressure of the groups 11, V, and VI species are very large at high temperatures which prevents, or complicates, processing above -3OO"C-6OO"C. Since the compound materials do not have stable native oxides, a dielectric film

must be applied to protect the wafer from undesired in-diffusion and to maintain surface integrity. The dielectric films of choice are Si,N,, SiO,, and the mixed "oxy-nitride" films, SiN,O, . To selectively dope the substrate, this film must be patterned appropriately. Due to the lower melting points of the compound semiconductors relative to silicon, these materials are subject to the creation of defects at lower temperatures. This phenomenon can radically alter the indiffusion behavior and electrical activity (site selection). Coupled with the high vapor pressures of the groups 11, V, and VI species, the diffusion must be carried out at relatively low temperatures to ameliorate decomposition and defect formation. This compromise entails extending the diffusion time to achieve the necessary time-temperature product. The protective film may be

"Double Diffusion Front" Behavior

Interstitial Impurity (Rapid Diffusion)

Substitutional Impurity Log (Concentration)

Distance into Semiconductor

Figure 10-10. Schematic diagram of a double diffusion front impurity profile (cf. Fig. 10-4). The net impurity profile results from the sum of the interstitial and substitutional impurity distributions. The electrical activity depends on the activation of these two components and any autocompensation due to site occupancy of the impurities in the host.


removed after the diffusion step to prevent further contamination or allow patterning in subsequent processes. Owing to the difficulties in carrying out diffusion-type processes, these methods have been supplanted by ion implantation and epitaxy. Further discussion of diffusion processes is presented in Sec. 10.4.

10.2.3 Epitaxial Methods In the epitaxial growth processes metalorganic chemical vapor deposition (MOCVD/ MOVPE), vapor phase epitaxy (VPE), liquid phase epitaxy (LPE), and molecular beam epitaxy (MBE), or gas-source/chemical beam epitaxy (GSE or CBE), the dopant species are normally incorporated during the deposition of the epitaxial layers. Group IV, group I1 transition elements, and group VI impurity species (as noted previously) are added to the melt in LPE, the gas phase in MOCVD and VPE, or effused from a Knudsen-typ cell or gas injector (MBE, and CBE/GSB respectively). In GaAs-based materials, the groups IV and VI elements act as n-type (donor) species, with the exception of carbon which acts as an acceptor, and Ge which exhibits a high degree of amphoterism. The group I1 elements are acceptors MBE crystal growth methods are covered in detail by Parker (1985), and MOCVD is discussed by Stringfellow (1989). See Chaps. 2 and 3 of this Volume for an additional discussion of these crystal growth methods. The range of doping concentration depends strongly on the nature of the impurity species, the purity of the sources, the chemistry of the growth process, the growth velocity, and the growth temperature. These parameters generally determine the background carrier concentration, which sets the lower limits of intentional doping. The thermodynamics of the multi-component system (i.e., solid solubility, ionic interactions,

513

misfit strain, point defects, etc.) limits the maximum atom concentrations. In this sense, the epitaxial layers generally achieve somewhat lower carrier concentrations than those of ion implantation processes since the latter approach is not tied so closely to the thermodynamics of the process. Donor concentrations in epitaxially grown material typically range from less than 5x 1015 cm-3 to greater than 5 ~ 1 0 ’ ~ c m - ~ . Acceptor concentrations are nominally in the - ~greater than 1019 range 5 - 10 x 10’’ ~ r n to crnp3.For HBT devices hole concentrations of > lo2’ cmP3have been created with carbon doping, although the use of the term “impurity” might be better replaced by “alloy component” at these levels. It should be noted that this is a doping tour-de-force since the electrical and physical properties of the GaAs degrade markedly for concentrations of carbon above -5x 1019cmP3 (George et al., 1991). The minimum concentrations are highly dependent on the growth apparatus as the background impurity concentrations and native defect structures in the epitaxial layers determine the minimum detectable change in the doping level. Recently, using gas-source epitaxial (GSMBE) methods, carbon concentrations above 1020cm-3 have been realized in GaAs (Abernathy et al., 1989), although the same caveats exist for high doping levels independent of the crystal growth method. Epitaxial growth processes provide significantly better control of the depth distribution of impurities than ion implantation, but, until recently, have had limited selected-area control capabilities. CBE/GSMBE methods are actively being explored for selected area growth (Tu, 1995; Shiralagi et al., 1996). The issues which limit the selected area growth are nucleation and growth phenomena and contamination in the patterned areas, as well as control of the growth rates on the various crystal planes exposed by the

514


process of ion implantation is of relatively low cost compared to epitaxial layer growth. This cost saving is due to a high wafer throughput relative to all other methods of creating an active layer, which is a significant point for fabrication costs. Also, the uniformity and reproducibility are adequate for most applications, the trade-off coming in the ability to create the tightly-controlled charge distributions required for ultra-high performance devices. However, as high volumes of epitaxial materials are being consumed and manufacturers add epitaxy capabilities, the material prices are falling, so reducing the offset in the final manufactured costs. The performance of epitaxy-based devices is typically far superior to that realized in ion implanted devices for a given set of design rules and circuit configuration. The performance advantage and yield improvements offered by epitaxial materials easily offset the higher costs of processing epitaxial materials for a number of applications. Furthermore, epitaxy-based heterostructures such as HBT, HEMT, VCSEL,

patterning. Recent advances in MOCVD have also shown some capability for controlled selective area growth (Linden, 1991). As was shown in Fig. 10-7, the device transfer characteristics are significantly better for epitaxy-based devices than for ion implanted structures. This is due to the tightly controlled charge distribution in a heterostructure device. Sidegating and backgating are also better controlled in heterostructure devices, as the charge distribution is readily isolated by etching or ion implantation processes. This latter point is illustrated in Fig. 10- l l . Principally, the performance improvements come from the significant differences in the charge distributions, the ability to isolate devices (interaction of the chemical species as well as damage), the creation of atomic displacement damage, and the interaction of the substrate and the charge distribution during device operation [see D’Avanzo (1982), Vuong et al. (1990)l. When doping compound semiconductors, many factors must be considered. The

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-

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Figure 10-11. Experimental results of sidegating effects in heterostructure FET devices.With optimized isolation at the device periphery, very large potential differences may be applied to adjacent devices with small interdevice spacing. The sidegating effect in devices that received a shallow isolation implant (dashed lines) relative to those devices that received an additional deep isolation implant (solid lines), within the same wafer. The y-axis is defined by 100 [ ~ d s ( v ~ s ) / ~ d s ( v ~ ~ = O ) ] , the x-axis is the voltage applied to a side-gate contact at the distances noted in the figure. Sidegating effects are mitigated to agreat degree with the deep isolation implant. [Figure from Vuong et al. (1990).] 0 1990 IEEE.

10.3 Isolation Methods

and others cannot be fabricated by ion implantation or any other methods. Additionally, it has been argued recently that the cost of producing a GaAs die on 150 mm substrates is substantially less than the cost of producing BiCMOS (silicon) devices on 200 mm substrates (Tomasetta, 1998).

10.3 Isolation Methods Electrical isolation is required to prevent interaction between devices in an integrated circuit. The objective is to limit or eliminate interdevice current flows and electric field effects to levels below those which affect the device operation. Circuit parasitics may be reduced by proper application of isolation techniques so that higher performance may be realized. Capacitances, inductive coupling, and leakage currents can be mitigated by appropriate isolation practices. In addition, electrons and/or holes may be better confined within the transistor cell. The use of isolation leads to more reproducible electrical characteristics, better control of the charge distribution in active devices, and similar control over the electrical characteristics of passive components such as resistors, inductors, and capacitors. There are two principal approaches to isolating devices in a compound semiconductor integrated circuit: ion implantation and “mesa” or “trench” etching. Each

‘Etched Mesa’

I-

515

method has its own advantages and drawbacks. Mesa/ trench isolation was developed first, and involves removing material to create an island or moat around the device. This approach can create substantial topological relief, which may complicate further wafer processing steps. As substrate material quality and device fabrication processes have improved, ion implantation has become the method of choice for isolation. Implantation permits a desirable planar morphology and the creation of finer device geometries which are needed in order to fabricate high density circuits with high yields and reliability. However, effective isolation of very shallow, or highly doped, layers often proves difficult in practice due to the Gaussian distribution of the ion implantation process. Implanting through photoresist or other capping layers can circumvent this problem by placing the peak of the ion distribution in the near-surface region.

10.3.1 Mesa Etching Mesa or trench isolation is an effective method for isolating discrete devices and active regions in integrated circuits. The technique involves defining regions surrounding the active devices with a photoresist layer or other masking materials, and subsequently etching away the exposed material to form isolated islands or “mesas” in the surface (Fig. 10-12). The etching can be Drain

Swrce _._ ..

“EtchedMesa’

/

Substrate

-l

Figure 10-12. An illustration of an n-channel FET isolated by an etched mesa process. The areas between adjacent devices may be ion-implanted or covered with a passivation layer to further enhance the isolation.

51 6


carried out using “wet” or “dry” chemistry methods (see Sec. 10.5 and Chap. 6 of this Volume). Mesa etching generally relates to a large low aspect ratio structure, whereas trench isolation refers to a high aspect ratio structure. A key requirement of the mesa definition process is to produce a morphology that is compatible with any subsequent processing steps. Excessively deep trenches, reentrant edges, or sharply sloped side walls will impair the creation of fine features, and may give rise to poor or nonexistent coverage of subsequent metal layers or dielectrics. Smooth features and rounded or gentle tran-

sitions at step-edges are generally preferred. Some of the key features of mesa isolation are illustrated in Fig. 10-13. If the trenches or mesas are incorrectly formed, as shown in Fig. 10-13 a, metallization layers and dielectrics will not deposit properly, leading to device failures (e.g., short or open circuits, leakage paths). Mesa-type structures such as those illustrated in Fig. 10-13b are desirable. The anisotropy of compound semiconductor materials becomes evident in the morphology created by the interaction of the etchant and the crystal structure, as shown in Fig. 10-14. Thus it is imperative to under-

Deposited S i SiQ& or SiO, Passivation

-

Thin or insufficierIt

Severely Undercut Mesa Semi-insulating Substrate

Semi-insulating Substrate

Figure 10-13. Cross section of an FET with mesa isolation. I n (a) the mesa is undercut excessively. Dielectric coverage and integrity are compromised. In (b) the mesa edges are optimally formed and the dielectric coverage is uniform.


Direction

51 7

GaAs Substrate

Direction

t

Direction

Direction

GaAs Substrate

I stand and control the etching process to produce the desired mesa or trench configuration. Etching characteristics, substrate crystallographic properties, and device implications were discussed, for example, by Lee (1982). Etch stop technology, as implemented in epitaxial materials, can be used very effectively to assist in the formation of isolation structures. An effective etch stop layer can provide precise location of the mesa ledge or trench bottom resulting from arresting the etch process, and provide extremely robust processes, for example, greater than 10000 to 1 selectivity in the InGaP-GaAs system (Ren et al., 1995). The ability to force the etchant into very fine features, i.e., liquid surface tension or gas pressure/density effects, limits the minimum spacing between devices and features. Similarly, to remove the reaction products or to dilute the etchant and arrest the etching process is particularly difficult for high aspect ratio, or closely spaced, features. (Details of etching chemistries and

I

Figure 10-14. Anisotropy of GaAs as revealed by chemical etchants. The limiting crystal planes are of { 111 } type, with arsenic or gallium planes exposed. This results from the nature of the zincblende crystal structure.

processes are presented in Sec. 10.5) As a result, devices must be separated to accommodate these process limitations at the expense of valuable semiconductor area. Thus the packing density and the integration level of the circuit are generally more limited when mesa isolation is used as opposed to ion implantation processes. Redeposition of the host materials or masking materials may occur during the etching process, which may inhibit the formation of well-controlled mesa morphologies, creating curved or corrugated surfaces, nonuniform mesa definition, leakage paths, etc. These effects must be avoided to successfully isolate devices with mesa technology.

10.3.2 Ion Implantation Isolation With ion implantation, the object is to render the material semi-insulating or highly resistive by the formation of deep levels and recombination centers resulting from the ion bombardment. Use of this

51 8


technique has the powerful advantage of maintaining surface planarity, which makes the definition of very fine features and multi-layer metallizations relatively straightforward. Thus better process integrity and greater complexity can be achieved with ion implantation as opposed to mesa etching methods. For successful isolation selection of the ion species, control of the ion flux, beam purity, and the ion energy are critical. The ion penetration depth is proportional to the ion energy, ion mass and host lattice atomic structure, molecular weights and composition. The concerns associated with ion implantation, as discussed in Sec. 10.2.1, are ion channeling, straggle, and tailing of the depth profile. However, for isolation processes it is usually desirable to extend the isolation as deeply into the substrate as possible, thus tailing may be a desirable feature

in this case, as shown in Fig. 10-15. The efficacy of the isolation is a function of the chemistry between the host and the implanted ions as well as the formation of defects. Some of the important ion implantation ranging data are summarized in Table 10-3 for a GaAs host crystal. Boron, hydrogen (protons), and oxygen are very effective species for ion implantation isolation. The isolation effect is created by the displacement of host-lattice atoms, the creation of a myriad of defect complexes, and the reactions of the host species with the implanted ions (e.g., A1-0 complexes in AlGaAs) (Donelly, 1981; Short and Pearton, 1988). Commonly used ions are oxygen, boron, and protons (H+) (Pearton et al., 1987; D’Avanzo, 1982). It is generally desirable to use heavier ions for the isolation implant, as greater atomic displacement occurs in the host. However, a significant com-

Figure 10-15. Ion implantation isolation schematic diagram. The peak of the ion range (R,) is the approximate position of maximum isolation. The displacement damage peak (maximum atomic displacement) will be some what shallower or deeper than R,, depending on the host and implanted species atomic numbers, the dose and the energy of the implantation. The approximate extent of the isolation is shown. Additional displacement occurs at the end-of-range, increasing the effective isolation depth.

51 9


Table 10-3. Ion-implantation ranging data for selected ion species in GaAs single crystal material Energy (keV)

20 50 100 150 200 300 380 a

Element H

B

C

0

Si

0.218/0.099 0.48010. 144 0.866/0.181 1.233/0.205 1.607/0.275 2.423/0.262 3.16U0.292

0.04410.034 0.124/0.070 0.255/0.115 0.382/0.145 0.504/0.170 0.733/0.207 0.905/0.229

0.039/0.030 0.10 1/0.060 0.208/0.098 0.313/0.125 0.41Y O . 147 0.606/0.182 0.75 U0.203

0.03010.022 0.07510.045 0.15410.076 0.233/0.100 0.3 16/0.121 0.462/0.152 0.567/0.172

0.018/0.013 0.04210.025 0.085/0.044 0.129/0.061 0.174/0.074 0.263/0.100 0.333/0.117

Gibbons et al. (1975); data are in micrometers; data are presented as depthlstandard deviation.

promise in the achievable depth arises for heavy ions at practical ion energies. Light ions, particularly protons, can be used for very deep isolation requirements if relatively high doses are required. The implanted ions may create a variety of atomic displacements in the crystal lattice. It is desirable to create defects which act as recombination centers to prevent or inhibit the transport of charge between devices. As mentioned in Sec. 10.2.1, these defects consist of atomic displacements, vacancies, interstitials, a variety of defect complexes, and antistructure (resulting from atomic site exchanges). Each defect alters the electrical characteristics of the host material, and in the aggregate serve to create the insulating regions between devices. At very high doses the lattice may be disordered to the point of amorphization. This can occur in GaAs at fluxes greater than lOI5 cm-* for oxygen or boron; protons require much larger doses (greater than 10l6~ m - ~“Softer” ). materials such as InP amorphize at slightly lower doses; hard materials like GaP or S i c require higher doses. Excessive damage can create a conductive region instead of insulating characteristics. In this case, extensive annealing may be required to recover the damage. It should be

noted that there are significant tradeoffs in the dose-energy relationships in the implantation process: simply increasing the dose or energy may actually enhance the interaction and leakage between devices, and also increase surface leakage due to excessive damage. The large density of states created with high dose implants may permit hopping conduction and tunneling processes for charge transport. A light dose implant may not create sufficient recombination centers to be effective; a low energy may create insufficient displacement damage or too shallow an isolation region (current flows underneath the isolation region). Each ion species has a unique “signature” in the isolation process. For example, B+ ions remove up to 200 electrons per ion when implanted into GaAs at 1 MeV (Davies et al., 1973). Oxygen ions, while less effective than B at removing electrons on a per-ion basis, have proven to be extremely effective at isolating GaAs and particularly AlAs or AlGaAs-containing structures (Favennec, 1976; Pearton et al., 1987; Short and Pearton, 1988; Ren et al., 1990). Oxygen produces a deep level in GaAs (Fig. 10-3, Sze, 1981, Chap. l), which captures electrons and may create a high resistivity characteristic with sufficient dose. In the Al-

520


GaAs material A1-0 complexes are formed which are highly effective recombination centers (Pearton et al., 1987; Short and Pearton, 1988). Protons are the ion of choice for deep isolation schemes (D’Avanzo, 1982). Being of low mass, the proton may be injected deep into the lattice even at modest energies, e.g., beyond 2 pm at an energy of 250 keV (Gibbons et al., 1975). It is interesting to note that the damage profiles do not generally coincide with the ion profiles due to the large mass differences between the host and most implanted species. This discrepancy is greater as the mass difference between the ion and the host atoms increases. Owing to the approximately Gaussian nature of the ion and damage distributions in the lattice, multiple implant se-

quences are generally needed to achieve a relatively smooth, total ion damage profile into the depth. This is illustrated in Fig. 10-16. When properly placed within the host lattice, multiple implants create a quasi-uniform, high resistivity volume in the implanted region. The drawback with the use of multiple implants is that the surface damage can be extensive, particularly at high doses or high energies, as well as extending process times and increasing macroscopic surface defect densities. The surface damage can lead to surface leakage paths or nonstoichiometric surface regions. For example, surface resistivity has been observed to fall by more than three orders of magnitude when very high energy isolation implants are carried out in GaAs (Liu et al., 1980).

Figure 10-16. Multiple implant isolation profile. In this case, ion implantation cycles are carried out at different energies. The deeper implants are performed at higher energies. End-of-range damage increases the isolation effectiveness and helps to smooth the net damage profile. With a large ion flux some amorphization or damage of the surface region may occur. A mild thermal anneal may be required to recover the crystal structure and stabilize the displacement damage profile without recovering the isolation effects.


One very powerful advantage of ion implanted isolation is that selected areas with complex geometries can be readily formed by patterned masking. Use of the selected area ion implantation methods for active region and isolation region formation allows for optimizing layout compaction and device isolation in the integrated circuit. To withstand very high energy ion bombardment, very thick blocking layers must be deposited on the surface, which can limit fine feature definition. Suitable ion blocks are thick photoresist layers, or photoresists with combinations of dielectrics or thin metals. Photoresist layers of 2-4 pm in thickness are typically employed to block 0, B, or H implants at energies of - 100 keV to -800 keV. With lighter ions, such as protons, the displacement of lattice atoms is significantly less than that obtained with heavy ions. Therefore the recovery of lattice disorder may occur with lower driving forces. For example, the damage created by H+implantation in GaAs anneals out at temperatures above about 400 “C. Protons create only small lattice displacements, and hydrogen diffuses rapidly out of the host leaving few electrically active defects (Pearton et al., 1990), The behavior puts significant constraints on processing temperatures and the viability of proton isolation for all but the lowest thermal budget processes. For most isolation processes a minimal thermal anneal is desirable, typically below -500°C for relatively short times. This “gentle” anneal prevents complete relaxation of the lattice, but eliminates some of the marginally stable atomic displacements and potential leakage paths while maintaining the high resistivity of the isolated region. On the other hand, for ion implantation doping it is necessary to anneal at temperatures in the range of 750 “C-900 “C to permit site selection by the impurities (activation) and

521

to remove electrically compensating displacement damage. This raises a conflict between the processes required to form the active layers and the need for isolation. For example, isolating underneath ohmic contact pads is not possible with present ion accelerator technologies. It should be noted that as the implantation process involves charged species interactions and significant energy is transferred to the lattice, the possibility of radiation damage and heating of the lattice during bombardment exists. The energy impinging on the wafer is of the order of hundreds of watts per square centimeter in a high-current implanter. If the wafer temperature rises above - 15O-20O0C, the effectiveness of the isolation process may be compromised as lattice displacements can anneal out during the implantation cycle. To minimize the self-heating, it is prudent to implant at the lowest practical beam current and ion energy, or control the substrate temperature during implantation. Electron bombardment can be used for isolation, but the damage created is subject to annealing out at very low temperatures. The annealing of electron-induced damage in GaAs has been observed to occur in two stages: 150-200°C and 200-300°C (Aukerman and Graft, 1967; Vook, 1964). This makes electron irradiation unsuitable for isolation as temperatures in wafer fabrication typically exceed these levels. Neutron damage is another method for isolating regions in compound semiconductors. The typical array of point defects and defect structures are produced by neutron irradiation. The damage induced by neutrons has been found to recover in two stages in a manner similar to electron-induced damage: at 200-300°C (minor displacements), and then recovers fully at 600-700°C (Lang, 1977). Thus the isolation created by neutron bombardment creates a stable isolation re-

522


gion only if processing temperatures are maintained below - 500°C. Beam blocking materials are generally transition metal layers in order to obtain sufficient stopping power for the neutron flux. One additional variation of ion implanted isolation is the creation of an isolation “box” for devices. For example, in devices utilizing n-type implants, a p-type implantation can be placed beneath the tail of the donor distribution. This buried-p layer creates a p-n junction isolation condition. By carefully selecting the dose and energy, the ptype layer can be nearly fully depleted, leading to minimal capacitance, a sharp n-type charge profile, and mitigation of short channel effects (Finchem et al., 1988; Matsunage et al., 1989; Onodera and Kithahara, 1989; Sadleret al., 1989). Typically, the buried p-type implant is used only under the channel region. However, it may be connected to an external bias to enhance the back-plane isolation with a depleted p-n

junction. An additional isolation implant or mesa processing may be used to create the “walls” of the box, thereby completely isolating each device, as illustrated in Fig. 10-17.

10.3.3 Sidegating and Backgating Sidegating and backgating are terms describing the interaction between devices in an integrated circuit laterally and from the back-plane region, respectively. These phenomena have plagued GaAs-based devices for many years (Vuong et al., 1990; D’Avanzo, 1982; Smith et al., 1988a; Lin et al., 1990), and arise from the electric fields induced in the material when the circuits are biased. The effects are realized as a modulation of the transistor channel current or the current flow in channel-resistors (Gray et al., 1990; D’Avanzo, 1982; Goto, 1988). The problems associated with sidegating and backgating are greatly influenced by the circuit layout, and, in particular, the spacing

Figure 10-17. A cross section schematic diagram of an FET isolated by ion implantation processing (or mesa etching). The device has a buried-p layer connected electrically to the low potential of the device. This addition serves to mitigate sidegating effects. The buried-p layer must be contacted through an additional p-type ion implantation adjacent to the nc contact implant (or diffusion). The gate is offset in the channel to reduce source resistance.


and differential voltages between nearby devices and the condition of the back-plane (biased or grounded). Additional phenomena in sidegating and backgating effects are the transient charging and discharging of deep states. Electric fields, such as those created in p-n junctions, implanted isolation regions, ohmic contacts, depletion regions (e.g., Schottky barriers), etc., all lead to exposure of the various deep level states (traps), relative to the Fermi level, which lie in the semiconductor energy gap as shown in Fig. 10-18 (see also Milnes, 1973, and Sze, 1981, Chap. 1). As the electric fields are altered first by biasing, then modulated during device operation, the deep traps charge and discharge as the bands bend. This leads to a secondary modulation of the charge transport in the devices, with response transients of sub-microseconds to minutes in duration, and strong temperature dependences.

Several competing processes may arise from these deep levels in or near active device regions: 1) charge domains may be launched from a source (anode) contact under moderately high electric field conditions, and 2) DC and AC electric fields may modulate the deep state charge conditions (Milnes, 1973). In GaAs, for example, charge domains may be created and injected from ohmic contacts when electric fields exceed 500 V cm-' to 1000 V cm-' between nearby devices (Ridley and Watkins, 1961; Ridley and Pratt, 1965; Kaminska et al., 1982). These charge domains travel through the semi-insulating substrate or buffer layer to the collecting contact (cathode or drain in a FET). The motion of these charge packets induces a time-varying electric field under the gate and thereby upsets the channel charge distribution causing a modulation of the device operating conditions (see, for example, Fujisaki and Matsunaga (1988)).

Semiconductor Surface Increasing reverse bias exposes additional deep states Emitted Charges (Deep Levels Empty)

@ 8 Fermi Level

523

/

-

Free charges may be recaptured by deep or shallow states ConductionBandEdge

------------

,

Shallow Donor Level

E3

N-type Semiconductor

Valence Band Edge

Figure 10-18. Schematic representation of the near-surface band bending in an n-type semiconductor. Shallow donors are partially ionized. Deep levels are occupied within 2 kTof the Fermi level, and filled below the Fermi level crossover points. When the state is lifted above E,, charges are emitted at rates proportional to their respective depths, the temperature, emission characteristics, and rate of band bending. The charges may be recaptured during relaxation processes and re-emitted, leading to an oscillatory condition.

-

524


In the case of field effects there are two main components. The DC contribution involves the equilibration of deep state capture and emission processes. This is typically a very slow process leading to long turn-on transients upon biasing, device latch-up, and an “improper” DC operating state. Depending on the material’s condition, these transients may be of the order of nanoseconds to minutes. The details of this quasi-equilibrium condition are affected by the operating temperature, and the temperature distribution in the device through the capture and emission rates and the concentrations of the deep states. The charge exchange processes can produce additional time constants in the temporal response as the device heats during operation. Localized anomalies may arise as different regions of the device may dissipate varying amounts of heat during operation. The AC effects are essentially resonances of the deep state capture and emission rates with the operating frequency of the devices. For example, in GaAs there are at least 20 known deep levels of electron- and hole-like characteristics in the energy gap (Martin et al., 1977). Thus, for a given temperature, electric field strength (biasing condition and voltage swings), active layer configuration, and circuit layout, a number of traps may be exposed within a device as shown in Fig. 1018. As the device changes state in response to an input, the trap exposure about the Fermi level is altered, and the emission or capture of charges by the trap(s) may be stimulated. This leads to the “resonance” condition. The electrical manifestations of deep levels may be observed as long time constant effects, impaired transient responses, “ringing” in the device characteristics, or an apparent lack of device gain (Lin et al., 1990; Vuong et al., 1990; Smith et al., 1988b). Similarly, the back-plane or substrate bias can modulate the channel charge distri-

bution in FETs through the electric field created between the back-plane and the channel, thus upsetting the threshold and current-carrying capability in the devices. Again, as the electric fields are modulated, the channel charge distribution responds with multiple time constants determined by the trapping behavior of the exposed deep levels, particularly those at the bufferinterface (epitaxial layers) or in the tailsubstrate of the implant profile. These effects are not subtle: sidegating and backgating phenomena, either static or dynamic, can lead to collapse of the transfer characteristics, or pinch-off resistors and transistors, as illustrated in Fig. 10-19. In extreme cases, sidegating can impact devices separated across an entire 3” (76 mm) wafer (Gray, 1989). The typical manifestations are devices operating well below expected performance levels, or the intermodulation effects as devices switch to different states and the electric fields are altered. These phenomena are well known and relatively well

SIDEGATE 2 yrn

-

8

4

-1.5

-0.5

-1.0 V,

0

0.5

(VOLT)

Figure 10-19. The effect of the sidegating voltage on I,, vs. Vgs in a depletion-mode HFET device. The sidegating potential is applied to a separate electrode separated 2 pm from the source of the test device. Note the strong effects of negative bias effectively depleting the channel charge and causing closure of the channel. Forward biasing the sidegate electrode has a negligible effect.

10.4 Diffusion

understood (D’Avanzo, 1982; Vuong et al., 1990; Smith et al., 1988a; Ridley and Watkins, 1961; Ridley and Pratt, 1965; Milnes, 1973). A highly effective method for isolation in GaAs devices has been discovered: a “lowtemperature buffer” (LTB) grown by MBE (Smith, 1988a). This approach capitalizes on the extensive defect structure created by epitaxial crystal growth at low temperature under strongly nonequilibrium growth conditions. The material produced by this process is nearly completely inactive, both electrically and optically (Kaminska et al., 1989). Smith et al., 1988b, has found that the DC isolation and DC sidegating immunity are greatly improved: negligible interactions are found for DC electric fields in excess of 10 kV cm-’. However, unless other measures are taken to displace device active regions well away from the LTB, the high-frequency performance of circuits fabricated on these buffer layers is drastically affected. It has been found that integrated devices operating at - 1 GHz, as fabricated with “standard” processing methods, are slowed to the kilohertz regime when constructed with the LTB structure without having sufficient isolation from the LTB (Lin et al., 1990). This effect was attributed to electron trap-related charge capture and emission with very long time constants. To circumvent these problems, a second relatively thick standard buffer layer must be grown on top of the LTB to minimize the effects on charge transport behavior in transistors (Smith et al., 1988aJ. Subsequently, the devices must be laterally isolated to prevent or mitigate the normal sidegating effects. “Low temperature” buffer layers have been greatly improved in the latter part of the 1990s, and are commonly used in epitaxy-based fabrication processes (Wang et al., 1997). The importance of controlling or eliminating interactions in compound semicon-

525

ductor-based devices continues to drive investigations into the trap-related, semi-insulating characteristics of GaAs and analogous effects in other III-V semiconductors. At the present time, there are methods for mitigating the sidegating and backgating effects, but it appears unlikely given the nature of the compound semiconductor materials and their defect structures, and the desirability of the semi-insulating behavior, that these problems will be totally eliminated.

10.4 Diffusion Diffusion and impurity redistribution are of great importance and consequence in device fabrication processes. Diffusion has been the subject of extensive investigation (Tuck, 1988). The intentional diffusion of impurities is required in numerous fabrication steps. Often, however, the diffusion of impurities and the interactions amongst the various materials present on, and in, the wafer are highly undesirable. As examples, p-n junctions generally become less abrupt and the electrical and physical (chemical) junctions may shift when the impurity species diffuse, or when mixed chemical species interdiffuse, such as with a GaAs : AlGaAs heterointerface. In heterostructure bipolar transistor (HBT) structures, the “misalignment” of the electrical and physical junctions strongly compromises the device electrical characteristics and device performance (Ali and Gupta, 1991). Rapid in-diffusion of gold in an ohmic contact region may cause device failure via punch-through (“spiking”) or lateral migration (Zeng and Chung, 1982). Silicon donor redistribution in HFET devices will alter the channel charge distribution, shift the device threshold voltage, the transconductance (gm), and affect the current carrying ability of the

526


channel (see Daembkes, 1991 and references therein, and Schubert, 1990). The diffusion behavior is characterized by a parameter known as the diffusion coefficient, and is controlled principally by the chemical potentials of the host and impurity atoms in the lattice, and the impurity concentration distribution(s). Defects, such as vacancies, interstitials, impurities, and the relative physical sizes of the host lattice atoms and the impurity, the bond strengths and the dimensions of the lattice interstices all affect the atomic mobilities and the diffusivity of the impurity atoms. Diffusion processes are mathematically represented by several empirical relationships known as Fick’s laws. The first of these laws considers the flux of a diffusing species (in one dimension), J, through a plane in a direction x, at any time (t): J=-D($

t

(10-1)

where C is the concentration, dC/dx is the concentration gradient, and D is the diffusivity. Equation (10- 1) describes the driving force behind diffusion: a concentration gradient, i.e., a chemical potential difference which, from thermodynamic arguments, must become negligible as the system reaches equilibrium. Equation (10- 1) is illustrated schematically in Fig. 10-20. The relative ease with which a given species moves in the lattice is embodied in the magnitude of the diffusivity. Fick’s second law relates the change of the concentration profile with time [taking the derivative of Eq. (10-l)] dC- d dt dx

( 10-2)

Equation (10-2) describes 1) how rapidly the material will redistribute in the host lattice, and 2) the concentration profile as a

I

Substitutional Impurity erfc behavior

Characterized by:

\

\

Distance into Semiconductor

Figure 10-20. Schematic diagram of a “erfc” diffusion profile, represented by a single-value diffusion coefficient, Do, and a unique activation energy, E,; k and T have their usual meanings.

function of time and distance. Using the grad operator, Eqs. (10-1) and (10-2) may be extended to accommodate the real threedimensional behavior of the diffusion process in the crystal lattice. Implicit in these descriptions is the temperature sensitivity of the diffusion process, which is accounted for in the diffusivity. The diffusivity is defined as D = Do exp ( - E J k T )

(10-3)

where Do is the diffusion constant, E, is the activation energy for the diffusion process, k is the Boltzmann constant, and T is the temperature (K). In addition, the diffusivity of an impurity is sometimes dependent on the concentration, typically being enhanced at higher concentrations. Therefore to realize a high degree of stability against elevated temperature processing, it is desirable that an impurity species have a large activation energy, a small diffusion constant (see, for example, Tuck, 1988 or Shewmon, 1963, and be present in reasonably low concentra-

527

10.4 Diffusion

tions (- 100 ppb to 100 ppm) to minimize impurity -impurity interactions in the lattice. The segregation coefficient k for an impurity species is a measure of the tolerance of the host lattice for the impurity atom. It is defined from solidification processes as the ratio of the concentration of the impurity incorporated into the solid relative to that in the liquid phase during crystal growth. With respect to the solid state, the segregation coefficient can be interpreted in terms of the additional driving force for diffusion: A small value of k implies a relatively large energy for redistributing the impurity in the host. In compound semiconductors most impurities have segregation coefficient values of less than one which represent an additional driving force for the out-diffusion behavior. The crystal lattice is distorted by the presence of the impurity atoms due to size and/or the chemical incompatibility. The extra energy available tends to drive the impurity species from the lattice. The free surfaces, or those surfaces and interfaces under strain due to mismatched physical properties (e.g., heterostructures, dielectric layers, metals, etc.), will also provide added energy for diffusion, and may act as sinks for the diffusing species. Also, the solid solubility limit places an upper limit on stable concentrations of impurities in the lattice: concentration above this level will increase the driving force for redistribution, precipitation, size exchange processes, and electrical compensation. In GaAs it has been observed that the diffusivities of the groups IV and VI donor type species are generally small, whereas the group I1 acceptor species tend to diffuse much more rapidly. Carbon, a group IV acceptor, is a notable exception, being extremely stable in most compound semiconductor lattices (Schubert, 1990; Schubert et al., 1990).

Two additional concerns for the processing of compound materials at elevated temperatures are the increased vibration frequency of the lattice atoms and the dissociation of the compound semiconductor material. The motion of the atoms in a compound semiconductor lattice can create a variety of electrically active point defects (Hurle, 1977; Van Vechten, 1975), and diffusion may cause an undesirable redistribution of the impurity atoms. As a result, the electrical properties of the material may be altered in an uncontrollable manner. For the compound semiconductor materials GaAs and InP, the dissociation rate is significant for temperatures above 600°C and 475 “C, respectively (Panish, 1974), and similarly for GaP and some 11-VI compounds. This is due to the high partial pressure of the group V (or group VI) species over the host material, as illustrated in Fig. 10-21 [after Thurmond (1965)l. The key point in this figure is the region around the congruent decomposition pressure. By controlling partial pressures of the various species the decomposition may be suppressed. Without some mechanism for protecting the surface region during high temperature processing, either with a cap layer or an overpressure of the group V species, the surface rapidly decomposes creating a metal-rich surface, enhanced dissolution of the surface layers, and destruction of the semiconducting properties. It is therefore critical to maintain a minimalistic approach to the thermal processing of most compound semiconductor materials. RTA (rapid thermal annealing) cycles or “low thermal budget” (i.e., lowest possible temperatures and minimal times) processing are needed to maintain the impurity profile and materials integrity in the near-surface region. For successful device fabrication, knowledge of the stability of the donor and acceptor species in the lattice is critical. The dif-

-

-

528


1200 1100 loo0 I

900

I

10“/T,

I

800 I

“C

IK

Figure 10-21. The equilibrium vapor pressure (in atm.) of As, Ga, As, and As, over GaAs as a function of lo4 T’. The total arsenic pressure (referred to As,) is approximately 1 atm. (lo5 Nm-*) at the melting point, 1238 “C. [Reproduced from Thurmond (1965). Reprinted with permission. 0 1965, Pergamon Press.]

fusion coefficient values for most usable impurities are in the range of lop3- lop6 cm2 s-l at the temperatures used for epitaxial crystal growth, ion implantation annealing, and wafer processing, and thus most species move quite rapidly in the lattice (Tuck, 1988, Chaps. 4,5; Shewmon, 1963). For example, one advantage of an epitaxial-grown MESFET device process sequence is the ability to minimize the thermal budget, leading to a limited redistribution of the donor impurities. In contrast, in a similar ion-implanted MESFET process, the thermal budget and maximum temperatures are extremely critical to the impurity distributions and activation. The resulting charge distribution, and the final device characteristics

are greatly affected by processing times of the order of seconds or tens of degrees, particularly for the ultra-thin, ion-implanted structures required for high-speed or low noise operation. On the other hand, high-temperature furnace or rapid thermal annealing of selfaligned MESFET and HFET devices is necessary and readily accomplished when refractory gate metals are used. The limited reactivity and stability of the refractory metals with most compound semiconductors permits the temperature to be raised above 800°C (for GaAs) sufficient to anneal the ion implantation damage, restore the lattice disorder, and activate the implanted species (Dautremont-Smith et al., 1990; Yamasaki et al., 1982; Shimura et al., 1992). At the same time, the impurities which provide charge to the channel may diffuse large distances (tens of nanometers), leading to uncontrolled device characteristics and poor performance, emphasizing the need for strict control and understanding of the timetemperature cycle impact. In other processes, if ion implantation is not used for doping, substantially lower thermal budgets may be used. Si redistribution during annealing processes was investigated in GaAs/AlGaAs heterostructure (HFET) materials (Schubert et al., 1988, 1990). It was found that the diffusivity of silicon was roughly ten times higher in AlGaAs than GaAs at 800°C. This places significant constraints on the device structures, particularly for HFET devices which may incorporate a “setback” (intentional spacing of the impurity species away from the channel region) to keep the ionized donors separated from the electrons that reside in the potential well (Sequeria et al., 1990; Baret al., 1993; Danzilioet al., 1992). In a typical annealing cycle the Si atoms may diffuse more then 5 - 15 nm, thereby placing a significant fraction of the Si atoms

10.4 Diffusion

in the channel region. This phenomenon will be realized as a reduced electron mobility and somewhat impaired electrical performance. One of the anomalies in the diffusion behavior of most acceptor species in compound semiconductors is the double diffusion front (Tuck, 1988; Gosele and Moorhead, 1981). In this case the impurity appears to have at least two distinct values for the diffusivity. These phenomena have been explained in terms of interstitialcy and substitutionality of the diffusing species. Interstitials have significantly lower activation energies for motion in the lattice, and therefore larger diffusion coefficients since there is no requirement for atomic site-exchange to allow motion within the crystal lattice (Gosele and Moorhead, 1981; Small et al., 1982). The interstitial atoms may therefore move very rapidly in the host material. The substitutional impurity, on the other hand, requires the presence of a vacancy or the exchange of adjacent lattice atoms to permit motion of the impurity. Such an exchange process requires the addition of significant amounts of energy, and the cooperative motion of several atoms. The activation energy for such a process is relatively large, the probability of site exchange is small, and the substitutional diffusion process is slow. The double diffusion behavior is illustrated in Fig. 10-22 for zinc in GaAs (after Tuck, 1988~).It is clear that there are at least two mechanisms operating in this case, with significant differences in diffusivity values as well as the relative concentrations of interstitial and substitutional impurities. Several investigations have been carried out to understand the behavior of anomalous diffusers such as Mg, Zn, and Be (Small et al., 1982; Cunnel and Gooch, 1960; Gosele and Moorhead, 1981). At the present time, although the mechanisms for explaining the double diffusion from behavior are well-ac-

529

Depth (pm)

Figure 10-22. Experimental diffusion profiles for zinc in GaAs at 1000°C. A, B, C, and D represent the zinc concentration profiles after 10 min, 90 min, 3 h, and 9 h, respectively. Note the two unique regions for the concentration profiles in each case. [Reproduced from Tuck (1988). Reprinted by permission of Adam Hilger/ IOP, 0 1988.1 Note: Ordinate axis label corrected from the original publication.

cepted, the precise understanding of the processes by which the species simultaneously select both types of diffusion paths has yet to be elucidated. As device processing continues to improve, more stable species, such as carbon, are being utilized for acceptor doping. However, carbon is not a panacea as the effectiveness for doping in a number of ternary and quarternary compound semiconductors is very limited. As mentioned above uncontrolled impurity redistribution can seriously affect device performance. These effects are often seen in one of the moore promising device structures, i.e., the heterostructure bipolar transistor (HBT) based on GaAdAlGaAs epitaxy (Ali and Gupta, 1991). Owing to “band gap engineering” (Capasso, 1987,1990) and the properties of GaAs-based and InP-based ternary compounds, an HBT device in these

530


It has been observed that the Be atoms redistribute so significantly in the lattice that this method of doping the p-base region is essentially impractical for use in controlled, reproducible HBT fabrication (Miller and Asbeck, 1985). Streit et al., (1992) claim to have solved the Be redistribution-related degradation problem by controlling certain growth parameters in the MBE growth of HBT structures, although these devices were operated at modest performance levels (Streit et al., 1992). Other p-type transition-metal species also behave in a manner similar to beryllium, but are not generally utilized for this reason. Accelerated device aging tests showed that Be doped base HBTs can be relatively stable to self-diffusion failure mechanisms under low to medium power conditions, as shown in Fig. 10-23 (Yamada et al., 1994). They found failures (under accelerated aging conditions) occurring at - 300 h, 230°C and an apparent activation energy of - 1.4 eV, which translated to projected operating lifetimes of - lo6lo7 h at a junction temperature of 125°C. Carbon, however, has been found to be very stable in compound semiconductor crystal lattices, and therefore appears to be the practical alternative for p-type doping in

materials is capable of switching in the hundreds of gigahertz, many times faster than the fastest silicon-based counterpart (Nubling et al., 1989; Nottenberg et al., 1989). Many of these HBT devices have been fabricated in MBE-grown epitaxial materials, using Be for the base dopant species (Kim et al., 1988; Miller and Asbeck, 1985; Streit, 1992). Investigations into the performance of Be doped base HBTs and the fundamental processes of diffusion of beryllium in GaAs have shown that this impurity diffuses extremely rapidly (Hafizi et al., 1990). This poses a difficult problem for the crystal grower and the process engineer, as significant impurity redistribution can occur during crystal growth. During even modest thermal processing, and subsequently during the device operation rapid diffusers can move in the crystal lattice, the latter effect being induced by elevated junction operating temperatures and the extremely high electric fields in the devices (Ali and Gupta, 1991). As a result of the Be redistribution at the emitter-base junction, the p-n junctions shift in an uncontrolled manner rendering the materials unsuitable for device applications (Hafizi et al., 1990; Yin et al., 1990).

0

-30

-60

5 -90

-2E 0

> 4

-120

Ta = 215°C f = 0.475 GHdPin = -30 dBm

-150

-240

I

0

I

--o- 215"C/no bias (hot control) -c25"Cho bias (control)

I

100

200

I

300

I

400

I

I ' I I 500 600 700

Stress Time (Hour)

I

800 900

Figure 10-23. A plot of the change in output voltage of a HBT-based circuit as a function of stressing time at 215°C. Parts which have not been subjected to current stress are shown as open circles and open squares. Parts which have been biased are shown as closed circles. At 2 1 5 ° C the output of the circuit degrades substantially up to 800 h. This indicates a change in the bases emitter junction, or a modification of the emitter contact resistance due to impurity diffusion. (Reproduced from Yamada et al. (1994). Reprinted with permission. 0 1994 IEEE.)

10.5 Etching Techniques

many III-V materials (Abernathy et al., 1989; Maliketal., 1989; Quinn, 1992- 1993).Carbon may be introduced into the lattice by ion implantation or during crystal growth when carried out with techniques such as metal-organic chemical vapor deposition (MOCVD) or gas-based molecular beam epitaxy methods (chemical beam epitaxy CBE or gas-source molecular beam epitaxy - GSMBE) (Abernathy et al., 1989; George et al., 1991). Several solid-phase carbon sources have been fabricated and used in standard MBE crystal growth (EPIKhorus, 1994;Maliket al., 1989).Holeconcentrations in HBT base layers exceeding lo2’ cm-3 have been realized without apparent problems with diffusion and redistribution. However, a significant lattice contraction occurs at these high carbon concentrations (above 3-5x 1019cmU3,George et al., 1991), with strong reductions in the hole mobility due to scattering events (Quinn, 1992- 1993). The formation of large numbers of line defects in base regions for these high carbon concentrations raises significant questions of long-term device reliability. Owing to the issues outlined in this section, there are only a limited number of solely diffusion-based processes remaining in compound semiconductor technology. For example, the JFET fabrication sequences are hybrid processes using diffusion of the p-type species to create the junction or highly doped p-contact region in an n-type material formed by epitaxy or ion implantation (Zuleeg et al., 1984, 1990; Wada et al., 1989). These diffusion processes are similar to those employed in silicon-based process sequences with the notable exception that they require very sensitive control of the process conditions. This is due to the large diffusivity of zinc or beryllium acceptor species, and the need to prevent dissociation of the host material due to the high vapor pressure of the group V elements.

-

531

The concern for rapid diffusivities arises also when considering reliability issues significant redistribution of any impurities or defects in the active regions of the devices will degrade performance and lead to field failures (Hafizi et al., 1990; GaAs IC 1992, 1993a). This has been observed in HBT devices, for example, where the performance characteristics decay rapidly as the device is operated under moderate to high stress conditions (Yamada et al., 1994). As previously, noted, the deterioration has been assigned to the redistribution of beryllium atoms in the base region of the device caused by thermal and electric field-aided drift of beryllium ions (Miller and Asbeck, 1985; Hafizi et al., 1990)

10.5 Etching Techniques Material removal may be carried out by “wet” chemistry, or by “dry” (vapor or plasmdsputtering) techniques. Etching processes can be used to delineate the features of active and passive devices, form electrical contacts, gate recesses, and vias, and create isolation trenches. The most critical issue is the ability to create an etched feature which has an optimal morphology compatible with the subsequent processing steps. The choice of wet or dry chemical etching methods depends upon the processing sequence, the required degree of etching control, the materials compatibility, and the availability of a suitable etchant for the target material. In addition, the etchant must not affect the masking or etch stop materials, and the other materials exposed during the etching process. Additional considerations are the control of undercutting of the mask layer (dimensional variation), the creation of anisotropic features, and the permissible process latitude.

532


Various etchants and methods may be used in the process sequence for defining device features or general etching processes. Anisotropy and materials selectivity are critical and very useful features of etchants and the different etching processes. The crystallographic sensitivity of the etching chemistry can be utilized to form selectively sloped side walls for smooth metal coverage or to create a controlled undercut to prevent metal continuity where desired (see Sec. 10.9, liftoff processes). At the same time, the undercutting of photoresist layers or other masking materials by lateral dissolution of the semiconductor, dielectric layers, or metals can give rise to very undesirable expansion or contraction of etched features. Reaction products are important in all aspects of etching, in both wet or dry methods. Such by-products may impede contact between the etchant species and the surface atoms. They can lead to anisotropic effects resulting from build-up on the various exposed crystallographic planes, or block the etching process entirely. Bonding of the reaction products to the surface may further alter the etching characteristics. In wet processes continual solvation of the reaction products into the solution alters the pH and therefore the chemical activity and the etching rates. In a similar manner, with dry etching, the poisoning of the plasma by reacted species may drastically alter the effectiveness of the etching process. Thus it is important to ensure adequate chemical flows in either wet or dry processes. The understanding of all of these competing effects is a critical element in developing a viable, controlled, and reproducible etching process. For both dry and wet etching processes, the main limitation (in typical compound semiconductor (CS) processing sequences) is the inability to readily etch gold, which is one of the principal metals in CS device fabrication. However, ion milling or liftoff pro-

cesses produce excellent results in gold metallizations, even with very fine geometries. It should be noted that significant efforts have been directed to creating aluminumbased metallization schemes for interconnects (Vitesse, 1990, 1995), and the use of titanium or tungsten-based metals to overcome the limitations of the liftoff processes needed for gold metallizations (GaAs IC, 1993b, Dautremont-Smith et al., 1990). Reactive ion etching or sputtering may also be used for the etching of various layers during processing. In this case, the rate(s) of sputtering the desired material(s) relative to that of the masking material(s) is crucial to the success of the process (Melliar-Smith and Mogab, 1978; Chapman, 1980). The chemical anisotropy of the compound semiconductor materials plays an important role in the formation of etched structures. The shape of an etched feature may be strongly influenced by the polar nature of the zincblende-type lattice and the anisotropic behavior of the etchant. For GaAs, anisotropic effects are further complicated by the existence of two standards for the substrate orientation. These two options are denoted “SEMI US” (wedge) and “SEMI E/J” (dovetail) (SEMI Standards, 1989). Both of these specifications adhere to the same electrical and physical characteristics as the SEMI standards, but they are rotated 90” about the (100) with respect to each other as shown in Fig. 10-24. As a result, the same chemical etchant may produce different (rotated 90°) etching features in the two wafer configurations. Thus, it is critical to understand the interactions of an etchant with the surface layers to ensure the formation of a desired morphology.

10.5.1 Wet Etching To remove undesired material(s) from the surface region, solutions of appropriate


533

(C)

UOH ETCH PIT

OF WAFEP

Figure 10-24. Crystallographic representations of the two standard configurations for gallium arsenide substrates. The etch pit configurations for each orientation are shown in (b) and (d) and on the central part of the crystal plane image. The etching response of the crystal with respect to the central axis is illustrated by the relative positions of the “V-groove” and “dovetail” etch figures. (a) V-groove option (known as the US standard); ( c )dovetail option (known as the E/J standard). Note that the minor flats are 180” in opposition between the two orientations. (Figure courtesy of SEMI, Mt. View, CA, reprinted by permission.)

chemicals (acids or bases and diluents) may be used. The etchant solution must be constantly in contact with the target material, and must typically be stirred or sprayed onto the wafer surface to ensure the constant replenishment of the etchant at the surface and to remove by-product materials (Shaw, 1981; Stirland and Straughan, 1976; Iida and Ito, 1971; Mukherjee and Woodard, 1985). The effects of stirring are typically observed as significant increases in etching rates relative to stagnant solutions, as shown in Fig. 10.25. Without agitation or replenishment, the etchants may produce significant undesired topological changes in the surface. Some means of arresting the etching process rapidly and uniformly must be provided to neutralize the etchant and com-

pletely remove the reacted material(s) in order to ensure reproducibility and control. Wet etching occurs by an oxidation process followed by solvation of the reacted species. The etching solution generally contains both the oxidizer and a solvent, and the CS-oxide species and reactants are preferably readily soluble materials. A complexing or buffering agent may be added to stabilize the etchant chemistry, and deionized water is commonly used as the diluent. A key issue in wet etching control is the boundary layer at the interface between the solution and the semiconductor surface. The schematic representation of the boundary region is shown in Fig. 10-26. The boundary layer controls the etching process through the exchange rates of the oxida-

534


50

1000

I

0

v)

\

"5

20

I

I

-

-

30

40

Figure 10-25. Etch-rate dependence on temperature and forced convection. The (8: 1 : I ) , etchant is H,SO,-H,O,-H,O with an addition of 50 wt.% citric acid. The ratio of H,O, (30%)to 50 wt.% citric acid is 1 : 1 by volume ( k = 1 in the figure). It can be seen that the effects of stirring are dramatic, as is the importance of temperature and therefore temperature control of the etchant and the etching rate. [Reprinted from Howes and Morgan ( 1 985). Reproduced with permission. 0 1985 John Wiley and Sons, Ltd. Figure caption modified by author (original data after Iida and Ito (1975), and Otsubo et al. (1976).]

10 I

1

\

%

x@\

Solution

.\

Stirring

100-

k=1

0

c

0

Lz CE

.-c

5 W

c

l0-

'

O

w

stirring

\ O

1

I 3 .O

I

3.2

Diffusion Boundary

I

O \ I

3.4

I

Bulk Fluid

I

Substrate Material

3.6

Convective Transport

'

Diffusion Limited TransportRegion

I 1 I

Turbulent or Laminar flow

I I DlsrolvedSpeclua Into Solvent Bulk

I

I I

tion-dissolution cycle, i.e., the removal rate of the surface materials relative to the arrival rate of fresh reactants to the surface. For extremely critical etching processes such as gate etching (FETs) or the emitterbase junction (HBTs), a weak oxidizer may be applied first, followed by a solvent solution so as to remove only a very thin surface

Figure 10-26. Schematic representation of the region adjacent to a semiconductor interface during chemical etching. The diffusion boundary layer is the controlling region for the transport of species to, and out from, the interface. A similar diagram can be utilized for gas-phase chemistry, with varying mean-free-path lengths and very high convective velocities in the bulk gas phase.

layer rather than maintaining a constant etching process. Repetition of the process results in a step-wise approach to the final gate trough depth and shape. While timeconsuming, this approach can provide an extremely high level of control. Table 10-4 presents a number of liquid etchants suitable for compound semiconductor materials.


Table 10-4. Common etchant compositions for compound semiconductors. Chemical formulation

Ratio

Reference

NH40H : H 2 0 2: H 2 0

1 : 2 : 20 3:1:50

Shaw (1981) Gannon and Neuse ( 1974) Adachi and Oe (1 983) Shaw (1981) Adachi and Oe (1 983) Adachi and Oe (1983) Adachi and Oe (1 983) Mori and Watanabe (1978) Adachi and Oe (1983)

I :8:40 HCI : HNO,

H,PO,: H202:H 2 0

1.3

5 : 1 : 20

I :9: I Br - MeOH

1 : 100

Choice of a specific chemistry depends on the morphology and degree of control desired in the fabrication sequence. There the two basic limiting mechanisms in wet etching: diffusion-controlled and reaction-rate-limited processes. In the diffusion-controlled case, the transport of reactant to the interface and the transport of the reacted products away from the interface are moderated by the diffusion boundary layer. Material transport limits the etching rate as diffusion coefficients in liquids are typically in the range of cm2 s-I. Therefore it may take a significant time for materials to reach the bulk liquid where convective flows (- cm s-I velocities) dominate. Additionally, there may also be an “incubation period” for etching initiation, i.e., the time required to come to a steady-state etching condition due to impeding surface layers or interfacial chemical imbalances. Typical wet etching rates are in the range of a few nanometers per minute to tens of micrometers per minute depending on the etchant agitation and dilution factors. For example, in

535

a gate etch process where control is crucial, the etch rate employed should be very slow. In contrast, for a backside via-etch a very high rate is needed to etch through (25 pm (- 1 mil) to 350 pm (- 14 mil) of substrate, while at the same time, a high degree of anisotropy is important to prevent lateral spreading and undercutting. Diffusion-limited etchants are relatively isotropic in general, as the surface reaction rate is orders of magnitude shorter than the residence time in the diffusion boundary layer. Agitation greatly affects the etch rates of diffusion-limited processes, as the diffusion boundary layer thickness is easily modulated by forced convective flow (see Fig. 10-26). Thus care must be exercised in wet etching processes to ensure stable, uniform and reproducible etching conditions. In the reaction-rate-limited case, the dissolution rate is determined by the rate of chemical interactions at the interface. Typically, reaction-rate-controlled etchants are anisotropic since the surface reactions are modulated by the density of atoms on the surface planes, and the availability of free electrons at the surface. Etching is therefore dependent on the surface atom density, the electrons configuration, the doping concentration, and any surface reconstruction. Convective flow generally has a minimal effect on reaction-rate-limited etchants, as the transport rate of etchant to the surface does not generally affect the reactions unless the solutions are highly dilute. Reaction-ratecontrolled etchants may either preserve the morphology existing at the initiation of etching, or more often, develop anisotropic shapes as crystallographic effects influence the local etch rate (exposing planes of higher or lower atom density). Reaction-rate-controlled etchants that exhibit strong anisotropy are very desirable for defining gates, mesas, vias, troughs, or other high-aspect-ratio features, but are

536


highly unsuitable for planarizing the surface or pre-crystal-growth surface preparation. In either case the formation of a remanent oxide layer can inhibit the interfacial reactions and affect material transport, thereby affecting the etch rate in both diffusion and reaction-rate-limited processes. Wet chemical also generally very sensitive to temperature, as illustrated in Fig. 10-25, and may also be sensitive to above bandgap light exposure (electron-hole pair generation). Etchant reactivity is nearly always enhanced by an increase in temperature, although depletion or exhaustion of the etchant solution accelerates at higher temperatures (Otsubo et al., 1976). Reaction-ratelimited processes are much more temperature-sensitive than diffusion-limited solutions. During the etching process, the reactions at the surface involve the breaking of many chemical bonds, and therefore energy is evolved. The temperature rise associated with the etching process can upset the local as well as the global etch rate, depending on the etching rate and the net free energy liberated in the reaction. Therefore it is optimal to provide relatively large volumes of etchant, and to provide temperature control to ensure stable etching conditions. The sensitivity to light is manifest through the creation of electron- hole pairs in the surface region, which may affect the charge exchange processes at the semiconductor-etchant interface. The presence of near or above bandgap energy may increase etching rates or create anisotropic effects from surface charge density differences. Thus care must be taken to control illumination of the wafers, the light intensity, and the spectral content, to ensure reproducible etching processes; etching in the dark is preferable. A difficulty with wet chemical etchants is maintaining the reproducibility of the chemistry and reaction conditions. Several

problems can arise in wet chemical etching processes: sensitivity to the etchant, temperature, the pH of the solution, chemical depletion, the presence of light, passivating layers, and the methods of application, e.g., immersion, agitation, spray and spin, etc. The etchant solutions deplete with usage (buffering may slow this process) and age (chemical breakdown during storage, heat, or exposure to air). Recirculating solutions, while reducing some waste handling issues may be more troublesome to control, because the solution chemistry is constantly changing. During use, the chemical potentials may be altered (the pH changes) and diluent species (water and other contaminants) are formed during the reactions, thereby diluting the solution. Light of an appropriate wavelength can increase the etching rates may-fold by creating electron-hole pairs at the surface or assisting in the breaking of bonds. The presence of an increased charge density (dopant species) will nearly always increase the reaction rates at the surface. Wet etching solutions often produce gaseous by-products (e.g., H,, O,, Cl,, Br,, or other volatiles). The formation of bubbles and bubble streaks on the wafer may inhibit or accelerate the etch rate depending on the nature of the surface reactions. This bubbling phenomenon may lead to nonuniform etching across the wafer surface, and can damage the surface morphology. For example, spiking at mask edges and openings can occur due to stagnation of the etchant material (Shin and Economou, 1991). Agitation or stirring can alleviate some of these problems. The use of spray etching methods avoids the difficulties of immersion-type etching baths, and can produce vastly superior terms of reproducibility and control of the etching process (Grim, 1989, 1990). However, the application rates must be sufficient to prevent etchant depletion, and uni-


formity can be more difficult to control with diffusion-controlled etches. Anodic etching is another “wet” method for removing the surface layers in a controlled manner. Here the wafer is fitted with an electrical contact, immersed in an etchant solution, and then biased to create a depletion region of the surface. The anodic oxidation reaction creates an interface charge which balances the impressed electric field. As etching proceeds, the surface potential is gradually equalized over the wafer surface, i.e., a relatively uniform surface oxide is created. Subsequently, this oxide may be removed by a suitable solvent and the process repeated until the desired amount of material is removed. In principle this method is well-controlled. In practice, significant problems arise with localized variation in the surface potentials, nonuniform current distribution, effects of localized charge (e.g., n- or p-type regions, semi-insulating regions, etc.), the impact of residues and surface contamination, and the presence of metals, which greatly complicate control of the etching uniformity. The high resistivity substrates of GaAs and InP commonly used in IC fabrication also cause problems owing to the limited current flow permitted with reasonable bias voltages. Furthermore, the etching occurs in discrete steps which creates a “digital” thickness change with each step and protracts the etching cycle greatly. Some of the additional problems associated with wet etching are the undercutting of the surface layers or masks due to capillary effects and chemical anisotropy. Surface tension, viscosity, anisotropy, solubilities, and convective flows all conspire to reduce the control over the critical dimensions, the morphology, and the uniform arresting of the etching process. The capillary effects may be realized as “blow-out’’or expansion of the feature peripheral dimen-

537

sions, and contraction (undercutting) of interior features. These phenomena also affect the control of the etching end-point when rinsing the etchant from the surface. Crystal lattice and etchant anisotropies, as well as flow-related effects and surface tension effects, can radically affect the shape of the etched feature. Some illustrations of different feature shapes are shown in Fig. 10-27. Once the desired chemistry is determined and understood, wafers may be routinely processed with wet etching methods. The etching of gates, vias, mesas, and channels are quite similar processes, the aim being to create a hole in, or a mesa on, the surface for the purpose of forming the gate trough, holes for interconnect vias, and isolation between devices, respectively. The selectivity of wet etchants can be exploited during fabrication by including etch stop layers in the epitaxial materials. With these materials, differential etch rates of 10000 to 1 can be realized (Ren et al., 1995). Wet etching may be used to subtractively define resistors or capacitor plates on or in the surface layers, although dry techniques are generally preferred for this process (see Sec. 10.5.2). In addition, wet chemical processes are typically used for the preparation of the substrate surfaces prior to crystal growth or processing. For additional information, see Williams (1990, Chap. 5). 10.5.2 Dry Etching

Dry etching of compound semiconductor materials encompasses the generic methods of plasma-based surface decomposition; sputtering, plasma etching (PE), reactive ion etching (RIE), reactive ion beam etching (RIBE), and electron-cyclotron resonance etching (ECRE). All of these etching technique involve the creation of excited or reactive chemical species which selectively

538


Reentrant Corner Prevents Metal or Dielectric Coverage

I Masking Layer

Strong Anlsotropy

+ Creates Faceted Structures

I

Undercut Feature

I

I

Substrate

-b

Substrate

I

Substrate

I

-

physically sputter, or react with, the target material(s) while minimally affecting the masking agent and those desirable materials that remain. Successful dry etching processes require careful selection of the reactive species, etching conditions, duration, control of the gas mixture, and the temperature Dry etching is typically carried out in a reduced pressure environment. High-volume vacuum pumps (for maintaining a low pressure), high-tension power supplies and field plates for developing a confined high electric field, controlled injection of the appropriate gases, an ion source (if needed),

Figure 10-27. A schematic illustration of various etched shapes which can be created by wet or dry etching techniques. In a) a strongly “undercut” shape is shown. This morphology would be ideal for a metal liftoff process, but undesirable for metal or dielectric coverage. In b), the crystal anisotropy has dominated the etching process, producing an etch morphology that has been limited along the ( 1 1 1 } crystal planes. Figure 10-27c illustrates a method by which very small features may be created: undercutting the masking material. Here a feature substantially smaller than the mask line is formed as material is removed from the exposed sides of the desired material. Depending on the etching conditions, anisotropy, and chemistry, vertical side walls, selectively curved side walls, or undercut features may be created, or highly selective etching may be carried out.

and monitoring of the process are required. Many configurations exist for this apparatus, but all systems contain the same basic components. A generalized system configuration is shown in Fig. 10-28. Dry methods are suitable for etching most of the materials present in a compound semiconductor integrated circuit process sequence. As with wet etching, gold is not etched by plasmas, although it can be sputter-etched, or ion-milled. Dry etching processes have excellent spatial resolution and the uniformity is typically very good, variation being of the order of a few percent across a 3” (76 mm) di-


539

Etchant and Ballast Gas Injectors

Figure 10-28. A schematic illustration of a generic plasma etching system. The plasma, containing a strongly reactive ion, is generated by RF excitation, with optional DC biasing. The reactive gas is injected into the plasma region and maintained in a dynamic vacuum condition. In this configuration, ions may directly bombard the water surface and induce damage in the semiconductor. A carrier or ballasting gas may be used to modulate the reactivity and etching rates. Rotation may be used to enhance the uniformity of the etching process. Heating may be used to accelerate or control the etching rate. Exhaust treatment may be required to handle toxic by-products.

ameter wafer in a well-controlled process (O’Neill, 1991). Plasma etching processes have been used to define laser facets, gate troughs, and isolation mesas, as well as to form top or through-wafer via structures. These methods have been used to define submicrometer gates (Sauerer et al., 1992), large diameter through-wafer vias (Chen et al., 1992), and achieve etch rates of 50 pm per hour (Kofol et al., 1992; see also Sec. 10.12). There are several mechanisms that remove material during all types of plasma etching: physical sputtering, chemical etching, and reactive ion etching. Complicating the reactant removal and promoting continued surface reaction are problems associated with the formation of reaction byproducts, surface and gas-phase polymerization, and other reaction inhibitors. These by-product materials act as contaminants in the plasma, as diluents in the gas stream and may block access of the surface to new reactant species or tie-up the reactant species in the gas phase through the formation of

complex molecules or other polymeric species. Chlorine-, fluorine-, or bromine-containing compounds are preferred for the etching gas. Such species as CCl, (Sato and Nakamura, 1982; Inamura, 1979), C1, (Donelly and Flamm, 1981), HC1 (Smolinsky et al., 1981), SiC1, (Sato and Nakamura, 1982), CF, (Schwartz et al., 1979; Harada et al., 1981), CCl,F, (Hosokawaet al., 1974; Smolinsky et al., 198l), and BC1, (Tokunaga et al., 1981; Hess, 1981) are commonly used in plasma or reactive ion etching systems. The etching rates of various materials can be balanced or controlled with additions of ballasting gases, such as argon or helium, and the total system pressure may be modulated to alter the plasma density and the impingement and interaction rates at the surface. A process utilizing these types of reactive chemical species is relatively hard on the apparatus, readily attacking the system components in the chamber, the gas control valves, feeds, injectors, pumping systems, pump fluids, and exhaust systems and waste

540


treatment facilities. The selection of system components and their exposure to the plasma or gas streams is critical for mitigating contamination of the semiconductors. Exhaust scrubbing and waste treatment is often required to prevent the polluting effects of the effluent gases. The excitation voltage and total RF and DC energy input to the plasma controls the ion creation rate and determines the ion energy distribution. There are frequency-dependent effects in the plasma, excitation being carried out typically at either -300455 kHz or 13.6 MHz (frequencies that do not interfere with communications bands) which alter the ionization efficiencies, ion densities, and energy distributions. The use of 13.6 MHz excitation results in minimal surface damage, while 300-455 kHz excitation tends to severely exacerbate the damage. This can be understood from the point of momentum transfer to the ions: at the lower frequency, ions can travel a significant distance during a cycle, readily impinging onto the surface, causing atomic displacements. At the high frequencies, however, the ions have substantially less time to accelerate into the surface region, and thus have a lower probability of damaging the surface atoms. In addition, the electric field strength and the geometry of the plasma excitation plates have a strong influence on the etching process by affecting the flow of ions to the wafer surface. The system pressure may be controlled over a moderate range which also changes the plasma density, the reactive ion density and formation rate, and thus the etching rate and selectivity (feature shape). Since the plasma contains a significant amount of energetic species, the temperature of the substrates rises typically to - 200 “C to - 300 “C during the etching cycle. Heating or cooling of the substrate may be required to control of etching process.

For the various materials exposed to the plasma during etching, the selectivity for removal is determined predominantly by the plasma-materials interactions, but also affected by the system operating pressure (impingement rates). For example, the etching of heterostructure materials (e.g., GaAs/ AlGaAs materials) may be carried out selectively or nonselectively by plasma methods depending on the gas chemistry and relative etch rates. Typical dielectric materials (oxides and nitrides) are readily etched by dry techniques, as are photoresists, the latter are removed particularly well in oxygen containing plasma (“ashing” processes). Nitrides are generally more etch-resistant than oxides. Most metals, except gold, are also etched easily in plasma containing reactive species such as C1, F, or Br (see Williams, 1 9 9 0 ~ )One . major concern in plasma etching is ensuring that the protective coatings maintain their integrity during the etching cycle (etch-rate issues). One difficulty with the phosphorus-containing compounds such as InGaP, GaAsP, or quaternary materials is that these materials do not etch readily in the typical plasma chemistries (Ren et al., 1993, 1995). A key to the successful implementation of plasma etching is controlling the damage induced by energetic ion bombardment of the exposed surfaces. This is especially true for devices using “shallow” p-n junctions or lightly-doped layers in the materials structures. Damage created by the injection or recoil of energetic ions can produce atomic displacements and create donors, acceptors, and deep levels, thereby alterating the charge in the surface region. The use of high frequency (13.6 MHz) excitation reduces there effects. To mitigate these effects there are parallel plate configurations with differing ratios between the upper and lower plate areas that control plasma confinement (density and impingement rate) and ion


guiding effects, and “downstream” designs wherein the plasma region is confined “upstream” well away from the substrates (Pearton et al., 1991). This latter design approach attempts to minimize the direct ion bombardment of the surfaces. Here the active species formed in the plasma are swept through the chamber and across the wafers by a flowing carrier gas stream. A multitude of other competing variables exist in the plasma system and process: the gas-phase composition, chamber materials, biasing of the substrates, ion damage thresholds for the substrate materials, as well as sputtering of the chamber materials. All of these system variables contribute to variations in the etching rates. Etch rates and profiles are strongly influenced by the pressure of the chamber, the gas chemistry, and even the slightest trace of contaminants in the etching chamber. Sputtering is the process of physically “blasting” atoms from the surface by atomic interactions. Typical sputtering systems have a source of energetic ions created by a DC or AC plasma in a diode configuration. The sputtering rates are controlled by the pressure, gas mixture, current, and voltage in the system. Argon ions are a preferred species as the gas is available relatively pure, is readily ionized, and the ion is massive. Charge separation in the plasma causes the argon ions to be attracted to the negatively charged (wafer) electrode. The ion impact sputters away the surface layers. Sputtering is carried out in relatively small volume chambers with a small spacing between the plates (- 10 cm). These systems are operated at total pressures of to - 1 Torr (0.13-133 N m-2). With a small chamber and close proximity of the plates, continuous redeposition may occur as it is difficult to extract the sputtered material rapidly from the center of the chamber. Contamination of the semiconductor material

54 1

can occur by redeposition and decomposition of the chamber materials, and by implantation by ion bombardment at the surface. “Passivation” of the surface or redeposition may slow the etching process by interfering with the sputtering rates of the desired species and create nonuniform etching profiles over the wafer surface. Etch masking must be quite robust to withstand the continuous ion bombardment in sputtering or plasma processes. Thick photoresist (PR) layers or multiple PR/metal layers may be used to resist the ion flux. A balance of etching rates between the mask materials and the semiconductor is generally the best achievable compromise in practice. Metal layers etch substantially more slowly than the semiconductor or photoresists. Thus relatively thin metal masking layers may be used to assist pattern definition, permitting very fine features to be created. Etch feature side wall definition is generally poorer with sputtering processes relative to other approaches. The high wall angles desired for deep trenching (isolation) cannot be achieved easily by sputtering, due to the limited interaction of the ions with the surface at high incident angles and the high probability of redeposition within the trench. RIE-type etching in much better suited to large-aspect-ratio etched structures. RIE/RIBE/PE processes operate at low pressures, in the range lop3- lop5Torr (0.13-0.0013 N m-2). RIE/RIBE chambers have relatively large electrode spacings, and lower energies (smaller potentials) are impressed, providing a cleaner environment for the etching process and somewhat reduced redeposition rates. The strongly enhanced etching comes from the reactivity of the ions rather than the energy imparted to the etchant species. Unlike plasma etching where the low-energy plasma consists of ions, radicals, and various electrons, pro-

542


tons, etc., an ion source (RIE) or directed ion beam (RIBE) creates a selected set of ionized species to affect the etching. These systems exhibit somewhat slower etching rates than those of sputtering processes, predominantly due to the limitations of the ion sources. Plasma etching tends to be isotropic, whereas RIE and RIBE can be used to control the etched morphology and have very limited sputter damage and redeposition. The latter two points are very critical in device structures that incorporate field effects for charge modulation (FET-type devices and lightly-doped structures, for example). PE operates at higher pressures than RIE/RIBE, with relatively low power, and etches at moderately low rates. While there is less surface damage created than with sputtering, PE still embodies a significant amount of damage and contamination from the plasma and chamber components. Operating at higher potentials generally leads to greater anisotropy in the etching, but greater damage to the surface due to implantation processes. RIE/RIBE carried out at higher bias voltages can produce near-vertical side walls due to impingement near 90". In RIE/RIBE the etching is caused predominantly by the reactive species rather than all of the particles in the plasma, as in PE . The ion source in RIE/RIBE provides a reactive ionized species containing a group VII (chlorine, fluorine, or bromine) atom or molecule. For most III-V materials, the chlorine and bromine compounds produce highly volatile reactants and are therefore preferred over the fluorine compounds (Burton et al., 1983; Ibbotson et al., 1983). Polymer formation is a concern with any of these compounds, particularly in the presence of photoresists. The objective is to provide selected, low-energy, reactive ions to the surface of the wafer where upon they

form volatile complexes with the surface atoms. This volatility limits redeposition as the complexes and compounds do not readily decompose or attach themselves to the surface of the wafer. A variety of halogenated compounds have been used as reactive ion sources: CF,, CCl,, BCl,, CBr,, or other chloro-fluoro carbons. CBr2C12, CHCl,, and C2C14have been found to readily form polymeric compounds and by-products, and are generally unsuitable for RIE/RIBE. Construction materials (chamber walls, shields, electrodes, etc.) for RIE/RIBE systems are of critical importance as the reactive species may cause the system components to decompose and contaminate the wafers. RIBE is differentiated from RIE by the use of collimation to create a directed beam of extracted ions from a high-density plasma source. This beam-like ion stream permits variation of the angle of incidence to the surface, thereby affecting the etching rates and morphology (Ide et al., 1992). Surface reactivity is not dependent on the incident angle to the first order, and therefore the side wall angle can be affected through the angle of incidence. The ability to control the interaction of the ions with the surface mitigates the problems of morphology control independent of the ion energy. RIE/RIBE are carried out in a parallel plate system, selecting the reacting ions by gas injection or ion extraction, under appropriate bias conditions. Etching occurs by chemical reaction and subsequent desorption of the reactants. The ability to create nearly vertical side walls at moderate bias voltages is a distinct advantage of RIBE. As with all plasma systems, RIE/RIBE etch rates are influenced by pressure, gas mixture, ion density, and excitation power. Problems may occur with polymerization between certain etchant gases and the reactant species, which can inhibit the etching.

10.6 Ohmic Contacts

543

Optical or Ion monitoring End Point Detection

Figure 10-29. A schematic illustration of an ECR-plasma etching system. The ion plasma, containing a strongly reactive species, is generated by exciting electron-cyclotron resonance of the desired chemical species. The source is located “upstream” from the etching chamber to protect the wafer from direct ion bombardment. A carrier or ballasting gas flows through the ion source and the chamber, assisting in the transport of reactive ions to the wafer. Electronic extraction may be used to pull ions from the source. Rotation or heating may be used to enhance or control the uniformity and rate of the etching process. Exhaust treatment is generally required to handle toxic by-products in compound semiconductor processing.

RIE/RIBE are significantly better than sputtering techniques for most applications, having lower damage due to the lower ion energies and reduced contamination (with proper chamber construction). Electron-cyclotron resonance etching (ECRE) processes involve the selective excitation of an ionized species through a high frequency resonant coupling process (Pearton et al., 1991). Figure 10-29 schematically outlines an ECRE configuration. The excited ions are typically created well away (“upstream”) from the etching chamber to minimize direct ion bombardment damage to the wafer. Ions are extracted from the ECR source by the electric fields and the pressure gradient in the system: The etching processes occur in a manner similar to RIE/RIBE. ECRE has the advantages of “clean” etching as it is carried out in a high or ultra-high vacuum environment, gives very minimal surface damage (with low to moderate extraction/accleration potentials), negligible redeposition, and reasonable etch rates (Pearton et al., 1991).

Run-to-run reproducibility is somewhat difficult to control in plasma techniques as there is no convenient and accurate method for monitoring the etching rate. Control of the end point may be enhanced by the incorporation of etch-stop layers, monitoring of the reaction product generation rate, or the presence of specific reacted species (chemical indicators) in the plasma or exhaust gases. These techniques can provide adequate end point detection to determine the completion of the etching cycle. Presently, the best control parameter is tracking of the reactant species evolution by residual gas analysis, optical absorption, or similar methods to determine an end point indication. Further development and refinement of gas-phase sensors will result in greatly improved control of plasma type processes.

10.6 Ohmic Contacts Ohmic contacts provide low resistance current paths and interconnection between

544


devices. The creation of the ohmic behavior is, and has been, a source of perpetual investigation and development activity in compound semiconductor materials (Braslau et al., 1987; Matino and Tokunuga, 1969; Schwartz, 1969; Edwards et al., 1972; Ostubo et al., 1977; Kaumanns et al., 1987). The underlying difficulty in creating an “ohmic” contact is that Schottky barriers are formed when most metals are brought into initial contact with the semiconductor surface (Schottky barriers are considered in detail in Sec. 10.7). Therefore some means of eliminating this barrier must be developed. The details of the mechanisms behind the formation of ohmic contacts are not yet fully understood in spite of more than 50 years of work [see Sharma (198l)l. From a theoret-

ical and physical standpoint an ohmic contact begins as a Schottky barrier, as shown in Fig. 10-30. The work function of the metal and semiconductor are initially offset as the Fermi energy is constant across the interface. This band offset creates a barrier to charge flow from the semiconductor to the metal, as attributed to the investigations of Schottky [see Chap. 5 in Sze (1981)], giving rise to a diode transfer characteristic. The Schottky barrier height is defined as the difference of the metal and semiconductor work functions (Pm- (Ps= (PB

(10-4)

As long as the quantity (PB is significantly greater than zero, a barrier to charge transport exists, and the flow of charge will not

Figure 10-30. Initial formation of a Schottky barrier prior to annealing to create an ohmic contact. In a) &, is the metal work function, x3is the electron affinity of the semiconductor, E, is the semiconductor energy gap, and E, and E, are the conduction and valence band energies, respectively. E, is the Fermi energy and q V , is the difference between the Fermi level and xs relative to the vacuum level. b) As the metal is brought into contact with the semiconductor, charge is exchanged to maintain a constant Fermi energy. This creates a depletion region, W, in the semiconductor to balance the electrons in the metal. The semiconductor energy bands “bend’ to reflect the charge distribution in the near-surface region. The Schottky barrier height is $ B , and the junction build-in potential is Vbi at equilibrium (no applied bias).

10.6 Ohmic Contacts

be linear with applied voltage (electric field strength). The formation of an “ohmic” contact to the semiconductor involves metallurgial reactions which create a transition from a Schottky barrier condition to a graded energy band structure with a negligible barrier height (Schwartz and Sarace, 1966; Schwartz, 1969; DiLorenzo et al., 1979). The initial formation of a depletion region (W) with the creation of a Schottky barrier is illustrated in Fig. 10-31. The width of this depletion region is proportional to the square root of the doping concentration (in the abrupt junction approximation) governed by the relation (Sze, 1981, Sec. 5.2)

( 10-6)

As the doping level is increased the depletion width shrinks, the interfacial electric becomes greater, and field emisfield (Emax) sion, thermionic emission, and tunneling processes may readily occur. It is desirable to have: 1) a small q3B such that k T / q is “large”, or 2) a degenerately-doped semi-

545

conductor so that tunneling and/or field emission processes have a high probability. A model for this latter point was discussed in the light of the depletion width being substantially smaller than the depth of the degenerate layer. Thus tunneling and thermionic emission processes are facile, and the barrier to transport is negligible (Popovic, 1978). Conversely, as the doping density decreases, the depletion width increases and the metallurgical junction must be formed deeper into the semiconductor to affect an ohmic behavior. Also, since there are fewer charges available in the semiconductor, the conductivity is reduced. All of these effects contribute to higher contact resistances for “lightly” doped materials, and make the formation of a high quality ohmic contact more difficult. There is no consensus on a precise model and understanding for the ohmic contact formation (see Sharma 1981, or Schwartz, 1969). Some investigators consider the interface to be a disordered alloy with “mobility gap” states (Peterson and Adler, 1976), while others interpret the interface as a transition from the metal through an amorphous region to the crystalline semiconductor material (Wey, 1976; Riben and Feucht, 1966). At present, resolution of these arguments remains unclear.

Figure 10-31. The creation of a depletion region of width W in the surface region of an n-type semiconductor. ED is the donor energy level relative to the conduction band edge, c ) ~E,, , Ev, E g , and EF have their usual meanings. Vbi is the built-in potential. The depletion width is inversely proportional to the carrier density as in Eq. (10-5).

546


Further investigations may some day shed light on the exact phenomena. For a more detailed theoretical development of ohmic contact electrical behavior see, for example, Chap. 5 in the book by Sze (1981). To eliminate the Schottky barrier and produce an ohmic behavior, a metal contact material must generally be alloyed into the semiconductor. The metal reacts with the semiconductor forming multiphase intermetallic compounds, lowering the barrier potential, and stretching the band-bending

into the semiconductor, as illustrated in Fig. 10-32. Electron (or hole) flow is impeded less and less as the alloying process advances. If the condition

-

glm- gls= glB 0 volts

( 10-7)

is met for an n-type semiconductor material, then the contact is considered to be ohmic in nature. For small positive values of $B (a small Schottky barrier height), significant tunneling and thermionic emission can occur permitting significant current flow with

Figure 10-32. Creation of an “ohmic” contact to a semiconductor. In a) the barrier height, &, is very small, presenting a negligible barrier to electron flow. h,,E,, E D , E,, E,, and E , have their usual meanings. In b) the surface region of the semiconductor is doped to an n+ degenerate condition (high electron density, Fermi level in the conduction band). The depletion width is dramatically narrowed. Thus tunneling processes may readily occur. Both of these processes may contribute to the ohmic behavior.

10.6 Ohmic Contacts

a small forward bias. Thus only a very small resistive component is realized. Surface states and surface charge may also affect the barrier height and charge distribution in the semiconductor, and therefore the I - V behavior (Spicer et al., 1989). This latter point is particularly important for devices which are lightly doped (“enhancement mode”) and therefore very sensitive to changes in near-surface depletion or the accumulation of charge. The contact resistance (R,) is derived from the thermionic I - V theory for an ideal Schottky contact. The definition of R, is

& = -n k T at V = O 4 Isat

(10-8)

A plot of log I vs. V should result in a straight line of slope q l ( n k T ) where n is the ideality factor from Schottky junction theory, k is the Boltzmann constant, q is the elementary charge, Tis the temperature, and Isatis the reverse bias saturation current. Typically, n is in the range 1 .O- 1.1 for a good ohmic contact; values very near 1.O are most desirable. Values of n greater than 1.1 indicate problems with the alloying cycle, the contact metallurgy, or highly resistive materials. A critical feature of the ohmic contact is the linearity of the I - V relationship: any diode-like characteristics are undesirable. Contact metals must be deposited on clean surfaces to prevent erratic intermixing of the metal and semiconductor during alloying, particularly with reactive species such as aluminum or titanium. Typically, at least one of the components of the metallization is a donor (e.g., Si, Ge, Sn,Se, or Te in ntype, 111-V compounds) or an acceptor (e.g., Zn, Cd, Be, or Mg in p-type materials) species in the host semiconductor. This will greatly increase the ease of ohmic contact formation as the effective doping density can create a highly degenerate layer in the

-

547

interfacial region of the metal and semiconductor. The alloying process causes intermixing of the metal, the doping species, and the semiconductor, as discussed above. However, many considerations arise in the process of alloying: chemical reactivity or inertness with the host semiconductor, diffusivity of the various species, the phase diagram for multi-component systems, surface tension, processing limitations (thermal and morphological) from previous steps, adhesion, defining geometry (masking), stability of the intermetallic phases, compatibility with the wire bonding metallurgy, etc. The phase diagram and the kinetics of the intermixing process determine, to a large extent, the achievable barrier reduction and thus the conductivities of the interfacial metallic region. It is desired that the contact resistance be as low as possible, typically in the range of to lop6 Q cm2 for n-type materials, and about ten times larger for p-type materials principally due to mobility differences. The range of interactions generate a large number of compromises in the development of a viable, manufacturable, and stable ohmic contact formation process. The fabrication of ohmic contacts begins with careful surface preparation, followed by deposition of metal(s) and/or metal alloys. There are a multitude of methods and metallurgical systems suitable for the formation of ohmic contacts to 111-V compounds (Sharma, 1981; Schwartz, 1969; Palmstrom and Morgan, 1985). Table 10-5 highlights a number of these metals systems; numerous other alloys have been evaluated. Predominantly, metallurgical systems based on Au-Ge, and more typically Au-Ge-Ni, are the most studied and in general use. For additional information see Sharma (198 l), Howes and Morgans (1985, Chap. 6), Williams (1990, Chap. l l ) , and the associated references therein.

548


Table 10-5. Ohmic metallizations. Metallization

In Sn Au-In Au-Sn Au-Ge Au-Ge-Ni Ag-In A1 Ag-Znn In-Zn

Semiconductor type

Reference

n n n n n n

Wronski (1969) Schwartz and Sarace (1966) Paola (1 970) Henshall (1977) Fukuta et al. (1976) Shih and Blum (1972), Kuan et al. (1983) Matino and Tokunaga (1969) Shih and Blum (1972) Ishihara et al. (1967) Matino and Tokunaga (1969)

n, P n P P

Evaporation methods are particularly useful for multi-component metallizations. While heating of the substrate material must be carefully controlled through the deposition rate and intentional heating or cooling of the wafer, control of the thickness and deposition rate are very good. Compositions can be controlled either through multiple deposition steps, co-deposition, or the use of alloys as charge materials. Sputtering and plating-type processes can also be used to deposit the metal on the semiconductor, although plating is rarely implemented for top surface metallizations in practice. Sputtering methods generally have lower deposition rates, can generate substantial damage in the semiconductor, and thickness control is indirect and difficult. On the other hand, sputter damage to the interfacial region may lead to lower contact resistance through the creation of defect states and disorder at the surface. Plating processes rapidly build up layer thicknesses, but tend to be rather “dirty” from the chemical standpoint, and have problems in relation to control of the surface morphology and layer thicknesses. In some processes, such as backside ohmic metallization of bonding pad formation,

where metal thickness control is relaxed but thick layers are desired, plating processes are the method of choice. Ohmic contact topology may be defined by standard photolithographic patterning methods after deposition (see Chap. 4of this Volume). Liftoff patterning, photoresist or dielectric assisted, is the most common method for the removal of unwanted metal (see Sec. 10.1 1.2), provided the deposition process has not created a completely uniform layer of metal over the photoresist or dielectric surface topology. Ion milling may be employed for patterning gold or goldbearing alloys, or tungsten-based contact materials. Aluminum and other non-gold bearing metallizations may be patterned by dry etching methods such as RIE (as discussed in Sec. 10.5.2). The annealing of most ohmic metallizations used in device fabrication is a very critical step. “Spiking” and other deviations from planarity can occur even with mild over-alloying (i.e., excessively high temperatures of extended alloy time), making subsequent processing more difficult (Gyulai et al., 1971; Zeng and Chung, 1982; Palmstrom et al., 1978; Miller, 1980). Spiking of the contact metal in the compound semiconductor systems is quite similar to that observed in the A1 :Si system at edges of contact windows. Lateral spreading has a negative impact on electric field distributions and may cause short-circuiting in fine geometries [see Goronkin et al. (1989)l. Roughness or texturing in the contact region is apparent after alloying especially if “overalloying” has occurred. Even 20-30°C overtemperatures (in the range of 400 “C for NiGeAu-based contacts to GaAs materials) or slightly extended cycle times can cause the metals to “punch through” active layers, as shown schematically in Fig. 10-33. Lateral spread of the contact materials may lead to uncontrolled electrical behavior in active

-

10.6 Ohmic Contacts

I

__

n ’ Laver .. I -.

nL Bulk GaAs Semiconductor

a)

and passive devices, such as low breakdown voltages or leaky characteristics. Roughness of the contact sites may also negatively impact subsequent mask alignment, photoresist depositions, and other processing steps. A minimal thermal budget is typically used for alloying processes employing a furnace, “hot plate”, or rapid thermal annealing (RTA) system. The objective is to minimize the metallurgical interaction while maximizing the conductivity of the alloyedcontact region. For n-type materials, using gold-based metallurgy, the alloying process is carried out at relatively low temperatures - 400 “ C ) and short times (of the order of tens of seconds to - 10 min), or in RTA systems with somewhat higher temperatures (- 500 “ C ) but shorter durations (ca. 30 s) the contact metallurgy is controlled sufficiently to create a reproducible, low-re-

549

Figure 10-33. Schematic representation of annealing effects on Ni-Au-Ge contacts to GaAs. In a) the metal regions have been deposited and defined by lithography. In b) the material has been annealed. The angular structure of the NiAs(Ge) crystal structure, represented by the shaded region, is characteristic of the metal-semiconductor interaction during annealing. This has been observed in several TEM investigations (Zeng and Chung, 1982; Parsey, 1990). Excessive annealing will produce punch-through of the metal below the n-layer, as shown.

sistance contact to the n-type materials [see Sec. V in Sharma (1981)l. Similarly, the Au-In and Au-Zn alloy families are commonly used for contacts to p-type materials. Owing to the lower carrier mobility, and thus the higher resistivity of p-type materials, a higher doping level is required to achieve low contact resistance (doping levels are usually greater than 1019 cmP3) to achieve a highly degenerate region. Even with high doping concentrations, contacts to p-type semiconductors are always of higher resistance than those to n-type materials. It is possible to form “nonalloyed” ohmic contacts to GaAs and other compound semiconductors provided sufficiently high doping concentrations exist in the surface layers. Typically, electron densities greater than 3-5 x 10’’ cmP3 are necessary for a low resistance, nonalloyed contact to n-type

-

550


material (Chang et al., 1971). If the semiconductor bandgap energy is small or can be reduced, for example, by the addition of an alloy component, e.g., In in In,Ga,As, the formation of nonalloyed contacts is facile. The use of In,,5Ga,,5As as a low resistance contact to HBT devices has attracted significant interest (Poulton et al., 1994; Huang et al., 1993). Keys to creating this type of contact are: 1) the relatively small bandgap of Ino.5Gao,5As(approx. 0.8 eV); 2 ) the degeneracy of the semiconductor (high surface doping concentration); 3) the formation of an extremely thin depletion region (< 10 nm) at the surface. Charge flows eas-

ily via tunneling and thermalization processes, as well as requiring only minimal electric fields to drift the charges across the metallurgial junction. Detailed analyses of the ohmic contact and interfacial reactions have been made by numerous techniques, among them, X-ray diffraction (Ogawa, 1988), Auger electron spectroscopy (Robinson, 1975), transmission electron microscopy (Kuan et al., 1983), scanning electron microscopy (Robinson, 1975), and secondary ion mass spectroscopy (Palmstrom et al., 1978). The information obtained has led to a detailed understanding of the interactions and con-

Weight P e r c e n t Gallium 0

10

20

30

40

50

60

70

80

90 100

L

t

Au

Atomic P e r c e n t Gallium

Ga

Figure 10-34. The Au-Ga phase diagram showing atomic percent (left figure) and weight percent (right figure) relationships. Numerous intermetallic phases can form in the temperature range -274°C to -491 "C, which can greatly affect the morphological and electrical behavior of annealed contacts (after Massalski, 1990, p. 370). Reprinted by permission of ASM International.

55 1

10.6 Ohmic Contacts

trol of the alloy process (see Howes and Morgan, 1985, Chap. 6). A number of investigators have studied the interaction of gold and gold-alloy materials with GaAs (Zeng and Chung, 1982; Vandenberg and Kingsborn, 1980) and InGaAsP (Vandenberg et al., 1982; Vandenberg and Temkin, 1984) and found that, as predicted from the phase diagrams, numerous intermetallic compounds form and evolve during the alloying process. For example, in the reaction of gold with GaAs, formation of the Au-Ga alloys occurs with the resulting loss of arsenic from the surface, and the creation of AuGa, and AuGa; p and y intermetallic phases are created, as shown in Fig. 10-34 (Massalski, 1986, pp. 258-261).

0 10 20

0

30

10

Au Figure 10-34. (continued).

40

20

Contact resistance in most ohmic contact systems has been found to increase if undesirable (high resistivity) phases form. For example, in the Ni-Au-Ge contact, if aAu : Ge or Ni-Ge are created in significant amounts, or if excess gold diffuses into the semiconductor surface region, the contact resistance will be increased. In contrast, the contact resistance will be lower if Ni-As and the in-diffusion of germanium occurs and Au : Ga forms. Schmid-Fetzer (1988) has recently reviewed the phase relationships and predicted interactions of a large number of metals for potential contacts to GaAs. Contacting thin layers (of the order of a few tens of nanometers) is a difficult task due to the necessity to consume some of the surface

Atomic P e r c e n t Gallium

50

70

60

30

40

80

50

60

Weight P e r c e n t Gallium

90

70

100

80

90

100

Ga

552


material, to form the correct phase(s), and the complication of uncontrolled in-diffusion processes due to surface defect formation. The varied and rapid diffusivity of the various component metals also complicates control of the alloying to very thin layers. Optimum thicknesses of n+ or p+ contact layers appear to be in the range of 25-50 nm.

10.7 Schottky Barriers and Gates A Schottky barrier is the rectifying contact which forms when a metal is brought into contact with a semiconductor material. This structure is a charge dipole which creates a depletion region analogous to a p-n junction diode. Schottky barriers are the heart of most FET-type devices. The charge flow in the transistor is modulated by the bias applied to the Schottky barrier gate metal during device operation. The “barrier

height”, in conjunction with the available charge density, determines the threshold of the switching action and the conduction state of the device at a given bias condition. In Fig. 10-35 the formation of a Schottky barrier is illustrated. The semiconductor material and the metal possess different work functions relative to the vacuum en, , and 4s, respectively. As the ergy levels, @ metal is brought into contact with the semiconductor, charge is exchanged between the materials so as to balance the chemical potential of the electrons and holes, i.e., the Fermi energy level is constant across the interface. The metal contributes 1 electron per atom, and the semiconductor typically l OP4 to lop6electrons per atom. Charge exchange creates the dipole layer and charge equilibrium is established. As a result of the imbalance in the charge density, a depletion region, “W”, is formed in the semiconductor.

-

x,

Figure 10-35. Schematic energy diagram of a Schottky barrier, $, is the metal work function, is the electron affinity, V,, is the built-in potential, E, is the energy gap, and E, and Ev are the conduction and valence band edges, respectively. q ! ~is~ the Schottky barrier height. After a metal is placed on the semiconductor surface, charge is exchanged to equilibrate the Fermi energy (EF). Since the semiconductor contains far less charge than the metal. the donor states (ED)empty producing a depleted region of width W.

553

10.7 Schottky Barriers and Gates

From Fig. 10-35 the relationship @m-xs= @B

(1 0-9)

may be observed. The difference between the electron affinity of the semiconductor, , and the metal work function, $m, is the Schottky barrier height, @ B . In principle each semiconductor-metal system should have a unique Schottky barrier height based upon the configuration of Fig. 10-35 (see Kahn et al., 1989). In reality, surface states, surface reconstruction, impurities, and defects may all act to “pin” the Fermi energy. Thus the barrier height values are confined to a relatively narrow range, as evident in Table 10-6. This phenomenon is the subject of intense investigation [see, for example, spicer et al. (1980), Brillson et al. (1983), and Williams (1982)], and remains unresolved at present. The current flow in a Schottky diode is described by the relationship

xs

I = I, { exp [ q V/(kT)] - 1 }

(10-10)

where q is the elementary charge, V is the applied voltage, k is the Boltzmann constant, and T is the absolute temperature. I , is the thermionic current I,=A* T 2 exp[-q $ B / ( k T ) ] }

(10-11)

where A* is the Richardson constant, @B is the Schottky barrier height, and the other symbols have their usual meaning. From Eq. (10-9) if then G B > O and the structure will be rectifying. Thus an ideal diode would have an infinitely large value of qB. In practice the largest possible value for the barrier height would suffice. For further development of the Schottky barrier theory see Simmons and Taylor (1983). Typically, $B is in the range of 0.5 V to 1.4 V for most important compound semiconductor as shown in Table 10-6, clustering around - 0.8 V for most metals on GaAs. The observed barrier height is related to the magnitude of the sem-

$,>x,,

Table 10-6. Schottky barrier heights on selected compound semiconductor Metal

Al Au Ag W Ti Ni Pt

Semiconductor material GaAs

AlAs

InP

0.80

-

0.90

1.20

0.80 0.83d

-

0.52‘ 0.52 0.54 -

-

-

0.77d

-

-

0.84

1.0

-

0.88

-

GaP

ZnSe

1.07

0.76

1.30 1.20

1.36 1.21

-

-

1.12 1.27 1.45

-

1.40

Values in electronvolts at 300 K; from Sze (1 98 1, p. 291); ‘ Sharma (1981); Waldrop (1984). a

iconductor band-gap, being about 0.5 - 0.6 of Eg , lower for materials with a small E,, and higher for wide gap ,materials such as Gap. For materials with small band gaps, such as InAs (0.42 eV), this factor places stringent requirements on device operation, necessitating cryogenic temperatures for viable transistor operation. The value of the Schottky barrier height does not appear to depend strongly on the metal work function, although from the physical description of the barrier formation [Eq. (10.9)] it should be directly tied to 9,. The “pinning” of the Schottky barrier height noted above has been attributed to the existence of surface states at the level of - 10l2 to - 1013cm2. These states can arise from carbon, oxygen, surface defects, or other contaminants chemisorbed or physisorbed on the surface. Numerous interpretations have been put forth to explain these effects. Brillson et al. (1983) have considered that a finite amount of intermixing occurs during the metal deposition process rather than an idealized, atomically abrupt interface. An effective metal work function is defined which integrates the effects of defects, clusters of metal, or semiconductor

554


species, etc. This leads to a “pinned” value for the Schottky barrier height. Spicer has postulated a “unified defect model”, depending on surface states from defects (e.g., vacancies) which gives rise to the pinning states. This behavior is discussed further by Williams (1982) and numerous theories exist for these pinning phenomena. Many investigations of the Schottky barrier phenomena have been carried out in an attempt to understand and control the interfacial charge states and the metallurgy of the metal-semiconductor junction so as to provide a stable and reproducible barrier height (Spicer et al., 1980; Pan et al., 1983; Brillson et al., 1983; Waldrop et al., 1982; Williams, 1982). While the barrier heights obtained under near-ideal conditions (e.g., invacuo cleaved surfaces) are relatively wellcharacterized, in practice, the variation induced by the processing chemistry and the materials properties requires significant efforts to provide a “reproducible” Schottky barrier height. However, the precise physical relationship of the energy gap, work function, and q5B is not fully understood, as remarked by many investigators (see review by Schmid-Fetzer, 1988). To form the Schottky-barrier gate structure, a metal (e.g., gold or aluminum) or metalloid (e.g., WSi, WN, TiWN, etc.) is deposited onto the CS surface and then patterned by standard photolithographic-etching processes. The demands of the fabrication process sequence place constraints on the formation of Schottky-barrier gates: the required thermal and patterning processes determine the permissible gate metallurgy. It is necessary to contend also with adhesion between the gate material and the semiconductor and the impact of subsequent processing steps on the chemical reactivity and stability of the metal-semiconductor system. Therefore the selection of suitable metals and metal alloys becomes relatively

limited (see Table 10-6). These materials may be used in combination to improve properties such as the electrical resistivity, but the barrier height is determined by the metal or metal alloy in contact with the semiconductor surface. The primary metal deposition methods are sputtering and evaporation. As in any deposition process, the surface and the material to be deposited must be extremely clean to prevent uncontrolled interfacial reactions or the creation of metal-insulator- semiconductor (MIS) structures. For most of the refractory metals, their melting points are sufficiently high that sputtering is the only viable deposition method; electron beam evaporation for these materials is either impractical or the deposition process will raise the temperature of semiconductor surface too high to prevent chemical interactions. On the other hand, sputtering readily creates surface damage and thus creates surface states (see Sec. 10.6). As previously noted, the formation of a Schottky barrier is extremely sensitive to the interfacial density-of-states. The corresponding variability in the barrier height, locally or globally, will affect the transistor threshold voltage, operating conditions, and reproducibility. Many of the metallurgical systems presented in Table 10-6, particularly in the case of refractory metals, may create significant stresses during deposition and fabrication, and also during device operation due to a mismatch in the lattice parameters, atomic configurations, and the existence of thermal expansion coefficient mismatch. These phenomena give rise to piezoelectric-type effects, and consequently, the transistor threshold voltage may shift. For example, the grain structure of a Schottky-barrier metallization, as deposited by various methods, is strongly dependent on the deposition rate and the deposition conditions (e.g., vacuum, plasma composition, target materials,

eB

etc.). Thus variations in may be anticipated. The microscopic details of the grain structure may also affect the gate metal resistivity and the susceptibility to electromigration at high current densities or high temperatures. These issues must be carefully addressed to achieve a stable Schottky barrier process. If the device fabrication process is carried out at relatively low temperatures, gate materials such as Ti-Pt-Au may be utilized (Wadaet al., 1989; Brown et al., 1989). Gold suffers from relatively poor adhesion to most compound semiconductors and also rapidly diffuses in most compound materials, even at low temperatures (ca. 250400"C), as does platinum. Thus there is a need to capitalize on the conductivity of gold, while maintaining process integrity. The Ti-Pt-Au system is commonly used for gate metals on GaAs. In this case, the titanium is used as an "adhesion promoter". The platinum layer serves as a diffusion barrier to prevent the gold from reacting with the titanium (see Massalski, 1986, pp. 298299) and subsequent gold-spiking into the GaAs (Goronkin et al., 1989). Palladium may be substituted for platinum with similar results. The gold provides a very low resistance path to support a high density current flow. As these metals are relatively compatible from a thermal expansion standpoint there are only small interlayer stresses, and little driving force for intermixing at


555

temperatures below ca. 600 "C, thereby producing a thermodynamically stable contact structure. For fabrication processes that employ nonalloyed or nonannealed contacts, aluminum, titanium, and tantalum have been found to be stable at temperatures up to 300°C. These materials can be used in the gate structure provided temperatures in subsequent process steps do not exceed roughly 200-250 "C and operating temperatures are limited to less than - 125-200°C. For devices which utilize an ion implantation and anneal step subsequent to the gate metal deposition (see Secs. 10.3 and 10.1l), the gate material must be stable at temperatures at least as high as the annealing temperature, typically in the range of 800°C to 1000°C. Self-aligned processes, such as the generalized approach shown in Fig. 10-36, require the use of ion implantation and annealing for defining the gate and channel regions. Several approaches exist for creating the self-aligned gate, among them, the selfaligned implantation for n+ layer technology (SAINT) (Yamasaki et al., 1982) and the self-aligned refractory gate integrated circuit process (SARGIC) (DautremontSmith et al., 1990; Dick et al., 1989). Any variation on this type of technology relies on the existence of a stable Schottkybarrier gate metallurgy. Typically, for selfaligned structures the gate material is a refractory or noble metal such as tungsten (Sze, 1981, p. 290), platinum (Fontaine et

-

1) Dielectric deposition, Open gate windows

Ion Implanted or Epitaxial Channel

Figure 10-36. Schematic flow of a "self-aligned" process wherein the gate metal layer is used to protect the FET channel from ion implantation and processing damage. Steps 1 and 2 define the channel and gate, step 3 is the self-aligning step. Step 4 provides the device isolation. Steps 5 to 8 define the ohmic contacts, first and second level interconnections, and passivation protection.

556


2) Gate metal deposition, Photolithography, Etching or liftoff to define gate

3) N'ion implantation. Anneal

n +ion implantation

4) Photolithgraphy, Isolation ion implantation

5) Photolithography, Ohmic metal deposition, Liftoff or etching, Alloying

Figure 10-36. (continued).

10.7 Schottky Barriers and Gates 6) Dielectriideposition, Via etch, Interconnect metal deposition, Patterning

7) Dielectric deposition, Via patterning, Metal 2 deposition, Patterning

8) Passivation and Contact pad via openings

Figure 10-36. (continued).

557

558


al., 1983; Sinha and Poate, 1974), Titanium (Matino), or an alloy or bi-layer such as WSi (Dautremont-Smith et al., 1990) W-N (Kikauraet al., 1988), Ti-W-N (Sadler et al., 1989), W-A1 (Inokuchi et al., 1987), or other similar combinations. These types of Schottky barrier material are relatively stable at high temperatures and exhibit only very limited reactivity with the compound semiconductor surface. However, it has been observed that metals such as tungsten must be treated extremely carefully as layers tend to lift from the semiconductor surface at temperatures above 400-500°C due to thermal expansion mismatch (the ratio of thermal expansion coefficients is greater than 10: 1). Also, all Ti-based gate structures can exhibit “gate sinking” under high stress operation. In this case, the metallurgical junction diffuses into the semiconductor and alters the electrical performance over time. Multi-layer metal-metalloid structures may be deposited to significantly reduce the electrical resistivity of the gate structure. For example, gold over W-Si, gold over TaSi, or tungsten over W-Si. Use of these layered structures is particularly important for device performance as silicide or refractory materials have a much higher resistivity than gold or gold-based alloys. Thus the current carrying capabilities are significantly lower. Electromigration and thermally-induced grain modification may also occur if the current densities are driven above lo5 A cm-* depending on the metals system (Irvin and Loya 1978; Irvin, 1982; Oates and Barr, 1994). Localized heating can occur in a resistive gate structure, thereby upsetting the device operating characteristics and accelerating the degradation processes (see Irvin and Loya, 1978; Irvin, 1982, and references therein). The use of such “bi-layer” or T-gate structures substantially enhances the current car-

-

rying capability (Maeda et al., 1988) and increases the operating speed of a transistor by lowering the gate RC time constant (Brech et al., 1997). A low-resistance gate is crucial to the performance of devices with submicrometer gate lengths, as the advantages of the small transit time through the gate region can be completely offset by the performance losses incurred from the RC effects of a high resistivity gate stripe. A gate structure known as the “T-gate” or “mushroom-gate” (Yuen et al., 1988; Beaubien, 1992; Wada et al., 1997; Thiede et al., 1998; Pobanz et al., 1998) can be utilized to further reduce the resistance of the refractory of high-resistivity gate structure while maintaining a very small effective gate length. The T-gate configuration is formed by deliberately undercutting the Schottky barrier material beneath the top metallization layer, or by providing a photoresist or other sacrificial layer to shape the top metallization during deposition following the definition of the fine gate feature on the surface. This undercut structure is also useful for self-aligned ion implanted processes to prevent the implanted ions from encroaching on the channel region. In cross section the gate has a T-shape with the current being carried predominantly in the low-resistivity top metal layer, as shown schematically in Fig. 10-37. Here the large, low-resistance top metal extends over the higher resistance Schottky barrier material in a Tconfiguration. Figure 10-38 shows an SEM cross section of a T-gate structure. The physical gate length in this figure is 100 nm, while the metal width of the cross is -0.5 pm. Wada et al. (1997) described a process for the fabrication of gates with dimensions of under 100 nm. Electron-beam or deep-UV lithography is required to achieve the sub-0.25 pm dimensions, whereas g-line or i-line photolithography is suitable for dimensions larger than -0.4 pm. Many “tricks”

-

559


Figure 10-37. Cross-section schematic diagram of a “T-gate” structure. Numerous combinations of compatible materials may be used for this gate configuration.

they formed a “spike-gate’’ structure, causing a buried extension of the T-gate to provide an extremely short gate length for power applications. The key to realizing successful device performance lies in the uniformity and reproducibility of the gate formation process, coupled intimately with the materials properties (thickness x doping product, charge profile, charge density, heterostructure etc.). Step and repeat lithographic systems can create minimum dimensions typically in the range of 0.25-0.5 pm in production environments. G-line (dimensions 0.5 pm), I-line (dimensions -0.25 pm), deep UV (- 0.15 pm), image reversal processes, or Xray flood exposure can be used to photolithographically define the fine features. FiveX or ten-X projection systems permit the writing of finer features than one-to-one projectors or contact aligners. Electron beam methods are capable of achieving -0.1 pm line widths and can perform near this level in a low-to-modest volume production environment, the trade-off being that the systems are relatively slow, expensive, and limited to gate level exposures at the present time. As designers continue to push for higher frequency performance and device dimensions shrink, it should be recognized that processes must evolve that can work macroscopically at the near-atomic level: consider that a 0.1 pm gate stripe is only about 350 atoms wide, while GaAs sub-

-

Figure 10-38. SEM micrograph of a T-gate structure. The physical gate length at the semiconductor surface is 100 nm. The width of the body is -0.5 pm. (Micrograph courtesy of Beaubien (1992).)

-

of interference or multiple pass exposures, intentional misalignment, multilayer resists, shadowing, etc. can be used in either process to achieve very fine gate geometries (Wang et al., 1997). Trade-offs regarding the selection of a fine-line process must be determined vis-a-vis device and process complexity, yield, process cost, and reliability. Devices fabricated with these fine features show superior high frequency performance due to the small RC time constant and a short gate length. A variation on the T-gate was proposed by Tanaka et al. (1997). Herein

560


strates are 100 mm in diameter, 150 mm substrates have entered production, and typical print fields in a step-and-repeat camera are 15-20 mm by 15-20 mm.

10.8 Annealing Annealing processes are required for activating ion implanted species, passivating surfaces and electrically active defects, and relieving stresses between layers of dissimilar materials. The underlying principle is to induce controlled atomic exchange within the wafer by thermal excitation. There are two basic approaches to this process: fur-

nace annealing (FA) and rapid thermal annealing (RTA). The two configurations are illustrated schematically in Figs. 10-39 and 10-40, respectively. Furnace annealing tends to be less stressful to the wafer as the rate of change of temperature is relatively slow, while the time at high temperature is relatively long. In RTA the object is to provide a rapidly changing, high peak temperature condition (typically hundreds of degrees higher than that in FA) to effect atomic level rearrangement in a very short time span. The drawback of RTA is the stress induced by rapid heating: the short time tends to preclude uniform heating and the exposure period is generally insufficient for ther-

-

................ ................ Tirne(rnin.)

Arsine, Phosphine Hydrogen or inert gas

Wafers

Furnace

Figure 10-39. A schematic diagram of afurnace annealing system. In the upper section of the figure, the time-dependence sequence is illustrated. The key issues are a relatively slow temperature rise and fall, and a lengthy time at the peak temperature. The lower half of the figure shows wafers heating parallel to the gas stream to minimize stresses due to heat retention and radiativelconductive thermal exchanges. Safety systems are mandatory for handling effluent gases when processing most 111-V or 11-VI compound semiconductor materials.

10.8 Annealing

TMaX

-

56 1

Typical Maximum Temperatures -700-1000°C 5-60 sec typical

ROOlll

Temp

Heating and cooling rates in the range -10 to 100’s of degrees per minute

-

Figure 10-40. A schematic diagram of a rapid thermal annealing (RTA) system. In the upper section of the figure, the time-temperature sequence is illustrated. The key issues are a relatively rapid temperature rise and fall, and a relatively short time at the peak temperature. The lower half of the figure shows a wafer constrained between a graphite (or other material) susceptor. This configuration, typical of present commercial systems, can process one wafer at a time. The susceptor acts to supply heat uniformly to the wafer to prevent slip and stress, and to slow the actual rates of heating and cooling. Exhaust gases must be treated by combustion or scrubbing for safety.

ma1 equilibration. The primary difference between these approaches is the nature of diffusion and redistribution of the impurities and defects behavior) due to the different time-temperature cycles. Annealing may be used for repairing the minor atomic displacements associated with ion implantation without causing the recovery of the gross displacement damage, as required for isolation processes; or, with a larger thermal budget, cause the ion im-

(m

planted species to site select (activate) and occupy a substitutional position in the lattice while simultaneously recovering nearly all of the atomic displacement damage; and also, for strain-relieving multi-layer materials structures with dissimilar physical properties, as are found in all integrated circuit fabrication sequences. Passivation may be realized through the “healing” of surface defects, the consolidation of deposited films, and the in-/out-diffusion of mobile

562


species such as hydrogen (Pearton and Caruso, 1989). Annealing may be carried out using a variety of heat sources such as stripheaters (Banerjee and Bakar, 1985), furnace-based processes (Woodall et al., 1981; Shigetomi and Matsumaro, 1983; Hiramoto et al., 1985), and RTA methods using lasers (Tsukada et al., 1983), rapid-cycling high intensity heat lamps (various types of IR generators) (Chan and Lin, 1986; Crist and Look, 1990), or arc sources (TabatabaieAlavi et al., 1983). The processes discussed here involve relatively high temperatures; low-temperature alloying and annealing processes are discussed relative to the formation of ohmic contacts in Sec. 10.6. On comparing FA and RTA methods, one finds the net thermal budgets to be significantly different. As an example, a furnace anneal cycle at 850 O C for 20 min is equivalent to a few seconds at 1000O C in terms of atomic diffusivities. In contrast, a typical RTA cycle may last only 5 or 10 s at 1000 C . During FA, the metastable defects and slightly displaced atoms relax during the heating cycle. While at temperature, longer range interactions take place, and site exchange and diffusion occur. During cooling, more active species continue to move slightly as the wafer returns to room temperature. The surface temperature achieved during RTA processes is not well-characterized as the heat sources (e.g., heat lamps) are operating many hundreds of degrees higher than the actual wafer temperature. Heat is being conducted and re-radiated from the surface region in a very dynamic condition. Also, the wafer topology may be very nonuniform: patterned layers of dielectric, metal, and semiconductor may be exposed, all of which have radically differing thermal and radiative properties. Thus strongly inhomogeneous thermal gradients are created in the wafer. It is the increased kinetic energy at O

the higher temperature that allows for very rapid atomic exchange and thus for rapid recovery of lattice damage and impurity site selection. Since the time at elevated temperature is so short in the RTA process, typical dopant species diffuse distances of the order of a few nanometers rather than tens or hundreds of nanometers in the case of FA. When a substrate is annealed after ion implantation, the donor and acceptor impurities generally become substitutional in the lattice and charge is provided to the semiconductor. The net amount of charge depends on 1) the number of donor or acceptor species present; 2) site selection probabilities (interstitialcy, autocompensation effects, the ionization state in the lattice), and 3 ) the degree of lattice recovery (point defect concentrations). For example, n-type regions with electron densities as high as 5 x l O I 9 cmP3have been created using very high dose implants (- 1015cmp2) and laser RTA techniques (Liu et al., 1980); p-type materials with hole densities up to 7 x 10l9 cm-3 have been formed using pulsed laser annealing (Kular et al., 1978). With furnace annealing processes, the peak charge densities achieved are somewhat lower than those obtained in RTA due to the quasi-equilibrium nature of the furnace anneal process. Typically, maximum n-type and p-type carrier concentrations of 3-5 x 10" cm-3, and 1 -2x 1019cmP3,respectively, are realized in GaAs with furnace annealing processes. Much effort has been expended in understanding and controlling the annealing process in compound semiconductors, building on the experience developed in silicon wafer fabrication. Owing to the volatility of the group 11, V, and VI species, thermal annealing of the compound semiconductors poses significant challenges. The behavior of GaAs materials under various conditions of capping and/or arsenic overpressure have been

10.8 Annealing

studied at great length with widely varying results [see, for examples, Woodall et al. (1981), Banerjee andBakar (1985), Tsukada et al. (1983) Crist and Look (1990), Asom et al. (1988), Look et al. (1986), Parsey et al. (1987)l. Site selection of impurities is affected by 1) the statistical nature of the atomic displacements, 2) the exchange processes that must take place to create a substitutional impurity, 3) the competing formation of point defects and defect complexes, etc. Since, in the compound semiconductors, there are two chemically and electrically distinct lattice sites, the charge state of an impurity can be either donor-like or acceptor-like, and in the case of interstitialcy the charge state may not be well-defined. Variations in activation have been attributed to inconsistencies in substrate properties (e.g., bulk and surface layer stoichiometry, impurities, out- and in-diffusion of both defects and impurities), the efficacy of “face-to-face” vapor exchange processes, and the interaction of the capping layers with the semiconductor surface layers (e.g., stresses, interdiffusion, contamination, etc.). The annealing of compound semiconductor materials may be carried out with or without a protective cap, or a group 11, V, or VI “quasi-equilibrium’’ overpressure atmosphere. In general, some method for maintaining the surface integrity is required to prevent decomposition of the surface regions due to the high vapor pressures of the group 11, V, and VI species, particularly with the phosphorus- or mercury-containing materials. The surface layers of compound semiconductors are subject to incongruent decomposition during heating due to the strongly mismatched vapor pressures of the respective components, as illustrated in Fig. 10-41 for GaAs, Gap, and InP (Panish, 1974). The vapor pressures of the group V species may be in the range of a few Pascal to many kilo Pascal at useable annealing

563

temperatures. Surface losses must be minimized lest the surface become conducting (more metallic) in nature as the surface becomes rich in the less volatile species. This latter effect will occur in the temperature regime about and above the congruent evaporation point. For GaAs-based materials, this is in the range of 580-620°C (Panish, 1974), and similarly, for InP -480-500°C. The group VI species tend to have lower vapor pressures than the group V elements, and thus somewhat more relaxed annealing conditions prevail for most 11- VI materials, although the same phenomena must be considered. However, in materials such as HgCdTe, the vapor pressure of mercury is extremely high and the vapors are toxic. Great care must be taken to prevent decomposition of HgCdTe and related compound semiconductors. In furnace annealing of GaAs, the initial rate of free-surface decomposition is of the order of a few monolayers per second at 50O-60O0C, depending on the heating rate, temperature, and presence of an atmosphere. In an equivalent RTA process, an uncapped surface decomposes at initial rates of tens of nanometers per second in GaAs; these rates are higher for phosphorus-containing compounds. The use of an overpressure of As, or P, vapor can reduce or prevent the decomposition by balancing the surface dissociation rate, while a cap layer will completely suppress loss of the volatiles, although diffusion into the cap or wafer surface may become an issue. “Overpressures” may be generated by heating solid sources of the host material, from elemental or compound sources, or by injection of the volatile component vapor species. Open tube or closed ampul methods have been used: practical considerations in the processing of large diameter wafers dictate the use of “open tube” methods, although significant safety measures must be

-

564

10 Compound Semiconductor Device Processing D4K/T,(Ga-AS,

In-P)

m4K/T,(Ga-P)

Figure 10-41. A plot of the vapor pressures of arsenic and phosphorous over GaAs, Gap, and InP (solid). The pressure scale is in log(atmospheres), and the temperature scales are in lo4 T-’ (in Kelvin). The vapor pressures are represented as the dimeric form of arsenic and phosphorus. (This figure is reproduced from Panish (1974). Reprinted with permission of North-Holland Publishing Co., Copyright 1974.)

in place for most compound semiconductors (Zuleeg et al., 1990). Furnace annealing of ion implanted GaAs is carried out typically for 20-30 min or more in the range of 700-900°C. Anneal-

ing processes carried out below about 700°C tend to be very protracted and are subject to large variation and irreproducibility (Henry, 1989-1991). Lower temperatures in the range of 500-700°C are used

10.8 Annealing

for materials containing phosphorus, and yet lower temperatures for materials in the 11-VI family (ca. 200-350°C). To prevent or minimize decomposition of the surfaces, the wafers are typically capped with a nitride or oxide film (Nishi et al., 1982; Campbell et al., 1986; Mathur et al., 1985). In some processes, “face-to-face” configurations have been implemented (Woodall et al., 1981), and in others the overpressure methods are employed without capping (Henry, 1989- 1991). Complications arise in each approach: removal of the capping material is a moderately difficult process and may damage the surface layer(s); the face-to-face approach subjects the wafer to yield-reducing damage from scratching and potential cross-contamination, and the overpressure method may have system and safety constraints due to the toxicity of the materials required in compound semiconductor processing. Owing to the relative “softness” of the compound semiconductor materials, the maximum annealing temperatures and the heating and cooling rates are much more critical than those used in silicon processing. For example, GaAs wafers may readily warp when furnace annealed in a vertical configuration at 850°C and withdrawn from the furnace at a rapid rate (effective dTldt of - 100- 1000°C per minute). Such warpage renders the wafer unsuitable for any further processing, as modern step-and-repeat or contact photolithography systems cannot focus on a surface with more than a few micrometers of local focal plane variation, or the wafer may fracture when brought into clamp contact with the photomask or other wafer handling tools. Annealing in a horizontal configuration has been accomplished, but consumes large areas in the furnaces, and is subject to the difficulties of maintaining a uniform and reproducible environment in a large volume. In addition,

565

stresses generated by rapid heating or cooling may create slip in the substrate, which can lead to short or open circuits after processing and facile cleavage of the water in post-process steps such as wafer thinning, back-surface metallizing, or dicing operations. The very rapid thermal cycling impressed in an RTA process makes the understanding and control of these stress-induced phenomena particularly important for maintaining wafer integrity. RTA processes, although inducing higher peak temperatures in the host wafer than furnace annealing cycles, essentially affect the same atomic-level reconstructions. RTA process conditions are typically in the range of 850- 1050°C for - 10-60 s (Banerjee and Baker, 1985; Tabatabaie-Alavi et al., 1983). They key issue in the RTA cycle is that the net thermal budget for the process is smaller than of the furnace-based processes. Thus, although the atomic-level excitation is greater due to the high temperatures, the short time prevents a significant redistribution for most impurities, defects, and the host lattice atoms, and yet allows the damage and atomic displacements to recover. This latter point is the principal advantage of the RTA annealing procedure relative to the furnace-based processes. As previously noted, greater carrier concentrations can be obtained with RTA processes versus furnace annealing, an effect attributed to the nonequilibrium conditions created in RTA processes (Tiku and Duncan, 1985). Rapid thermal annealing has been investigated for several years with mixed results (Kular et al., 1978; Kasahara et al., 1979; Immorlica andEisen, 1976; Fan et al., 1982; Arai et al., 1981; Ito et al., 1983). The successful implementation of RTA has been strongly dependent on the configuration of the annealing apparatus and the environment within the process chamber, as well as the details of the time-temperature cycle.

566


RTA processes have been developed to anneal the wafers under atmospheres of As, ASH,, P, PH, , H,, N,, or Ar to mitigate surface decomposition effects. The difficulties in this approach lie in developing a uniform and reproducible thermal environment in a wafer with a patterned, and possibly metallized, surface in conjunction with the necessity of maintaining the surface integrity. The low thermal diffusivity of the compound semiconductor materials contributes significantly to the creation of localized temperature gradients in the wafer, which may be undesirable in terms of stress and electrical property uniformity. The thermal shock induced in the wafer from the extremely rapid rise or fall of the wafer temperature and stresses generated from nonuniform heating due to the varied reflective and absorptive properties of the fabricated wafer, must be carefully considered and understood for successful implementation of RTA processes. Stresses generated in annealing arise from basically two phenomena: differential thermal expansion and physico-chemical interactions. The process of depositing a metal layer may expose the wafer surface to temperatures in excess of 1000"C in a metal evaporation system, or varying in the hundreds of degrees for sputtering-based depositions. While the bulk of the material may not achieve this high temperature during the process, the surface layers do realize this thermal insult. Upon cooling, stresses will build up from the large differences in the thermal expansion coefficients between the metal, the semiconductor, and the other layers, such as dielectric films. Typically, this difference in expansion coefficients is of the order of 5 : 1 to 10 : 1 between the different materials. If care is not taken in the annealing cycle, this differential contraction/expansion can create sufficient stress to delaminate the structure, fracture

fine features, or induce piezoelectric effects. An annealing process can also be used to relax stresses that arise from the process sequences and the incompatibilities of the multiple layers of dissimilar materials which comprise the fabrication of the device. A furnace anneal at relatively low temperatures (below 450-500 "C), with an appropriate neutral or protective atmosphere for times ranging from a few minutes to several hours can be used to alleviate stresses. The object of this cycle is to permit some interatomic exchange and relaxation to create a transition region between the dissimilar materials. Crystal slip may occur more readily with RTA processes than furnace annealing, due to the large thermal stresses (i.e., the thermal gradients between the front and rear surfaces, the finite thermal diffusivity of the semiconductor materials, and the metal thermal conductivity, etc. (Pearton and Caruso, 1989)). Slip in the (1 10) crystal directions and dislocations can be generated in the peripheral region of the wafer, due to the large radial and axial thermal gradients enhanced by the radiative characteristics of the wafer edges. The mechanical failure and disruption of the crystal lattice leads to poor performance or failure of devices fabricated in these regions (Miyazawa et al., 1983; Ishii et al., 1984; Suchet et al., 1987). Stresses induced in the RTA process can lead to warping, delamination of dielectric layers, and damage to fine-featured components (e.g., separation of resistor films, cracking of metal traces, etc.), particularly at step edges. By careful design of the heating systems, the use of heat shields, susceptors, cover wafers, or heat spreaders, the RTA approach can be made to produce a viable wafer with minimal deleterious effects. In the deposition of dielectric materials. the chemical compositions may be adjusted to reduce the stress generated in the anneal

-

10.9 Dielectrics and Interlayer

and thus lead to greater resistance to the effects of thermal cycling. However, even a low-stress film may create tension or compression in the range of lo9 to > 10” dyn cm-’ ( lo4 to > lo5 N), which is sufficient to alter the device electrical characteristics. This latter point is the result of the polar nature of compound semiconductor crystal lattices and resulting piezoelectric effects. The problem associated with such compositional variation is that the film properties are determined by the chemical make-up and may therefore be in conflict with the design requirements (e.g., the capacitance dielectric value or the isolation and standoff voltage capabilities). In the case of a dielectricover-gate stripe, stresses in this critical area may shift the threshold voltage, which can lead to erratic circuit performance from thermal cycling effects. The metallization/ dielectric “sandwich” structures, e.g., capacitors or inductors, and multi-level metals, formed when passive components and interconnections are fabricated must also be stable to the thermal cycle. The respective materials properties and compatibility are very important if delamination or blistering resulting from excess stresses at the respective interface is to be avoided. In HBT devices, the breakdown voltage of the emitterbase or collector-base junctions may be reduced by improperly deposited dielectric layers. Interface and deep-level states may be passivated in compound semiconductors by appropriate implantation processes (e.g., low energy protons), followed by a gentle, low-temperature annealing cycle (Pearton and Caruso, 1989). As hydrogen rapidly out-diffuses from compound semiconductors (Pearton et al., 1987), temperatures in the range of 300-400 “C must be used for the annealing process. Also, with this high diffusivity the thermal excursion and thermal budget of any subsequent process

-

-

567

steps are drastically limited if the effect of the hydrogen is to be maintained (see Sec. 10.3). Reproducibility of the annealing process in crucial in order to obtain reproducible device performance. The statistical nature of impurity site selection, and related compensation and defect formation processes, necessitates tight control of the annealing environment. If high temperature anneals are used, such as are necessary for ion implantation annealing, then considerations must be taken of the thermal history of the wafer from previous process steps, the impact on impurity and defect redistribution in subsequent processing, and the ability of the materials to withstand the additional thermal cycling. One of the conditions impressed on the fabrication sequence is that sequential steps must be carried out with continually lower thermal budgets to prevent uncontrolled reactions, undesirable phase formation, and additional in-diffusion and punch through of the junction and contact regions. Therefore, careful planning and a detailed understanding of the material’s properties and the thermodynamics and kinetics of the processes are required.

10.9 Dielectrics and Interlayer Isolation Electrical and mechanical isolation is required between the various layers of semiconductor and metals in a device. For example, the formation of capacitors requires a dielectric material to isolate the electrode plates. In the case of an inductor the coil runners must be isolated from the substrate or any other metallizations. The formation of a capacitor is illustrated in Fig. 10-42. Typically, this structure is formed as either an nf layer covered by a dielectric (Fig. 1042a), or as one of the first level metals cov-

568

10 Compound Semiconductor Device Processing Effectivedimension of capacitor 4

I

I

*

"Second"Level M e t a l l

N Channel Isolation

Substrate

Isolation

Effective dimension of capacitor 4

I

I

First Metal Layer

Substrate

ered by a dielectric, followed by an upper level metal which defines the capacitor area (Fig. 10-42b). In this application, the properties and perfection of the dielectric layer are critical to the reproducibility and yield of the capacitors. An inductor may be formed as a spiral in a single layer of metal with a bridge or via to connect the center of the coil. Stacked inductors are also possible using multiple metal layers and vias. The complexity of modern circuit designs demands multiple metallization layers to interconnect the devices and the signal transmission lines, provide for power bus routing, and to permit adequate circuit compaction. Each of these metal layers must be

LL

Figure 10-42. Schematic cross sections of capacitor structures. In a) a channel-based capacitor is illustrated. In b) the capacitor is formed from the first and second levcl metal\, with the dielectriL between them The thickne\\ and pertection of the diclcctric layer is critical to the leakage and breakdown properties of the structure in both cases. The effective areal dimensions of the capacitor are determined by the lengths of the upper level metal pad.

isolated with a dielectric layer. The dielectric material must possess a suitable dielectric strength and dielectric constant, uniformity of thickness and physical properties, and be deposited with a high degree of layer integrity to minimize short circuits. The dielectric layers also play a critical role in controlling the density of surface states and pinning of the Fermi level at the semiconductor surface. These properties may affect the value and control of the device thresholds in MESFET, HFET (MODFET), and MISFET-type devices fabricated on GaAs, InP, and other compound semiconductor materials [see Daembkes (1991), and articles and references therein].

10.9 Dielectrics and lnterlayer

The dielectric material serves to reduce surface leakage by “tying up” dangling bonds and passivating the surfaces. A dielectric layer may also be used to protect the compound semiconductor from chemical attack and contamination during processing, and to provide mechanical protection of the surfaces. An encapsulating dielectric film may be used to prevent surface decomposition during annealing procedures. This is a crucial application in most III-V and I1-VI compounds due to the volatility of the component species. To assist in the formation of air bridge metallizations, dielectric layers may be used to form the post-andbridge structures. Thus understanding of the dielectric material, the deposition process, and potential interactions at the interfaces are critical for achieving reproducible device characteristics. It is an unfortunate fact that the compound semiconductor materials do not have the strong, stable native oxide available in silicon technology. For example, in GaAs the native oxides Ga,O, and As20, (y=3.5) are very weak, being readily soluble in a variety of liquids. The suboxides (Ga20and As20) are quite volatile at common processing temperatures. These oxides, which form rapidly in air, are one source of interfacial states as the surface bond configuration and chemistry are strongly modified by the oxidation process. The native oxides also tend to be inhomogeneous in their properties due to strong local variation in the chemical composition and bonding (Watanabe et al., 1979). In part, this is due to the large difference in vapor pressure and reactivity of the constituent elements. Other oxide layers, for example those formed with glycol-based solutions, have been found to be electrically inferior to most deposited dielectric materials and have therefore received little attention (Hasegawa and Hartnagel, 1976). Dissolution of the group 111 and

569

group V oxides may readily be carried out with HC1- or NH,OH-based chemistries. This is convenient for surface preparation, but emphasizes the limited utility of the native species for integrated circuit applications. Thus alternative deposited dielectric materials must be used for CS device fabrication. For most applications, the suitable dielectric materials are SiO,N,, Si,N,, and SiO,. Device performance criteria dictate the optimum value of the dielectric constant. The dielectric constant depends strongly on the chemical composition; the composition of the materials is determined by the deposition chemistry and the apparatus configuration. It should be emphasized that these materials are rarely, if ever, stoichiometric. Therefore, care must be exercised in deposition to achieve a homogeneous, uniform and low-stress film. The application of a dielectric layer embodies many compromises. Optimally, it is desirable to have a low dielectric constant for high-speed operation. The tradeoff in the use of SO,, Si,N,, and SiO,N, is the value of the dielectric constant: nitride films are best for capacitors, but the oxide is optimum for runners due to the lower dielectric constant and a resulting lower capacitance. Mixed oxy-nitride materials have dielectric constants intermediate between SiO, and Si,N,, which permits a compromise in the circuit fabrication-performance relationship. For example, the dielectric constant for SiO, (x-2) is significantly less than that of Si,N, (x-3, y-4) as shown in Table 10-7, along with other interesting dielectric materials. Alternative dielectrics have received some attention during the late 1990s for special applications. Circuit designers recognize certain advantages of “high k” dielectrics, but design and layout constraints may force impractically small dimensions, which obviate the advantages.

570


Table 10-7. Values of dielectric constants for selected dielectrics. Material

GaAs SiO, Si,N, Pol yimide Ta205

TiO, SrTiO, A m

Dielectric constant (relative)

Reference

13.1 4-5 5.5-7.5 -3.5 20-2s 14-110 50- 100 9.5

Sze (I98 I , App. H) Williams (1990, p. 295) Williams (1990, p. 295) CRC (1978) Williams (1990, p. 295) CRC (1978) Nishitsuji et al. (1993) CRC (1986)

A lower capacitance may be realized with SiO,, a highly desirable feature for highspeed circuits. However, much thinner SiO, dielectric layers must be deposited to achieve a given capacitance value (relative to materials with larger dielectric constants) or, alternatively, large areas of the circuit must be committed to these devices with the resulting cost increase and yield reduction. In the case of very thin layers, the integrity of the film becomes a yield-limiting factor. Most of these dielectric layers can be deposited with relatively low stresses, if the process is carried out under optimized conditions. Typical stress levels are in the range of lo9- 10” dyn cm ( lo4- lo6 N). Values of lo9 dyn cm (lo4 N) or less are considered strain-free, while those above 10’’ dyn cm ( lo5 N) can create problems with yield and reliability (layer adhesion, thermal cycling effects). Another issue with stress is the piezo-electric (PE) effects arising from the polar nature of the compound semiconductor lattice. Interlayer stresses may generate significant anisotropic threshold shifts due to the PE effects; thus the gate orientation with respect to the substrate crystallographic orientation becomes important. In Si,N,. films on GaAs, stress typically increases with increasing Si fraction. At the

same time, the dielectric film resistivity varies with the silane concentration in the deposition atmosphere, making the electrical isolation less effective, i.e., higher leakage currents may be observed. Hydrogen incorporation also increases with lower deposition temperatures. Excessive hydrogen content may cause dielectric “blistering” during subsequent high temperature processes. An optimum balance of the properties in silicon nitride materials has been obtained with “near-stoichiometric” film compositions (see Williams, 1990, Secs. 8.3.1, 13.3, and references therein). A caveat to the use of dielectric materials is the mechanical incompatibility between most such materials and the compound semiconductors. The thermal expansion coefficients of dielectric materials are typically quite different from metals or the host semiconductor. Thus deposition of the dielectric layer can increase the levels of stress during thermal excursions. Thermal cycling caused by device operation can produce failures in metallization lines and contacts from cyclic fatigue, particularly at steps and edges. This effect is illustrated schematically in Fig. 10-43.Cyclical stresses can also give rise to shifts in device characteristics arising from the PE effects in the compound semiconductor. The PE effects and the fabrication process-related phenomena, as they affect the device threshold and operation, must therefore be clearly understood to achieve proper and reliable circuit operation. The deposition of dielectric films may be carried out by a variety of techniques. Evaporation methods for dielectric material deposition are well understood but have limited applicability for compound semiconductor processing. This method suffers from exposure of the substrate to very high temperatures, dielectric composition control is very difficult, and variation in the film composi-


571

Figure 10-43. Detail of a metal line over a dielectric step. With continued thermal cycling, the differential expansion may induce fractures and microcracking in the metal lines. Similarly, dielectric over-layers may crack due to expansion of the metals beneath. Steps and edges are most suscep tible owing to the concentration of stresses.

tion occurs with time due to depletion of the various components from the source charge at varying rates. The control of stoichiometry and the materials properties are also complicated by the fact that elemental and molecular evaporation rates are very difficult to balance in a high vacuum (HV or UHV) deposition environment. Sputtering methods may be used for deposition but surface damage can be significant unless great care is taken to optimize deposition processes. Stoichiometry is generally variable throughout the film on the microscale, which may affect the physical properties as well as the etching characteristics. Aging of the sputtering target(s) may also cause a gradual shift in the dielectric composition and properties. Lattice damage can occur from ions and surface atoms being driven into the surface region: resputtering of surface atoms also occurs during deposition. It is critical that no low frequency (e.g., 455 kHz) excitation is implemented in these systems as the plasma will severely

damage any exposed semiconductor surface regions. Hydrogenation of the surface region is also a problem, especially with the use of silane, hydrogen, and/or ammonia feed gases. The incorporation of hydrogen in various forms alters the dielectric properties in an uncontrolled manner and produces a time-varying effect in the film, due to out-diffusion of the hydrogen species during subsequent processing, or even during device operation (Pearton et al., 1987). Standard CVD processes require relatively high deposition temperatures to drive the gas phase reactions. Typically, deposition takes place at temperatures greater than 500- 1000°C, which is incompatible with most metallizations used for ohmic contacts and interconnects. Temperatures in this range are also too high for most compound semiconductor materials: surface decomposition may occur during the deposition cycle, as the vapor pressures of the group V species, e.g., PA, and P,, for example, are significant at these processing temperatures

572


(see Fig. 10-41, and Panish (1984), for example). The deposition method of choice appears to be plasma-enhanced chemical vapor deposition (PECVD). This is due to the relatively low temperatures (- 175-400°C) developed in these processes, and the enhanced controllability of the reactor systems. The plasma serves to create energetic reactive species, with the energy imparted by electrical excitation rather than direct thermalization. The plasma may be generated with DC or AC fields, in a variety of system configurations: each approach has its proponents (Gupta et al., 1983; Tsubaki et al., 1979). In PECVD processes the pressures are typically of the order of lop3Torr (0.13 N rn-,). The excitation in the plasma imparts energies in the range of a few hundred electronvolts or less. Thus there is only minimal surface damage due to free electron or ion bombardment (Meiners, 1982). The chemically reactive species are generated at low effective temperatures with the plasma. Only a very small fraction of the available molecules are ionized by these interactions: most of the plasma is neutral and therefore relatively “cool” and unreactive. The substrate may be heated or cooled, but it is necessary to raise the substrate surface temperature to only 150-300°C for high quality deposition. The self-heating effects during deposition can raise the substrates into this temperature range; active cooling may be desirable for process reproducibility. The low temperature of this process generally allows direct monitoring of the gas-phase reactions, reaction species, and by-products by the characteristic emission or absorption energies (Havrilla et al., 1990), or analysis of the exhaust stream by RGA techniques. These type of measurements can be readily adapted to process control or end-point detection.

-

The PECVD method offers great flexibility: the dielectric density, composition, refractive index, and dielectric constant can be varied by controlling the deposition conditions. The PECVD processes can be used to create layers of AlN, Si,N,, SiO,, Ta,O, , TiO,, and other materials. A1N appears to be a promising new material for use in GaAs and related materials. It possesses a thermal expansion coefficient well matched to GaAs, but the deposition-related damage is presently significant and the material is rather hard to remove without creating additional damage to the surface (Gamo et al., 1977). Growth rates in PECVD tend to decrease with increasing operating pressure or higher deposition temperatures, while the refractive index generally increases with a higher deposition temperature. Suitable gases for deposition and etching are reactive species: chlorines, fluorines, ammonia, silane, hydrogen, oxygen, and nitrogen-containing compounds. Noble gases such as argon may be used as diluents to moderate the deposition process. The major drawback to utilizing PECVD processing is that the process has many variables: gas pressure, chamber and substrate temperatures, flow rates, gas compositions, etching rates, the evolution of by-product materials, the electrode geometry, the excitation method (DC or RF and excitation frequency), the input power, the plasma energy density, the system configuration, substrate rotation, etc. (Gupta et al., 1983). These variables present a formidable obstacle to process development, and complicate process control. For process consistency, contamination from pumps, leakage at vacuum seals (processes are not operated in UHV conditions), chamber materials, and residual species such as Si, 0, H, C, N, etc. must be considered. As a result, a stable, robust operating condition can be difficult to achieve and sustain. Another concern in the PECVD


method is that deposition occurs over the entire chamber, complicating the control and stability of the process. Careful maintenance and consistent cleaning are required to maintain process integrity refully designed experimental methods 'and the application of statistical process control monitoring, a robust and reproducible process may be obtained (Havrilla et al., 1990). Barrel (or plate-type) PECVD reactor designs can be used for deposition (or etching) processes (Fig. 10-44). In a barrel reactor the electrode plates in the chamber may be neutral or floating relative to the ground potential. Various susceptor and chamber configurations are possible. Biasing the wafer plate can enhance or retard the deposition process, or alter the selectivity of the deposition. A low energy ion flux is thus created between the upper plate and the wafer surface. Local perturbations in the electric field on the wafer surface can readily deflect the incoming ions. It is generally more difficult to control an etching process on a fine scale in this type of system, due to the low ion energy and small accelerating field strength. This makes a barrel-type reactor best suited for relatively coarse processes, e.g., deposi-

573

tion of thick, noncritical layers, etching of large features, or ashing of photoresist layers, due to problems associated with localized and nonuniform electric fields on the metallized and/or patterned wafers. Controlled gas flows, critical to achieving a uniform etching process, are also difficult to maintain uniform in a barrel design due to nonuniform and nonsymmetric heating effects, convection, and generally asymmetric injection and pumping of the effluent species in commercial systems. Radial flow, rotating susceptor reactor designs have proven quite good for achieving uniform film deposition. A generalized configuration is shown in Fig. 10-45. New commercial systems, such as those developed by ElectroTechTM,or PlasmaThermTM, are capable of 1% control of thickness over a 3" (76 mm) diameter GaAs wafer (O'Neill, 1991). In this configuration the electrode temperature can be controlled, if desired, to enhance or retard the surface reaction rate. Reactant gases and ion species are much better distributed in the radial reactors relative to the barrel-type designs which leads to improved film characteristics and thickness uniformity. In a radial reactor the plasma is

Figure 10-44. A schematic illustration of a RF-excited, barrel-type configuration for PECVD of dielectric films. The plasma above the wafer creates the active species for deposition. The energy of the excited species may be quite high and cause damage to the semiconductor surface. Susceptor rotation may be incorporated to improve uniformity. Heating and bias may be supplied to the wafers to assist deposition.

574


Figure 10-45. A schematic illustration of a high-performance, radial flow configuration for PECVD of dielectric films. The plasma is generated above the wafers, creating the active species for deposition. A radial flow is set up by the injection and exhaust configuration, improving the uniformity of the deposition. As in most plasma-type systems, the energy of the excited species may be quite high and cause damage to the semiconductor surface. Susceptor rotation may be incorporated to improve uniformity. Heating and bias may be supplied to the wafers to assist deposition.

confined between the excitation plates, with a quenched region adjacent to the plate surfaces (space charge region). Ions are accelerated through the space charge region by the electric field and impinge on the wafer surface. Several investigators have introduced “downstream” (indirect) systems, wherein the plasma excitation and active species are generated “upstream” (with respect to the location of the substrates and the gas flow), well removed from the deposition region. The reactive materials are extracted from the source cell with the gas stream, and flow across the wafers. Deposition occurs on the wafer surface if the thermal conditions are appropriate. This configuration is shown in Fig. 10-46. It has been found that the use of such a downstream deposition process greatly reduces the plasma-induced ion damage in the surface regions (Meiners,

1982). A limitation to this approach is the total reactive ion current extractable from the source and the lifetime of the ionized species in the gas stream. Another approach to CVD deposition is photo-stimulated CVD. In this embodiment, a CVD chamber is fitted with windows to permit selected-wavelength light to impinge on the gases and/or the substrate. The added stimulation generates the desired species with reduced electrical energy input. The technique has advantages similar to PECVD: low deposition temperatures as well as a great selectivity for the excitation of specific molecular species by choice of the optical excitation energy (Peters, 1981). Photo-enhanced CVD induces less surface damage than the standard PECVD techniques, and by utilizing a downstream type configuration direct ion bombardment damage of the surface can be avoided.

10.9 Dielectrics and Interlayer

575

Figure 10-46. A schematic illustration of an ECR-plasma CVD system. The plasma is generated by tuned electron-cyclotron resonance of the desired species in a cell well removed from the deposition region. A carrier gas flow or extraction potential transports the active species to the wafers. Minimal damage is imparted in the wafer in this configuration. Rotation of the wafers may be provided to improve the uniformity of the deposition. Heating or bias may be supplied to the wafers to assist deposition.

Electron-cyclotron resonance (ECR) is a relatively new method for creating a plasma while mitigating the damage induced by the ion and electron bombardment (Kondo and Nanishi, 1989; Takamori et al., 1987; Sugata et al., 1988). Here the plasma excitation is provided in the usual manner with the addition of a very high frequency RF excitation signal. Selective excitation is achieved by choosing the excitation frequency to resonate with the desired ion species cyclotron frequency. These selected ions absorb the energy and create the plasma for deposition. A relatively high excitation power is required in this approach, and therefore the downstream configuration is used for obvious reasons. Another class of dielectric materials are polyimides. These materials are polymeric organic films with relatively low dielectric constants: typical values are 3.5. Polyimides are very stable dielectrics: some compositions are capable of tolerating exposure to temperatures greater than 500°C (Dupont, 1976). These materials are best suited as an encapsulant or capacitor dielec-

-

tric, for inductor isolation, or for isolation of second (and higher) metal levels. These materials are also useable for the standoff of metal runners in air bridge configurations, although the large capacitances may present a problem at very high frequencies. Moisture absorption and swelling can be an issue with polyimide materials. Incorporation of those layers must take packaging integrity into account to ensure long term reliability. Polyimides may be deposited with dispensehpin systems, as are used for photoresist coating. The major drawbacks to the application of polyimides are: 1) the extended curing time required to drive off the solvents and crosslink the polymer chains (ca. 1 h or more at elevated temperatures), and 2) control of the thickness owing to the high viscosity of the liquid phase. Following the curing, the polyimide film can be patterned with standard photolithographic methods. However, only specific etchants and some plasmas will attack polyimide materials. They can be etched with oxygen plasmas (asher), or with strongly basic solutions. Appropriate solvents or alcohols

576


may also be used for pattern development, but care must be taken to minimize softening or other damage to the film. One great advantage of the polyimides is their dielectric strength: typical values are lo6 V cm-'. This property, coupled with the high dielectric constant, makes these materials very attractive for use in high voltage circuits or for achieving very fine feature sizes. In PECVD and related deposition methods, film growth rates are in the range of 10-50 nm min-I, and useful films are typically 50- 1000 nm thick. The polyimide film thickness is controlled through the fluid viscosity and the spin speed and acceleration program in the spinner system. Very thin films (< 100 nm) can be deposited, but integrity generally suffers. All types of dielectric films can be evaluated with standard ellipsometric instruments to determined thickness and the dielectric constants. Other instruments, such as interferometers, are used to determine the compressive or tensile stress conditions in the deposited films. Pinholes or failures in the film integrity are a continual problem resulting from wafer surface contamination, the formation of large clusters or particulates in the plasma and on the chamber surfaces, or difficult surface topology. Multiple process cycles can be used to alleviate or minimize this problem. The impact of dielectric films and surface states on the channel saturation currents (Jsat), the device threshold voltage (Vth), and reverse breakdown voltage (VbJ effects are poorly understood. Sputtering of PECVD typically produce ion damage depths less than 50- 100 nm, but can have a damage depth in GaAs up to twice the expected ion range under improper deposition conditions (Williams, 1990, Chap. 9). Significant surface depletion effects occur from this damage, and can result in erratic device behavior. The surface state effects are especially

-

important for enhancement mode or lowcurrent devices, where the charge is very close to the gate or of low density, and thus the conducting channel is more sensitive to local perturbations in the surface electric field strength. Post-growth annealing may help stabilize the dielectric film properties by equilibrating the interface charge balance and the interfacial chemistry, and also relaxing built-in stresses (Weiss et al., 1977). All of these issues are crucial to the fabrication of high-performance, high-reliability integrated circuits in compound semiconductors, and are the subject of continuous investigation and development.

10.10 Resistors Biasing networks, feedback control, voltage and current dividers, load terminators, and balancing applications all require the use of resistors. Resistors may be formed utilizing the conducting channels (active regions) in the surface of the wafer, or constructed as separate thin film layer structures. The channel-based resistor structures may be formed using the n-layer to the n/n+ layers (ion implanted or epitaxially grown layers), as illustrated in Fig. 10-47a. This approach demands tight control of the sheet resistances in the layer(s) for a controlled resistance value. A thin film resistor is typically deposited above the first dielectric layer, as shown in Fig. 10-47b, but may be placed in any convenient location within a multi-layer metal scheme. A resistor requires a conductive stripe and at least two contacts. A channel-type structure will require some form of peripheral isolation to define the resistor body dimensions. Thus the fabrication of resistors must be carefully considered when planning the process sequence. Either a trench, mesa, or ion implantation scheme must be used to

10.10 Resistors

577

Figure 10-47. In a) a cross section of a channel-based resistor is illustrated. The effective length of the resistor is “1”. Ohmic contacts define the effective length. The width is determined by perimeter isolation [mesa or implant (shown)]. A dielectric layer is used to protect the resistor body during subsequent processing steps. Figure 10-42b illustrates a resistor structure made with a thinfilm resistor material. The layer is deposited on a dielectric as shown, and patterned by photolithographic methods. Metal contact pads are deposited and patterned on the ends of the resistor. Taps may be placed along the resistor body, if required. The effective length of this resistor is /, with the width determined by the lithography. Controlling the thickness or the chemical constituents in the film provides a high degree of control over the resistor properties.

define the body of the resistor and to isolate the contact region for channel-type resistors; deposited film resistors may be defined by photolithography and etching or lift off processes. Greater latitude is permitted for the deposited film structures built on dielectric layers, as the resistor bodies can meander over the surface (with some restrictions) without consuming valuable active area. A larger range of resistivity values is accessible to the thin process relative to the channel-type structures. The processing asso-

ciated with the resistor fabrication must not exceed the thermal constraints of the preceding processing sequences. The resistance value ( R )achieved in a resistor is defined by the relationship (10-12) where p is the resistivity of the conducting medium, L is the length, and W is the width of the resistor body; t is the layer thickness, implant thickness (- 2 AR& or the total ac-

578


tive epitaxial layer thickness, 2 R, is the sum of the contact resistances, and W, is the effective contact width. A resistor structure is shown in detail in Fig. 10-48. If multiple conducting layers are used in the resistor stripe, such as in an n+-n layer structure, Eq. (10-12) is modified to accommodate parallel conduction effects. For practical resistor structures, the contact resistance will be negligible (typically much less than one percent of the resistor value), and well within the resistor process variations. Resistors formed with the semiconductor conducting layers are relatively easy to implement. No additional mask levels are needed as the channel can be patterned with the process sequences of ohmic metallization and isolation. Typical resistivity values are in the range of 100-1000 Q/ 0 , but this range may easily be extended with additional ion implantation and annealing steps. If the resistor is isolated with a mesa etch, then additional process steps may be necessary. The topology and design rule limitations with a mesa configuration must be considered in light of subsequent process steps and consumption of semiconductor area (cost). The implementation of channel-type resistors has several drawbacks: surface depletion (surface states) can affect the charge in the resistor stripe, surface potential offsets may arise with dielectric deposition, a relatively large temperature coefficient of

-

resistivity exists (bandgap energy coefficient, impurity ionization, mobility effects) saturation of the current-carrying capability can occur, heating or cooling effects alter the charge density and carrier mobility, and slow domain oscillations and high frequency (Gunn-type) oscillations can arise from charge injection into the substrate. All of these effects, described below, compromise the performance of such a resistor structure. Careful layout (with respect to power distribution busses, proximity to critical nodes, etc.) is necessary to minimize interactions with the resistors and other circuit components. The realities of device fabrication manifest themselves in resistor structures in the following manner. Surface depletion can decrease the available charge in the resistor stripe, and generally leads to higher resistance values than expected. Owing to process-induced variations in the layer thicknesses, charge density, dimensional tolerances, surface states, and surface contamination effects (leakage currents), the resistance may actually increase or decrease in an uncontrolled manner. Layers of high sheet resistivity, with their correspondingly low-charge density, are more susceptible to these variations. The application of a dielectric film will tend to ameliorate the effects of surface states, but can aggravate control of the resistance owing to the generation of stress and piezoelectric effects.

Figure 10-48. Detail of a resistor structure showing the critical dimensions and features. The contact resistance is predominantly at the interface of the metal and the semiconductor. The bulk resistivity determines the dimensions of the resistor relative to the needs of the circuit design. W, is the effective contact width, W is the effective width of the resistor stripe, t is the effective thickness of the layer, and L is the effective length.

10.10 Resistors

The magnitude of these effects in subject to the dielectric film composition, surface preparation, and deposition conditions. Thermal effects must also be considered, as carrier mobilities decrease with heating (proportional to T-”’). Thus the resistor value increases when significant power is dissipated in the circuit or the resistor. In addition, when temperatures are very high (> 100°C), the effects of band-gap narrowing may also begin to influence the transport properties, again altering the resistivity. This behavior is of importance to the designers, as compensation networks may have to be build into the circuit to accommodate these changes in resistance. Since the resistor body in this configuration is essentially the transistor conducting channel, it is subject to the same current saturation limits as the transistors. For most compound semiconductor materials, channel saturation occurs at electric field strengths of - 1000-5000 V cm-’ (Sze, 1981d, pp. 44, 325). While these effects can be mitigated by careful design and control of the voltage drop across the resistor, it presents an additional restriction for the device designer and process engineer. Attempts to exceed the saturation values will lead to excessive heating and accelerated failure. Critical field effects may arise from both DC and AC operating conditions when the resistors are biased. Above the critical field strength, charge may be injected into the regions surrounding the resistor (isolation regions or the semi-insulating substrate). Selfoscillations may then occur in the compound semiconductor material. These oscillations may be realized as “slow domains” (Ridley and Walkins, 1961; Ridley and Pratt, 1965; Kaminska et al., 1982, and Sec. 10.3.3) or high frequency, Gunn-type oscillations (Sze, 1981, Chap. 11). In GaAs slow domains can be created when the electric field strength exceeds roughly 500- 1000 V

579

cm-’ (Kaminska et al., 1989); Gunn oscillation are created at a field strength in excess of roughly 3000V cm-’ (see (Sze, 1981d, Chap. 11). The oscillations will add to the dispersion in the device characteristics. A major consideration in the use of channel resistors is the heat dissipation. The thermal conductivity ( K) of GaAs is only - 0.48 W cm-’ K-’ (EMIS, 1990, Sec. 1.8), and the thermal diffusivity is only -0.27 cm2 s (EMIS, 1990, Sec. 1.9). In InP these values are -0.56 W cm-’ K-’and -0.4 cm2 s, respectively (EMIS, 1991, Sec. 1.8 and 1.9). Therefore care must be taken to avoid excessive local heating and thermal runaway conditions, particularly if a resistor body is adjacent to an active device. The last concern for channel-type resistors is the large distributed capacitance which arises from the depletion effects along the length of the resistor. The capacitance is of particular concern for “long” resistor stripes (high-resistance values), which can lead to intractable RC time constant problems and a significant reduction in device operating speeds. Inductive parasitics also arise with long meandering resistors, which again can limit high-frequency operation and create unexpected operating instabilities. Thin film resistors may be constructed on the semiconductor surface (with implant isolation beneath the resistor body and contact regions), or above the first or subsequent dielectric layer(s) by the deposition and patterning of thin layers of Cr, Ni-Cr (nichrome), TaN, or other materials (see Table 10-8). These resistor films have specific resistance values in the range of - 10-1000 R/U which provides a suitable range of resistor values. The deposition and patterning of these films on the semiconductor surface are subject to many of the effects that affect the channel-type structure de-

580


Table 10-8. Thin film resistor materialsa. Metal

Resistivity range (Q/a

Cr Ti NiCr TaN a

13 55-135

60-600 280

Temperature coefficient (PPm K-’)

3000 2500 200 - 180 to -300

From Williams (1990, p. 306).

scribed above. The formation of a thin film structure involves depositing a uniform layer of the resistor material, then photolithographically defining the appropriate pattern. Etching of the exposed material is carried out using plasma-etching techniques. Lift-off methods may also be implemented, using photoresist or dielectric-assisted techniques. Contact metals are then deposited on the resistor stripe as desired, patterned, and annealed to alloy the contact to the resistor body. Tapped resistor structures can be readily fabricated. These tapped resistor structures may be used for tuning high-frequency response or circuit gain characteristics, using laser ablation or current pulses to break the film at a desired location. By depositing the thin film layer on the dielectric, numerous advantages are gained: relatively easy control of the resistance

value, a trimming capability (laser trimming or focused ion beam (FIB) repair), reduction of the distributed capacitance, and design and layout flexibility at the expense of an additional masking level. The thin films are typically less than 100 nm thick, and therefore have a limited impact on the topology. Evaporation and sputtering processes are the deposition methods used for resistor fabrication: plating processes are insufficiently well controlled. A caveat with these thin film structures is that continuity is strongly affected by pinholes and inhomogeneities in the film. Therefore, a robust, high integrity film must be produced (slow deposition rates and multiple passes are recommended). High current densities in the thin film resistor can result in electromigration problems, localized heating, and catastrophic failure, particularly at the junction of the contact pad and the resistor body. These effects are similar to electromigration failures in drainhource or gate metallizations. This failure mechanism is illustrated schematically in Fig. 10-49 (see Magistrali et al., 1992). The adhesion of the resistor film to the semiconductor or dielectric material is a critical issue. This problem is typically surmounted by the deposition of a dielectric layer over the resistor to protect the thin film layer from damage, stresses, and confine the film. Control of the resistance value is in-

Region ?f Failure

Pile-up

Current ‘Crowding

Figure 10-49. A schematic picture of film resistor failure. The electromigration-induced transport of material (“electron wind”) causes a high resistivity region to form near one contact. Some material is transported to the opposite end of the resistor. The loss of material creates a “hot spot” which ultimately fails catastrophically.

10.1 1 Metallization and Liftoff Processes

fluenced by the variations in film thickness, defined width, and film composition. Film resistors may be trimmed by laser ablation methods to “fine tune” the resistance value at the time of testing. More recently, with the advent of the FIB techniques, the resistor stripes may be repaired, or built-up, albeit this approach is presently limited to very costly circuitry. Fringing capacitance effects are minimized by the use of deposited film resistors, as the charge in the semiconductor is well removed from the resistor stripe. The dielectric constant of the dielectric layer may be optimized and a minimized capacitive coupling may be effected with a thin film structure. This can lead to significantly reduced RC time constants relative to channel-type resistors. In principle, the limit to current flow in a thin film resistor is the maximum current density supported by the material. This is constrained practically by electromigration phenomena, the heating-related effects, the materials’ temperature coefficients, and the maximum power dissipation of the resistor and substrate materials. As the dielectric materials are well behaved, there is little concern for charge injection, oscillations, and nonlinearity in the thin film structures deposited on dielectric layers even when operated at high bias levels.

10.11 Metallization and Liftoff Processes A metallic conductor is required to provide the interconnection of devices, interlevel and back-plane connections (vias), and for electrical and thermal conduction paths to the external environment. The conductor material must have the following properties: a high electrical and thermal conductivity, be electrically and mechanically stable, be chemically inert yet paternable by fabrica-

581

tion-compatible chemistries, possess good adhesion characteristics, be corrosion resistant, ductile, and compatible with the processing sequences which follow the deposition and definition steps. The key issue for metallization and interconnect processes is minimizing the electrical resistivity in runners and vias to prevent excessive power dissipation and the concomitant loss of signal, as well as the operating speed limitations due to RC time constants and heating effects, while utilizing minimal geometries. Au, Al, Ti, Ta, W, Ge, various silicides, and numerous gold-based alloy materials are compatible with most compound semiconductor processes (Howes and Morgan, 1985, Chap. 6; Williams, 1990, Chap. 11). However, to prevent undesired chemical and metallurgical reactions, many of these materials must be used in a “multilayer” configuration, i.e., a barrier layer and high conductivity “bulk” metal(s). In addition, the interconnection metal must be stable to electromigration processes which arise at current densities above - lo5- lo6 A cm-* (Davey and Christon, 1981; DiLorenzo and Khandelwal, 1982, p. 345; Williams, 1990, Chap. 20; Irvin, 1982). Furthermore, this stability must be maintained under highly stressful testing and operating conditions, e.g., accelerated aging, testing and operation at elevated temperatures, high bias, and high humidity. Only then can a material be called suitable for use in compound semiconductor devices. Unlike the aluminum metallization common to silicon-based products, metallizations for CS devices must be stable for tens of thousands of hours at very high operating temperatures, ca. 200 -250 “C. Metallization schemes are a major issue in IC interconnects. A “two level” process prevents minimal dimension devices from being fabricated due to the dominant problem of power routing. Thus lower perfor-

582


mance, lower yields and higher cost circuits would be realized. Three-level (Lee et al., 1989) and four-level (Vitesse, 1990, 1995; TriQuint) interconnect schemes provide for flexibility in signal and power routing, and allow for significant circuit compaction and optimization of the signal and power distribution. In multi-layer metallization schemes, the control signals are typically carried in the lower layers, while the power distribution and ground connections are handled in the upper layer(s). Vias are used to complete the interlayer connections. A commercial four-layer metallization process is illustrated schematically in cross section in Fig. 10-50. In this figure, the interconnection is made from an upper metal layer to a lower level metal directly. The multi-layer configuration shown in Fig. 10-51 is a “post-andrunner” structure. The interconnect layers would be created by sequential metallization over dielectric, patterning, and some form of via-fillhelected-area metallization. The interconnect runners are formed by aluminum or gold-based metal deposition

processes, and photolithographic patterning techniques. The posts may be formed during the interconnect metal deposition or, for example, selective-tungsten CVD processes (Wilson et al., 1993) as shown in Fig. 10-52. Each subsequent metal layer is generally printed with a slightly larger critical dimension as a result of circuit topology constraints. A substantial amount of planarization may be realized as a side benefit of the larger dimensions. However, as is evident in Fig. 10-52, this is not always required. So far, chemical-mechanical polishing has not been necessary in CS device processing. This is due partly to the greatly relaxed geometries necessary to obtain extremely high performance in CS devices, and the somewhat lower integration levels common to CS applications. The number of mask levels in CS processing rarely exceeds 13- 15 plates, even for highly complex circuits in the range of 100000 to 500000 gates (Brown et a1.,1998; Vitesse, 1995), whereas a bipolar silicon process might have 28-30 plates, or more, giving rise to very rough to-

’tI]

Mask levels

i}

Procesf

Technolcqy

4 layers of Aluminum Interconnect

Conventional state-of-the-art Silicon Interconnect

MESFET

GaAs

Proprietaryto Vitesse

GoA‘ Wafer

Multiple 4 inch wafer venhrs

Figure 10-50. A schematic cross section of a four-layer interconnect metal scheme. Aluminum is utilized for the upper level metal layers in these MESFET ICs. (Figure courtesy of C. Gardner, Vitesse Semiconductor Corporation, Camarillo, CA.)


583

Figure 10-51. Details of a “post-and-runner” multi-level metallization scheme. Two levels of metal are shown above the ohmic contact. The via plug may be formed by selected area chemical vapor deposition or by blanket deposition and etching. A substantial amount of planarization may occur in this type of structure as the dielectric layer tends to smooth out height variations and steps. This structure may be continued above the two layers by successive depositions and patterning.

Figure 10-52. An SEM cross section micrograph illustrating the details of a four-layer “post-and-runner” metallization process. The via plugs are selected-area CVD tungsten, with a titanium adhesion layer and gold main metal on each tungsten plug. The magnification marker is 1 ym; the via diameters are approximately 1 ym, and the interconnect metal layer thickness is approximately 400-500 nm. (Figure courtesy of Dr. M. Wilson, Cray Computer Co., Colorado Springs, CO.)

pology. In any case, the larger dimensions of the upper level metallizations have the distinct advantage of a higher current carrying capacity, ideal for low-loss power distribution busses. A four-level “post-andrunner” metal interconnect scheme is shown in a SEM micrograph (Fig. 10-53). This type of multi-layer process has proven to be reliable and manufacturable with high yields (Mickanin et al., 1989; Wilson, 1989). The circuit compaction permitted by multi-level metallization allows for significantly improved high-speed performance. This is achieved predominantly by optimizing the routing through various levels of interconnect and minimizing the distance between critical nodes in the circuit. At present, the use of fourth metal-level power

584


Figure 10-53. An SEM micrograph of a four-layer “post-and-runner” metallization process with interlayer dielectric removed. This figure illustrates the beauty and utility of the multi-layer metallization process. The fine geometry lines are gate fingers of nominally 1 pm in dimension. The increasingly larger metal lines are evident at higher levels. (Figure courtesy of Dr. W. Mickanin, TriQuint Semiconductor, Inc., Beaverton, OR.)

routing with relaxed design rules can approach 50% surface area utilization for both power and ground distribution lines (Vitesse, 1990). Since adding an additional metallization layer only requires relaxing the critical dimensions (due to surface topology), a via process, and a dielectric layer, there is no theoretical limit to the number of levels of metal. The performance requirements of up to 50-100 GHz and a million or more devices do not demand development above four or perhaps five metal levels.

10.11.1 Metallization In the manufacture of compound semiconductor devices, the interconnect metallizations are still predominantly gold and gold alloy based. Aluminum-based metallization processes are being introduced to fabrication sequences (see Vitesse, 1990), but the use of aluminum and aluminum alloys, while well understood in the silicon in-

dustry, is subject to the same constraints as are found in silicon processing: e.g., the formation of Au-A1 intermetallic compounds with undesirable high resistivity (e.g., “purple plague”, see Irvin and Loya, 1978; and Irvin, 1982), and concerns for long term reliability from alloying materials such as copper, modest current carrying capability, and wire-bonding issues. To minimize the metallurgical reactions and rapid in-diffusion of gold, barrier metals such as Pt, Pd, W, or Ti must be used between the contact layer (semiconductor or metal) and the gold interconnect layers. While there barriers perform the function of blocking the intermixing of the contact metals, they add complexity to the process sequence, and ultimately act only to slow the eventual intermixing process. Numerous metallizations have been tried in the compound semiconductor field. The reader is referred to Sec. 10.6, and Howes and Morgan (1985, Chap. 6), for additional supporting discussions. As the processing of compound semiconductor devices matures, aluminum alloys are being used in an increasing number of applications. Aluminum and aluminum alloys have the distinct advantage of being patterned readily by reactive ion etching, ion milling, or lift-off methods, as well as relatively low cost. Gold can be effectively patterned by lift-off or ion milling processes. Submicrometer features may be patterned readily in any of the common metallization systems used in compound semiconductor device fabrication. The aluminum layers are commonly alloyed with copper to stabilize the material against electromigration failure. In silicon devices, copper has not been found to affect device performance. For GaAs, copper is a deep acceptor with at least four deep levels in the lower half of the energy gap (see Fig. 10-3) (Kullendorf et al., 1983). This can give rise to slow transients and erratic de-


vice behavior under certain bias or operating conditions (strongly related to device design and structure). For GaAs digital applications, the A1-Cu system (with barrier layers) appears to be suitable. In the case of RF or mixed signal applications, the process sequences and device structures and operating points are significantly different, and may result in compromised device performance. In InP materials, copper has at least three deep acceptor states, and, in fact, high concentrations of copper give rise to a semiinsulating characteristic and copper precipitation (Leon et al., 1992). Thus great care must be exercised when using Al-Cu metallizations. Gold-based interconnects, on the other hand, are problematic in the silicon case (carrier lifetime-killer centers), but are highly effective for compound semiconductor devices, and have been field-proven as reliable for more than twenty-five years. Typically, gold-based gates and interconnections are utilized in processes that do not use ion implantation beyond the formation of the junction, isolation, and contact layers. This is due to the rapid diffusion and metallurgical reactions which occur at temperatures of - 350-500°C in most compound semiconductors. A common interconnect metallization used in GaAs device fabrication is the Au/Pt/Ti system (Niehaus et al, 1982). Here the titanium layer is used to enhance the adhesion. The platinum layer acts as a diffusion barrier against gold interdiffusion, and to mitigate the reaction of titanium and gold which occurs at -200°C. Since gold and platinum have high conductivity, this “sandwich” structure produces very low resistivity interconnects. An interconnect for higher temperature applications is based on Ti-WIAu. The Ti-W layers are used to contact the semiconductor and provide a diffusion barrier to the gold, while the gold layer carries the majority of the current. This contact has been found to be stable

585

to - 500-6OO0C, although adhesion problems due to differential thermal expansion (stress), and degradation mechanisms are not yet completely controlled. In addition, sputter deposition must be carefully controlled to prevent leakage currents due to surface damage (Kohn, 1979; Day et al., 1977). Interdiffusion is a problem with a number of desirable materials due to the reactivity of GaAs and InP with a wide range of metals. These reactions are well understood through the phase relationships for these systems. For example, aluminum on GaAs interdiffusion has been observed at - 250 “C and extended times (Mukherjee et al., 1979; Sealy and Surridge, 1975). It should be noted that for aluminum-based metallizations, 250°C is quite near the “2/3 melting point” criteria used in metallurgy for defining stability to interdiffusion, and thus such interactions are expected. For further understanding of potential intermetallic phase formations, see Massalski (1986). As previously discussed, barrier metals or alloying elements can be used to improve the stability and minimize interdiffusion in the contact regions. High temperature interconnects and metallization are used when the wafer may be subjected to high processing temperatures as required for ion-implantation annealing. These materials were discussed in Sec. 10.6 in the context of gate formation. Such interconnect configurations are typically constructed from refractory metals such as Ti-W, W-Si, Ti-W-Si, W-N, Ta-N, and Ta-Si (some of these materials may also be used for thin film resistor stripes). It has been found that these materials withstand temperatures well in excess of 850 “C without significant interdiffusion [see Dautremont-Smith et al. (1990)l. There are significant limitations in the metal line widths, achievable by different patterning methods. The electron beam

586


(e-beam) writing system has achieved dimensions below 100 nm in the laboratory, but this is a very daunting proposition for the fabrication line where control, low cost, and reproducibility are required. An example of a -0.1 pm e-beam-exposed, T-gate structure was shown in Fig. 10-38. Typically, gate dimensions as small as 0.35 pm are printed by step-and-repeat systems (Williams, 1990; Wilson et al., 1993), whereas “0.25 pm” or smaller technology is implemented with e-beam methods (Danzilio et al., 1992). Smaller gate features require multi-layer offset photoresist patterning, electron beam, or other short wavelength processes such as deep ultraviolet exposure. Owing to instrument throughput constraints, the e-beam is only used to write the finest gate features, not the general metallization patterns. The step-and-repeat systems can control line widths down to - 0.4 pm using the G-line, and - 0.3 pm using the I-line, from high intensity mercury vapor light sources. Figure 10-54 shows a - 0.36 pm gate feature defined by G-line exposure. Finer features can be produced by careful control of the photoresist thickness, exposure conditions, multi-layedmulti-exposure photoresist and metal thicknesses. Figure 10-55 schematically illustrates a method of offsetting multiple photoresist layers and implementing directional metal deposition to achieve finer metal line geometries. In the upper metallization levels there are fewer constraints in the metal line dimensions, but patterning and dimensional control may be complicated by the topology. Partial planarization by dielectric deposition can relieve these problems. Ion milling or sputtering methods may be used for metal pattern definition. This process requires a high vacuum system and appropriate high current ion sources or plasma excitation systems. In the ion milling process, a high flux ion source is used to sput-

ter the unwanted metal atoms from the exposed surface. In sputtering processes, an ion plasma is created above the wafer surface which removes metal atoms by physical sputtering processes. Argon, or chlorinecontaining compounds, are typically used for the source gases. Nitrogen gas may be added to ballast or control the ion milling rates. The patterning of fine features is limited by the spacing of adjacent metal runners due to shadowing of the ions by the topology of the metal and the pre-existing wafer surface. The photoresist or other defining layer (e.g., a second metal, a dielectric layer, or a combination of photoresists and metals or dielectrics) add to the topological relief. Ion milling is relatively slow compared to liftoff processes, although it leaves a very smooth surface and is not subject to edge burring and adhesion-strength limitations. Sputtering is relatively rapid and can be used to etch fine features. One of the concerns in ion milling or sputtering is that in

Figure 10-54. A SEM micrograph showing a recessed gate opening. The magnification marker is 1 pm. The trench dimension is 0.356 pm at the bottom, printed by G-line photolithography. This dimension represents the limit to G-line lithography with single pass step-and-repeat exposure systems, and standard photoresists. (Micrograph courtesy of P. A. Grasso, S. E. Lengel, A. F. Williams, Lucent Technologies, Inc., Reading, PA.)


507

Figure 10-55. A schematic view of a method for creating fine features with process-limited photolithography. a) A layer of photoresist is deposited and exposed at a controllable dimension. A second layer of photoresist is deposited on the wafer and exposed with a specific offset to the original pattern. Clearing the exposed photoresist leaves a bilayer offset feature as shown in b). Subsequent metal deposition, preferably at a substantial angle, produces a fine metal feature of dimension much less than the photolithography limit, if desired.

the process of etching, residual ion damage and redeposition of sputtered species may occur, which can lead to surface-state-induced electrical effects or leakage paths in devices. In most process tools, only a single wafer or a few wafers can be etched at a time, leading to a limited throughput in the apparatus. The topic of ion etching was discussed in Sec. 10.5 in a more general context. The criteria and utilization presented therein are applicable to metallization patterning.

10.11.2 Liftoff Processes Liftoff procedures are implemented when metallizations are incompatible with chemical etchants, when rapid, high throughput processes are desired, or when ion-based patterning is undesirable. The as-deposited metal layers are required to be ductile and adherent in order to permit the selective separation of the unwanted metal from the wafer surface. In addition, the control of step, edge, and side-wall coverage is critical for

588


providing a “weak link” to permit separation of the metal film. Metals that are deposited by evaporation or plating meet these criteria and are generally quite well suited for liftoff processes. These patterning methods are particularly effective for gold or gold-based materials, as deposited gold layers are nearly “dead soft”. Sputtered metal layers, and particularly refractory metals, are more difficult to liftoff successfully due to high adhesion to all surfaces, relatively good conformal coverage of steps and edges, and their tendency to be harder in the as-deposited state. Liftoff processes involve the creation of high aspect ratio trenches or undercut pattern features in the patterned photoresist or a)

dielectric layer(s), coupled with a “directional” type of metal deposition process. The metals are deposited over this patterned sacrificial film. Then the metal layer and sacrifical film is stripped off by mechanical, chemical, or chemo-mechanical means, so “lifting” the unwanted metal from the surface. To successfully carry out the liftoff process, complete, full thickness metal coverage at the edges of the photoresist or dielectric layers is highly undesirable. Electron beam or resistance-heated evaporation methods are best suited to the deposition of metal layers due to the highly directional nature of the evaporation process, resulting in “poor” edgehidewall or corner coverage, as illustrated by Figure 10-56.

Metal Flux

Semi-insulatingSubstrate

&&

Gate feature after removal of / photoresist and metal layers.


Figure 10-56. A schematic illustration of an optimal liftoff metal coverage. a) The key to a clean metal liftoff lies in the thin or nonexistent coverage of the side walls of the gate or metal trench feature. b) The thin lines of metal part readily form the main metal line when the photoresist of patterning material is removed from the wafer, leaving the desired metal line pattern.


Other methods of metallization, such as sputtering or plating, tend to provide a more uniform surface coverage, and thus are less well suited to liftoff techniques, unless the sacrificial layer is shaped to create a thin parting line in the metal. The thickness of the dielectric or photoresist, and the edge definition, play a critical role in the perfection of the liftoff procedure by influencing the thickness of the metal coverage during deposition. The metal at step edges and corners is typically much thinner than the bulk regions of the metal film. Therefore the edges are much weaker than the bulk and easily parted at these sites. Ideally, there is no metal film continuity and the undesired material will liftoff without residue. The thinning or lack of coverage at the feature edges is also important for the prevention of burring and the elimination of interlayer short circuits. However, great care must be exercised in lifting off the metal, as many desired metal traces have steps and edges in their topology. Several methods of “lifting” the undesired metal are available. All of the methods rely on a solvent (water or organic chemicals) or an etchant to dissolve the sacrificial layer. Typical photoresists are quite soluble in acetone or other organic solvents. Sacrificial dielectrics films may be dissolved with HF or other suitable acids or bases. This latter approach has been used for large area liftoff of epitaxial films (Fan, 1990; Yablonovich et al., 1990) by utilizing sacrificial AlAs or AlGaAs layers. Subsequently, the unwanted metal and the sacrificial layer are floated or “scrubbed” off the surface of the semiconductor wafer with agitation, a high pressure fluid spray, or other mechanical means. As uncontrolled physical/mechanical scrubbing can be quite damaging to the remaining metal, most processes use deionized water or other solvents at moderate pressures and flows to remove

589

the metal and residual photoresist or dielectric materials. Metal recovery systems are used to reclaim precious metal wastes in these processes. Static electricity can be an issue with solvents or other chemistries flowing over a highly resistive substrate, leading to circuit damage. Surfactants or other materials may be added to the fluid streams to reduce static charge build-up. The adhesion of the metal to the desired surfaces must be strong in the as-deposited state or the metal layer may be removed from undesired areas during the liftoff. At the same time, poor adhesion of the metal to the sacrificial dielectric or photoresist layer is highly desirable. In addition, relatively thin metal layers must be used to prevent tearing of the metal or lifting off of the desired layer. Edge lifting and undercutting may occur if the adhesion to the desired contact region is insufficient. Burring can be a problem with liftoff processes owing to the ductility of the metals in the as-deposited state. The liftoff processes may tear the metal at the parting lines if there is incomplete separation of the deposited metal film. This result could be due to excessive metal coverage or thickness variations, grain structures anomalies, adhesion variations, particles, etc. Small burrs will be left along the edge of the metal line in this case. This problem is illustrated in Fig. 10-57. The burrs can protrude through the next level of dielectric causing short circuits between the metal layers. Careful preparation and wellcontrolled deposition conditions are required to ensure clean removal of the unwanted metal. Figure 10-58 illustrates a “clean” edge definition on a multi-fingered air bridge structure created with liftoff methods. The air bridge was constructed by a sacrificial layer post-and-runner process. At present there is no solution for complete amelioration of the problems of edge lifting and minor tearingburring of the

590

10 Compound Semiconductor Device Processing Metal Flux


gate feature after removal

Semi-insulating Substrate _____

b)

Figure 10-57. An illustration of a burr formed on a metal feature due to improper trench edge definition or excessive metal layer thickness. In this case the burr may extend along the metal line or be an isolated fine point. This may cause interlayer shorting due to poor dielectric coverage in subsequent process steps.

metal layer. Good process methodology and process control can produce excellent, reproducible results with liftoff processes. A minor amount of yield reduction may occur from open circuits, electrical contact resistance variations, burring, and short circuits. While these drawbacks can be quite serious, many materials cannot be successfully etched or ion milled, thus liftoff processes are the only viable alternative. It should be noted that commercial liftoff-based processes are quite robust, and presently operate with high yields.

10.12 Backside Processing and Die Separation Backside processing is carried out when the wafer must be thinned or if a back-surface metallization layer is needed. It is highly desirable to thin a compound semiconductor wafer to improve device performance from both the thermal and electrical standpoint. For example, thin wafers and the use of backsurface ground planes are critical to the RF performance of microwave devices. The spacing of the top surface conductors to the ground plane (back surface), i.e., the wafer thickness, creates a controlled

591

10.12 Backside Processing and Die Separation

Figure 10-58. Secondary electron micrographs of air bridge structures formed by liftoff methods. The marker is 10 pm in both images; the span dimension is approximately 25 pm. In a) a “sea” of approximately 125 air bridges over interconnect metal lines is presented. In b) a high magnification image of a few air bridges is presented. Note the moderate take-off angle of the bridge, leading to high strength and high reliability, and the elimination of electrical shorting. Bridge structures such as these readily withstand backside processing. (The micrographs are courtesy of P. A. Grasso, S. E. Lengle, A. F. Williams, Lucent Technologies, Inc., Reading, PA.)

impedance condition for transmission lines, which is required for stable microwave performance. It may be necessary to link the top surface ground lines to the back surface ground plane, i.e., through-wafer vias are required. Source or emitter vias (for FET or HBT devices, respectively) provide low im-

pedance connections to the ground (Furukawa et al., 1998). In addition, thinner substrates and through-wafer vias permit vastly improved heat extraction from the devices. As the thermal conductivity of GaAs and InP is significantly less than that of silicon, this is a critical issue, as shown in Table 10-9. Thus by thinning the wafer, greater power may be dissipated per unit area for a given temperature rise, permitting compact, high-power devices without compromising performance. If no backside processing is required, the wafer would pass to die separation, as described in Sec. 10.12.2. One of the key issues in the backside process flow is attention to detail; the importance of this point cannot be over-emphasized. Since the front side process is now completed, it becomes an extremely expensive proposition to damage the active circuitry while thinning and metallizing the back surface. There is a great amount of handling in the backside process which can subject the wafer, in a relatively weak condition, to significant abuse. Breakage, contamination, and physical damage (e.g., scratches and chips) may occur at each of the mounting, grinding, polishing, cleaning, etching, metallization, and demounting steps, which encompass the backside process sequence (Fig. 10-59). In comparison to silicon fabrication, compound semiconductor materials are much “softer” (the hardness of GaAs is approximately one-tenth that of silicon), and have facile cleavage, which emphasizes the importance of careful handling to avoid Table 10-9. Thermal conductivity of selected semiconductorsa. Silicon

1.5b

Gallium arsenide

Indium phosphide

0.48

0.56d

Values in W cm-’ K-’ at 300 K; Sze (1981, App. H);‘EMIS(1990, Sec. 1.8);dEMIS(1991,Sec. 1.8). a

592


+Q Demount

Grind (oneor two-step)

I

Cleaning

Photolithography Through-wafer IR Alignment

Optiinal: ElechicalTestin~

. I

-1

Scribeand-Cleave

Mount to Substrate or Tape

-

or Pick Die

Figure 10-59. An example of process flow options for creating back surface metallizations, through-wafer vias, die separation, and the selection of viable devices.

chips and breakage. Finished die costs are highly dependent on the success of this final process step. Very little information on the complete backside processing sequence has been made available in the public domain, as it is considered highly proprietary. The process flow description herein is drawn from the authors’ experience and discussions with other experts, and represents a “hybrid” view of the backside issues. 10.12.1 Backside Processing

The process involves a multitude of steps to complete the wafer process flow as shown in Fig. 10-59. The principal tasks to be accomplished are: mounting, grinding, cleaning, polishing, and if required, masking, via etching and finally, metallization. Following these processes the wafers will be electrically tested and optically inspected, the useable die separated by various means, and the die passed to assembly and packaging.

Mounting involves fixing the wafer topface-down onto a supporting substrate to facilitate the grinding or lapping processes and subsequent handling in a thinned condition. This mount must be physically strong, stiff, extremely flat, and not damaged by the thinning processes. Sapphire or quartz mounts, ground and polished to optical flatness, are suitable for this task. Silicon wafers or other materials may be used if back-to-front alignment is not required. The wafers may be affixed to the mount by an IR-transparent adhesive (e.g., paraffin, beeswax, or other readily soluble, noncontaminating materials of low melting point). Adhesive tape products, such as NITTO tape are also suitable for mounting. It is critical to ensure that the mount is free of particulates and that the wafer is parallel to the mount surface. The wafer must not be subjected to excessive stress or pressure during the mounting procedure, and great care must be taken to prevent damage to the front side structures. This latter point is particularly

10.1 2 Backside Processing and Die Separation

important when air bridge technology is employed. Wafer thinning is a slow, labor-intensive process even with automated apparatus. The initial grinding or lapping of the back surface may remove up to -95% of the original thickness, with an accuracy of a few micrometers (-0.1 mil). The wafer may be ground to a thickness slightly greater than the final target value, and then chemically polished or etched as desired. The etching step removes grinding damage and achieves the final thickness and surface quality suitable for via etching and/or metallization. High precision grinding apparatus is required for this task, with well controlled stock removal rates to prevent damage to the wafer and to ensure accurate thickness control. Fine diamond grit (1 - 10 pm nominal) grinding wheels can produce a good surface flatness at economical grinding rates without generating excessive damage to the substrate. Commercial vertical spindlehorizontal pass grinding units can achieve very good control and reproducibility of the thickness and surface quality (Lapinsky, 1991). Following the grinding procedures, the wafer and mount are carefully cleaned to remove grinding residues. This step involves a detailed inspection of the wafer to identify any surface damage, fractures, or chipping of the edge. The wafer may then be chemo-mechanically polished to the final thickness, removing the gross damage from the grinding and preparing the surface for metallization or masking and via definition. The final polish chemistry is typically based on NaOCl or NH,OH etching solutions as they are anisotropic and produce a superior surface finish (Stirland and Straughan, 1976). For InP substrates, mixtures of bromine and methyl alcohol are typically employed (Chin and Barlow, 1988). Chemomechanical etching tends to slightly round

593

the wafer profile as polishing occurs. Therefore care must be taken to maintain the flatness and parallelism of the wafer surface. In addition, the polishing systems must be well-characterized to achieve an accurate final thickness as the material removal rates vary strongly with polishing pressure and solution pH. In a well-controlled process, variation can be maintained within 2.5 pm (0.1 mil) to 5 pm (0.2 mil) for a final thickness ranging from 100-250 pm (Lapinsky, 1991). Wafers for certain microwave or high power applications are thinned to as little as 25 pm (1 mil) (Niehaus et al., 1982). At this thickness the wafer will readily conform to corrugations in the NITTO mounting tape. The mounted wafer is now ready for backside metallization. As shown in Fig. 10-59, there are two paths: photoresist deposition and exposure of the via pattern to create the front-to-back contacts, or, if vias are not required, the mounted wafer is cleaned and passed to metallization. Typically, a 4 mil (100 pm) or thinner wafer will not be demounted as cleavage is quite facile in compound semiconductor materials; 250 pm (10 mil) thick wafers can be carefully handled without a carrier. Thorough cleaning is again critical to the success of the process, as adhesion of the photoresist and the initiation of etching are strongly influenced by the surface condition. The photoresist masking layer for backside processing must be significantly thicker that required for the front surface processing. Owing to the very extended etching times needed for opening vias through hundreds of micrometers of substrate, the masking layer must be much more robust, although the precision of the critical dimensions is more relaxed than for front side processes. Multi-layer masking techniques may be used to minimize via “blowout” (expansion significantly beyond the

594


patterned dimensions) and damage to the substrate (edge lifting, pinhole leakage, etc.). For example, additional layers of photoresist, or metals such as Ni or Cr, could be applied on top of the base photoresist layer. In this case, the photoresist layer may be only a few hundred nanometers thick, and the metal layer of the order of 50 nm thick. Exposing a through-wafer via pattern requires a “front-to-back” infrared aligner system. In this apparatus the front surface metallization pattern is imaged through the carrier and wafer using sub-bandgap infrared light The alignment of the via mask pattern is referenced to the target contact pads on the front surface. Exposure is carried out as with normal photoresist techniques (see Chap. 4 of this Volume) with the exception that very extended or multiple exposure times may be required. In multi-layer processes several passes through this sequence are necessary. The through-wafer vias are etched in a manner described in Chap. 6 of this Volume and Sec. 10.5. Reactive ion etching is becoming the preferred method, as the morphology and aspect ratio of the via may be controlled through the etching conditions (pressure and gas compositions). With wet chemical methods, the vias tend to expand laterally as vertical etching proceeds even with highly anisotropic etchants, although very smooth via walls result with wet chemistry methods. It is difficult to control the final “over-etching” of the target areas and minimize the damage to the front surface if etchants leach around the metal contact pads. Also, the aspect ratio of the via and the side-wall structure is critical to the metallization process: severely undercut edges, re-entrant corners, or curved side walls (Fig. 10-60a), or vertical side walls and sharp corners (Fig. 10-60b), will prevent or complicate successful metallization coverage, leading to unsatisfactory continuity, high resistivity, and poor reliability.

Metallization steps are carried out after careful cleaning of the etched wafer. Residues are often left on the surface due to polymerization or overheating from the ion plasma during RIE, or residual by-products from the chemical etching procedures. It is crucial that any foreign materials are removed as the metallization quality may be affected or inhibited entirely. There are several approaches to backside metallization: 1) deposit a thin layer of metal(s), form a plug in the via hole, and then deposit a thick, full surface metal layer over the entire wafer; 2) deposit a thin metal layer for contacting, and then use a “solder” flow process to fill the vias and provide the full surface metal cover age. Many variations of these general approaches exist. Metallization may be carried out in two or three steps: the first to provide an intimate conformal seed metal layer to ensure ohmic contact to the exposed (back surface) metal pads on the front surface (Fig. 10-61), then to “plug” or “fill” the vias, and the third step to completely contact the surface and the vias creating the ground plane. The via may or may not be completely filled. The final process entails the addition of a planarization metal deposition or the application of a thick back surface metallization. The first metallization may be an adhesion promoting layer (e.g., titanium), or a layer of gold or gold alloy. The plug process should appropriately fill a via and be relatively planar. When the final metal layer is formed it must be adherent, uniform in thickness, and planar. Examples of the plug process are shown in Figs. 10-62 and 10-63. In Fig. 10-62 an SEM micrograph shows a view of a via hole. The morphology of the wall of the via is apparent. A series of via plugs with top surface contact pads is shown after etching away the substrate in Fig. 10-63. The surface morphology of the via perimeter is evident on the gold plugs. It is clear that the

10.12 Backside Processing and Die Separation

595

Back Surface of Wafer

Figure 10-60. Illustrations of undesirable via morphologies. In Fig. 10-60a, the effects of undercutting or re-entrant corners are evident. Metal coverage and continuity are compromised by these conditions. Figure 10-60b highlights the additional problems of sharp corners and vertical side walls. Here the filling of the via may be compromised by the vertical wall, and the sharp corners enhance stress localization.

Figure 10-61. Schematic illustration of a well-defined through-wafer via. The corners of the via are rounded to enhance continuity and minimize stresses. The seed plating is continuous and the filling metal shows only limited underfilling. A planarization metal layer is shown (optional). The final back surface metal layer provides the continuous back-plane conductor.

596


Figure 10-62. As SEM micrograph of a via hole after etching. The diameter of the via is approximately 100 pm. Note the gentle curvature of the top region of the via. (Figure courtesy of Dr. A. Colquhoun, Daimler-Benz Research Center, Ulm, Germany.)

acteristics. Solder-fill approaches can provide a via fill at relatively low cost. The plug metallization must be compatible with plated or evaporated gold or gold alloys typically used for the ground plane formation, and subsequent die attachment processes. The back surface metal plate-up is normally many micrometers thick and uniform in coverage to ensure uniform electrical and thermal contact, low resistance, and to withstand the alloying and reaction that occurs during mounting of the finished die to the package. For this reason, plating methods (electro or electro-less) are optimal, although evaporated or sputtered metals may be used. The key issue during the metal deposition process is to keep the wafer temperature below the softening point of the adhesive material (the wafer is still mounted on a carrier). Plating may be carried out at temperatures below lOO"C, which is compatible with most adhesives, whereas evaporation may expose the wafer to very high surface temperatures, and sputtering methods can raise the temperature to well above 200°C. To circumvent the heating problem, evaporation or sputtering may be carried out in steps, although there are penalties in system throughput, the metal film qualities, and the cost associated with this type of process sequence. Active cooling may be necessary to help control the temperature rise. As in front surface metallizations, an adhesion promoter such as nickel or titanium may be used to improve the adherence of the back surface metal. When using electroplating processes it is difficult to produce a uniformly thick metal layer owing to the high resistivity of semi-insulating substrates (GaAs or InP) and the finite electrical contacts. A metal seed layer is required to initiate the plating process. Current flow necessary to induce plating is inhibited in the substrate, and current spreads through the

-

Figure 10-63. An SEM micrograph of a series of through-wafer vias after removing the GaAs substrate. The top surface contact pads form a cap on the filled via metal. Via diameters are slightly larger than 100 pm. These vias are used to form a ground plane for 2 20 GHz device operation. (Figure courtesy of Dr. A. Colquhoun, Daimler-Benz Research Center, Ulm, Germany.)

-

shape of the via hole is critical for achieving continuity between the back plane and the front surface contacts. Plugs may be formed by selected area filling with gold, gold-based alloys, or other metal solders, or by plating processes with good filling char-

10.1 2 Backside Processing and Die Separation

seed layer from the electrical contacts. The metal build-up generally occurs more rapidly in areas close to the contact(s), especially if high plating currents are used. The use of highly conductive, adhesion-promoting layers and substantial seed metal thickness can greatly reduce this problem by increasing the in-plane conductivity. There is additional concern for interactions of gold with GaAs and InP with respect to long-term stability under severe operating conditions. Barrier metals such as nickel, platinum, or palladium may be incorporated in the back surface metal layers to reduce the interaction of gold or solder metals with the GaAs substrate (Parsey et al., 1996). However, it has been shown that gold-based metallurgy is very stable under high-stress reliability testing (Irvin, 1992). References such as Massalski (1986) should be consulted for further understanding of the relevant phase diagrams. At this point the wafer may be demounted from the supporting plate. The wafer is now quite fragile and easily damaged by mishandling. Several cleaning steps are required before the wafer may be passed to testing and evaluation. The adhesive materials and any undesired materials that were placed on the front surface as a protective coating must be removed. As before, no residues may be left on any surfaces as they will impede electrical contact to the back surface as well as the bonding pads on the front surface. The wafer may be transferred to a supporting carrier such as a NITTO tape handling system (Nitto). Here the wafer is gently pressed onto a polymer film which is supported by a tensioning ring carrier. The film and ring are capable of supporting the wafer mechanically during testing, die separation, and “pick and place”. As the polymeric film is plastic, separating the die is accommodated by expanding the film after the “streets and alleys” are cut or formed.

597

10.12.2 Die Separation The wafer must now be electrically tested to identify the good die. After testing and marking (ink dot or X - Y die location map) the die must be separated for mounting in packages. Several methods exist for separating the die: scribe-and-cleave (diamond scribe or laser ablation using varied mechanical stresses to cleave the wafer along the scribe lines) and sawing (typically with diamond blades). The first approach is best suited to wafers with thin or no backside metallization, although if the metal layer is less than a few micrometers thick this tends not to be an insurmountable problem. The latter method is required for very thick backside metallizations because of the malleable nature of gold. With diamond or laser scribing, a groove is scored or ablated, respectively, in the “streets and alleys” between adjacent die. The groove acts to focus the mechanical stresses when the wafer is flexed on a suitable pad by a roller-type device or impacted by a cleaving bar. The use of a roller-type method is not well suited for devices using air bridge metallizations unless great care is exercise in the scribing and the mechanical handling: the air bridges are easily crushed. Also, detritus from the diamond scribe or laser ablation processes may be lodged around the air bridges leading to short circuits or other damage, unless the surface is encapsulated. Recently, an apparatus for “scribe-andcleave” processes has been introduced to compound semiconductor technology (Dynatex). This instrument uses an automated diamond scribe system coupled to a precision impact bar which rides below the backside of the wafer is indexed in two dimensions while the impact bar is snapped up to the back surface at each scribe line The sharp impact breaks or cleaves the wafer

598


without excessive force, and has been found to be suitable for die separation when air bridge metallizations are used, although the cautions of contamination apply due to use of the diamond scribe. It is important to note that these processes perform best when photolithography is carried out aligned to the preferred (1 10) cleavage directions in the compound semiconductors. Attempting to die separate along other crystal directions generally leads to failure and low yields. The second method of separation is diamond sawing (AT, Disco). In this approach, the wafer is placed on a precision indexing table and then moved beneath a rotating diamond wheel to cut a groove in the “streets” on the wafer surface. The blade width is typically - 10 pm (0.0004 in) to 100 pm (0.004 in), creating a cut roughly 25% wider than the actual blade dimension. Diamond sawing is the “least clean” method to separate the die. As noted above, the wafers should be encapsulated to protect the surfaces from damage and contamination. However, this may be in conflict with the testing and evaluation sequence. Use of the diamond blade, the coolant/lubricant fluid, and the generation of chips and other rubbish creates significant contamination of the wafer surface and necessitates careful cleaning procedures to remove the residual materials. After the “x” and “y” groove pattern is cut, the wafer may be mechanically stressed to cleave the substrate along the grooves, as noted above. The same constraints apply here to the use of the mechanical flexing approach for cleaving the wafer. In some cases the wafer may be sawn completely through the back surface metal. Great precision is demanded in the cutting process to avoid excessive damage to the substrate carrier film layer. Vibration imparted into the wafer during sawing is of substantial detriment to GaAs and InP materials, as they are quite brittle. Edge dam-

-

age, fractures, and undesired cleavage can readily occur during the sawing operation. One step remains before the die may be selected: physically separating the die. In the case of NITTO tape or similar materials, this step is effected by stretching the polymer film. The spacing between the separated die is expanded to allow mechanical chip handling devices to remove the chip from the film, or to permit human handling, without damage to adjacent die. Exposure to chemicals or UV light may be used to reduce adhesion between the wafer and the carrier to facilitate the removal of the die from the film. “Pick-and-place’’ is a process of selecting the good die and locating them in a chip carrier or package cavity. This is done either manually or with automated systems. Vacuum pickups are employed to avoid the damage and yield losses associated with tweezers or mechanical clamping devices. In the case of expanded film carriers either method may be used. Solid wafer carriers (e.g., sapphire or quartz) do not lend themselves to effective die separation, and therefore require manual chip selection in the latter case, further cleaning processes may be necessary to remove residues. The identity of the die and the location within the wafer are known from the testing sequence and may be maintained prior to assembly. Following completion of the pick- and-place operation, the die are subjected to additional visual inspection with the survivors passing to assembly and test.

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Handbook of Semiconductor Technology Kenneth A. Jackson, Wolfaana Schroter

Copyright 0WILEY-VCH Verlag GmbH, 2000

11 Integrated Circuit Packaging Daniel I. Amey

E . I . DuPont de Nemours Inc., Dupont Electronic Materials. Wilmington. DE. U.S.A.

List of Symbols and Abbreviations ........................................ 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Package Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Integrated Circuit Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3 11.4 Die Attachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5 Microinterconnect Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6 Wire Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tape Automated Bonding (TAB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.7 Flip Chip or Solder Bump . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.8 11.9 Package Sealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.10 Rent’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.11 Thermal Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.11.1 Thermal Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.11.2 Cavity-Up/Down . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.12 Package Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13 JEDEC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13.1 Dual In-Line Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13.2 Flatpack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13.3 Chip Carrier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13.4 Small Outline Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13.5 Grid Array Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13.6 Hybrid Circuit Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.14 Package Attachment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.15 Electrical Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.16 Other Package Selection Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.17 Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.18 Multichip Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.18.2 Multichip Packaging Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.19 Change and Repair . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.20 Change Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.21 Repair Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.22 The Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.23 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

608 610 610 612 614 614 615 616 618 619 620 621 621 624 624 624 626 626 627 628 628 630 631 633 635 636 637 637 637 640 641 642 644 645

608

11 Integrated Circuit Packaging

List of Symbols and Abbreviations 9

P P TI T2

6, eCA

0, 0, 01 1 0J2 0J3 ~ J A

OJC

0, ATAB BGA

cc

c4 CERDIP CMOS CQFP DIP ECL EIA EIAJ FQFP FRU IC IEC IEEE I/O ISHM JEDEC LCC LFPM LGA LIF LSI MCM MCP

number of logic gates number of pins dissipated power average die junction temperature ambient air temperature relative dielectric constant case-to-air thermal resistance thermal resistance of the die thermal resistance of the heat sink material thermal resistance of the die-to-package interface thermal resistance of the package-to-heat-sink surface thermal resistance of the heat-sink-to-air (film resistance) junction-to-air thermal resistance junction-to-case (exterior) thermal resistance thermal resistance of the package material TAB ball grid array ball grid array chip carrier controlled collapse chip connection ceramic dual in-line package complementary metal-oxide semiconductor ceramic quad flatpack dual in-line package emitter coupled logic Electronics Industries Association Electronics Industry Association of Japan fine pitch quad flat pack field replaceable unit integrated circuit International Electrotechnical Commission Institute of Electrical and Electronics Engineers input -output International Society of Hybrid Microelectronics Joint Electron Devices Engineering Council leadless chip carrier linear feet per minute land or leadless grid array low insertion force large scale integration multichip module multichip packaging


MSI PBGA PGA PLCC PWB QFP QUIP SIMM SIP SMTA SMTPGA

so

SOJ SOP SOT SSOP TAB TCE TCM TQFP TSOP VLSI ZIF ZIP

medium scale integration plastic ball grid array pin grid array plastic leadless chip carrier printed wiring board quad flatpack quad in-line package single in-line memory module single in-line package Surface Mount Technology Association surface mount pin grid array small outline SOP with leads in a J configuration small outline package small outline transistor shrink small outline package tape automated bonding thermal coefficient of expansion thermal conduction module thin quad flatpack thin shrink small outline package very large scale integration zero insertion force zigzag in-line package

609

610


11.1 Introduction A package as defined in JEDEC Standard No. 99 is “An enclosure for one or more semiconductor chips that allows electrical connection and provides mechanical and environmental protection”. A wide variety of package types exist having different shapes, materials, styles, terminal forms, terminal pitch and terminal count. Terminal count is a general, generic term referring to pins, leads, pads, solder bumps, etc., and is often used interchangeably with the term which describes a specific configuration. Thousands of package variations exist, each meeting specific application requirements. Designers selecting an integrated circuit (IC) are faced with an “alphabet soup” of package types - BGA, PGA, LGA, LCC, TSOP, TSSOP, QFP, MQP, etc., etc., etc., - from which to choose; but it has not always been this way. In the 1960s the choices were few, with the dual in-line package (DIP) the most popular type. Since then, each decade has seen a doubling of the number of basic package types available to the designer, thus making the choice of a package type more difficult and critical to the success of the overall packaging approach. Packaging and interconnection has limited, and will continue to limit electronic system performance. It is rare for a package type to disappear from the scene. This is illustrated in Table 11-1. The DIP quickly replaced the TO5 style package for ICs; but after 30+ years, the DIP still remains in widespread use in electronics packaging. Package types and variations evolve without replacing existing types, resulting in the proliferation we have today. Some of this is due to the early identification of the potential or need for a new type, the long gestation period for a package to become widely applied due to the establishment of the infra-

structure to apply the package (asssembly equipment, test tools, etc.), and investment in both the factory and the field. But, due to rapid change, the required investment is not just the investment in the new approach but also that of the prior packaging approach. This investment drag on technology insertion is one of the major reasons the DIP has enjoyed such a long life. Packages have changed and will continue to change to develop denser, thinner, lighter single chip packages and proliferation of types will continue. As has long been the case, no one package type can suit the needs of the many and varied applications in the electronics industry.

11.2 Package Functions Semiconductor circuits continue to place new demands on circuit packages and interconnections for efficient circuit packaging. Package trends are toward increasingly higher terminal counts, higher thermal dissipation, higher packaging densities (more interconnections per square inch) and multichip packaging to improve electronic system performance with increased functionality and capabilities. In the 1950s and early 1960s discrete semiconductor devices and electronic components such as transistors, resistors, and capacitors with axial and radial lead terminals were predominant. As semiconductor technology improved, and more and more components could be put on a silicon chip, the number of pins on the TO-type semiconductor packages were not sufficient. ICs used circular TO5 packages with 10 and 12 leads in a circular pattern, the pin limit for the package and the printed circuit interconnect technology for that time (about 1963). This resulted in the need for, and introduction of, the DIP and the DIP has

61 1

11.2 Package Functions

Table 11-1. Integrated circuit package types. Package type Dual in-line package Flat pack Chip Carrier Leadless chip carrier Plastic leaded chip carrier Grid array Pin grid array Leadless (land) grid array Small outline or small outline IC Small outline J lead Tape automated bonding In-line packages Single in-line package Zig-zag in-line package Quad in-line package Single in-line memory module Quad flat pack Molded ring carrier Fine pitch quad flat pack Thin quad flat pack Shrink small outline package Thin small outline package Thin shrink small outline package Grid array Ball grid array Plastic ball grid array TAB ball grid array Surface mount pin grid array Metric TAB Multichip module MCM pin grid array MCM ceramic quad flat pack Shrink DIP Memory cards Large 1/0 SIMMs

Acronym

1960s

1970s

1980s

19905

DIP FP

0 0

0 0

0 0

0

LCC PLCC

0

0 0

0 0

0 0

PGA LGA

0

0

0 0

0 0

0

0 0

0 0

0

0

0

0 0 0

0 0 0 0

0 0 0 0

0

0

0

0

cc

SO or SOIC SOJ

TAB SIP ZIP QUIP SIMM (SIP)

0

0

QFP TAPEPAK * FQFP TQFP SSOP TSOP TSSOP

0 0 0 0 0

BGA PBGA ATAB SMTPGA

0 0 0 0 0

TAB MCM MCM PGA MCM CQFP

SIMM (SIP)

served as the workhorse package for many years and will continue to be a primary semiconductor package type for many, many years to come. However, in the mid-l970s, as the semiconductor technology advanced into

0

0 0

0

0

0 0 0

0 0 0

0 0

0 0 0

medium scale integration (MSI) and large scale integration (LSI), more and more components and capabilities became possible on the silicon die or chip, but there were not enough pins or terminals in the DIP or other in-line styles to practically

61 2


support the logic that could be fabricated on a single die. This led to the need for different package types; the large pin (or terminal) count packages such as chip carriers and pin grid arrays (PGAs), the fine pitch QFPs and now ball grid arrays (BGAs)and multichip modules (MCMs). It is a fact of life that more pins can always be used. Multichip packaging is the latest direction for packages and modules. Multichip packaging is not new for it has been applied in both military and commercial applications for over 25 years. Ceramic hybrid technology, the original MCMs, provided the functional equivalent which the state-of-the-art semiconductor technology could not economically provide as a single die. As semiconductor technology advanced, those functions in the multichip package were, or were capable of being, replaced by single-chip functions with higher performance or capability. Yet, there was still the need/desire for capability beyond what single chip packaging could provide in the military and high performance markets which continued the growth of the hybrid industry and the same needs are now moving multichip packaging in ceramic, thin film and printed wiring technologies into the mainstream. More on that later. Single chip package types are still the basis for multichip packages and single chip packages will continue to be used in high volume. Multichip functions will become single chip functions or packages as semiconductor technology continues its relentless speed and density advancement. In the foreseeable future few barriers are predicted to limit this advancement. MCMs are another package technology evolving to further expand the packaging engineering toolbox. Proliferation of variations will continue and the complexity in choosing the “right” pack-

age will become greater and continue to drive interconnection technology. It must be emphasized that no one package or packaging technique can satisfy all applications. Each packaging approach has its advantages and disadvantages which must be considered in a system analysis of the complex technology, application requirements, manufacturability, maintainability, and cost tradeoffs typical of an electronic system as well as the unique, companyspecific practices (and biases) which exist in any company.

11.3 Integrated Circuit Processing It is important to understand the microinterconnect technology used in semiconductor packaging. Figure 11-1 depicts the major integrated circuit fabrication steps (for wire-bonded circuits) from the unprocessed wafer through the masking and wafer processing steps, also referred to as “front-end processing”, and the packaging steps from wafer mounting through sealing or encapsulation, the “back-end processing”. The wafer, with its hundreds or thousands of identical circuits, is mounted on a carrier with a heat releasable adhesive or wax. Wafer dicing is the sawing of the wafer to create the individual die, or chip, that will be packaged. Die attachment or die bonding is the physical attachment of the die to the package or substrate for mechanical attachment and heat conduction. Electrical contact is sometimes a function of the die attachment. The interconnection from the die to the package, leadframe, or substrate is shown as wire bonding (tape automated bonding steps are shown in Fig. 113) and interconnections at this stage are sometimes referred to as the “microinterconnect” to distinguish them from the interconnections external to a package. Note

-

61 3

+ l

m SILICONWAFER

11.3 Integrated Circuit Processing

MASK MAKING

MASK INSPECTDN 8 VERIFICATION

WAFER PROCESSING

r-l PROBETEST

? l WAFER MOUNTING

I +

WAFER SAWINGOICING

I OPTICAL INSPECTDN

-I

PACKAGES OR LEADFRAMES

GOLD OR ALUMINUM WIRE

DIE EONDING

DIE SEPARATION

& LOAD IN WAFFLE PACK

' I

H

OPTICAL INSPECTION

I

LIDS OR PLASTICS

H I

1

SEALING OR ENCAPSULATION

FINALTEST

I I

that flip chip or solder bump microinterconnection does not use the die attach step for the solder bumps serve to both attach and electrically interconnect the die. Sealing or encapsulation provides for the protection of the die from the environment. Note the various points where test is performed. Wafers are tested in a probe test where each individual die in the wafer is tested to

Figure 11-1. The major integrated circuit fabrication steps.

determine if it is functional. Typically only key DC characteristics are tested. Faulty circuits are identified with a spot of ink to indicate to subsequent assembly steps that the die is not functional. The final test, after all the packaging and assembly operations are complete, is the stage where full functional and AC testing and sorting for electrical and environmental performance is

61 4

1 1 Integrated Circuit Packaging

accomplished. Testing at intermediate packaging stages is not practical so that a great deal of value is added between the last two test steps. The packaging represents a significant portion of the overall cost of a circuit.

11.4 Die Attachment There are four primary ways for the physical attachment of the die to the package or substrate: alloy or eutectic bonding, solder attachment, low temperature glass frits, and adhesive bonding. Dice that have been separated from the wafer may be in a “waffle pack” (a plastic case with a square array of pockets with a die in each pocket) for manual bonding to a package or substrate or they may be mounted on a releasable carrier that keeps the dice in a precise, uniform position (as they were fabricated) after the dicing operation for use in automated attachment equipment. Typically the equipment is pick-and-place style with a heated vacuum tip collet that picks up the die and moves it to the package or substrate which is on a heated platen. The collet has a mechanical action scrubbing the die on the package surface and a eutectic bond is formed between the silicon die and the gold plating in the package die attach area. For a larger die, a solder or gold alloy preform in the form of a thin (about 1 mil, i.e., -25 pm) wafer is placed between the package die attach area and the die. The back of the die is metallized with gold and the die attach area is also gold. The assembly is heated in the 300°C range where the preform flows and attaches the die to the package. Low temperature glass flowing in the 300-400 “Crange is also applied with ceramic packages. Epoxies are also used, particularly in hybrid circuits and MCMs. When epoxies are

used there are organics present in the package that may be of concern for some applications where contamination may result. The epoxies are typically one-part materials and may be filled with metallic particles for good thermal and electrical conductivities. One criterion for acceptable die attachment has been established for the amount of material around the perimeter of the die. Typically military packaging requires a good fillet between a minimum of three sides of the die and the package base. This has been established for mechanical attachment but does not necessarily give an indication of the overall integrity of the die attachment, which is important in high dissipation circuits. X-rays and acoustic microimaging are means to examine the die attach to determine void free attachment for good thermal properties (DiGiacomo, 1989). Diodes with dedicated leads for thermal sensing and thermal resistance test equipment are also used. All of these test or analysis techniques can add significant cost to a circuit and should be carefully applied to any design or product specifications. Thermal performance is, however, an increasingly critical parameter that affects reliability and electrical performance, so the extra cost of insuring die attach integrity may be well justified in high performance, high price circuits. See the section on thermal management (Sec. 11.11).

11.5 Microinterconnect Methods Figure 11-2 shows three microinterconnect attachment or bonding methods: wire bonding, flip chip (also called solder bump or “C4” for controlled collapse chip connection), and tape automated bonding (TAB).The left side of the figure shows the orientation of the die with respect to the

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