Angle-Resolved Photoemission

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Studies in Surface Science and Catalysis 74 ANGLE-RESOLVEDPHOTOEMISSION Theory and Current Applications

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Studies in Surface Science and Catalysis Advisory Editors: B. Delmon and J.T. Yates

Vol. 14

ANGLE-RESOLVED PHOTOEMISSION Theory and Current Applications

Editor S. D. Kevan Physics Department, University of Oregon, Eugene, OR 97403, USA

ELSEVIER

Amsterdam -London

-New York -Tokyo

1992

ELSEVIER SCIENCE PUBLISHERSB.V. Sara Burgerhartstraat 25 P.O. Box 21 1, IOOOAEAmsterdam, The Netherlands

ISBN: 0-444-88 183-2

0 1992 Elsevier Science Publishers B.V. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, withoutthe prior written permission of the publisher, Elsevier Science Publishers B.V., Copyright & Permissions Department, P.O. Box 521,1000AM Amsterdam,The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from theCCCaboutconditionsunderwhich photocopiesofpartsofthispublicationmay bemadeinthe U.S.A. All other copyright questions, including photocopying outside of the U.S.A., should be referred to the copyright owner, Elsevier Science Publishers B.V., unless otherwise specified.

No responsibility is assumed by the publisher for any injury and/or damage t o persons or propertyas a matterof products liability, negligence or otherwise, or from any useoroperation of any methods, products, instructions or ideascontained in the material herein. This book is printed on acid-free paper. Printed in The Netherlands

V

PREFACE

The technique of angle-resolved photoemission (ARP) is at an interesting period in its development. In the past 15 years, a theoretical foundation has been laid upon which most current experiments are interpreted: conservation of parallel momentum, approximate conservation of perpendicular momentum, broadening mechanisms, and prediction, detection, and characterization of intrinsic and extrinsic surface states. It thus appears that ARP can be applied in a relatively straightforward fashion to a wide variety of problems of current and standing interest in solid state and surface physics and chemistry. However, increasingly sophisticated experiments are testing and limiting the application of some of these simple concepts: many body and other final state effects, static and dynamic disorder, theoretical treatment of excitation spectra. In the same period, significant improvements in experimental and theoretical methodology have been attained. The techniques for preparing and characterizing surfaces and interfaces have progressed to the point where reasonably complex yet well-defined systems can be prepared: elemental surfaces of all sorts, metal-metal and metalsemiconductor interfaces, semiconductor heterojunctions, compound and alloy surfaces. The constant improvement in computer technology and in codes for calculating electronic structure have allowed the "routine" introduction of self-consistency, improved treatments of exchange and correlation, and relativistic effects. The first few steps in actually calculating the excitation spectrum of simple systems have recently been reported. Finally, the increased availability and improved quality of synchrotron radiation sources have made the technique more powerful, more generally applicable, and more diverse in the everincreasing array of sub-fields being spawned. The rate at which new storage rings and beam lines dedicated to the production of soft x-rays are being proposed, constructed, and commissioned suggests a very bright and busy future for the technique. This confluence of events is allowing ARP to be applied in many laboratories around the world to a variety of systems. This confluence also makes the present an opportune time to produce a researchlevel monograph on the subject. As yet, no comprehensive treatise exists. Very good reviews of ARP by Plummer and Eberhardt, Himpsel, and Williams, Srivastava, and McGovern have appeared. The several books on photoemission as a whole generally contain but one chapter dealing with ARP. None of these reviews, however, comes close to a comprehensive treatment of this very large and growing field. Indeed, it is unlikely that

vi

any one small set of authors would endeavor to write a monograph at the level and in the detail the field warrants. What is needed is a reference book that will be of general use both to long-time workers in the field as well as to the uninitiated graduate student just learning how to apply the basics to their particular problem. This is the goal of the current monograph. The first chapter provides an introduction to the motivations, methodologies, and terminologies of the technique, and briefly discusses "the party line" for interpreting ARP data. The next two chapters discuss in detail the physics of the photoemission process and the current understanding of its precise relationship to crystalline electronic structure, primarily €or bulk, three-dimensional states. After a brief review of the one-step, single particle theories, these chapters will focus on the "crucial issues" which all-to-often are not adequately addressed in interpreting experimental results. These would include, for example, the physics of quasiparticle excitation and other many-body effects, the applicability of the local-densityapproximation-calculated electronic structures to photoemission data, and the various contributions to linewidths and shapes. The next eight chapters discuss various wellestablished and currently active experimental applications of the technique. All but chapter 7 are focused upon measurement of intrinsic and extrinsic (i.e., adsorptioninduced) electronic states in two and three dimensions. Chapters 4 and 5 survey the surface electronic structure of metals and semiconductors, respectively, as probed by ARP, and its impact upon surface stability and reconstructive behavior. Chapter 6 discusses more complex metals and metallic compounds and is included as an avenue to test simple data analysis models. Chapters 8-10 center on the application of ARP in studying the electronic and geometric structure of relatively simple atomic and molecular adsorption systems. Chapter 11 discusses the somewhat more complex application to thin film systems. Chapter 7 is the only one specifically directed toward core-level ARP measurements, wherein ARP can provide valuable surface structural information. All of these subjects are quite active in various laboratories around the field. The final chapters examine applications which are still being developed and which hold significant promise for the future. Chapter 12 reviews the application to ferromagnetic systems, an area which has been revolutionized by the ability to distinguish the spin of the excited electron at arbitrary energy and emission angle. Chapter 13 is included to demonstrate the time-reversed application of ARP, inverse photoemission, which, as a complement to ARP, allows the unoccupied levels to be probed. The next chapter reviews recent efforts to apply pumpprobe techniques, using lasers as the pump, to study the dynamical properties of surfaces in real time. Finally, chapter 15 discusses the most recent and perhaps most dramatic application of ARP to highly correlated electronic behavior.

vii

CONTENTS Preface

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

v

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

ix

Introduction .............................................................. N.V. Smith and S.D. Kevan

1

The Physics of Photoemission ............................................... J.E. Inglesfield and E.W. Plummer

15

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

63

Surface States on Metals ................................................... S.D. Kevan and W. Eberhardt

99

Surface States on Semiconductors ............................................ G.V. Hansson and R.I.G. Uhrberg

145

List of Contributors

Quasiparticle Excitations and Photoemission S.G. Louie

Metallic Compounds and Ordered Alloys: Carbides and Nitrides, Applicability of Simple and Sophisticated Theories to More Complex Systems L.I. Johansson, and C.G. Larsson

.....

213

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

243

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

291

Molecular Chemisorptian .................................................. H.-J. Freund and M. Neumann

319

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

371

Photoelectron Diffraction D.P. Woodruff Atomic Chemisorption A. Goldmann

Metallic Films on Metallic Substrates K. Jacobi

viii

Thin Films on Semiconductors R.D. Bringans

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

Spin- and Angle-Resolved Photoemission from Ferromagnets E. Kisker and C. Carbone

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

435

469

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

509

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

553

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

571

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

595

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

601

Inverse Photoemission P.D. Johnson

Multi-Photon Photoemission J. Bokor and R. Haight

New Frontiers: Highly-Correlated Electronic Behavior R.F. Willis and S.D. Kevan

Future Prospects in Angle-Resolved Photoemission S.D. Kevan Index..

ix

LIST OF CONTRIBUTORS 1) Introduction N.V. Smith, AT&T Bell Laboratories, 600 Mountain Ave., Murray Hill, N.J. USA 07974, and S.D. Kevan, Physics Department, University of Oregon, Eugene, OR. USA 97403.

The Physics of Photoemission J.E. Inglesfield, University of Nijmegen, Faculty of Science, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands, and E.W. Plummer, Department of Physics, David Rittenhouse Laboratory, University of Pennsylvania, Philadelphia, PA. 19104-6396.

2)

3) Quasiparticle Excitations and Photoemission S.G. Louie, Department of Physics, University of California, Berkeley, CA. 94720.

Surface States on Metals S.D. Kevan, Physics Department, University of Oregon, Eugene, OR. USA 97403, and W. Eberhardt, Institut fur Festkorperforschung, Kernforschungsanlage Julich GmbH, Postfach 1913, D-5170 Julich, FRG.

4)

Surface States on Semiconductors G. Hansson and R. Uhrberg, Department of Physics and Measurement Technology, Linkoping Institute of Technology, S-581 83 Linkoping, Sweden.

5)

Metallic Compounds and Ordered Alloys 6) L.I. Johannson, Department of Physics and Measurement Technology, Linkoping University,S-581 83 Linkoping, Sweden; and C.G. Larsson, Department of Physics, Chalmers University f Technology, S-41296 Goteborg, Sweden. 7) Photoelectron Diffraction D.P. Woodruff, Department of Physics, University of Wanvick, Coventry CV47AL UK. 8) Atomic Chemisorption A. Goldmann, Gesamthochschule Kassel, FB 18 Physik, Heinrich-Plett-Strasse 40, 3500 Kassel, FRG

Molecular Chemisorption H.J. Freund, Lehrstuhl fur Physikalische Chemie I, Ruhr-Universitat Bochum, Postfach 10 2148, 4630 Bochum 1, FRG; and M. Neumann, Fachbereich Physik, Universitat Osnabruck, Barbarastrasse 7, 4500 Osnabruck, FRG.

9)

10) Metallic Films on Metallic Substrates K. Jacobi, Fritz-Haber-Institut der Max-Planck Gesellshaft, Faradayweg 4-6, D-1000 Berlin 33 FRG.

X

Thin Films on Semiconductors R.D. Bringans, Xerox Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, Ca. 94304 11)

12) Spin- and Angle-Resolved Photoemission from Ferromagnets E. Kisker, Institut fur Angewandte Physik, Universitat Dusseldorf, Universitatstrasse 1,4000 Dusseldorf 1, FRG, and C. Carbone, Institut fur Festkorperforschung der Kernforschungsanlage Julich GmbH, Postfach 1913, D-5170 Julich, FRG. 13) Inverse Photoemission P.D. Johnson, Physics Department, Brookhaven National Laboratory, Upton, N.Y. USA 11973. 14) Multi-Photon Photoemission J. Bokor, AT&T Bell Laboratories, Crawfords Corner Road, Holmdel, N.J. USA 07733, and R. Haight, IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, N.Y. USA 10598.

15) New Frontiers: Highly Correlated Electronic Behavior R.F. Willis, Physics Department, 104 Davey Building, Pennsylvania State University, University Park, PA 16802, and S.D. Kevan, Physics Department, University of Oregon, Eugene, OR. USA 97403. 16) Future Prospects in Angle-ResolvedPhotoemission S.D. Kevan, Physics Department, University of Oregon, Eugene, OR. USA 97403.

1

Chapter 1

INTRODUCTION N.V. SMITH AND S.D. =VAN

From humble beginnings in the early 1970's, angle-resolved photoemission spectroscopy (ARPES) has become established as an indispensable tool for the investigation of solids and their surfaces. This book represents an attempt to assemble in one volume an account of the large variety of work now going on. This opening chapter sets the work against the larger perspectives of the history of the photoelectric effect and of the electronic structure of condensed matter. It offers also a brief treatment of past and present experimental methods, and a brief account of our current understanding.

1. HISTORICALBACKGROUND 1.1 Prehistory Interest in the angular dependence of the photoelectric effect can be traced back to the early decades of this century. Jenkin (1) has written an entertaining and informative history which covers this period, and he documents how a number of Nobel laureates (W. H. Bragg, C. T. R. Wilson, A. H. Compton, W. Bothe, C. D. Anderson and E. 0.Lawrence) contributed to this topic before moving on to other (and evidently more rewarding!) endeavors. The history by Jenkin confines itself to the angular dependence of X-ray photoemission. We attempt here to fill in some of the gaps relating to ultraviolet photoemission and its angular dependence. Our treatment is not exhaustive, but is intended rather to sound a few historical keynotes which resonate strongly with current activity. In the 1920's, the angular dependence of photoemission from alkali metals was investigated by Ives and coworkers at the Bell Telephone Laboratories (2). Their apparatus is shown in Fig 1. These pictures exemplify not just the delightful scientific artwork of an earlier generation but also the two main experimental approaches still in use today: a single movable electron collector, or a sectored collector. The work of Ives and his group was closely linked with their technological interest in the use of alkali-based photocathodes in the emergent industry of television and in the possibilities of videotelephony. One question of physics raised in this work, however, has lost none of its savor in the intervening decades, namely, the vectorial photoeffect, which is concerned with the differences in emission intensity associated with the polarization of the incident radiation. The next landmark occurs in 1945 with the publication by Fan of a theory of the bulk origin of the photoelectric effect (3). This paper, which does not appear to have had

2

F

I

b

Fig. 1 Early angle-resolved photoemission apparatus of Ives and coworkers reproduced from Ref. 2. The method on the right employs a moveable electron collector; that on the left employs a stationary sectored collector. much impact at the time, presented a view of the photoemission process contrary to the prevailing notion that the photoelectric effect was a surface phenomenon (4). The Sommerfeld model of a metal treats electrons confined in a potential well V(r) of rectangular shape. Optical excitation occurs only if VV#O, and this condition, in the Sommerfeld model, occurs only at the surface. If we allow the existence of some atomic structure within the well, we have VV#O in the interior and the existence of a bulk contribution to the photoelectric effect. The Fan paper treats the bulk potential by Fourier synthesis, what in modern parlance we would call a nearly-free-electron (NFE) or pseudopotential model. Figure 2, reproduced from the Fan paper, shows the k-space geometry for optical excitations within a hypothetical NFE metal. We recognize here a number of results which have subsequently been rederived by others (5,6). Surfaces of constant photon energy are planes. Surfaces of constant electron energy are spheres which intersect these planes. Thus the angular distribution of photoelectrons will be about cones (6).

3

1.2 Photoemission as a Soectroscooy The transformation of photoemission into a spectroscopy, as opposed to an interesting and useful physical phenomenon, took place some time in the late 1950s, or early 1960's. The contributions of Spicer (at Radio Corporation of America, and later at Stanford University), Apker, Taft and Phillip (General Electric) and Gobeli and Allen

ll.

V

Fig. 2 Diagram reproduced from Fig. 1 of the 1945 paper by Fan (Ref. 3) showing the kspace geometry for the bulk photoelectric effect. (Bell Labs) are especially important. Parallel efforts were being made in Europe by Mayer and associates (Clausthal). Some future historian of science might wish to note that photoemission research in the United States appears to have been driven not so much by the desire for fundamental knowledge for its own sake but by the imperatives of the burgeoning television industry. The key discovery in this early period was the establishment of the primacy of the bulk photoelectric effect. The personal memoir of W. E. Spicer on his early days at RCA (7) is particularly revealing on this point. He was confronted at the start of his work by a large literature of photoemission experiments performed in ill-defined vacuum using an interpretive approach dominated by the Sommerfeld model. This body of work he found "basically useless". The historical turning point came with the routine attainability of ultrahigh vacuum and the ability to prepare samples which were atomically clean and the availability of bulk band structure calculations for purposes of comparison. A major landmark was the publication in 1964 by Berglund and Spicer (8) of photoemission energy spectra on Cu and Ag. These spectra displayed in a spectacular way the edges of the d bands at respectively 2 eV and 4 eV below the Fermi level. The sight of

4

these spectra convinced one of the authors (NVS), then a graduate student, that he wanted to be a photoemission spectroscopist. He was not alone in this aspiration. There followed an explosive effect to use photoemission in the determination of the densities of states and other electronic properties of a wide variety of materials. The reader is referred to the compendium by Cardona and Ley (9) for a summary of this activity up to about 1977. In the early 1970's, photoemission began to diversify. There was a reawakening in the interest in the angular dependence of photoemission (see Section 1.3 immediately following). The attractive features of synchrotron radiation were also recognized (10, 11). Spin asymmetry in photoemission was detected (12). Surface effects in photoemission, having been in eclipse for a decade, now began to reassert themselves. Band-gap surface states were observed on clean silicon (13, 14). Electronic states associated with adsorbed molecules were observed (15). Even the elusive surface photoelectric effect was unambiguously isolated (16). 1.3 Angle-resolved Dhotoemission sDectroscoDy Photoemission work in the 1960's was almost exclusively angle-integrated. An exception was the work of Gobeli, Allen and Kane in 1964 (17). In a notably prescient paper, Kane argued that the E(k) band structure could in principle be mapped from angular dependent photoemission spectra (IS). This paper recognizes the indeterminacy of kL, the internal perpendicular component of the electron wave vector, and contains within it the energy-coincidence strategy for overcoming this obstacle. Ten years were to elapse however before a band structure was actually mapped (19). Experimental work on the angular possibilities of photoemission spectroscopy started in earnest in the early 1970's. Using a sectored-collector apparatus similar to that in Fig. 1, Gustafsson et al. (20) showed in 1971 that the photoemission from Ag(ll1) was indeed distributed about cones of constant energy, as anticipated in the work of Fan (3) and of Mahan (6). At about this time the following events occurred: Feuerbacher and Fitton showed that normal photoemission from W(100) was dominated by a surface state just below the Fermi level (21); Wooten et al. demonstrated strong angular dependences in photoemission from GaAs (22); Koyama and Hughey, using synchrotron radiation, observed an angular dependence in photoemission from polycrystalline gold (23); and Williams et al. found that the photoemission spectra from MoS2 varied in a spectacular fashion with angle of emission (24). The work of Wooten lends itself to an interesting anecdote. At that time, he was at the Livermore Laboratory, and the underlying motivation for his work was the need to develop better photodetectors to monitor emissions from underground detonation of nuclear devices (25). The first formal demonstration of band mapping using ARPES was published by Smith, Traum and DiSalvo in 1974 (19). In order to circumvent the indeterminacy of k L these workers performed their measurements on the two-dimensional layer-compounds TaS2 and TaSe2 They monitored the variation in energy E of peaks in the photoemission

5

spectrum with polar angle 0 of emission, and then obtained the parallel component of the electron wave vector using

k 11

= ( 2 1 n E / f i ~ )sin ~ / ~8,.

The resulting E(k11) dispersion curves were in good agreement with the first principles band calculations (26). Equation [l] is now the standard algorithm in the reduction of angle-resolved photoemission data. The use of synchrotron radiation to enhance the capabilities of band mapping and to identify wave function symmetry using polarization selection rules was soon established (see below). The work of this era is captured in the compendium by Feuerbacher, Fitton and Willis (27). A number of more mature reviews are also available (28-31). Following this hesitant start, ARPES has burgeoned into a major industry. Activity shows no sign of slackening. Subsequent chapters of this book represent an attempt to organize and to summarize this large body of material. 2. CURRENT UNDERSTANDING AND PRACTICE With some qualifications, there is now a general consensus on the physics of the photoemission process and on how ARPES data should be interpreted. This has been the subject of extensive experimental and theoretical work in the past 20 years. Indeed, these issues were the primary focus of previous monographs and reviews of photoemission which can be found in the literature. The modern extensions pertaining to the theoretical foundations of ARPES can be found in the next two chapters of this book. 2.1 Photoexcitation Drocess (i) Basic Formula. ARPES is intimately tied to investigations of the electronic structure of crystalline systems. Except in the case of very high photon fluences (see Chapter 14), the process is very well described by lowest order time-dependent perturbation theory and thus by Fermi's Golden Rule, derived in Chapter 2: J=(k/4r2)

1 I (Qf I (e/2mc)(A*P +

P.A) I qi) I

6(E-Ei-hw)

i This expresses the observed photocurrent . Iat final energy E in terms of the initial and final state many-body wave functions, respectively q i and qf, and the dipole operator of the incident photon field. Fermi's Golden Rule provides the essence of the so-called singlestep, ultimately quantum mechanical model for photoemission. In general, the many-body wave functions are not known. In order to understand and to interpret a photoemission experiment at a given energy and momentum, various approximations are made. The validity of these, described briefly below, is addressed throughout this book.

6

(ii) IndeDendent Darticle awroximation. A common approximation in applying [2] is to assume that the initial and final state electronic wave functions may be approximated as independent particle states. In this case, qi and qf can be written as product functions of band states. By virtue of Bloch's theorem, these can be labelled by their energy and twoor three-dimensional crystal momentum, depending on the degree of surface localization. Since the energy and momentum of the final-state eiectron is measured, the dispersion relation of the final-state quasiparticle dispersion relations can often be determined. A further approximation is commonly made that these quasiparticle dispersion relations are related to the ground state calculated band structure. The validity of these two major approximations is of central concern in the following two chapters. The validity of the independent particle picture must be examined on a case-by-case basis. For example, "residual" atomic effects (Cooper minima (32), Fano-like resonances (33), shake-up structures (34) etc.) are commonly observed in photoemission spectra from solids. These suggest a higher degree of electron correlation, and thus many-body effects, than the independent particle approximation allows. One of the outstanding problems in solid state physics, understanding the coexistence of, and interplay between, localized electron correlation phenomena and delocalized, band-structure effects is currently also a major focus for ARPES (35). In condensed matter systems the importance of these effects is significant if the on-site correlation energy between two electrons in a band is comparable to the band width. The future of such studies is explored in Chapter 15. One facet of ARPES in which many-body effects can never be entirely neglected is final-state lifetime broadening (36). This damping is of both fundamental and practical interest since it ultimately limits the resolution of the technique. ARPES owes its surface sensitivity to the strong inelastic scattering which the final state electron experiences as it leaves the crystal. The photoelectron is thus endowed with a finite mean-free-path and lifetime. Moreover, photoemission is a final state spectroscopy which measures the energy of the (N-1) particle system relative to that of the N-particle system. The hole states below the Fermi level will also have a finite lifetime due to refilling by radiationless processes. Both of these lifetimes are of order seconds, so that the loss of energy resolution due to uncertainty broadening can be substantial. In the spirit of Fermi liquid theory, these effects are often treated heuristically by allowing the self-energies of the final state quasiparticles to be complex (see Chapters 2 and 3). The imaginary parts are then inversely related to the quasiparticle lifetimes. The use of complex self-energies appended to electron-energy-band calculations is not rigorous, nor is it theoretically satisfying. The above discussion indicates that photoemission spectra cannot be accurately compared to ground state calculations in any case. Recent theoretical advances are allowing quasiparticle spectra to be calculated directly (37). These advances and their impact upon the analysis of ARPES data are examined further in Chapter 3. (iii) Surface Photoeffect. The surface photoelectric effect arises when the dipole operator in the Golden Rule is transformed into a gradient of the electrostatic potential

/

using the commutation relation between the momentum operator and the unperturbed Hamiltonian. The difference between the bulk and surface photoeffects has become blurred since it is now clear that both can exist in the same spectrum. It is generally accepted that the "original" surface photoeffect which is produced by the rapid potential variation near the surface, is most easily measurable in simple metals with very weak bulk pseudopotential. While this was first suggested from total photoyield experiments (16), it has been usefully studied more recently in simple metals using the polarization dependence of the photoemission cross section at photon energies near the plasma frequency (38). 2.2 Phenomenology The manifold of angular parameters in a modern photoemission experiment is illustrated in Fig. 3. Most important are 8, and 4,, the polar and azimuthal angles of electron emission relative to the sample normal and the crystal axes.

++M

CRYSTAL

MAGNET1ZATl ON Fig. 3 All the angles. This diagram is intended to shown all the angular parameters of a fully characterized photoemission experiment. Other angles are oP and $, the polar and azimuthal angles of photon incidence. The degree of polarization of the incident radiation is also significant and is generally expressed as a ratio between amplitudes of electric vector perpendicular (s-polarization) and parallel (p-polarization) to the plane of incidence. Circular or elliptical polarization corresponds to a phase angle A between the s and p components. Finally, we recognize

8

the possibility of a spin asymmetry of the emitted photoelectrons, up or down relative to some appropriately chosen spin-quantizationdirection. No experiment, as far as we are aware, has had variational control over all of these angular and directional parameters. The typical experiment confines itself to some subset of these angles depending on the particular physical phenomenon under investigation. Indeed, the selection of subsets serves as a convenient way to categorize the area of study -band mapping, photoelectron diffraction, symmetry, spin detection and so on. (i) SamDle Orientation. The sample in an ARPES investigation is generally a single crystal of known orientation and of high surface quality. In the case of semiconductors or layered compounds, the surface can be produced by cleavage in vacuum. In the case of most metals and those semiconductor surfaces not achievable by cleavage, a nearly perfect surface may be produced by appropriate cycles of ion bombardments and annealing, or in some cases by vapor deposition film growth. The conditions of surface cleanliness and surface order are established using in situ Auger spectroscopy and low energy electron diffraction (LEED). It is now routine to create ordered overlayers of adsorbed atoms and molecules on these clean surfaces.

(ii) Band MaDDing. The principal angles of concern are 8, and de, the take-off angles of the photoelectrons. The polar angle 8, determines the parallel momentum k in II the crystal azimuth defined by de Herein lies the basis of the bandmapping capability of ARPES. This is a vast topic which will be pursued extensively in the following Chapters. (iii) Photoelectron Diffraction. The emphasis in photoelectron diffraction (PhD) is on the determination of atomic structure rather than electronic structure. The basic notion is to excite electrons out of core levels and to examine the angular distribution. The diffraction patterns observed should, in principle, reveal the environment of the emitting atom. The feasibility of PhD was demonstrated in 1978 (39-41). The topic has now reached considerable maturity, and is treated in Chapter 7. A review by Fadley is also available (42). There are two basic choices of angular variable. One is to hold 8, constant (usually at normal emission, 8, = 0) and to monitor the core photoemission cross section a function of energy E by exploiting the continuum nature of synchrotron radiation. The other approach is to hold ee constant at some off normal Be P 0 position and to measure the azimuthal (4,) dependence of the cross section by rotating the sample. (iv) Svmmetry considerations. The direction of incidence of the photons is specified in Fig. 3 by the angles ePand $y Of more significance is the state of polarization of the incident beam. If the incident beam is linearly polarized, we may distinguish between s and p polarization depending on whether the electric vector is perpendicular or parallel to the plane of incidence.

9

The photon polarization enters into the cross section through the square of the momentum matrix elements as indicated in [ 2 ] . The final state $f is a plane wave at the detector, so we may infer something about the angular dependence of the wave function of the initial state $i by variations of A, the electromagnetic vector. It should be emphasized that a quantitative treatment is quite difficult since A changes from its exterior value to its value inside the solid over a length scale comparable with the sampling depth of the photoemission experiment (43). Many applications of [ 2 ] ,however, are qualitative, and are concerned with identifying odd or even symmetry for the initial state wave function (44). (v) SDin asymmetry. There is a class of experiments which measure the spinpolarization of photoemitted electrons. In such experiments, we must specify a direction of spin quantization. There are two basic physical origins for spin asymmetry. The first is relativistic effects (i.e. spin-orbit interaction) whose detection requires circularly polarized light; the appropriate direction of spin quantization is either the surface normal or the propagation direction of the incident photons. The second is exchange (i.e. magnetic) effects; the appropriate direction of spin quantization direction is the applied magnetic field. These matters are elaborated in Chapter 12. The reader is referred also to the chapters on photoemission in the books by Kirschner (45) and by Feder (46). (vi) Inverse Dhotoemission. The early 1980's witnessed the emergence of angle-resolved inverse photoemission. The inherent cross section for inverse photoemission is lower than that for forward photoemission by the ratio r = (A \A )2, e P where xe and are respectively the wavelengths of the photoelectron and photon. In the P ultraviolet region, we have ra result which explains the relatively late development of inverse photoemission. The angular variables, however, remain unchanged except, of course, that the directions of the electron and photon in Fig. 4 must be reversed. This topic is treated in Chapter 13. Other reviews (e.g. Refs. 47 and 48) are available in the literature.

3. MODERN INSTRUMENTS We offer here a brief general overview of the methods presently in use for angle resolved photoemission spectroscopy. For a more detailed treatment the reader is referred to the review by Leckey (49). Specifics will be treated where appropriate in the individual Chapters. 3.1 Movable Analners The workhorse of the ARPES industry is the spherical deflection analyzer (SDA). Other kinds of electrostatic dispersive instruments which have been used include cylindrical mirror analyzer (CMA), plane mirror analyzers (PMA), elliptical mirror display analyzer (EMDA), 127' cylindrical deflection analyzer (CDA) and others (see Refs. 49 and 50).

10

The 180 SDA is especially well adapted to angle-resolved photoemission for a number of reasons. It can be easily matched to axial input optics composed of cylindrical electron lenses. One such design by one of the authors (SDK) (Ref. 51) is shown in Fig. 4. The four-element input optics permits the angular acceptance and energy resolution to be adjusted by externally applied voltages. Another attractive feature of the SDA is its point-to-point focussing and the fact that the output focal surface is plane, which lends itself well to parallel detection using microchannel plates. The SDA is inherently angle-selective, and a crude angle-resolved experiment can be done simply by tilting a sample in front of a fixed SDA. It is now common practice, however, to mount a modest-sized (typically 50 mm radius) SDA on a one-axis or two-axis goniometer, thereby permitting considerable versatility in the choice of angles of emission. Such instruments are commercially available from a number of manufacturers. These may be regarded as the modern-day version of the movable collector approach of the 1920's illustrated in Fig. 1.

Fig. 4 Layout of a spherical deflection analyzer (SDA), workhorse of the ARPES industry, from Ref. 51.

11

3.2 Multidetection As indicated above, the data-taking capacity of a SDA can be enhanced by using a microchannel plate to perform parallel detection over a range of values of the electron energy E. This practice is now quite commonplace. Other workers have sought to exploit the two-dimensional nature of microchannel plates to perform parallel detection over two variables. The different approaches can be categorized according to the choice of the two variables. In the so-called display analyzers the choice of variables is 8, and de. An early such instrument, built by Rowe and coworkers (SZ), was an adaptation of a multigrid LEED optics permitting a visual display of the photoemission over a large part of the o,, de field. One can think of this as a modern version of the sectored-collector approach of the 1920's illustrated in Fig. 1. Such instruments are really high-pass filters for the electron energy E, and the energy spectrum must be extracted by differentiation of the photocurrent with respect to retarding voltage. This necessity is eliminated in the elliptical mirror display analyzer (EMDA) perfected by Eastman and coworkers (53). It consists of sets of retarding grids (high pass filters) and reflecting grids (low pass filters) permitting the selection of a narrow A E band pass. For the purposes of band mapping, a more appropriate pair of variables would be E and 8,. The aim of such experiments is to determine the E(se), or equivalently E(k 11 ), dispersion relations for one or two high symmetry azimuths. Thus the azimuthal angle be

U

Ba8e Plate

Fig. 5 Layout of the E, ee-multidetecting toroidal analyzer of Riley and Leckey (Ref. 54).

12

is not a particularly useful choice as a continuous variable. An especially noteworthy (E, e,)-multidetecting instrument is the toroidal analyzer of Leckey and Riley (Refs. 49 and 54) a section of which is shown in Fig. 5. Photoelectrons are collected from the sample over a plane containing the surface normal and brought to a focus on a microchannel plate, where contours of constant E and ee are respectively concentric circles and radial lines. This instrument is very well adapted to operation in the synchrotron arena, where beam time is precious and there is a premium on fast data taking. Another very noteworthy (E, ee)-multidetecting instrument is the magnetic deflection instrument perfected by Uveque (Ref. 55). It permits display of the E(k 11 ) band structure on a fluorescent screen in real time. Results obtained on the layer compound GaSe are shown in Fig. 6. This work symbolizes in a rather spectacular way the fulfillment of the dream expressed 25 years ago by Kane (18) that it should be possible to map the energy bands of solids directly from experiment.

m r m

r

r

mk

r

km

Fig. 6 ARPES results on the layer compound GaSe by Uveque Ref. 55). Upper row of panels: (E, 8 ) images taken in real time on a fluorescent screen or four different sample azimuths. d d d l e row: images after processing to enhance band structure effects, and converted to (E,k ) coordinates. Lower row: band structure diagrams corresponding to the experimental kimuths.

6

13

3.3 Time-of-Flipht Methods Time-of-flight (TOF) instruments offer an alternative to deflection instruments in the measurement of electron energy spectra. Indeed, a rather early angle-resolving photoemission instrument built by Bachrach, Skibowski and Brown (56) exploited the pulsed time structure of synchrotron radiation to do TOF energy analysis. The TOF instruments come into their own when the main aim is to do time-resolved photoemission measurements (57). See Chapter 14 for an elaboration of this topic. We are now witnessing the development (58) of photoemission instruments capable of TOF energy analysis combined with two-angle multidetection. REFERENCES: Chapter 1 1.

2. 3. 4.

5.

6. 7. 8. 9. 10. 11.

12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 3 1. 32.

J. G. Jenkin, J. Electron. Spectroscopy 23, 187 (1981). H. E. Ives, A. R. Olpin and A. L. Johnsrud, Phys. Rev. 32,57 (1928). H. Y. Fan, Phys. Rev. 68,43 (1945). A. Hughes and L. DuBridge, Photoelectric Phenomena (McGraw-Hill, New York, 1932). N. V. Smith and W. E. Spicer, Phys. Rev. 188,593 (1969). G. D. Mahan, Phys. Rev. B2,4334 (1970). W. E. Spicer, in Chemistry and Physics of Solid Surfaces IV, edited by R. Vanselow and R. Howe (Springer-Verlag, Berlin, 1982). C. N. Berglund and W. E. Spicer, Phys. Rev. 136, 1030 (1964); ibid., 136,1044 (1964). M. Cardona and L. Ley, Photoemission in Solids (Springer-Verlag, Berlin, VoI I, 1978, Vol II 1979). D. E. Eastman and W. D. Grobman, Phys. Rev. Lett. 28,1327 (1972). G. J. Lapeyre, A. D. Baer, J. Hermanson, J. Anderson, J. A. Knapp and P. L. Gobby, Solid State Commun. 15, 1601 (1974). U. Banninger, G . Busch, M. Campagna, and H. C. Siegmann, Phys. Rev. Lett. 25, 585 (1970). L. F. Wagner and W. E. Spicer, Phys. Rev. Lett. 28, 1381 (1972). D. E. Eastman and W. D. Grobman, Phys. Rev. Lett. 28,1378 (1972). D. E. Eastman and J. Cashion,Phys. Rev. Lett. 27, 1520 (1971). S. A.Flodstrom and J. G. Endriz, Phys. Rev. Lett. 31,893 (1973). G. W. Gobeli, F. G. Allen, and E. 0. Kane, Phys. Rev. Lett. 12,94 (1964). E. 0.Kane, Phys. Rev. Lett. 12,97 (1964). N. V. Smith, M. M. Traum, and F. J. DiSalvo, Solid State Commun. 15,211 (1974). T. Gustafsson, P. 0. Nilsson, and L. Walldkn, Phys. Lett. A37, 121 (1971). B. Feuerbacher and B. Fitton, Phys. Rev. Lett. 29,786 (1972). F. Wooten, T. Huen, and H. V. Winsor, Phys. Lett. A36,351 (1971). R. Y. Koyama and L. R. Hughey, Phys. Rev. Lett. 29,1518 (1972). R. H. Williams, J. M. Thomas, M. Barber, and N. Alford, Chem. Phys. Lett. 17, 142 (1972). F. Wooten, private communication. L. F. Mattheiss, Phys. Rev. B8,3719 (1973). B. Feuerbacher, B. Fitton and R. F. Willis, Photoemission and the Electronic Properties of Surfaces, (Wiley, New York, 1978). B. Feuerbacher and B. Fitton, in Electron Spectroscopy for Surface Analysis, H. Ibach, ed. (Springer, Berlin, 1977). R. H. Williams, G. P. Srivastava and I. T. McGovern, Rep. Prog. Phys. 43, 1357 (1980). E. W. Plummer and W. Eberhardt, in Adv. Chem. Phys. Vol49, edited by I. Priogoine and S. A. Rice (Wiley, New York, 1982). F. J. Himpsel, Adv. Phys. 32, 1, (1983). J.W. Cooper, Phys. Rev. 128,681 (1962).

14

33. for a review, see J. W. Allen, "Resonant Photoemission of Solids with Strongly Correlated Electron", in Synchrotron Radiation Research Advances in Surface Science, R.Z. Bachrach, ed. (Plenum, New York, 1990). 34. C. Guillot, Y. Ballu, J. Paigne, J. Lecante, K.P. Kain, P. Thiry, Y. Petroff, and L. Falicov, Phys. Rev. Lett. 39, 1632 (1978). 35. Narrow Band Phenomena, J.C. Fuggle, G.A. Sawatzky, and J.W. Allen, eds. (Plenum, New York, 1989). 36. J.B. Pendry, in Photoemission and the Electronic Properties of Surfaces, B. Feuerbacher, B. Fitton and R. F. Willis, eds. (Wiley, New York, 1978). 37. M.S. Hybertson and S.G. Louie, Phys. Rev. Lett. 55, 1418 (1985); M.S. Hybertson and S.G. Louie, Phys. Rev. B34, 5390 (1986); J.E. Northrup, M.S. Hybertson, and S.G. Louie, Phys. Rev. Lett. 59,819 (1987). 38. H.J. Levinson, E.W. Plummer, and P.J. Feibelmann, Phys. Rev. Lett. 43,952 (1979). 39. S. D. Kevan, D. H. Rosenblatt, D. Denley, B. -C. Li and D. A. Shirley, Phys. Rev. B20, 4133 (1979). 40. D. P. Woodruff, D. Norman, B. W. Holland, N. V. Smith, H. H. Farrell and M. M. T r a m , Phys. Rev. Lett. 41,1130 (1978). 41. S. Kono, C. S. Fadley, N.F.T. Hall, and Z. Hussain, Phys. Rev. Lett. 41, 117 (1978). 42. C. S. Fadley, Pro Surf. Sci. 16,275 (1984). 43. P. J. Feibelman, bhys. Rev. Bl2, 1319 (1975). 44. J. Hermanson, Solid State Commun. 22, 19 (1977). 45. J. Kirschner, Polarized Electrons at Surfaces, (Springer-Verlag, New York, 1985). 46. R. Feder, Polarized Electrons in Surface Physics, (World Scientific, Singapore, 1985). 47. V. Dose, Surf. Sci. Rep. 5,337 (1985). 48. N. V. Smith, Rep. Prog. Phys. 51, 1227 (1988 . 49. R. C. G. Leckey, J. Electr. Spectr. 43,183 (1 87). 50. N. V. Smith and S. D. Kevan, Nucl. Instr. and Methods 195,309 (1982). 51. S. D. Kevan, Rev. Sci. Instr. 54,1441 (1983). 52. S. P. Weeks, J. E. Rowe, S. B. Christman and E. E. Chaban, Rev. Sci. Instrum. 5Q, 1249 (1979). 53. D. E. Eastman, J. J. Donelon, N. C. Hien and F. J. Himpsel, Nucl. Instr. and Methods 172,327 (1980). 54. R. C. G. Leckey and J. D. Riley, Ap 1. Surf. Sci. 22/23,196 (1985). 55. G. U v e ue, Rev. Sci. Instr. 59, 8!9 (1988); 57 1042 (1986); G. Uveque and J. Robins, $id. 58, 1456 (1987). 56. R. Z. Bachrach, M. Skibowski and F. C. Brown, Phys. Rev. Lett. 37,40 (1976). 57. R. Haight, J. Bokor, J. Stark, R. H. Storz, R. R. Freeman, and P. H. Bucksbaum, Phys. Rev. Lett. 54, 1302 (1984). 58. D. J. Trevor, L. D. Van Woerkom and R. R. Freeman, Rev. Sci. Inst. 60,1051 (1989).

3

15

Chapter 2

THE PHYSICS O F PHOTOEMISSION J.E. INGLESFIELD AND E.W. PLUMMER

1

Introduction

In angle-resolved photoemission the study of the energy and angle dependence of the phot,oemitted electrons provides information about the electronic excitations of the solid. In the simplest picture, these excitat,ions correspond to the one-electron states of band theory, and much of this volume is concerned with the invaluable information about surface and bulk band structure which can be found from the photoemission spectrum. Many features in the spectrum correspond to surface and bulk processes. Surface photoemission comes from electrons in the top few angstroms of the solid, and if the surface is periodic it conserves the component of the electronic wave-vector K parallel to the surface. As the energy of the outgoing electron equals the energy of the initial state plus Rw, the dispersion of surface states, for example, can immediately be mapped out from the photoemission spectrum. In bulk photoemission on the other hand, the component of the Bloch wave-vector perpendicular to the surface kl is also conserved (approximately) in the transition and the bulk band structure can be mapped out. Actually, the surface plays an integral role in photoemission - the electrons have to pass through the surfa.ce on their way to the detector, and the mean free path of these electrons is rather short inside the solid, typically around 10 for photoelectrons with a kinetic energy of 50 - 100 eV. These effects must be included in an accurate description of photoemission. I n this chapter we shall concentrate an the way that one-electron energy bands show up in photoemission, in spite of the complicated electron-electron interactions in solids. These bands really describe the excitations of quasiparticles - screened electrons or holes - and much of the current interest in photoemission (and iiiverse photoemission) is centred on the differences between the quasiparticle states, and the energy bands of conventional density functional theory. The electron-electron interaction can also lead to extra features in the photoemission spectrum - satellites - and we shall see how these can originate. Finally we turn to the electromagnetic field itself, discussing its screening by the electrons.

2 2.1

The photoemission process The final state in the Golden Rule

In angle-resolved photoemission, the energy distribution of electrons travelling in a particular direction is measured. To see how this measurement is related to the electronic structure of the solid we must first understand the wave-function of this final state [l, 2, 3, 41. Switching on the light in the remote past, the wave-function of an electron initially in state q5* is given at t = 0 by the perturbation theory expression [5]:

16

G is the Green function for the system, and the perturbation is:

+

SH = L ( A . p p.A). 2nzc

(2)

with frequency w . We shall study the form of t,he vector potential A in greater detail in section 6. As the electrons reaching the detector are free, let us express G in terms of the free electron Green function Go using Dyson’s equation [5]:

G = Go(1

+ TGo),

(3)

where T is the operator describing the scattering of the emitter. The free electron Green function is given in Hartree atomic units by:

’

where k2/2 is the energy of the emitted electrons, E = E, +FLU. rent a long way from the emitter this can be expanded: GO(r,r’)

-

exp(ikr)

-~

2x7-

exp( -ik.r‘),

As we measure the photocur-

(5)

where k is directed towards the detector: kr

k=-,

By substituting (3) and (5) into (1) we obtain the asymptotic form of the photoelectron

with: q5f(r)= exp(2k.r). This wave-function contains the physics of the famous three-step model [S]: working from the right, the photoelectron is excited by SH, scattered by the crystal, and then propagates to the detector. We can rewrite this as:

where:

+

I4f) = (1 G 3 ’ ) I4f). So the photocurrent per unit solid angle is finally given by:

This expression for the photocurrent corresponds to the Golden Rule [2, 3, 71, with a final state wave-function given by (10). This is the time-reversed LEED state [3]: the final state is obtained by shooting the plane wave e x p ( 4 k . r ) at the sample, letting the sample scatter it via (1 + GOT),and finally taking the complex conjugate. This is not particularly mysterious, because in photoemission the electron which reaches the detector was scattered by the atoms in the emitting sample in the distant past, whereas in most scattering problems this takes place in the future. The energy density of these final states is given by k/8a3 per unit solid ‘e

=h=

n1=

1 au.

17

angle, and when multiplied by the Golden Rule factor of 27r we immediately recover (11). The Golden Rule expression can be generalized to the case where there are many occupied electronic states in the emitter, giving for the photocurrent per unit solid angle and per unit energy:

J ( k )=

.c,k

I ($r I 6 H I

$1)

l2 & ( E- E, - hw).

(12)

1

It can also be generalized to the real case of interacting electrons [l]. The initial state is then the ground state of the N-electron system 1 N , 0); the final state is labelled by the wave-vector k of the electrons reaching the detector, and the state s of the ( N - 1) -electron system left behind, 1 k; N - 1, s ) . This final state can be found by preparing the [ N - 1)-electron system in state s , shooting a free-electron wave with wave-vector -k at the system and letting them interact - finally taking the complex conjugate of the resulting N-electron wave-function.

2.2

Transitions to the final state

As we shall see throughout this book, a great deal can be learnt from photoemission spectra by applying conservation rules [S, 9, lo]. The first of these - energy conservation - is ensured by the &function in the Golden Rule expression (12):

E = E; + hw

(13)

from the measured energy E of the photoelectrons and the photon energy hw we can immediately deduce the energy of the initial state E,. Moreover, in photoemission from a periodic solid surface, the wave-vector component parallel to the surface K of the initial and final states is equal t o within a surface reciprocal lattice vector; this is because the vector potential entering the matrix element in (12) varies comparatively slowly (at least parallel to the surface - see section 6). As surface states have a discrete energy at fixed K , they show up as sha.rp features in the angle-resolved photoemission spectrum [figure I ) , and by applying these two conservation rules their dispersion ca.n be mapped out [S. 101 (section 4). Inside the solid, the LEED state ($;) corresponding to shooting exp(-ik.,r) at the surface consists of the linear superposition of bulk solutions of the Schrodinger equation, with energy E and wave-vector component K , which matches onto the incident wave over the surface. In general these solutions are Bloch waves travelling away from the surface corresponding to the energy bands, together with evanescent waves decaying into the crystal from the surface [11]; in an energy gap of the bulk band structure the wave-function is made up entirely of evanescent waves. These evanescent waves are solutions of the Schrodinger equation which are not allowed in an infinite crystal, but which can occur in the case of a crystal with a surface. We would then expect the matrix element in (12) to be large for bulk initial states with the same total wave-vector ( K , k,) as a travelling wave component of the final state, giving a direct transition. By measuring the energy of direct transitions as a function of photon energy, the initial state bands can then be mapped out - if the perpendicular component of wave-vector inside the solid, k 1 , can be determined [S, 10) (section 4). The presence of the surface means, of course, tha.t kl is not strictly a good quantum number except deep in the solid, and this is why the final state (and initial state) wave-functions contain evanescent wave components near the surface. So the photoemission spectrum also reflects the local density of states at the surface with fixed wave-vector component K - the continua of bulk states reflected by the surface as well as the discrete surface states [ l l ] [figure 1). In fact, even the travelling wave component of the final state wave-fiinction is damped by many-body effects, giving a finite mean free path (section 3.2), and this has the effect of smearing out direct transitions (section 3.4) and enhancing surface sensitivity.

-

18

I

I

I

I

I

I

“

“

I

-20 -18 -16 -14 -12 -10 - 8 -6 -4 - 2

0

INITIAL STATE ENERGY (eV)

Figure 1: Normal emission photoemission from Mg(0001), AI(001) and Be(0001) [9]. Direct bulk transitions are indicated by the arrows, and surface states by the shading.

19

2.3

Calculating photo emission

A calculation of the photoemission spectrum can help with the identification of features as either surface or bulk, and by “tuning” t,he potential felt by the electrons to obtain optimal agreement with experiment, information can be obtained about the energy shifts and broadening effects due to the electron-electron interactions (section 3). The necessary ingredients of such a calculation are an accurate way of finding the electronic states both in the bulk and at the surface, a proper evaluation of the matrix elements, and a way of putting in the many-body effects of lifetime broadening for the initial state and the finite mean free path of the photoelectron (sections 3.2, 3.3). A computer package to do this was developed by Pendry and his co-workers [la]. The starting point is to rewrite the Golden Rule expression for the photocurrent using the following relationship between the sum over states i in (12) and the Green function [5]:

1 $,(r)$;(r’)b(E - E,) = -%nG(r, r’;E) i

7r

- this sum over states is called the spectraEfunction, and we shall meet it again in section 3.1. So we can write (12) as [12]:

J(k) = -%njdrJdr’l/.j(r)sHG(r,r’; k 47r3

E - hw)SH$j(r’).

This expression is very convenient, because it involves the Green function for the initial states, rather than the individual states themselves. In evaluating (15) on the computer, several approximations have to be made. First it is assumed that the vector potential in SH is spatially constant, neglecting the screening effects we shall discuss in section 6. This means that 6 H can be transformed to VV form [12], where V is the potential felt by the electrons. It is assumed that this potential has the muffin tin form inside the solid, that is, a spherically symmetric atomic-like potential at each atomic site, and a flat potential in the interstitial region between the atomic muffin tins. This form of potential gives the electronic states very well for reasonably close-packed systems, but is not satisfactory for open structures like diamond. At the surface, a simplified (one-dimensional) form of the surface barrier is used - usually a step barrier, though recent work uses a barrier taken from self-consistent surface electronic structure calculations [13]. With these simplifications, the way that the program works is as follows. The photoelectron state $r, the time-reversed ( i . e . complex conjugated) LEED state, is calculated using a layer is expanded scattering approach in which the solid is divided up into layers of atoms. in plane waves between the layers, and the reflection and transmission properties of each layer are calculated, giving the probability amplitudes for a plane wave with parallel waveG, where G vector component K to be reflected and transmitted into plane waves K is a two-dimensional layer reciprocal lattice vector. By repeated reflection and transmission operations, the full wave-function for an electron incident on the whole semi-infinite crystal can be determined. Knowing $, J dr’G(r, r’; E - tLw)6H$,(r‘) can be found. In this expression, SH$f acts as a source of electrons for which G describes the propagation in the lower energy (initial) state. An immediate simplification is that 6 H (2.e. VV) is non-zero only inside the muffin tins and at the surface barrier, and then the layer-adapted multiple scattering technique can be used to find the whole wave-field of J dr’GbH$,. As an example of photoemission calculations, figure 2 shows results calculated by Konig et a1 [13] for normal photoemission from Ag(001), at a range of photon energies, compared with experiment [14]. These were obtained using theii extension of the Pendry program to include the more accurate surface barrier. There is fairly good agreement with experiment, and the main features in the spectra are reproduced by the calculation: in particular, this work clearly

+

20

.

.. ..

..._

h u ( PI’) 40

45

55

60

65

70

75

Figure 2: ( a ) Normal emission spectra from Ag(001) at different photon energies, compared with (b) calculated spectra [13].

identifies state B in figure 2(a) as a surface state. The main discrepancy is that the peaks lie about 1 eV closer to the Fermi energy than in experiment, due to shifts in the quasiparticle energy bands compared with the density functional values (section 3.3.1).

3 3.1

Quasiparticles in photoemission Quasiparticle self-energy

Many aspects of photoemission can be described in a single particle picture, as a transition from an occupied one-electron orbital to the state describing the propagation of the photoelectron. In reality the solid is an immensely complicated many-body system of electrons all interacting with one another, but for many purposes this simply results in the screening and decay of the hole left behind and of the photoelectron. These screened, decaying single particle states are the quasiparticles [15, 161, whose wave-functions satisfy a single particle Schrodinger equation:

containing the self-energy (or optical potential) C, which is complex and energy-dependent. The real part of C describes the screening of the quasiparticles, shifting the energy from the Hartree value, and the imaginary part the decay or inelastic scattering processes. The quasiparticle wave-functions (or amplitudes) are given by the matrix elements:

#(r) = ( N

4(r)

-

1,i\&r)lN,O), hole states

= (N,Ol&r)lN

+ l , j ) , electron states.

(17)

Here is the electron annihilation operator, and the hole quasiparticle describes the hole in the ith excited state of the ( N - 1)-electron system, and the electron quasiparticle describes the extra electron in the j t h state of the ( N 1)-electron system. The initial state energy bands measured in photoemission are really the bands of the hole quasiparticles. The imaginary part of the self-energy, which corresponds to the decay of the hole, gives each state a finite energy width (161. The imaginary part of C felt by the photoelectron comes from inelastic scattering processes which cause the spatial decay of the quasiparticle amplitude into the solid, away from the surface [16]. The decay length (+2 to give the decay in intensity) corresponds to the mean free path, one of the factors which determines surface sensitivity in photoemission. To understand the quasiparticle properties of the final state more fully, let us go back to the many-body Golden Rule (section 2.1) [17]. Writing the matrix element between the many-body states as:

+

(k; N - 1,s 16H I N,O) = /dr(k; N - 1,s I G+(r)$(r) [ N,O)SH(r), we can insert a complete set of states of the ( N - 1)-electron system:

(k;N-

1,s

16H 1 N,O) = x / d r ( k ; N - 1,s 1 $+(r) 1 N - l , j ) S H ( N - 1,j 1 &(r) N , 0). j

(19) The matrix element ( N - l,jl$(r)lN, 0) is just the quasiparticle amplitude fof the hole state j . However, the matrix element describing the photoelectron (k;N - l,s]$+(r)lN- 1,j) is not an ordinary quasiparticle amplitude as in (17). An electron quasiparticle amplitude describing the propagation of an electron asymptotically in the would be (k; N, Ol~+(r)lN,O), (time-reversed) plane-wave state k incident on the N-electron system in the ground state; in (k; N - l,sJ$+(r)lN - l , j ) , the electron is incident on the ( N - 1)-electron system in an excited state s, and changes the state from s to j .

22

Fortunately, the matrix element (k; N - l , s J G + ( r ) J N - l , s ) , in which the photoelectron does not change the state of the ( N - 1)-electron system, behaves like the usual quasiparticle amplitude. The term j = s in (19) is the intrinsic contribution to the photoemission matrix element [l],for which the photocurrent can be written as:

k

I d+(r) 1 N - l , s ) G H ( r ) A ( r , r ‘ ; E - b ) x 6H(r’)(N - 1,s I &r’) 1 k; N - l , s ) ,

J(k) = G / d r / d r ’ ( k ; N - l , s

(20)

where A is the interacting spectral function [lS]:

d ( r , r ’ ; E ) = ~ ( N , O ( $ + ( r ’ ) I N - l , s ) ( N - l , sI G ( r ) I N , 0 ) 6 ( E - E o + E , ) .

(21)

3

This has the same form a.,s (la), with the initial state 4, replaced by the hole quasiparticle amplitude ( N - l,s[$(r)[N,O), and the final state by the photoelectron quasiparticle (k; N - 1, sl&+(r)lN - 1, s). The relationship between the interacting spectral function and the interacting single particle Green function (or propagator) is the same as (14). As we shall see later in this chapter and elsewhere in this volume, A describes satellites as well as quasiparticle states associated with single particle energy bands. The intrinsic contribution to photoemission dominates at high enough photon energies, so that the photoelectron escapes before the other ( N - 1) electrons can respond to it [l]. Let us now study the photoelectron quasiparticle in detail. It can easily be shown that the matrix element appearing in (19) satisfies a system of coupled Schrodinger equations [17]:

h is the one-electron part pf the Ilamiltonian, including the Hartree potential, and density fluctuations (N - 1 , j 1 $+$ I N - 1,a) couple the components of the generalized quasiparticle; v is the Coulomb potential, and the s u m excludes the Hartree-like term 1 = j . Ek,+is the energy of the many-body final state I k; N - l,s), that is, E E,. This system of equations can be reduced to a single equation for (k; N - 1 , s I $+(r) 1 N - l,s), assuming that this is the dominant component [17]:

+

x (k; N - 1 , s 1 &+(r”)1 N - 1,s) = ( E k , s - E , ) ( k ; N - 1,s

I &+(r)I N - 1,s).

Here, G is the Green function for the one-electron part of the Hamiltonian, and:

fi,s(r) = /dr’(N

-

1 , s /4+(r‘)d(r’)1 N

-

l,l)v(r’,r).

(24)

(23) is an effective single particle equation for the photoelectron quasiparticle amplitude, containing the self-energy:

This is essentially the same self-energy that appears in (16) [17, 181, evaluated at the energy of the emitted electron.

23

0,

I

,

,

,

,

,

,

,

,

,

1 " " " " ' l

Figure 3: Real and imaginary parts of the self-energy of an electron gas at different densities as a function of wave-vector relative to X.17 [16, 191.

3.2

Mean free path of the photoelectron

When we solve the Schrodinger equation (23) for the (time-reversed) photoelectron, the solution at the energy of measurement E corresponds to a state decaying into the solid [16]. Neglecting band structure effects, the wave-function inside the solid has the form:

+; and when y is small compared with

N

exy i k l z exp - 7 2 ,

(26)

kl:

So the escape depth is given by: kl

d = ___ (28) 21BnC) - the factor of 2 comes from squaring the wave-function to find the intensity. Only the normal component of the electronic motion is involved in the decay, which is why surface sensitivity can be increased by going to large emission angles. The mean free path itself is given by:

where k is the total wave-vector inside the solid (more generally, the group velocity). In a free electron metal, C has a small imaginary part until the electron energy measured relative to the Fermi energy exceeds the plasmon energy (figure 3) 116, 191. A new channel then opens up into which the photoelectron can be scattered by exciting a plasmon. In terms of (as), state 1 consists of the hole state s plus a plasmon, and the imaginary part of the

24

f 0 a m 0 L L

+4

Energy Above Fermi Level (eV)

Energy Above F e r m i Level (eV)

Figure 4: Mean free pat,li as a function of electron energy in A1 and Ag. The lines correspond to different theories, and the points to experiment [22]. potential comes from (25) when E 2 El - E,. Below the plasmon frequency the photoelectron can be scattered out of the elastic cha.nne1 by exciting electron-hole pairs, but we see from figure 3 that they give a small contrihntion to the imaginary part of the self-energy. For a nearly free electron metal like A1 the mean free path should drop sharply at the plasma frequency, and then gra.dually increase with increa.sing energy. This behaviour is found rather generally, in fact, with a minimum in the mean free path of about 5 A at an electron energy of typically 20 eV [20, 211. A theoretical analysis of electron mean free paths in a wide range of elements and compounds has been carried out by Penn [22] and Tanuma e t a2 [23], making use of optical data for the dielectric function to which the electronic self-energy can be related. Results for A1 and Ag are shown in figure 4, together with experimental data from overlayer experiments and photoemission - a.greement, is rather good. I n a,ctual photoemission and LEED calculations, the imaginary part of the self-energy is assumed to be constant spatially, right up to the surface, and this seems a good a.pproxima,tion [24]. The imaginary pa.rt of the self-energy conies from real transitions scattering out of the elastic cha.nnel, hut C also has a real part coming from virtual transitions. These are related by a Kramers-Kronig dispersion relation [lG]. For electrons with energies greater than the plasmon energy, the real part of the self-energy gradually becomes less attractive as the electron energy increases [19] (figure 3). This shift comes from the inability of the electron gas to screen the photoelectron when it is moving fast. There is experimental evidence that this shift is quite important: for example in photoemission calculations for Cu( I l l ) , an upward shift in the inner potential felt by the photoelectron is needed to obtain the right photon energy-dependence of the intensity [ 2 5 ] . Beam threshold measurements for the diffraction of low energy electrons from Cu(ll1) show a 4 eV shift in the real part of the self-energy between 20 and 120 eV kinetic energy 1261, and theoretical a.nalysis of the low energy electron diffraction from Cu(OO1) over an extended energy range ( u p to 700 eV) [27] exhibits an energy-dependence consistent with the beam threshold measurements and the theoretical calculations shown in figure 3. The effect of the energy-dependence of the self-energy can be seen in the inverse photoemission 3xperiments of Speier e t al [as]. In these experiments the quasiparticle amplitude for the 2lectron in its high energy initial state incident on the solid is essentially the same as that for the time-reversed photoelectron. Speier ef a1 [2S] found upward shifts in spectral features in the bremsstra.hlung isochromat spectra for Ni, Cu, Ag and Pd relative to the density of unoccupied states calculated with an energy-independent ground state potential (figure 5). N

25

Figure 5: Bremsstrahlung isochromat spectrum for Ag (top curve), compared with the calculated density of states (bottom curve) and the broadened density of states (middle curve) (281.

3.3

Spectral function of hole states

The core states, energy bands and surface states measured in photoemission correspond to quasipa.rticle states in the hole spectral function A, defined in (21). This enters directly in the intrinsic contribution to the photocurrent (20), which dominates at high photoelectron energies when the outgoing photoelectron does not, change the sta,te of the ( N - 1)-electron system [I]. In (21) we wrote the spectral function in terms of the individual hole excitations of the system, but it is convenient to rewrite this in terms of the interacting Green function or propagator, upon which the diagrammatic and pcrt.urha.tion approach to many-body theory is based. The Green function is given by:

G(r,r';E) = s

(N,O14+(rf)P- I , ~ ) ( N 1,sI4(r)W,O) E - Eo t E, -is

sumsover the excitations of the ( N - 1)-electron system (hole states) and the (N+l)-electron system (electron states) [16]. It is time-ordered, meaning that the denominator for the hole states contains -is, and for the electron states t76. Comparing with (21) we see that for E < 0 (we take the Fermi energy as our zero), A is related to G by:

-

the same as the non-interacting result (14). The Green function satisfies the inhomogeneous version of the Schrodinger equation (16), containing the self-energy [16]:

-

1 2

(--V*+V(r)-

J

E)Q(r,r';E)+ dr"C(r,r";E)O(r",r’,;E) = -6(r-r').

(32)

All the difficulties of the many-body prohlein reside in determining C, but gradually experience is building up in finding the self-energy in simple metals [29, 301 and semiconductors [31], and photoemission provides an invaluable way of testing the theories.

26

Quasiparticle states correspond to peaks in the spectral function A( E ) . For a particular hole state, the Green function varies i n energy like: 1

(33)

4(E)- E-C-(Z(E))'

where c is the energy of the state using the Hartree potential, and (C) is the expectation value of the self-energy. If Z varies slowly with energy, and its imaginary part is small, we then find a quasiparticle peak in A a t energy c A, lifetime broadened to width r', with A = %C, and r = I&CI [is]: n

+

Such a quasiparticle is a solution of the Schrodinger equation (16) at a particular Bloch wavevector, with a complex (analytically continued) eigenvalue (c A X ) [16]. Compare this with the photoelectron quasiparticle which is a scattering solution of (16) at real energy, and consequently complex wave-vector. Not all the structure in A corresponds to quasiparticles, which are usually considered as those states for which there is a one-to-one relationship with energy bands; there are also many-body satellites. However, quasiparticle states are particularly important,, and a constant theme of recent work is that they are often surprisingly well defined.

+ +

3.3.1

Core states and satellites

Photoemission from localized core states shows a shifted and lifetime-broadened quasiparticle peak, and satellite structure. The valence electrons screen the core hole left behind, reducing the energy needed to remove the core electron. This interaction between the core hole and the remaining electrons inevitably leads to the possibility of electronic excitations - plasmons in the case of nearly free electron metals, as well as electron-hole pairs - this gives the satellite structure. To study the core hole spectral function, we shall describe the screening properties of the valence electrons in metals like Na or Al in terms of plasmons, writing the Hamiltonian as [32, 331:

The first term, summed over pla.smon modes, just counts the number of plasmons in each mode the second term gives the unrelaxed energy of and multiplies this by the plasmon energy the core hole e:, or zero when the core st,at,eis occupied - 6+, b are hole creation and annihilation operators; the final t.erm contains the potent,ial energy of interaction between the hole and the plasmons - ( u z a q ) gives the amplitude of the plasmon cha,rge density fluctuation, and A,, is a measure of the potential which t,liis produces at the core. The eigenstates of (35) fall into two classes. Clearly, when the core st;lte is occupied, H just reduces t.o the simple harmonic oscillator for plasmons, with energies: ~

3

~

;

+

E

=T

+

I ~ W ~r i p 2

+ ngw3 + . ..

(36)

where rip is the number of pla.smons in mode q. When the core state is empty the Hamiltonian becomes: 4

This can be diagonalized with new plasmon variables:

27

W*Ec-3Wp

W+€c-2Wp

W’Ec-

Wp

W‘Ec

kinetic energy

Figure 6: Spectral function for a core state i n a free electron gas with the density of Na (rs = 4 ) (displaced by the photon energy hw to give the intrinsic photoemission spectrum) [l]. giving: B

So the energies of the system with a core hole are: E = t: -

+ nlwl + n2w2 +

Xilw,

n3W3

+ .. .

(40)

9

and the spectral function consists of a core peak at energy L , = e: - C , Xi/wq, together with plasmon satellites [33]. The spectral function d ( w ) calculatd for a. core state in a free electron gas with the density of N a (rS = 4 a.u.) is shown in figure 6 [I]. As well as the no-loss peak at t, there are the satellites corresponding to exciting one, two,. . . plasmons, with line-shapes resulting from the plasmon dispersion. When the interaction between the core hole and the remaining electrons is included, the total integrated weight in the spectral function is the same as in the noninteracting case - weight is transferred from the core line to the satellites; moreover, the centre of gravity of the spectral function lies at the unrelaxed core energy c t - the Koopman’s theorem value [33]. This is generally true, for more complicated interactions than we have assumed in (35). Unfortunately these moments results for d do not go over to the photoemission spectrum except in the intrinsic limit of high photon energies, and in the case of plasmon satellites extrinsic plasmon excitation persists even at high photoelectron energies [l, 17, 341. Although the spectral features remain, their weight changes because of extrinsic effects, in which the excitation of plasmons by the photoelectron becomes important (section 5 ) . As well as the plasmons, the core hole can excite electron-hole pairs in the electron gas. Unlike the plasmons, the electron-hole pairs in a metal start with zero energy, so the corresponding satellite begins at the screened core energy. Moreover, the effect of the core hole on the electron gas in its ground state is to modify each one-electron wave-function, resulting in zero overlap between the Sla.ter deterniinant wave-functions of the many-electron system with and without the core hole [35]. This wipes out the 6-function of the core state quasiparticle peak shown in figure 6. It is replared by a power law singularity in the spectral function [l]:

d(E)

-

(t.

1 - E)l-a’

where (Y can be found from the phase shifts of the electrons at the Fermi energy due to the core hole potential: 2

n=--

H2

C(2+ I)&;, 1

(42)

28

il 1-

Ot1078

1076 1074 1072 BINDING ENERGY (OW

1070

Figure 7: Na 1s and 2s photoemission spectra, showing the asymmetric shape of the no-loss peak, fitted by the Doniach-SunjiC lineshape and a Lorentzian at the surface plasmon satellite (solid line) [3S]. to quote the famous Nozitres-de Dominicis result [36). So far we have neglected the lifetime of the hole, due mainly to Auger processes in which an electron drops down from a higher level and a second electron is excited. If these do not interfere with the interactions with plasmons and electron-hole pairs, the full spectral function can be obtained by convoluting the infinite lifetime result, that is (41) close to ccr with a Lorentzian like (34). This gives the Doniach-SunjiC lineshape [37]:

where we write f for the gamma-function, and r is the lifetime broadening. In general this provides an excellent fit to experimental data, and has been applied to a wide range of core states. In a study of photoemission from nearly free electron metals, Citrin et al. [38) obtained the core spectra shown in figure 7 for the N a 1s and 2s levels. Allowing for phonon effects, they found t1ia.t their results could be fitted with (43), with an asymmetry parameter a of 0.20 and lifetime broadening I? of 0.2s eV for these levels. a can also be found from the scattering properties of a static, self-consistently screened core hole via (42), in good agreement with the Na experiments. The lifetimes are harder to calculate, but for the deep 1s hole i t is mainly due to intra-atomic Auger processes and an atomic calculation gives good agreement. The 2s lifetime is dominated by interatomic processes involving valence electrons, but reasonable theoretical estimates can be made for this too. 3.3.2

Valence band quasiparticles

Most electronic structure calculations for the valence states in a solid and at a surface are based on density functional theory, which is designed to give ground state properties correctly, like the total energy and charge density [39]. Although the one-electron wave-functions and energies in

29

density functional theory do not in principle correspond to quasiparticle excitations, the energy bands are often in good agreement with photoemission measurements. The discrepancies will be studied in section 4.3. In density functional theory, the ground state charge density po(r)of the system is written in terms of effective one-electron wave-functions which satisfy a Schrodinger equation containing the exchange-correlation potential Vzc(r) as well as the Hartree potential V.(r) and the potential due to the ions [40]:

V,, corrects VH to describe the effects of exchange - the fact that electrons with the same spin cannot be at the same place at the sa.me time - and the correlated motion of the electrons. Usually Vzc(r) is calculated in the local density approximation, in which it is taken as the exchange-correlation potential of a uniform electron gas with the same charge density as at point r. Density functional theory is remarkably succesful in describing the charge density and energetics of solids and surfxes, but apart from the highest occupied energy level which in (44) have no rigorous meaning as oneequals the ionization energy, the individual t , ’ ~ electron excitation energies. This is unlike the quasiparticle equation (16), for which the c;’s are the excitation energies which enter the hole spectral function. Unlike the self-energy C in (16), the exchange-correlation potential is local, real, and energy-independent. The discrepancies between density functional energy bands and the actual quasiparticle excitations appearing in (16) are due to energy-dependent energy shifts coming from the real part of the self-energy, and lifetime broadenings due to the imaginary part (34). A particularly important energy shift occurs in semiconductors, for which density functional theory generally gives a gap between the valence and conduction bands which is too small [31], but in the following section we will also discuss shifts in met,als. The GW approximation [16] provides a valuable method for calculating C, and this is the way that the free electron results of figure 3 were found. The reason why density functional theory continues t o be the starting point for describing valence band quasiparticles is that it is relatively straightforward to implement; the self-energy is much more difficult to determine even in the GW approximation, and up to now it has been calculated only for semiconductors (311 and s-p bonded metals [29]. The lineshape of surfa,ce states, localized states lying in bulk energy gaps, should in principle be Lorentzian, due to the energy broadening of the imaginary part of the self-energy (section 4.1) [41, 421. Of course the surhce s h t e does not necessarily feel the same self-energy as neighbouring bulk states, but in the ca.se of .4l(OOl) the surface state below E.P extends deep into the solid (431, and we would expect the value of the self-energy to be bulklike. In this case, the apparent lineshape of this state is asymmetric (figure 1) [44], because it lies so close to the bulk band edge that the Lorentzian overlaps with the smeared-out band edge [43]. This does not mean that there is any mixing between the s u r f x e state and bulk quasiparticle amplitudes - the surface state quasiparticle is still spatially localized. In the case of Be(0001) the surface state has the expected Lorentzian lineshape (421 (section 4.1).

3.4

Quasiparticles in direct transitions

The energy broadening of the hole quasiparticle combines with the momentum broadening of the photoelectron, due to the exponential decay of its wave-function away from the surface, to give a width to direct transitions. To obtain this we go back to the Golden Rule, writing

30

the spectral function for the hole state as:

is the initial state band structure, and r h is the energy broadening of this state. The contribution of the final state to the squared matrix element in the Golden Rule (20), in which k L is conserved, is proportional to the spectral function for the photoelectron:

- Eh(k1)

re

kl) c
a

c3 W W

20

z

0

a I-

0 W

10

1 W

r

0.5

1 .o

CRYSTAL MOMENTUM k

N

(i-')

Figure 18: Plot of the free electron bands in the direction normal to the (110) face of N a [55]. The shaded region illustrates the energy uncertainty in the final bands due to lifetime effects.

45

'

-4.0 15.0

25.0

35.0

45.0

55.0

65.0

75.0

Photon Energy (eV)

Figure 19: Peak position for normal cinission spectra from N a ( l l 0 ) . The data is from Jensen and Plummer [55] and the theory from Shung ef d. [74]. state with an initial energy of -2.0eV measured from the Fermi energy ( E F = 3.24eV) with a wave-vector k I = 0.30a.u. The heavy arrow in figure 18 shows this direct transition. If the photon energy is reduced, the transition comes from an initial state with a smaller k l and an energy closer to the bottom of the band. A t hw = Eg = 16.8eV the transition comes from the bottom of the band. If the photon energy is increased from the original value of 26eV then the initial state moves to larger kl and closer to the Fermi energy. At hw=32 eV the direct t,ransition comes from the Fermi energy, and in the single particle picture no direct transitions should be seen between 32 and 38 eV, where a transit,ion from the Fermi energy to the next higher final stat,e band will be seen again. As t,he photon energy is increBed beyond this value the direct transition is from initial states moving down in energy, reaching the bottom of the band at hw=67 eV. The experimental results of Jensen a.nd Plummer [55] in this direction are shown by the heavy dots in figure 19, compared with the predictions of the free electron model which are shown by the solid line. Qualitatively the peak positions in the photoemission spectra behave just as predicted from figure 18 and equation 60. It should be noted that N a shows better agreement with free electron theory than almost any other material that has been investigated. Yet there are two notable exceptions to the agreement: firstly, the bottom of the experimental band is not as deep as predicted theoretically; and secondly, a peak appears at the Fermi energy in the photon energy range between 32 aiid 38 eV where no transition should be allowed. The latter issue has attracted considerable attention [6S, 74, 75, 761 but will not be discussed in this chapter. The difference between the measured and calculated values for the bottom of the band is in principle the self-energy correct,ion. Jensen and Plummer [55] reported that the bottom of the measured band is 2.5 eV below the Fermi energy, compared with the theoretical

46

-0.8

4.4

0.0

0.4

0.8

k" (A')

Figure 20: Measured quasiparticle dispersioii for Na [56], compared with the LDA or free electron band structure [72]. The dashed line is the calculated band in the RPA [15]. value of 3.2 eV. In the extremum searching procedure [56, 671, data like those shown in figure 19 are used to determine only one point in the dispersion curve of the initial state - the extreme point. In favourable circumstances the data is fitted by a curve, like the dashed curve in figure 19 which represents a transition from an initial state with an effective mass of 1.28 into a free electron final state band, and from this fit the deepest point is determined. This gives the extremum for K = 0, in other words E, at k = 0. Then, another photon sweep is made with the analyzer fixed at a new value of K from which the extremum energy is determined, and the procedure [56]. is repeated to give the band structure along the line k = (K,O) Figure 20 shows the data for the experiiiiental quasiparticle band structure for Na obtained in this way, compared with theory. The solid curve is the single particle band obtained from the density functional band calculation [72], the same as the non-interacting free electron band, while the dashed curve gives the quasiparticle band calculated in 1965 by Hedin (151 within the random phase approximation (RPA) for an electron gas with the density of Na. It is obvious that the experimental and theoretical quasiparticle bands are appreciably different. The difference between the measured quasiparticle band and the single particle band ( i . e . the )I (figure 3), solid curve) is %E. A slight problem arises since %E # 0 at EF (unlike % whereas the experimental data are referenced to EF. The change in %E with respect to the Fermi energy can be determined, defined by:

ABI=(k) = [E,(k)- E ~ l e x p- [ & ( k ) - EF]theory.

(61)

The experimental data shown in figure 20 are plotted in figure 21 to show the k-dependence of &E [56]. The Hedin calculation for the self-energy [15] is shown as the solid line, marked RPA. The discrepancy between the RPA calculation and the experimental results generated several papers, attempting to improve upon the RPA calculation [29, 30, 77, 78, 79, 801.

47

W F )

Figure 21: Comparison of the experimental and theoretical self-energy correction A%Z(k) [56]. The various theoretical curves are explained i n tlie text. Experimentally the band narrowing seen i i i figure 20 for N a was also reported to have been confirmed by x-ray absorption measurements [Sl]. There seemed to be a straightforward procedure for improving the self-energy calculation that, produced remarkably good agreement with the experimental data [29, 561. Hedin’s GW approximation was used, in which the self-energy is calculated as the first term in an infinite series containing successively higher powers of the dynamically screened Coulomb interaction [15, 161. Hedin employed the free electron Green function and the Lindhard dielectric function (i.e. RPA, without exchange-correlation) for screening the electron-electron interaction [15, 291. An immediate improvement in the a.greement between theory and experiment was achieved by incorporating into the G W scheme a more realistic dielectric function for the electron-electron screening. Northrup ef nl. [29] used a density functional (LDA) dielectric function in a calculation that also included the effect of the ion cores in the Green function. They reproduced the measured quasiparticle Iiands for N a , and their %kX is shown as the dashed line labelled LDA in figure 21. ‘This t,ype of t,heory is now commonly referred to as time-dependent LDA [S2]. Lyo and t’lummer (561 developed a scheme to calculate the selfenergy self-consistently within the G\I! approximation using different, models for the dielectric function. This calculation showed that good agreement with experimental data for a wide range of simple (s-p bonded) metals could be achieved if the long wavelength limit of the dielectric function included the effects of exchange and correlation - a local correction to the RPA . There are many examples in the literature where there are systematic differences between the measured and calculated bands. Probably the most studied discrepancy occurs in Ni, where there is a N 1 eV difference between theory and experiment, 2-3 eV below the Fermi energy [S3]. The difference between theory and experiment has been measured for the intermetallic NiAl [69], and shows a simi1a.r trend to Ni as a function of energy below E F , except that the magnitude is a factor of 2.5 smaller. I n bot,h of these cases the difference has the same sign as in the case of Na, i.e. the occupied quasiparticle Ixmds are narrower than single particle band structure calculations predict. For Ag the reported difference has the opposite sign, as can be seen from figure 2 [13]. Takahashi et el. [S4] have made a comparison of the measured

bands in the high T, superconductor BizSrzCaCuzOS. In the light of the discussion above, it would seem that what is needed for the future is a considerable theoretical effort focused on including the real band structure with an LDA dielectric function in a GW-type calculation of the self-energy, or to develop another equivalent model for treating many-body effects. Wrong! There is in fact no theoretical justification for the LDA procedure outlined above. A calculation which should be better than the GW approximation for the electron gas predicted a broadening instead of a narrowing of the single particle bands [79], and Mahan and Sernelius [30] have shown that if vertex corrections are included properly in a calculation of C, a cancellation occurs which gives back almost the same answer as that obtained by Hedin [15] in the RPA. Vertex corrections describe the correlation between the position of the electron and the positions of the other electrons in the screening charge: the LDA calculation by Northrup et al. [29] includes such corrections in the dielectric function, but Mahan and Sernelius showed that these are largely cancelled by including the vertex correction in the numerator of the selfenergy expression [30]. Their theoretical result for B E is shown in figure 21 by the dashed line labelled G W f . This all presents a theoretical problem which should keep many-body theoreticians occupied for years. But there is a much more serious problem related to the interpretation of angle-resolved photoemission. One of the golden rules of angle-resolved photoemission is that peaks which move with photon energy at fixed K come from bulk transitions, and peaks that are fixed as the photon energy is changed are two-dimensional surface states and surface resonances. In a series of important papers [74, 761, perhaps just a.s seminal as his early work on photoemission theory [3], Mahan and his collaborators have shown that even in transitions identified as bulk-like, surface effects can distort the lineshape. In section 3 it was pointed out that the reduction in symmetry at the surface allows for non-kl-conserving transitions. The amplitude of these surface transitions must be added coherently to the amplitude of the bulk transitions, leading t o the possibility of interference. Shung and Mahan [76] have calculated the photoemission from Na(llO), treating the bulk and surface emission on an equal footing, and they have shown that this interference can lead to measurably large distortions in the position and lineshape of the “bulk” transition. This can lead to discrepancies between the apparent binding energy and the actual energy of the quasiparticle initial state involved in the transition. This suggests that in many applications accurate photoemission calculations, such as those described in section 2.3 [12, 131, may be necessary. In further work, Shung et al. [74] again calculated the photoemission spectra of Na, but this time fully incorporating the self-energy effects as well as the surface effects. They found that both ?%E and %C for the initial and final states contribute to the distortion of the measured photoemission spectra. The crosses in figure 19 are from this calcula.tion, and are in excellent agreement with t,he photoemission data in the low photon energy range. The theory sta.rts off from an RPA quasiparticle band structure (figure 20); the additional band-narrowing shown in figure 19 at low photon energies is a consequence of the smearing-out of the bands - mean free path effects in the final state bands (shown schematically by the shaded regions in figure 18), coupled to the equivalent lifetime effects in the initial state bands. This effect is reduced appreciably at higher photon energies, where the mean free path of the photoelectron is longer and the effect of damping in the final state band is reduced. This calculation indicated that the simple first order expression for the peak shape given by equation 49 is not correct, and that appreciably asymmetric peaks will be observed in the photoemission spectrum. Subtle lineshape asymmetries may be present in the data from the alkali metals that could not be detected due to the low cross-section for excitation [55, 56, 681. In contrast, the signalto -noise and background are adequate for A1 and Be to evaluate the lineshape of a direct transition [9]. Figure 22 shows the fit to the direct transition from the bottom of the Be band seen in normal emission from the (1120) surface of Be at a photon energy of 100 eV. The direct transition is fitted with a Lorentzian lineshape with a FWHM of 3.45 eV (with

-

49

:.,a

16

14

12

10

8

6

Binding Energy (ev)

4

2

*-**a4

0

Figure 22: Normal emission photoemission spectrum [rom Be( 1120) taken at a. photon energy of 10s eV [SS]. The direct transition is fitted by a Loreiitzian line-shape. The insert is the direct transition peak recorded at a photon energy of 30eV normal to the (0001) face [52].

50

a x2 = l.l), in good agreement with the measurements on Be(0001) shown in the insert for a photon energy of 30 eV [52]. The clear theoretical prediction by Shung et al. [74] is that

the lineshape of the peak, and consequently the peak position, in the photoemission spectra for transitions from the bottom of the unoccupied band depends upon the photon energy (see figure 19, for Na). This prediction is not substantiated by the two Be spectra shown in figure 22, or from measurements on Mg [64], Na [55] or K [68]. This is an area where more and better experimental data and theoretical calculations are required. Experimentally the surface interference effect could be completely eliminated by using s-polarized light and measuring at the non-normal r points in the second surface Brillouin zone. In principle, &E and SmIC for the final bands can be obtained experimentally from the real and imaginary parts of the optical potential deduced from a fit to the low energy electron diffraction data [27].

5

Plasmon satellite shake-up and time scales

111 section 3.3.1 we saw that the core hole spectral function in simple metals contains plasmon satellites, and here we shall study their excitation in the photoemission process. The state corresponding to the n’th plasmon satellite is Ik; N - l , c , n ) , in other words a photoelectron in the asymptotically free electron state k, and the ( N - 1)-electron system containing core hole c and excited into the n’th plasmon mode. From (19) we see that there are two ways in which the system can be excited into this state. The first, is the intrinsic contribution:

/dr(k;N-l,c,n

( 5 + ( r ) I N - l , c , n ) s H ( N - l , c , n I $ ( r ) IN,O),

(62)

which we can interpret (reading from the right) as the creation of the core hole and the plasmon excitation occurring together, followed by the propagation of the photoelectron which does not change the state of the system. The other way of exciting the system is the extrinsic contribution:

in which the creation of the core hole leaves the electron gas in its ground state, but the outgoing photoelectron excites the n’th plasmon mode. The intrinsic and extrinsic contributions to the total transition matrix element (19) are coherent, and they interfere with one another in exciting plasmons - the core hole and the outgoing electron have opposite charges 187, 881. The result of this is that the intensity of the plasmon satellites is only significant when the photoelectron has a kinetic energy greater than (typically) 50 eV [89, 90, 911. This has been explained using both semi-classical and quantum mechanical models [92,93, 94, 95, 181. To lowest order i n the coupling with the plasmon, the matrix element describing the creation of the core hole and the corresponding excitation of the plasmon in the intrinsic contribution is [17]:

Here 4c is the core electron wave-function, 6u, is the potential of the plasmon with energy w,, and Y~ is a coupling constant to the plasmons which can be found from dielectric response function theory [96]. The other amplitude entering the intrinsic contribution can be approximated by the plane wave of the photoelectron: (k; N - 1,c,17 I 4 + ( r ) I N - l , c , n ) = e x p ( - i k . r ) .

(65)

51

I

, I

A

/’ / /

3 /

/

I

I I I

,

/

/

/’ ,

-055

I

I

-050

-045 -0.41 iaul %1$2 Figure 23: Surface plasmon satellite fiom a core a t the surface of a free electron gas with the density of A1 1951. J is the photocui I ent noiinal to the surface, as a function of electron kinetic energy measured from the no-losr line at (hw Ec). The broken curve shows the intrinsic contribution; full cuives are tlie total pliotocurrent at (hw E,) = ( A ) 1.2, (B) 2 , (C) 4, (D) 8, (E) 12 a.u.

+

+

In the extrinsic contribution, the core hole amplitude is just:

and from a perturbation treatment of t.he theory presented in section 3.1 [17] it follows that:

where G is the Green function of the photoelectron (the free electron Green function in this model), evaluated at the energy of the photoelectron Ek plus the plasmon energy. This describes the way that the photoelectron is scatateredfrom one free electron state to another by interacting with tlie plasmon. Substituting these amplitudes into (59) and (60) we can find the shape and strength of the plasmon sat,ellit.es. Results for the surface plasinon satellite i l l A1 arc shown in figure 23 for photoemission from a core at the surface [95]. The width of t,he satellite comes from the plasmon dispersion, and we see that the intrinsic and extrinsic contrihutions c,ancel a t the minimum energy-loss end of the satellite, corresponding to the excitation of the long wavelength surface plasmons. This is because the long wavelength plasnions are excited by the average potential which is zero for photoelectron. The shorter wavelcngth plasmons can be excited by the core the core-hole hole photoelectron even at low kinetic energies of the photoelectron. From the figure we see that the interplay between intrinsic arid extrinsic processes leads to more structured satellites as the electron kinetic energy increases, rediiciiig eventually t o the intrinsic contribution alone. Similar behaviour is found for the bulk plasmon satellite, and it has been suggested that the main reason why the satellit,es are not apparent a t low kinetic energies is that they are so featureless that they merge into the background of other inela.stic loss processes [95]. These quantum mechanical results are i l l very good agreement with a semi-classical treatment in which it is assumed that. the photoelectron follows a classical trajectory from the core, and the resulting time-dependent perturlmtion excites the plasmons (figure 24) (951. T h e validity of the semi-classical approach nieaiis that w e can use a time-scale argument to decide

+

+

52

3

iI

i

WOl

f) IOU1

fi

Figure 24: Surface plasmon satellite from a core 10 a.u. in from the surface, at (ftw+E,) = ( A ) 2 and (B) 12 a.u. [95]. The full curve is the quantum mechanical calculation; the broken curve is the semi-classical calculation in which the photoelectron has the energy prior to plasmon loss; the chain curve is the semi-classical calculation in which the photoelectron has the energy after plasmon loss. when plasmons will show up [97]: plasmons with a particular wavelength will only be strongly excited if the electron separates by at least this distance in one plasmon period. For example, the peak in the surface plasmon satellite (figure 23) corresponds to a plasmon wavelength of about 40 a.u., with a period of 14 a.u., so we expect it to show up at an electron kinetic energy of about 4 a.u. - in good agreement with the proper calculation. At lower kinetic energies the perturbation due to exciting the core electron is switched on adiabatically as far as exciting the plasmon is concerned, and at higher kinetic energies it is a sudden perturbation which “shakes up” the plasmon. Many-body satellites can have much more complicated photon energy-dependence than this, with resonance behaviour in cases where there are different transitions which can lead to the sanie final state [l].

6

Screening of the electromagnetic field

Section 2 derived the transition matiix element for photoemission using the Golden Rule, with the induced photocurrent per unit solid angle and per unit energy given by equation 12. The matrix element connecting the initial and final states is M I , = ($,lA . p p . A\&), where p is the momentum operator -zhV and A is the vector potential. It is normally assumed that the spatial variation of A is very small on an atomic scale and that V . A = 0. With these assumptions, which are rigorously true in a vacuum, the matrix element can be written as:

+

hfjf

0: A o .

($,rlVl’l$t),

(68)

where V is the potential felt by the electrons. It is this form of the transition matrix element that is used in almost every calculation of a n angle-resolved photoemission spectrum (section 2.3). The intent of this section is to point out how important the local electromagnetic

53 corrections can be and to illustrate liow the intera.ction of the incident field with the solid can be described theoretically and pictured physically. Photoemission from a simple metal again offers a. good starting point from which the basic principles may be illustrated. If a. metal was really free electron like, the only place where an electroil could be excited by ail incident photon would be a t the surface. Inside the metal it is impossible to simultaneously conserve energy and momentum, or in the framework of (68), V V = 0 inside the material. At the surface, V V # 0 and electrons can be excited (the crystal moves). This is the surface photoelect,ric effect. Mackinson pointed out in 1937 that in the surface region the rapid variations in the electromagnetic field could be as important as the abrupt change in the potential [98]. Remember that in the classical calculation there is a discontinuity a t the surface in the component of the electric field perpendicular to the surface. In a microscopic representation of t h r fields there are rapid oscillations in the surface region which depend in detail upon the incident frequency and the electron density of the solid [99]. The following describes what is known experimentally and theoretically about the importance of the local fields a t the surface. Philosophically there are t,wo approaches to incorpora.ting the induced fields into equation 12 for the pliotocurrent. The first wonld be to consider both the initial and final states as the true many-body stat.es of the system. Then $1 would conta,iii the response of the electrons to the incident field as a true many-hody wave-function. The second approach, which is much more appealing for photoemission calculal ions, is to keep the wave-functions single particle-like and put all of the ma.ny-body screening effects into the effective field. Here we will start with the latter approach and then finish t.liis section by describing the many-body wave-functions in terms of the normal modes of tlie electron gas a t the surface [100]. T h e vector potential inside the solid A(r) can be writ,ten as:

+

A ( r ) = AO AA(z),

(69)

where A0 is the vector potential out,side the solid, and AA the variation in A inside the solid, which is a function of 7 . With this definition the matrix element M I , can be written in the form: Afjz

=&.($jIpl~bt)

+ ($/lAA.p+p.AAI$t).

(70)

The first term is the ordina,ry surface pliotoelcctric effect described by (68) and the last term results from the microscopic variations in the fields at the surface. The last term is zero unless there are longitudinal electromagnetic waves or rapidly varying transverse fields. Such fields may exist only i n the presencca of sources of electric fields, in other words inside ina.tt,er. The matrix element in (70) has been evaluated theoretically for the surface of a jellium metal with the density of A l and compared directly to experiment [101, 1021. Figure 25 shows the comparison of the calculation of the intensity of the Fermi edge emission from an Al( 100) sample i n normal emission as a function of photon energy in the energy range of the surface and bulk plasmons [102]. The bulk plasmon in A1 is at about 15 eV, where there is a minimum in the experimental cross-section. Feibelman’s calculation shown by the solid line is in quantitative a.greement with t.he d a t a if the local field variations are included [loll. The dashed line in this figure is the calculated intensity if only the first term in (70) is included. It is quite obvious that in this photori energy regime the local field variations dominate the cross-section, and analysis of the theory indicates that the p . AA term in (70) is in general the most important. Quite generally the local field corrections i n tlie photoemission matrix element are going to he important whenever there are rapid clia.nges in the dielectric response of the system, either spatially or as a function of frecluency. This is a common occurrence near the threshold for core level excitation and is refrrretl to a.s resonant photoemission. In contrast, the frequency-dependence of the surface dielectric rcsponse is much more difficult to measure and

54

Faml Emldon From Al(lO0) 1.0

0.5

0

I0

(1

12

13

14

16

10

17

10

19

Proton Energy (eV)

Figure 25: Measured and calculated photoemission intensity from the Fermi energy of Al( 100) as a function of photon energy [101, 1021. The solid curve contains local field effects while the dashed line has only the macroscopic field included. The theory and experiment are plotted on the same absolute scale. consequently has mostly been in the province of the theorist [99, 1031. It is now understood that the peak in the cross-section of the emission from A1 shown in figure 25 at about 12 eV is associated with a pole in the surface response function [loo], and as such is really a normal mode of the electrons at the surface. Normal modes of the electron gas are truly many-body effects, therefore in all the theoretical investigations of these modes $, is a many-body wave-function, and consequently the perturbing electromagnetic field in the photo-excitation matrix element should be the applied field Ao. It is an interesting lesson in science to see how these two approaches (single particle us many-body) proceded in parallel without recognizing that they were discussing the same physical effect. The most common normal mode of the electrons at the surface is the surface plasmon, but in fact this mode is determined by the bulk properties, since it occurs when e = -1. In 1970 Bennett suggested that there may be additional surface modes (1041, and in 1975 Eguiluz et al [lo51 described the nature of these modes. They are higher order oscillations of the electron gas, referred to as “multipole modes”, in contrast to the usual surface plasmon which is a monopole mode. Considerablc theoretical interest developed concerning the nature of these modes [106, 107, lOS, 109, 110, 1111, but as there was no evidence that these modes had ever been observed experimentally the field remained a bastion for theorists. The suggestion by Schwartz and Schaich [log] and Kempa and Gerhardts [110] that the multipole mode might be the origin of the enhanced photoyield shown in figure 25 went almost unnoticed. In 1990 measurements of the inelastic loss spectra as a function of momentum transfer from surfaces of the alkali metals revealed the presence of two distinguishable normal modes, the surface plasmon and one multipole mode [112]. Theoretical analysis of the surface response function for jellium showed conclusively that the multipole mode was in fact the origin of the enhancement in the photoyield [loo]. Once it was recognized that there was a new mode at the surface, its presence was identified in the spectra obtained from various surface spectroscopic techniques. Figure 26 compares the spectra from K (curve a ) and Al (curve b) obtained from inelastic electron scattering (ELS), photoemission or photoyield (PY) and inverse photoemission (IPS). The solid line in the top panel is the ELS data for K [loo], where three peaks can be seen: the surface plasmon, the multipole mode and the bulk plasmon. The data points are from photoyield measurements made in 1974. These PY data show only the multipole mode, because light cannot couple to either the surface plasmon or the bulk

55

~~~

~

0.6

0.7

0.8

0.9

o/op

1.0

1.1

1.2

Figure 26: Comparison of the electron loss data (ELS) [loo] with the photoyield (PY) [101, 113) and inverse photoemission (IPS) [114] data for ( a ) I< and ( h ) Al. The observed modes are the surface plasmon (SP), the multipolc mode (Mhl) and the I,ulk plasmon (BP).

56

plasmon unless the surface is rough [113]. The bottom panel shows the data for Al, where in the ELS spectrum the niultipole mode cannot be resolved due to the intensity and width of the surface and bulk plasmon. The photoyield data is reproduced from figure 25, and shows only the multipole mode for a flat surface. The inverse phot,oernission data [I141 should only show the multipole mode if the surface was smooth. Local fields a.t. the surface a.re an import.ant, past, of t,he complet,e picture of aagle-resolved photoemission and appear as coninion features in a variety of surface spectroscopies. More attention needs to be paid to the emission angular dependence at photon energies where the cross-section is dominated by local field efFect,s.

57

References 111 C.O. Almbhdh and L. Hedin, Handbook on Syn~hrot~ron Radiation vol. 1, ed. E.E. Koch

(North Holland), 607 (1983) [2] I. Adawa, Phys. Rev. 134, A788 (1964) [3] G.D. Mahan, Phys. Rev. B2, 4334 (1970) [4] A. Liebsch, Phys. Rev. B13, 544 (1976)

[5] E.N. Economou, Green’s Functions in Quantum Physics (Springer), (1979)

[6] W.E. Spicer, Phys. Rev. 112, 114 (1958) [7] P.J. Feibelman and D.E. Eastnian, Phys. Rev. B10, 4932 (1974) [8] F.J. Himpsel, Adv. Physics 32, 1 (19S3) [9] E.W. Plumrner, Physica Scripta T17, 1% (1987) [lo] E.W. Plummer and W. Eberhardt. Adv. Chem Phys. 49, 533 (1982)

[ l l ] J.E. Inglesfield, Rep. Prog. Physics 45, 223 (19S2) 1121 J.F.L. Hopkinson, J.B. Pendry and D.J. Titterington, Comp. Phys. Commun. 19, 69 (1980) [13] U. Konig, P. Weinberger, J. Rediriger, €1. Erschbauiner and A.J. Freeman, Phys. Rev. B39, 7492 (1989) [14]

H.A. Padmore, C. Norris, C.C. Smith, C.G. Larsson and D. Norman, J.Phys. C: Solid State Phys. 15, L155 (1982)

[15] L. Hedin, Phys. Rev. 139, A796 (1965) [16] L. Hedin and S. Lundqvist, Solid State Physics vol. 23, eds. F. Seitz, D. Turnbull and II. Ehrenreich (Academic), 1 (1969) [17] J.E. Inglesfield, Physica Scripta T17, 89 (1987) [IS] W. Bardyszewski and L. Hcdin, Pliysica Scripta 32, 439 (1985) [I91 R.1. Lundqvist, Phys. Status Solitli 32, 273 (1969) 1201 D.P. Woodruff, The chemical physics of solid surfaces and heterogeneous catalysis vol. 1, eds. D.A. King and D.P. Woodruff (Elsevier), 81 (1981) [21] C.J. Powell, J. Elect. Spectroscopy 47, 197 (1988)

[22] D.R. Penn, Phys. Rev. B35, 4S2 (1987) [23] S. Tanuma, C.J. Powell and D.R. Pelin, J . Elect. Spectroscopy 52, 285 (1990) [24] J.C. Inkson, Surface Sci. 28, 69 (1971) 1251 P.O. Nilsson and C.G. Larsson, Phys. Rev. B27, 6143 (1983)

58

[26] S.A. Lindgren, L. Walldh, .J. Rundgren and P. Westrin, Phys. Rev. Letters 50, 368 (1983) [27] B. Blum, H. Davis and E.W. Plurnmer, to be published [2S] W. Speier, R. Zeller and J.C. Fuggle, Phys. Rev. B32, 3597 (1985) [29] J.E. Northrup, M.S. Hyhertsen and S.G. Louie, Phys. R.ev. Letters 59, 819 (1987) [30] G.D. Mahan and B.E. Sernelius, Phys. Rev. Letters 62, 2718 (1989) [31] R.W. Godby, M. Schluter and L.J. Sham, Phys. Rev. B 36, 6497 (1987) [32] B.I. Lundqvist, Phys. Kondens. Ma.ter. 6 , 193 (1967) [33] D.C. Langreth, Phys. Rev. B1, 471 (1970) [34] C.H. Tung and R.H. Ritchie. Phys. Rev. B16, 4302 (1977) [35] P.W. Anderson, Phys. Rev. Letters 18, 1049 (1967) (361 P. Nozikres a.nd C.T. de Dominicis, Phys. Rev. 178, 1097 (1969) [37] S. Doniach and M. SunjiC, J. Phys. C: Solid S h t e Phys. 3,285 (1970) 1381 P.H. Citrin, G . K . Wertheim and Y. Baer, Pliys. Rev. B16, 4256 (1977)

[39] A.R. Williams and U. von Ba.rth, in Thcory of the Inhomogeneous Electron Gas, eds. S. Lundqvist and N.H. Ma.rch (Plenum) [ 1983). [40] W. Kohn and L.J. Sham, Phys. Rev. 140,A1133 (1965) [41] S.D. Kevan, N.G. Stoffel and N.V. Smith, Phys. Rev. B31, 1788 (1985) 1421 R.A. Bartynski, E. Jensen, T . Gustafsson and E.W. Plummer, Phys. Rev. B32, 1921 (1985)

[43] J.E. Inglesfield and G.A. Benesh, Surface Sci. 200, 135 (1988) [44] H.J. Levinson, F. Greuter and E.W. Plummer, Phys. Rev. B27, 727 (1983) [45] J.A. Knapp, F.J. Hirnpsel and D.E. East,nian, Phys. Rev. B19, 4952 (1979) [46] T.C. Chiang, J.A. Knapp, hl. Aono a n d D.E. Eastman, Phys. Rev. B21, 3513 (1980) [47] H. Winter, P.J. Durham and G.M. Stocks, J . Phys. F: Metal Phys. 14, 1047 (1984) [48] H. Winter, P.J. Durham, W.M. Ternmerman a n d G.M. Stocks, Phys. Rev. B33, 2370 (1986) [49] E.W. Plummer, T. Gustafsson, D.R. Hanianii, I. Linda,u, D.L. Mills, C. Quate and Y.R. Shen, Advancing Materials Research, ed. P.A. Psaras and H.D. Langford (National Academy Press), 283 [ 1987) 1501 M.Y. Chou, P.K. Lam and M.L. Cohen, Phys. Rev. B28, 4179 (1983) [51] The anomalous properties of Be2 are discussed by R.O. Jones and 0. Gunnarsson, Rev. Mod. Phys. 61,689 (1989), and the binding energy 1ia.s been measured by V.E. Bondybey and J.H. English, J. Chem. Phys. 80, 568 (1984)

59

[52] E. Jensen, R.A. Bartynski, T. Gustafsson, E.W. Plummer, M.Y. Chou, M.L. Cohen and G.B. Hoflund, Phys. Rev. €330, 5.500 (19S4)

[53] U.O. Karlsson, S.A. Flodstroiii, R. Engelhardt, W. Gadeke and E.E. Koch, Solid State Commun. 49, 711 (1984) [54] E. Jensen, R.A. Bartynski, T. Gustafsson and E.W. Plummer, Phys. Rev. Letters 52, 2172 (1984)

[55] E. Jensen and E.W. Plunimer, Pliys. Wcv. Letters 55, 1912 (1985) (561 In-Whan Lyo and E.W. Plummer, Phys. Rev. Letters 60, 1558 (1988)

[57] T.L. Loucks and P.H. Cutler, Phys. Rev. 133, A819 (1964) [58] E.V. Chulkov, V.M. Silkin and E.N. Shirykalov, Surface Sci. 188, 287 (1987) [59] R. Yu and P.K. Lam, private communication

[60] M. Seel, Phys. Rev. B28, 778 (1983) 1611 P.O. Gartland and B.J. Slagsvold, Solid State Commun. 25, 489 (1978) [62] G.V. Hansson and S.A. Flodst,rom, Phys. Rev. B18, 1562 (1978) [63] L. Hedin and B. Lundqvist, J. Phys. C: Solid State Phys. 4, 2064 (1971) [64] R.A. Bartynski, R.H. Gaylord, T. Gustafssoii and E.W. Plummer, Phys. Rev. B33, 3644 (1986) [65] J.B. Pendry, Low Energy Electron Diffract.ion (Academic Press) (1974) [SS] D.W. Jepsen, F.J. Himpsel a n d D.E. Eastman, Phys. Rev. B26, 4039 (1982) 1671 W. Wohlecke, A. Baalmann and M. Ncuniann, Solid State Commun. 49, 217 (1984) [68] B.S. Itchkawitz, In-Whan Lyo and E.W. Plummer, Phys. Rev. B41, SO75 (1990) [69] S.-C. Lui, J.W. Davenport, E.W. Pltimnier, D.M. Zehner and G.W. Fernando, Phys. Rev. B42, 1582 (1990) [70] F.J. Himpsel, D.E. Eastman and E.E. Koch, Phys. Rev. B24, 1687 (1981) [71] G. Watson, B. Lee and E.W. Plutnmer, to be published [72] W.Y. Chin and J. Callaway, Phys. Rev. B11, 1324 (1975) [73] J.W. Davenport, Bulletin APS 33, 518 (19SS) [74] K.W.K. Shung, B.E. Sernelius and G.D. Mahan, Phys. Rev. B36,4499 (1987)

[75] A.W. Overhauser, Phys. Rev. Lett.ers 55, 1916 (1985) [76] I

(5)

where the y's are the field operators in second quantization notation, )O>is the ground-state wavefunction, and T is the time order operator. An especially useful quantity is the diagonal elements of G in orbital basis representation

where the c t and c are creation and annihilation operators for the single particle states. Physically the single-particle Green's function gives the amplitude of finding a particle in state p at time t = z if one is created into that state at time t = 0. For a noninteracting electron system, this definition leads to a single particle Green function Go given by (for simplicity of notations, we set fi = 1 and the crystal volume v = 1)

where f is the usual Fermi factor. The time Fourier transform of Eq. (7) gives

where 6 is a positive infinitesimaland qp is O+ if the state p is above the Fermi energy Ef and 0- if below. Or equivalently, expressed in a spectral weight function A(p,o),

with A(p,w) for the noninteracting system given by a delta function

69

The contour C runs infinitesimally above the real axis for w < p and below the real axis for w > p where p is the chemical potential. Since in general the spectral function is just proportional to the imaginary part of the Green's function: 1 A(r,r',w) = - Ilm G(r,r',w)l . x

(1 1)

Equation (10) tells us that the single particle Green's function of a noninteract, energy required to add a paring system is characterized by a pole at E ~ the ticle in state p to the system. Thus one expects that in general, if the diagonal matrix element of A with respect to a one-particle state is sharply peaked as a function of energy for an interacting many electron system, then it is meaningful and useful to speak of a particle-like excitation (see Fig. 1). This corresponds to a pole in the Green's function at a complex energy, and a A(p,o) of the form

A(P,m) =

i 27F ZP

- [Ep - PI

k&

Fig. 1. Qualitative picture of spectral function A(k,E).

The physical content of this picture can be clearly seen by substituting Eq. (12) back to Eq. (9) and obtain for positive z

where rpis the imaginary part of Ep. G, in this particular single-particle orbital basis, describes a propagation amplitude which is oscillatory with characteristic energy given by Re(Ep). This leads to the usual interpretation that the peak position in A is the quzlsiparticle energy (real part of EP) and the width relates to the lifetime of the quasiparticle (imaginary part of Ep). For an interacting many-particle system, finding the quasiparticle properties is then equivalent to solving for the appropriate single-particle orbitals which give rise.to sharp peaks in the diagonal matrix element of A and solving for the position of these peaks in the complex energy plane.

3.

GREEN’S FUNCTION THEORY OF QUASIPARTICLE ENERGIES In this section, we briefly discuss a formulation for solving the singleparticle Green’s function and hence the energies and wavefunctions of quasiparticles in real solids. For simplicity of notation, we suppress the spin indices associated with the electron. 3.1.

Jhe Self FnerFor a many-electron Hamiltonian

H=

2

where h(ri) = pi /2m + Vion(ri) and V,(rij) = e2/lri - r,], the single-particle Green’s function can be shown, via the equation of motion of G, to satisfy

where VH is the usual Hart‘ree potential and Z is called the electron self energy operator which is a functional of G. Equation (15) can be solved formally in the so-called quasiparticle approxirnation by expressing

71

where Erik and Wnk are eigenvalues and eigenfunctions to the homogeneous equation

We may now identify the pole structure of G(r,r',a) with the solution to this equation. Given the self energy operator Z, the problem of solving for the quasiparticle properties is then one of solving Eq. (17), the quasiparticle equation. This equation is similar in form as the Schrodinger equation in one-electron theories. However, owing to electron-electron correlation effects, Z(r,r',m) is now a nonlocal, nonHermitian and energy dependent operator giving rise to a complex Erik. This comes about because the exchange interaction is nonlocal and electron screening is intrinsically energy dependent in a solid. And, as discussed above, the real part of Erik gives the quasiparticle energy and the imaginary part gives the lifetime. The quasiparticle energy is often written 0 as a sum of a single-particle term, En, plus a self-energy znk due to exchange-correlation effects.

This description of excited states of the interacting electron system in terms of quasiparticles depends on the lifetime of the quasiparticle being sufficiently long on the time scale of the relevant experimental probes. For energies near the Fermi level of a metal or the gap region of a semiconductor, the quasiparticles are well defined allowing us to pursue this description. Near the bottom of the occupied bands, for example, lifetime effects are certainly appreciable. Here, in discussion of interpretation of structures in the photoemission spectra, we are primarily concerned with the real part of the selfenergy operator, i.e. the energy of the quasiparlicle.

72

To solve the quasiparticle equation, a useful formulation is to express the self-energy operator in terms of the dynamically screened interaction W: W( r,r’;co) =

E-l(r’,r’’;co)VC( r”,r’)dr’‘

(19)

where E(r,r’,co) is the time-ordered dielectric response function of the system. The dielectric function is related to the irreducible polarization propagator P by E(r,r’;co) = S(r - r’)

-

P(r,r”,o)Vc( r” - r’)dr”

.

(20)

In this formalism, C can be obtained formally by a set of coupled functional derivative equations which are2

j

C(1,2) = i W(1+3)G(1,4)r(423)d(34)

(21a)

P(1,2) = 4

(21c)

G(1,3)G(4,1+)r(342)d(34)

where r as defined is often referred to as the vertex function. The index 1 is a shorthand notation representing the coordinates (r1,tl) and spin. 1+ denotes (rl ,tl + 6) with S a positive infinitesimal. The set of coupled equations given above may be used to generate a series expansion for C in terms of powers of G and W. For example, a starting iterative solution to Eq. (21) is obtained by setting Z = 0 in Eq. (21d) which gives the simple expression

13

and a first order expression for Z as ~ ( 1 , 2= ) i G(1,2)W(1+,2) .

(23)

Successive iteration of Eqs. (21a-d) would lead to correction terms with increasing higher power of W to Eq. (23). This is schematically illustrated in Fig. 2. For a system with large polarizabilify, this series expansion is advantageous over the conventional one in terms of the bare Coulomb interaction and the noninteracting Green's function. W, being the dynamically screened interaction, is much weaker and thus should lead to a significantly more rapid convergence in the expansion for Z. Mathematically, since W and the dressed Green function can be expressed as series expansions in the bare quantities, each term in Fig. 2 is a partial summation over terms in a conventional expansion.

z= 2

+ 2

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

......

__ . ...

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

1 + 2 3.

1 + 2

._,.., . ..:.

.

.. 1

..........:-... ........

1 + 2

1

Fig. 2. Diagrammatic expansion of Z in the screened Coulomb interaction

.

.

The GW ADDrOXlmatlon In practical calculations for real materials, the electron self-energy operator has only evaluated to first order in the dynamically screened Coulomb interaction W and the dressed Green function G. This approach is called the GW approximation since C is given by Eq. (23). Or, more explicitly, the selfenergy operator is given by (after Fourier transformation to energy space)

3.2.

74

E(r,r';E) = i

I dw -e-iSw G(r,r';E - w)W(r,r';w) 2x

(24)

where 6 = O+. In this approximation the calculation of the quasiparticle properties reduces to computing Z using Eq. (24) and then solving Eq. (17). As seen from the structure of Eqs. (16), (17), and (24), the quasiparticle energies together with Z and G must be obtained in a self-consistent fashion. Hence, even in this first-order theory, first-principles calculation of the electron excitation properties is a major computational task. The two essential ingredients in the theory are the dynamical dielectric response function and the dressed electron Green's function. Both have to be treated adequately to obtain quantitative results that may be compared with experiment. Note that if W is replaced by the bare Coulomb interaction in Eq. (24), then C becomes the usual exchange operator. The quasiparticle equation, Eq. (17), reduces to the single-particle equation in Hartree-Fock theory. Thus, in this way, one can think of the Hartree-Fock energies as an approximation to the quasiparticle energies. The dielectric function contains the dynamical screening response of the electrons which gives rise to correlation effects going beyond bare exchange. Although, as in any perturbation series, an a priori determination of convergence is difficult, the GW approximation has yielded very good results in comparison with experiment for a wide range of materials. Because of computational difficulties, there have been only limited ~tudies2~12-15 of the effect of higher order terms or vertex corrections on the quasiparticle energies and they were on the uniform electron gas. Even for this simple model case, estimates of the effect of vertex corrections vary considerably. CALCULATION OF THE ELECTRON SELF-ENERGY There is a long history of previous work dating back to the early 1960's on trying to calculate the electron self energy in solids along the approach discussed above.16 The band gap problem of the semiconductors gave impetus to the development of several recent theories. Wang and Pickett7 applied the local density functional approach for the self-energy operator to semiconductors. Horsch, Horsch, and Fulde8 used a linked cluster expansion variational approach to include the effect of electron correlations. Strinati, 4.

75

Mattausch, and Hankeg formulated a tight-binding approach to evaluate Z in the GW approximation. In application, each of these approaches has required empirical input at some stage. First-principlescalculations for real material~5~10~11 are now possible. The work of Hybertsen and Louiesllo and subsequently those of Godby, Schluter, and Sham1 calculated the electron self-energy operator without using empirical input. In particular, the approach developed in Ref. 10 has been applied to compute the quasiparticle properties of a variety of solid-state systems including semiconductors and simple metals as well as surfaces, interfaces, superlattices, and small metal clusters. We describe briefly here the approach and discuss some of the results in the subsequent sections. To calculate the self-energy operator in the GW approximation, the crystalline Green's function and the dynamically screened Coulomb interaction are required input. Both qualities are crucial in determining the final self energy and have to be adequately calculated with all the important physical processes included for the material under consideration. Jhe C r v W e Green's Function In the approach of Ref. 10, a quasiparticle approximation is employed for the Green's function resulting in an expression for G [Eq. (16)] which is similar to the independent particle case. This approximation assumes that all the weight in the spectral function is in a narrow quasiparticle peak which is then approximated by a delta function. The Green's function is constructed initially using the LDA wavefunctions and eigenvalues. For the examples described below, they are obtained with the ab idio pseudopotential method. In principle, the self-consistent Green's function should be obtained by iteration using the successively calculated quasiparticle wavefunctions and energies. It turns out, however, that the LDA eigenvectors are extremely good approximations to the quasiparticle wavefunctions,'O with overlap between the two which is often better than 99.9%. The Green function in practice is then subsequently updated only with the quasiparticle spectrum from Eq. (1 7). There is only very limited experience on the importance of including the detailed structure in the spectral function for the quasiparticle energies.* Comparison of calculated energies with experiment show that Eq. (16) is an 4.1.

76

excellent approximation for semiconductors and insulators and for the s-p metals. However, as in the case of vertex corrections, only a posteriori experience truly justifies the approximation. And, the validity of Eq. (16) and Eq. (24) remains to be assessed for systems with highly correlated electrons. 4.2.

Jhe Screened d -C Io w i e l d Fffea Evaluation of the screened Coulomb interaction requires the full dielectric response function (both the spatial and time dependences) of the system. Because of charge density inhomogeneity, the dielectric response function E(r,r';w) of a solid is a function of r and r' separately. This functional dependence reflects the fact that the response in a solid can be significantly different depending on the location of the perturbation. In Fourier space, for a crystal, the dielectric function is a matrix in the reciprocal lattice vectors G . The off-diagonal elements of EGG(q,w) give the so-called local field effects in screening which describe the variation in the electron polarizability at different positions in the unit cell. For semiconductors and insulators, it is shown10 that the offdiagonal elements must be included in the evaluation of Z,i.e. local field effects are essential in determining the quasiparticle energies. The frequency dependence of E (or the dynarnical screening effects) are also found to be significant for obtaining quantitatively correct results. The dielectric matrix is calculated in two stages in the Hybertsen-Louie approach. The static dielectric matrix . Making the standard assumption that the energy dependence of the matrix element &k(E) = cnklZ(E)lnk> is linear for E near Erik and that Erik = Erik, the first-order solution is given by 4.3.

Here pf;ck is the matrix element of the LDA exchange-correlation potential and

is the dynamical renormalization constant which may be shown to be the same as the 2 in Eq. (1 2). BULK MATERIALS The quasiparticle approach has been applied to study the excitation spectra of a range of bulk materials. We give several illustrative examples

5.

78

here. 5.1.

Semiconductors and- 1

A first application and major success of the first-principles self-energy approach described in the last section is the quantitative resolution of the band gap problem in semiconductors and insulators. The calculated minimum gaps1* for several selected materials are compared with experimental values19~20in Table 1. Although, in principle, energy gaps deduced from direct and inverse photoemission experiments ought to be different from those measured in optical experiments because of electron-hole interactions. For semiconductors, the differences are usually minor. As seen in Table 1, the calculated quasiparticle gaps are in dramatic better agreement with experimental values than the LDA and HF results. Germanium is no longer predicted as a metal. In general, agreement with experimental values for the gap of semiconductors is at the level of 0.1 eV. We note that the quasiparticle gaps were calculated using input consisting of only the atomic numbers of the constituent elements and the crystal structure. It is found that both local field effects and dynamical screening in the dielectric response are crucial in obtaining quantitatively accurate band gaps for semiconductors. This is because calculation of the gap requires the difference in self energies between the occupied valence band maximum state and the empty conduction band minimum state. These states in general have wavefunctions residing in different regions of the crystalline unit cell (bonding vs. antibonding sites) where the dielectric response can be significantly different owing to local field effects. The frequency-dependence of screening leads to a dynamical renormalization factor Z (Eq. 26) of typically 0.8-0.85 for semiconductors.10 This degree of renormalization is modest, implying that quasiparticles are well-defined in semiconductors. However, this frequency dependence in the self energy of the electrons, which reflects the mixing of the electron degrees of freedom with the elementary excitations (plasmons), is non-negligible in determining quantitatively the quasiparticle energies. In Fig. 3, the calculated quasiparticle band structure for Ge is shown and compared to the energies deduced from angle resolved photoemission21 and inverse photoemi~sion22~23 experiments. The overall agreement between theory and the experimental results of Wachs et d.for the occupied

79

10

1

8

6

4

2

z o v

F

-2

Q)

C

w -4 -6 -8

o Experiment

o I+H

-10

Typical error

-12 -14

L

A

r

A

X

Wave vector i; Fig. 3. Calculated quasiparticle energies of Ge versus direct (0,Ref. 21) and inverse (0,Refs. 22 and 23) photoemission data. states are excellent. Along the A direction the dispersion agrees well with theory for all the bands. The binding energy near the X point seems to be larger in experiment than in theory. The discrepancies are, however, well within the experimental error estimates shown in Fig. 3. Although angle-

80

resolved inverse photoemission studies are less common and typically have poorer energy and angular resolution, the calculated conduction band energies of Ge have been quantitatively verified by the data of Refs. 22 and 23. A similar level of agreement with photoemission experiment has been observed for other insulating materials including a wide rage of gap size (metallicity) as well as ionicity. In Table 2, the calculated bandwidths of the three homopolar materials are compared to photoemission results. The agreement in general is good, but the theory seems to give systematically slightly too small a bandwidth. Some results together with experimental data20t24-26for the ionic insulator LiCl are given in Table 3. A more detailed comparison for the conduction band states at the L point in the Brillouin zone with inverse photoemission data is given in Table 4 for Si and Ge.22 The agreement is again very good, within 0.1 -0.2 eV. Since, as discussed above, photoemission experiments measure the quasiparticle energies whereas optical transitions contain possibly additional electron-hole interactions, comparison of these results to optical data has been made in an effort to extract the influence of excitonic effects.22 Optical TABLE 2. Comparison of calculated bandwidth with photoemission data for the homopolar materials. (Energy in eV.)

diamond Si Ge a Ref. 19

Quasiparticle

Expt.

23.0 12.0 12.8

24.2 f 1a 12.5 0.6a 12.9 f 0.2b

*

b Ref. 21

measurement of the second indirect edge in Si places the Llc state 2.1 eV above the valence band edge.27 This is nominally 0.3 eV different from the inverse photoemission result in Table 4. However, since the experimental error bar is large and the quasiparticle theory result falls almost exactly halfway between the two experimental results, the significance of excitonic effects for this case remains an open question.

81

TABLE 3. Quasiparticle results (in eV) for Lice are compared with experiment for gap E,, Ce 3p bandwidth W3p, and the separation between the Ce 3s and 3p bands E3,, - E3s. J

ice

Theorv

Fxot. 9.4a 4.0 f 0.2b 11.6 & 0.5C 11 .O k 0.6d

9.1

3.8

a Ref. 20

b Ref. 24

CRef. 25

dRef. 26

TABLE 4. Comparison of the calculated conduction band critical point energies at L relative to the valence band edge to the results of angle resolved inverse photoemission experiments for Si and Ge.. ~

Si

r25’v+ Llc r25’v+bc

Theory

Expt.a

2.27

2.4 f 0.15 4.15 k 0.1

4.25

Ge r 8 v --f kic r 8 v + hc r8v +4 . 5 ~ r 8 v + hc

0.75 4.3 4.43 7.61

0.8 4.2 f 0.1 7.8 f 0.1

Comparison of calculated quasiparticle energies with other optical data shows that excitonic effects do not appear significant in bulk semiconductors. The experimental optical transition energies19.28-31 are given in Table 5 together with the calculated transition energies for the crystals diamond, Si, and Ge. The experimental values are from high precision electroreflectance and wavelength modulation spectroscopy measurements. It should be pointed

82

TABLE 5. Comparison between theory and experiment for optical transitions in Ge, Si, and diamond. (Energies in eV.) LDA

Quasiparticle Theory

Expt.

0.30 -0.07 2.34 2.56 3.76

0.30 0.71 3.04 3.26 4.45

0.297a 0.887a 3.006a 3.206a 4.501a

2.57 3.26 2.72 4.58

3.35 4.08 3.54 5.51

3.4b

Ge r7v

+r 8 v

rev +r7c r 8 v + rG, r8v r& x5v xx --j

--j

Si

r2sv+ rlw

r 2 v V -+ rZc

k’v-+ L l C

L3’v -+ L3c

4.2C 3.45b 5.50b

Diamond r25’v-+r15c r25v rTc x4v + X l C

+

a Ref. 28

5.5 13.1 10.8

bRef. 29

7.3d 15.3k5e 12.5C

7.5 14.8 12.9 CRef. 19

dRef. 30

Wef. 31

out that in addition to neglecting electron-hole interactions, the calculated energies correspond to transitions at symmetry points in the quasiparticle band structure. The actual critical points in the experimental optical spectra from which the transition energies are identified may be away from these symmetry points. This introduces an intrinsic but small uncertainty in the comparison of experiment to theory. As seen from the Table, the theoretical results are typically within 0.1-0.2 eV of the experimental values for all transitions except for the very high energy ones in diamond, where the experimental uncertainties are rather large. The accuracy of the present results is a major improvement over previous ab inifio band calculations. It is comparable to what is obtainable from empirical schemes such as the Empirical Pseudopoential Method6 in which the photoemission and optical data are fit to several adjustable parameters.

83

'

-3 -30

3

'

-1 -15

-1

'

-15

I -20

-10

0

10

20

-I0

-5

0

5

Ib

-10

-5

0

5

10

I

-3 -15 -10

-5

0

5

10

15

20

(ev)

Fig. 4. Differencebetween calculated quasiparticle energies and LDA eigenvalues.

Figure 4 displays the difference between the quasiparticle energies and the LDA eigenvalues as a function of the quasiparticle energies for four

a4

insulating materials. Several striking trends may be observed. The manybody corrections to the LDA values, defined by bnk = Erik - &nk, are dominated by a jump at the band gap. This may be understood in terms of a change of the wavefunction character from bonding to antibonding as the gap is crossed. The self energy operator Z is nonlocal with a range which extends over about a bond length.1oll1 It is therefore considerably more sensitive to a change of the nodal structure in the wavefunction than any local potential such as that used in the LDA. In addition to the jump, there is a rather smooth energy dependent part to the correction which is quite large for some of the large gap materials. Also the magnitude of the corrections associated with the valence band states relative to those of the conduction band states are materials dependent. This has important implications on the theory of Schottky barriers and band offsets at semiconductor interfaces since the relative position of the band states are required in determining these junction properties. Also, as we see below, the many-body corrections to LDA surface state energies are not necessarily the same as for the bulk states. Thus, the corrections are not just a simple shift of the LDAconduction bands relative to the valence bands. There appears no simple empirical rules which would allow a determination of the quasiparticle energies quantitatively, especially for surface and defect states, without performing a detailed microscopic calculation.

&mle

MetaIS Comparison of standard band structure energies with photoemission and other spectroscopic data also shows sizable discrepancies for metals4 These again may be attributed to exchange-correlationeffects. Thus far, most of the quasiparticle calculations on metals however have been carried out either for the jellium model or for the simple s-p metals.’6.32-38 A few exceptions are some work on the d-band metals using a simplified version of the GW approximation.39 A case of particular interest is the bandwidth of the alkali metals. Although these are conceptually the simplest of the metals, the measured bandwidth from recent angle-resolved photoemission experiments4140 showed a substantial disagreement of nearly 30% with the corresponding free electron values or results from band calculations using LDA methods. 5.2.

85

1 .o

0.0

-1.0

8

w

-2.0

-3.0 0.00

0.50

1.00

Fig. 5. Comparison of calculated quasiparticle energies (filled circles) with LDA eigenvalues (dashed line) and experimental data from Ref. 4 (crosses) for Na. The experimental data for Na is given in Fig. 5 together with the calculated quasiparticle band structure.36 The surprisingly large observed bandwidth reduction in this case is explained by the self-energy effects. The occupied bandwidth is reduced from the LDA value of 3.16 eV to a value of 2.52 eV when self-energy corrections are included. This value is in excellent agreement with the photoemission values of 2.5 f 0.1 eV (Ref. 4) and 2.65 f 0.05 eV (Ref. 40). However, the origin of the dispersionless feature just below the

86

Fermi energy is still a subject of debate. The calculated quasiparticle energies for Na are also consistent with recent X-ray absorption edge measurements,41 which are sensitive to the position of the empty density of states features deriving from the gap at the Brillouin zone face. The experimental results indicated a 16% contraction in the width of the unoccupied part of the spectrum just above EF. The calculation36 predicted an 18% reduction. Similar narrowing of the occupied states has been calculated for other simple metals37.38 with good agreement with experiment. It is found that the inclusion of exchange-correlation effects in the dielectric screening going beyond RPA is important for the self energy of the alkali metals. But, on the other hand, local field effects do not play a significant role. In general, for a metal, a reduction in bandwidth from the free electron value is expected if the density is such that the electron density parameter r, is greater than one.38 TABLE 6. Quasiparticle energies in eV calculated for Al, relative to EF, compared to experimental angle-resolved photoemission results of Levinson et a/.(Ref. 42).

Theory

Experiment

- 1.51 - 2.89

- 1.15

- 1.00

- 2.39

- 0.95 - 2.4

- 0.87

- 0.90

0.25 0.90 - 4.39 -1 0.01

- 4.55 - 10.6

- 2.83

In Table 6 the calculated quasiparticle energies for Al are compared with experimental values determined from angle resolved photoemission by Levinson et al.42 Overall, the agreement between theory and experiment is

87

again very good. There is however one discrepancy. The calculation gives a value for the X1 state at -1.51 eV below the Fermi level, but the experimental spectra place it at -1.15 eV. On the other hand, the X4, Z1,Z3, and W3 states are all found to be within 0.1 eV of the experimentally determined energies. This difference in the placement of the X1 level results in a calculated gap at X of only 1.38 eV whereas the experimental value is 1.68 eV. The origin of this difference between theory and experiment remains unclear at this time. The quasiparticle bandwidth for Al is 10.01 eV. It is about 6% smaller than experiment. Some of the discrepancy for the bandwidth (also observed in the case of semiconductors) may result from the plasmon pole approximation which tends to overestimate the bandwidth narrowing for systems with rs = 2.

There have been several alternative theorie~32.33~35 proposed for the observed band narrowing in the alkali metals. The work of Ref. 32 and Ref. 33 are both done in the context of the jellium model and include coupling to spin fluctuations in addition to density fluctuations in the electron self-energy, but using rather different models. Results in Ref. 33 gave bandwidths which are too small by approximately 10-20°/0. On the other hand, Ref. 32 obtained bandwidths which are systematically too large. Shung et a1.,35 on the other hand, attribute part of the narrowing of the Na bandwidth to the photoemission process. They found that the measured valence-band width should depend on the range of photon energies. However, no such dependence is seen in A more accurate determination of the effect of the surthe e~periments.4~40 face on the measured photoemission spectrum of Na (including the unexplained flat feature near EF) would require a calculation of the self-consistent surface potential, including atomic relaxation and full response function. SURFACES AND CLUSTERS The self-energy approach has been extended and applied to the excited-state properties of semiconductor surfaces,43-46 heterojunctions,47 superlattices,48 and small metal clusters.49 We briefly discuss here some examples of surface and cluster calculations and the corresponding comparisons with experiment. Since the electronic and geometric structures of these systems are much less intuitive and more difficult to determine unambigu-

6.

88

ously from experiments, the predictive aspect of the self-energy approach here makes it especially valuable in these studies. As a simple illustration of many-body effects on the quasiparticle surface-state energies, we consider the case of the As capped Si(ll1) and Ge(ll1) surfaces. At saturation coverage, these surfaces have a very simple geometry which is a 1x1 structure with the As atoms replacing the outermost layer host atoms.50 The surface is chemically inert and highly stable against reconstruction. There have been very extensive photoemission studies on their surface-state spectra,50 making these surfaces an ideal case for a manybody calculation. Moreover, these are systems of considerable intrinsic importance because of the interest in growth of GaAs on covalent semiconductors. As for bulk materials, the calculations43 involve, first, a determination of the surface geometric structure by total energy minimization and then evaluation of the quasiparticle energies for both the bulk and surface states. A 12layer slab in a repeated supercell geometry was used to simulated the properties of the surface. Figure 6 depicts the calculated quasiparticle energies for the As-capped Si(ll1) with the shaded areas corresponding to the projected bulk quasiparticle band states. The quasiparticle surface-state bands are given together with the LDA surface-state bands for comparison. Very similar results have been obtained for the As/Ge(lll) surface. In Fig. 6, the occupied surface-state band corresponds to the lone-pair states on the chemisorbed As atoms. The calculaton also predicted an empty surface-state band which corresponds to localized states splitting off from the conduction band continuum of Si. The effects of going beyond LDA for the surface state energies can be clearly seen. As compared to the LDA results, the occupied surface-state band has a slightly lower energy and broader dispersion. Both features turn out to be necessary for better agreement with photoemission experiment. The effects of quasiparticle corrections to the energies of the empty surface states are much more dramatic. These states are substantially shifted upward in energy, opening up the energy gap between the occupied and empty surface states by nearly an extra 1 eV at some k-points. Figure 7 compares the calculated lone-pair surface-state energies with results from angle-resolved photoemission experiments50 for As/Si(l 11) and As/Ge(ll 1). For both surfaces, the agreement is excellent in both the place-

89

4

3

-2 2 - 1 h

Y 5a , o -1 -2 -3 M

-

K

Fig. 6. For the As capped Si(111) surface, the calculated quasiparticle surface bands are plotted against the bulk projected bands in the surface Brillouin zone. The LDA surface band energies are also shown (dashed li nes). ment and the dispersion of the surface bands and is well within the estimated uncertainties of +_ 0.1 eV with experiment and theory. Since there is no adjustable parameters in the theory, this lends strong support that the calculated electronic and geometric structures are correct. The empty surface states should be accessible to experimental observation using techniques such as inverse photoemission, surface optical transitions or scanning tunneling spectroscopy. Recent scanning tunneling44 and inverse photoemission experiments51 have indeed given quantitative confirmation to the theoretical predicitons in Fig. 7 for the empty states.

90

0

n

3 -1 a,

W

h M

-3

'

-

M

I

I

-

K

0

-1 A

P a, c

W

-2

-3

M

K

Fig. 7. The calculated occupied surface band is compared to photoemission results (Ref. 50) for As capped G e ( l l 1 ) surface (upper panel) and As capped Si(ll1) surface (lower panel).

91

2.5 2.0

1.5

1.o

s Q)

a

a W

I

0.5 0.0 -0.5 -1 .o

-1.5 -

r

-

J

Fig. 8. Quasiparticle surface-state bands for Si(ll1) 2x1 compared to photoemission (Ref. 53) and inverse photoemission (Ref. 54) experiments. An example of a surface with a more complex structural reconstruction is the Si(ll1) 2x1 surface. This surface has a n-bonded chain reconstruction

92

which extends to 5 layers below the topmost surface layer. Figure 8 compares the calculated quasiparticle surface-state band structure46 with results from photoemission52153and inverse photoemission54 experiments. The plot is for states with k-vector parallel to the K-bonded chain of Si surface atoms. The agreement between theory and experiment is again very good for both the occupied and empty surface states. The calculated surface state band gap of 0.62eV is in agreement with the direcvinverse photoemission gap of 0.75 eV and is substantially larger than the LDA gap of 0.27 eV. However, the optically measured surface-state gap for this surface is found to be only about 0.45 eV at low temperatures.55 This discrepancy between the photoemission results with the optical data may in fact be an indication of the breakdown of the free quasiparticle picture ininterpreting the optical transitions for this case, and other effects such as electron-hole interactions (enhanced by the reduced dimensionality at the surface) need to be included in considering the optical data. Another interesting example of surface calculation is that of the photoemission properties of the clean GaAs(ll0)surface which has a (1x1) relaxed geometry of the buckling type. The geometric structure of this surface is now quite well-determined both theoretically and experimentally. Its excited-state properties are however far from well-determined. In particular, various experiments and theories are giving conflicting results for the position of the empty surface states. Figure 9 depicts the calculated quasiparticle surface-state bands45 for the relaxed GaAs(l10)surface together with four sets of experimental data.56-59 For the occupied surface states, the theory agrees very well with the data from angle-resolved photoemission experiment.56 The controversy is with the empty surface states. The calculation is in good agreement with one set of inverse photoemission data57 (IPE-1) and with results from a laser excited/probe (2-step) photoemission experiment.59 But it is in disagreement with the interpreation of data from a second inverse photoemission measurement (IPE-2).58 First-principles study of the kind we have here is thus useful in helping to unravel the physics of a situation with conflicting experimental results. For the present case of the GaAs(ll0) surface, it seems clear that taking theory and all the experimental results together, a low-lying band of surface states with a band minimum in the bulk gap is favored. The above examples show that quite accurate surface-state energies

93

3.2

2.4

1.6

2

1

z

08

C

w

0

VBM

-0.8

-1.6

-

r

R

M

-

X'

-

r

Fig. 9. Comparison of the GaAs(l10) calculated quasiparticle surface band structure with various experimental data (see text). may be obtained using the self-energy approach. Comparing to the LDA results, the quasiparticle calculations yield the correct surface excitation energies by substantially opening up the gap between empty and occupied surface states. This is quite similar in the behavior of self-energy correction to the bulk-state energies. However, analysis43 of the surface calculations showed that the quasiparticle corrections to the surface states can be quite different from those of the bulk. The differences arise both from change in screening at the surface (hence a change in the self-energy operator) and from change in character of the surface-state wavefunction from those of the bulk states. As a consequence, an accurate determination of the excitation spectra of a surface will generally require a full quasiparticle calculation and

94

- Present

- - - LDA

0

5

15

10

20

NUMBER OF ATOMS P E R CLUSTER

Pre s ent

- - - LDA

2’ 0

5

LO

15

20

NUMBER O F ATOMS P E R CLUSTER

Fig. 10. Absolute values of the highest-occupied quasiparticle energies of alkali-metal clusters and in the LDA with the jellium-sphere-background model. (a) Nan and (b) Kn (n = 2, 8, 18, and 20). Experimental ionization potentials are given by solid circles (Ref. 60). is not expected to be obtainable from a ground-state LDA study and knowledge of the bulk spectra only.

95

The self-energy approach has also been applied to clusters. The calculation49 was carried out using a positive-jellium-backgroundmodel for the alkali metal clusters. This model has been quite successful in explaining a number of ground-state properties of these clusters including the occurrence of the famous "magic" numbers in their mass abundance.60 In calculating the quasiparticle energies, a real space formalism for dielectric screening including local field effects was developed. Figure 10 depicts the absolute values of the highest-occupiedquasiparticle energies for Nan and Kn clusters with n = 2, 8 , 18, and 20. These energies may be compared with available experimental ionization potentials.60 As seen from the figure, the agreement between theory and experiment is satisfactory with both the trend and magnitude of the ionization energies well reproduced. The systematic lowering of the experimental ionization energy as compared with theory may reflect an inadequacy of the jellium-positive-background model for these clusters. Another possible explanation is that the experimental ionization potentials for metal clusters depend on the temperature. Hotter clusters are expected to give smaller ionization potential. The calculations were carried out at T = 0. SUMMARY AND CONCLUSION The interpretation of the photoemission spectra of solids requires the concept of quasiparticles. In this Chapter, a self-energy approach for calculating the quasiparticle energies from first principles is discussed. The approach, which involves a first-order expansion of the electron self-energy operator in the screened Coulomb interaction, is shown to be well-founded as well as applicable in practical computations for real materials. Selected examples of application of the method to bulk crystals, surfaces, and clusters are presented. Results from the calculations have successfully explained the major features in the photoemission and optical spectra of these systems. And, in many cases, the theory has been predictive. The overall agreement between calculated energies and experimental data is generally at the level of a tenth of an eV for semiconductors and simple metals. This ability of theory in computing accurate excitation energies from first principles is a very recent development, and it is a major improvement over using, as quasiparticle energies, eigenvalues from methods based on local density functional formalism or the Hanree-Fock approach. Although application of the

7.

96

present quasiparticle method to transition metals and other more highly correlated electron systems remains to be made, its successes so far have been quite impressive and encouraging. The use of this approach together with total energy methods for structural determination should provide a theoretical framework which enables us to calculate the electron excitation spectra of many materials from first principles. ACKNOWLEDGEMENT This work was supported by NSF Grant No. DMR88-18404 and by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Sciences Division of the U.S.Department of Energy under Contract No. DE-AC03-76SF00098. The support of a Guggenheim Foundation Fellowship is also gratefully acknowledged. REFERENCES 1. 2.

3. 4.

5. 6. 7.

8. 9. 10. 11.

12. 13. 14. 15. 16.

See, for example, chapter by J. E. lnglesfield and by G.A. Sawatzky. For a review see L. Hedin and S. Lundqvist, Solid State Physics 23, 1 (1969). P. Hohenberg and W. Kohn, Phys. Rev. 136,8864 (1964); W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). E. W. Plummer, Surf. Sci. 152/153, 162 (1985); E. Jensen and E. W. Plurnmer, Phys. Rev. Lett. 55, 1912 (1985). M. S. Hybertsen and S. G. Louie, Comments Cond. Mat. Phys. 13, 223 (1987). M. L. Cohen and J. R. Chelikowsky, Electronic Structure and Optical Properties of Semiconductors (Springer-Verlag, Berlin, 1988). C. S. Wang and W. E. Pickett, Phys. Rev. Lett. 51,597 (1983); Phys. Rev. B 30, 4719 (1984). S. Horsch, P. Horsch, and P. Fulde, Phys. Rev. B 29, 1870 (1984). G. Strinati, H. J. Mattausch, and W. Hanke, Phys. Rev. Lett. 45, 290 (1980); Phys. Rev. B 25,2867 (1982). Also, W. Hanke, Th. Golzer, and H. J. Mattausch, Solid State Commun. 51, 23 (1984). M. S. Hybertsen and S. G. Louie, Phys. Rev. Lett. 55,1418 (1985); Phys. Rev. B 34, 5390 (1986). R. W. Godby, M. Schluter, and L. J. Sham, Phys. Rev. B 35,4170 (1987). P. Minnhagen, J. Phys. C 7, 3013 (1974); J. Phys. C 8, 1535 (1975). A. H. MacDonald, J. Phys. F 10, 1737 (1980). T. K. Ng and K. S. Singwi, Phys. Rev. B 34, 7743 (1986). X. Zhu and A. W. Overhauser, Phys. Rev. B 33,925 (1986). For an excellent review of pre-1969 work, see Ref. 2.

97

17. 18.

M. S. Hybertsen and S. G. Louie, Phys. Rev. B 35,5585(1987);35, 5602 (1987). J. E. Northrup, M. S. Hybertsen, and S. G. Louie, Phys. Rev. Lett. 59, 81 9 (1987);Phys. Rev. B 39,81 98 (1 989).

26. 27. 28. 29. 30. 31.

Zahlenwerte und Funktionen aus Naturwissenshaften und Tecknik, in Vol. 111 of Landolt-Bornstein (Springer-Verlag, New York, 1982),Pt. 17a. G.Baldine and 6. Bosacchi, Phys. Status Solidi 38,325 (1970). A. L. Wachs eta/., Phys. Rev. B 32,2326 (1985). D. Straub, L. Ley, and F. J. Himpsel, Phys. Rev. Lett. 54,142 (1985); Phys. Rev. B 33,2607(1986). F. J. Himpsel, unpublished. R. T. Poole, J. G. Jenkin, R. C. G. Leckey, and J. Liesegong, Chem. Phys. Lett. 22,101 (1973). T. Ohta, S.Kinoshita, and H. Kuroda, J. Electron. Spectrosc. Relat. Phenorn. 12,169 (1977). L. 1. Johanson and S. B. M. Hagstrom, Phys. Scr. 14,55 (1976). R. Hulthen and N. G. Nilsson, Solid State Commun. 18,1341 (1976). D. E. Aspnes, Phys. Rev. B 12,2797(1975). R. R. L. Zucca and Y. R. Shen, Phys. Rev. B 1,2668(1 970). R. A. Roberts and W. C. Walker, Phys. Rev. 161,730(1967). F. J. Hirnpsel, J. F. van der Veen, and D. E. Eastman, Phys. Rev. B 22,

32.

T. K. Ng and K. S. Singwi, Phys. Rev. B 34,7738 (1986); 34,7743

19. 20. 21. 22. 23. 24. 25.

1967 (1980). (1986).

35.

X. Zhu and A. W. Overhauser, Phys. Rev. B 33,925(1986). A. H. McDonald, M. W. C. Dharma-Wardana, and D. J. W. Geldart, J. Phys. F 10,1719 (1980);A. H. McDonald, ibidl0, 1737 (1980). K. W. K. Shung, 6. E. Sernelius, and G. Mahan, Phys. Rev. B 36,4499

36.

J. E. Northrup, M. S. Hybertsen, and S. G. Louie, Phys. Rev. Lett. 59,

33. 34.

(1987). 37. 38. 39. 40. 41. 42. 43. 44.

45. 46.

819 (1987). M. Surh, J. E. Northrup, and S. G. Louie, Phys. Rev. B 38,5976 (1988). J. E. Northrup, M. S. Hybertsen, and S. G. Louie, Phys. Rev. B 39,8198 (1989). F. Sacchetti, J. Phys. F 12,281 (1982);M. Schreiber and H. Bross, J. Phys. F 13,1895 (1983). 1. Lyo and E. W. Plummer, Phys. Rev. Lett. 60,1558 (1988). P. H. Citrin eta/.,Phys. Rev. Lett. 61,1021 (1988). H. J. Levinson, F. Greuter, and E. W. Plummer, Phys. Rev. B 27,727 (1983). M. S.Hybertsen and S. G. Louie, Phys. Rev. Lett. 58,1551 (1987); Phys. Rev. B 38,4033(1988). R. S.Becker, 6. S. Swartzentuber, J. S. Vickers, M. S. Hybertsen, and S. G. Louie, Phys. Rev. Lett. 60,116 (1988). X.-J. Zhu, S.6. Zhang, S. G. Louie, and M. L. Cohen, Phys. Rev. Lett. 63,2112 (1989). J. E.Northrup, M. S. Hybertsen, and S. G. Louie, to be published.

98

47. 48. 49. 50.

51.

S. B. Zhang, D. Tomanek, S. G. Louie, M. L. Cohen, and M. S. Hybertsen, Solid State Commun. 66, 585 (1988). M. S.Hybertsen and M. Schluter, Phys. Rev. B 36,9683(1987);S.B. Zhang, M. S. Hybertsen, M. L. Cohen, S. G. Louie, and D. Tomanek, Phys. Rev. Lett. 63,1495 (1989). S.Saito, S.B. Zhang, S. G. Louie, and M. L. Cohen, Phys. Rev. 40,

3643 (1 989). R. D. Bringans, R. I. G. Uhrberg, R. Z. Bachrach, and J. E. Northrup, Phys. Rev. Lett. 55,533(1985);R. 1. G.Uhrberg, R. D. Bringans, M. A. Olmstead, R. Z. Bachrach, and J. E. Northrup, Phys. Rev. B 35,3945 (1987). W. Drube, R. Ludeke, and F. J. Himpsel, Proceedings of the 79th International Conference on the Physics of Semiconductors,ed. W.

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Zawadski (Inst. of Physics, Polish Academy of Sciences, 1988),p.637. F. J. Himpsel, P. Heimann, and D. E. Eastman, Phys. Rev. B 24,2003 (1981);F. Houzay, G. M.Guichar, R. Pinchaux, and Y. Petroff, J. Vac. Sci. Technol. 18,860 (1981). R. I. G.Uhrberg, G. V. Hanson, J. M. Nicholls, and S. A. Flodstrom, Phys. Rev. Lett. 48,1031 (1982). P. Perfetti, J. M. Nicholls, and B. Reihl, Phys. Rev. B 36,6160 (1987). F. Ciccacci, S.Selci, G. Chiarotti, and P. Chiaradia, Phys. Rev. Lett. 56,

56.

A. Huijser, J. van Laar, and T. L. van Rooy, Phys. Lett. 65 A, 337

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13456 (1988). R. Haight and J. A. Silberman, Phys. Rev. Lett. 62,815 (1989). W. D. Knight, K. Clemenger, W. A. de Heer, W. A. Saunders, M. Y. Chou, and M. L. Cohen, Phys. Rev. Lett. 32,2141(1984).

99

Chapter 4 SURFACE STATES ON METALS S.D. KEVAN AND W. EBERHARDT

1. INTRODUCTION

Over the past decade angle resolved photoemission spectroscopy (ARP) has matured from a new and exotic technique into a very powerful tool to determine the electronic structure of solids, surfaces, and interfaces. Measuring not only the kinetic energy hut also the direction of the photoexcited electrons and thus the components of the electron momentum vector, allows a determination of all relevant quantum numbers of the electronic states of a solid including the ones located at the surface. ARP is indeed the only existing spectroscopic technique that allows a direct and unambiguous determination of a two o r three dimensional band structure E(k) of a solid or a surface. These band structures have been calculated for many decades, and the basic concepts can be found in any elementary solid state physics textbook. It is therefore very fascinating now to have an experimental technique at hand to verify these calculations. Even more important than this connection with t h e theory of electronic structure in crystalline solids is the technological impact generated by these measurements. The electrctn interactions between the individual atoms forming a solid or a surface, as reflected by the electronic structure, determine all the properties of the material. While the mechanical stability, acoustic properties, electrical and thermal conductivity, or magnetism are generally related to bulk electron interactions, other properties like corrosion or embrittlement as well as the catalytic activity of a material are related to the electronic structure of internal a n d external surfaces. In semiconductor technology, metal semiconductor or semiconductor semiconductor interfaces largely determine the electrical characteristics of a device. Even though the systems in technical applications are very complex and often do not have the perfect two or three dimensional periodicity required for a strict application of ARP, very valuable information can be obtained by studying ideal "model" systems. Two dimensional systems like the interior and exterior surfaces of a solid have their own localized or quasilocalized electronic eigenstates. These states are the two dimensional analogues of the electronic states associated with point defects like shallow and deep band gap levels in semiconductors, or spin polarized resonances associated with transition metal impurities in a free electron host. The defect levels associated with the termination of the perfect crystal structure at the surface are called surface states or resonances. These states have properties which are quite different from the bulk electronic structure of the host. Moreover they are, because of their two dimensional nature, distinct from most other defect levels and therefore easily recognizable.

100

Like other types of defect levels, surface states and resonances have a profound influence on the physical and chemical properties of a surface. Historically this has been more obvious for semiconductor surfaces (see chapter 5). For example the dangling bond states created by forming a surface are often partially satisfied by driving a reconstruction or relaxation of the surface layers. The existence of surface states on semiconductor surfaces has long been postulated to explain surface band bending effects and the Schottky Barrier formation. O n metal surfaces the relationship between the electronic structure and other surface properties is neither so obvious nor intuitive. This is largely due to the more complicated nature of metallic relative to covalent bonding. Thus establishing a linkage between the electronic structure, measured by ARP, and other surface properties such as the geometrical structure, surface dipole layer formation, dynamical properties, and chemical reactivity is one of the most important goals in surface physics. This linkage will be the first step toward an intuitive understanding of these complex phenomena. This goal has been vastly aided by the development of efficient and accurate codes for the calculation of the surface electronic structure from first principle. By coupling ARP data with these calculations in the past decade, the field has progressed to a point where a fairly detailed understanding of simple surfaces has been attained. In this chapter we focus on the surface states and resonances which exist on nominally clean and well ordered metal surfaces, the interactions these support, and the phenomena i n which they participate. W e will exclude metal/semiconductor and metal/metal interfaces, since of this type of research is discussed in later chapters of this volume. W e will start by presenting two simple empirical models, which provide some intuition when and where surface states might occur, what their properties might be, and what they tell us about the surface. We will the describe how a surface state can be identified experimentally and which of its properties can be measured using ARP. We will then review some of the experimental and theoretical results for surface states on various metal surfaces. Finally we will try to assess the overall significance of the work accomplished to date in terms of its relevance to surface properties in general. There are several previous reviews of A R P which provide similar yet less complete information about surface states on metals. These include chapters in books focussing primarily on angle integrated photoemission by Feuerbacher, Fitton , and Willis,' N.V. Smith? and P r ~ t t o n and , ~ articles written by Feuerbacher and W i l l i ~ Plummer ,~ and Eberhardt: and HimpseL6 In addition there exist numerous reviews on surface electronic structure theory, which make extensive reference to surface states on metals and at least recently compare theory with experimental r e s u ts.7-14 ~ Theoretical Concepts for Surface States It is a useful endeavor to try to develop an intuitive understanding of why a surface state exists and what its properties might be. This will lead naturally to a better understanding of the impact that surface states might have on other surface properties. The first step in quantifying the surface electronic structure is a classification of the possible types 1.1

101

o f electronic states that may occur at the surface of a perfect crystal. Obviously tlic' hull;

elcctronic states will extend into the surface region, where they are reflected !>I ilic v:iL'iiiiiii Iurt-ier. True surface states on the other hand, exist only ;it the surface ;ind li:t\c :1ii espoiic'iiti~rllydecaying wave function both i n the direction into the solid i t i i c l ;iI.\ti iiiio i l i c v m i u i i i . I n energy/momenturn space these states are restricted t o regions wticrc IIO Ivilk ii:ites of the same symmetry and qtianttini number are allowed to exist. The \wvc 1'iiiii.iiiiii of the surface state would otherwise mix with the bulk wave function and the st;itc woiild i i o t tic confined to t h e surface region of the crystal. This is the case f o r a surf'Ice rc.sl)11: II)cc. \vhicli may also be viewed as a modification of the wave function of a bulk c l e c i r o i i i c \I:IIC i i w r i l i c surface.

>

w

w>

3 0

A

Auc

BULK STATE b

SURFACE RESONANCE

Fig. I Electronic wave functions in the surt'ace region. Fig. I shows schematically the differen1 types of electron wave functions o l w t - w t l iii lie stirface region. Bulk states (c) exist with periodically varying amplittide tliroughoui [tic

crystal. I f these bulk states are high enough in energy, i.e. above t h e vactitiiii I crystal, then they match to free electron states in the vacuum antl the electrons i i i ~ I i c z c states c ~ leave i the solid (e). Surface states ( a ) are localized strictly to the surfacc i-c'$oii of ilir crystal, l ~ obviously t are periodic i n the two dimensions parallel t o the stii-f;t~~c. S i i i ~ l : ircsonances (b) are equivalent to bulk wave functions with ;in enlarged ariipliiutlc iii tlii, surface region of the crystal. Vacuum electronic states (d), which cannot be iiiiitclic~l ill

~ ~

cncrgy antl momentum to crystalline wave functions in the interior are present i n [ l i e . w i ~ l ~ i ~ i-cgions as evanescent states. These evanescent states contribute a large amoiint ( ( 1 I I l c photoemission process and they are for example responsible for some of the "liackgrriiiiitl" 5igii;iI observed which cannot be explained as direct interband transitions.

102

The goals of several early phenomenological models which will be described Iwieily below1-'-18 were to give an intuitive understanding of why a surface state exists and u h i t its properties might be. These models were based on extensions of simple, empirical iiio(1eIs ol' l i t i l k hand structure: the nearly free electron model and the tight binding model. 111 t l i c w simple models band gaps are located either at the center of the Brillouin zone or iit tlic m i c ' Ix)und;iries, and consequently that is where the early models predict the surface st:iie\ to exist. Later the existence criteria were extended by Gurman and Pendry" t~ includc si:iies existing in gaps located at arbitrary points in the Brillouin zone. The earliest attempts to understand and predict the existence of surface states extended nearly free electron models of bulk band structure to semi infinite crystals.' ’.I2 These non-self-consistent models used empirical pseudopotential parameters, i i i i t l ilie electrostatic potential at the surface was assumed to jump abruptly from the inner pteiiiial to tlie v;~ciiiini level at an arbitrary distance from the plane of the surface ;itom. l'hc Schriicliriger equation was solved for energies both within the bulk band and ;ik;f)fcrr pro.jectetl band gaps. Within the bulk bands all three momentum componeiits :ire r w l . corresponcling to a freely propagating state. For states located in the gaps, however. the iiionieiitum normal to the surface ( lu) must necessarily be complex, assuring ;I finite penetration depth of the state. Thus the surface state decays evanescently into the bilk with :in exponential decay constant related to the imaginary part of k i . Successful matching I)!' this state to a wave function decaying into the vacuum barrier leads to ;I st:itioii;ii-!. noriiializahle eigenstate, located within a band gap. Stirface states Iocaied iii ;I hyliridiz~itional band gap have been labelled Shockley states. The surface state on Al[OO I ). which will be discussed later is well-described as a Shockley state, since i t exists i i i :I zoiie Ix)unclai-y hybridizational band gap which is characterized adequately I)! one pseutlopotential coefficient. The existence criteria for a Shockley state depends upon the choice of the termixitiiig potential at the surface. The step potential used in the original models'7 required m;itcliiiig l o ;I single exponentially decaying wave function outside the surface. There irewll\ ;I coiistr:iint o n the sign of the dominant pseudopotential coefficient VG. I f VG > 0, w i t h the origin of the coordinate system on the lattice planes, the matching condition is nor p)sle and ;I state will not exist. Conversely, precisely one state will exist when VG < 0. Receiit tre:itiiients used a more realistic image potential outside the The existciicc criterion is relaxed somewhat and two or more surface localized states may exist, reg;irtlles of the sign of VG. Other properties of Shockley states such as their energy and ev;iiiesceiii decay length are also determined by a combination of the characteristics of the hiilk h i i d gap a n d of the assumed crystal Since the properties of b u l k livt~riilizaiiciii~il gilx are generally well understood, these states can provide a very useful prolw ( 1 1 the prol7erties of the potential describing the termination of the crystal. As a testing grountl iolfir-st-principles computations, they have been instrumental in demonstrating tlie riece.ssity I'oi;ich ieviiig self-consistency in surface calculations.

103

A second intuitive model which predicts surface states is based on the tight-binding or Huckel model for band structure.17 This is the natural counterpart to the pseudopoterltial based theories. The model assumes localized orbitals located on a semi-infinite lattice which interact weakly and only with their nearest neighbors. The surface perturlxition is introduced through an empirical parameter A which describes the difference in self-eiiergy o f the orbitals located on the surface plane relative to those of the bulk. Again there exists a hulk band of energies of total width W. Unlike the pseudopotential models, in this model a surface localized state will not split from the bulk band unless x = 4A/W > 1. I f this criterion is satisfied, a surface state splits from the bulk band by an amount

AE, = A(l-I/x)* These are useful and intuitive results. The magnitude of W is directly related to tllc hybridization integrals between neighboring sites or, in three dimensions, between I:itiice planes. It therefore is a measure of how much the layers normal to the surface interact. I f this integral is small, as in the case of core levels, neighboring layers do not interact

:it :ill.

and the surface level splits from the bulk level by an amount equal to A. If A a W, the

perturbation is smaller than the interaction between layers and a surface state will n o t split off. In the limit of small X , the pseudopotential model is probably more applicable. Surface states which are well described using this tight binding model are often called Tamm si:ites. 'The important factors distinguishing Tamm states are a lack of hybridization between Ixiiid\ and fairly localized orbitals, both of which lead to small band widths. This is :tiways appropriate for surface core levels. In addition valence surface states which split off very narrow d-bands on several low index noble metal surfaces are good approximations to Tamm states (see Section 2.1). The empirical parameters in this model clearly coiit;iiii usef~ilinformation about the surface. A, for instance, tells us about the magnitude o f the surface perturbation experienced by an electron. Other wave function parameters ;itso clepend on x in a systematic way.17323 Of course, these paradigmatic models of surface states on metal surfaces c;in iioi IC precisely realized in real systems. Indeed, many states have been observed which do n o t I i I either the Shockley or the Tamm paradigm exactly. The most obvious case, where tliis \\,ill occur is on transition metal surfaces. We can have significant s-d hybridization, for ex:iinple. leading to surface states which are intermediate between Tamm and Shockley states. I n addition, the relatively narrow d-bands undergo significant band hybridization among themselves. Gaps open throughout the bulk Brillouin zone, wherever bands of thc s:tnie symmetry approach, in some cases leading to projected gaps and surface states. Moreovei-. paps can be opened through other symmetry breaking forces such as the spin oihit interaction (Sec. 2.2). Surface states of all types can be observed in such gaps. State-of-the-art self consistent calculations yield not only the energy-momeiitiiiii parameters but also the charge distribution associated with surface state the wave functions. This gives a "visual" confirmation of the degree of surface localization. An example of the calculated charge density for a highly localized d-like surface state on Pd( 111) is shown i n

104

d - LIKE SURFACE STATE

Fig. 2 Top: Charge density contours for a highly-localized d-like surface stilte on Pcl( I I I ) . Bottom: Total charge density in the surface region (from Ref. 24). Fig. 2.24 This state and others, for example, on C U ( O O I ) ~and ~ > ~Ni(O01)29 ~ are welldescribed by the Tamm model. Most of the very successful surface electronic structure calculations approximate the solid by a small number of atomic layers in the appropriate geometry. For computational reasons, this number is so small that these calculations (lo n o t give continuous bands but rather a whole series of discrete states. It can become difficult t o distinguish computationally such surface states if the bulk penetration is too large. l’he computational criterion for a surface state then depends on where the state is locakcl i n energy-momentum space and how much of the charge of the state is located in the oulemiost layer. The first experimental evidence for the existence of a surface state on a metal surfrice was obtained in field emission studies of W(OOl)3O Later the same state was also observed tising ARP?1>32 At about the same time as these early experimental obser\iarions. calculaotions predicting the existence of surface states in hybridizational band gaps in niet:\Is were reported by Pendry and F o r ~ t m a n nand ~ ~ Forstmann and H e i ~ ~ Application e . ~ ~ of these calculations to W(OO1) was not possible however, and the precise origin of this surface state o n W(OO1) was undetermined until recent calculations were able to include relaLivis!ic effects (Sec. 2.2). The prediction and experimental observation of surface states on nietal surfaces has now been accomplished for almost all the low index surfaces of the metallic elements in the periodic system. This was achieved almost exclusively by ARP. We present a few more basic concepts of surface states and their existence criteria before we discuss why ARP is such a powerful tool in identifying surface states and how one

105 SURFACE NORMAL

t I

Fig. 3 Bulk face-centered cubic Brillouin zone, and the projection onto the (001) stir-face Brillouin zone. actually goes about identifying surface states using ARP.

Surface states are truly two-

dimensional states, which decay evanescently into both the bulk and the vacuum. Only two components of crystal momentum, those parallel to the surface (kII ), are well defined f o r these states. Thus by definition surface states exist within a region of three-dimensional energy-momentum space, where no bulk states of the same symmetry are allowed to exist. Most conveniently this is within an absolute energy gap in the bulk band structure. However, as we will see later, surface states are not limited in their existence to ahsolure gaps. To be more precise, the condition for the existence of a surface state is defined such that for a certain parallel momentum k 11, there are no bulk states of the same syrnmeiry ror any momentum normal to the surface (lu). Otherwise the surface state would couple to (his hulk component. We thus say surface states have to exist in symmetry projected bulk I x i r i c l

gaps. Their wave functions are effectively excluded from penetrating into the bulk of tlie material by energy and momentum conservation. We use Al(OO1) as an illustrative example of a surface which has a well defined surface state. Aluminum has the fcc crystal structure. The Brillouin zone for a fcc c y t ; i l a n d the projection onto the (001) surface Brillouin zone (SBZ) are shown in Fig. 3. I n Fig. 7 w e show a calculated band structure of aluminum along the high symmetry directions irsing o n l y the two largest pseudopotential coefficients. This matches very closely the Ixintls calculated using more sophisticated techniques36 A careful look at Fig. 3 reveals that tlie hulk states along r-X of the bulk Brillouin zone are projected onto the center of the SBZ, which is generally labelled r. This point r corresponds to a parallel momentum of li 1 =

106

out in the SBZ along both symmetry azimuths. Thus even though there is no absolute band gap in the occupied bands of aluminum, a well defined surface state may nonetheless exist on the ( 0 0 1 ) ~ ~ 7 and ~ ~ (111)38 7 ~ ~ -surfaces ~ ~ of aluminum. Experimental verification of these states will be discussed below. It is possible for an electronic state with significant surface character to exist outside of one of these projected band gaps, if this state has a well defined symmetry distinguishing it from the underlying continuum of bulk states. Thus this state is still ;I true surface state, since coupling to the bulk states is symmetry forbidden. If on the other hand the surface and bulk states are of the same symmetry, mixing will occur and the state becomes a surface resonance. A surface resonance is a resonance in the classical sense and is analogous, for example, to a Fano resonance in atomic physics. Its wave function penetrates the bulk to infinity, but it has a n enhanced surface amplitude like a surface state as indicated schematically in Fig. lb. The degree of surface localization for a surface resonance depends on the strength of the coupling between the quasi-discrete state and the b u l k continuum. A n electron in a resonant state will thus have a finite probability of tunneling into the bulk continuum and therefore it will be lifetime broadened energetically. Naturally, the upper limit on the inverse lifetime of a surface resonance is the width of the bulk band in which it is embedded. We thus have a very simple picture of three types of levels found near a surface. A true surface state has zero band width in the direction normal to the surface. It therefore does not exhibit any dispersion with change in normal momentum. A surface resonance has a nonzero width which is less than or equal to the width of the bulk band in which it is embedded, and the bulk band has a width given by the solution of the Schrodinger equation deep inside the crystal. In principle any or all of these states might be observed i n ;I photoemission spectrum. The procedures for isolating the contributions from these three different classes of states and the characterization of the surface features is described nest. We will see in section 2.3 that these categories can and will break down when the three types of states are energetically very close to one another at the same parallel momentum.

Exnerimental Characterization of Surface Electronic Levels The application of ARP to study surface localized levels is straight-forward. Energy and k 11 are conserved in the photoemission process and these, together with the symmetry and electron spin on a magnetic surface or when relativistic effects are important, are the only relevant "quantum numbers" characterizing a surface state. The difficulties with the I .2

non-conservation of the normal momentum component, which have to be overcome in determining bulk band structures using ARP, pose no problems in determining the dispersion of surface states. We assume in the following that the one-electron approximation is adequate for the description of the valence state photoemission process. The breakdown of this approximation, which is signalled experimentally by the presence of shake-up satellites in the spectra, is discussed in more detail e l ~ e w h e r e ~and l , ~in~ Chapter2 of this volume. In most cases we are not interested in the absolute intensity of a feature

107

1Z.O.OJ

lZO.Il

lld.O.I.5l

l~,LIl

lO.O.0l

k ($1

Fig. 4 Calculated band structure of aluminum using four plane waves a n d t w o pseudopotential coefficients. Note the nearly-free-electron gaps which open at the X and 1points (from Ref. 35). Aluminum is a nearly free electron metal with a fairly large pseudopotential coefficient V200. This opens a gap at the X point of the bulk band structure such that there are no bulk states between roughly 2.2 eV and 3.0 eV below the Fermi level. From the projection shown in Fig. 3 and from the calculated band structure shown in Fig. 4 we t l l u \ know that at r of the SBZ of tu(0Ol) there exists a band gap for these energies. This is exactly the condition under which we expect a surface state to exist. (0,O).

-%

- 0

G

8 -1 Y

2 - -2

t

r -3

Fig. 5 Aluminum band structure projected onto the mirror planes of the (001) surfacc. Brillouin zone. Data points are the experimentally determined surface state dispersion (Ref. 20). There are several ways to present these projections of bulk states onto t h e SBZ. Most common is to plot the projected bulk bands at any given energy as a function of parallel momentum along the symmetry directions of the SBZ. Such a projection is shown in Fig. 5 for Al(001). In this case the SBZ is a square and the symmetry azimuths are labcllecl A and C. In this figure, the shaded regions indicate projected gaps in the bulk bands o f eveii symmetry under reflection in the mirror planes normal to the surface. The projected gap at t h e zone center described above is observed to pinch off slowly at parallel momenta further

108

observed in the photoemission spectrum, since this is determined by matrix element effects which do not readily give additional information about the surface electronic structure. However, the relative intensity of a photoemission feature measured as a function of photon energy or of the orientation of the photon polarization vector relative to the crystal lattice and the detector does yield important information about the symmetry of the wave functions as we will show below. In a typical ARP experiment the photoelectron emission angles, the incident photon energy, the polarization, and the crystal orientation are held fixed while an energy distribution curve (EDC) of the emitted electrons is recorded. The energy of the photohole can be readily determined relative to the Fermi energy EF. The magnitude of the initial and final state parallel momentum (in A-’) can be calculated for any spectral feature at ;I measured kinetic energy Ek (in eV) via the standard algorithm: k 11 = 0.512 J E k sin

0

(2)

The polar emission angle relative to the surface normal is d. The vector components of k 1 can thus be calculated if the azimuthal emission angle is known. The ARP final state consists of a photohole and a photoelectron. Momentum conservation dictates that the parallel momentum components of these two be identical modulo a surface reciprocal lattice vector. The momentum of the photon is small at VUV energies and can be neglected. I n this way the quasiparticle two-dimensional energy dispersion relation, E(k 11 ), can be determined. This is what we generally use in comparison with a ground state band structure calculation. Many body and self-energy effects introduce some complications in this comparison, since the binding energy determined in photoemission is not the true ground state energy of the system. These effects have been discussed in more detail in chapters 2 and 3. For convenience we exclude these many body effects from the discussion in this chapter even though we are well aware of their presence. The discussion above indicated the importance of the determination of the symmetry of a given state. This can be achieved with a polarized excitation source like synchrotron radiation and has been applied extensively. To show this simple principle, we consider the symmetry properties of the Fermi Golden Rule matrix element, which governs the photoemission process I = 2s/h

I< i I A

.PI f

>I2

6(Ef-E;-

hw)

(3)

where < i I and 1 f > are the initial and final state wave functions, A is the vector potential of the incident light, P is the momentum operator, and the 6-function ensures energy conservation. All these functions are necessarily continuous in space. In order to have nonzero photocurrent at the detector, both the final state and the matrix element as a whole must be totally symmetric with respect to any symmetry operation of the crystal. This means that the product of the initial state wave function and the dipole operator A P must be symmetric. Changing the direction of the polarization of the incoming photon with respect to the crystal lattice and the detector thus allows us to determine the initial state symmetry.

-

109

This js most often done for emission in a mirror symmetry plane, where at least two symmetry representations exist, odd and even upon reflection. If the polarization vector i s located within the mirror plane where the detector is located, then the dipole operator is even and only even initial state wave functions contribute to the photoemission current. If, on the other hand, the polarization vector is normal to the detection plane, then the dipole operator is odd and only odd initial state wave functions contribute. For emission along the normal of the low index planes of the fcc and bcc lattice these symmetry selection rules have been pointed out by HermansonP3 The general symmetry selection rules for optical excitation in the fcc and bcc lattices have been tabulated by Eberhardt and H i m p ~ e and l~~ by B e n b ~ w for~ the ~ hcp lattice. A difficulty often encountered in these studies is distinguishing the spectral features which arise from surface states as opposed to ones caused by bulk interband transitions. While there is no absolute procedure for accomplishing this, several tests have been developed to aid in this process. Historically the first test applied was the so called "crud test". Exposing an atomically clean surface to impurities will preferentially change the surface related features like surface states and resonances in the spectrum, since their existence is dependent on surface perfection and the particular shape of the surface potential. Even though this concept seems to be quite intuitive and has been applied frequently, this test by itself is the least perfect criterion for the proof of existence of a surface state. For example, certain well known surface states do not change when the surface is covered with a particular adsorbate.46 Moreover, the notion that surface states "disappear" when the surface is exposed to an adsorbate does not make sense physically. The charge at the surface does not get completely removed by the adsorbate, but rather on the adsorbate-covered surface it is located in different regions of energy/momentum space than on the clean surface. This means in practice that surface states of the clean surface will be observed to shift and maybe to broaden in energy upon adsorption. Sometimes they \+ill completely disappear out of a particular photoemission spectrum, but then also other interface states will show up at a different place of the energy/momentum space at [lie surface. An example of a successful crud test is shown in Fig. 6 for the state located a t the center of the SBZ of A I ( O O ~ ) . The ~ ~ spectra were accumulated at normal emission (8 = O ) , so that kll = 0 from eq. (2). The upper spectra were collected from the clean surface, while the lowest three were collected from a surface which had been exposed to increasing amounts of oxygen. The feature at a binding energy of 2.75 e V below the Fermi level (EF) i s significantly reduced in intensity following the exposure, indicating its possible origin its 21 surface feature. Comparing the energy at r of this feature with the projected hand structure, Fig. 5. we get further evidence that this feature is caused by a surface state, since its existence falls within a projected band gap. The fact that we compare an experimental result with a projection of calculated bands can lead to some difficulties if many body effects distort the experimental measured energies (see Chapter 2). It is preferable although not always possible to determine the bulk states and projected gaps experimentally.

110 I

I

I

I

I

Al(lO0)

CLEAN

80 L 160 L 200 L

-4

-2

INITIAL ENERGY I

d

Fig. 6 Al(OO1) normal emission spectra indicating the sensitivity of the surface state to contamination by oxygen (Ref. 37). Fig. 7 illustrates the application of polarization selection rules to determine the symmetry of this states Here the spectra are taken with synchrotron radiation and the angle of incidence of the light is varied. A. this angle increases, measured relative to the surface normal, the polarization component in direction of the surface normal increases, whereas the component parallel to the surface decreases. Clearly the surface state emission is stronger, when the light incidence is more grazing to the surface. This indicates that the state is excited by the polarization component of the light normal to the surface. Thus the dipole operator is even with respect to all symmetry operations and the initial state must be even as well. A more definite criterion for the proof of existence of a surface state than the "crud test" is the lack of dispersion as a function of the component of momentum normal to the surface. As explained in chapter 3, the bulk band structure or more exactly the quasiparticle band dispersions for bulk states can be readily obtained using ARP. Since a true surface state has zero band width in a direction normal to the surface we expect to observe experimentally that its energy will not change with change in final normal momentum. Sometimes this test can lead to ambiguous results, since dispersionless features can show u p in the photoemission spectrum which originate from flat or dispersionless bulk bands. Nevertheless, this is a necessary condition for the existence proof of surface states. Surface resonances, due to their intermediate character, might appear to disperse slightly. An

-

111

NORMAL EMISSION AP (100)

-5

-4

-3 -2

-1

E,

INITIAL ENERGY (eV1 Fig. 7 Dependence of Al(O01) surface state intensity on the angle of photon incidence. additional difficulty is caused by bulk "density-of-states" features arising through indirect (momentum non-conserving) transitions from regions of high initial state density. These regions are naturally associated with bulk band edges such that often these features appear to be very close to a band gap. An example of the absence of dispersion of a true surface stare with riornial momentum is given for the Al(OO1) surface state in Fig. 8. This figure shows EDC's collected at normal emission geometry from Al(OO1) as a function of photon energy.35 Since 6 = 0, eq. 2 shows that kll = 0 even though the total final state momentum is roughly proportional to JEk. Thus k~varies significantly for the spectra shown in Fig. 8. However, the binding energy relative to the Fermi level of the surface state feature distinguished earlier is observed not to change. The large intensity variations seen are due to variation in the coupling to the final state wave function, and will be discussed more fully in Sec. 2. I . Successful application of several of these tests provides compelling evidence that a state is indeed a surface state. Distinguishing a surface resonance is still more coniplicated, since it is degenerate with a bulk continuum. Since "normal" bulk states may also be modified at the surface by adsorbates the boundaries become rather vague and the process of distinguishing a surface resonance from a "modified" bulk states is a semantic exercise. After the surface character of a given photoemission feature has been ascertained, it is a simple exercise to determine the dispersion relation by varying the emission angle to vary the final and initial state parallel momentum according to eq. 2. Strictly these tests would have to be repeated for all parallel momenta, but that is usually not done in practice. An example of this is presented in Fig. 9, again for our model case of Al(O01). These

112

.zo

-15 -10 - 5

EF

INIT1AL -STATE ENERGY ( eV I

Fig. 8 Demonstration of the lack of dispersion of the Al(OO1) surface state as a function of l u (from Ref. 35). EDC's were collected as a function of emission angle in the C 1) [loo] azimuth.38 The surface state disperses symmetrically about the normal emission direction. The measured dispersion relation is shown in Fig. 5 along with the projected bulk bands as discussed earlier26,35,37 This surface band exhibits parabolic dispersion centered at r with an effective mass of roughly 1.18 times the free electron mass. This dispersion relation is in reasonable accord with calculations based on the local density approximation using the ~ , date ~ ~ no calculations of the excitation spectrum densi ty functional a p p r ~ a c h . ~To including many body corrections like described in chapter 2 and 3 have been undertaken for this system. Having discussed the basics on both the theoretical and also the experimental side we will now show some examples of how these type of studies have increased our understanding of metal surfaces. Section two of this chapter will deal in more detail with general phenomena of surface states and resonances on simple metals, whereas section three provides a more detailed investigation using ARP of several interesting surface phenomena. The final section projects some of the future possibilities in this field. 2.

SIMPLE SURFACE STATE PHENOMENA After ascertaining the existence of a surface band and perhaps measuring. its dispersion relation, it is often desirable to characterize its properties further in order to

113

Fig. 9 Spectra of Al(OO1) as a function of emission angle indicating the dispersion of the surface state in the c symmetry azimuth (from Ref. 38).

establish correlations with other surface properties. In this section, we give a brief account of additional information that can often be extracted from ARP measurements. Surface Localization of the Wave Function The data presented in Fig. 8 provides useful empirical and sometimes semiquantitative information about the spatial extent of the surface state wave function normal to the surface. The charge density of this state actually is spread out over several lattice planes normal to the surface. If the final state wavelength is matched to the lattice spacing normal to the surface, then optimum coupling is achieved and the contributions from a11 lattice planes add constructively to the total photocurrent. Destructive interference at intermediate final state wavelengths can nearly quench emission from the surface st;ite. Thus surface states extending in charge density over several lattice planes often exhibit characteristic oscillations in cross section, whereas the surface-localized d-like surface states like that shown in Fig. 2 more or less follow the atomic cross section behavior of their tl-like origin and do not exhibit these oscillations. Thus by measuring the variation of the cross section of surface states with photon energy, we can estimate whether the state is located just at the outermost lattice plane or whether it extends into the solid. The first effort47 which documented and utilized this effect was for a well-known surface state existing near EF on C ~ ( I I ~ ) Measurements . ~ ~ ~ ~ of~ the - ~ intensity ~ of this 2.1

114

W IV

1

32

Surface State on Cu (111)

hu = 30 r

70

50 I

1

1

I

110 eV

90 !

I

l

l

'0

12

k l (2da)

00

binding energy. eV

Fig. 10 a) Photon energy dependent normal emission Cu(l1l) spectra. Note the dramatic intensity oscillation of the two surface states S1 and S3. b) Intensity of S1 as a function of !iL.

surface state (Figs. 10a and b) as a function of photon energy at normal emission were found to exhibit a pronounced maximum near hu = 70 eV. This corresponds closely to a final k i near the L-point in the second bulk Brillouin zone (see Chap. 2). The large cross-section for the surface state at this momentum gives experimental verification that the real part of the surface state momentum normal to the surface is given by the zone-boundary L-point momentum. This is in accord with the simple models described in section 1.1, given the existence of a bulk projected gap at L. Moreover, the width of the intensity distribution in Fig. 10b reflects qualitatively the imaginary part of the normal momentum and thus [lie decay length of the surface state wave function into the bulk. A simple model based on the tight-binding algorithm was developed to explain these data. This yielded a measure of the

115

decay length in reasonable accord with calculations. More recently, models based on t h e pseudopotential mode138>50t51 and (equivalently) a geometric structure factor52 have been applied to yield quantitatively similar results for the sp surface state C u ( l l 1 ) and also for similar states on Ag(ll1) and Au(ll1). A useful application of these ideas was reported recently for the zone center state o n The energy of the state was varied within the gap by depositing small amounts of alkali atoms on the surface. As the state approached the band edge, the penetration length was observed to increase, an effect which was quantitatively documented. While the measured decay lengths are in fairly good accord with surface calculations, they differ systematically from what would be predicted from an analytic continuation of the calculated bulk bands into to the complex plane. In some cases, surface state intensity oscillations can be large enough that a state is not visible at some photon energies. A good example exists on Al(111). The pseudopotential coefficient V l l l is about one quarter the magnitude of V200 for this metal, leading to a much smaller bulk band gap at L than at X (see Fig. 4). These coefficients are the same sign, however, and the pseudopotential model thus predicts a surface state t o exist o n both surfaces. A surface state located on Al(111) would be predicted to penetrate much further into the bulk than one on Al(OOl), implying a more sharply peaked intensity distribution. This intuitive result has recently been observed38 The decay length was determined to b e longer than the sampling depth of the photoemission probe and thus could not be experimentally determined. The long penetration length had delayed both experimental and computational characterization of this Al( 111) state. A similar search of copper low-index surfaces at a variety of photon energies indicated the existence of several states which had not previously been d e t e ~ t e d . ~ ' The opposite extreme from these slowly decaying sp-like states is offered by the previously-mentioned d-like Tamm states observed on the noble metals and j 9 The existence of these states arises from a symmetry-related decoupling of layers n o r m a l to the surface. For example, at the M point of the surface Brillouin zone on Cu(OO1). the tixy orbitals are completely nearest-neighbor antibonding within a layer and completely nnnbonding to similar orbitals in nearest neighbor layers. This results in an extremely flat bulk band along the bulk X-W-X line at the top of the copper d-bands. This projects onto M, and ii highly localized Tamm-like state naturally results (Fig. 2). A plot of the intensity of this state as a function of final momentum normal to the surface23 (Fig. 11) is essentially flat, indicative of the predicted extreme surface localization. It is interesting to search for similar localized states on other noble metal low index surfaces. The lower symmetry on Cu(ll1) renders the bulk layers normal to the surface less completely decoupled and thus the bulk band has some width. A Tamm-like state does exist,50*55 but with a splitting from the bulk band 50% smaller than that observed on Cu(OO1). This can b e semiquantitatively explained by Eq. 1 in Sec. 1.1. O n Cu(Oll), where the symmetry is still lower, no related state has been observed. Similar states have been ~ 911 ~l),~ ,Au(001) (lxl), and Au(001) ( 5 ~ 2 0 ) . ~ ~ observed on Ni(OOl),29 ~ g ( 0 0 1 ) , 2 ~ 9 ~Au(

116

Pi i il I

* * 1

1

I I

lk fR

R'.

o Ag (000

cu (001)

Fig. 11 Intensity of the Tamm-like surface states at M on Cu(OO1) and Ag(001) as a function of ILL (from Ref. 23). SDin-Orbit Interaction and Surface Electron States 2.2 One aspect of surface electronic structure which has been increasingly studied in recent years is the impact of the spin-orbit interaction. Dispersion relations will be significantly perturbed by the spin-orbit interaction only when bands approach to within the atomic spin-orbit parameter for the atomic levels included in the band. The symmetry of the electron states is lowered below that of the geometric point group of the surface, and interactions which would otherwise be symmetry-forbidden can occur. The band topologies can be significantly altered as is the case, for example, in semiconductor band structures near the fundamental band gap. New projected band gaps can be produced in which additional surface states and resonances are situated. The existence criteria for such states have not been determined, and are presumably not as intuitive as those for the nearly-free-electron and tight-binding types of surface states. Alternatively, interactions between surface bands or between surface and bulk bands of different nominal symmetry are allowed. The first suggestion that the spin-orbit interaction may lead to the existence of a surface state was for the very first surface state ever observed on a metal surface, that is, the so-called Swanson hump state near the Fermi level on W(O01).6°761 Despite the fact that this is one of the best-studied surfaces from both an experimental and computational point of view, the precise character of this state was uncertain until recently. The difficulty lies in the strongly hybridized relativistically-calculated bands for tungsten along r-X, the line which projects onto the center of the surface Brillouin zone. Early suggestions that the

117

-,I

-I

-6

INITIAL

4 ENERGY

BELOW EF I.VI

I-ig. 12 a ) Norm:il emission spectra of Bi( 1 1 1 ) at two temperatures indicating the existeiicc of :I surface state, labelled A. b) Experimental and calculated energy h a n d s ; i n d stirkicc tlcnaity of slates f o i- Bi( 1 I I ) (from Ref. 73). surface level was a true state located in a spin-orbit gap62 were followed by nearly ek'ery interpretation p o ~ s i b l e . h ~The - ~ ~advance in computational capabilities has been improved to the point where the spin-orbit interaction can be adequately included in a surf:ice slah calculation, hut only in a partially self-consistent way.70-72 These calculations have shown that ttic existence of the Swanson hump feature is not dependent on the spin-orhit iiiter;ictioii. I t i s essentially a tlZ2-like Tanim state ptrshetl o u t of a hulk continutim. \VhiIc [lit' spill-orhit iriter;iction appears to affect the Swanson hump only to 3 m i n o r extent. i t is important to realize that a significant amount of experimental and coniptitationiil development a n d effort has occurred as a result of its existence. A clearer example of a surface state which exists i n a gap opened by the spin-or-l>it interaction was reported for Bi( 11 In this case, the bulk hands are of sp character, and t l i i i s :ire simpler than on W(OO1). The A R P spectra which indicate the existence of thc hiirface state are reproduced in Fig. 1221. The peak at Ep, = 0.5 eV satisfies ;ill the criteria t o r being :I surface state. There is, however, no projected gap in the non-relativistic hiilk Ixintl structure. Rather, 21s shown in Fig. 12b, a gap opens when two bulk bands of differcn\ y i i n e t r y attempt t o cross near this binding energy. This crossing is disallowed by the spinorbit interaction, and a small gap is thereby produced which supports a surface state. Other spin-orbit induced surface levels have recently been observed. Wincott, e!. al.,

have reoorted verv high energv resolution mectra of Cu(OO1) showing a second tl-like

3

2

1

EF

Binding Energy (eV) Fig. 13 a) Photoemission spectra of Mo(Ol1) in the A azimuth as a function of k I The unusually rich spectra result from a spin-orbit induced avoided crossing between krf:rcc hands of differing nominal symmetry. The resulting surface band dispersions and thc projected bulk continutim are shown in b). (from Ref. 76) surface state at M which resides in a narrow spin-orbit gap.s8374 Recent experiments 011 W(O1 I ) , Mo(Oll), and Ta(Ol1) have detected spin-orbit induced surface states and also surface resonances.75-7' The gap shown in Fig. 12b occurs due to the effect of symmetry-breaking spin-orbit interaction on bulk electron states. The same avoided crossing must occur between two .scrt$rce bands whenever they are energetically close. The effect has recently been observed esperiinentally o n Mo(O1 1) and W(O1 l ) , where the bulk band projection esliiliiis overlapping odd and even symmetry gaps, both of which support surface state^.^'^^^ The surface bands are forced to hybridize under the influence of the spin-orbit interaction. The spectra for Mo(O1 1) in t h e vicinity of the spin-orbit induced hybridization ;ilony A are qui!r complex (see Fig. l h ) , and produce the surface band dispersions shown in Fig. 131,. Spinorbit induced avoided crossings roughly 0.3-0.4 eV in width are observed in both syminetry azimuths in the vicinity of small projected bulk gaps which are essentially the intersection of gaps of odd and even symmetry. Theoretical7' and experimental result^^^^^* indicate that this spin-orbit induced interaction between bands of different nominal symmetry plays ;I key role i n the clean-surface reconstrtiction observed on W(OO1) (Sec. 3. I).

119

Another system where the spin-orbit interaction appears to have a pronounced influence on a surface electronic level occurs on the Tamm-like state o n Ag(OOl)23357,5s ;I[ M just above the d-hands, similar to the state observed on Cu(001) described i n the I;~at section. The symmetry decoupling of dxy orbitals in neighboring planes is broken by the spin-orbit interaction, and the associated h u l k hands acquire some width near the X Imints of the bulk Brillouin zone. There is thus expected to be enhanced communication between the layers on Ag(001) relative to Cu(OO1) due primarily to the larger 4tl spin-orlit parameter. From the discussions of Sec. 1.1 and 2.1, one might expect t h a t this communication will manifest itself as a non-zero decay length for the surface state w;we function on Ag(001). The results shown in Fig. 11 indicate that the ideal of ;I surface witc intensity which tracks the relatively smooth atomic cross section is nearly re;ilized for Cu(O0l) but not for Ag(001). This confirms qualitatively the expected result. The situatioii on Ag(001) is more complicated, however, since the observed splitting between the h i i l k and surface bands is less than the calculated hulk band width by about SO meV, placing the w r h c e level in the projected continuum. The hulk band width is dominated by the atomic spin-orbit parameter and thus the calculation should be fairly accurate. The silver st:itc appears to be a resonance due t o the spin-orbit interaction, a conclusion which is difficult t o verify with ARP spectra2' showing two well-separated features (one surface and one 1~111;) ;it :I

II per pe ntli cii I;ir mom en t a. Recent experiment al work preze n ts

11i c ;I different interpret at i o n of t t i e e I e ct I-() are structure near M o n A g ( O O p Fairly similar spectra to those reported interpreted in terms of three peaks rather than just two. There are the same surface and

'

bulk features discussed ahove in addition to ii second surFace state existing in a spin-orbit

induced gap located below the bulk continuum. This interpretation also suggests ; i n anomalously small bulk band width. To date, calculations for this surfacex2 do n o t really solve this enigma, since these are only scalar relativistic. Moreover, they tend to overestimate the splitting o f the surface hand from the hulk by a factor of 2-3, and predict one 01more lower lying surface resonances which are not experimentally observed. Firrtheitheoretical input will be required to solve this discrepancy in the interpretation. 2.3

Surface State Linewidths and LineshaDes The observed peak widths in ARP spectra are normally attributed to lifetimc broadening o f the final hole and electron states.56,83-86 These lifetimes and their relation t o peak widths are of fundamental interest because they determine things such ;is enel-gy resolution of electron and optical spectroscopies, in addition to the momentum resoliltion 0 1 ARP. Simple phenomenological models based on a direct-transition model (see chapter 2 ) relate the final state lifetimes to the observed ARP linewidths. It happens that these broadening phenomena are particularly simple in the case of an intrinsically 2D state such ;IS a surface state.

For example, in the case of emission normal to the surface, the peak witltti i s

predicted t o be83

120

c

A

+65

BINDING ENERGY (eV)

Fig. 14 High resolution photoemission spectra of the zone-center Cu( 1 1 1) s u r f x e state ; I S ;I function of k 11. Note the anomalous increasing linewidth f o r decreasing hindin, enel-?! ( f r o m Ref. 49). I'

\vhei.e rll and re are the final state hole and electron inverse lifetimes, and vll ;tiid vc :trc thc corresponding hand velocities normal to the surface. For a two-cliniensional st;itc, vjl i \ necessarily zero and r = rh.83 The final state hole decays primarily by Iioiii-~i~li~ili\,~~ Auger-like processes, the phase space for which goes to zero for state near EF. We t l i t i h ciii I)reclict that a surface band crossing EF should have zero fiinclamental w i d ~ h . .Jlii\ pi-ediction is qualit;Ltively observed for the Tamrn states observed on Cu(00I) : i n d CII( I I I ) . I n this case, the states lie energetically above the d-band, and only a ~iii;iIl tlc.ii.;iLy 1 1 1 t'lectrons at higher energy in the sp-band are available to fill the pliotohole. Thiis ;I VCI-! narrow photoemission feature is observedz3~s5-s9~74,81 Even though the relationship expressed by Eq. 4 is significantly modified foi- eniisrioii

angles away from the surface normal,87 the conclusion concerning the vanishing lincn4tltli for ;I surface state crossing EF remains valid. In recent years, sufficient esperiiiieiit:il resolution has become available to test the limits of validity of this prediction. T h i s \\':I\ clonc some time ago for the sp-like surface state on Cu( 1 ll).40188 A sampling of rlit'se d ; i r : i i i sho\vn i n Fig. 14. The surface state (observed to be dotibled clue 1 0 the use 01' a i l .+\II

121

resonance lamp) exhibits parabolic dispersion about the zone center. The Iiypot Iic5is concerning vanishing linewidth as the surface state crosses EF is clearly observed n o t to Iic valid. The anomalous broadening was attributed to surface imperfections, a fact whicli n ~ 1 5 later used to study deviations from perfection more s y s t e m a t i ~ a l l y . More ~ ~ ~ ~sigiiific:iiit ~ and more fundamental deviations from the simple lifetime model are observed foi- (1-1 ikc surface states near EF on transition metals. Recent results on surface localized state\ o i i W(O1 1) and Mo(O1 for example, invoked broadening via cre:ition of phonon5 eitlicr during o r after the excitation event.

Sorface Resonant Levels Surface resonances present a particularly interesting problem which impacts dii*crw areas of surface physics and chemistry. There are at present no general models whicli give intuition about when a surface resonance will exist or what its properties might he. I n addition, resonances are not well-described by most first-principles ci)iiil)tit;itioii:il techniques since these utilize slabs having a finite number of layers 10 mimic the I ~ i l kiii ;I tr;ici;ihle way. We note that the simple phase model presented in a I;iter chapter t o IircdicI the energies of image-potential states has been adapted successfully to predict ;in sp-surf:ice rcsonance on C L I ( O O ~ ) This . ~ ~ model is not generally applicable in more complic:itctl situtions. Recently, an embedding technique developed some time ago95 to ;illow ;I s1;iIi IO be appended to a semi-infinite bulk crystal has become both popular and c~)i~ii~tit~ttioii:ill! ~ n a n a g e a b l e . ~The ~ ' ~future ~ promises a more complete theoretical treatment of 511 rl;ic.c resonances. As explained i n Sec. 1.1, a surface resonance should be entliwecl with :I i - c v ) i i : i i i L ' L ' lifetime corresponding t o the tunneling rate out of the quasidiscreet level and i n t o thc h ~ i l l i coiitiiiiium. This resonance width has been the subject of much attention for :icIsorptioii systems a s it forms the physical basis for c h e m i s ~ r p t i o n . ~ ~ - ' ~The ' ' study of intrinhic ~tirl':icc resonances from this point o f view is also of interest since the tunneling is :I tlyn:imic;il phenomenon which determines surface-bulk charge transfer rates and surface dipole 1:iyciformation. As explained in the introduction, experimental studies of surf'ice resonances arc essentially identical to sttidies of intrinsic surface states. One often applies the 5'1llle rc51\ I0 ascertain surface character, albeit with less certainty due t o the mixed 2D-3D chai-;ictcr ill' :I hiirface resonance. I t is likely that many features that have been called states are actually riioi-e prcci\cly I:ihelled resonances. On semiconductor surfaces, for example, surface features are i1orm:illy c;~lIcdsurface states even though these often lie outside the absolute band gap. A siii-f:icc stare lying in a symmetry-projected band gap will often be weakly coupled to the coritiniiiiiii via the spin-orbit interaction (see Sec. 2.2). In these cases, the distinction is norimlly I I O I important since the resonant coupling t o bulk states is small, anti the wave-funelion i t essentially 2D in character. A more interesting case is offered by recent results on the much-stucliecl ('ii(00 I ) A reasonably well-defined feature was observed in the miclclle of the s u r I ' ~ i c c wrface.

2.4

L

122

Ta(Ol1)

4

hv=40eV

2

A

EF

Binding Energy (eV) 1.0

0.4

0.8

Parallel Momentum

1.2

(Ad')

Fig. lS a ) bottom: Surface energy bands and projected bulk bands in the A mirror plane of Ta(0l I). Solid circles indicate the band exhibiting surface characteristics and demoiistr;ite the surface-bulk "avoided crossing". The corresponding surface feature linewiclth ;IS ;I function of kll is shown in the top panel. b) Sampling of the coresponding A R P spectra. 131-illoiiinzone which obeyed all the criteria to be labelled a surface m t e . However. no y:ip exists in the experimentally-measured bulk copper band structure, and t h u s this 5i;itc appears to be a surface resonance which is approximately predicted by calculations.-’I A novel way to study surface resonant coupling using ARP is t o observe ilie S I ; I I C resonance transition, since it can then be isolated from other types of broadeniiiy mechanisms. While this is not possible for most types of resonances, it often occurs i i i ilic' case of a surface resonance since a surface band dispersion relation located in ii pro.jcctctl gap must eventually cross into ;I projected continuum. This is demonstrated by recent rewlt\ on Ta(Oll)." As shown in Fig. 1%. on this surface there is a large projected gap :it i l i c center of the SBZ which pinches off in both symmetry azimuths. The gap supports :I surfacc st:ite o n both t h e clean and hydrogen-covered snrfaces, similar to that described for Ti(000 1 ) in Sec. 3.2. The surface bands milst disperse into the continuum somewhere in the Brillouin zone, thereby becoming resonances. The ARP spectra shown i n Fig. 1Sb exhil3it ;I

123

phenonienon which is approximately described an avoided crossing between S L I r h c e ; i i i O bulk bands at a klI value of 0.3-0.4 A-1.78 The surface band acquires the btilk char;ictcr. while at the same time the bulk band becomes the surface resonance. The resonance is 0.5 eV broader than the state (Fig. 15a, top panel). An important implication of these results is that the terms surface state, bulk state, and surface resonance become ambiguous when the energies of these features are similar at a given momentum. 3.

SELECTED TOPICS IN SURFACE STATES ON METALS

The application of ARP to study surface states o n simple metal surfaces is now wellestablished, and useful information can be attained in a routine fashion. This is howevcr :iii active field with several trends of current and future interest. We review a few of tlicsc iii this section. Surface States and Surface Dvnamical ProDerties Surface states are unusual in the sense that they are truly two-dimensional in iiatiiiw. I t is therefore natural to ask whether the variety of interesting physical phenomena ohscr\,ctl in low-dimensional systems might not also occur at surfaces and be driven hy the two-

3.1

dimensionality of surface bands. For example, the integral and fractional qu:liittiii1 1-l;iIl effects observed in semiconductor inversion layers and heterostructures result front tlic formation of quantized Landau levels in a 2D electron gas. The higher level o f degeneracy and also the increased importance of correlation and many-body effects might l e a d to ;I higher level of complexity and possibly to the observation of new physical phenomena :II metal surfaces. The ongoing interest in thin-film superconductivity also suggests interesting surface analogs. Some of these experiments will ultimately be limited only by o t ~ :tI>ili[y r I(, procluce surfaces with a high degree of perfection. Phenomena in which lowered dimensionality plays a key role often involve electronic screening and the generalized wave vector(q)- and frequency(w)- dependent elect roiiic susceptibility, X(q,w). In the random phase approximation, xo(q,w), the bare susceptiliility takes the formZo3

where f(k) and t(k) are the Fermi factor and band energy at wave vector k. l ' h i > electronic susceptibility must be normalized by the electronic self-energy ~ ( w (zee ) chapter 3) in order to treat shorter-range phenomena, so that x(q,w) = xo(q,w)/[l- C ( W ) x " ( ( I , w ) ] . Eq. 5 suggests that x"(q,w) may be singular, and these singularities translate into instatiilitie5 of some sort. Since ARP measures the energy bands of occupied states, in principle useful information about electronic screening can be extracted. The Fermi factors in the numerator of Eq. 5 require the creation of an electron-holc pairs with wave vector q. At small w , xo(q,w) can exhibit an anomaly when the h i 1 d energies at k and k + q are similar, i.e., they must both be near the Fermi Icvel: - I ' I t t h:ri.tS

124

Fig. 16 Surface Fermi contours for clean and hydrogen-covered W(O11). The s h x l c d regions is the projection of the experimental bulk Fermi surface onto the surface Brilloiiiri zone (from Ref. 90). functional form of the resulting xo(q,w) is strongly dependent on dimensionality. Foiexample, integration of Eq. 5 for a 3 D free electron gas yields a mild logarithmic singtihrity in slope in x"(q,w) at q = 2 k ~ This . becomes a discontinuity in slope in two dimensions aiid ;I singularity in the magnitude of xo(q,w) in one dimension. In bulk systems, this scrce1)ilig often is manifested by unusual anomalies observed in the dispersion relations for low-energy elementary excitations which indicate dynamical coupling with the electron gas. I n sevcrc cases, these anomalies "freeze in" and the lattice reconstructs, as in the Peierls-like ch:irgedensity-wave distortions observed, for example, in quasi-1D and -2D metals,104 or ii spindensity wave is formed, as, for example, in bulk chromium.105 3.1.1

Fermi surface of clean and hydrogen covered W(110)

An important feature of phenomena observed in low-dimensional systems is th:t1 tlicy

occur o n an energy scale which is very small compared to the occupied electronic 1x1110 nklili of the systems under consideration. Thus while the bulk of ARP studies to date have explored all the occupied levels near a surface, generally only those very close to the I-erini level can have a very pronounced impact on the subtle effects associated with Iowet-ed dimensionality. For this reason, there has recently been increasing interest in careful measurements of surface bands in the vicinity of the Fermi level. Bulk three dimensional Fermi surfaces are commonly determined by de Haas van Alphen or related meiisureiiiciits. Unfortunately these bulk-sensitive methods cannot be readily applied t o the deterinii1:ttion of ;I 2D Fermi surface at a surface o r interface. ARP can be used to determine [lie I-crmi

125

Work Function Change (mev)

0

W(0ll)

-

A

+H

bQ,

J 1

11-1 L

Y

a

0.0

0.2

0.4

0.6

Hydrogen Coverage (rnonolayers) Fig. 17 Change in Ferrni wave vector, along the line A in Fig. 16, with hydrogen co\era::c the corresponding work function change. Note the change in slope at recoiistrtictioii (from Ref. 90).

iind

level crossings o f the various bands with reasonable precision and thus to map out the Feriiii surface throughout the SBZ. As an example we show here in Fig. 16 the data of Gaylord et al.oO for the L w t ) dimensional surface Ferrni surface of clean and hydrogen saturated W( 110). The datn poinls show the Fermi level crossings of surface states and resonances throughout the S I C superimposed onto the projections of the bulk Fermi surface.lo6 The clean surface has Iwtli electron and hole orbits. An electron orbit centered around C extends across the first S I X boundary line P-H and surrounds the projection of the bulk electron jack. Three different hole orbits are observed; one is centered around C and the other ones are found at the SI%% boundaries, one along the line P-N-P and the second one along the line P-H. C)iily lllc electron orbit and the last mentioned hole orbit are true surface states, located in ;I gap of the projected bulk bands. The other features are surface resonances embedclecl i n l o tlic projected bulk states. These data suggest unusual behavior of the bare susceptibility. Neglecting rii:ltrix element effects, anomalies appear in integrating Eq. 5 when segments of the Ferrni surt'ace have parallel tangents, and are most severe when the curvatures are similar. For e x a n i l k the sections of the electron orbit along the lines A and R can be strongly coupled t o thc nearby segments of the hole orbit centered at N. This might appear as a Kohn anoinaly i n the surface phonon dispersion relations.'07 Hydrogen chemisorption rapidly attenuates the hole-orbit states. The electroiiorbit state shifts to higher binding energy, resulting in expansion of the Fernii surface. Ultimately the Fermi surfaces in two neighboring SBZs contact each other at the sharp points near H in Fig. 16. This results in the appearance of two hole orbits observed along the P-N-P and P-H lines.

126 I

.

.

.

.

,

.

.

.

.

.

.

.

.

.

.

.

.

.

.

1.1 1 1-01 0.92 0.82

n

W

W

Z

3

1 EF=O Binding Energy (eV)

2

0.76 0.70 0.64 0.54 0.44 0.38 0.31 0.24 0.17 0

Fig. 18 Photoemission spectra of W(00l)jn the E azimuth as a function of k 11. The nondispersive band near EF for k / / - 0.5 A' was suggested to drive the ~ ( 2 x 2 )reconstrucrion (from Ref. 80). Recently this surface has been observed to reconstruct upon adsorbing >0.5 monolayers of hydrogen.lo8 It is observed that the change in magnitude of the stirI';ice Fermi wave vector is approximately linear with hydrogen coverage, with a change in slope near half monolayer coverage, as plotted in Fig. 17. This smooth shift with changing i n coverage is also observed for the surface states observed on Ni(ll1) and P d ( l l 1 ) discussed below. One might speculate that the reconstruction is related to the change of morphology ;issociated with the merging of neighboring Fermi surfaces. However the merging occurs at ;I milch smaller coverage of about 0.2 to 0.3 ML. Thus there seems to be no direct connection between the change in Fermi surface morphology and the geoirierric reconstruction of this surface. This is supported by the observation that Mo(Ol1). which does not reconstruct.109 exhibits similar 2D Fermi surface behavior.92 3.1.2 Clean surface reconstruction of W(OO1)

In 1978, Tossatti suggested that the surface reconstruction of W(001) might be driven hy ii Peierls-like instability o f the electron gas,'" similar to the one operative iii layered quasi-2D transition metal dichalcogenides. lo4 This suggestion, which enjoyed signil'ic:inr popularity for a time, was largely rejected in favor of a tocat driving meclianisrn. 1 - 1 1'.

''

127

-1

.o

0

1 .o

Fig. I0 Surface Fermi contours for clean W(001). The shaded region centered along the L: mirror plane reflects the extent o f the non-dispersive band in Fig. 18 (from Ref. 80). Indeed, an early Fermi surface determination indicated insufficient nesting to support ;I charge-density-wave type of mechanism. A recent calculation for Mo(001). howevei-. suggests that Fermi surface nesting may play an important if not determining role in driving the slightly incommensurate reconstruction observed on that surface.l l 5 An incommensurate structure is difficult to explain within a model based purely upon local bonding considerations. It is unlikely that completely different mechanisms are operative O I I two otherwise so similar surfaces. Indeed, recent atom diffraction results o n W(O0 I ) sugge\t the existence of an incommensurate phase on that surface above room temperature,' " although these results contradict all existing electron and x-ray diffraction data.' 18-120 A more recent 2 D Fermi surface determination on W(001) is at odds with the previous work, and suggestive of the apparently delicate interplay between localized aiid delocalized mechanisms.80 A sampling of the ARP spectra from that study i n the relevant C azimuth is shown in Fig. 18. Near EF, these exhibit a surface band which begins with the intense Swanson hump feature near the zone center (kll = 0.0 A-’), disperses tow;ircI I N I does n o t cross EF, and then disperses away from EF before reversing direction i i i i c l ci-ossiiig near the M symmetry point. The resulting Fermi surface is shown in Fig. 19. The crossiry near M forms a well-defined hole pocket similar to that observed on W(O11). Tlie size of this pocket i s considerably over-estimated by all existing c a l c ~ ~ l a t i o n This s . ~ is~ due ~ ~ ~ ~ ~ ~ ~ i n part to the influence of the spin-orbit interaction along c, where odd and even projected gaps overlap significantly (see Sec. 2.2). The shaded region in Fig. 19 indicates the region of "3’

128

k-space where the surface band is too close to the Fermi level to be measured accurately. A vector connecting shaded regions on opposite sides of the SBZ (i.e., q = 2 k ~ is ) slightly incommensurate with the lattice and is in rough accord with the periodicity seen in the atom diffraction measurements. This delocalized, CDW-like driving force is actually not incompatible with the local mechanism, since the coupling occurs over a large portion of kspace and is thus in some sense localized. These results suggest further first-principles computations are in order to understand these W(OO1) and Mo(001) reconstructions comp I e t ely. 3.1.3 Non-adiabatic surface interactions The adiabatic or Born-Oppenheimer approximation, which implies the separability of

electronic and nuclear wave functions, is always suspect in metallic systems where electronic excitation energies extend to zero energy. Superconductivity is perhaps the most dramatic manifestation of the breakdown of adiabaticity. The interactions described in the previous section provide good examples as well. The general importance of non-adiabaticity cannot he over-stated: breaking or making a chemical bond is in some sense a non-;idi;ilxitic process. We anticipate that non-adiabaticity plays an important role i n a variety of surf:icc. processes including transport, chemistry, ion neutralization, etc.

W(OO1): h v = 4 2 eV, A Ira

n

w

U

z

~~

1

4 3 2 1 EF=O Binding Energy (eV)

Fig. 20 Photoemission spectra of clean (dashed curve) and hydrogen-covered (solid curve) W(OO1) demonstrating the existence of a H-induced feature near EF near X (from Ref. 114).

129

The criterion for the breakdown of adiabaticity is the existence of a significant density of electrons (or pairs of electrons in the case of superconductivity) with a velocity which is comparable to nuclear velocities, at an energy close to EF. The flat band near EF observetl on W(OO1) is a good candidate, and a subtle interaction between electronic and static and dynamic geometrical structures results. Adsorbate vibrations can also be damped non-adiabatically when there is ;i 1;ri-g~ density of surface-localized electrons near EF. The first direct observation of this phenomenon was in a surface infrared reflection-absorption study of W(001)-2H which observed an asymmetric adsorbate vibrational mode, characteristic of a discrete oscillator (the vibration) coupled non-adiabatically to a continuum (the electron-hole pair spectr~rn).A ~ ~narrow ~ ? ~ band ~ ~ of adsorbate-induced surface states was predicted to exist near EF. A recent ARP study has detected such a band, as shown in Fig. 20.124 'I'he symmetry of the band suggested a reassignment of the adsorbate vibration. This sysccni provides an excellent example of how ARP can engage in a useful interplay with otlieilower-energy surface probes. The existence of such adsorbate-induced bands appears n o t 10 be too uncommon; recent results for W(OOl)-tC, Mo(OOl)+H, and W(OIl)+K, W ( O 1 I ) t 0% Mo(Ol1) t 0 indicate similar phenomena occur on those surfaces. The Crud Test Revisited: Hydrogen ChemisorDtion 3.2 An important and growing application of the ARP technique to surface states on inet:il\ amounts to a careful application of the "crud test" (Sec 1.2). Any adsorbate on a surkrcc does not remove all charge from the surface region, as the crud test implies, but rather l l i e surfrice states of the adsorbate-covered surface are located in different areas of energy/momentum space than the electronic states of the clean surface. In principle, using ARP we can study formation of the chemisorption bond, momentum by momentum. While recent efforts studying the interaction between electronegative and electropositive adsorbctl atoms and the underlying surface bands appear promising,543125-127 by far the most w o r k iii this area has been done on hydrogen chemisorption. The results for tungsten and molybdenum surfaces reviewed in the last section are one example of this type of study. Hydrogen atoms, having only one 1s electron, are by definition the simplest chernisorption system. Therefore, various theoretical approaches have been tested on thi. model chemisorption system. These theoretical descriptions range from extensions of (lie Newns-Anderson impurity to quantum chemical methods128 on one hand to solid state band structure calculation^^^^^^^^^^^ and the jellium description of the substratc o i l the other hand.131-135 By their nature each of these models will emphasize a difl'ereiit aspect of the adatom substrate interactions. Some describe the adsorbate substrate bond :is ;Ldirected chemical bond128 or interactions with specific surface states24i129,130 wherca\ other^'^'-'^^ have the interaction delocalized because of the delocalized nature of !lie substrate. The study of hydrogen interaction with metals is not only of interest as a model system for chemisorption but it also has many practical applications. The role o f

130

chemisorbed hydrogen in heterogeneous catalysis is obviously very important h u t nevertheless far from being understood. In materials science, the formation and properties of metal hydrides as well as hydrogen embrittlement of steel and other structural materials are important research areas. This also extends to the application of transition metals ;IS hydrogen storage elements. With the possibilities and well known environmental advantages of a hydrogen based energy economy these technological aspects of the interaction of hydrogen with metals will become even more important in the future. The study of the electronic structure of hydrogen on metal surfaces by ARP largely deals with the changes induced in the surface electronic structure rather than with extrinsic molecular or atomic electronic levels. Hydrogen is dissociated upon chemisorption and exhibits only a very weak Is electron derived band-like state. This is in contrast to other chemisorption systems like CO or NO having quite strong bands derived from the molecular electronic states which often are non-degenerate with substrate electronic states. 3.2.1 Hydrogen saturated surfaces Because of the somewhat elusive character of the hydrogen induced changes i n the surface electronic structure some of the initial attempts to determine the electronic structure

of a hydrogen covered metal surface failed. The first successful studies of this kind we1-r perfommed on H on Ti(OOOl)136 and for H on N i ( l l l ) , P d ( l l l ) , and Pt(ll1) surfaces."" The latter work dealt especially with the phenomenon that the hydrogen induced states on these surfaces could only be clearly detected at low temperatures near 100 K. Room temperature adsorption resulted in no or rather small changes in the surface electronic structure, even though hydrogen was definitely chemisorbed as evident from thermal desorption spectra and a change in work function of the surfaces, Fig. 21 shows the normal emission spectrum for hydrogen on Ti(0001) compared to the emission of the clean surface.136 The peak at EF in the spectrum of the clean surface is quenched by hydrogen adsorption and corresponds to the emission of the surface state of the clean surface. The hydrogen covered surface exhibits a hydrogen 1s derived band at 6.9 eV below EF and another strong emission feature at 1.3 e V below EF. These two features at r correspond in the simplest possible explanation to the bonding-antibonding level combination for the hydrogen chemisorption bond. The bonding state exhibits a Is1 dispersion with a band width of 2.4 eV, whereas the antibonding state is essentially tlat in dispersion but exists only about halfway into the SBZ, not quite to the point where the g;ip iii the projected band structure ceases to exist129 (see Sec. 2.4). The bonding split-off state has hydrogen Is character with a strong admixture of metal 3d-character, whereas the antibonding state originates mostly from the surface state of the clean surface shifted by the interaction with the hydrogen atoms. For hydrogen on Pd( 111) the picture is slightly more complicated because this surface has more intrinsic surface states. These states are shifted by the chemisorption of hydrogen even though they might not be directly involved in the chemisorption bond. Fig. 22 shows ;I plot of the SBZ projected band structure of Pd(ll1) with and without hydrogen. The

131 l

l

i

l

l

~

l7

j

NORMAL EMISSION AREDC f i w = 2 2 eV

-Ti(0001l-H(1x1) ---- Ti (0001l

n

S,p I

I

- POLARIZATION I

I

I

1

I

1

I

-5

1 I'

a

I N I T I A L ENERGY ( e V 1 Fig. 21 Photoemission spectra of clean and hydrogen-covered Ti(0001) exhibiting the bonding and antibonding states in hydrogen chemisorption (from Ref. 129). experimental data points137 are compared to the calculated surface states ( s o l i t l The agreement throughout most of the SBZ between theory and experiment is rather good, except near the M point of the SBZ, where some minor discrepancies are observed. This has been discussed in more detail e 1 ~ e w h e r e . l The ~ ~ hydrogen Is derived band is again split off from the bottom of the bulk sp-band and all the surface states of tlic clean surface are shifted to higher binding energies when hydrogen is chemisorbecl. ' I l i e cross section and the coverage dependent studies discussed below are strong evidence f o r ;I large substrate 4d admixture in the H 1s derived band. The surface state on Pd( 11 1). which i\ equivalent to the antibonding state found for the Ti(OOO1) surface, is unoccupiecl on Pd( I I I ) arid thus is located above EF. The existence of this state, at least on the clean sirrf;.ice, has been verified by inverse p h o t o e m i ~ s i o n . ~ ~The ~ , ' comparison ~~ between experiment a n d theory points toward the threefold hollow position as the hydrogen adsorption site o n this surface, but no definite distinction can be made as to whether the hydrogen atoms are located in the fcc o r hcp hollow sites. This whole research area of hydrogen chemisorption on metals is a very nice example demonstrating how a positive interaction between theory and experiment can stimulate research in both directions. In the first round, comparing the ARP1367137 results shown i n Fig. 21 and Fig. 22 with state of the art electronic structure calculation^'^^^^^^ it became obvious that, even though most of the possible adsorbate structures could be ruled out. based upon the spectroscopic information alone the adsorbate geometry coiild not bc uniquely determined. This was somewhat disappointing because these were quite extensive data sets, where a lot of work had been put into both theory and experiment. The principal

132

(a)

CLEAN P d ( l l t ) SURFACE STATES

(b)

H, ADSORPTION 0 - I -2 - 3

E,

- 4

- 5

I

I

n i i

I

r

1

w

P

Fig. 22 Surface band dispersion curves and projected bulk continuum in the mirrorsymmetry planes for clean and hydrogen-covered Pd(1ll) (from Refs. 128 and 129).

question, which still remains to b e answered even as of today, is how well theory and experiment should be expected to agree with each other. Assuming that the experiment really tells us what nature is about (see Chapters 2 and 31, we have to be concerned niostly about the theory. These calculations are of the highest quality, but nevertheless conlain certain approximations, mainly with respect to the treatment of exchange and correlation. Also both calculation^^^^^^^^ use special but different sets of Gaussian wave functions to describe the charge distribution in the surface region. This is done fully self-consistently l l u t nevertheless the degree of localization of the surface states seems to depend on t h e Ixisk sets used in these theoretical schemes. three to f o u r For H on Ti(OOO1) there were, according to Feibelman et "sl.'ectroscopicaIly acceptable" adsorption geometries which all produced about the sanw electronic structure, characterized by the split off hydrogen 1s derived band ant1 the antibonding state at -1.3 e V derived from interaction of the intrinsic surface state with the

133

hydrogen atoms. Possibly this choice could be narrowed down somewhat by requiring niore stringent agreement between theory and experiment, as discussed in Ref. 5 but there is still n o unique solution for the adsorbate structure based upon the spectroscopy alone. Including into the calculations a scheme to evaluate the total energy of the system and thus to further determine the heat of adsorption for the hydrogen atom let Feibelman e t narrow down the choice for the adsorption sites of H on Ti(OOO1) to propose the "long bond length fcc" surface site as the most likely adsorbate geometry. As already mentioned atlove in the equivalent studies of hydrogen chemisorption on Pd(l1 1)138 the results point toward hydrogen chemisorption in the three fold hollow site on the surface, where the question remains open, whether the hcp or fcc surface site should be favored. Recent total energy calculations for hydrogen chemisorption on R u ( O O O ~ find ) ~ ~ that ~ the fcc site is abotit 0. I eV lower in energy per hydrogen atom and thus should be favored on that surface. 3.2.2 Coverage-dependent studies The most puzzling result of the early studies was the existence of an "invisihle" hydrogen adsorption phase corresponding to saturation coverage at room temperature.137s138 Hydrogen is clearly present on these surfaces under these conditions, with a coverage equivalent to approximately 0.5 saturation coverage at 90 K for Ni(l1 I ) and 0.3 for Pd( 111), as evident by thermal desorption and nuclear m i c r ~ a n a l y s i s . ~ ~ ~ ~ ~ Absolute coverage studies using the latter143 found that for D on Pt(ll1) at 300K and 5 . 5 ~ 1 0 'Pa ~ the coverage is o = 0.15 monolayer, substantially less than previously estimated. Nevertheless, apart from a work function change this room temperature adsorption state is spectroscopically almost "invisible". This applies not only to photoemission studies, but to low energy electron energy loss vibrational spectroscopy as well.144

I

I

- 10

I

I

I

I

I

-5 E - E,(eV)

I

I

I

I

I

0

Fig. 23 Normal emission ARP spectra of Pd( 111) as a function of hydrogen coverage ( f r o m

Ref. 46).

134 Pd(l11) + Ht

K Surface Stales

- 6.0

1

H 1s s p on ~ State at

r

50

100%

50%

OW

H, Coverage

Fig. 24 Summary of results for coverage-dependent hydrogen adsorption on Pd(ll1). Upper panels show the energies of surface bands, while the bottom panel shows the work function change. The angle resolved photoemission data on Ni, Pd, and Pt(ll1) discussed abow were taken for saturation coverage at low temperatures (90K). This coverage corresponds 10 the adsorption of one monolayer of hydrogen atoms. Therefore it is not surprising, that t h e H induced split off band exhibits a (1x1) dispersion. For a coverage less than oiic monolayer, down to about 0.5 on Ni(ll1) or 0.3 on Pd(ll1) the hydrogen induced changes i n the surface electronic structure are still visible. At the lower coverages the total band width of the H 1s split-off state is reduced, but somewhat unexpectedly this band still exhibits ;I (1x1) periodicity with the substrate in its d i ~ p e r s i o n .At ~ ~the same time a continuous shift of the intrinsic surface states back toward the position of the clean surface has been observed. This is illustrated in Fig. 23 and Fig. 24. Fig. 23 shows normal emission AREDC'\ of hydrogen on Pd( 111) as a function of hydrogen coverage. The results for all the surfx.t. features of this surface are summarized in Fig. 24 as a function of hydrogen coverage. The reduced width of the split-off state together with the continuous shift of the intrinsic surface states cause us to rule out the formation of adsorbate islands as explanation for the (1s I ) dispersion of the split-off band. This is also consistent with the large H-H repulsion fourid for the adsorbed Thus the (1x1) periodicity can only be explained I)!

135

the large admixture of substrate d-character as suggested by the theoretical analysis of the orbital content in this state.130,137 Both at the zone center and at the zone boundary this state is largely characterized by substrate d-states "pulled down" by the presence of the Hatoms on the surface. This also causes the relatively large cross section of this state compared to the emission of the substrate sp-band, which is barely visible in the spectra. This substrate d admixture to the H Is split-off band also causes the difference in the band width between the P d ( l l 1 ) and Ni(ll1) surfaces. The band width of the H induced band on Ni is about twice as large (4.2 eV) as on Pd ( 2 eV), which cannot be solely explained by the 10% decrease in lattice constant between Pd and Ni. Moreover, an isolated monolayer of H-atoms in the correct spacing to match the P d ( l l 1 ) surface has a calculated band width of 4 eV,145 or twice the actually measured band width for H on Pd(ll1). Thus the width of the hydrogen Is induced band on Ni(ll1) corresponds roughly to the estimate for the monolayer, whereas the band width on Pd(ll1) is way too small. Additionally, the shape of the H induced split-off band on Pd deviates strongly from the "normal" parabolic band shape and exhibits an almost flat dispersion from the halfway point to the zone boundary. The explanation for both, the unusual dispersion and small band width of H on Pd( 111) lies in the interaction with the Pd d electrons. At the zone boundary the location of the split off state is largely determined by the energy of the bulk substrate d-bands and the surface component split off the bottom of these bands. The exact nature of the H adsorbate layer for sub-monolayer coverage is still a mystery. We have reconciled the observation of a (1x1) periodicity in the H induced band by the strong admixture of substrate d-states and ruled out island formation because of the continuous, almost linear shift of the intrinsic surface states with coverage and t h e strong repulsion between adsorbed hydrogen atoms. Whether the H-atoms actually form a kind of delocalized lattice gas,147 where the average distance varies with concentration, or whether the atoms are adsorbed in fixed threefold hollow positions with a random distribution of vacancies is as yet unresolved. Also, because of the strong repulsion between the H-atoms they could move into a subsurface p ~ s i t i o n , ' ~which ~ , ~ ~for ~ both Ni(111)138 and R u ( O O ~ ) ~is~ calculated ' to have a lower binding energy. Thus these sites would not be occupied without some further stimulation. Moreover, the subsurface hydrogen is supposed to change the symmetry of the surface state near EF at the center of the SBZ.I4' We have experimentally checked the symmetry of this state and did not observe a change in symmetry at low hydrogen coverages46 The latest turn in the mutual stimulation between theory and experiment are the calculations by M.Y. Chou and J.R. Chelikowski for hydrogen chernisorption on R U ( O O ~ ) . ~ ~ ' These total energy calculations demonstrate that for hydrogen monolayer adsorption on Ru(001) the fcc three fold hollow surface site is definitely the energetically favored adsorption site. It takes substantial energy (0.7 eV/atom) to push a hydrogen atom from this position into the subsurface site. This is illustrated by the potential energy curve shown i n the top panel of Fig. 25. However if the coverage is doubled, the hydrogen repulsion for the surface sites becomes so strong that now the energetically favored chemisorption geometry

136 -1.8

-

f

-2.2

-I r I

g

yf

s

C)

-

I

-

-2.4 -2.8

-2.8

HIRu (0001)

-I

-3.2’.

I

I

I

I

-1

0

I

I

I

I

-0.8

I: -1.4 -1.6 -1.1)

-3

-2

1

2

3

Poaitlon of Hydrogen Atom (0.u.)

Fig. 25 Potential energy curve for hydrogen motion perpendicular to the surface layers of Ru(0001), at one (a) and two (b) monolayer coverages (from Ref. 141). has half the adsorbed hydrogen atoms occupy the octahedral subsurface sites just below the fcc surface sites, where the other half of the adsorbed hydrogen atoms are located. Thus for the complete monolayer the chemisorbed surface atoms provide an attractive force for adsorption in the subsurface positions, as indicated by the potential energy curve in the bottom panel of Fig. 25. This model does not contradict the general observations about the sequential filling and depletion of these sites. Since the subsurface site becomes favorable for adsorption only after completion of the first surface layer of hydrogen atoms, in adsorption the surface sites still are occupied first. On the other hand in thermal desorption the surface hydrogen atoms are expected to be removed first, but as soon as the surface site is unoccupied, the chemisorption in the connected subsurface site is energetically less favorable such that this hydrogen atom will move into the vacated surface site. Thus de fact0 in desorption the subsurface layer gets depleted first. 3.2.3 The hydrogen dissociation mechanism All hydrogen chemisorption studies described above implicitly assume that the hydrogen molecule is dissociated upon contact with the metal surface and then chemisorbed as two independent hydrogen atoms. This assumption is verified experimentally by the complete isotope sdrambling of an H2/D2 mixture upon desorption. In this context, it is of special interest that the bond strength of hydrogen atoms and the desorption temperature on Cu and Ni surfaces are quite but Cu does not dissociate the H7, molecules.

137 I

~

NI / C u 11111

I

~

I

~

hv = 9.5 eV

INiIlll) hv:95eV

/II

k,,=O

il I .J I

E,=O

2

I

I

L

Energy above E,

I

I

,

6 lev1

1

E,=O

1

1

,

1

1

1

1

2

L 6 Energy above E, lev1

Fig. 26 Inverse photoemission spectra at normal electron incidence for clean and nickelcovered copper (left), and clean and copper-covered nickel (right). The difference between these two surfaces is in the existence of a dissociation harrier oil Cu(ll1). The height of this dissociation barrier has been experimentally determined i n H 2 scattering experimentslS1 to be 3-5 kcal/mole. Hydrogen permeation studies give an even higher value for this barrier152 from the analysis of the desorption velocity and angular profile, which might be due to direct desorption from a subsurface bound state. While there were different theoretical models proposed explaining the nature of this dissociation barrier1s3-156 experimentally the possible electronic origin of this barrier was only recently explored by studies of the modification of electronic structure of Cu( 11 1) a n d N i ( l l 1 ) surfaces by adsorption of epitaxial monolayers of Ni or Cu, respe~tively.'~' The

model presented by Harris and Andersson,lS6 was essentially confirmed by these experiments. I n this model the main interaction between the H2 molecule and the surface is through the sp-electrons. On both surfaces these s electrons must orthogonalize to the ug orbital of the approaching H2 molecule. On Cu this can only be accomplished by shifting the s electrons up in energy and therefore this leads to a considerable activation barrier. On the Ni surface on the other hand, the d-holes at the Fermi surface may serve as sink for the metal s electrons through a change in s-d hybridization, which costs much less energy. This model is very similar in its nature but not its language to the quantum chemical approach taken bv t ~ p t 0 n . l ~ In ' this description a large density of states near EF allows the substrate

138

orbitals to adjust to the approaching H2 molecule and maximize bonding interaction, while minimizing Pauli repulsion between the states. The presence of d-holes in the electronic structure of a monolayer of Ni o n Cu(ll1) is demonstrated by the left panel of Fig. 26. The bottom curve shows the inverse photoemission spectrum of the C u ( l l 1 ) surface under normal incidence of the electrons. This curve shows a step like rise at the Fermi level EF and a peak at 4.25 eV assigned to an image potential state. Upon deposition of a pseudomorphic monolayer of Ni onto this surface, the top curve is obtained, which is dominated by a large peak at EF. The persistence of the image potential state near 4.2 eV is evidence for a well ordered surface. Measurements of the dispersion of the hole states near EF show that the hole states extend only over a small region of momentum space near the center of the SBZ. The well known surface state on C u ( l l 1 ) still exists on this composite surface without any noticeable change in dispersion. This modified surface is able to dissociate hydrogen, whereas the bare Cu(ll1) surface does not. Upon hydrogen chemisorption the hole state emission is strongly attenuated. Combining these inverse photoemission studies with angle resolved photoemission experiments on the same surface systems Frank et al.157 find that the total density of states at EF for the composite surface is not much larger than for the clean Cu surface, since these holes are only present within a small fraction of the two dimensional SBZ. On the other hand, deposition of a monolayer of Cu, which also grows pseudomorphically on Ni( 11l), causes hardly any change in the inverse photoemission spectrum. This system displays the equivalent d-holes, but now for a semi-infinite Ni crystal. as shown in right side of Fig. 26. However this surface does not dissociate hydrogen anymore. This indicates that the dissociation mechanism is directly related to the immediate states at the surface. The localized d-holes of the substrate do not extend far enough to have any effect on the dissociation, even though they are clearly visible in the inverse photoemission spectrum. These experiments confirm the theoretical model of the hydrogen dissociation mechanism of Harris and A n d e r ~ s o nto~ the ~ ~ extent that they show the importance of surface localized d-holes for this step. We have to add here that the attenuation of the dhole derived peak in the inverse photoemission spectrum upon hydrogen exposure of the composite Ni on Cu(ll1) surface is related to the bonding of the hydrogen atoms and not necessarily to the dissociation. Obviously the photoemission and inverse photoemission do not monitor the actual dynamic dissociation process, but only cause and effect. Nevertheless this result is another important step forward in gaining a better understanding of the interaction of hydrogen with transition metal surfaces. CONCLUSIONS AND FUTURE POSSIBILITIES I n this chapter, we have reviewed physical phenomena of interest in the area of surface electron states which exist on nominally clean metal surfaces. We began with a historical perspective of why surface states exist and what their properties might be. We 4.

139

followed with several examples of increasing sophistication, ultimately to indicate the fairly good fundamental understanding we have in this area. While the review cannot be comprehensive for such a large and active field, we have tried to capture a few of the interesting and important current trends. We now use this as a basis for speculation about what might be important research areas in the future. Obvious extensions of the current work exist in preparing and measuring novel surfaces of unusual materials and films. This is the subject of several of the following chapters, and we leave a description of the future in these areas to those chapters. Instead, we mention a few subjects of general interest in the surface chemical physics communities. Much of the unexplored frontier in this area lies in very high resolution studies. The ultimate goal is to make contact with the subtle electronic phenomena studied in other areas of surface and solid state physics. For example, the self-energy of an electron is modified by the electron-phonon interaction so as to modulate energy bands as they cross the Fermi level. This effect is also reflected in the low temperature specific heat of metals, and is ultimately related to the formation of the superconducting gap. It has not been measured t o date by ARP, primarily due to the lack of adequate energy and angle resolution and possibly of an adequately narrow photoemission feature. To do so would provide a very useful, momentum-resolved probe of the dynamical coupling between electrons and phonons. The best chance of measuring this fundamentally important phenomenon is with ARP studies of 2D metallic states, as these are intrinsically narrow. These wiggles in dispersion relations near EF can turn into gaps if the electron-phonon interaction is strong enough so that the lattice reconstructs or the system becomes superconducting. Related phenomena may he observable on magnetic systems which undergo a spin-density-wave transition. C a p anisotropy, a phenomenon of significant current interest in the high temperature superconductivity field, should b e a fairly general phenomenon which ARP is just beginning to address. The idea of the breakdown of the Born-Oppenheimer approximation also clearly linked to these high resolution experiments. With better resolution and sensitivity than currently available, we may be able to provide very concise and useful information in systems which exhibit nonadiabatic adsorbate vibrational damping. An important theme will continue to be to understand interactions between adsorbates and electrons in the vicinity of the surface. This will be increasingly important as the sophistication of surface phonon measurements improves. We have in mind extensions of the experiments reviewed i n Sec. 3.1 and 3.2 to other adsorbates which are more strongly interacting than hydrogen. The field from these adsorbates is screened by Fermi surface electrons, which in turn are scattered by the adsorbate potential. This interaction is fundamentally the source of lateral adsorbate interactions. A complete understanding of such energetically weak interactions will be important in achieving a general knowledge of surface phenomena.

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Chapter 5

SURFACE STATES ON SEMICONDUCTORS GORAN V . HANSSON AND ROGER I . G .

1

UHRBERG

INTRODUCTION

The atomic and e l e c t r o n i c s t r u c t u r e of semiconductor s u r f a c e s and i n t e r f a c e s a r e of widespread s c i e n t i f i c and t e c h n o l o g i c a l i n t e r e s t , and s t u d i e s of semiconductor s u r f a c e s have become a v e r y a c t i v e a r e a

i n t h e f i e l d of s u r f a c e s c i e n c e /l-lO/. P h o t o e l e c t r o n spectroscopy

i s t h e main t o o l f o r i n v e s t i g a t i o n s of t h e e l e c t r o n i c s t r u c t u r e of semiconductor s u r f a c e s . By t h e use of a n g l e - r e s o l v e d photoemission t h e complete s u r f a c e s t a t e band s t r u c t u r e h a s been determined f o r s e v e r a l s u r f a c e s . Due t o t h e i n t i m a t e r e l a t i o n s h i p between t h e atomic and e l e c t r o n i c s t r u c t u r e of a semiconductor s u r f a c e , it has f u r t h e r m o r e been p o s s i b l e t o use i n f o r m a t i o n about t h e s u r f a c e e l e c t r o n i c s t r u c t u r e t o draw important c o n c l u s i o n s concerning t h e atomic geometry of semiconductor s u r f a c e s /11-13/. A r i s i n g from t h e c o v a l e n t c h a r a c t e r of most semiconductors t h e r e i s a v e r y l a r g e change i n t h e e l e c t r o n i c s t r u c t u r e a s s o c i a t e d w i t h t h e b r e a k i n g of bonds i n t h e formation of a s u r f a c e . I t i s well known t h a t semiconductor s u r f a c e s i n g e n e r a l r e l a x o r r e c o n s t r u c t by rebonding and moving t h e s u r f a c e atoms t o reduce t h e s u r f a c e f r e e e n e r g y . A wide v a r i e t y of e x p e r i m e n t a l t e c h n i q u e s has been a p p l i e d t o t h e s t u d y of semiconductor s u r f a c e r e c o n s t r u c t i o n s and d u r i n g t h e l a s t few y e a r s t h e r e has been a remarkable p r o g r e s s i n t h e unders t a n d i n g of s e v e r a l of t h e s e r e c o n s t r u c t i o n s . More t h a n twenty y e a r s have now p a s s e d s i n c e t h e f i r s t evidence of photoemission from semiconductor s u r f a c e s t a t e s was r e p o r t e d i n

experiments on c l e a v e d S i ( l l 1 ) s u r f a c e s /14/. During t h e e a r l y p e r i o d t h e main o b j e c t of photoemission s t u d i e s was r e l a t e d t o t h e q u e s t i o n s of whether t h e r e a r e any s u r f a c e s t a t e s i n t h e bulk band gap and whether t h e s u r f a c e e l e c t r o n i c s t r u c t u r e i s m e t a l l i c o r semiconducting. From a n g l e - i n t e g r a t e d photoemission s t u d i e s it became e v i d e n t t h a t t h e s u r f a c e band s t r u c t u r e s of many semicond u c t o r s have band gaps t h a t a r e r e l a t e d t o r e l a x a t i o n a n d / o r r e c o n s t r u c t i o n of t h e s u r f a c e s . I n t h e l a s t few y e a r s t h e r e has been

146

a l a r g e number of a n g l e - r e s o l v e d p h o t o e l e c t r o n s p e c t r o s c o p y (ARPES) s t u d i e s , which have g i v e n v e r y d e t a i l e d i n f o r m a t i o n a b o u t t h e s u r f a c e e l e c t r o n i c s t a t e s . I n s e v e r a l cases, a s f o r t h e S i ( l l l ) 2 x l and 7x7 s u r f a c e s , t h e i n f o r m a t i o n a b o u t t h e s u r f a c e e l e c t r o n i c s t r u c t u r e from ARPES s t u d i e s and t h e o r e t i c a l c a l c u l a t i o n s g i v e s s t r o n g s u p p o r t f o r t h e r e c o n s t r u c t i o n models t h a t a r e a l s o p r e f e r r e d from a m u l t i p l i c i t y of o t h e r e x p e r i m e n t s s u c h a s s c a n n i n g tunneling-microscopy

(STM), t r a n s m i s s i o n - e l e c t r o n - d i f f r a c t i o n

(TED)

and H e a t o m - s c a t t e r i n g . I n t h i s c h a p t e r w e w i l l g i v e a s u r v e y o f t h e ARPES s t u d i e s of semiconductor s u r f a c e s t a t e s by d i s c u s s i n g s e v e r a l o f t h e most w e l l - s t u d i e d s u r f a c e s . E x p e r i m e n t a l s t u d i e s on o t h e r semiconductor s u r f a c e s are summarized i n a compendium and f o r a d i s c u s s i o n of t h e s e r e s u l t s , w e r e f e r t o a r e c e n t , e x t e n s i v e review paper /15/. 2

CHARACTERISTICS OF SEMICONDUCTOR SURFACE STATES A s u r f a c e of a c r y s t a l b r e a k s t h e t h r e e - d i m e n s i o n a l

bulk period-

i c i t y and t h e r e i s an a s s o c i a t e d change i n t h e e l e c t r o n i c s t r u c t u r e . The Bloch states of t h e i n t e r i o r of t h e c r y s t a l have t o b e matched t o s t a t e s d e c a y i n g e x p o n e n t i a l l y from t h e s u r f a c e i f t h e energy i s below t h e vacuum l e v e l . The matching c o n d i t i o n s c a n g i v e rise t o an increase o r decrease i n t h e surface l o c a l density of s t a t e s f o r a c e r t a i n e l e c t r o n e n e r g y . S t a t e s w i t h s i g n i f i c a n t l y i n c r e a s e d amplitude a t t h e s u r f a c e , r e l a t i v e t o t h e p e r i o d i c bulk values, a r e c a l l e d s u r f a c e r e s o n a n c e s . There can a l s o e x i s t new s t a t e s , c a l l e d s u r f a c e s t a t e s , t h a t a r e completely l o c a l i z e d t o t h e s u r f a c e r e g i o n . These a r e e l e c t r o n i c s t a t e s w i t h e n e r g y , E i , and wavevector p a r a l l e l t o t h e s u r f a c e , k,,

,

such t h a t E i (k//)i s w i t h i n a f o r b i d d e n gap o f

t h e b u l k band s t r u c t u r e p r o j e c t e d o n t o t h e s u r f a c e B r i l l o u i n zone. A b a s i c u n d e r s t a n d i n g of s u r f a c e s t a t e s was a l r e a d y o b t a i n e d by

t h e 1 9 3 0 ' s /16,17/ and, d u r i n g t h e l a s t decade i n p a r t i c u l a r ,

there

h a s been a s t r o n g development i n c a l c u l a t i o n a l methods f o r t h e o r e t i c a l s t u d i e s of s u r f a c e e l e c t r o n i c s t r u c t u r e . For a number of semiconductor s u r f a c e s , s e l f - c o n s i s t e n t l y c a l c u l a t e d s u r f a c e e l e c t r o n i c s t r u c t u r e s have now been r e p o r t e d and i n combination w i t h energy-minimization

schemes i t h a s been p o s s i b l e t o c a l c u l a t e t h e

l o w e s t e n e r g y c o n f i g u r a t i o n f o r d i f f e r e n t t y p e s of r e c o n s t r u c t i o n s . T h e band d i s p e r s i o n s Ei (k//)of s u r f a c e s t a t e s and s u r f a c e r e s o n a n c e s from s u c h c a l c u l a t i o n s can b e d i r e c t l y compared w i t h e n e r g y d i s p e r s i o n s o b t a i n e d from ARPES measurements.

147

T h e o r e t i c a l s t u d i e s show t h a t s u r f a c e s t a t e s on semiconductors can o f t e n be d e s c r i b e d a s v e r y l o c a l i z e d bonds a t t h e s u r f a c e s , e . g . d a n g l i n g bond o r back bond s t a t e s . S u r f a c e resonances,

which by

d e f i n i t i o n a r e d e g e n e r a t e w i t h bulk s t a t e s , can on t h e o t h e r hand have a v a r y i n g degree of l o c a l i z a t i o n i n t h e s u r f a c e r e g i o n . There

i s no a b s o l u t e d e f i n i t i o n f o r how s t r o n g s u r f a c e l o c a l i z a t i o n a s t a t e s h o u l d have t o be d e f i n e d a s a s u r f a c e r e s o n a n c e . From t h e e x p e r i m e n t a l p o i n t of view, it i s g e n e r a l l y d i f f i c u l t t o conclude whether a s u r f a c e r e l a t e d photoemission f e a t u r e i s due t o a s u r f a c e s t a t e o r a s t r o n g s u r f a c e resonance, u n l e s s it i s c l e a r where t h e edges of t h e p r o j e c t e d bulk bands a r e . T h i s has i n p r a c t i c e l e d t o t h e f a c t t h a t a c t u a l s u r f a c e resonances i n e x p e r i m e n t a l s t u d i e s a r e o f t e n denoted a s s u r f a c e s t a t e s .

I n t h e p r e v i o u s d e s c r i p t i o n of s u r f a c e s t a t e s / r e s o n a n c e s it was i m p l i c i t l y assumed t h a t t h e s u r f a c e s t a t e band s t r u c t u r e i s charact e r i s t i c of a s u r f a c e w i t h p e r f e c t two-dimensional

periodicity,

i.e.

t h e i n t r i n s i c s u r f a c e s t a t e band s t r u c t u r e . Another important c l a s s of s u r f a c e s t a t e s on semiconductor s u r f a c e s i s t h e d e f e c t - r e l a t e d s u r f a c e s t a t e s . I n t h e c a s e of a low-doped semiconductor w i t h n o

i n t r i n s i c s u r f a c e s t a t e s i n t h e bulk band gap, a small number of d e f e c t s t a t e s i n t h e band gap can have a major e f f e c t on t h e s u r f a c e band bending,

s e e below. During t h e 1 9 7 0 ' s t h e r e were some contro-

v e r s i e s concerning t h e e x i s t e n c e of s u r f a c e s t a t e s i n t h e bulk band gaps of c l e a v e d 1 1 1 - V compound semiconductors. I t was e v e n t u a l l y shown by c a r e f u l s t u d i e s of t h e s u r f a c e F e r m i l e v e l p o s i t i o n on nand p-doped c r y s t a l s t h a t t h e occurrence of s u r f a c e s t a t e s i n t h e gap was r e l a t e d t o d e f e c t s on t h e c l e a v e d s u r f a c e s f o r s e v e r a l of t h e s e semiconductors. Although t h e s e s t u d i e s /18,19/ were made using c o n t a c t p o t e n t i a l d i f f e r e n c e measurements,

it i s possible t o get the

same i n f o r m a t i o n from energy s h i f t s of photoemission s p e c t r a . A d i r e c t o b s e r v a t i o n of photoemission from d e f e c t s t a t e s i s however, i n most c a s e s , n o t p o s s i b l e because t h e d e f e c t d e n s i t y i s t o o low and t h e emission from l o c a l i z e d d e f e c t s w i l l be d i s t r i b u t e d over a l l emission a n g l e s . S u r f a c e s t a t e s i n t h e band gap of semiconductors w i l l a f f e c t t h e p o s i t i o n of t h e Fermi-level

(chemical p o t e n t i a l ) a t t h e s u r f a c e . For

s u r f a c e s w i t h a very high d e n s i t y of s u r f a c e s t a t e s i n t h e gap, t h e Fermi l e v e l can appear pinned a t a c e r t a i n p o s i t i o n i n t h e gap i r r e s p e c t i v e of t h e doping. Concurrent w i t h t h e F e r m i - l e v e l p i n n i n g t h e r e i s a band bending i n t h e n e a r s u r f a c e r e g i o n which depends s t r o n g l y on t h e doping.

148

I n Fig. l ( a ) i s shown a h y p o t h e t i c a l band diagram o f a n n+-doped semiconductor c l o s e t o a s u r f a c e w i t h s u r f a c e s t a t e s i n t h e gap. I f both b u l k and s u r f a c e c o u l d be e l e c t r i c a l l y n e u t r a l t h e energy bands would b e f l a t u p t o t h e s u r f a c e and t h e F e r m i l e v e l of t h e s u r f a c e would be a t t h e s o - c a l l e d n e u t r a l l e v e l Eo. T h i s i s o b v i o u s l y a none q u i l i b r i u m s i t u a t i o n , s i n c e t h e Fermi-level

i s not c o n s t a n t

throughout t h e c r y s t a l . E l e c t r o n s w i l l flow from t h e bulk of t h e c r y s t a l t o t h e s u r f a c e , making t h e s u r f a c e n e g a t i v e l y charged and t h e b u l k c l o s e t o t h e s u r f a c e p o s i t i v e l y charged, r e s u l t i n g i n t h e s i t u a t i o n shown i n F i g . l ( b )

.

I t i s q u i t e s t r a i g h t f o r w a r d t o deduce t h e r e l a t i o n s h i p between

t h e s u r f a c e d e n s i t y of e x c e s s e l e c t r o n s , n s , t h e band bending, VB, and t h e doping c o n c e n t r a t i o n N, / 2 0 / :

n,

=

( 2 c e0

vB N,

(1)

/e)1/2

where K i s t h e s t a t i c d i e l e c t r i c c o n s t a n t of t h e semiconductor. There a r e two o p p o s i t e cases t h a t a r e of p a r t i c u l a r importance f o r ARPES s t u d i e s on semiconductor s u r f a c e s .

The f i r s t c a s e concerns t h e p o s s i b i l i t y of u s i n g h i g h l y doped c r y s t a l s t o s t u d y normally empty s u r f a c e s t a t e s . For c l e a v e d G e ( l l l ) 2 x l s u r f a c e s t h e s i t u a t i o n i s very f a v o r a b l e f o r making ARPES s t u d i e s of s t a t e s above t h e n e u t r a l l e v e l , s i n c e t h e Fermi l e v e l i s known t o be pinned c l o s e t o t h e v a l e n c e band edge. For an n-doping c o n c e n t r a t i o n of lxlO1* cm-3 t h e e x c e s s s u r f a c e charge i s e s t i m a t e d t o be = 3x1Ol2 e l e c t r o n s p e r cm2, which corresponds t o = 0 . 0 0 5 e l e c t r o n s p e r s u r f a c e atom. I n s t u d i e s by N i c h o l l s e t a l . /21/ on

-Ev

F i g . 1. ( a ) H y p o t h e t i c a l band diagram of an n+-doped semiconductor with s u r f a c e s t a t e s i n t h e gap, assuming t h a t both b u l k and s u r f a c e could be n e u t r a l . S h o r t and long l i n e s denote empty and f i l l e d surface s t a t e s , respectively. (b) Band diagram a f t e r e l e c t r o n s have been t r a n s f e r r e d t o t h e s u r f a c e and e q u i l i b r i u m has been e s t a b lished.

149

emission from t h e minimum of t h e a n t i b o n d i n g (almost empty) s u r f a c e

s t a t e band on G e ( l l l ) Z x l , t h i s c o n c e n t r a t i o n of e x c e s s e l e c t r o n s was e a s i l y d e t e c t a b l e . I t can be e s t i m a t e d , t h a t t h e s e n s i t i v i t y of t h e ARPES experiment i s a t l e a s t enough t o d e t e c t = 5 ~ 1 0 -e l~e c t r o n s per s u r f a c e atom f o r e l e c t r o n s i n t h i s almost empty band. The high s e n s i t i v i t y i s p a r t l y due t o t h e s t r o n g a n i s o t r o p y i n emission from t h e m i n i m u m of a s u r f a c e s t a t e band.

i s exemplif i e d by t h e e r r a t i c s h i f t s of ARPES s p e c t r a of moderately doped The second c a s e , f o r which band bending i s important,

semiconductors w i t h no i n t r i n s i c s u r f a c e s t a t e s i n t h e band gap. Small changes i n t h e number of d e f e c t s t a t e s i n t h e gap, a s a r e s u l t of c o n t a m i n a t i o n o r v a r y i n g s u r f a c e t r e a t m e n t s , can sometimes be a problem. Consider f o r example t h e c l e a v e d ( 1 1 0 ) s u r f a c e of a 111-V compound semiconductor l i k e GaAs. For a c r y s t a l with a doping of lXlOl7

~ m a- s~ h i f t of t h e Fermi l e v e l by 0 . 2 eV can be accomplished i . e . of t h e o r d e r of l ~ l O - ~

by 5x1Ol1 s u r f a c e s t a t e s p e r c m 2 ,

e l e c t r o n s p e r s u r f a c e atom. This number i s l a r g e r t h a n t h a t e s t i m a t e d a s t h e s e n s i t i v i t y of ARPES f o r o b s e r v i n g t h e normally empty s u r f a c e band on G e ( l l 1 ) Z x l . However, because of t h e more i s o t r o p i c emission from d e f e c t induced s u r f a c e s t a t e s , t h e s e a r e more d i f f i c u l t t o observe i n a n a n g l e - r e s o l v e d photoemission experiment. S i n c e t h e e x p e r i m e n t a l t e c h n i q u e and t h e p h y s i c s of photoemission a r e d e s c r i b e d i n c h a p t e r s 1 and 2 , we w i l l h e r e o n l y v e r y b r i e f l y i n t r o d u c e t h e b a s i c i d e a s n e c e s s a r y f o r d i s c u s s i n g ARPES s t u d i e s of semiconductor s u r f a c e s t a t e s . I n an AWES experiment, with photons of energy hv, t h e k i n e t i c energy E k i n i s measured f o r e l e c t r o n s e m i t t e d a t an a n g l e Be from t h e s u r f a c e normal. I n t h e absence of i n e l a s t i c s c a t t e r i n g , t h e energy and p a r a l l e l wavevector conserva t i o n f o r p h o t o e l e c t r o n s , e x c i t e d from a s t a t e with i n i t i a l energy E i and p a r a l l e l wavevector ki,/, can be w r i t t e n : Ekin = E i

+

hv - Q

(2)

E; i s d e f i n e d r e l a t i v e t o t h e Fermi l e v e l EF and Q i s t h e semicond u c t o r work f u n c t i o n . S i n c e t h e wavevector of t h e photon u s u a l l y can be n e g l e c t e d i n ARPES experiments, t h e p a r a l l e l wavevector compon e n t , k,,,

i s conserved t o w i t h i n a s u r f a c e r e c i p r o c a l l a t t i c e

v e c t o r G s . The r e l a t i o n s h i p between e m i s s i o n a n g l e and p a r a l l e l wavevector i s given by e q . ( 4 ) .

By m e a s u r i n g t h e k i n e t i c e n e r g y , E k i n , of e l e c t r o n s g i v i n g r i s e t o a c h a r a c t e r i s t i c photoemission f e a t u r e , as f u n c t i o n o f emission a n g l e , Oe, one c a n o b t a i n a d i s p e r s i o n c u r v e E i ( k / / ) . For e m i s s i o n f e a t u r e s which a r e due t o d i r e c t t r a n s i t i o n s i n t h e b u l k , s u c h d i s p e r s i o n c u r v e s w i l l i n g e n e r a l b e photon energy dependent, s i n c e f o r a given k/,-value

t h e r e i s a r a n g e o f i n i t i a l e n e r g i e s from

which d i r e c t t r a n s i t i o n s c a n o c c u r . I n c o n t r a s t , f o r e m i s s i o n f r o m a s u r f a c e s t a t e band t h e d i s p e r s i o n c u r v e o b t a i n e d i s p h o t o n e n e r g y i n d e p e n d e n t a n d t h e ARPES e x p e r i m e n t g i v e s t h e two-dimensional s u r f a c e band s t r u c t u r e , i . e . E i ( k / / ) . I n t h e s t r i n g e n t o n e - s t e p d e s c r i p t i o n o f t h e p h o t o e m i s s i o n pro-

cess it i s n o t p o s s i b l e t o s e p a r a t e t h e e x c i t a t i o n o f t h e e l e c t r o n from t h e t r a n s p o r t t o and t h r o u g h t h e s u r f a c e . I t i s a l s o n e c e s s a r y t o t a k e i n t o a c c o u n t t h e e f f e c t s of e l e c t r o n a n d h o l e l i f e t i m e s when t h e p h o t o e m i s s i o n p r o c e s s i s d e s c r i b e d i n more d e t a i l . A m a j o r consequence of e x t e n d i n g t h e t h e o r y beyond t h e s i m p l e s t t h r e e - s t e p model i s t h e i n t r o d u c t i o n o f mechanisms f o r b r o a d e n i n g i n t h e p h o t o e m i s s i o n s p e c t r a . O f p a r t i c u l a r i m p o r t a n c e i s t h e r e l a x a t i o n of t h e c o n d i t i o n of k l - c o n s e r v a t i o n i n t r a n s i t i o n s c o r r e s p o n d i n g t o e m i s s i o n from b u l k s t a t e s n e a r t h e s u r f a c e . I t i s c l e a r f r o m p h o t o e m i s s i o n s p e c t r a t h a t t h e r e a r e s u c h b r o a d e n i n g mechanisms, which g i v e r i s e t o k , / - r e s o l v e d i n t h e surface region /22/.

e m i s s i o n from t h e d e n s i t y of s t a t e s

T h i s p r e s e n t s a problem when t r y i n g t o

i d e n t i f y e m i s s i o n from s u r f a c e s t a t e s / r e s o n a n c e s i n p h o t o e m i s s i o n s p e c t r a , s i n c e s u c h k / / - r e s o l v e d e m i s s i o n from band e d g e s i n t h e bulk e l e c t r o n i c s t r u c t u r e w i l l a l s o g i v e rise t o photon energy independent d i s p e r s i o n s E i ( k / / ). I t c a n sometimes be d i f f i c u l t t o p r o v e t h a t a c e r t a i n f e a t u r e i n

a p h o t o e m i s s i o n s p e c t r u m i s due t o a s u r f a c e s t a t e / r e s o n a n c e . There

are t h r e e c r i t e r i a o f t e n u s e d t o s u p p o r t t h e i d e n t i f i c a t i o n of e m i s s i o n from s u r f a c e s t a t e s / r e s o n a n c e s : 1) t h e e n e r g y o f t h e o b s e r v e d f e a t u r e l i e s w i t h i n a g a p o f t h e

p r o j e c t i o n o f t h e b u l k band s t r u c t u r e o n t o t h e s u r f a c e B r i l l o u i n zone. 2 ) t h e measured d i s p e r s i o n E i (k//)i s i n d e p e n d e n t o f p h o t o n e n e r g y

3) t h e f e a t u r e i s s e n s i t i v e t o c h e m i s o r p t i o n o f a t o m s o r molecu-

les on t h e s u r f a c e . The f i r s t c r i t e r i o n i s n o r m a l l y ( i n t h e a b s e n c e o f s t r o n g d i f f u s e

151

s c a t t e r i n g ) s u f f i c i e n t f o r i d e n t i f y i n g a s u r f a c e s t a t e , however i n many cases t h e u n c e r t a i n t y i n t h e p o s i t i o n s of t h e bulk band edges

are l a r g e enough t o make i t d i f f i c u l t t o u s e . Furthermore, when emission from band edges can be c o n s i d e r e d a s a p o s s i b i l i t y t o e x p l a i n a f e a t u r e , n e i t h e r of c r i t e r i a 1 and 2 a r e c o n c l u s i v e . We f i n d t h a t t h e u s e of well-ordered

c h e m i s o r p t i o n s y s t e m s t o modify

t h e s u r f a c e e l e c t r o n i c s t r u c t u r e of semiconductor s u r f a c e s i s very v a l u a b l e f o r t h e i d e n t i f i c a t i o n of s u r f a c e s t a t e s and s u r f a c e r e s o n a n c e s . T h e t h i r d c r i t e r i o n must however be used w i t h g r e a t c a r e s i n c e a l s o bulk f e a t u r e s a r e a f f e c t e d by a d s o r p t i o n of atoms o r molecules due t o i n c r e a s e d s c a t t e r i n g of t h e e m i t t e d e l e c t r o n s .

3

CLEAVED S i (111)2x1 AND Ge (111)2x1 SURFACES The c l e a v e d S i ( l l 1 ) and G e ( l l 1 ) s u r f a c e s have been s t u d i e d exten-

s i v e l y w i t h a n g l e - r e s o l v e d photoemission /23-57/

and t h e e l e c t r o n i c

s t r u c t u r e s of t h e s e two s u r f a c e s a r e p r e s e n t l y w e l l u n d e r s t o o d . Both s u r f a c e s a r e b e l i e v e d t o r e c o n s t r u c t a c c o r d i n g t o t h e x-bonded chain model o r i g i n a l l y s u g g e s t e d f o r t h e S i ( l l l ) 2 x l s u r f a c e by Pandey / l l / . F i g . 2 ( a ) shows a schematic view of t h e x-bondei model f o r t h e

G e ( l l l ) 2 x l s u r f a c e a s o b t a i n e d i n c a l c u l a t i o n s g i v i n g t h e geometry w i t h minimum energy / 5 8 / . For both s i l i c o n and germanium t h e recons t r u c t i o n g i v e s rise t o a f i l l e d bonding d a n g l i n g bond band, t h a t is found below t h e v a l e n c e band edge i n ARPES s t u d i e s , and an a n t i bonding dangling-bond band t h a t d i s p e r s e s from t h e conduction band

I

Ge (11112.1

F i g . 2 . ( a ) B a l l and s t i c k model of t h e energy-minimized x-bonded c h a i n geometry f o r G e ( l l l ) 2 x l / 5 8 / . ( b ) S u r f a c e B r i l l o u i n zones f o r t h e diamond-structure ( 1 l l ) l x l and ( 1 1 1 ) Z x l s u r f a c e s .

152

r e g i o n down i n t o t h e a b s o l u t e band gap. I n e a r l y low-energy e l e c t r o n d i f f r a c t i o n (LEED) s t u d i e s by Lander

e t a l . /59/ it was f i r s t found t h a t c l e a v e d S i ( l l 1 ) s u r f a c e s a r e r e c o n s t r u c t e d and e x h i b i t 2x1 LEED p a t t e r n s , b e c a u s e of a d o u b l i n g of t h e u n i t c e l l a l o n g a < Z l l > - d i r e c t i o n . F i g . 2 ( b ) shows t h e shape of t h e s u r f a c e B r i l l o u i n zone f o r b o t h t h e u n r e c o n s t r u c t e d 1x1 and t h e r e c o n s t r u c t e d 2x1 s u r f a c e . There a r e t h r e e e q u i v a l e n t -type d i r e c t i o n s and t h e LEED-pattern i s o f t e n a s u p e r p o s i t i o n of p a t t e r n s from domains o r i e n t e d a l o n g e a c h of t h e s e e q u i v a l e n t d i r e c t i o n s . I n o r d e r t o d e t e r m i n e t h e s u r f a c e s t a t e band s t r u c t u r e w i t h a n g l e r e s o l v e d p h o t o e m i s s i o n it i s e s s e n t i a l t o s t u d y a single-domain s u r f a c e , which can be o b t a i n e d w i t h h i g h p r o b a b i l i t y f o r b o t h S i (111)2x1 and G e (111)2x1 s u r f a c e s by s p e c i a l c l e a v a g e t e c h n i q u e s .

3 . 1 S t u dies o f t h e b o n d i n a d a n a l i n s bond band on S i ( l l l ) 2 x l E a r l y e v i d e n c e f o r s u r f a c e e l e c t r o n i c s t a t e s on t h e c l e a v e d S i ( l l 1 ) - s u r f a c e was o b t a i n e d i n p h o t o e l e c t r i c y i e l d measurements i n t h e p i o n e e r i n g work of A l l e n and Gobeli / 6 0 / .

The f i r s t photo-

e l e c t r o n e n e r g y d i s t r i b u t i o n c u r v e s showing e m i s s i o n from s u r f a c e s t a t e s on t h e c l e a v e d S i ( l l 1 ) s u r f a c e w e r e o b t a i n e d from a n g l e i n t e g r a t e d measurements by Eastman and Grobman / 6 1 / ,

and by Wagner

and S p i c e r / 6 2 / . The same c l e a r e v i d e n c e f o r s u r f a c e s t a t e s n e a r t h e t o p of t h e v a l e n c e band was a l s o o b t a i n e d i n l a t e r a n g l e - i n t e g r a t e d measurements by I b a c h and Rowe / 6 3 , 6 4 / . S i n c e t h e more powerful t e c h n i q u e of a n g l e - r e s o l v e d photoemission was f i r s t a p p l i e d t o t h e c l e a v e d S i ( l l 1 ) s u r f a c e by Rowe e t a l . /23, 2 4 / t h e r e h a s been a l a r g e number o f s t u d i e s o f t h e e l e c t r o n i c

s t r u c t u r e of t h e S i ( l l l ) 2 x l s u r f a c e /25-52/.

Up t o 1981 it seemed

t h a t a l l g r o u p s r e p o r t e d d i f f e r e n t r e s u l t s f o r t h e d i s p e r s i o n of t h e dangling-bond band. I n a review p a p e r by Plummer and E b e r h a r d t / 6 5 / a comparison was made between t h e r e s u l t s of Rowe e t a l . / 2 3 / ,

Parke

e t a l . / 2 5 / , Hansson e t a l . / 3 0 / , Houzay e t a l . /34/, and Himpsel e t a l . /36/.

Since a l l s t u d i e s r e p o r t e d d i f f e r e n t r e s u l t s , t h e s i t u -

a t i o n seemed v e r y c o n f u s e d . One r e a s o n f o r t h e s m a l l o v e r l a p between t h e r e s u l t s of t h e d i f f e r e n t groups is t h a t t h e S i ( l l l ) 2 x l s u r f a c e h a s low symmetry and t h e d i s p e r s i o n was r e p o r t e d f o r i n e q u i v a l e n t directions i n different studies. An u p d a t e d review o f t h e c o n s i s t e n c y of ARPES measurements on

S i ( l l l ) 2 x l s u r f a c e s was g i v e n i n 1983 i n r e f . 43. I t was p o s s i b l e t o b r i n g t o g e t h e r e x p e r i m e n t a l d a t a from Uhrberg e t a l . / 3 1 , 3 8 / ,

153

Himpsel e t a l . /36/,

Houzay e t a l . /34/

,

and Rowe e t a l . /23/ and

form a c o n s i s t e n t p i c t u r e of t h e d a n g l i n g bond band d i s p e r s i o n . F u r t h e r s u p p o r t f o r t h i s d i s p e r s i o n was l a t e r o b t a i n e d i n t h e s t u d i e s by Mirtensson e t a l . / 4 8 /

and Bokor e t a l . / 5 1 / .

Early

d i s p a r a t e r e s u l t s from Parke e t a l . /25/ and Rowe e t a l . /23/ could be e x p l a i n e d a s multidomain e f f e c t s and b u l k c o n t r i b u t i o n s ,

respec-

t i v e l y . The most r e c e n t , d e t a i l e d h i s t o r i c a l review and d i s c u s s i o n

of t h e c o n s i s t e n c y of d i f f e r e n t ARPES s t u d i e s on S i ( l l l ) 2 x l has been given i n r e f . 1 5 . I t w a s concluded t h a t t h e r e i s indeed a l a r g e degree of c o n s i s t e n c y between t h e v a r i o u s ARPES experiments and a p l a u s i b l e e x p l a n a t i o n was a l s o g i v e n f o r a recent d i s p a r a t e r e s u l t /42/.

What h a s been d e s c r i b e d above a s c o n s i s t e n t r e s u l t s on t h e dangl i n g bond d i s p e r s i o n of c o u r s e c o n t a i n some v a r i a t i o n i n t h e d e t a i l s of t h e r e p o r t e d d i s p e r s i o n s . The bandwidth of t h e d a n g l i n g bond band v a r i e s between 0 . 6 and 0 . 8 eV, which, a t l e a s t p a r t i a l l y ,

is a

r e s u l t of d i f f e r e n t a n g u l a r r e s o l u t i o n s . The a b s o l u t e p o s i t i o n of t h e band v a r i e s by 0 . 2 5 eV between extreme c a s e s , which can be r e l a t e d t o u n c e r t a i n t i e s i n t h e e x p e r i m e n t a l l y determined Fermi l e v e l (EF) p o s i t i o n combined w i t h v a r i a t i o n s of t h e p i n n i n g p o s i t i o n of EF a t t h e s u r f a c e . An example of t h e agreement between d i f f e r e n t experiments, t h a t o r i g i n a l l y were i n t e r p r e t e d q u i t e d i f f e r e n t l y , i s shown i n F i g . 3 . Angle-resolved p h o t o e l e c t r o n s p e c t r a p r o b i n g t h e e l e c t r o n i c s t r u c -

t u r e a l o n g t h e long a x i s ,

r-j,

of t h e s u r f a c e B r i l l o u i n zone (SBZ)

a r e shown i n F i g . 3a (from r e f . 3 8 ) . The dominating s t r u c t u r e A has a s t r o n g energy d i s p e r s i o n w i t h maximum energy a t a p o l a r a n g l e of approximately 45O,

which corresponds t o emission from s t a t e s a t t h e

SBZ boundary f o r t h e photon energy used ( 1 0 . 2 e V ) . f o r emission from s t a t e s a l o n g t h e r - j - l i n e

Similar r e s u l t s

have a l s o been o b t a i n e d

i n t h e s t u d i e s by Houzay e t a l . / 4 2 / and MBrtensson e t a l . / 4 8 / . I n F i g . 3b some e a r l i e r photoemission r e s u l t s from t h e work by

Himpsel e t a l . / 3 6 / a r e shown. The s u r f a c e s t a t e emission was i n t h i s c a s e o b t a i n e d a s t h e d i f f e r e n c e between s p e c t r a from t h e c l e a n 2x1 r e c o n s t r u c t e d s u r f a c e and s p e c t r a from t h e hydrogen exposed

1x1-H s u r f a c e . Besides t h e s t r o n g upwards d i s p e r s i o n found along t h e r-j-line

t h e r e i s a weak downwards d i s p e r s i o n a l o n g t h e i=’-J’-line.

I n t h e o r i g i n a l p a p e r by Himpsel e t a l . / 3 6 / it w a s proposed t h a t t h e s u r f a c e s t a t e peak was a s u p e r p o s i t i o n of emission c o n t r i b u t i o n s from two f l a t bands and t h a t i n t e n s i t y v a r i a t i o n s l e d t o an apparent

s,1lllc12xll

A

SURFACE STATE

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si I l l l i - H I l x l i SUBTRACTED

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.

.

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-1

L 0 . W -1

$=G

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INITIAL ENERGY BELOW Ev lev)

t

'2 E -10 J'

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WAVE VECTOR

Fig. 3. ( a ) ARPES s p e c t r a probing t h e s u r f a c e e l e c t r o n i c s t r u c t u r e along t h e f-3 symmetry l i n e i n t h e 2 x 1 S B Z . Peak A and shoulder A ' are surface s t a t e contributions / 3 8 / . ( b ) ARPES d i f f e r e n c e s p e c t r a between c l e a n and hydrogen expose_d S i ( l l l ) 2 x l s u r f a c e s / 3 6 / . S u r f a c e s t a t e s a r e probed along t h e T-J and symmetry l i n e s . From r e f . 5 0 . ( c ) Comparison between experimental and t h e o r e t i c a l / l o / r e s u l t s f o r t h e s u r f a c e s t a t e d i s p e r s i o n on S i ( l l 1 ) Z x l . Data p o i n t s 0 , 0 from Uhrberg e t a l . / 3 8 / and m , D from Himpsel et a l . / 3 6 / have been From r e f . 5 0 . s h i f t e d -- 0 . 1 5 e V upwards r e l a t i v e t o E,.

r-3'

band d i s p e r s i o n . This s u g g e s t i o n s t i m u l a t e d a l o t of d i s c u s s i o n concerning c o r r e l a t i o n e f f e c t s and t h e v a l i d i t y of t h e s i n g l e p a r t i c l e i n t e r p r e t a t i o n of photoemission from s u r f a c e s t a t e bands /66-68/.

Regardless of t h e ambiguity i n t h e e v a l u a t i o n of t h e d a t a ,

155

it was c l e a r t h a t any c a l c u l a t e d s u r f a c e s t a t e bands f o r t h e , a t t h a t t i m e , w e l l e s t a b l i s h e d b u c k l i n g model /69/ could not e x p l a i n t h e photoemission r e s u l t s . The i d e n t i f i c a t i o n of s t r u c t u r e A a s a s u r f a c e s t a t e i s c l e a r s i n c e it d i s p e r s e s f a r i n t o t h e gap of t h e p r o j e c t i o n of t h e bulk bands. I n F i g . 3c t h e d i s p e r s i o n of t h e s u r f a c e s t a t e band i s shown r e l a t i v e t o t h e edge of t h e p r o j e c t e d bulk v a l e n c e bands. The d a t a p o i n t s a r e from Uhrberg e t a l . /38/ and Himpsel e t a l . / 3 6 / , and t h e i n c l u d e d t h e o r e t i c a l s u r f a c e s t a t e band d i s p e r s i o n i s from a c a l c u l a t i o n by Pandey u s i n g an energy-minimized v e r s i o n of h i s a-bonded c h a i n model /11,70/. There was a b r e a k t h r o u g h i n t h e u n d e r s t a n d i n g of t h e S i (111)2x1 s u r f a c e , when Pandey, a f t e r i n v e s t i g a t i n g many different possible surface reconstructions,

proposed t h e new 71-

bonded c h a i n model. The e l e c t r o n i c s t r u c t u r e of t h i s model was found t o be c o n s i s t e n t with t h e e x p e r i m e n t a l r e s u l t s of Himpsel e t a l .

/36/, i f t h e main photoemission peak was a s s o c i a t e d w i t h a s t r o n g l y d i s p e r s i n g band i n s t e a d of two almost f l a t bands w i t h i n t e n s i t y v a r i a t i o n s . The e x i s t e n c e of a h i g h l y d i s p e r s i v e s u r f a c e s t a t e band

was f i n a l l y proven by Uhrberg e t a l . /38/ through an a n a l y s i s of t h e s u r f a c e s t a t e peak width and d i s p e r s i o n i n h i g h - r e s o l u t i o n ARPES s p e c t r a l i k e t h e ones i n F i g . 3 a . A s seen i n F i g . 3c, t h e r e i s very good agreement between t h e o r y and experiment concerning t h e shape of t h e d i s p e r s i o n of t h e s u r f a c e s t a t e band. The s t r o n g p o s i t i v e d i s p e r s i o n found i n t h e o u t e r h a l f of t h e ?->-line f o r t h e u n d e r s t a n d i n g of t h e 2 x l - r e c o n s t r u c t i o n ,

i s very s i g n i f i c a n t s i n c e o u t of t h e

many models i n v e s t i g a t e d , o n l y t h e x-bonded c h a i n model has r e s u l t e d i n t h i s k i n d of d i s p e r s i o n .

Besides t h e main s u r f a c e s t a t e band, t h e r e i s a s m a l l f e a t u r e A '

i n F i g . 3a, t h a t has been a s s i g n e d t o a s u r f a c e s t a t e . The energy of t h i s f e a t u r e i s w i t h i n t h e p r o j e c t e d bulk band gap n e a r t h e j - p o i n t a s shown i n F i g . 3 c . The weak s h o u l d e r h a s v e r y c o n s i s t e n t l y been reported near t h e %point i n

d i f f e r e n t studies /36,38,42,48/.

The

o r i g i n of t h i s emission was a p o i n t of c o n t r o v e r s y f o r some t i m e . Himpsel e t a l . /36/ s u g g e s t e d t h a t t h e emission was from t h e same s u r f a c e s t a t e band a s i s seen i n t h e normal d i r e c t i o n . This w a s r u l e d o u t by Uhrberg e t a l . / 3 8 / who proposed t h a t emission from secondary domains, t h a t were r o t a t e d by f 120

r e l a t i v e t o t h e main

domain, was s t r o n g enough t o be s e e n . I t had been found t h a t m u l t i domain c l e a v e s gave a peak a t t h e same energy and a n g l e s a s t h e c o n t r o v e r s i a l s h o u l d e r . Although it i s d i f f i c u l t t o r u l e o u t t h i s

156

e x p l a n a t i o n , t h e above mentioned c o n s i s t e n c y of t h e i n t e n s i t y of t h e s h o u l d e r i n d i c a t e s t h a t it i s a f e a t u r e c h a r a c t e r i s t i c of a s i n g l e domain c l e a v e . An e x p l a n a t i o n of t h i s second s u r f a c e s t a t e w i t h i n t h e K-bonded c h a i n model h a s been s u g g e s t e d through t h e o r e t i c a l c a l c u l a t i o n s by S e l l o n i and B e r t o n i /71/,

who found a second s u r f a c e

s t a t e / r e s o n a n c e l o c a t e d below t h e d a n g l i n g bond band a t k / / - p o i n t s close t o

3.

Through t h e y e a r s t h e r e have been s e v e r a l f u r t h e r s u g g e s t i o n s t h a t backbond s u r f a c e s t a t e s / r e s o n a n c e s have been d e t e c t e d i n ARPES experiments on S i ( l l l ) 2 x l s u r f a c e s /24,25,30,36,37/.

The main

s u p p o r t f o r t h e s e s u g g e s t i o n s have been e i t h e r an e x p e r i m e n t a l l y determined l a r g e contamination s e n s i t i v i t y o r agreement w i t h some c a l c u l a t e d backbond s t a t e d i s p e r s i o n s . However no c o n c l u s i v e evidence f o r t h e s e backbond resonances have been p r e s e n t e d . Since emission from bulk d i r e c t t r a n s i t i o n s h a s been shown t o be both i n t e n s e and contamination s e n s i t i v e /45/,

we f i n d it q u e s t i o n a b l e

whether any t r u e backbond s u r f a c e resonance was i d e n t i f i e d i n t h e s e s t u d i e s on t h e c l e a v e d S i ( l l l ) 2 x l s u r f a c e . I t c e r t a i n l y would be very h e l p f u l t o have a d e t a i l e d c a l c u l a t i o n of where t o e x p e c t backbond s u r f a c e s t a t e s w i t h i n t h e x-bonded

c h a i n model.

3 . 2 S t u di e s of t h e bo n d i n s d a n a l i n a bond ba nd on G e ( l l l ) 2 x l Evidence f o r s u r f a c e e l e c t r o n i c s t a t e s on t h e c l e a v e d G e ( l l 1 ) s u r f a c e was f i r s t found i n p h o t o e l e c t r i c y i e l d measurements on d i f f e r e n t l y doped germanium c r y s t a l s / 7 2 / .

Independent of doping,

t h e Fermi l e v e l was pinned c l o s e t o t h e v a l e n c e band edge and two groups of s u r f a c e s t a t e s j u s t below and above t h e v a l e n c e band maximum were c o n s i d e r e d t o be r e s p o n s i b l e f o r t h e observed p i n n i n g of t h e Fermi l e v e l . P h o t o e l e c t r o n s p e c t r a c l e a v e d germanium,

(angle-integrated)

from

showing emission from s u r f a c e s t a t e s , were f i r s t

r e p o r t e d by Eastman and Grobman / 6 1 / .

They found a 0 . 7 eV wide

s u r f a c e s t a t e band c e n t e r e d a t about 0 . 7 5 eV below t h e valence band edge. A s i m i l a r s u r f a c e s t a t e d i s t r i b u t i o n was l a t e r observed by Murotani e t a l . /73/ and Rowe / 1 4 / .

Rowe a l s o i d e n t i f i e d f o u r more

s t r u c t u r e s a s i n t r i n s i c s u r f a c e s t a t e f e a t u r e s . However, no f i r m support f o r t h i s i d e n t i f i c a t i o n w a s presented. The f i r s t ARPES s t u d y of t h e c l e a v e d G e ( l l l ) 2 x l s u r f a c e w a s r e p o r t e d by N i c h o l l s e t a l . / 5 3 / . They used photons i n t h e range 7.4-11.6

eV,

and i n accordance w i t h t h e S i ( l l l ) 2 x l s u r f a c e t h e

dominating s t r u c t u r e i n t h e s p e c t r a corresponds t o a h i g h l y d i s p e r s i v e d a n g l i n g bond s t a t e . The d i s p e r s i o n , E i ( k / / ) , was s t u d i e d along

157

- - -

the r-J-K-r-lines

i n t h e s u r f a c e BZ a n d c o n s i s t e n t r e s u l t s w e r e

o b t a i n e d for t h e t h r e e d i f f e r e n t photon e n e r g i e s used ( 8 . 6 , 10.2, and 11.0 eV)

.

I n a s t u d y o f t h e A-bonded c h a i n model o f t h e G e ( l l 1 ) Z x l s u r f a c e by N o r t h r u p a n d Cohen / 5 8 / ,

t h e y compared t h e c a l c u l a t e d d i s p e r s i o n

of t h e d a n g l i n g bond band w i t h t h e e x p e r i m e n t a l r e s u l t s from r e f . 53 a n d f o u n d good a g r e e m e n t c o n c e r n i n g t h e s h a p e o f t h e d i s p e r s i o n , w h i l e the a b s o l u t e energy w a s about 0 . 8 e V t o o high.

S i n c e t h e y used

t h e l o c a l - d e n s i t y a p p r o x i m a t i o n , which does n o t c a l c u l a t e removal

e n e r g i e s , such a d i s c r e p a n c y i n t h e a b s o l u t e energy is r e a s o n a b l e . The s i m i l a r i t y i n t h e s h a p e o f t h e d i s p e r s i o n s was c o n s i d e r e d a s

s t r o n g s u p p o r t f o r t h e x-bonded

c h a i n model.

The a p p l i c a b i l i t y o f t h e A-bonded c h a i n model w a s l a t e r q u e s t i o n -

ed when c o n f l i c t i n g ARPES r e s u l t s were o b t a i n e d by S o l a l e t a l . /55/ u s i n g p h o t o n e n e r g i e s i n t h e r a n g e 35-50 e V . A s i g n i f i c a n t l y d i f f e r e n t d i s p e r s i o n was p r e s e n t e d a l o n g t h e f - j - l i n e

w i t h a measured

b a n d w i d t h o f o n l y 0 . 2 5 e V compared t o 0 . 7 5 e V i n r e f . 5 3 . Although

it h a d b e e n r e p o r t e d i n r e f . 53 t h a t 2 0 . 5 e V of t h i s d i s p e r s i o n w a s o b s e r v e d w i t h i n t h e p r o j e c t e d b u l k band g a p , it was c l a i m e d by S o l a l

e t a l . t h a t b u l k c o n t r i b u t i o n s i n t h e s p e c t r a c o u l d have i n f l u e n c e d t h e m e a s u r e d v a l u e f o r t h e d a n g l i n g bond d i s p e r s i o n . S i n c e t h e d i s p e r s i o n o f s u r f a c e s t a t e s s h o u l d be independent o f t h e photon e n e r g y , it was i m p o r t a n t t o d e t e r m i n e w h e t h e r t h e o b s e r v e d d i f f e r e n c e s were s t i l l d u e t o t h e d i f f e r e n t p h o t o n e n e r g i e s u s e d . F u r t h e r ARPES s t u d i e s on t h e G e ( l l l ) 2 x l s u r f a c e were t h u s c a r r i e d o u t w i t h r e s o n a n c e r a d i a t i o n o f 1 6 . 8 a n d 2 1 . 2 eV-photon s y n c h r o t r o n r a d i a t i o n of 2 1 . 2 ,

e n e r g y and w i t h

3 2 . 0 , a n d 3 5 . 0 eV-photon

e n e r g y by

Nicholls et a l . /56/. A summary o f t h e d i f f e r e n t e x p e r i m e n t a l r e s u l t s f o r t h e d a n g l i n g

bond b a n d d i s p e r s i o n a l o n g t h e f - 3 - l i n e

i s given i n F i g . 4 (from

r e f . 5 6 ) . The s o l i d c u r v e shows t h e ARPES peak p o s i t i o n i n t h e

e a r l i e s t 10.2-eV d a t a , w h i l e t h e crosses w e r e o b t a i n e d by a n a l y z i n g t h e p e a k p o s i t i o n i n d i f f e r e n c e s p e c t r a o b t a i n e d by s u b t r a c t i n g

spectra f o r a h y d r o g e n e x p o s e d s u r f a c e f r o m s p e c t r a f o r t h e c l e a n s u r f a c e . The o p e n c i r c l e s show t h e d i s p e r s i o n m e a s u r e d b y S o l a l e t

a l . /55/,

w h i l e t h e s q u a r e s a n d f i l l e d c i r c l e s are f r o m r e f . 5 6 . A s

s e e n i n F i g . 4 t h e d i s p e r s i o n o b t a i n e d by S o l a l e t a l . i s much

smaller t h a n t h a t o b t a i n e d i n t h e o t h e r s t u d i e s , i n p a r t i c u l a r o n e c a n n o t e t h a t t h e a g r e e m e n t b e t w e e n t h e t w o s t u d i e s u s i n g 35-eV p h o t o n e n e r g y i s v e r y p o o r . One d i f f e r e n c e b e t w e e n t h e two 35-eV s t u d i e s , which m i g h t be s i g n i f i c a n t ,

is t h a t the dispersion was

158

-

2

+

10.2 Diff. spectra

0

35 Sclal e t a1

I

Y

W

g L w

O

m

u > W CL

Z, -0.5

-t L

a

z

-1 .o

5

F

F i g . 4 . Comparison between e x p e r i m e n t a l r e s u l t s /_53,55,56/ f o r t h e d a n g l i n g bond d i s p e r s i o n on G e ( l l l ) 2 x l a l o n g t h e T-J symmetry l i n e . From r e f . 5 6 . measured a t room t e m p e r a t u r e d i r e c t l y a f t e r c l e a v a g e i n r e f . 56, w h i l e i n t h e s t u d y by S o l a l e t a l . t h e sample w a s c o o l e d t o 20 K a f t e r c l e a v a g e . T h i s c o u l d , a t l e a s t i n p r i n c i p l e , lead t o temperat u r e dependent changes i n t h e e l e c t r o n i c s t r u c t u r e o r t o a higher l e v e l of c o n t a m i n a t i o n t h a t would e f f e c t t h e d a n g l i n g bond dispersion. I n t h e room t e m p e r a t u r e s t u d i e s r e p o r t e d i n r e f s . 5 3 and 56 t h e r e

i s a s m a l l d e c r e a s e i n t h e measured d i s p e r s i o n w i t h i n c r e a s i n g photon energy. This r e f l e c t s a d e c r e a s e i n t h e k,,-resolution,

as

t h e k i n e t i c e n e r g y o f t h e e m i t t e d e l e c t r o n s i n c r e a s e , which w a s d i s c u s s e d i n some d e t a i l i n r e f . 5 6 . To summarize, t h e d i s p e r s i o n o f t h e f i l l e d d a n g l i n g bond band on t h e G e ( l l l ) 2 x l s u r f a c e h a s been s t u d i e d f o r a wide r a n g e of p h o t o n e n e r g i e s . F o r room t e m p e r a t u r e s t u d i e s t h e r e s u l t s are v e r y c o n s i s t e n t , g i v i n g a s t r o n g l y d i s p e r s i n g d a n g l i n g bond band i n good a g r e e m e n t w i t h c a l c u l a t i o n s u s i n g t h e x-bonded

c h a i n model /50/.

3 . 3 2 an-na

d-nu

b

m band on G e a n d SifU.l)-&l

A c c o r d i n g t o t h e c a l c u l a t i o n s of t h e e l e c t r o n i c s t r u c t u r e of t h e x-bonded c h a i n model t h e d a n g l i n g bond s t a t e s s h o u l d form o n e f i l l e d ( b o n d i n g ) a n d one empty ( a n t i b o n d i n g ) d a n g l i n g bond b a n d on t h e

159

n e u t r a l G e and S i ( l l l ) 2 x l s u r f a c e s .

As w a s d i s c u s s e d i n S e c t i o n 2 ,

it i s p o s s i b l e t o occupy p a r t s of s u c h a n empty band by u s i n g h i g h l y n-doped c r y s t a l s . The f i r s t ARPES s t u d y o f t h i s t y p e w a s m a d e by N i c h o l l s e t a l . / 5 7 / u s i n g h i g h l y n-doped G e ( l l l ) 2 x l s a m p l e s . F o r t h e d o p i n g l e v e l u s e d ( = 1 ~ 1 0 ~~ r8 n - ~ S, b ) t h e e s t i m a t e d o c c u p a t i o n l e v e l of t h e almost empty b a n d i s 0 . 0 0 5 e l e c t r o n s p e r s u r f a c e atom,

i . e . 0 . 5 % o f t h e almost empty band f o r t h e 2x1 r e c o n s t r u c t e d s u r f a c e w i l l be o c c u p i e d a t t h e band minimum. High r e s o l u t i o n ARPES s p e c t r a , p r o b i n g t h e e l e c t r o n i c s t r u c t u r e o f a h i g h l y n-doped G e ( l l l ) 2 x l s a m p l e a l o n g t h e T - z - l i n e t h e 3-point,

a r e shown i n F i g . 5a (hv

=

close t o 10.2 e V ) / 5 7 / . I n a very

limited a n g u l a r range around t h e j - p o i n t

a s h a r p f e a t u r e , B,

s p o n d i n g t o e m i s s i o n from t h e a n t i b o n d i n g band, level.

corre-

i s s e e n a t t h e Fermi

I n t h e s a m e a n g u l a r r a n g e t h e f i l l e d d a n g l i n g bond band, A,

i s a t i t s maximum e n e r g y . A t = 0 . 9 e V below EF, t h e r e i s a s m a l l shoulder,

similar t o t h e shoulder seen a t t h e 3-point

s p e c t r a f r o m S i ( l l l ) 2 x l . The s t r o n g p e a k ,

-1.6

eV,

i n ARPES

seen i n a l l s p e c t r a near

i s due t o t r a n s i t i o n s i n t h e b u l k .

The i n t e n s i t y o f e m i s s i o n from t h e two s u r f a c e s t a t e b a n d s h a s a v e r y s t r o n g p o l a r i z a t i o n dependence. t w o 3-points,

I n F i g . 5b, s p e c t r a a and d,

on o p p o s i t e s i d e s of t h e s u r f a c e normal

(see i n s e t i n

F i g . S a ) , a r e p r o b e d w i t h l i g h t i n c i d e n t a t 60° f r o m t h e s u r f a c e n o r m a l . I n s p e c t r u m c, e m i s s i o n f r o m t h e 3 - p o i n t

w a s obtained with

8 i = Oo a n d t h e e m i s s i o n from b o t h t h e f i l l e d a n d t h e a l m o s t empty b a n d i s v e r y much r e d u c e d , which i s c o n s i s t e n t w i t h t h e e x p e c t e d p o l a r i z a t i o n d e p e n d e n c e o f b o n d i n g and a n t i b o n d i n g n - s t a t e s

w i t h pz-

c h a r a c t e r . S p e c t r a b and e i n F i g . 5b show t h e e f f e c t on t h e s u r f a c e

s t a t e e m i s s i o n o f moderate e x p o s u r e s t o e x c i t e d hydrogen, a f t e r which t h e s u r f a c e s t i l l e x h i b i t e d a 2x1 LEED p a t t e r n . T h e r e a r e p r a c t i c a l l y no e l e c t r o n s r e m a i n i n g i n t h e a n t i b o n d i n g band a n d t h e bonding state emission i s s i g n i f i c a n t l y reduced, while t h e bulk emission i s l a r g e l y unaffected.

I n F i g . 5c t h e experimentally o b t a i n e d d i s p e r s i o n s / 5 1 / f o r t h e f i l l e d a n d a l m o s t empty s u r f a c e s t a t e b a n d s a r e shown t o g e t h e r w i t h t h e b a n d s c a l c u l a t e d f o r t h e n-bonded c h a i n model / 5 0 / .

The measured

d i s p e r s i o n o f t h e f i l l e d d a n g l i n g - b o n d b a n d ( A ) i s t h e same as found i n e a r l i e r s t u d i e s on undoped a n d l i g h t l y n-doped c r y s t a l s / 5 3 , 5 6 / . The o b s e r v e d s u r f a c e s t a t e band g a p ( 0 . 5 e V ) i s i n v e r y good a g r e e m e n t w i t h t h e band g a p f o u n d i n a b s o r p t i o n e x p e r i m e n t s w i t h p h o t o t h e r m a l d i s p l a c e m e n t s p e c t r o s c o p y ( 0 . 5 e V ) / 7 5 / and o p t i c a l

160

......

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

-2 -1 0 ENERGY BELOW E,

(eV)

P

3

r-j

F i g 5. ( a ) Photoemissi.on s p e c t r a probing t h e symmetry l i n e f o r t h e ( 1 1 1 ) 2 x 1 s u r f a c e of a h i g h l y n-doped Ge-crystal / 5 1 / . Peaks A and €3 correspond t o t h e bonding and anti-bonding d a n g l i n g bond band, r e s p e c t i v e l y . hv = 1 0 . 2 eV. b ) S e l e c t e d ARPES s p e c t r a showing t h e p o l a r i z a t i o n dependence and contamination s e n s i t i v i t y of photoemission from t h e bonding and anti-bonding s u r f a c e s t a t e s on G e ( l l l ) 2 x l / 5 7 / . c ) Comparison between t h e measured s u r f a c e s t a t e d i s p e r s i o n s / S 7 / and t h o s e c a l c u l a t e d f o r t h e n-bonded c h a i n model of t h e G e ( l l l ) 2 x l s u r f a c e / 5 8 / . From Ref. 5 7 . II

r e f l e c t i v i t y ( 0 . 5 eV) / 1 6 / and t h e agreement between t h e observed band gap v a l u e s i m p l i e s t h a t p o s s i b l e e x c i t o n i c e f f e c t s a r e q u i t e small i n t h e a b s o r p t i o n experiments. There a r e s t r o n g s i m i l a r i t i e s between t h e measured d i s p e r s i o n s and t h o s e c a l c u l a t e d f o r t h e

x-

bonded chain model concerning t h e shape of t h e f i l l e d (bonding) band and t h e p o s i t i o n i n k l l - s p a c e of t h e minimum of t h e antibonding band. The agreement between experiment and t h e o r y i s q u i t e s a t i s f a c t o r y s i n c e t h e underestimation of t h e band gap and t h e e r r o r i n a b s o l u t e p o s i t i o n of t h e f i l l e d band can be expected /ll/ a s t h e l o c a l - d e n s i t y approximation was used i n t h e c a l c u l a t i o n . The p r e s e n t photoemission experiments a r e a l s o c o n s i s t e n t with a number of p r e v i o u s s t u d i e s using s u r f a c e c o n d u c t i v i t y , Kelvin probe, and photoemission y i e l d measurements on d i f f e r e n t l y doped G e c r y s t a l s , which have shown t h a t t h e Fermi l e v e l i s pinned c l o s e t o

161

t h e valence-band

edge a t t h e s u r f a c e independent o f t h e doping. For

h e a v i l y p-doped

s a m p l e s , t h e b a n d s are f l a t up t o t h e s u r f a c e , w h i l e

f o r h e a v i l y n-doped

samples t h e bands are b e n t upwards. S i n c e t h e

g a p b e t w e e n t h e b u l k v a l e n c e band a n d t h e a n t i b o n d i n g s u r f a c e s t a t e band i s 5 0 . 1 e V , d e f e c t induced v a r i a t i o n s i n t h e Fermi level p o s i t i o n a c r o s s t h e s u r f a c e are l i m i t e d t o t h i s narrow energy r a n g e . T h i s c o u l d b e t h e r e a s o n why ARPES s p e c t r a f r o m t h e G e ( l l l ) 2 x l s u r f a c e h a v e b e e n f o u n d t o be s i g n i f i c a n t l y b e t t e r r e s o l v e d t h a n f r o m t h e S i ( l l l ) 2 x l s u r f a c e . I n s t u d i e s o f t h e a n t i b o n d i n g band on t h e S i ( l l l ) 2 x l s u r f a c e by M a r t e n s s o n e t a1 / 4 8 / ,

t h e minimum o f t h e

empty s u r f a c e s t a t e band was f o u n d t o be = 0 . 4 e V a b o v e t h e v a l e n c e b a n d e d g e , p e r m i t t i n g a l a r g e r d e f e c t i n d u c e d v a r i a t i o n of t h e Fermi l e v e l p o s i t i o n over t h e cleaved s u r f a c e . I n summary, ARPES s t u d i e s o n t h e S i a n d G e ( l l l ) 2 x l s u r f a c e s have p r o v e n t h e e x i s t e n c e o f a f i l l e d d a n g l i n g bond band w i t h a s t r o n g d i s p e r s i o n s e p a r a t e d by a = 0 . 5 e V band g a p from a n a n t i b o n d i n g d a n g l i n g bond b a n d . T h e r e i s a l s o s t r o n g s u p p o r t f o r t h e i d e n t i f i c a t i o n of a weak s t r u c t u r e n e a r

5

(A')

as an i n t r i n s i c s u r f a c e

s t a t e . T h e s e f e a t u r e s a r e a l l c o n s i s t e n t w i t h r e s u l t s from c a l c u l a t i o n s o f t h e e l e c t r o n i c s t r u c t u r e s f o r t h e n-bonded

chain

model f o r b o t h s u r f a c e s . 4

ANNEALED (111) SURFACES OF S i AND G e I t i s p o s s i b l e t o p r e p a r e c l e a n Si a n d G e ( l l 1 ) s u r f a c e s by therm-

a l o r laser a n n e a l i n g such t h a t s m a l l areas of t h e s u r f a c e s e x h i b i t v a r i o u s r e c o n s t r u c t i o n s . I n scanning-tunneling-microscopy

studies,

e x t e n d e d a r e a s w i t h 7x7, 2x1, and 2x2 symmetry h a v e b e e n r e p o r t e d f o r t h e S i ( l l 1 ) s u r f a c e , as w e l l a s s i n g l e u n i t c e l l s e x h i b i t i n g 5x5,

9x9, 2x2, ~ ( 4 x 2 )a n d 43x43 symmetry /78-80/.

The G e ( l l 1 ) s u r -

f a c e h a s b e e n o b s e r v e d h a v i n g r e g i o n s w i t h 7x7, c ( 4 x 2 ) , c ( 2 ~ 8 and ) ~ 2x2 symmetry / 8 0 / .

F o r p r e p a r a t i o n of macroscopic s u r f a c e s needed

f o r e . g . p h o t o e m i s s i o n a n d LEED s t u d i e s , i t i s r e l a t i v e l y e a s y t o o b t a i n S i ( l l 1 ) s u r f a c e s w i t h 7x7 a n d q u a s i - 1 x 1 symmetry a n d G e ( l l 1 ) s u r f a c e s w i t h ~ ( 2 x 8 )symmetry. I n t h e f o l l o w i n g s e c t i o n s w e summar i z e t h e e x p e r i m e n t a l r e s u l t s f o r ARPES s t u d i e s on t h e S i ( 1 1 1 ) 7 x 7 a n d G e ( l l l ) - c ( 2 x 8 ) s u r f a c e s . F o r a more e x t e n s i v e r e v i e w i n c l u d i n g a d i s c u s s i o n o f t h e r e s u l t s on q u a s i - 1 x 1 s u r f a c e s w e r e f e r t o r e f . 1 5 .

162

4 . 1 %far.!

s t a t e s on t h e S i ( l l 1 ) 7x1 s u r m

The most s t a b l e r e c o n s t r u c t i o n o f t h e S i ( l l 1 ) s u r f a c e h a s a 1x7 s u r f a c e u n i t c e l l , i . e . t h e u n i t c e l l i s 4 9 t i m e s l a r g e r t h a n on a h y p o t h e t i c a l i d e a l , u n r e c o n s t r u c t e d , 1x1 s u r f a c e . The 1x7 recons t r u c t i o n i s o b t a i n e d by a n n e a l i n g a c l e a n S i ( l l 1 ) s u r f a c e , where t h e d e t a i l s o f t h e a n n e a l i n g p r o c e d u r e t h a t i s needed, depend on whether t h e c l e a n s u r f a c e h a s been o b t a i n e d by c l e a v i n g , s p u t t e r i n g o r heat c l e a n i n g . Ever s i n c e t h e 7x7 r e c o n s t r u c t i o n w a s f i r s t o b s e r v e d i n LEED-experiments by S c h l i e r and Farnsworth i n 1 9 5 9 /81/ it h a s been a c h a l l e n g e f o r s u r f a c e s c i e n t i s t s t r y i n g t o u n d e r s t a n d semiconductor s u r f a c e r e c o n s t r u c t i o n s , and it i s c e r t a i n l y one of t h e most e x t e n s i v e l y s t u d i e d s u r f a c e s b o t h e x p e r i m e n t a l l y and theoretically. A l a r g e number of models h a s been proposed t o e x p l a i n t h e a v a i l able e x p e r i m e n t a l d a t a , b u t none o f t h e s u g g e s t e d models c o u l d be c o n s i d e r e d a s r e l i a b l e , u n t i l Takayanagi e t a l . / 8 2 / proposed a model f o r t h e 1x7 r e c o n s t r u c t i o n based on r e s u l t s from t r a n s m i s s i o n e l e c t r o n d i f f r a c t i o n experiments. This model, r e f e r r e d t o a s t h e DAS (dimer, adatom, s t a c k i n g - f a u l t ) model, a l s o a c c o u n t s f o r STM, ions c a t t e r i n g and X-ray d i f f r a c t i o n d a t a / 8 3 - 8 8 / . I n t h e model t h e r e are 1 2 adatoms, 6 r e s t atoms, 9 dimers and one c o r n e r h o l e per s u r f a c e u n i t c e l l , and i n one h a l f o f t h e u n i t c e l l t h e r e is a s t a c k i n g fault. S i n c e t h e 1x7 s u r f a c e i s s o complex one might imagine t h a t t h e r e would be many d i f f e r e n t s u r f a c e s t a t e s c o r r e s p o n d i n g t o t h e h i g h number o f i n e q u i v a l e n t atoms i n t h e s u r f a c e u n i t c e l l . Furthermore, t h e l a r g e s i z e of t h e u n i t c e l l w i l l l e a d t o a l a r g e number of bands even f o r e q u i v a l e n t s u r f a c e atoms. E . g . , i f an i d e a l 1x1 s u r f a c e w a s t r e a t e d a s a s u r f a c e w i t h 1x7 p e r i o d i c i t y , t h e r e would be 4 9 dangl i n g bond bands i n t h e s m a l l 7x1 s u r f a c e B r i l l o u i n zone and t h e s e bands would form a c o n t i n u o u s d e n s i t y o f s u r f a c e s t a t e s t h a t i s h a l f - f i l l e d . For a r e c o n s t r u c t e d 7x1 s u r f a c e t h e l o w e r i n g o f t h e symmetry w i l l l e a d t o energy gaps a t t h e B r i l l o u i n zone e d g e s . There w i l l b e a s e p a r a t i o n of t h e s u r f a c e s t a t e s i n t o d i f f e r e n t manifolds of bands which correspond t o t h e d i f f e r e n t t y p e s o f s u r f a c e s t a t e s on t h e r e c o n s t r u c t e d s u r f a c e . The energy s e p a r a t i o n between t h e bands w i t h i n a manifold m u s t be s m a l l and one can h a r d l y expect t o r e s o l v e i n d i v i d u a l bands i n ARPES s t u d i e s , u n l e s s t h e m a t r i x elements f o r t r a n s i t i o n s make one band i n a manifold dominate i n each spectrum. I t s h o u l d be n o t e d t h a t , i n t h e f o l l o w i n g s e c t i o n s , t h e d e n o t a t i o n of t h r e e d i f f e r e n t s u r f a c e s t a t e s / b a n d s (Sl, S2 and

163

S3)

on t h e 1x7 s u r f a c e , i s u s e d f o r t h r e e s e p a r a t e m a n i f o l d s w i t h a n

unknown number o f b a n d s from t h e 7x1 band s t r u c t u r e . T h r o u g h o u t t h e l a s t t w e n t y y e a r s a l a r g e number of p h o t o e m i s s i o n s t u d i e s o f t h e s u r f a c e e l e c t r o n i c s t r u c t u r e on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e h a s b e e n p u b l i s h e d /29,31-35,44,46,64,89-105/. A l r e a d y by

1964 A l l e n a n d G o b e l i /14/ h a d p u b l i s h e d t h e f i r s t p h o t o e l e c t r o n e n e r g y d i s t r i b u t i o n c u r v e s showing d i f f e r e n c e s between t h e c l e a v e d

2x1 s u r f a c e a n d t h e c l e a v e d a n d a n n e a l e d ( s u p p o s e d l y 7x7) s u r f a c e . F o r t h e a n n e a l e d s u r f a c e t h e y f o u n d a c h a r a c t e r i s t i c e m i s s i o n from j u s t b e l o w t h e Fermi l e v e l , which t e n t a t i v e l y was a s s i g n e d t o s u r f a c e s t a t e s t h a t h a d moved up i n t o t h e g a p . T h i s i n t e r p r e t a t i o n

i s i n good a c c o r d w i t h t h e p r e s e n t u n d e r s t a n d i n g o f t h e S1 s u r f a c e

s t a t e , see below. I n t h e s e e a r l y s t u d i e s t h e p h o t o n e n e r g y was v e r y low, 5 6.2 e V , which made i t p o s s i b l e t o s t u d y e m i s s i o n from t h e S1 s u r f a c e s t a t e o n l y . R o w e e t a l . /64,89/ d i d s e v e r a l a n g l e - i n t e g r a t e d s t u d i e s w i t h h i g h e r p h o t o n e n e r g i e s and e m i s s i o n from a l l t h r e e s u r f a c e s t a t e s Sl, S2 a n d S 3 c o u l d be o b s e r v e d f o r t h e f i r s t t i m e . The f i r s t a n g l e - r e s o l v e d p h o t o e m i s s i o n s t u d y on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e was made by Eastman e t a l . /go/. The a n g l e - r e s o l v e d s p e c t r a showed s i g n i f i c a n t i n t e n s i t y v a r i a t i o n s i n t h e s u r f a c e s t a t e e m i s s i o n w i t h a n g l e , w h i l e v e r y s m a l l e n e r g y d i s p e r s i o n s were r e p o r t e d . With t h e mixed s , p - p o l a r i z a t i o n

employed, t h e S3 s u r f a c e

s t a t e w a s s t r o n g a t h i g h a n g l e s o f e m i s s i o n , w h i l e t h e r e was o n l y a weak f e a t u r e a t t h e same e n e r g y i n n o r m a l e m i s s i o n . I n a low p h o t o n e n e r g y (hv

=

10.2 e V ) ARPES s t u d y on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e b y

Hansson e t a l . /91/, t h e e m i s s i o n from Sl and S2 was c h a r a c t e r i z e d w i t h r e s p e c t t o e n e r g y d i s p e r s i o n , p o l a r i z a t i o n d e p e n d e n c e and c o n t a m i n a t i o n s e n s i t i v i t y . The a g r e e m e n t w i t h t h e r e s u l t s o f Eastman

e t a l . /90/ w a s good, e . g . a s t r o n g m e t a l l i c e d g e (S1) was r e p o r t e d a n d t h e e m i s s i o n from b o t h S1 and S 2 was f o u n d t o b e s u p p r e s s e d f o r normal i n c i d e n c e o f t h e l i g h t . High p h o t o n - e n e r g y

ARPES s t u d i e s

(hv = 20-90 e V ) were r e p o r t e d by

Houzay a n d c o w o r k e r s /31-34/. The S 2 s u r f a c e s t a t e s e e n i n normal e m i s s i o n was shown t o h a v e s t r o n g v a r i a t i o n s i n i n t e n s i t y w i t h phot o n e n e r g y . I n c o n t r a s t t o t h e p r e v i o u s s t u d i e s o n l y a s m a l l metal-

l i c e d g e (S1) w a s r e p o r t e d and i t w a s p r o p o s e d /34/ t h a t t h e m e t a l -

l i c edge i s a r e s u l t o f e x t r i n s i c e f f e c t s . S i m i l a r l y , a s m a l l m e t a l l i c e d g e w a s a l s o r e p o r t e d by Hansson e t a l . /30/ on 7x7 s u r f a c e s o b t a i n e d by a n n e a l i n g o f 2 x i s u r f a c e s . A s d i s c u s s e d by Eastman e t a l . /92/, a n u n d e r s i z e d m e t a l l i c e d g e c a n be d u e t o

164

e x p e r i m e n t a l parameters l i k e e m i s s i o n a n g l e , p o l a r i z a t i o n and photon e n e r g y o r due t o improper a n n e a l i n g of t h e 7x1 s u r f a c e . The d i s p e r s i o n s o f t h e s u r f a c e s t a t e s on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e a l o n g t h e h i g h symmetry d i r e c t i o n s , Neddermeyer e t a l . / 9 8 / ,

ri?

and FM, h a v e been s t u d i e d by

Uhrberg e t a l . /102/ a n d Mgrtensson e t a l .

/105/ and t h e r e s u l t s of t h e l a s t s t u d y a r e d e s c r i b e d below. The

e a r l i e r s t u d i e s gave q u i t e s i m i l a r r e s u l t s , a l t h o u g h s l i g h t l y small e r d i s p e r s i o n s were r e p o r t e d . T h i s can p r o b a b l y be a t t r i b u t e d t o t h e somewhat p o o r e r r e s o l u t i o n i n t h e s p e c t r a i n r e f s . 98 and 1 0 2 .

F i g . 6a shows A W E S s p e c t r a from t h e s t u d y by Mdrtensson e t a l . /105/

f o r v a r i o u s a n g l e s of e m i s s i o n a l o n g t h e [lo?] a z i m u t h a l

d i r e c t i o n . The i n c i d e n t r a d i a t i o n was p - p o l a r i z e d w i t h 2 1 . 2 e V photon e n e r g y . There a r e t h r e e s t r u c t u r e s S l , S2 and S3,

in the

r a n g e 0-2 e V below t h e F e r m i l e v e l , which a r e due t o e m i s s i o n from t h e p r e v i o u s l y e s t a b l i s h e d s u r f a c e s t a t e s . T h e r e i s a l s o a number of o t h e r s t r o n g f e a t u r e s i n t h e s p e c t r a , t h a t a r e i n t e r p r e t e d as e m i s s i o n from b u l k b a n d s . I n r e f . 102 Uhrberg e t a l . a n a l y z e d b u l k contributions t o 21.2-eV

s p e c t r a l i k e t h e o n e s i n F i g . 6a, and e . g .

t h e s t r o n g b r o a d peak r a p i d l y d i s p e r s i n g from -3 t o -4

e V around 15’

e m i s s i o n a n g l e can be i d e n t i f i e d a s due t o d i r e c t t r a n s i t i o n s from t h e s e c o n d topmost v a l e n c e band. A s t r o n g s u p p o r t f o r t h e s u r f a c e

s t a t e i n t e r p r e t a t i o n of S,

S2

and S3 i s g i v e n by t h e c o n s i s t e n c y of

t h e i r d i s p e r s i o n s f o r d i f f e r e n t phot,on e n e r g i e s , which i s n o t found

for the other structures i n the spectra. The S1 s u r f a c e s t a t e h a s a peak p o s i t i o n t h a t i s 2 0 . 2 e V from t h e Fermi l e v e l and t h e h i g h e n e r g y c u t o f f i s s i m i l a r t o t h e Fermiedge o f a metal s u r f a c e . T h i s m e t a l l i c c h a r a c t e r of t h e 1 x 7 s u r f a c e h a s a l s o b e e n found i n e l e c t r o n - e n e r g y - l o s s

measurements, where it

r e s u l t s i n a v e r y s t r o n g b r o a d e n i n g of t h e e l a s t i c p e a k /106/. The i n t e n s i t y of e m i s s i o n from t h e S 1 s u r f a c e s t a t e has a c h a r a c t e r i s t i c v a r i a t i o n w i t h t h e p a r a l l e l wavevector, k,,, i . e . maximum e m i s s i o n i n t e n s i t y i s o b t a i n e d a p p r o x i m a t e l y h a l f w a y between t h e f - p o i n t

and

t h e 1 x 1 s u r f a c e BZ boundary / 9 3 / . A s mentioned above, it has been s u g g e s t e d t h a t t h e S,

s t r u c t u r e r e s u l t s from e x t r i n s i c e f f e c t s / 3 4 / ,

s i n c e i t was s e e n w i t h v e r y low i n t e n s i t y i n some s t u d i e s . I t i s i n t e r e s t i n g t o n o t e t h a t i n t h o s e s t u d i e s /30,34/

the reported

s p e c t r a were a l l o b t a i n e d a t e m i s s i o n a n g l e s f o r which t h e i n t e n s i t y of S,

i s low anyway, i . e . i n normal e m i s s i o n o r a t h i g h a n g l e s . I t

now seems t o be g e n e r a l l y a c c e p t e d t h a t S1 i s a n i n t r i n s i c s u r f a c e s t a t e o f t h e 7x7 s u r f a c e .

165

I

I

I

I

I

I

I

I

I

I

I

I

I

I

LI I

-6 -4 -2 O ENERGY BELOW E, (eV)

ENERGY BELOW E,

(eV)

F i g . 6 . ( a ) Photoemission s p e c t r a r e c o r d e d from S i ( 1 1 1 ) 7 x 7 f o r e m i s s i o n a l o n g t h e [ l o l l a z i m u t h a l d i r e c t i o n . E x c i t a t i o n w i t h pp o l a r i z e d 21.2-eV r a d i a t i o n i n c i d e n t a t 45' /105/. (b) Normal-emission s p e c t r a from S i ( 1 1 1 ) 7 x 7 f o r v a r i o u s photon e n e r g i e s . The a n g l e of i n c i d e n c e of t h e photons i s O i = 15' and t h e p o l a r i z a t i o n v e c t o r i s i n t h e (Oil) p l a n e , 15’ from t h e [Zllld i r e c t i o n . From r e f . 5 2 . The second s u r f a c e s t a t e S2 i s seen c l e a r l y i n a l l s p e c t r a i n F i g . 6 a . I t has o f t e n been d e s c r i b e d a s a d i s p e r s i o n l e s s f e a t u r e , however, t h e r e i s a small = 0 . 1 eV p o s i t i v e d i s p e r s i o n from

r

to

0.5(r-K). The d i s p e r s i o n s of t h e s u r f a c e s t a t e s a l o n g t h e main symmetry l i n e s

r-k

and

T-fi a r e shown i n F i g . I t o g e t h e r with t h e

v a l e n c e band edge a s p r o j e c t e d o n t o t h e 1x1 s u r f a c e B Z . A v a l u e of 0.63 eV f o r E,-E,

was used, which has been r e p o r t e d as an average

v a l u e f o r many 1x7 s u r f a c e s w i t h a maximum d e v i a t i o n of = 0 . 0 7 eV /107/.

The energy of S 2 i s 0 . 8 - 0 . 9 e V b e l o w t h e F e r m i l e v e l i n t h e

whole s u r f a c e BZ which means t h a t it i s l o c a t e d i n t h e p r o j e c t e d bulk band gap, except f o r k / / - p o i n t s c l o s e t o

f.

F i n a l l y , t h e S3 s u r f a c e s t a t e i s c l e a r l y seen a t h i g h a n g l e s i n F i g . 6 a . I n t h e [lOi] azimuthal d i r e c t i o n , S j has a n e g a t i v e d i s p e r s i o n of = 0 . 3 eV f o r i n c r e a s i n g emission a n g l e s a n d it f a l l s

166

It-

M

-

-

K -rloiI

r

WAVEVECTOR

F i g . 7 . The e x p e r i m e n t a l l y measured d i s p e r s i o n s o f s u r f a c e s t a t e s on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e . D a t a from r e f . 1 0 5 . w i t h i n t h e p r o j e c t e d bulk band gap i n a l a r g e r e g i o n around t h e

E-

p o i n t as s e e n i n F i g . 7 . I n t h e [ 2 i i ] a z i m u t h , S3 d i s p e r s e s down t o

i t s a b s o l u t e minimum e n e r g y , = 2 . 0 e V below EF, a t t h e M-point r e s u l t i n g i n a t o t a l bandwidth o f

= 0.4 eV.

F o r t h e f u r t h e r d i s c u s s i o n o f S 3 , it i s i m p o r t a n t t o n o t e t h a t it

i s n o t p o s s i b l e t o f o l l o w t h i s s t r u c t u r e from h i g h e m i s s i o n a n g l e s a l l t h e way t o normal e m i s s i o n . I n s t e a d w e a s s o c i a t e t h e e m i s s i o n s e e n i n t h e normal d i r e c t i o n ,

a t -2.0

eV,

t o e m i s s i o n from b u l k

s t a t e s . I t h a s been p r o p o s e d i n two s t u d i e s u s i n g 21.2-eV /90,97/

radiation

t h a t e m i s s i o n from S3 c a n be s e e n i n t h e normal d i r e c t i o n

a n d t h a t it i s t h e n e x c i t e d by l i g h t p o l a r i z e d p a r a l l e l t o t h e surface. Since p-polarized

l i g h t at a high angle of incidence w a s

u s e d t o o b t a i n t h e 21.2-eV

s p e c t r a i n F i g . 6a, t h i s t y p e of e m i s s i o n

should be suppressed. F i g . 6b shows normal e m i s s i o n s p e c t r a , o b t a i n e d w i t h a n a n g l e o f l i g h t i n c i d e n c e Oi=15' and t h e p o l a r i z a t i o n v e c t o r i n t h e (Oil) plane /52/.

A s s e e n when comparing t h e 21.2-eV

spectrum i n F i g . 6b

w i t h t h e normal e m i s s i o n s p e c t r u m i n F i g . 6a, t h e r e are v e r y s t r o n g p o l a r i z a t i o n e f f e c t s . When t h e p o l a r i z a t i o n v e c t o r i s c l o s e t o p a r a l l e l t o t h e [ 2 1 1 1 d i r e c t i o n a l o n g t h e s u r f a c e , t h e e m i s s i o n from t h e S 1 and S2 s u r f a c e s t a t e s i s v e r y much r e d u c e d w h i l e a s t r o n g f e a t u r e a p p e a r s a t 2 . 0 e V below EF i n normal e m i s s i o n . From t h e p h o t o n e n e r g y dependence o f t h e p e a k p o s i t i o n it m u s t , however, be c o n c l u d e d t h a t t h i s s t r u c t u r e i s due t o e m i s s i o n from t h e b u l k . F u r t h e r c o n f i r m a t i o n of t h i s a s s i g n m e n t i s o b t a i n e d from s i m i l a r s t u d i e s on t h e S i ( l l l ) 2 x l s u r f a c e , where t h e same b u l k c o n t r i b u t i o n

167

h a s b e e n i d e n t i f i e d a s b e i n g due t o d i r e c t t r a n s i t i o n s from t h e two t o p m o s t v a l e n c e b a n d s , which a r e d e g e n e r a t e a l o n g t h e a p p r o p r i a t e l-L l i n e i n t h e b u l k BZ /45/.

I n some earlier s t u d i e s /90,97/, normal e m i s s i o n u s i n g 2 1 . 2 - e V

t h e p o l a r i z a t i o n dependence of

p h o t o n e n e r g y had b e e n u s e d t o con-

c l u d e t h a t t h e S1 and S2 s u r f a c e s t a t e s h a v e S3

s t a t e w a s a s s i g n e d t o have

A3

A l symmetry, w h i l e t h e

symmetry. From t h e p h o t o n e n e r g y

d e p e n d e n t d a t a i n F i g . 6b it c a n i n s t e a d b e i n f e r r e d t h a t t h e p o l a r i z a t i o n d e p e n d e n c e o f t h e s t r u c t u r e a t 2 . 0 e V below EFI s e e n i n n o r m a l e m i s s i o n , r e f l e c t s t h e A 3 symmetry o f t h e t o p m o s t t w o b u l k b a n d s . We f i n d t h a t , f o r a l l t h r e e s u r f a c e s t a t e s S l , S2 and S 3 i n F i g . 6 a , t h e p o l a r i z a t i o n d e p e n d e n c e i s q u a l i t a t i v e l y t h e same. J u s t

as f o r S 1 and S p . t h e

S3 s u r f a c e

s t a t e e m i s s i o n i s s u p p r e s s e d when

t h e p o l a r i z a t i o n v e c t o r of t h e photons i s p a r a l l e l t o t h e s u r f a c e /102/.

T h i s i s c h a r a c t e r i s t i c f o r s-p,

t y p e o r b i t a l s and t h e p o l a r i -

z a t i o n d e p e n d e n c e t h u s i m p l i e s a l a r g e s-p,

( d a n g l i n g bond) c o n t e n t

i n a l l three s u r f a c e s t a t e s . T e s t s o f t h e c o n t a m i n a t i o n s e n s i t i v i t y have been u s e d t o s u p p o r t

t h e i d e n t i f i c a t i o n o f s u r f a c e s t a t e s . I n r e f . 102 b o t h 0 2 and C12 e x p o s u r e s w e r e u s e d t o modify t h e s u r f a c e i n o r d e r t o r e d u c e t h e i n t e n s i t y o f e m i s s i o n from s u r f a c e s t a t e s . I t w a s f o u n d t h a t low e x p o s u r e s of oxygen h a d a l a r g e r e f f e c t on t h e S1 s u r f a c e s t a t e t h a n on S2,

w h i l s t c h l o r i n e had t h e o p p o s i t e e f f e c t . A c o m p a r i s o n between

ARPES s p e c t r a from t h e S i ( l l l ) 2 x l a n d 7x7 s u r f a c e s i s a l s o u s e f u l

f o r i d e n t i f i c a t i o n of b u l k a n d s u r f a c e c o n t r i b u t i o n s . I t i s c l e a r t h a t t h e r e a r e no f e a t u r e s i n t h e 2x1 s p e c t r a t h a t c o r r e s p o n d t o t h e S l , Sz and S 3 s t r u c t u r e s ,

while t h e r e a r e bulk t r a n s i t i o n s t h a t a r e

f o u n d i n s p e c t r a from b o t h s u r f a c e s . The o r i g i n o f t h e s u r f a c e s t a t e s on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e h a s r e c e n t l y b e e n d i s c u s s e d by N o r t h r u p /108/. H e p e r f o r m e d model c a l c u l a t i o n s f o r (111) s u r f a c e s w i t h o n e S i adatom per u n i t c e l l i n

4 3 x 4 3 o r 2x2 s u r f a c e p e r i o d i c i t i e s . These adatom u n i t s a r e e s s e n t i a l components i n t h e DAS model of t h e 7x7 s u r f a c e . I n p a r t i c u l a r t h e 2x2 s u r f a c e g e o m e t r y w i t h o n e 3 - f o l d c o o r d i n a t e d adatom a n d one rest

a t o m p e r u n i t c e l l can s i m u l a t e t h e l a r g e t r i a n g u l a r u n i t s cont a i n i n g 1 2 adatoms a n d 6 r e s t atoms p e r 7x7 u n i t c e l l i n t h e DAS-

model. F o r t h e 2x2 adatom geometry t h r e e s u r f a c e s t a t e s a r e f o u n d , a l l w i t h a p p r e c i a b l e s-p, ( d a n g l i n g bond) c h a r a c t e r . The s t a t e labelled

i s composed o f s u b s t r a t e d a n g l i n g bond s t a t e s c o u p l e d t o

adatom p z o r b i t a l s , which a r e p r e d i c t e d t o form a p a r t l y f i l l e d m a n i f o l d o f b a n d s on t h e 1x7 s u r f a c e . X2 i s a d o u b l y o c c u p i e d

168

d a n g l i n g bond s t a t e l o c a l i z e d on t h e rest atoms, a n d f i n a l l y C3 i s composed o f s u b s t r a t e d a n g l i n g bond o r b i t a l s c o u p l e d t o adatom px

,&

and py o r b i t a l s . The e n e r g y p o s i t i o n s a n d d i s p e r s i o n s o f t h e

and C3 s u r f a c e s t a t e b a n d s f o r t h e 2x2 a n d 43x43 model g e o m e t r i e s g i v e v e r y s t r o n g s u p p o r t f o r i d e n t i f y i n g C1 , C p and C3 w i t h t h e S1, Sg and S 3 s u r f a c e

s t a t e s s e e n i n ARPES m e a s u r e m e n t s .

H a m e r s e t a l . /log/ v e r y r e c e n t l y d e v e l o p e d a new method, current-imaging-tunneling o b t a i n energy-resolved

s p e c t r o s c o p y (CITS) which w a s u s e d t o

real-space

images o f t h e f i l l e d and empty

s u r f a c e s t a t e s o f t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e . I t was shown, v e r y conv i n c i n g l y , t h a t t h e S1 s u r f a c e s t a t e i s l o c a l i z e d on t h e p o s i t i o n s i n t h e 1x7 u n i t c e l l which c o r r e s p o n d t o t h e adatoms i n t h e DASmodel a n d t h e S2 s u r f a c e s t a t e i s l o c a l i z e d on t h e rest atom p o s i t i o n s . H a m e r s e t a l . a l s o f o u n d some e v i d e n c e f o r t u n n e l i n g from a lower l y i n g s u r f a c e s t a t e , a s s i g n e d t o adatom backbonds,

which

would c o r r e s p o n d t o t h e s t a t e S 3 . Thus, b a s e d on t h e o r e t i c a l c a l c u l a t i o n s a n d CITS s t u d i e s , t h e r e i s p r e s e n t l y a good u n d e r s t a n d i n g o f t h e o r i g i n o f t h e d i f f e r e n t s u r f a c e s t a t e s o b s e r v e d i n ARPES e x p e r i m e n t s on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e .

4.2.

G e ( l l 1 ) -c ( 2 &

The c l e a v e d G e ( l l l ) 2 x l s u r f a c e i s m e t a s t a b l e a n d upon h e a t i n g t o

= 3OO0C it t r a n s f o r m s t o a more s t a b l e s u r f a c e which e x h i b i t s a complex LEED p a t t e r n w i t h 1 / 2 a n d 1 / 8 o r d e r s p o t s . I n s e v e r a l r e c e n t s t u d i e s t h e LEED p a t t e r n h a s b e e n a s s i g n e d t o a t h r e e - d o m a i n

~(2x8)

r e c o n s t r u c t i o n . S i n c e t h e r e a r e some e x p e c t e d 1/4 o r d e r s p o t s m i s s i n g i n t h e ~ ( 2 x 8 )LEED p a t t e r n , t h e i n t e r n a l s t r u c t u r e of t h e ~ ( 2 x 8 )u n i t c e l l h a s t o a c c o u n t f o r t h e c o r r e s p o n d i n g s t r u c t u r e f a c t o r c a n c e l l a t i o n s , as h a s b e e n d i s c u s s e d b y Chadi and Chiang

/llO/ and Yang and Jona / l l l / . I n t h e f i r s t a n g l e - i n t e g r a t e d p h o t o e m i s s i o n s t u d y on a n n e a l e d G e ( l l 1 ) s u r f a c e s by Murotani e t a l . / 7 3 /

t h e e x i s t e n c e of s u r f a c e

s t a t e s c l o s e t o t h e v a l e n c e band e d g e was s u g g e s t e d . F u r t h e r s u p p o r t f o r t h i s i d e n t i f i c a t i o n was o b t a i n e d i n p h o t o e m i s s i o n y i e l d measurements by G u i c h a r e t a l . / 1 1 2 / ,

i n which a s u r f a c e s t a t e band

0 . 6 e V below t h e v a l e n c e band e d g e was f o u n d . H i m p s e l e t al. /93/ s t u d i e d t h e a n g u l a r d i s t r i b u t i o n s o f p h o t o e l e c t r o n s from t h e t h e r m a l l y a n n e a l e d G e (111)-c ( 2 x 8 ) a n d t h e l a s e r a n n e a l e d G e (111)1 x 1 s u r f a c e s . On b o t h s u r f a c e s t h e y f o u n d two s u r f a c e s t a t e s a t - 0 . 1 eV a n d -1.3 e V r e l a t i v e t o t h e v a l e n c e band e d g e , which e x h i b i t e d

169

c h a r a c t e r i s t i c e m i s s i o n p a t t e r n s w i t h i n t h e 1 x 1 s u r f a c e B Z . The

f i r s t s t u d i e s of t h e d i s p e r s i o n s o f t h e s u r f a c e s t a t e band s t r u c t u r e

w e r e p r e s e n t e d by B r i n g a n s a n d Hochst / 1 1 3 ,

114/, who r e p o r t e d two

a l m o s t f l a t b a n d s c o n s i s t e n t w i t h t h e r e s u l t s o f Himpsel e t a l . /93/.

Yokotsuka e t a l . /115/ r e p e a t e d t h e s e measurements w i t h b e t t e r e n e r g y r e s o l u t i o n and more d e t a i l s f o r t h e d i s p e r s i o n s o f t h e s u r f a c e s t a t e b a n d s were f o u n d . F o r c e r t a i n e m i s s i o n a n g l e s t h e r e were t r i p l e t s t r u c t u r e s i n t h e s p e c t r a i n d i c a t i n g t h a t t h e r e are a t l e a s t t h r e e d i f f e r e n t s u r f a c e s t a t e b a n d s . Yokotsuka a n d c o w o r k e r s a l s o s t u d i e d t h e e m i s s i o n from t h e G e ( l l l ) - c ( 2 x 8 ) s u r f a c e a s t h e temper a t u r e w a s r a i s e d and t h e s u r f a c e f i n a l l y t r a n s f o r m e d i n t o a 1x1 r e c o n s t r u c t e d s u r f a c e /116/. A t h i g h e r t e m p e r a t u r e s a weak s t r u c t u r e c o r r e s p o n d i n g t o a n o t h e r w i s e empty s u r f a c e s t a t e a p p e a r e d j u s t a b o v e t h e Fermi l e v e l . The a n g u l a r dependence o f t h e e m i s s i o n from t h i s s t a t e w a s f o u n d t o be t h e same a s t h a t of t h e m e t a l l i c s t a t e on t h e S i ( 1 1 1 ) 7 x 7 s u r f a c e . S t r o n g s i m i l a r i t i e s between t h e a n g u l a r d i s t r i b u t i o n s o f t h e two l o w e r l y i n g s u r f a c e s t a t e s on S i ( 1 1 1 ) 7 x 7 a n d G e ( l l l ) - c ( 2 x 8 ) had a l s o p r e v i o u s l y b e e n r e p o r t e d by Himpsel e t

a l . Both Himpsel e t a l . / 9 3 /

and Yokotsuka e t a l . /116/ s u g g e s t e d

t h a t s i m i l a r b u i l d i n g b l o c k s a r e p r e s e n t on t h e S i ( 1 1 1 ) 7 x 7 a n d G e ( l l l ) - c ( 2 x 8 ) s u r f a c e s and t h a t t h e l o n g r a n g e o r d e r i n g of t h e s e b u i l d i n g b l o c k s a f f e c t s t h e o c c u p a t i o n of t h e s u r f a c e s t a t e n e a r t h e Fermi l e v e l . T h e r e h a v e r e c e n t l y been p u b l i s h e d s e v e r a l d e t a i l e d s t u d i e s of t h e s u r f a c e s t a t e / r e s o n a n c e b a n d s t r u c t u r e on t h e G e ( l l l ) - c ( 2 x 8 ) s u r f a c e . The e n e r g y d i s p e r s i o n s of t h e s u r f a c e s t a t e c o n t r i b u t i o n s , measured a l o n g t h e

F-l?

l i n e i n t h e s u r f a c e BZ i n t h e d i f f e r e n t

e x p e r i m e n t s , a r e shown i n Fig. 8 ( f r o m r e f . 1 1 7 ) . Data p o i n t s from Yokotsuka e t a l . /115/ and N i c h o l l s e t a l . / l l E /

are p l o t t e d assu-

ming a d i f f e r e n c e o f 0 . 1 5 e V between t h e v a l e n c e band maximum and t h e F e r m i l e v e l . The d a t a p o i n t s from B r i n g a n s e t a l . /119/ a r e s h i f t e d by 0 . 2 5 e V t o o b t a i n b e t t e r o v e r a l l a g r e e m e n t . F i n a l l y , t h e r e s u l t s from A a r t s e t a l . / 1 1 7 / a r e summarized a s f u l l drawn d i s p e r s i o n c u r v e s f o r f o u r s e g m e n t s of t h e s u r f a c e s t a t e band s t r u c t u r e . A p a r t from a weak, r a p i d l y d i s p e r s i n g s h o u l d e r r e p o r t e d by A a r t s e t a l . n e a r normal e m i s s i o n , t h e r e i s good a g r e e m e n t between t h e f o u r s t u d i e s u s i n g d i f f e r e n t photon e n e r g i e s and t h i s i s s t r o n g s u p p o r t f o r t h e i d e n t i f i c a t i o n of t h e f e a t u r e s as s u r f a c e states/resonances. A c e r t a i n spread i n t h e data points i s t o be e x p e c t e d , s i n c e t h e f e a t u r e s are n o t e a s y t o r e s o l v e and, f u r t h e r -

170

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;21.2 eV

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Fig, 8 . Summary o f t h e [ O l l l - d i r e c t i o n on t h e p o i n t s from r e f s . 115, while t h e r e s u l t s from

-

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1.o

0.5

1.5

coii>

measured s u r f a c e s t a t e d i s p e r s i o n s a l o n g t h e G e ( l l l ) - c ( Z x 8 ) s u r f a c e , from r e f . 117. Data 118 and 1 1 9 a r e shown w i t h d i f f e r e n t symbols, r e f . 1 1 7 are shown a s c u r v e s .

more, b u l k c o n t r i b u t i o n s c a n i n t e r f e r e , as most o f t h e measured s u r f a c e s t a t e band s t r u c t u r e i s n o t i n t h e p r o j e c t e d 1x1 b u l k band gap

-

I t i s c l e a r from F i g . 8 t h a t t h e s u r f a c e s t a t e band s t r u c t u r e

along t h e

f‘-E l i n e i s more c o m p l i c a t e d t h a n j u s t t h e two a l m o s t

flat

bands t h a t w e r e p r o p o s e d i n t h e f i r s t ARPES s t u d i e s . I n t h e l a t e r high r e s o l u t i o n s t u d i e s , t h e r e a r e resolved f e a t u r e s a t intermediate e n e r g i e s found a t two p o s i t i o n s a l o n g t h e T-k-line, v a l u e s of 0 . 3 and 0 . 6 A-1

i . e . f o r k,,-

r e s p e c t i v e l y . The s u r f a c e s t a t e band

s t r u c t u r e h a s a l s o been s t u d i e d a l o n g t h e [1211 and [Zii] a z i m u t h a l d i r e c t i o n s /115,117-119/ and s m a l l e r d i s p e r s i o n s o f t h e bands have c o n s i s t e n t l y been found i n t h e s e d i r e c t i o n s i n t h e d i f f e r e n t experiments. In p a r t i c u l a r ,

u n l i k e f o r s p e c t r a i n t h e [Oli] azimuth,

no d i s p e r s i n g f e a t u r e s a r e s e e n i n between t h e two r e g i o n s , t h a t have s o m e t i m e s been d e s c r i b e d a s c o n t a i n i n g f l a t b a n d s . I n summary, w e f i n d t h a t q u i t e c o n s i s t e n t r e s u l t s have been reported f o r t h e e l e c t r o n i c s t r u c t u r e of t h e G e ( l l l ) - c ( 2 x 8 ) surface. With m o d e r a t e r e s o l u t i o n i t a p p e a r s t o c o n s i s t of t w o r a t h e r f l a t bands, w i t h t h e topmost band dominant n e a r normal e m i s s i o n w h i l e t h e

l o w e r band h a s h i g h e r i n t e n s i t y a t h i g h e r e m i s s i o n a n g l e s . With h i g h e r r e s o l u t i o n it h a s been p o s s i b l e t o f i n d s i g n i f i c a n t f i n e

171

s t r u c t u r e i n t h e d i s p e r s i o n l e a d i n g t o t h e i d e n t i f i c a t i o n of f o u r s u r f a c e s t a t e bands. Since t h e G e ( l l l ) - c ( 2 x 8 ) s u r f a c e has, so f a r , a l w a y s c o n t a i n e d t h r e e d i f f e r e n t l y r o t a t e d domains i t i s c l e a r t h a t t h e p h o t o e m i s s i o n s p e c t r a s h o u l d be i n f l u e n c e d b y m u l t i - d o m a i n

e f f e c t s a s w e l l as p o s s i b l e d i s o r d e r b e t w e e n t h e d o m a i n s . I t c e r t a i n l y would b e v e r y h e l p f u l f o r t h e e v a l u a t i o n o f t h e p h o t o e m i s s i o n d a t a and t h e u n d e r s t a n d i n g o f t h e e l e c t r o n i c s t r u c t u r e , i f it c o u l d b e p o s s i b l e t o p r e p a r e s i n g l e - d o m a i n s o f t h e ~ ( 2 x 8 )r e c o n s t r u c t i o n by some s p e c i a l method.

5

S i ( 1 0 0 ) AND G e ( 1 0 0 ) SURFACES The e q u i l i b r i u m s u r f a c e p e r i o d i c i t i e s o f t h e S i and G e ( 1 0 0 ) s u r -

f a c e s r e m a i n a m a t t e r o f d i s c u s s i o n i n t h e l i t e r a t u r e . F o r reviews o f t h e p r e s e n t u n d e r s t a n d i n g we r e f e r t o r e c e n t p u b l i c a t i o n s by

H a m e r s e t a l . /120/,

Lambert e t a l . / 1 2 1 / ,

Kubby e t a l . / 1 2 2 /

and

r e f e r e n c e s t h e r e i n . The b a s i c 2x1 r e c o n s t r u c t i o n i s g e n e r a l l y accepted t o e n t a i l t h e formation of dimers, c r e a t e d through p a i r i n g o f t h e n e a r e s t n e i g h b o r s u r f a c e a t o m s . I n t h e room t e m p e r a t u r e STM s t u d i e s of S i ( 1 0 0 ) by Hamers e t a l . / 1 2 0 /

a l . /122/

and G e ( 1 0 0 ) b y Kubby e t

i t w a s found t h a t t h e s e d i m e r s are o r d e r e d i n domains o f

rows o r i e n t e d a l o n g t h e p e r p e n d i c u l a r

[ O l l ] and

[ O l i l d i r e c t i o n s and

t h e two t y p e s o f domains a r e s e p a r a t e d by monatomic s t e p s . The d i s t a n c e b e t w e e n t h e rows i s t w i c e t h e l a t t i c e c o n s t a n t o f t h e u n r e c o n s t r u c t e d s u r f a c e , r e s u l t i n g i n a n a p p a r e n t 2x1 r e c o n s t r u c t i o n . I n h i g h r e s o l u t i o n images o f t h e G e ( 1 0 0 ) s u r f a c e , a n asymmetry of

most o f t h e d i m e r s i s f o u n d , which i s a t t r i b u t e d t o a b u c k l i n g o f t h e d i m e r s . I n g e n e r a l , t h e rows o f d i m e r s h a v e a n a p p a r e n t z i g - z a g s t r u c t u r e i n STM-images,

i n d i c a t i n g t h a t t h e d i r e c t i o n of buckling

a l t e r n a t e s from d i m e r t o d i m e r a l o n g a row. C o n c e r n i n g t h e o r d e r b e t w e e n n e i g h b o r i n g rows, a l o c a l ~ ( 2 x 2 )symmetry o c c u r s when t h e b u c k l i n g i n two rows a r e i n p h a s e , w h i l e a ~ ( 4 x 2 )symmetry o c c u r s when t h e b u c k l i n g i s 180’ o u t o f p h a s e . I n t h e STM-images p r e s e n t e d , t h e m a j o r p a r t c o n s i s t s of z i g - z a g r o w s b u t t h e i n d i v i d u a l ~ ( 2 x 2 ) a n d ~ ( 4 x 2 )domains a r e s m a l l , i n d i c a t i n g a weak c o r r e l a t i o n between t h e p h a s e o f t h e b u c k l i n g i n n e i g h b o r i n g r o w s . Although o n l y v e r y

s m a l l r e g i o n s were f o u n d t o h a v e t r u e 2x1 symmetry, t h e s u r f a c e a s p r e p a r e d b y Kubby e t a l . e x h i b i t e d a s h a r p 2x1 LEED-pattern. T h e r e

was no e v i d e n c e o f q u a r t e r o r d e r s p o t s o r s t r e a k s t h a t would b e i n d i c a t i v e o f ~ ( 4 x 2 )o r ~ ( 2 x 2 domains ) extending over l a r g e r regions.

172

Top view

Top view

IOlil

Side view

Side view

............................. domain b

( a ) IDEAL

(b) ASYMMETRIC DIMERS

i

(c) TWO-DOMAIN 2x1 SBZs

F i g . 9. ( a ) S c h e m a t i c views of t h e u n r e c o n s t r u c t e d S i ( 1 0 0 ) s u r f a c e . ( b ) The asymmetric dimer-model o f t h e S i ( 1 0 0 ) 2x1 s u r f a c e . (c) Superimposed s u r f a c e B r i l l o u i n zones of t h e two d i f f e r e n t S i ( 1 0 0 ) 2x1 domains, i n t h e r e p e a t e d zone scheme. I n o t h e r LEED /123-125/

and H e d i f f r a c t i o n /121/ s t u d i e s of t h e

G e ( 1 0 0 ) s u r f a c e a t room t e m p e r a t u r e , b e s i d e s s t r o n g 2x1 s p o t s , a d d i t i o n a l s t r e a k s passing through t h e q u a r t e r o r d e r p o s i t i o n s of t h e ~ ( 4 x 2 )and t h e c e n t e r p o s i t i o n of t h e ~ ( 2 x 2 )d i f f r a c t i o n p a t t e r n s have been r e p o r t e d . These d i f f r a c t i o n s t u d i e s and t h e STMs t u d y /122/ t h u s i n d i c a t e t h a t t h e G e ( 1 0 0 ) s u r f a c e a t room temperat u r e h a s a m i x t u r e of r e g i o n s w i t h ~ ( 4 x 2 )and ~ ( 2 x 2 )symmetry and t h a t d e p e n d i n g on t h e sample p r e p a r a t i o n t h e y can b e l a r g e enough t o b e e v i d e n c e d i n LEED and H e d i f f r a c t i o n .

I n s t u d i e s of t h e tempera-

t u r e dependence, b o t h Kevan / 1 2 3 , 1 2 4 / and Lambert e t a l . /121/ have r e p o r t e d i n c r e a s e d i n t e n s i t y of t h e ~ ( 4 x 2 )f e a t u r e s w i t h d e c r e a s i n g t e m p e r a t u r e i n d i c a t i v e of a g r a d u a l s u r f a c e o r d e r i n g of t h e ~ ( 4 x 2 ) phase. I n STM-images of t h e S i ( 1 0 0 ) s u r f a c e , most of t h e d i m e r s a p p e a r t o b e symmetric / 1 2 0 / . The s u r f a c e a l s o c o n t a i n s a h i g h d e n s i t y of vacancy-type d e f e c t s , which c o u l d l o c a l l y s t a b i l i z e an a l t e r n a t i n g ( z i g - z a g ) b u c k l i n g of t h e d i m e r s a t room t e m p e r a t u r e .

I t was a r g u e d

t h a t t h e o b s e r v a t i o n of symmetric d i m e r s i n d e f e c t - f r e e r e g i o n s c o u l d r e f l e c t t h e time-averaged c o n f i g u r a t i o n o f d i m e r s t h a t a r e d y n a m i c a l l y b u c k l i n g , on a t i m e s c a l e s h o r t compared t o t h e STM measurement t i m e . Schematic views of t h e i d e a l (100) s u r f a c e and t h e asymmetric dimer model o f t h e ( 1 0 0 ) 2 x 1 r e c o n s t r u c t i o n a r e shown i n F i g . 9 ( a , b ) .

173

N o t e t h a t t h e a s y m m e t r i c d i m e r s o b s e r v e d i n STM a r e a l t e r n a t i n g

a l o n g t h e dimer r o w s a n d f o r m r e g i o n s w i t h 2x2 or ~ ( 4 x 2 )s y m m e t r y . Fig.

9 ( c ) shows t h e s u r f a c e B r i l l o u i n z o n e s c o r r e s p o n d i n g t o t h e

dominating

two-domain

(100)2x1 reconstruction t h a t normally has

b e e n o b s e r v e d i n LEED i n c o n j u n c t i o n w i t h r e p o r t e d ARPES s t u d i e s on both S i a n d G e ( 1 0 0 ) 2 x l . 5.1

Si ( 1 0 0 ) 2 x 1

T h e f i r s t e v i d e n c e of p h o t o e m i s s i o n from s u r f a c e s t a t e s o n t h e S i ( 1 0 0 ) 2 x l s u r f a c e was p r e s e n t e d i n t h e a n g l e - i n t e g r a t e d

s t u d i e s by

A s u r f a c e s t a t e s t r u c t u r e w a s o b s e r v e d a t -1.1

Rowe and Ibach /89/.

eV b e l o w E F . A more d e t a i l e d p i c t u r e o f t h e s u r f a c e e l e c t r o n i c s t r u c t u r e w a s presented i n t h e f i r s t angle-resolved photoemission This study w a s performed along

s t u d y b y Himpsel a n d Eastman / 1 2 6 / .

t o avoid ambiguities due t o the superposition

the [010]-direction,

of e m i s s i o n f r o m t h e t w o t y p e s o f 2 x 1 d o m a i n s , r o t a t e d by 90' r e l a t i v e t o each o t h e r . E q u i v a l e n t k / / - p o i n t s a r e p r o b e d f o r t h e t w o d o m a i n s a l o n g t h e [OlO] - d i r e c t i o n ,

which s h o u l d r e s u l t i n i d e n t i c a l

s u r f a c e s t a t e c o n t r i b u t i o n s from t h e t w o domains. A dominant s u r f a c e

s t a t e s t r u c t u r e l o c a t e d 0 . 7 eV below EF a t

J’,

t o 1 . 2 e V b e l o w EF a t

f,

d i s p e r s i n g downwards

was o b s e r v e d i n t h e s t u d y .

dominant s u r f a c e state s t r u c t u r e , a peak a t -0.7

'

I ,

..

'

s5

'

'

'

'

Besides t h i s

e V close t o

5' a n d

I

... I I'

s5

LLI

3

3w m

.

10.2 eV

15.0 eV a21.2 eV A

. -

r

1.0 Jab

WAVE VECTOR (A*')

- [OlO]

-1

r

[oii]

0.5 J

r

+ WAVE VECTOR (A-'

0.5

)+

[0111

F i g . l c . - ( a ) E x p e r i m e n t a l s u r f a c e band s t r u c t u r e for S i ( 1 0 0 ) 2 x 1 a l o n g T-J’ i n t h e [OlO] a z i m u t h a l d i r e c t i o n ( f r o m r e f . 1 4 0 ) . Data p o i n t s f o r s t r u c t u r e S,, f r o m r e f . 1 2 8 , h a v e a l s o b e e n i n c l u d e d i n t h e f i g u r e . The s o l i d l i n e shows t h e u p p e r e d g e o f t h e p r o j e c t e d b u l k v a l e n c e - b a n d s i n t h e - 1 x 1 SBZ. (b) Experimental s u r f a c e state b a n d s t r u c t u r e a l o n g t h e T-J’ a n d r-3 s y m m e t r y l i n e s / 1 3 8 / .

174

a s h o u l d e r a t -1.3 e V a t ?I were a l s o i d e n t i f i e d as s u r f a c e s t a t e emission. S i n c e t h e s e e a r l y s t u d i e s , a l a r g e number of a n g l e - r e s o l v e d s t u d i e s has been performed on t h e S i ( 1 0 0 ) 2 x l s u r f a c e / 1 2 7 - 1 4 0 / ,

and

t h e y have r e s u l t e d i n a v e r y d e t a i l e d and c o n s i s t e n t p i c t u r e of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e . The s u r f a c e band s t r u c t u r e a s obtained i n some r e c e n t a n g l e - r e s o l v e d photoemission s t u d i e s of t h e S i ( 1 0 0 ) 2x1 s u r f a c e /128,138,139/ s u r f a c e s t a t e s , S1-S5,

i s summarized i n F i g . 1 0 . A l t o g e t h e r f i v e

have been observed i n t h e [ O l O ] azimuth,

while only S1 and S5 have been i d e n t i f i e d i n t h e [Oli] and [Oll] symmetry d i r e c t i o n s . Below i s given a b r i e f d e s c r i p t i o n of t h e various surface s t a t e s , but f o r a d e t a i l e d discussion o f , e.g. the degree of c o n s i s t e n c y between t h e d i f f e r e n t a n g l e - r e s o l v e d photoemission s t u d i e s r e p o r t e d i n t h e l i t e r a t u r e , we r e f e r t o r e f . 1 5 . F i g . l l ( a ) shows some photoemission s p e c t r a , from a s t u d y by Goldmann e t a l . /131/, probing t h e s u r f a c e e l e c t r o n i c s t r u c t u r e along t h e [OlO] azimuthal d i r e c t i o n . Besides t h e S 1 and S2 s u r f a c e s t a t e s , t h a t f i r s t were i d e n t i f i e d by Himpsel and Eastman /126/, Goldmann e t a l . a l s o r e p o r t e d a s t a t e , S4, around t h e j ' - p o i n t .

symmetrically d i s p e r s i n g

All t h e s e t h r e e s u r f a c e s t a t e s a r e , a t t h e 3 ' -

p o i n t , w i t h i n t h e band gap of t h e bulk band s t r u c t u r e p r o j e c t e d onto t h e 1x1 s u r f a c e B Z . The e x i s t e n c e of t h e dominant d i s p e r s i n g s u r f a c e s t a t e s t r u c t u r e

(Sl), o r i g i n a l l y r e p o r t e d i n r e f . 1 2 6 , was f i r s t confirmed i n s t u d i e s by van Hoof and van d e r W i e l / 1 2 7 / /128/.

and by Uhrberg e t a l .

I n t h e s e two s t u d i e s , photoemission s p e c t r a were a l s o

o b t a i n e d a l o n g t h e [Oll] and [ O l i l d i r e c t i o n s

(see Fig. 9 ( c ) ) i n

o r d e r t o determine t h e d i s p e r s i o n a l o n g both t h e

r-3

and

r-3'

symmetry l i n e s . Due t o t h e presence of two t y p e s of domains, s u r f a c e s t a t e emission from t h e

r-3

and

F-3' l i n e s

w i l l be superimposed i n

t h e s p e c t r a f o r such d i r e c t i o n s . An i d e n t i f i c a t i o n of t h e d i s p e r s i o n s along t h e two symmetry l i n e s was proposed based on symmetry arguments /128/.

Both groups r e p o r t e d a very small

d i s p e r s i o n (< 0 . 1 e V ) a l o n g t h e 0 . 1 e V ) along t h e

r-3'

line.

I=-3 l i n e and a l a r g e d i s p e r s i o n

A l l t h r e e experiments,

d i f f e r e n t photon e n e r g i e s 13 eV /126/, 2 1 . 2 e V / 1 2 1 / ,

(=

performed a t and 1 0 . 2 eV

/128/, gave a c o n s i s t e n t p i c t u r e e x c e p t f o r s m a l l d i f f e r e n c e s i n t h e

bandwidth and a b s o l u t e energy. L a t e r ARPES s t u d i e s /129-140/ have a l s o been v e r y c o n s i s t e n t and t h e d i s p e r s i o n of S 1 shown i n F i g . 1 0

i s t y p i c a l f o r a high r e s o l u t i o n study.

175

-

Si ( 1 0 0 ) 2 x l towards [ O l O l

' 2 5 '

-2 - 1

0

'

10'

L -2 - 1 0

INITIAL-ENERGY BELOW E,

F=O

-2

-L

-6

-8

-2 -1 lev)

0

-lC

Initial state energy Ei(eV]

F i g . 11. ( a ) A n g l e - r e s o l v e d p h o t o e m i s s i o n s p e c t r a (hv = 2 1 . 2 e V ) o b t a i n e d a l o n g t h e [OlO] a z i m u t h a l d i r e c t i o n f o r v a r i o u s a n g l e s of e m i s s i o n (8,) ( f r o m r e f . 1 3 1 ) . The s u r f a c e s t a t e s S,, S, and S , a s w e l l a s s e v e r a l b u l k s t r u c t u r e s a r e i n d i c a _ t e d i n t h e s p e c t r a . The maximum i n t h e d i s p e r s i o n of S , o c c u r s a t J ' (8, = 3 6 ' ) . ( b ) P h o t o e m i s s i o n s p e c t r a from a h i g h l y n-doped S i ( 1 0 0 ) s a m p l e , o b t a i n e d a t 2 1 . 2 e V p h o t o n e n e r g y , f o r v a r i o u s a n g l e s of e m i s s i o n ( 8 , ) a l o n g t h e [OlO] a z i m u t h a l d i r e c t i o n . The s u r f a c e s t a t e S, and a t t h e 3 ' shows n a r r o w i n t e n s i t y maxima a t t h e ? - p o i n t (8,=0") p o i n t (8,=34') /139/. ( c ) Dependence o f t h e s u r f a c e s t a t e e m i s s i o n i n t e n s i t i e s on t h e a n g l e of i n c i d e n c e ( 8 , ) /139/. S t r u c t u r e S 2 , which l i e s w e l l w i t h i n t h e p r o j e c t e d b u l k band gap, has been observed around

3 ' i n p r a c t i c a l l y a l l ARPES e x p e r i m e n t s i n

which t h e [ O l O ] d i r e c t i o n was p r o b e d /126,128,130-132,134-140/.

It

h a s b e e n s u g g e s t e d t h a t t h e e x i s t e n c e o f ~ ( 4 x 2 )a n d 2x2 r e c o n s t r u c t i o n s c o u l d e x p l a i n t h e p r e s e n c e of s t r u c t u r e S2 / 2 9 / . reconstruction the

For a 2x2

3' p o i n t would c o r r e s p o n d t o a r - p o i n t i n t h e

s e c o n d 2x2-SBZ and t h u s t h e S 2 s t r u c t u r e would c o r r e s p o n d t o t h e d a n g l i n g bond s t a t e a t a f - p o i n t .

However, a s w a s p o i n t e d o u t i n

r e f . 1 3 2 , i n p h o t o e m i s s i o n s t u d i e s where s t r u c t u r e S2 i s w e l l r e s o l -

176

ved /128,132/ t h e e n e r g y i s f o u n d t o be s i g n i f i c a n t l y l o w e r ( 0 . 1 5 eV) t h a n the energy a t

r,

which r u l e s o u t t h i s e x p l a n a t i o n .

r e s o l u t i o n s t u d i e s /132,136/,

In high

t h e s t r u c t u r e S2 f u r t h e r m o r e w a s found

t o h a v e a d i s p e r s i o n minimum a t

3 ' . This i s incompatible with an

e x p l a n a t i o n i n t e r m s of s c a t t e r i n g from t h e r e g i o n w i t h a h i g h dens i t y of states c l o s e t o

?.

One way t o o b t a i n f u r t h e r i n f o r m a t i o n a b o u t S 2 i s t o p e r f o r m s t u d i e s on s i n g l e - d o m a i n

2x1 s u r f a c e s . Single-domain S i ( 1 0 0 ) 2 x l

s u r f a c e s h a v e b e e n o b t a i n e d on S i ( 1 0 0 ) s a m p l e s which a r e c u t o f f a x i s b y t y p i c a l l y 4O. I n t h e s t u d y by B r i n g a n s e t a l . /133/, t h e d i s p e r s i o n o f t h e d a n g l i n g - b o n d s t a t e S1 a l o n g t h e

r-3 and I;-3'

l i n e s w a s unambiguously d e t e r m i n e d , a n d f o u n d t o c o n f i r m t h e e a r l i e r r e s u l t s on two-domain s u r f a c e s / 1 2 8 / . s u r f a c e s /133/, >'-point

I n t h e s t u d y o n s i n g l e domain

it a l s o was c o n c l u d e d t h a t S2 i s n o t o b s e r v e d a t t h e

a l o n g a [Oll] symmetry d i r e c t i o n . I n a l a t e r s t u d y by

U h r b e r g e t a l . /15,138/, i n which a l s o t h e [ 0 1 0 ] - d i r e c t i o n was probed,

s t r u c t u r e S2 w a s o b s e r v e d j u s t as c l e a r l y a s f o r t h e t w o -

domain S i ( 1 0 0 ) 2 x l s u r f a c e s . C o n s i d e r i n g a l l t h e i n f o r m a t i o n a b o u t s t r u c t u r e Sg w e f i n d t h a t it i s a c h a r a c t e r i s t i c s u r f a c e s t a t e band on s i n g l e - d o m a i n

a s w e l l as two-domain

Si(100) surfaces exhibiting

2x1 LEED p a t t e r n s . The s u r f a c e s t a t e s t r u c t u r e S4 was f i r s t o b s e r v e d i n t h e s t u d i e s by Koke e t a l . /130/ a n d Goldmann e t a l . /131/ ( s e e F i g . l l ( a ) ) and t h e d i s p e r s i o n w a s f o u n d t o be t h e same f o r b o t h 1 6 . 8 5 a n d 21.2 e V p h o t o n s . The S 4 s u r f a c e s t a t e h a s a l s o b e e n s t u d i e d by J o h a n s s o n and coworkers w i t h photon e n e r g i e s of 2 1 . 2 e V , eV /140/.

T h e obtained d i s p e r s i o n around

1 6 . 8 5 e V / 1 3 1 / and 1 5 . 0

3' i s v e r y s i m i l a r t o t h a t

o b s e r v e d by K o k e e t a l . /130/, a n d it i s shown i n F i g . 1 0 . There i s some e x p e r i m e n t a l e v i d e n c e t h a t S4 i s d u e t o e m i s s i o n from t h e dimer b o n d s . F i r s t l y , t h e S 4 s u r f a c e s t a t e i s n o t r e d u c e d t o t h e same e x t e n t as t h e s t a t e s S 1 and S 2 , when n o r m a l l i g h t i n c i d e n c e is u s e d , which i n d i c a t e s a h i g h e r d e g r e e o f p x r p y c h a r a c t e r f o r t h e S4 s t a t e

/137,140/. S e c o n d l y , hydrogen c h e m i s o r p t i o n s t u d i e s / 1 3 1 / h a v e shown t h a t f o r t h e ( d i m e r i z e d ) monohydride p h a s e , S i ( 1 0 0 ) 2xl:H, t h e s t a t e s S1 a n d S 2 w i t h d a n g l i n g bond c h a r a c t e r a r e removed a n d S4 r e m a i n s , w h i l e a l l t h r e e s u r f a c e s t a t e s a r e removed on t h e d i h y d r i d e p h a s e , Si(100)1x1:2H. A weak s u r f a c e r e l a t e d s t r u c t u r e

(S3) w a s o b s e r v e d i n t h e e a r l y

s t u d y by Uhrberg e t a l . /128/. The s t r u c t u r e w a s a s s i g n e d to e m i s s i o n from a s u r f a c e resonance ( o v e r l a p p i n g i n e n e r g y w i t h t h e b u l k b a n d s ) s i n c e it showed t h e same s e n s i t i v i t y t o c o n t a m i n a t i o n a s

177

t h e dangling-bond s t a t e . A contamination s e n s i t i v e s t r u c t u r e w a s a l s o o b s e r v e d a t t h e same i n i t i a l e n e r g i e s a n d i n t h e same p a r t o f t h e SBZ i n t h e s t u d y by Koke e t a l . / 1 3 0 / . photon e n e r g y /139/

I n a d d i t i o n , a t 21.2 e V

a contamination s e n s i t i v e s t r u c t u r e i s observed

with a d i s p e r s i o n overlapping with t h o s e r e p o r t e d f o r 1 0 . 2 e V /128/ and 16.85 e V /130/.

The p r e s e n c e of a n e m i s s i o n s t r u c t u r e f o r a l l

t h r e e photon e n e r g i e s with a similar behaviour supports t h e o r i g i n a l s u r f a c e r e s o n a n c e i n t e r p r e t a t i o n . However, t h i s a s s i g n m e n t i s n o t unambiguous a n d more s t u d i e s a r e n e e d e d b e f o r e a p o s i t i v e a s s i g n m e n t c a n b e made. The a n g l e - r e s o l v e d p h o t o e m i s s i o n t e c h n i q u e h a s a l s o b e e n employed i n s t u d i e s o f t h e n o r m a l l y empty s u r f a c e b a n d s . I t w a s shown i n t h e s t u d y by M s r t e n s s o n e t a l . /132/

t h a t by u s i n g h i g h l y n-doped

s a m p l e s ( p = 6 d c m ) a l a r g e enough p o p u l a t i o n o f t h e "empty" s u r f a c e states could be achieved t o f a c i l i t a t e a direct observation of t h e s e s t a t e s i n photoemission.

A new s u r f a c e s t a t e s t r u c t u r e

see F i g s . 1 0 a n d l l ( b , c ) , was o b s e r v e d a t t h e F e r m i l e v e l a n d t h e e m i s s i o n was l o c a t e d i n a v e r y s m a l l k / / - r e g i o n a r o u n d and a r o u n d t h e J ' - p o i n t i n b o t h t h e [ O l l ] , [Oli] a n d [ 0 1 0 ] - d i r e c t i o n s . I n t h e f i r s t s t u d y of t h i s s t a t e /132/ 1 0 . 2 e V p h o t o n s were u s e d , (S5),

r

a n d q u i t e l o w i n t e n s i t y of t h e Fermi s t r u c t u r e w a s o b t a i n e d . I n

l a t e r s t u d i e s u s i n g h i g h e r photon e n e r g i e s c o n s i d e r a b l y h i g h e r i n t e n s i t y of e m i s s i o n h a s been o b t a i n e d / 1 3 6 , 1 3 9 / .

E.g., i n t h e

s p e c t r a i n F i g . l l ( b , c ) , obtained with 2 1 . 2 e V photon energy, t h e e m i s s i o n i n t e n s i t y from t h e F e r m i s t r u c t u r e i s s i m i l a r t o t h e i n t e n s i t y f r o m t h e f i l l e d s u r f a c e s t a t e b a n d (S1)

/139/. I n s t u d i e s

u s i n g s y n c h r o t r o n r a d i a t i o n i n t h e r a n g e 8-27 e V t h e r e l a t i v e e m i s s i o n i n t e n s i t y from t h e Fermi s t r u c t u r e w a s f o u n d t o i n c r e a s e m o n o t o n i c a l l y w i t h photon energy /139/.

From t h e n a r r o w k , , - l o c a l i -

z a t i o n of t h i s s t a t e t h e r e a l - s p a c e e x t e n s i o n o f t h e wave f u n c t i o n w a s c a l c u l a t e d t o be 2 30 A /132/. Due t o t h i s l a r g e v a l u e it was

concluded t h a t t h e s t r u c t u r e s a t t h e Fermi-level

c o u l d n o t b e due t o

l o c a l i z e d d e f e c t s t a t e s , b u t were i n s t e a d due t o e m i s s i o n f r o m minima of a n a l m o s t empty d i s p e r s i n g s u r f a c e b a n d . A s p o i n t e d o u t i n t h e s t u d y by M h r t e n s s o n e t a l . / 1 3 2 / t h e s e s t a t e s , c o r r e s p o n d i n g t o

t h e bottom of t h e empty band, a r e r e s p o n s i b l e f o r t h e F e r m i - l e v e l p i n n i n g o f t h e S i ( 1 0 0 ) s u r f a c e on n-doped

samples.

A small s t r u c t u r e c l o s e t o t h e Fermi level

i n t h e s t u d y by Goldmann e t a l . / 1 3 1 /

at

r

w a s a l s o observed samples.

on l i g h t l y p-doped

T h i s s t r u c t u r e w a s f o u n d t o be h i g h l y l o c a l i z e d a r o u n d t h e l= p o i n t

178

s i m i l a r l y t o t h e s t r u c t u r e o b s e r v e d f o r t h e h i g h l y n-doped samples

/132/, b u t i n c o n t r a s t t o t h e r e s u l t s f o r t h e h i g h l y n-doped s u r f a c e t h e F e r m i - s t r u c t u r e was n o t o b s e r v e d a t 3 ' . The Fermi s t r u c t u r e w a s i n t e r p r e t e d b y Goldmann e t a l . /131/ a s due t o e x t e n d e d defect s t a t e s on t h e s u r f a c e , i n a c c o r d a n c e w i t h t h e i n t e r p r e t a t i o n o f a s i m i l a r s t r u c t u r e on Ge(100)Zxl (see s e c t i o n 5 . 2 ) . It i s worth n o t i n g t h a t f o r t h e h i g h l y n-doped samples /132/ t h e i n t e n s i t y of t h e Fermi-structure a t

5'

was found t o b e h i g h l y reduced when normal

l i g h t i n c i d e n c e was u s e d . The geometry i n t h e e x p e r i m e n t by Goldmann

e t a l . /131/ was s u c h t h a t l i g h t i n c i d e n t c l o s e t o t h e normal w a s u s e d ( e i = 6 " ) , when p r o b i n g s t a t e s c l o s e t o t h e 3' p o i n t , which must have s u b s t a n t i a l l y reduced t h e p o s s i b i l i t y of o b s e r v i n g t h e Fermis t r u c t u r e . An a l t e r n a t i v e e x p l a n a t i o n t o t h a t p u t f o r w a r d by Goldmann e t a l . i s t h a t t h e p r e s e n c e of donor-type d e f e c t s on t h e S i ( 1 0 0 ) s u r f a c e l e a d s t o a s m a l l b u t f i n i t e o c c u p a t i o n a t t h e minima of t h e a n t i b o n d i n g dangling-bond band. I t i s o u r e x p e r i e n c e , t h a t

r e p e a t e d h e a t t r e a t m e n t s and hydrogen e x p o s u r e s of S i ( 1 0 0 ) s u r f a c e s can r a i s e t h e s u r f a c e F e r m i l e v e l p o s i t i o n on l i g h t l y doped c r y s t a l s /139/. T h e s t r u c t u r e a t t h e F e r m i - l e v e l would t h e n n o t be due t o

e m i s s i o n from d e f e c t s t a t e s b u t i n s t e a d due t o e m i s s i o n from s u r f a c e band s t a t e s .

F u r t h e r s t u d i e s a r e needed t o f u l l y c h a r a c t e r i z e t h e

F e r m i s t r u c t u r e on t h e p-doped samples t o f a c i l i t a t e a comparison

with t h e r e s u l t s f o r t h e h i g h l y n-doped s a m p l e s . A d e t a i l e d and c o n s i s t e n t p i c t u r e o f t h e s u r f a c e band s t r u c t u r e

h a s emerged from t h e a n g l e - r e s o l v e d p h o t o e m i s s i o n s t u d i e s , a s was i l l u s t r a t e d i n F i g . 1 0 . I t was e a r l y e s t a b l i s h e d t h a t t h e S i ( 1 0 0 ) 2 x l s u r f a c e i s semiconducting / 8 8 , 1 2 6 / .

The s u r f a c e s t a t e band gap

between t h e S 1 and S5 s u r f a c e bands has been d e t e r m i n e d t o be 0 . 1 e V /132/. The e a r l i e s t s u g g e s t e d models f o r t h e s u r f a c e geometry,

i n c l u d i n g vacancy, c h a i n , and symmetric dimer models, a l l gave metallic s u r f a c e s t a t e b a n d s . T o a c c o u n t f o r t h e s e m i c o n d u c t i n g s u r f a c e e l e c t r o n i c s t r u c t u r e , a m o d i f i c a t i o n of t h e dimer model was p u t f o r w a r d by Chadi /141,142/ w i t h s u p p o r t from e n e r g y m i n i m i z a t i o n c a l c u l a t i o n s . T h i s model c o n s i s t s of asymmetric d i m e r s i n a 2x1 arrangement on t h e s u r f a c e and i s shown i n F i g . 9 ( b ) . The c a l c u l a t e d e l e c t r o n i c s t r u c t u r e f o r t h e asymmetric dimer model /141,143/ showed a s e m i c o n d u c t i n g s u r f a c e w i t h a dangling-bond

dispersion i n quali-

t a t i v e agreement w i t h t h e ARPES r e s u l t s f o r t h e d i s p e r s i o n of S1 /126/. However, some d i s c r e p a n c i e s a l r e a d y e x i s t e d a t t h i s s t a g e ,

e . g . t h e t i g h t - b i n d i n g c a l c u l a t i o n gave a dangling-bond band t h a t was more t h a n twice a s wide a s t h e e x p e r i m e n t a l s u r f a c e s t a t e band

179

( 1 . 2 e V compared t o 0 . 5 e V ) . A s e l f - c o n s i s t e n t

pseudopotential

c a l c u l a t i o n for t h e same s t r u c t u r e /143/ g a v e a b a n d w i d t h of t h e r i g h t magnitude b u t t h e dangling-bond band w a s l o c a t e d = 0.8 e V t o o high i n energy. Improvements i n t h e a b s o l u t e e n e r g y a n d e s p e c i a l l y i n t h e band w i d t h o f t h e d a n g l i n g - b o n d b a n d were o b t a i n e d i n l a t e r c a l c u l a t i o n s by Bowen e t a l . /144/ a n d by Mazur a n d Pollmann /145,146/.

The

c o m p a r i s o n s b e t w e e n t h e o r y a n d t h e e x p e r i m e n t a l r e s u l t s /144,145/ f o r t h e S 1 b a n d from r e f s . 1 2 6 , 1 2 7 a n d 1 2 8 w e r e v e r y f a v o u r a b l e for t h e a s y m m e t r i c d i m e r m o d e l . However, t h e s u p p o r t i s e s s e n t i a l l y based on o n l y o n e s u r f a c e s t a t e band,

t h e dangling-bond

band ( S l ) ,

w i t h some a d d i t i o n a l s u p p o r t b a s e d on t h e a g r e e m e n t b e t w e e n t h e c a l c u l a t e d d i m e r bond b a n d and s t r u c t u r e S, f o u n d i n e x p e r i m e n t s . The s u r f a c e s t a t e s which c a n n o t be e a s i l y a c c o u n t e d f o r by t h e a s y m m e t r i c 2 x 1 dimer-model a r e S 2 , S4 and S g ( a t

r ) . Around

Sg s t r u c t u r e c a n be e x p l a i n e d b y t h e empty d a n g l i n g - b o n d

j’ t h e

b a n d which

shows a minimum a t t h i s symmetry p o i n t i n most c a l c u l a t i o n s . The s u r f a c e band c a l c u l a t i o n s u s u a l l y show s e v e r a l s u r f a c e s t a t e s / r e s o n a n c e s i d e n t i f i e d a s d i m e r bond and back-bond s t a t e s . I n t h e c a l c u l a t i o n s by Pollmann e t a l . /13,141/ t h e s e s u r f a c e r e s o n a n c e s

were f o u n d c l o s e t o

and 3' i n t h e e n e r g y r a n g e 1-4 e V below t h e

v a l e n c e b a n d maximum. A m a t c h i n g o f t h e e x p e r i m e n t a l b a n d s w i t h c a l c u l a t e d b a n d s i s d i f f i c u l t however, s i n c e o n l y t h r e e k , , - p o i n t s o v e r l a p b e t w e e n t h e e x p e r i m e n t a l l y p r o b e d [OlO]- d i r e c t i o n

(F-3' )

and

t h e symmetry l i n e s s t u d i e d i n t h e c a l c u l a t i o n . For S 2 t h e r e does n o t

s e e m t o be a n y r e a s o n a b l e e x p l a n a t i o n i n a n y o f t h e t h e o r e t i c a l band s t r u c t u r e s p r e s e n t e d for t h e 2x1 d i m e r model of t h e S i ( 1 0 0 ) s u r f a c e . I t h a s been s u g g e s t e d t h a t S p c o u l d be a n a r t i f a c t due t o t h e

p r e s e n c e of t h e two 2x1 domains on t h e s u r f a c e .

A s d i s c u s s e d above,

s t u d i e s on s i n g l e - d o m a i n S i ( 1 0 0 ) Z x l s u r f a c e s h a v e shown, however, t h a t S2 i s a l s o p r e s e n t on t h e s e s u r f a c e s w i t h t h e same r e l a t i v e i n t e n s i t y compared t o t h e d a n g l i n g bond s t a t e S 1 . D e s p i t e t h e f a c t t h a t t h e s u r f a c e band s t r u c t u r e c a l c u l a t i o n s f o r t h e d i m e r model g i v e good a g r e e m e n t w i t h e x p e r i m e n t a l d a t a f o r t h e d a n g l i n g - b o n d b a n d S1, w e f i n d t h a t more d e t a i l e d c o m p a r i s o n s have t o b e done,

s i n c e o n l y a s m a l l number o f t h e e x p e r i m e n t a l s u r f a c e

s t a t e s h a v e so f a r b e e n a c c o u n t e d f o r . F u r t h e r t h e o r e t i c a l a n a l y s i s of t h e e l e c t r o n i c s t r u c t u r e o f a l t e r n a t i n g asymmetric dimers w i t h 2x2 or ~ ( 4 x 2 )symmetry i s l i k e l y t o improve t h e u n d e r s t a n d i n g of t h e S i ( 1 0 0 ) 2 x 1 s u r f a c e with a seemingly i n h e r e n t d i s o r d e r e d d i s t r i b u t i o n o f symmetric and asymmetric d i m e r s .

180

5.2

G e ( 100)2x1 and c (4x2) s u r f a c e s

ARPES s t u d i e s of t h e photon energy dependence o f e m i s s i o n i n t h e

normal d i r e c t i o n from Ge(100)2x1 s u r f a c e s have been r e p o r t e d by Nelson e t a l . / 1 4 8 / ,

Neave e t a l . / 1 4 9 /

and H s i e h e t a l . /150/.

Although t h e sample s u r f a c e s w e r e p r e p a r e d q u i t e d i f f e r e n t l y , t h e e x p e r i m e n t a l r e s u l t s a r e v e r y c o n s i s t e n t . Nelson e t a l . p r e p a r e d t h e s u r f a c e by a r g o n i o n bombardment and a n n e a l i n g , w h i l e Hsieh e t a l . a l s o u s e d h o m o e p i t a x i a l l y MBE-grown G e ( 1 0 0 ) 2 x 1 s u r f a c e s . F i n a l l y , Neave e t a l . s t u d i e d Ge(100) s u r f a c e s grown by MBE on GaAs(100) s u b s t r a t e s . I n a l l t h r e e s t u d i e s /148-150/,

s t r o n g , dispersive

f e a t u r e s c o u l d be i d e n t i f i e d a s d i r e c t t r a n s i t i o n s from t h e b u l k v a l e n c e bands and t h e r e w e r e a l s o two n o n - d i s p e r s i v e

features a t

=0.6 e V and ~ 1 . 3e V below t h e v a l e n c e band e d g e . I n t h e work by Nelson e t a l . and Neave e t a l . t h e s e n o n - d i s p e r s i v e f e a t u r e s were a t t r i b u t e d t o s u r f a c e s t a t e s . In a l a t e r study t h e s u r f a c e s t a t e i n t e r p r e t a t i o n f o r low p h o t o n e n e r g i e s was c h a l l e n g e d by Hsieh e t a l . , who concluded t h a t t h e s e s t r u c t u r e s were o v e r l a p p i n g w i t h b u l k t r a n s i t i o n s . Although t h e y , a l s o for t h e h i g h e r p h o t o n e n e r g i e s , o f f e r e d a l t e r n a t i v e e x p l a n a t i o n s of t h e s t r u c t u r e s i n terms of b u l k e m i s s i o n , t h e y concluded t h a t most l i k e l y t h e r e a r e two s u r f a c e s t a t e s g i v i n g e m i s s i o n a t -0.5

and -1.3 e V i n t h e normal e m i s s i o n

s p e c t r a f o r h i g h photon e n e r g i e s . I n an a t t e m p t t o r e s o l v e t h e c o n t r o v e r s y , Kruger e t a l . /151/ t h e o r e t i c a l l y s t u d i e d t h e e l e c t r o n i c s t r u c t u r e o f t h e asymmetric dimer model f o r t h e ( 1 0 0 ) 2 x 1 s u r f a c e s o f G e and S i . Using t h e s e l f c o n s i s t e n t s c a t t e r i n g t h e o r e t i c a l method t h e y c a l c u l a t e d wave-vector r e s o l v e d l a y e r d e n s i t y of s t a t e s a t d i f f e r e n t p o i n t s i n t h e s u r f a c e BZ.

Two s u r f a c e s t a t e s , c o r r e s p o n d i n g t o a d a n g l i n g bond s t a t e on

t h e r a i s e d dimer atom and a back-bond s t a t e , were found n e a r t h e e x p e r i m e n t a l l y found e n e r g y p o s i t i o n s . I t was shown t h a t t h e topmost s t a t e ( t h e d a n g l i n g bond s t a t e ) i s a w e l l d e f i n e d s t a t e o n l y i n t h e o u t e r p a r t s of t h e s u r f a c e BZ, w h i l e it becomes a v e r y b r o a d and weak r e s o n a n c e a t

r,

decaying slowly i n t o t h e b u l k . D i f f i c u l t i e s i n

i d e n t i f y i n g t h i s s u r f a c e r e s o n a n c e i n measurements of t h e e m i s s i o n i n t h e normal d i r e c t i o n can t h u s be e x p e c t e d f o r Ge(100) 2x1, w h i l e f o r S i ( 1 0 0 ) 2 x l t h e d a n g l i n g bond s u r f a c e s t a t e remains a pronounced r e s o n a n c e a l l t h e way up t o t h e F - p o i n t . I n t h e p a p e r by Nelson e t a l . /148/ t h e s u r f a c e s t a t e d i s p e r s i o n s were r e p o r t e d f o r t h e LO111 a z i m u t h a l d i r e c t i o n , which c o r r e s p o n d s t o t h e i=s d i r e c t i o n f o r one 2x1 domain-type and t h e

Fj’

direction

181 S i ( 1 0 0 ) 2 x l t h e r e w a s a l s o e m i s s i o n i n a narrow a n g u l a r r a n g e around t h e 3'-point

o f t h e 2x1 s u r f a c e BZ. F i n a l l y , t h e t e m p e r a t u r e

d e p e n d e n c e o f e m i s s i o n i s o p p o s i t e f o r S i a n d G e . For S i ( 1 0 0 ) 2 x l t h e peak h e i g h t i n c r e a s e s w i t h d e c r e a s i n g t e m p e r a t u r e ,

which p r o b a b l y

j u s t r e f l e c t s t h e change i n t h e F e r m i - D i r a c d i s t r i b u t i o n ,

i.e. the

e l e c t r o n s p i l e up a t t h e minimum o f t h e a l m o s t empty b a n d . The t o t a l number o f e l e c t r o n s i n t h i s band i s e x p e c t e d t o be c o n s t a n t f o r S i r s i n c e t h e minimum of t h e s u r f a c e s t a t e b a n d i s 0 . 4 e V a b o v e t h e v a l e n c e b a n d e d g e which e x c l u d e s t h e r m a l e x c i t a t i o n from t h e v a l e n c e band. What c o u l d be t h e r e a s o n f o r t h e i n c r e a s e o f t h e m e t a l l i c p e a k with i n c r e a s i n g temperature f o r Ge(100)? F i r s t l y , t h e increase i n t h e number o f s u r f a c e s t a t e e l e c t r o n s n e a r t h e l=-point

(seen i n

normal e m i s s i o n ) , can r e f l e c t a s i g n i f i c a n t change i n t h e e l e c t r o n i c s t r u c t u r e a s t h e s u r f a c e d i s o r d e r s , a s w a s s u g g e s t e d by Kevan /124/. Secondly,

s i n c e t h e e n e r g y o f t h e m e t a l l i c peak i s v e r y c l o s e t o t h e

v a l e n c e b a n d e d g e on G e ( 1 0 0 ) , i t i s p o s s i b l e t h a t t h e o c c u p a t i o n of t h e s u r f a c e s t a t e b a n d i s due t o t h e r m a l e x c i t a t i o n from t h e b u l k e n e r g y b a n d s , i n which case t h e s i m u l t a n e o u s o c c u r r e n c e o f t h e change i n o r d e r o f t h e s u r f a c e would be a c c i d e n t a l . I n c o n c l u s i o n , t h e i n f o r m a t i o n o b t a i n e d i n ARPES e x p e r i m e n t s on G e ( 1 0 0 ) s u r f a c e s i s somewhat f r a g m e n t a r y . T o d e s c r i b e and u n d e r s t a n d t h e s u r f a c e e l e c t r o n i c s t r u c t u r e s o f t h e G e ( 1 0 0 ) 2 x l and ~ ( 4 x 2 ) s u r f a c e s t h e r e i s a g r e a t n e e d f o r e x t e n s i v e b a n d mapping s t u d i e s . The o r i g i n o f t h e m e t a l l i c s u r f a c e s t a t e i s s t i l l a n open q u e s t i o n ,

a n d it would p r o b a b l y be v e r y h e l p f u l t o s t u d y t h i s s t a t e on h i g h l y n-doped

c r y s t a l s , where t h e r e s h o u l d b e more e l e c t r o n s i n t h i s

state.

6

CLEAVED (110) SURFACES OF 1 1 1 - V

SEMICONDUCTORS

F o r 1 1 1 - V compound s e m i c o n d u c t o r s , t h e ( 1 1 0 ) s u r f a c e s e x h i b i t simple 1x1 r e l a x a t i o n s , while t h e p o l a r

(111) a n d ( 1 0 0 ) s u r f a c e s a r e

c o n s i d e r a b l y more complex, o f t e n e x h i b i t i n g a l a r g e number of rec o n s t r u c t i o n s . I n b o t h t h e o r e t i c a l and e x p e r i m e n t a l s t u d i e s of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e o f 1 1 1 - V compound s e m i c o n d u c t o r s u r faces,

t h e emphasis h a s t h e r e f o r e been on t h e ( 1 1 0 ) s u r f a c e . I t i s

t h e o n l y non-polar

s u r f a c e a n d it c a n b e e a s i l y p r e p a r e d i n a c l e a n

and s t o i c h i o m e t r i c s t a t e i n s i t u , a s i t i s t h e n a t u r a l c l e a v a g e plane. S i n c e GaAs i s t h e t e c h n o l o g i c a l l y most i m p o r t a n t 1 1 1 - V compound

182

f o r t h e o t h e r 2x1 domain-type.

These d i s p e r s i o n s a r e q u i t e s i m i l a r

t o t h e r e s u l t s of Uhrberg e t a l . /128/ f o r t h e same a z i m u t h a l d i r e c t i o n on S i ( 1 0 0 ) 2 x l . Although t h i s l i m i t e d s e t of r e s u l t s i s c o n s i s t e n t w i t h t h e c a l c u l a t e d d i s p e r s i o n s f o r t h e asymmetric dimer model,

it seems v e r y l i k e l y t h a t f u r t h e r d e t a i l e d s t u d i e s of t h e

e l e c t r o n i c s t r u c t u r e of t h e Ge(100)2x1 s u r f a c e w i l l i d e n t i f y s u r f a c e s t a t e s t h a t cannot be e x p l a i n e d by t h e asymmetric dimer model,

just

l i k e t h e case f o r t h e Si(100)2xl surface. High-resolution

ARPES s t u d i e s on t h e Ge(100) s u r f a c e by Kevan and

S t o f f e l /123,124/

c o n c e n t r a t e d on t h e emission from a p r e v i o u s l y not

observed m e t a l l i c s u r f a c e s t a t e , which was observed o n l y o v e r a very narrow range of p a r a l l e l momenta n e a r t h e c e n t e r of t h e s u r f a c e BZ. The emission was found t o slowly d i s a p p e a r a s t h e t e m p e r a t u r e was lowered from room t e m p e r a t u r e t o 7 1 K . T h i s behaviour was d e s c r i b e d a s a m e t a l - i n s u l a t o r t r a n s i t i o n , which was found t o be c o i n c i d e n t with t h e g r a d u a l t r a n s i t i o n of t h e LEED p a t t e r n from 2x1 t o ~ ( 4 x 2 ) . The emission from t h e s u r f a c e s t a t e a t t h e Fermi l e v e l and some LEED p r o f i l e s a r e shown i n F i g . 1 2 f o r d i f f e r e n t s u b s t r a t e t e m p e r a t u r e s (from r e f . 1 2 3 ) . The p h y s i c a l o r i g i n of t h e m e t a l l i c s u r f a c e s t a t e i s not p r e s e n t l y c l e a r . I n r e f . 1 2 4 Kevan s u g g e s t e d t h a t d e f e c t dangling bond s t a t e s appeared i n t h e b u l k band-gap

due t o d i s o r d e r of t h e

c (4x2) r e c o n s t r u c t i o n , induced by f l i p p i n g s i n g l e dimers. From t h e narrow k/,-range FWHM),

f o r which t h i s s t a t e was observed

(

Ak = 0 . 0 9 A - l ,

it was concluded t h a t t h e m e t a l l i c s t a t e was r e l a t e d t o

d e f e c t s with an e s t i m a t e d r e a l space e x t e n t of 10-12

A, i . e .

approximately t h r e e d i m e r s . T h i s e s t i m a t e was l a t e r q u e s t i o n e d by Mdrtensson e t a l . /132/,

who d e r i v e d a lower l i m i t of 30

A for the

r e a l space e x t e n t of t h e s u r f a c e s t a t e s . Since t h e s u r f a c e s t a t e t h u s e x t e n d s over a t l e a s t 50 atoms, i t was s u g g e s t e d t h a t t h e m e t a l l i c peak i s n o t due t o emission from l o c a l i z e d d e f e c t s , but t o emission from t h e bottom of an almost empty d i s p e r s i n g s u r f a c e s t a t e band p i n n i n g t h e Fermi l e v e l . T h i s e x p l a n a t i o n could account f o r t h e f a c t t h a t t h e k/,-range,

f o r which t h e emission was observed,

i n c r e a s e d w i t h t e m p e r a t u r e /123/,

s i n c e a temperature increase w i l l

l e a d t o an i n c r e a s e d o c c u p a t i o n i n s t a t e s away from t h e m i n i m u m of t h e almost empty band. I n t h e experiments by Kevan e t a l . on G e ( 1 0 0 ) , l i g h t l y n-doped

c r y s t a l s w e r e used,

so a f i n i t e occupation

of e l e c t r o n s i n such a band i s e x p e c t e d . We want t o p o i n t o u t h e r e t h a t , whether a semiconductor s u r f a c e a p p e a r s a s m e t a l l i c o r n o t ,

183

ARP

LEED

0 5 BINDING

EF

ENERGY ( e v )

0

2

4

MOMENTUM TRANSFER

F i g . 1 2 . L e f t h a l f : The t e m p e r a t u r e d e p e n d e n t p h o t o e m i s s i o n n e a r t h e F e r m i - l e v e l , s e e n i n normal e m i s s i o n s p e c t r a from t h e Ge(100) s u r f a c e u s i n g 2 0 eV p h o t o n e n e r g y . R i g h t h a l f : LEED i n t e n s i t y p r o f i l e s e x t e n d i n g from t h e ( 0 , O ) beam t o t h e (1,1/2) beam a t t h e s a m e t e m p e r a t u r e s . T h e g r a d u a l a p p e a r a n c e of a p e a k a t 2 . 2 A-1 i s i n d i c a t i v e o f t h e t r a n s i t i o n t o a n o r d e r e d ~ ( 4 x 2 )s t r u c t u r e . From r e f . 123. d e p e n d s on t h e d o p i n g o f t h e b u l k s e m i c o n d u c t o r . E . g . ,

t h e (111)2x1

and ( 1 0 0 ) 2 x 1 s u r f a c e s o f h i g h l y n-doped S i - c r y s t a l s a p p e a r to b e

m e t a l l i c , s i n c e t h e r e c a n be a n a p p r e c i a b l e o c c u p a t i o n of e l e c t r o n s i n s u r f a c e s t a t e b a n d s i n t h e b u l k band-gap,

which would be empty

f o r u n c h a r g e d s u r f a c e s o f undoped s i l i c o n . T h e r e a r e some s t r o n g s i m i l a r i t i e s between t h e m e t a l l i c s t a t e s on Ge(100)Zxl and S i ( 1 0 0 ) 2 x l s u r f a c e s , suggesting similar o r i g i n s . F i r s t l y , the emission f r o m both s t a t e s i s s t r o n g l y l o c a l i z e d around t h e normal d i r e c t i o n . S e c o n d l y , t h e y have t h e same p h o t o n e n e r g y dependence, i . e . t h e i n t e n s i t y of t h e metallic s t a t e s relative t o t h e o t h e r s t r u c t u r e s i n c r e a s e monotonically w i t h photon energy i n t h e range 1 4 t o 2 1 e V /123,139/. There are a l s o s i g n i f i c a n t d i f f e r e n c e s i n t h a t t h e metallic s t a t e on G e ( 1 0 0 ) was o n l y s e e n n e a r t h e s u r f a c e n o r m a l , w h i l e on

184

s e m i c o n d u c t o r it h a s become a p r o t o t y p e f o r basic s u r f a c e s t u d i e s on t h i s t y p e o f s e m i c o n d u c t o r . Both t h e cleaved and t h e s p u t t e r e d and a n n e a l e d G a A s ( l l 0 ) s u r f a c e s g i v e a 1x1 p a t t e r n i n LEED e x p e r i m e n t s , and t h e r e i s s t r o n g e v i d e n c e i n t h e e l e c t r o n e n e r g y dependence o f t h e s p o t i n t e n s i t i e s t h a t t h e s u r f a c e has a large r e l a x a t i o n / 1 5 2 / . A schematic v i e w o f t h e s u r f a c e atom c o n f i g u r a t i o n i s g i v e n i n F i g .

1 3 ( a , b ) . The r e l a x a t i o n i s c h a r a c t e r i z e d by a d i s p l a c e m e n t o f t h e A s atoms o u t o f t h e s u r f a c e p l a n e and o f t h e G a atoms i n t o t h e c r y s t a l , g i v i n g r i s e t o a bond r o t a t i o n a n g l e a. The Ga-As

bonds on t h e f i r s t

s u b s u r f a c e p l a n e c o u n t e r r o t a t e b y a s m a l l a n g l e . The g r o s s f e a t u r e s o f t h e G a A s ( l l 0 ) r e l a x a t i o n h a s been a c c e p t e d f o r a l o n g t i m e , b u t d u r i n g t h e mid-80's

some c o n t r o v e r s i e s a r o s e c o n c e r n i n g t h e magni-

t u d e o f t h e bond-angle

r o t a t i o n a n d t h e changes i n bond l e n g t h s . A

r e c e n t r e v i e w of t h e h i s t o r i c a l development of t h e d e t e r m i n a t i o n of t h e G a A s ( l l 0 ) r e l a x a t i o n h a s been g i v e n by Duke and P a t t o n / 1 5 2 / .

The e l e c t r o n i c s t r u c t u r e of t h e G a A s ( l l 0 ) s u r f a c e h a s been s t u d i e d e x p e r i m e n t a l l y and t h e o r e t i c a l l y by a l a r g e number of g r o u p s

/153-182/. One m a j o r q u e s t i o n h a s been w h e t h e r t h e r e a r e a n y s u r f a c e

states i n t h e a b s o l u t e , fundamental gap. For a n unrelaxed s u r f a c e geometry t h e d a n g l i n g bond s t a t e s on t h e A s and Ga atoms a r e c a l c u l a t e d t o b e w i t h i n o r v e r y n e a r t h e band gap, while t h e y a r e pushed o u t o f t h e g a p by c e r t a i n r e l a x a t i o n s . E a r l y e x p e r i m e n t a l d a t a on Fermi l e v e l p i n n i n g i n p h o t o e m i s s i o n measurements /183/ and c o n t a c t p o t e n t i a l d i f f e r e n c e measurements /184/ s u g g e s t e d t h a t t h e r e w e r e empty s u r f a c e s t a t e s i n t h e g a p . However, it w a s c o n v i n c i n g l y shown b y s e v e r a l g r o u p s /185-187/ t h a t t h e s e s t a t e s a r e d e f e c t s t a t e s a b s e n t on h i g h q u a l i t y c l e a v e s . P a r t i a l y i e l d measurements

/188/ a l s o g a v e some e v i d e n c e f o r empty s u r f a c e s t a t e s i n t h e gap, s i n c e e x c i t a t i o n s of G a 3d e l e c t r o n s i n t o empty s u r f a c e s t a t e s below

(a) Side view

(b) Top view

a (c) SBZ

x

i=

X'

F i g . 1 3 . S c h e m a t i c view of t h e bond a n g l e r e l a x a t i o n model f o r t h e ( b ) t o p view, (c) surface G a A s ( l l 0 ) s u r f a c e . ( a ) s i d e view, B r i l l o u i n zone.

185

t h e c o n d u c t i o n b a n d e d g e seemed t o b e p o s s i b l e

.

The low v a l u e o f

t h e e x c i t a t i o n t h r e s h o l d was l a t e r e x p l a i n e d by s t r o n g e x c i t o n i c i n t e r a c t i o n s between t h e e l e c t r o n e x c i t e d t o t h e empty s u r f a c e s t a t e a n d t h e G a 3d c o r e h o l e / 1 8 9 / .

I t i s now w e l l e s t a b l i s h e d t h a t t . h e r e

a r e n o i n t r i n s i c s u r f a c e s t a t e s i n t h e a b s o l u t e b a n d g a p of GaAs ( 1 1 0 )

.

From c o n t a c t p o t e n t i a l d i f f e r e n c e measurements on c l e a v e d 1 1 1 - V ( 1 1 0 ) s u r f a c e s by H u i j s e r and c o w o r k e r s / 1 8 , 1 9 /

t h a t besides GaAs n e i t h e r o f GaSb,

it w a s c o n c l u d e d

InAs o r I n P have i n t r i n s i c

s u r f a c e s t a t e s i n t h e a b s o l u t e band g a p . F o r Gap, however, l e v e l on n-doped

the Fermi

( 1 1 0 ) s u r f a c e s was p i n n e d a t = 0 . 5 e V below t h e

c o n d u c t i o n b a n d e d g e , i n d i c a t i n g t h e e x i s t e n c e of a n empty s u r f a c e s t a t e band i n t h e band g a p . O c c a s i o n a l l y , on t h e o t h e r s u r f a c e s , d e f e c t s t a t e s i n t h e gap were o b s e r v e d t o a f f e c t t h e Fermi l e v e l p o s i t i o n . T h i s c o u l d e x p l a i n why i n some e a r l i e r s t u d i e s , on f o r example InP,

t h e r e had b e e n r e p o r t s o f i n t r i n s i c s u r f a c e s t a t e s i n

t h e gap.

6.1

ARPES s t u d i e s o f G a A s ( l l 0 )

P h o t o e m i s s i o n s t u d i e s on G a A s ( l l 0 ) s u r f a c e s h a v e b e e n p e r f o r m e d by many d i f f e r e n t g r o u p s / 9 0 , 1 5 3 - 1 6 8 / ,

c o v e r i n g a wide r a n g e o f

p h o t o n e n e r g i e s f r o m 9 t o 1 0 0 e V . S e v e r a l o f t h e s e s t u d i e s have been concerned w i t h t h e photon energy dependence o f t h e e m i s s i o n i n t h e normal d i r e c t i o n /90,153,161-165/.

I t can be concluded t h a t emission

a r i s i n g f r o m b u l k t r a n s i t i o n s h a s b e e n i d e n t i f i e d o v e r t h e whole photon energy range, while t h e only suggested s u r f a c e s t a t e i n t h e s e n o r m a l e m i s s i o n s t u d i e s i s a v e r y weak s h o u l d e r a t = 0 . 1 e V below t h e v a l e n c e band e d g e , t h a t was r e p o r t e d by M i l l s e t a l . / 1 6 1 / . ARPES s t u d i e s on G a A s ( l l 0 ) i n v e s t i g a t i n g e m i s s i o n from s u r f a c e

s t a t e s / r e s o n a n c e s h a v e b e e n p u b l i s h e d by Knapp a n d c o w o r k e r s /1541 5 6 / , W i l l i a m s e t a l . /157/, H u i j s e r e t a l . / 1 5 8 / , /166/

and M g r t e n s s o n e t a l . / 1 6 8 /

Solal et a l .

a n d t h e r e s u l t s a r e summarized i n

t h e e n e r g y b a n d d i a g r a m i n F i g . 1 4 . The most e x t e n s i v e e x p e r i m e n t a l s u r f a c e s t a t e d i s p e r s i o n s a r e from t h e s t u d y by H u i j s e r e t a l . . To o b t a i n t h e measured d i s p e r s i o n s t h e y used b o t h H e I ( 2 1 . 2 I (16.8 eV)

s e v e r a l d i f f e r e n t c o l l e c t i o n geometries. E . g . , t h e ??.-line

ev) a n d

Ne

r a d i a t i o n and t h e y s t u d i e d t h e photoemission using t h e d i s p e r s i o n s along

w e r e m e a s u r e d w i t h f o u r d i f f e r e n t g e o m e t r i e s , by u s i n g

p o s i t i v e o r negative angles of l i g h t incidence,

f o r emission angles

e i t h e r on t h e Ga, o r t h e A s d a n g l i n g bond s i d e o f t h e n o r m a l . The

186

h

2

........

HUlJSer et al

Y

Knspp, Eastrnan e t a1

>

-. -, -.-

(3

Knapp and Lapeyre

K

w Z w

0

W i l l i a m s e t a1

-. ._..-

-..

Solal e t al

1

5 t

r i b t e n s s o n e t al

z

SURFACE WAVEVECTOR Fia. 14. Summary of the experimental surface state bands reported fo; the GaAs(ll0) surface orientation of the surface BZ relative to the surface unit cell is shown in Fig. 13(c). To identify the emission from surface states, they used contamination tests (lo5 - lo6 L of hydrogen) and studied the dispersions with two different photon energies. Unfortunately, very little primary data, i.e. spectra or measured peak energy positions, were published in the paper by Huijser et al. /158/, so it is difficult to assess the credibility of the measured band dispersions and their interpretation as surface state bands. It is somewhat surprising that it seems that practically all structures seen by Huijser et al. could apparently be interpreted as due to surface states/resonances, especially since bulk transitions dominate the normal emission spectra in the same photon energy range /161,164,165/. In the summary of reported surface state dispersions in Fig. 14, there is rather good agreement between different experiments concerning some major features in the photoemission spectra, like the energy positions of the uppermost surface state bands at the X and 2' points. A l s o in unpublished ARPES studies by Aust / 1 6 1 / using 21.2 eV radiation, good agreement was obtained with the results of Huijser et al. /158/ concerning the dispersion of the topmost surface state band and the peak positions at the f and 2 ' points.

187

However, e x c e p t f o r t h e topmost band, t h e d i s p e r s i o n s away from t h e high s y m m e t r y p o i n t s were s i g n i f i c a n t l y d i f f e r e n t from t h e r e s u l t s of H u i j s e r e t a l . . Considering t h e l a c k of r e p r o d u c i b l e r e s u l t s concerning most of t h e f e a t u r e s r e p o r t e d , w e f i n d t h a t t h e r e i s a need f o r a new e x t e n s i v e band mapping s t u d y b e f o r e t h e s u r f a c e s t a t e band s t r u c t u r e can be e s t a b l i s h e d . I t would a l s o be very h e l p f u l i f t h e c o n t r i b u t i o n s from bulk emission i n t h e off-normal d i r e c t i o n s could be a n a l y z e d i n d e t a i l . T h e o r e t i c a l s t u d i e s of t h e e l e c t r o n i c s t r u c t u r e of G a A s ( l l 0 ) have been performed by many groups u s i n g d i f f e r e n t computational t e c h n i q u e s i n o r d e r t o i n v e s t i g a t e s e v e r a l d i f f e r e n t model geometries f o r t h e r e l a x a t i o n of t h e s u r f a c e /156,171-181/. The c a l c u l a t e d s u r f a c e s t a t e band s t r u c t u r e s have a l o t i n common, b u t t h e r e a r e a l s o s i g n i f i c a n t d i f f e r e n c e s , r e l a t e d t o t h e model used o r t o t h e t y p e o f c a l c u l a t i o n u s e d . For d e t a i l e d comparisons between t h e c a l c u l a t e d s u r f a c e s t a t e band s t r u c t u r e s and t h e r e s u l t s from ARPES s t u d i e s , we r e f e r t o t h e o r i g i n a l t h e o r e t i c a l p a p e r s . I n g e n e r a l , t h e r e i s good agreement between t h e c a l c u l a t e d ,

occupied d a n g l i n g

bond band on t h e A s s u r f a c e atoms and t h e topmost e x p e r i m e n t a l l y observed band. Although t h e agreement i s not s o good f o r t h e o t h e r e x p e r i m e n t a l l y observed bands,

i t has been p o s s i b l e t o a s s o c i a t e a

c a l c u l a t e d s u r f a c e s t a t e / r e s o n a n c e /176/ t o each of t h e s t r o n g f e a t u r e s s e e n i n t h e ARPES s p e c t r a from H u i j s e r e t a l . /158/. I n c o n c l u s i o n , ARPES s t u d i e s o n t h e G a A s ( l l 0 ) s u r f a c e have i n d i c a t e d a l a r g e number of s u r f a c e s t a t e s o r r e s o n a n c e s , some of which have been r e p o r t e d o n l y i n a s i n g l e and b r i e f l y r e p o r t e d s t u d y . From LEED,

medium-energy

i o n - s c a t t e r i n g and t h e o r e t i c a l c a l c u l a t i o n s

s t r o n g s u p p o r t f o r t h e bond a n g l e r e l a x a t i o n model h a s been o b t a i n e d

/152/. C a l c u l a t i o n s of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e u s i n g t h i s model can a t l e a s t q u a l i t a t i v e l y e x p l a i n most of t h e r e p o r t e d s u r f a c e s t a t e f e a t u r e s . For t h e topmost s u r f a c e s t a t e band, d i f f e r e n t e x p e r i m e n t s have given a c o n s i s t e n t d i s p e r s i o n , which i s i n good agreement with c a l c u l a t i o n s f o r t h e A s d a n g l i n g bond band. I n particular,

t h i s s u r f a c e s t a t e band i s found o u t s i d e t h e a b s o l u t e

band gap i n b o t h experiments and c a l c u l a t i o n s . 6.2

GaSbf 110)

GaSb i s a 1 1 1 - V compound semiconductor with a band s t r u c t u r e s i m i l a r t o e . g . t h a t of GaAs. However, due t o t h e l a r g e atomic number of Sb, r e l a t i v i s t i c e f f e c t s , l i k e s p i n - o r b i t

splitting, are

more i m p o r t a n t f o r GaSb. The e l e c t r o n i c s t r u c t u r e of GaSb has been

s t u d i e d q u i t e e x t e n s i v e l y by C h i a n q a n d Eastman /190/. They d e t e r mined t h e b u l k b a n d e n e r g y d i s p e r s i o n s , E ( k ) , a n d c r i t i c a l p o i n t s , u s i n g ARPES s t u d i e s o f t h e c l e a v e d G a S b ( l l 0 ) s u r f a c e . C o n c e r n i n g t h e s u r f a c e e l e c t r o n i c s t r u c t u r e o f G a S b ( l l O ) , C h i a n g a n d Eastman p r o b e d e m i s s i o n from t h e

r

a n d M p o i n t s o f t h e s u r f a c e BZ, b u t t h e y d i d n o t

r e p o r t a n y e m i s s i o n from s u r f a c e s t a t e s a t t h e s e symmetry p o i n t s .

A d e t a i l e d ARPES s t u d y o f t h e e m i s s i o n n e a r t h e v a l e n c e band edge

w a s r e c e n t l y p r e s e n t e d by Manzke e t a l . /191/. They u s e d v e r y h i g h energy and angular r e s o l u t i o n i n t h e i r s t u d i e s of t h e cleaved G a S b ( l l 0 ) s u r f a c e . I n t h e normal e m i s s i o n s p e c t r a i n F i g . 1 5 ( a ) , e m i s s i o n f r o m t h e t o p m o s t t h r e e v a l e n c e b a n d s a r e i n d i c a t e d by A, B, a n d C , w h i l e a weak c o n t r i b u t i o n i n t e r p r e t e d a s s u r f a c e s t a t e e m i s s i o n i s d e n o t e d S S . C o n s i s t e n t w i t h s t u d i e s on o t h e r 1 1 1 - V

(110)

s u r f a c e s , t h e s u g g e s t e d s u r f a c e s t a t e e m i s s i o n i n t h e normal d i r e c t i o n h a s v e r y low i n t e n s i t y a n d it i s d i f f i c u l t t o s e p a r a t e it from e m i s s i o n f r o m t h e t o p of t h e v a l e n c e b a n d . F i g . 1 5 ( b ) shows t h e ARPES s p e c t r a f o r o f f - n o r m a l e m i s s i o n a l o n g t h e r % ' - l i n e i n t h e s u r f a c e B Z . F o r b o t h 1 7 e V a n d 2 1 . 2 eV p h o t o n e n e r g y a n a r r o w f e a t u r e , SS, i s o b s e r v e d on t h e h i g h k i n e t i c e n e r g y s i d e o f t h e s p e c t r a . As shown i n t h e l o w e r r i g h t p a r t o f F i g . 1 5 ( b ) , t h e m e a s u r e d d i s p e r s i o n o f t h i s s t r u c t u r e i s t h e same f o r b o t h photon e n e r g i e s , s u p p o r t i n g a s u r f a c e s t a t e i n t e r p r e t a t i o n o f t h e f e a t u r e . I n t h e l o w e r l e f t p a r t o f F i g . 1 5 ( b ) it c a n be s e e n t h a t t h e s t r u c t u r e v e r y r a p i d l y d i s p e r s e s down i n e n e r g y a s t h e d e t e c t i o n a n g l e i s c h a n g e d away f r o m t h e n o r m a l d i r e c t i o n . T h i s e x c l u d e s t h e p o s s i b i l i t y t h a t t h e e m i s s i o n i n t h e normal d i r e c t i o n i s r e l a t e d t o d e f e c t s , i n which case t h e e m i s s i o n would be more i s o t r o p i c and non-dispersive.

The t o t a l d i s p e r s i o n o f t h e f e a t u r e SS i s 1.1 e V

along t h e ??'-direction,

which i s t h e same v a l u e a s t h e d i s p e r s i o n

o f t h e p r o j e c t e d v a l e n c e band e d g e , i . e . t h e b u l k r L - d i s p e r s i o n

as

r e p o r t e d by Chiang a n d Eastman /190/. I t i s r e a s o n a b l e t o d i s c u s s a l s o a n a l t e r n a t i v e i n t e r p r e t a t i o n of SS. I . e . ,

it c o u l d b e d u e t o i n d i r e c t

( a n d i n some s p e c t r a d i r e c t )

t r a n s i t i o n s from t h e p r o j e c t e d b u l k b a n d e d g e . I n f a c t , some m a j o r f e a t u r e s i n ARPES s p e c t r a from 1 1 1 - V s e m i c o n d u c t o r s , peak = 4 e V below E,

l i k e the strong

s e e n f o r p h o t o n e n e r g i e s i n t h e r a n g e 21-24

eV

i n F i g . 1 5 ( a ) , h a v e c o n s i s t e n t l y b e e n a s s i g n e d t o t r a n s i t i o n s from c r i t i c a l p o i n t s i n t h e o n e - d i m e n s i o n a l d e n s i t y o f s t a t e s /163,190, 192/.

One m a j o r c o n c l u s i o n drawn by Manzke e t a l . /191/ w a s t h a t t h e

p r o p o s e d s u r f a c e s t a t e b a n d l i e s w e l l w i t h i n t h e f u n d a m e n t a l gap,

189 hv = 17eV

hr = 112eV

kinetic energy

F i g . 1 5 . ( a ) Normal emission s p e c t r a from G a S b ( l l 0 ) f o r d i f f e r e n t photon e n e r g i e s /191/. A i s due t o d i r e c t t r a n s i t i o n s from t h e uppermost b u l k band, while SS has been a s s i g n e d t o a s u r f a c e s t a t e . T h e i n s e t shows t h e e x p e r i m e n t a l band s t r u c t u r e c l o s e t o t h e valence band maximum i n t h e rKX d i r e c t i o n of t h e bulk BZ. ( b ) ARPES s_p_ectra showing t h e p o l a r a n g l e dependence of emission a l o n g t h e r X ' - d i r e c t i o n f o r 1 7 and 2 1 . 2 eV photon e n e r g y . Right i n s e t : The d i s p e r s i o n of t h e SS f e a t u r e a t 1 7 e V ( s o l i d c i r c l e s ) and 2 1 . 2 e V (open c i r c l e s ) . L e f t i n s e t : S e l e c t i o n of h i g h e s t r e s o l u t i o n s p e c t r a (AE = 5 0 m e V ) f o r 17-eV photon e n e r g y . From r e f . 1 9 1 . s i n c e t h e s u r f a c e s t a t e maximum was r e p o r t e d t o be ( 0 . 1 9 f 0 . 0 3 ) eV above t h e t o p of t h e bulk valence bands. I n t h e h i g h r e s o l u t i o n s p e c t r a i n F i g . 1 6 ( a ) t h e y were a b l e t o r e s o l v e two c o n t r i b u t i o n s s e p a r a t e d by 0 . 1 9 e V i n t h e h i g h energy peak i n t h e normal emission s p e c t r a o b t a i n e d w i t h 23 e V photon e n e r g y . NOW, c o n s i s t e n t w i t h t h e p r e v i o u s s u g g e s t i o n t h a t SS could be due t o emission from t h e topmost (heavy h o l e ) valence band, one may a t t r i b u t e t h e second c o n t r i b u t i o n t o bulk emission from t h e l i g h t h o l e band. A schematic

190

(a)

-

0

1 I 23eV

*17eV

Y)

f 13

n

1I I

0 I

-

) .

t c W c .-c

-0.1 0 0.1 WAVEVECTOR 1

(6’

kinetic energy F i g . 1 6 . ( a ) High r e s o l u t i o n normal e m i s s i o n spectra a t 1 7 a n d 23 e V p h o t o n e n e r g y . I n t h e l o w e r p a r t a r e shown t h e G a u s s i a n p e a k s res u l t i n g from a f i t o f t h e 23-ev s p e c t r u m i n t o two components /191/. ( b ) S c h e m a t i c e n e r g y d i a g r a m o f t h e b u l k bands o f GaSb n e a r t h e v a l e n c e band e d g e a t t h e r - p o i n t , showing t h e e f f e c t s o f s p i n - o r b i t splitting. d i a g r a m o f t h e b u l k b a n d s n e a r T, u s i n g e x p e r i m e n t a l l y o b s e r v e d band

masses f o r GaSb /193/ a n d assuming a s i m i l a r s h a p e f o r t h e bands a s o b t a i n e d i n d e t a i l e d r e l a t i v i s t i c c a l c u l a t i o n s on G e /194/, i s shown i n F i g . 1 6 ( b ) . T o p r o b e t h e maximum e n e r g y p o s i t i o n o f t h e l i g h t h o l e band w i t h direct t r a n s i t i o n s it i s n e c e s s a r y t o have the c o r r e c t p h o t o n e n e r g y . One c a n estimate, a s s u m i n g e . g . f r e e e l e c t r o n f i n a l b a n d s , t h a t t h e d i r e c t t r a n s i t i o n from t h e l i g h t h o l e band w i l l d i s p e r s e down by 0 . 1 9 e V f o r a change i n t h e p h o t o n e n e r g y by = 1 eV.

I n fact, one can n o t e t h a t t h e r e i s a s t r o n g photon energy

dependence o f t h e s h a p e o f t h e combined A, SS p e a k i n F i g . 1 5 ( a ) and t h e p e a k seems t o b e most n a r r o w i n t h e 24-eV s p e c t r u m . The s t r o n g e s t e v i d e n c e a g a i n s t a s u r f a c e s t a t e l y i n g 0 . 1 9 e V w i t h i n t h e b u l k b a n d gap,

i s t h a t p r e v i o u s measurements of t h e

c o n t a c t p o t e n t i a l d i f f e r e n c e s between n- and p-type surfaces /19/

GaSb(ll0)

have shown t h a t t h e r e i s no Fermi l e v e l p i n n i n g by

s u r f a c e s t a t e s i n t h e g a p . T o summarize, a n i n t e r e s t i n g n a r r o w f e a t u r e s e e n n e a r t h e p r o j e c t e d v a l e n c e band e d g e i n ARPES s t u d i e s on t h e G a S b ( l l 0 ) s u r f a c e i s , s o f a r , t h e o n l y s u g g e s t e d s u r f a c e

s t a t e on t h i s s u r f a c e . D e s p i t e t h e v e r y h i g h r e s o l u t i o n i n t h e r e p o r t e d ARPES s t u d i e s , w e c a n n o t y e t c o n s i d e r t h e i d e n t i f i c a t i o n o f t h i s s u r f a c e s t a t e as e s t a b l i s h e d .

191

7

MBE-GROWN

111-V SEMICONDUCTOR SURFACES

The d e v e l o p m e n t of t h e MBE

( m o l e c u l a r beam e p i t a x y ) - t e c h n i q u e h a s

made it p o s s i b l e t o p r e p a r e p o l a r s u r f a c e s o f 1 1 1 - V compound s e m i c o n d u c t o r s w i t h a wide r a n g e o f a n i o n ( o r c a t i o n ) c o n c e n t r a t i o n s i n t h e s u r f a c e l a y e r . F o r a d e s c r i p t i o n o f t h e u s e of MBE f o r sample p r e p a r a t i o n w e r e f e r t o c h a p t e r 1 3 . Below t h e r e i s a r e v i e w o f t h e ARPES s t u d i e s o f MBE-grown p o l a r GaAs s u r f a c e s . The GaAs(100) s u r f a c e i s c e r t a i n l y one o f t h e t e c h n o l o g i c a l l y most i m p o r t a n t s e m i c o n d u c t o r s u r f a c e s , s i n c e it i s t h e n o r m a l l y u s e d s u r f a c e i n e p i t a x i a l g r o w t h o f GaAs/GaAlAs s t r u c t u r e s f o r d e v i c e a p p l i c a t i o n s . The b u l k GaAs c r y s t a l i s b u i l t up by e q u i d i s t a n t , a l t e r n a t i n g G a and A s monolayers i n t h e [ l O O I - d i r e c t i o n .

Depending

on t h e r e l a t i v e c o n c e n t r a t i o n o f Ga a n d A s i n t h e m o d i f i e d s u r f a c e l a y e r s o f a GaAs(100) c r y s t a l and t h e method o f p r e p a r a t i o n , it i s p o s s i b l e t o c r e a t e a l a r g e number o f r e c o n s t r u c t i o n s . Commonly o b s e r v e d r e c o n s t r u c t i o n s a r e , i n o r d e r of i n c r e a s i n g A s t o G a s u r f a c e atomic r a t i o s , t h e c ( 8 ~ 2 4x6, ) ~ c ( 6 ~ 4 1x6, ) ~ Zx4/c ( 2 ~ 8 ) ~ ~ ( 4 x 4 1 ,a n d As-covered 1 x 1 s u r f a c e s / 1 9 5 / .

F o r t h e ~ ( 8 x 2 )s u r f a c e

t h e r e i s some u n c e r t a i n t y i n t h e o r d e r i n g b e c a u s e o f t h e wide r a n g e of G a / A s c o n c e n t r a t i o n s r e p o r t e d f o r t h i s r e c o n s t r u c t i o n /195,196/. The m i x i n g o f 2x4 and ~ ( 2 x 8 )r e c o n s t r u c t i o n s i s c a u s e d by v a r i a t i o n s i n t h e l o n g r a n g e o r d e r a n d t h e mixed p h a s e h a s o f t e n b e e n d e s c r i b e d a s a 2x4 r e c o n s t r u c t i o n , due t o d i f f i c u l t i e s i n o b s e r v i n g t h e u n i q u e ~ ( 2 x 8 )f e a t u r e s i n t h e RHEED p a t t e r n s . The c r y s t a l s t r u c t u r e o f GaAs c a n a l s o b e d e s c r i b e d a s a s t a c k i n g of d o u b l e - l a y e r s i n t h e [ I l l ] - d i r e c t i o n , e a c h d o u b l e - l a y e r i n g o f one G a - l a y e r and o n e A s - l a y e r .

I f the crystal i s separated

i n t o two h a l v e s i n between two d o u b l e - l a y e r s , t e r m i n a t e d and t h e o t h e r As-terminated. a r e d e n o t e d as t h e (111) and

(777)

consist-

o n e h a l f w i l l b e Ga-

The c o r r e s p o n d i n g s u r f a c e s

s u r f a c e s , r e s p e c t i v e l y . By

c h a n g i n g t h e d e t a i l s o f s u r f a c e p r e p a r a t i o n it i s p o s s i b l e t o v a r y t h e r e l a t i v e s u r f a c e c o n c e n t r a t i o n s of Ga a n d A s , which c a n r e s u l t i n d i f f e r e n t s t a b l e s u r f a c e r e c o n s t r u c t i o n s . F o r t h e (111) ( i d e a l l y Ga-terminated)

s u r f a c e a 2x2 p e r i o d i c i t y h a s b e e n r e p o r t e d i n

e l e c t r o n d i f f r a c t i o n e x p e r i m e n t s on b o t h MBE-grown and s p u t t e r e d and a n n e a l e d s u r f a c e s . The ( i i i ) - s u r f a c e c a n , however, e x h i b i t s e v e r a l d i f f e r e n t reconstruction p a t t e r n s . In order of decreasing A s content 2x2, 43x43-

R30°, 419x419-

R23.4'

and mixed 3x3 a n d 1 x 1

r e c o n s t r u c t i o n s have been obtained /191/.

192

7.1

GaAs (100) s u r f a c e s

The e l e c t r o n i c s t r u c t u r e of MBE-grown GaAs(100) s u r f a c e s h a s been s t u d i e d by Larsen and coworkers /198-204/,

Bachrach e t a l . /205/ and

Chiang e t a l . /206/. Both Bachrach e t a l . and Chiang e t a l . r e p o r t e d angle-integrated

s p e c t r a from f i v e r e c o n s t r u c t i o n s , and d i f f e r e n c e s

i n t h e i r r e s p e c t i v e s p e c t r a were a s s i g n e d t o d i f f e r e n c e s i n e i t h e r t h e s u r f a c e e l e c t r o n i c s t r u c t u r e o r t h e s u r f a c e d i f f r a c t i o n of e l e c t r o n s e m i t t e d from t h e s u r f a c e and t h e b u l k . I n t h e s t u d y by Chiang et a l . a n g l e - r e s o l v e d photoemission i n t h e normal d i r e c t i o n was s t u d i e d over a wide range of photon e n e r g i e s and s t r o n g bulk c o n t r i b u t i o n s w e r e found t o dominate t h e emission f o r a l l s u r f a c e s s t u d i e d , i . e . t h e ~ ( 2 x 8,) 1x1, ~ ( 6 x 4,) and ~ ( 4 x 4 )s u r f a c e s . N o s u r f a c e s t a t e emission c o u l d be i d e n t i f i e d i n t h e normal emission spectra. E x t e n s i v e s t u d i e s of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e of t h e 2x4/c(2x8)

(denoted 2x4) and ~ ( 4 x 4 )phases have been performed by

Larsen e t a l . /198-203/.

They combined s t u d i e s of a n g l e - r e s o l v e d

photoemission from t h e v a l e n c e bands and c o r e l e v e l s with RHEED s t u d i e s and t h e o r e t i c a l c a l c u l a t i o n s of t h e s u r f a c e e l e c t r o n i c s t r u c t u r e , t o develop models f o r t h e s e A s r i c h s u r f a c e s . By u s i n g t h e t u n a b i l i t y of s y n c h r o t r o n r a d i a t i o n and by comparing t h e s p e c t r a from s u r f a c e s with d i f f e r e n t r e c o n s t r u c t i o n s t h e y were a b l e t o i d e n t i f y bulk and s u r f a c e c o n t r i b u t i o n s t o t h e photoemission s p e c t r a . The s u r f a c e s t a t e band s t r u c t u r e o b t a i n e d f o r t h e G a A s ( 1 0 0 ) - 2 ~ 4 / ~ ( 2 ~s 8 u r) f a c e i s shown i n F i g . 1 7 ( a ) d i s p l a y e d i n a 2x1 s u r f a c e B r i l l o u i n zone / 2 0 1 / .

The s u r f a c e BZ:s f o r t h e 1x1, 2x1,

and 2x4 r e c o n s t r u c t i o n s a r e shown i n F i g . 1 7 ( b ) . The a u t h o r s argued /201,203/ t h a t t h e main c o n t r i b u t i o n t o t h e r e c o n s t r u c t i o n of t h e GaAs(001)2x4 s u r f a c e ( u s i n g t h e i r n o t a t i o n ) i s t h e two-fold p e r i o d i c i t y a l o n g t h e [ ? l o ] - d i r e c t i o n ,

i . e . i n the s a m e

azimuthal d i r e c t i o n a s t h e A s d a n g l i n g bonds on t h e i d e a l s u r f a c e , and t h a t it i s t h e r e f o r e r e l e v a n t t o compare t h e e x p e r i m e n t a l l y o b t a i n e d bands w i t h c a l c u l a t i o n s f o r a 2x1 r e c o n s t r u c t e d s u r f a c e . Larsen e t a l . c a l c u l a t e d t h e s u r f a c e s t a t e bands f o r a 2x1 model corresponding t o a f u l l monolayer of asymmetric As-dimers. assumption of a f u l l As-layer

The

was s u p p o r t e d by t h e measured c o r e

l e v e l i n t e n s i t i e s . The main c o n c l u s i o n s from t h e comparison between t h e o r y and experiment were, f i r s t l y , t h a t a l t h o u g h t h e r e i s no oneto-one

correspondence between t h e e x p e r i m e n t a l and c a l c u l a t e d bands,

one should e x p e c t a number of s u r f a c e s t a t e bands i n t h e range 0 . 5 -

193

( a ) GaAs(001I-ZxL Surface bands 0

I

111 .1

SBZ

12.11

SBZ 01

( 2 4 SBZ

J

I

r

J2,i

1

Jzri

F i g . 1 7 . ( a ) The e x p e r i m e n t a l l y o b t a i n e d s u r f a c e s t a t e bands f o r t h e ( 2 x 8 ) s u r f a c e . Open and f i l l e d symbols i n d i c a t e t h e GaAs ( 0 0 1 ) - 2 ~ 4 / c energy p o s i t i o n s of s h o u l d e r s and peaks i n ARPES s p e c t r a , r e s p e c t i v e l y . hv = 2 9 e V ( s q u a r e s ) , hv = 21.2 e V ( t r i a n g l e s ) o r 2 0 < hv < 32 eV ( c i r c l e s ) . From r e f . 2 0 1 . ( b ) The s u r f a c e B r i l l o u i n zones f o r 1x1, 2x1, and 2 x 4 r e c o n s t r u c t i o n s of t h e GaAs(001) s u r f a c e . 1 . 6 eV below t h e v a l e n c e band edge. Secondly, t h e o b s e r v a t i o n of a

s u r f a c e s t a t e band ( S q ) a t = -3 eV along t h e &xl-K2xl s t r o n g s u p p o r t f o r a d i m e r i z a t i o n of As-atoms

l i n e provides

on t h e 2x4/c(2x8)

s u r f a c e , s i n c e t h i s band i s i n good agreement with t h e c h a r a c t e r i s t i c c a l c u l a t e d dimer bond band. I t was a l s o emphasized t h a t emission from t h i s band was not found on o t h e r s t u d i e d GaAs(100) s u r f a c e s .

I n t h e i r s t u d i e s of t h e ~ ( 4 x 4 )r e c o n s t r u c t e d s u r f a c e , Larsen e t a l . /202/

r e p o r t e d emission from one s u r f a c e s t a t e band (S1)

d i s p e r s i n g from - 0 . 3

eV a t

f' t o - 1 . 0 eV a t Jlxl. From core l e v e l

s t u d i e s it was concluded t h a t t h e occurrence of a 0 . 6 eV s h i f t e d A s 3d component was evidence f o r A s atoms bonding e x c l u s i v e l y t o o t h e r As atoms. The i n t e n s i t y of t h e A s 3d emission a l s o i n d i c a t e d more than a complete A s l a y e r on t h e s u r f a c e . A ~ ( 4 x 4 )model of As-dimers on t o p of a f u l l A s l a y e r was suggested t o e x p l a i n t h e c o r e l e v e l r e s u l t s , while no e x p l a n a t i o n f o r t h e S1 s u r f a c e s t a t e band was given.

I n summary, except f o r t h e G a A s ( 1 0 0 ) - 2 x 4 / c (2x8) s u r f a c e , t h e e l e c t r o n i c s t r u c t u r e s of GaAs(100) s u r f a c e s a r e not well known. To improve t h e understanding it seems n e c e s s a r y t o have a wide range of experimental t e c h n i q u e s t o reduce t h e u n c e r t a i n t i e s i n s t o i c h i o m e t r i e s . Furthermore,

i n c o n j u n c t i o n with t h e o r e t i c a l c a l c u l a t i o n s ,

one must l i m i t t h e number of p o s s i b l e r e c o n s t r u c t i o n models. Isola-

194

t e d s t u d i e s o f t h e s u r f a c e e l e c t r o n i c s t r u c t u r e on t h e d i f f e r e n t

s u r f a c e s w i l l p r o b a b l y b e o f l i m i t e d v a l u e , s i n c e f o r a w e l l founded d i s c u s s i o n of s u c h r e s u l t s , it i s n e c e s s a r y t o have a n a c c u r a t e e s t i m a t e of t h e s u r f a c e s t o i c h i o m e t r y .

7.2

__-

G a A s ( l l 1 ) m d (111) s u r f a c e s

The e l e c t r o n i c s t r u c t u r e s o f GaAs (111) and b e e n s t u d i e d w i t h ARPES /207-211/

(iii) s u r f a c e s

a n d a l a r g e number o f s u r f a c e

s t a t e b a n d s have b e e n p r o p o s e d . J a c o b i e t a l . /208/ a n g l e - r e s o l v e d p h o t o e m i s s i o n from t h e 2x2, on t h e

(777)

have

43x43,

studied the

a n d 419x419 p h a s e s

s u r f a c e u s i n g 2 1 . 2 a n d 1 6 . 8 e V r a d i a t i o n . They

e v a l u a t e d t h e d i f f e r e n c e s i n t h e s p e c t r a f o r t h e 2x2 a n d 419x419 p h a s e s a n d a t t r i b u t e d t h e s e t o c h a n g e s i n t h e s u r f a c e s t a t e s . From t h e i r e x t e n s i v e s t u d i e s of e m i s s i o n a l o n g t h e [iOl],

[ i i 2 1 , and

[211] a z i m u t h s , t h e y s u g g e s t e d a n i d e n t i f i c a t i o n of f i v e d i f f e r e n t s u r f a c e s t a t e bands on t h e G a A s ( i i i ) 2 x 2 s u r f a c e . T h r e e o f t h e s e , observed a t = 1.8, = 4 . 0 ,

a n d = 6 . 6 e V below t h e v a l e n c e band edge,

r e s p e c t i v e l y , were r e p o r t e d t o e x h i b i t t h e e x p e c t e d 2x2 symmetry i n t h e surface BZ:s.

F o r t h e 419x419 s u r f a c e o n e s u r f a c e s t a t e band

d i s p e r s i n g from 0 . 4 e V a t

r

t o 1.0 eV a t

glxl was i d e n t i f i e d .

From t h e p o l a r i z a t i o n dependence o f t h e two topmost b a n d s on t h e ( i i i ) 2 x 2 s u r f a c e , t h e s e were a t t r i b u t e d t o t h e l o n e p a i r o r b i t a l s on As-atoms

i n t h e s u r f a c e l a y e r . However, a b u c k l i n g r e c o n s t r u c t i o n of

t h e 2x2 s u r f a c e , t h a t was c o n s i d e r e d as b e i n g c o n s i s t e n t w i t h t h e d a t a , was l a t e r r u l e d o u t u s i n g t h e r e s u l t s o f e n e r g y m i n i m i z a t i o n c a l c u l a t i o n s / 2 1 2 / . When e x a m i n i n g t h e p r o c e d u r e t o e v a l u a t e s u r f a c e s t a t e c o n t r i b u t i o n s from d i f f e r e n c e s p e c t r a u s e d by J a c o b i e t a l . /208/,

some words of c a u t i o n a r e n e e d e d . F i r s t l y ,

c h a n g e s i n band-bending,

i f t h e r e a r e any

even i d e n t i c a l b u l k c o n t r i b u t i o n s from t h e

two s u r f a c e s w i l l g i v e rise t o s t r u c t u r e i n t h e d i f f e r e n c e s p e c t r a . Secondly, c h a n g e s i n t h e s u r f a c e geometry w i l l a l s o a f f e c t e m i s s i o n from t h e b u l k . ARPES s t u d i e s o f t h e ( 1 1 1 ) 2 x 2 a n d ( i i i ) 2 x 2 s u r f a c e s have been r e p o r t e d by B r i n g a n s and Bachrach / 2 0 9 , 2 1 0 / .

F i g . 1 8 ( a ) shows t h e

measured d i s p e r s i o n s of s u r f a c e r e l a t e d s t r u c t u r e s o b s e r v e d i n t h e

[Oli] a z i m u t h . It i s g r a t i f y i n g t h a t t h e f i v e s u r f a c e r e l a t e d f e a t u r e s r e p o r t e d a t l= by J a c o b i e t a l . /208/

for the (iii)2x2

s u r f a c e were a l s o found i n t h e s t u d y by B r i n g a n s and Bachrach / 2 0 9 / . There a r e , however, d i f f e r e n c e s i n t h e i n t e r p r e t a t i o n o f t h e s e features, i . e . i n t h e later study t h e features a t 0.3,

1 . 7 5 , and 3 . 1

195

.[lii]

[ o i i]

[i2i]

(iii)

Fig. 18. ( a ) Measured d i s p e r s i o n s o f s u r f a c e r e l a t e d f e a t u r e s i n ARPES s t u d i e s on GaAs(111)2x2 a n d ( i i i ) 2 x 2 s u r f a c e s . Data t a k e n a t 1 7 , 2 0 , 22, 25 a n d 2 7 e V are shown by , x , a n d + symbols r e s p e c t i v e l y . Open symbols c o r r e s p o n d t o w e a k e r f e a t u r e s . L i n e s t h r o u g h t h e G a A s ( i i i ) 2 x 2 d a t a a r e r e p e a t e d t o show 2x2 symmetry. From r e f . 2 0 9 . ( b ) The s u r f a c e B r i l l o u i n zone f o r G a A s ( 1 1 1 ) 2 x 2 i s shown by t h e f u l l l i n e a n d t h e 1 x 1 z o n e i s shown b y t h e b r o k e n l i n e .

+,

e V b e l o w Em

were i n t e r p r e t e d a s s u r f a c e s t a t e s , w h i l e t h e f e a t u r e s

a t 2 . 7 a n d 1.0 e V w e r e a t t r i b u t e d t o b u l k t r a n s i t i o n s , t h a t were o b s e r v e d i n t h e normal d i r e c t i o n b e c a u s e o f s u r f a c e s c a t t e r i n g i n t h e 2x2 r e c o n s t r u c t e d s u r f a c e l a y e r . A s shown i n F i g . 1 8 ( a ) , B r i n g a n s and Bachrach a l s o found s t r o n g s u r f a c e r e l a t e d e m i s s i o n i n b e t w e e n t h e two u p p e r m o s t f u l l - d r a w n b a n d s , s u g g e s t i n g o n e more s u r f a c e s t a t e band i n t h i s e n e r g y r e g i o n . I n t h e comparison between t h e

( 1 1 1 ) 2 x 2 and

( i i i ) 2 x 2 surfaces it

was c o n c l u d e d , t h a t t h e e l e c t r o n i c s t r u c t u r e of t h e two s u r f a c e s a r e r e m a r k a b l y d i f f e r e n t . The d i s p e r s i o n s o b t a i n e d o n t h e ( 1 1 1 ) 2 x 2 s u r f a c e showed a n a p p a r e n t 1 x 1 symmetry, i n s t e a d o f t h e 2x2 symmetry o b s e r v e d f o r s e v e r a l f e a t u r e s on t h e ( T i I ) 2 x 2 s u r f a c e . F u r t h e r m o r e , t h e p o l a r i z a t i o n d e p e n d e n c e o f t h e t o p m o s t s u r f a c e f e a t u r e showed

196 o p p o s i t e b e h a v i o u r f o r t h e two s u r f a c e s . T h i s i s c o n s i s t e n t w i t h c a l c u l a t i o n s f o r relaxed geometries /213/,

where t h e p , - l i k e

dang-

l i n g bond band was f o u n d t o b e t h e t o p m o s t o c c u p i e d band on t h e

(Ti?)

s u r f a c e , w h i l e i t w a s a p,-band

on t h e (111) s u r f a c e .

I n c o n c l u s i o n , l a r g e d i f f e r e n c e s h a v e been o b s e r v e d i n t h e e l e c t r o n i c s t r u c t u r e o f GaAs(111)2x2 a n d ( i i i ) 2 x 2 s u r f a c e s , a n d a l s o between t h e ( i i i ) 2 x 2 and ( i i i ) q 1 9 x d 1 9 s u r f a c e s . So f a r , i t h a s n o t b e e n p o s s i b l e t o compare t h e measured s u r f a c e s t a t e d i s p e r s i o n s w i t h a n y band c a l c u l a t i o n s f o r t h e r e c o n s t r u c t e d s u r f a c e s . C o n c e r n i n g t h e experimentally obtained surface state dispersions, t h e correct i d e n t i f i c a t i o n of s e v e r a l o f t h e o b s e r v e d s u r f a c e r e l a t e d f e a t u r e s r e m a i n s t o be e s t a b l i s h e d .

8

11-VI

AND I V - V I

The 1 1 - V I

SEMICONDUCTOR SURFACES compound s e m i c o n d u c t o r s a r e c o n s i d e r a b l y more

and IV-VI

i o n i c than t h e 111-V

semiconductors / 2 1 4 / ,

and t h e y c a n be s e p a r a t e d

i n t o t h r e e c a t e g o r i e s a c c o r d i n g t o t h e i r c r y s t a l l i n e s t r u c t u r e . They c a n form i n t h e c u b i c z i n c b l e n d e s t r u c t u r e ( e . g . C d T e ) , i n t h e hexagonal w u r t z i t e s t r u c t u r e t u r e ( t h e IV-VI

( e . g . ZnO), o r i n t h e r o c k s a l t s t r u c -

s e m i c o n d u c t o r s , e . g . P b S e ) . Some of them,

l i k e ZnS

o r CdS, can a p p e a r i n e i t h e r z i n c b l e n d e o r w u r t z i t e s t r u c t u r e . Reviews o f t h e e x p e r i m e n t a l l y o b t a i n e d LEED-patterns s t o i c h i o m e t r i e s o f d i f f e r e n t Zn- a n d C d - c h a l c o g e n i d e b e e n g i v e n by T a k a h a s h i a n d E b i n a / 2 1 5 , 2 1 6 / . polar cleave surfaces,

and s u r f a c e

s u r f a c e s have

I n g e n e r a l , t h e non-

i . e . t h e (110) s u r f a c e o f t h e z i n c b l e n d e

s t r u c t u r e a n d t h e (lOi0) a n d (1170) s u r f a c e s o f t h e w u r t z i t e s t r u c t u r e e x h i b i t 1 x 1 LEED-patterns and a n n e a l e d p o l a r or non-polar

a f t e r cleavage,

while t h e s p u t t e r e d

s u r f a c e s e x h i b i t LEED-patterns

i n d i c a t i n g s u p e r s t r u c t u r e s o r even f a c e t t i n g . Concerning t h e atomic geometry o f t h e n o n - p o l a r /215,216/

( 1 1 0 ) and (1070) s u r f a c e s it was c o n c l u d e d

t h a t r e s u l t s from LEED I - V

a n a l y s i s i n d i c a t e t h a t probably

a l l t h e s e s u r f a c e s have r e l a x e d g e o m e t r i e s a l t h o u g h t h e LEED symmetry i s 1x1. A r e l a x a t i o n of t h e Z n T e ( l l 0 ) and Z n S e ( l l 0 ) s u r f a c e s h a s b e e n p r e d i c t e d from e n e r g y - m i n i m i z a t i o n c a l c u l a t i o n s by Chadi /211/.

An o u t w a r d r e l a x a t i o n o f t h e a n i o n s i m i l a r t o t h e r e l a x a t i o n

o f t h e G a A s ( l l 0 ) s u r f a c e w a s f o u n d t o lower t h e e n e r g y o f t h e s e s u r f a c e s . A f a i r l y good a g r e e m e n t c o n c e r n i n g t h e d i s p l a c e m e n t of s u r f a c e atoms i s o b t a i n e d between L E E D - r e s u l t s total-energy

minimization c a l c u l a t i o n s / 2 1 1 / .

/218,219/ a n d t h e

197

8.1

The c l e a V ed C d T e i l 10) s u r f a c e

T h e C d T e ( l l 0 ) s u r f a c e i s p r o b a b l y t h e most w e l l - s t u d i e d

11-VI

semiconductor s u r f a c e a s f a r as e x p e r i m e n t a l s t u d i e s of t h e elect r o n i c s t r u c t u r e a r e c o n c e r n e d . S e v e r a l d i f f e r e n t g r o u p s /216,2202 2 6 / h a v e p e r f o r m e d ARPES s t u d i e s a n d some of them have d i s c u s s e d

p o s s i b l e c o n t r i b u t i o n s from s u r f a c e s t a t e s i n t h e s p e c t r a . I n o t h e r s t u d i e s t h e focus has been on comparisons w i t h t h e t e c h n o l o g i c a l l y and s c i e n t i f i c a l l y i m p o r t a n t Cdl-xHg,Te

/225/

and Cdl_,MnxTe

/221/

alloys. S i l b e r m a n e t a l . / 2 2 5 / a n d Magnusson e t a l . / 2 2 6 / h a v e measured t h e n o r m a l e m i s s i o n s p e c t r a from C d T e ( l l 0 ) f o r p h o t o n e n e r g i e s i n t h e r a n g e 13-26 e V . The s p e c t r a shown i n F i g . 1 9 ( a ) were o b t a i n e d w i t h t h e p o l a r i z e d r a d i a t i o n i n c i d e n t a t 15O from t h e s u r f a c e normal and t h e E-vector w i t h i n t h e ( i l O ) - p l a n e / 2 2 6 / .

Magnusson e t a l .

r e p o r t e d t h a t d i r e c t t r a n s i t i o n s i n t h e b u l k d o m i n a t e i n t h e normal d i r e c t i o n s i n c e f e a t u r e s A-D

a l l a r e d i s p e r s i n g w i t h photon energy,

f u r t h e r m o r e t h e s t a t i o n a r y s t r u c t u r e a t - 6 . 2 e V below t h e F e r m i

.-

e n e r g y w a s i n t e r p r e t e d a s b e i n g due t o b u l k e m i s s i o n a s i t h a s maximum i n t e n s i t y when d i r e G t t r a n s i t i o n s a r e e x p e c t e d from a f l a t p o r t i o n o f t h e b u l k band s t r u c t u r e . The s p e c t r a shown i n F i g . 19(a) a r e c o n s i s t e n t w i t h t h e s p e c t r a of Silberman e t a l . ,

although t h e r e

a r e l a r g e d i f f e r e n c e s between t h e two s e t s o f d a t a b e c a u s e v e r y d i f f e r e n t p o l a r i z a t i o n s o f t h e l i g h t w e r e u s e d . Examples o f t h e s e s t r o n g p o l a r i z a t i o n e f f e c t s were a l s o g i v e n i n t h e s t u d y by Silberman e t a l . . I n t h e c a s e of l i g h t p o l a r i z e d mainly a l o n g t h e s u r f a c e n o r m a l , t h e e m i s s i o n i s d o m i n a t e d by e x c i t a t i o n s t o t h e s i m p l e [ k + (110)4Wa] f r e e e l e c t r o n p a r a b o l a /225/.

Excitations t o other free-electron

( p r i m a r y cone e m i s s i o n )

l i k e b a n d s and i n d i r e c t

t r a n s i t i o n s h a v e t o be i n v o k e d t o e x p l a i n some o f t h e f e a t u r e s s e e n , i n p a r t i c u l a r , with s-polarized

light /226/.

An i m p o r t a n t c o n c l u s i o n

i n t h e p r e s e n t c o n t e x t i s t h a t no e v i d e n c e f o r s u r f a c e s t a t e s h a s been found i n t h e normal e m i s s i o n s p e c t r a . Magnusson e t a l . / 2 2 6 /

a l s o d i d q u i t e e x t e n s i v e o f f - n o r m a l ARPES

s t u d i e s on C d T e ( l l 0 ) s u r f a c e s , i n v e s t i g a t i n g t h e s u r f a c e e l e c t r o n i c s t r u c t u r e along t h e

r%I%'F symmetry l i n e s i n t h e s u r f a c e

BZ.

In F i g .

1 9 ( b ) ARPES s p e c t r a , o b t a i n e d w i t h 18-eV p h o t o n e n e r g y , a r e shown,

which p r o b e t h e e l e c t r o n i c s t r u c t u r e a l o n g t h e r % ' - l i n e . A l l f e a t u r e s s e e n a t s m a l l e m i s s i o n a n g l e s , 8,

c

.-It C

a

c

C Y

Binding energy (eV)

Fig. 8 . ARUP-spectra in normal emission for different light polarization directions of CO(2xl)p2mg/Ni(llO) (full lines) in comparison with the clean Ni(ll0) surface (broken lines) in the region of the metal emissions (ref. 63). between the one for C O / A g and CO/Cu which leads us to expect more intense satellites, and corroborates the ideas presented. In our discussion so far we have only considered the molecule induced peaks at binding energies higher than the metal states, i.e. those states that correspond to "molecular" ion states. However, as is obvious from Fig.1 there are levels of the adsorbate system within the region of the metal projected density of states, due to the coupling of unoccupied molecular states to occupied metal states. There have been several attempts to identify these states (refs. 61-63). The most recent one was done on the system CO(2xl)p2mg/Ni(llO), whose structure will be discussed in detail in connection with intermolecular interactions (ref. 26). The symmetry and high CO density of this system allows to measure the adsorbate induced

334

peaks in the d-band region of the Ni substrate (ref. 63). Fig.8 shows a selected set of spectra that demonstrate the intensity, symmetry and energy position of the CO induced, d-like states for this system. The spectra of the clean surface are given as dashed curves for comparison. The usually dominant CO molecular ionizations (ref. 26) are not shown in this figure. The various peak intensities are strongly polarization dependent, and, together with the measured dispersion, discussed in the section intermolecular interactions, support an assignment of these features to CO-2n-Ni-3d states, To summerize the results so far, the ARUP-spectra are found to reflect the bonding with the surface. It is possible to differentiate between physisorbed, weakly chemisorbed, and strongly chemisorbed CO adsorbates. However, the differences in the habit of the spectra for various chemisorbed systems are rather unpronounced which limits the applicability of photoemission with respect to fingerprinting. On the other hand, ARUPS is sensitive to the local site symmetry via the angular emission pattern, as well as the angular dependence of resonance features in the ionization cross-section. For special cases the back-bonding states in the region of the metal substrate states can be identified. In order to appreciate in more detail how these aspects of photoemission have been used to study molecule surface interactions under the influence of variations of the substrate and co-adsorbed species we briefly review selected results of adsorbates on clean and precovered surfaces: 2.1

Pure adsorbates

2.1.1 Hz

Even though HZ adsorbates have a lot of appeal to be the model system to study molecular adsorption very little has been done with respect to the application of ARUPS. The reason is, of course, that in general, at routinely accessible temperatures hydrogen adsorbs dissociatively to form atomic adsorbates. To our knowledge only angle integrated spectra have been published for adsorbed molecular H2 (ref. 6 4 ) . Whether one should look at hydrogen adsorbates with coverage 8 = 2 as containing atomic (2H) or quasimolecular HZ is probably a matter of semantics. Christmann et al. (ref. 6 5 ) have studied these systems with ARUPS and observed band dispersions as large as 4 eV and binding

335

energies for the hydrogen induced features close to 10 eV below EF .

4? 50/l~

.-

:?.

0.5L; T = 240K hw = 36eV

Fig. 9. ARUP-spectra of CO/Fe(lll) for various light incidence and electron emission angles as indicated in the inset ( E n i n in eV). Top and bottom panels differ by the CO exposure. The top panel corresponds to saturation coverage (ref. 66). 2.1.2 co As documented in the previous section the adsorption of CO has been extensively investigated with ARUPS. The orientation of the CO molecule has been found to be parallel to the surface in the case of Ag(ll1) (ref. 101, and upright in many chemisorbed systems (refs. 24-40). Recently, some systems have been studied where CO shows photoemission patterns different from the usual behaviour. Fig.9 presents spectra for CO/Fe(lll) (ref. 6 6 ) . The 5a/ln-band is clearly split, and the 4 0 intensity is not

336

completely attenuated in the forbidden geometry indicating a possible tilt of the CO molecules or a strong distortion of the 4 0 wavefunction. Spectra have been reported for CO/Cr(llO) (ref. 2 9 ) and CO/Fe(100) (refs. 67) where the authors claim flat lying CO. These are the only cases where strongly chemisorbed CO appears to be oriented parallel to the surface.

I

.

FellllVN,

; T*llK

1.

2-pol .?'

Fclllll/N,

2- pol nornol

normal emission

cmission

..., ...

-._ . '

.

%

4 ! LZSN

32 5rv 30 0.v 275.v ZI5.Y

-I

1

bl

b2

ho 17 5SV

LZ 5rv

37 5."

32 I*

17%"

-

I pol 60'off nwmol

E,

emission -

2

L

6

6

10

12

E,,"l*'

Fig. 10. ARUP-spectra of Nz /Fe(lll) for grazing light incidence and normal emission (left panel), and s-polarization (near normal incidence, right panel) and two electron emission angles (bl: normal emission; b2: off-normal(600) emission). For each measurement geometry typical spectra at different photon energies are plotted (ref. 72).

337

2.1.3 Nz Nz on Fe(ll1) has been the model system to investigate the mechanism of ammonia synthesis (ref. 68). It is known that NZ dissociation is the rate limiting step, and that there exist molecular precursor states for dissociation where NZ has been presumed to be side-on bonded to the iron surface (ref. 69). Via ARUPS a strongly inclined NZ species was identified (ref. 70) in addition to a vertically bound Nz species which only exists at lower temperature. Fig.10 shows a set of angle resolved spectra at low temperature (vertically bound N2) and higher (T=llOK) temperature (Nz bound inclined). Fig.lOa reveals the a-shape resonance in normal emission for z-polarized light at T o the VW mode is the equilibrium mode, whereas A s o holds for the SK and the FM mode. Bauer

379

(6) has pointed t o the f a c t t h a t f o r the FM ( l a y e r by l a y e r ) mode A s o has t o be f u l f i l l e d f o r each new layer. This w i l l be the case o n l y when adsorbate and s u b s t r a t e are very s i m i l a r :

TA

= TS, TI = 0. From t h i s simple argument i t be-

comes c l e a r t h a t t h e SK mode i s t h e most l i k e l y one.

It has t o be noted t h a t

f o r p r a c t i c a l cases the above argument i s not very h e l p f u l : Exact

‘I

values are

n o t known i n most cases, and the e q u i l i b r i u m c o n f i g u r a t i o n may n o t be reached, since t h e m o b i l i t y o f the incoming atoms may n o t be l a r g e enough. Thus, pending on substrate temperature, observed,

de-

d i f f e r e n t metastable c o n f i g u r a t i o n s may be

and i t has t o he proven experimentally which growth mode occurs i n

each case.

Fiq. 2: Auger i n t e n s i t i e s from Mo substrate and Pd adl a y e r as f u n c t i o n o f evapor a t i o n steps. From (8).

5

0

10 15 NUMBER OF 1 mnn DOSES OF Pd

20

25

From an experimental p o i n t o f v i e w i t i s most d i f f i c u l t t o v e r i f y t h e FM mode, since some s c a t t e r o f experimental p o i n t s may round o f f t h e breaks i n t h e Auger

curves.

The most important p o i n t

i s to

have a l l

settings f o r

the

evaporation source, the AES detector and sample p o s i t i o n w e l l reproducible. The best curves are published by Bauer and h i s coworkers. One example i s shown i n f i g . 2. I t e x h i b i t s r e a l l y s t r a i g h t l i n e s f o r the Is(Mo) as w e l l as f o r IA(Pd). I n o t h e r cases, where a d d i t i o n a l data are c o l l e c t e d depending on thickness, t h e s c a t t e r of t h e data may increase g r e a t l y . One o f these examples i s presented i n

3, where a k i n d o f SK mode i s demonstrated f o r Ag/A1(111)

fig.

(19).

from our group

One c l e a r l y recognizes a break a f t e r one ML and a s t r a i g h t l i n e up t o

about 4 ML. By evaluating the data i n d e t a i l we found a completion o f t h e M L up t o 87% before the second l a y e r s t a r t s growing and estimated the c l u s t e r on t o p

o f t h e f i r s t ML t o be 3-4 l a y e r s t h i c k . As Rhead e t a l .

(3) have pointed out t h e r e are several o t h e r more com-

p l i c a t e d growth modes possible besides t h e three simple cases o f f i g .

1. For

380

rt

I

1

I

I

I

I

Fiq. 3: Auger intensities for Ag layers vapor deposited onto Al(111) as function of evaporation time. The kinetic energies of the Ag and A1 transitions are given in parentheses. The sample temperature was 300 K. From (19).

I

I C

200

-

LOO 600 EVAPORATION TIME I s

800

instance, it is quite possible that real exponential behavior is exhibited over the whole thickness range or starting with the second layer for the SK mode, if there is simultaneous multilayer growth. This mode can be operative for high supersaturation and low substrate temperature when the atoms may adsorb at the site, where they hit the surface, Furthermore, the discussion above breaks down, if the sticking coefficient varies with thickness (which is, on the other hand, very unlikely for metallic adsorbates and rather low substrate temperatures). Another underlying assumption is the neglect o f interdiffusion, which has to be checked in each case. NOBLE METALS The noble metals Cu, Ag and Au are the most frequently studied among the thin metal film systems. This is certainly due to the importance of these metals as electrical conductors. Besides this, the investigations are facilitated by the chemical inactivity of these metals. In the following we discuss each of the three metals separately. Some conclusions are drawn in section 3.4, where some tables of BE are presented. 3

3.1 Comer There are two major ARUPS studies of Cu on Ag(001) (21,22) which confirm pseudomorphic growth up to a thickness of 2-3 Cu layers. These Cu layers are expanded by 13 % relative to bulk Cu. The large misfit induces more strain than can be sustained by the adlayer during FM (layer-by-layer) growth. Therefore, after 2-3 ML the system switches to the SK mode as can be seen from the deterioration of the LEE0 pattern and the shallow slope of the AS curves.

381

Fiq. 4: Series of AR spectra taken along the Z azimuth for 1 ML Cu on Ag(001). The photon energy is 30 eV. Three bands of features (indicated by the tick marks) are attributed t o Cu 3d states and are seen to disperse in energy as 0 i s varied. The Cu 3d origin of the features is established by comparison with data from clean Ag and from Ag with 2-6 monolayers of Cu coverage, Emission at 0 = 40" originates near the M symmetry point. From (21).

-a

-6

-4

Energy

-2

0

(eV)

Fig. 4 exhibits a series of ARUP spectra taken in the TM azimuth for different angles of emission 0 (21). Especially, above the upper edge of the Ag 4d emission of the substrate at about 4 eV, well resolved Cu-derived peaks can be seen exhibiting some dispersion. The 20 band structure is presented in fig. 5, as it is deduced by the authors from all measured spectra including those of fig. 4. By using well suited angles and photon energies also states near 5 eV are identified as Cu states which overlap with the Ag bands from the -

-

-

Ag(OO11* 1 ML

Cu

-I

Fiq. 5: 2D band structure of the Cu monolayer. Features displaying clear A 1 or ’c2 symmetry are indicated by solid circles while open circles represent A1 or Z7 states. The remaining features are plotted as triangles or, in the case o f unresolved peaks, as error bars soannina the Drobable ’peak posit\ons. Bands are drawn through the points in qualitative agreement with theory (23,24). Bands with C2 or A2 symmetry are indicated by dashed lines. The shaded area indicates the projection o f the Ag 4d bulk band structure. From L

4

l

2

-

'.

I -4

-5 I

I5

10

05

0

05

I0

(21)

-

382

substrate. For the ML only peaks are taken, which increase in intensity also for the 2 and 3 ML thicknesses. Other Cu-induced features are not discussed, since in the Ag 4d region there is no way to differentiate between redistributed Ag features and real interface states. The former effect may arise from increased scattering due to the higher density of defects at the interface compared to the clean Ag(001) surface. Thus, it is interesting to note that (a) the derived band width of the Cu ML (3.15 eV) is essentially identical to that reported for bulk Cu (3.20 e V ) , and (b) the bands are more tightly bound than bulk Cu bands by only 0.25 eV. These findings agree best with a calculation for a Cu ML on Ni(001) (23) indicating that the lattice constant is only o f minor importance for the 20 band structure. For the same system (Cu/Ag(001)) Smith et al. (22) arrive at a somewhat different 20 band structure, which i s shown in fig. 6. There is a further band resolved nearer to EF and, more important, the total width of the ML bands is only 1.5 eV and lying completely above the substrate 4d emission. This finding led the authors to vary the result of a ML calculation (24) in order to explain their result as pointed out in the caption of fig. 6.

Fiq. 6: Energy bands of the Cu (100) mono1 ayer on Ag(100). Full curves, LCAO bands calculated by Smith et al. (24) for an isolated Cu(100) monolayer, after reducing the energy dispersion by a factor o f 1.8 in order to correct for the Cu lattice expansion and rigidly shifting the bands 1.2 eV away from the Fermi level. From (22).

I

R

r

1 X

The second well defined Cu adlayer system is Cu/Ru(0001) (25-27), which has the advantage of being composed of two immiscible components. Cu grows pseudomorphically up to one ML on the Ru(0001) surface with a 5 % tensile strain with respect to the Cu(ll1) bulk lattice, which is largely reduced compared to the Ag(001) surface. Houston et al. (25) have been able to separate a true interface state which is, according to their slab calculations, localized in the Cu and outermost Ru layers. Guided by their calculations they have been able to separate this state from the Ru substrate emission near the ?t point at 1.5 eV

383

Fiq. 7: ARUP spectra taken with He1 radiation at normal incidence and an electron emission angle of 52" for Cu on Ru(0001) are shown as functions of Cu coverage. The intensity of the various curves has been normalized at the Fermi level, EF. The individual curves are matched to their corresponding Cu coverages in monolayers by the solid lines while the saturating behavior of the interface state at approximately -1.4 eV is identified by the dashed lines. From

(25).

-6.0 -5.0 4.0 -3.0

-2.0

-1.0

0.0

BINDING ENERGY-OV

below EF, as shown in fig. 7. From this figure it is also seen that the Cu ML emission evolves at nearly the same energy as the Cu 3d emission for higher coverages. Houston et al. did not try further t o extract a 2D band structure. They stressed that for 1 ML or less "the Cu 3d levels mix stronqly with the Ru 4d states". This may become even more clear from their calculated bands as shown in fig. 8. They point out that without a strong interaction between the first Cu layer and the Ru substrate a pseudomorphic growth with a 5 % tensile strain would be difficult to understand. They felt this to be in contradiction

aa

9 s w

-20

F

-

persions along the r - K s.ymEfmetry line for a five-layer Ru(0001) film covered on both ’faces by a 1 ML 1x1 Cu overlayer. States indicated by ,. heavy lines and arrows are ’strongly weighted on the outer Cu overlayers and first underlying Ru layers of the film.

384

Fiq. 9: ARUP spectra (normal emission, mixed s/p polarization) from Cu/Ru bilayers as a function of the Cu coverage (OCU= 0.38... ? 5 ML), at a fixed photon energy of 30 eV. Since only the Cu d-band position is to be shown, the curves have not been normalized with respect to their absolute intensity. The dotted line represents the spectrum o f the uncovered Ru(001) surface. The Cu was evaporated with the substrate at 1000 K. From (26).

\

ML

038

.- _.

, - 00 I

-1 E -0 F initial energy lev 1

-8 -7 -6 -5 - L -3 -2

to the analysis o f Vickerman et al. (26), which found the Cu 3d and Ru 4d emission just added "without any hint of a stronq electronic interaction". Fig. 9 presents some of their data (26). They evaluated also a 20 band structure as shown in f i g . 10 and found their results of the ML to be in agreement with the work of Richter e t al. (27). q.0

-

,

I

1

-% -1

Fiq. 10: 20 band structure of the Cu film on Ru(0001). The open circles refer to a 0.82 ML film ( h a = 28 eV). The squares (ha= 30 eV) and the diamonds ( R w = 50 eV) refer to a 2 ML Cu film. The solid circles indicate the position of the Cu d-bands as obtained experimentally in (28) for Cu on NixCui-x(ll1). From (26).

%

m

$ -2 e

-2 -3 .-

.-C

-c

-5

P parallel momentum

ii,,

385

In order to separate the adlayer from the substrate state an interesting experiment was performed by Shek et al. (29) for Cu on Pt(ll1). From LEEO and AES they argued that the ML grows pseudomorphically, giving rise to a tensile stress of 9 %.By using synchrotron radiation at ho= 150 eV they suppressed the Pt 5d emission, since the Cooper minimum lies at this energy for Pt. They observed the Cu emission at 2.65 eV and a weak shoulder at 3.5 eV developing for coverages between 0.75 and 1.0 ML. From their core-level measurements they concluded that the Cu adatoms are essentially neutral in spite of the large electronegativity difference between Cu and Pt. The work function, as measured from the PE EDC’s, decreased by 1.26 eV during completion of the ML. We turn now to what we believe is another class of substrates - the spmetal substrates. Fig. 11 presents the result of the pioneering work of Abbati et al. (30). Cu was deposited onto a freshly cleaved Zn(0001) surface. LEEO indicated a pseudomorphic adlayer, but an AES study was not performed at that time. In agreement with their tight-binding calculation they found for the Cu ML a shift of 1.2 eV to larger binding energies and an appreciable narrowing of the 3d emission. These results have been quite consistently interpreted: The band narrowing in the ML is due to the decreased number of neighbors from 12 to 6 with respect to bulk Cu. The distance between EF and the 3d band is increased. since the average density of states in the lower part of the conduction band is decreased. Thus, the shift to higher BE may be seen as a consequence of the SP charqe decompression at the surface with respect to the bulk. The final d occupancy was found to be 9.963, i.e. larger than the value 9.886 obtained for the bulk. Thus the Cu species is more atomic in the over1 ayer

.

Fiq. 11: Energy distribution curves for (a) one Cu ordered monolayer on Zn(0001) face, (b) about one ML’ of Cu on a polycrystalline Zn film, and (c) thick Cu layer. Theoretical results are given for (d) the local density of states of a Cu overlayer and the total density o f states of (e) Cu and Zn, (f) bulk Cu, and (9) the isolated monolayer. From

-

(30)

386

It is worthwhile to explain in more detail what is meant by "sp charge decompression". It is connected to the normalized atom approach (31) pointing back to the beginning of band structure calculations (31). For example, let us consider the transition from the Cu atom with its 3d10 4s1 configuration to bulk Cu. By the interaction in the bulk both the 3d10 and the 4sl level broaden into bands and overlap strongly. Furthermore, the center of gravity of the d band is shifted to smaller energies by more than 5 eV so that the bottom of the s band (which is actually an sp band due to the admixture of states) falls well below the bottom of the d band. The local charge distribution around the atom is also changed. The sp states which are spatially more extended than the d states, are somewhat compressed into the atomic unit cell in the bulk. Introducing now a surface means a "sp charge decompression" into the vacuum. Within this model the d band should move back to higher energies as it is observed for the Cu ML here (30). It is interesting to note that a quite similar result has been found for Cu on different surfaces o f Al, which belongs also to the group of sp-metal substrates. Di Castro and Polzonetti (32) have found a ML emission peaked at 4.2 eV, which shifts to 2 eV for thicker layers. They measured on polycrystalline A1 films. From their Auger intensities as function of thickness they deduced some interdiffusion between A1 and Cu for the first layer. An ARUPS investigation for Cu on Al(111) was performed by Barnes et al. (33). From their Auger intensities versus thickness curves they concluded that

INITIAL

ENERGY

EiieV)

'

Fiq. 12: ARUP spectra at normal emission from Cu films grown on Al(111) at Ts = 300 K. Also shown is emission from a semi-infinite Cu(ll1) single crystal. Incident radiation: He1 (ha= 21.22 eV). From (33).

e s s e n t i a l l y l a y e r growth takes place below 300

K besides some i n t e r f a c i a l mix-

i n g i n t h e ML. Fig. 12 e x h i b i t s t h e main r e s u l t o f Barnes e t a l . (33). There i s a whole t r a n s i t i o n r e g i o n from the ML t o about 10 ML w i t h i n which t h e Cu 3d emission i s s h i f t e d towards EF by about 1.5 eV. The C u ( l l 1 ) 3d band has been developed o n l y a t about 10 ML. The broad ML and sharp 10 ML-ARUP spectra a r e i n good agreement w i t h t h e long-range disorder f o r t h e ML and a weak C u ( l l 1 ) LEED p a t t e r n f o r 10 ML. Finally,

i t i s i n t e r e s t i n g t o note t h a t these r e s u l t s are i n very good

agreement w i t h o l d e r angle-integrated XPS measurements (34). 3.2 S i l v e r Among t h e noble metals, Ag i s most i n t e n s i v e l y studied and t h e Ag ML i s best defined w i t h respect t o i n t e r d i f f u s i o n and a l l o y formation. Tobin e t a l . (35,36)

i n v e s t i g a t e d Ag on Cu(OO1). Ag forms a hcp ML g i v i n g r i s e t o a ~ ( 1 0 x 2 )

s t r u c t u r e as i n d i c a t e d i n f i g . 13. Normally two domains develop so t h a t t h e FR and % d i r e c t i o n s

cannot be separated i n t h e (110) plane.

For one surface t h e

authors c l a i m t h a t they have been able t o prepare a s i n g l e domain Ag adlayer (36).

I n fig.

14 some normal emission spectra are shown f o r C u ( l l l ) ,

Ag(ll1)

and Ag overlayers o f d i f f e r e n t thickness. The BE are given i n t h e 4 t o 5 eV interval for different

photon energies. For normal emission

kll= 0 and kl

is

REAL SPACE

RECIPROCAL SPACE

F i q . 13: Depiction o f one o f t h e two o r thogonal domains o f c(10x2)Ag/Cu(001) in r e a l space. The Ag atoms are shown as f i l l e d c i r c l e s and t h e Cu(OO1) surface l a t t i c e as squares. The a c t u a l r e g i s t r y w i t h t h e subs t r a t e i s unknown. The s u r f a c e - B r i l l o u i n zones of Cu(OO1) and both u n d i s t o r t e d hexagonal Ag domains as w e l l as t h e paths across each zone taken when r o t a t i n g o f f normal i n t h e Cu(OO1) planes (110) and (100) are shown. Only t h e domain associated w i t h (c) was observed w i t h LEED. From (35).

388 s-pol

23-eV Photon energy

He I

m

,

r

.-VI

L

o(

L

U C

-e Q

h .In f

m

c

E -

Binding energy (eV)

I l l 10

5

I

I

,

,

I

I 1

EF

Binding energy (eV)

Fiq. 14 (left): Mapping of the binding energies (BF) o f the silver features vs photon energy for (a) Ag(lll), (b) 5 ML, (c) 4 ML, and (d) 2 ML o f c(lOxZ)Ag/ Cu(OO1). The band i i i states (BF > 4.5 eV) at 2 ML become bands 4, 5, and 6 in Ag(ll1). The weak leading shoulder in Ag(ll1) at BF near 4.2 eV is shown with open circles and i s due to band iv. (e) Normal-emission spectra collected with hw = 23 eV for curve A Ag(lll), curve B 5 ML of c(10x2)Ag/Cu(001), curve C 4 ML, curve 0 2 ML, and curve E clean Cu(OO1). From (35). F i q . 15 (riqht): ARUP spectra taken of clean Cu(OO1) (lower member o f each pair) and 1) ML of c(lOxZ)Ag/Cu(001) (upper member of each pair), with s-polarized He1 radiation. The angle listed is the polar emission angle 0 versus the surface normal. Each spectrum is normalized to the largest Cu d-band peak. From

(36).

389

Fiq. 16: 20 band structure for Ag on Cu(100) observed at near-monolayer coverages. The triangles at BF near 4.8 eV at ?; are the averaged values of the spin-orbit split peaks observed with s- and p-polarized He1 and NeI radiation.

I

Y

10

08

06

k II

02

02

-6

I

06

04

08

I

-4

I

I

I

-2

10

I Z Z 14

k II

I

-8

a4

L 6 0 I

,

EF

INITIAL ENERGY(&)

Fiq. 17 (left): ARUP spectra from 1.2 A (1/2 monolayer) of Ag on Ni(001) taken with a photon energy ho= 22 eV and kl along Ni[llO]. The polar emission angles 0 are indicated. Features which are due to the presence of the Ag overlayer are marked with arrows. The inset shows a schematic drawing of the Brillouin zone of monolayer Ag(ll1). From (37). Fiq. 18 (riqhtl: Comparison of the 20 band structure a 0.5 ML Ag on Niflll) (data indicated by crosses: energy scale on the left-hand side) to the 2D dispersion relations from a near-monolayer coverage o f Ag on Cu(OO1) (data indicated by squares; energy scale on the right-hand side). In both cases k, is along the direction o f the Ag overlayer. The smooth solid and dashed curves are proposed band dispersions of bands 1-6. From (37).

390

varied with ho. It is necessary for a 2D band structure that the dispersion relation be independent of kl. Fig. 14 indicates that this requirement is nicely fulfilled for the 2 ML features between 4 and 5 eV. Fig. 15 presents some ML spectra for s-light from a He1 laboratory light source. The ML spectra are compared with the clean Cu(OO1) spectra indicating a fairly large overlap between Ag and Cu states down to an energy of 5 eV. Thus, this system certainly demanded some care to unambiguously figure out the 2D band structure of the Ag ML as shown in fig. 16. The investigations of this kind seem to be at the very beginning, where trends have to be figured out first. Therefore, the study of Shapiro e t al. (37) is very useful, in which they measured the Ag films on Ni(ll1) and Ni(100) substrates. Surprisingly, they found the 2D band structure to be practically identical for both substrates. With respect to the results for Ag on Cu(100) note the normal emission spectrum of fig. 17, which exhibits only one strong peak for both substrates. Fig. 17 demonstrates also that Ni is better suited as substrate than Cu, since its 3d states are better separated from the Ag 4d adlayer states. Interestingly, Shapiro et al. have been able to demonstrate that the 20 band structures of Ag on Ni and Ag on Cu are very similar, if one admits a rigid shift in energy of only 0.32 eV to higher BE for Ag on Cu as shown in fig. 18.

Fiq. 19: Normal-emission ARUP spectra taken with a photon energy of 22 eV from Cu(ll1) covered by various thicknesses of Ag as indicated. From (38).

J

1.8

I

l

l

I

0.6

0.4

0.2

EF

Binding Energy (eV)

Besides the 20 band structure of the adlayer, the evolution of surface states is very important for an understanding o f the electronic structure o f thin metal films. This question was studied carefully for Ag on Cu(ll1) (38)

391

which grows e p i t a x i a l l y w i t h a 13 % l a t t i c e contraction. We w i l l comment on t h e very l a r g e amount o f t h i s c o n t r a c t i o n l a t e r . Fig. 19 e x h i b i t s the surface s t a t e a t t h e L-gap and i t s changes from C u ( l l 1 ) t o A g ( l l 1 ) . For the 0.5 ML f i l m two peaks can be seen, one from the bare C u ( l l 1 ) surface and one f o r t h e Ag ML. The continuous s h i f t o f the Ag surface s t a t e w i t h l a y e r thickness i s explained by t h e degree o f i t s l o c a l i z a t i o n . Two o t h e r substrates have been used t o support Ag f i l m s , namely Pd(100) and

P t . Supported by Pd(100) Ag forms a p ( l x 1 ) e p i t a x i a l adlayer i n t h e range between 1 and 10 ML (39). The ML spectrum e x h i b i t s one strong Ag peak near 4.5 eV (Fig. 20). One recognizes t h a t t h e bulk spectrum develops r a t h e r l a t e a t about 10 ML. Capehart e t a l . (40) have found a two-peak spectrum f o r Ag on Pd(100) a t the

7

point.

By comparing these data w i t h t h e i r c a l c u l a t i o n s they have been

a b l e t o d e r i v e t h e symmetry o f the peak, which i s a l ( = d3z2-r2) peak and e(= dxy,yz)

f o r the 4.6

f o r t h e 6 eV

eV peak. A s i m i l a r double peak i s found on

Pt(100) and P t ( l l 1 ) (41).

F i q . 20: ARUP spectra measured normal t o t h e surface o f an Ag/Pd(100) overlayer system a t v a r i o u s coverages o f Ag. Photon beam o f 21.22 eV was i n c i d e n t a t t h e angle o f 15" r e l a t i v e t o t h e surface normal i n t h e (001) plane. From (39).

-800

-600

-LW

-200

J

-OW

E, leVi

Now we t u r n again t o t h e sp-metal substrates.

I n f i g . 21 we show the A1 XPS

r e s u l t o f Egelhoff Jr. (42) f o r Ag on Al(100). For t h e sub ML species the Ag 4d emission i s centered a t about 6.4 eV. These measurements agree very n i c e l y w i t h more r e c e n t r e s u l t s f o r Ag on A l ( 1 1 1 )

from our l a b o r a t o r y (19).

From c a r e f u l

AES a n a l y s i s we found SK growth mode w i t h a w e l l defined Ag ML. e x h i b i t s t h e t r a n s i t i o n from 0.8 ML t o bulk Ag(111),

evidenced by LEED. Between the ML, which i s pseudomorphic, Ag(ll1) f i l m a t

Fig.

22

the l a t t e r being f u r t h e r and t h e e p i t a x i a l

O > 10 ML t h e r e i s a broad t r a n s i t i o n r e g i o n w i t h o u t any LEED

392

Binding Energy, eV Fiq. 21: Valence band XPS spectra f o r Ag on Al(100) a t t h e i n d i c a t e d Ag t h i c k nesses. From (42).

F i q . 22: ARUP spectra f o r Ag l a y e r s o f d i f f e r e n t thickness on an A l ( 1 1 1 ) subs t r a t e . The spectra were taken a t normal emission. Angle o f incidence o f t h e l i g h t (ho=21.2 eV) was 45" w i t h respect t o t h e surface normal. From (19).

ENERGY BELOW EF(eV)

393

i

I ii

;

@ I0

D

HF

:

212 ev

uI

I

: 6 a e~

r

-

1.5

1 ML A g on A l ( 1 l l )

0.5

0

4

1

M

05 k,, [k’l

10

1.5

Fiq. 23: 20 band s t r u c t u r e o f an Ag ML on Al(111). From (19).

p a t t e r n and w i t h a broad PE spectrum as shown i n f i g . 22. The ML s t a t e e x h i b i t s r a t h e r sharp, d i s p e r s i n g peaks. From t h e whole s e t o f d a t a a 20 band s t r u c t u r e was derived as shown i n f i g . 23. The 20 Ag band s t r u c t u r e found f o r A l ( 1 1 1 )

is

much s i m p l e r than those found f o r t h e Cu and N i substrates as shown above.

3.3 G o l d The e l e c t r o n i c s t r u c t u r e o f Au f i l m s i s l e s s f r e q u e n t l y studied than t h a t o f Cu or Ag f i l m s . As d-metal substrates o n l y Pd (43), P t (41), (45-48)

have been used. The data from Au on P d ( l l 1 )

W (44) and Cu

(43) are measured i n an

angle-integrated mode and are n o t backed by an a d d i t i o n a l AES o r LEE0 analysis. The ML i s c h a r a c t e r i z e d by peaks a t 1.5,

3.1,

4.3,

and 5.9. From (43) one r e c -

ognizes t h e strong overlap between the Pd substrate- and Au o v e r l a y e r - s t a t e s so t h a t o n l y t h e peak a t 5.9 eV i s w i t h o u t doubt mainly Au 5d derived. The s t r o n g i n t e r a c t i o n between Au and Pd manifests i t s e l f a l s o by Au d i f f u s i o n i n t o Pd, which can be achieved by a 30 s anneal t o 670 K. The r e s u l t i s a s h i f t o f t h e Au 5d emission t o smaller BE by several t e n t h s o f an eV. From t h i s change t h e authors (43) assume i m p l i c i t l y t h a t t h i s d i f f u s i o n s t a r t s o n l y a t e l e v a t e d temp e r a t u r e s and n o t already a t 300 K. The spectra f o r A u / P t ( l l l )

(41) taken i n an angle-integrated mode e x h i b i t

f e a t u r e s a t 1, 3, 4 and 5.8 eV BE f o r t h e Au ML. I t i s i n t e r e s t i n g t o note t h a t t h e r e s u l t s f o r Pt(100) and Pt(997) substrates g i v e n by t h e same authors look v e r y much t h e same as f o r P t ( l l 1 ) .

On W(110)

Au forms an ordered p ( l x 1 )

394

overlayer which is compressed by 3.4 %. This compression is released at a thickness of 3-4 ML, when the LEED pattern vanishes. By XPS a rather broad twopeak structure is found for the ML with peaks at about 4.0 and 6.2 eV (44). In this work also the Au 4f levels have been studied carefully as shown in fig. 24. For the ML the 4f BE is shifted by 0.31 eV to higher energies, i.e. opposite t o the surface core-level shift. The reason for this shift is not clear at the moment. It may be due to a strong hybridization o f the Au and W valence orbitals or - with respect to bulk Au - to a reduced shielding by the 2D Au 6s band.

Fiq. 24: Gold 4f spectra for various coverages of Au on W(100). (a) 0.8 ML; (b) 2.4 ML; (c) thick Au layer. From (44).

BlNOlNG ENERGY teV1

We turn now to the Au/Cu(001) system, which has been studied very recently different groups (45-48). The investigation of this pair goes back to the pioneering work of Palmberg and Rhodin (1) who interpreted their ~(2x2)structure found at room temperature as a Cu Au surface alloy. They also showed by LEED that the transition into the ~(2x2) structure proceeds at temperatures above 250 K. Very recently Graham (45) found by low energy ion scattering that the Cu(lOO)-c(2~2) Au surface is very similar to the Cu3Au(100) surface. Wang et al. (46) came to the same conclusion by a LEEO analysis. In fig. 25 (45) some spectra are compared for Cu(lOO), Cu(lOO)-c(2~2)Au, and Cu3Au(100). For He1 and O = 0” (normal emission) the intensity of the Au 5d states is weak compared to the Cu 3d substrate emission. Furthermore, the similarity between the Cu(lOO)-c(2x2)Au and the Cu3Au emission is obvious. At the r point the B E ’ S are 5.2 and 6.3 eV. These states exhibit a weak dispersion of by

-

395

I

I

I

I

I

I

I

I

He1

"Cu 1100l-c~ZX21Au'

i'i W

-

t

cu11001

-

I I I I I I I I I

8

4

0

BINDING ENERGY ( e V )

8 4 0 BINDING ENERGY (eV)

Fiq. 25: ARUP spectra o f Cu3Au(100), "Cu(lOO)-c(2xZ)Au" and Cu(100). The emission i s normal t o the surface ( l e f t ) and off-normal i n the (010) plane ( r i g h t ) From (45).

about 0.4 eV. A t t h e M p o i n t a surface s t a t e i s found a t 1.6 eV which i s known t o l i e a t 1.8 eV f o r Cu(100). The greater width o f the Au 5d bands, i.e. extension down t o g r e a t e r BE,

their

i s i n agreement w i t h r e s u l t s from o t h e r authors

(46) f o r photon energies between 24 and 40 eV. For the same system Knapp e t a l . (47) have v a r i e d the thickness o f t h e Au layer. They have found an ordered ML a t 220 K e x h i b i t i n g a ~ ( 1 2 x 2 ) LEE0 p a t t e r n i n analogy t o t h e c(1Ox2) p a t t e r n f o r Ag on Cu(100).

As shown i n f i g .

have analyzed t h e B E ' S as f u n c t i o n o f Rw. Obviously,

26 they

the sample temperature

was 300 K throughout these measurements so t h a t a l l t h i c k e r l a y e r s grow on t o p o f t h e ~ ( 2 x 2 ) reconstructed one. V a r i a t i o n o f the photon energy is very h e l p f u l i n separating 20 from 30 bands. For normal emission the 20 d i s p e r s i o n is e l i m i nated, since t h e momentum i s zero. Thus, any v a r i a t i o n o f

BE i n d i c a t e s emission from a bulk (30) sample. Therefore, f o r 30 bands a d i s p e r s i o n w i t h hw i s expected and can be c l e a r l y seen f o r Cu(100) (OML) and A u ( l l 1 ) i n f i g . 26. For 2 ML, a s t a t e a t 4.7 eV evolves, which i s 2D i n character. The s t a t e a t 6.5 eV i s 20 f o r a 1 ML coverage b u t not f o r 2 o r 3 ML. According t o t h e authors t h i s i s due t o a change i n mean f r e e path o f t h e outgoing photoelectrons. It i s i n t e r e s t i n g t o note t h a t the bulk A u ( l l 1 ) photoelectron spectra are seen o n l y f o r thicknesses 2 12 ML.

396

-% 5-

. . . . . . . . ... . + ......... ................................

1 .-

L. ..........?...........L...........

I '

lm[.

..... . .. ..*...... .. .... ....:

2.01..

8 -

w

.

..

2MLiML;:.

*

3M_t it . 3

*.

6Mcj

1 2W 12w[

6 Mc'

i

Ad11111 J

J

. ................... .......... "’.I ......... .: . ....... ...... i ..... ........ ...... '. i ......:" . .. . . . . ........ ._ j . . . . . ..

.(

4.0-

a.

6.0-

.

I

1..

1

PHOTON D E W Y (eVJ

Fiq. 26: P l o t o f Au/Cu(100) BE r e f e r r e d t o EF versus photon energy f o r 0, 1, 2, 3, 6 and 12 ML coverages. From (47).

I n a recent paper t h e same group (48)

has measured t h e unreconstructed

Au ML on a Cu(100) surface e x h i b i t i n g t h e ~ ( 1 4 x 2 ) s t r u c t u r e below 220 K. As a r e s u l t o f t h e 2D band mapping three bands are observed a t 6.3 eV

(7)

(2).

and 3.5 eV

Furthermore,

(T), 4.7 eV

the Au 4 f core l e v e l s s h i f t by 0.33

higher BE during the t r a n s i t i o n from p(lx1)

eV t o

a t 190 K t o ~ ( 2 x 2 ) a t 300 K

observed f o r the 0.5 ML coverage. I

1

I

I

1 1 - 1

I

1

I

.. . .,-.. ,

.. , .. .

.

.

. . .. ...... . . .._..-.. . ..... : . .... . . . . . ... . ...-. . . .. -. ,..._-.._ ..,.,........... .__.... . . -.r.:

F i q . 27: ARUP spectra f o r Au l a y e r s on A l ( 1 1 1 ) . The spectra are taken a t normal emission f o r W o = 21.2 eV. (a) 1 ML o f A12Au on top o f Al(111); (b) 1 ML A12Au

i

I

p l u s 1 ML Au; (c) intermediate s t a t e ; (d) bulk Au thickness l a r g e r than 10 ML. From

(49).

.......... I

I

I

I

I

5

I

I

...-. I

1

(a1 L OPE,

BINDING ENERGY lev)

397

Now we t u r n t o the second group o f substrates, the sp metals. Egelhoff has found q u i t e d i f f e r e n t spectra f o r Au adlayers on Al(100) (34). The sub ML emiss i o n i s centered a t 7 eV w i t h an FWHM o f 4 eV i n p a r t due t o t h e reduced energy r e s o l u t i o n o f XPS. Recently, we have found several d i f f e r e n t Au 5d spectra on a

A1 (111) surface depending on coverage and evaporation c o n d i t i o n s as i n d i c a t e d i n f i g . 27 (49). The LEED p a t t e r n i n combination w i t h r e f l e c t i o n e l e c t r o n mic-

r o s c o p i c studies f o r the bulk Al2Au a l l o y from the l i t e r a t u r e i n d i c a t e d t h a t i n the ML an A12Au(lIO) l a y e r was formed. The r e s u l t o f the ARUPS study o f f i g . 27 i s t h a t t h e Au 5d l e v e l s s h i f t t o smaller BE w i t h an increasing l a y e r t h i c k ness,

i.e.

an increasing Au 5d overlap.

Thus,

s t a t e (b) i n f i g .

understood as an Au ML on top o f the f i r s t A12Au a l l o y layer.

27 can be

T h i s geometry

leads t o a Au 5d overlap s i m i l a r t o t h a t i n a AuAl a l l o y . State (c) i s i n t e r mediate between the Au ML and bulk Au, as was found i n a s i m i l a r k i n d o f Ag on

Al(111)

(19).

F i n a l l y , a t about 10 ML t h e bulk A u ( l l 1 ) spectrum i s measured.

Q u i t e obviously, t h e l a t t i c e mismatch between A12Au and Au prevents an ordered phase i n t h e t r a n s i t i o n region.

3.4 Conclusions about noble metals We have noted already t h a t o f a l l metals the noble metals have been most e x t e n s i v e l y studied as t h i n m e t a l l i c f i l m s . Therefore, one can t r y t o evaluate some general conclusions. For t h i s purpose we have summarized the BEF values i n t a b l e s 1 t o 3.

For the angle-resolved mode the values a t

are taken. We are

t a k i n g i n t o account mainly the experimental r e s u l t s here and comment on theor e t i c a l r e s u l t s i n t h e summary below. As we have already pointed out, there are two groups o f substrates, t h e dand sp-metal substrates, which induce a q u i t e d i f f e r e n t behavior o f t h e noblemetal adlayer.

For the sp-metal

substrates the BEF are s h i f t e d g e n e r a l l y t o

higher values. S o , t a k i n g t h e most intense peak a t 2.7

eV t o 4.2

7.0 eV f o r Au.

eV f o r Cu, from 4.6 eV t o 5.7

?, these

mean s h i f t s a r e from

eV f o r Ag,

and from 6.2

eV t o

I t seems t h a t t h e i n t e r a c t i o n o f t h e noble metals w i t h d-metal

substrates i s stronger than w i t h sp-metal substrates. For most o f t h e Ag and Au adlayers t h e r e i s a c o n t r a c t i o n o f the ML w i t h respect t o the b u l k i n t e r a t o m i c distances. The reason f o r t h i s c o n t r a c t i o n may be two-fold.

(a) I t may be i n -

duced by a tendency t o b i n d the adatom t o s p e c i f i c substrate-surface s i t e s . (b)

It may a l s o w e l l be t h a t a metal ML tends t o develop i t s own next-neighbor d i s tance, which i s smaller than i n the bulk. This can be understood by the reasona b l e i d e a t h a t t h e bonding t o neighbor atoms i n t h e l a y e r s above and below t h e ML weakens t h e bond strength w i t h i n the ML. We have found an example which exh i b i t s such behavior. Ag grows pseudomorphically on an A l ( 1 1 1 )

surface,

until

a t about t h e complete ML coverage i t becomes f u r t h e r contracted from about 1 % i n t h e pseudomorphic phase t o 5.6 % i n t h e compressed phase (5O).This

tendency

398

o f the Ag ML t o c o n t r a c t by about 6 % may a l s o e x p l a i n the unusually l a r g e c o n t r a c t i o n o f 13 % f o r Ag on C u ( l l 1 ) which was reported above. There are only few examples f o r a compression i n a r e l a t i v e l y weakly bound ML (51),

which can

be due t o the f a c t t h a t most experimental examples are f o r d-metal substrates.

It may be i n t e r e s t i n g t o note t h a t by a recent t o t a l energy c a l c u l a t i o n a l a t -

an unsupported A1 l a y e r (52). I n an experiment one i s n o t able t o work w i t h an unsupported ML. Therefore, a d e l i c a t e t i c e c o n t r a c t i o n o f 7 % was found f o r energetic balance has t o be sustained.

I n order t o prepare a ML t h e r e must be a

l a r g e enough adatom-substrate i n t e r a c t i o n t o prevent 3D c l u s t e r growth; b u t n o t

so l a r g e as t o prevent t h e overlayer from contracting. Coming back t o t h e d i f f e r e n c e i n BEF on d- and sp-metal substrates, we propose t h a t t h i s m a y be i n p a r t due t o the l a r g e r c o n t r a c t i o n o f t h e adlayer on a d-metal

substrate.

This c o n t r a c t i o n counteracts the decompression o f t h e sp

electrons, which i s a general property o f the monolayer and which t o Abbati e t a l .

(30)

-

-

according

induces the downward s h i f t o f t h e BE. This counteract-

i n g compression seems t o be so e f f e c t i v e t h a t t h e observed 2D band widths are, s u r p r i s i n g l y , as l a r g e as the 30 ones, as noticed by many authors. A t t h e moment, we have t o admit t h a t i t i s n o t clear, t o which e x t e n t t h i s explanation i s c o r r e c t o r whether other mechanisms are more important.

One c e r t a i n l y has

a l s o t o consider the d i r e c t adatom d-level t o substrate d-level case o f u n f i l l e d d bands

-

interaction I n

which are n o t considered i n t h i s s e c t i o n

-

t e r a c t i o n can be so strong t h a t t h e adlayer i s - also e l e c t r o n i c a l l y

t h i s in-

-

just a

c o n t i n u a t i o n o f the bulk substrate and cannot be discussed as a separate 2D i d e n t i t y . On the other hand, f o r the Cu, Ag, Au case one would expect a decrease o f

the

adatom-substrate

interaction with

the

increasing

separation

between EF and t h e d band from Cu t o Au. For t h e cases discussed here such a tendency cannot be deduced. I n t h e noble-metal case studies we have presented many examples

-

which may

be somewhat confusing a t f i r s t . But the reason i s q u i t e simple. I t i s j u s t n o t p o s s i b l e a t the moment t o c l a s s i f y a s i n g l e experimental r e s u l t as more o r l e s s representative. Furthermore, i t i s n o t so simple t h a t t h e 20 band s t r u c t u r e i s completely d i f f e r e n t between d i f f e r e n t substrates. There i s a n i c e example presented i n f i g . 18 showing t h a t t h e Ag

on Cu(100) and Ag on Ni(100) e x h i b i t the

same 2D band s t r u c t u r e t a k i n g i n t o account o n l y a small energy s h i f t o f 0.3 eV. There are s i m i l a r i t i e s between t h e 2D band s t r u c t u r e s o f a noble metal on d i f f e r e n t substrates, and we have t r i e d t o f i g u r e them out. F i n a l l y , we want t o s t r e s s t h e f o l l o w i n g important observation which p a r t l y explains t h e complicated spectra. We b e l i e v e t h a t a l a r g e p a r t o f the observed peaks o r bands are i n t e r f a c e s t a t e s having a l a r g e substrate d character. This p o i n t was made by Houston e t a l . a t all.

(25) who d i d n o t e x t r a c t a 20 band s t r u c t u r e

It seems t o us t h a t t h i s p o i n t becomes r a t h e r evident f o r t h e best

399

documented Ag case. I f one compares the 2D band s t r u c t u r e s f o r Ag on N i and Cu

23, one i s l e d t o the conclusion t h a t t h e

i n f i g . 18 and f o r Ag on A1 i n f i g .

two h i g h - l y i n g bands between 5.7 and 7.0 eV are t h e pure Ag bands, whereas t h e o t h e r l o w - l y i n g bands on Cu and N i may be l a r g e l y substrate-derived.

We b e l i e v e

t h a t t h i s i d e a should be used as a guide i n f u t u r e work i n order t o shed l i g h t on t h i s r a t h e r complicated phenomenon. Our many examples i n d i c a t e f i n a l l y t h a t one should n o t i n v e s t i g a t e systems w i t h a complete overlap i n energy o f t h e adlayer and substrate d-states.

TABLE

1

Binding energies r e f e r r e d t o EF o f Cu 3d e l e c t r o n s i n ML f i l m s o f Cu on d i f f e r e n t substrates.

Angle-integrated ( A I )

and angle-resolved

(AR)

(at

7;) modes

are indicated.

Substrate

Ref.

Mode

Ag,polyc.

12

Al

Ag(100) Ag (100)

(21 22

IAR AR

Ru (1000)

26

AR

Ru (1000)

27

Al

hw (eV)

BEF(eW)

8.6

1

30 21.2

2.5

I

2.66 2.75

3.33 3.42

30

2.7

3.5

21.2

2.75

2.47

I

Pt(ll1)

29

Al

Zn (1 000)

30

Al

21.2

3.8

Al, polyc.

31

A1

21.2

4.2

AI (1 11)

33

AR

21.2

4.15

Al (100)

34

At

150

1300

2.65

3.5

4.5

400

TABLE 2

Binding energies referred to EF of Ag 4d electrons in ML films of Ag on different substrates. Angle-integrated (AI) and angle-resolved (AR) (at 7) modes are indicated.

TABLE 3

Binding energies referred to EF of Au 5d electrons in ML films of Au on different substrates. Angle-integrated (AI) and angle-resolved (AR) (at 7) modes are indicated. Substrate

Pd (1 11)

1R (111)

hw lev)

Ref. Mode 43

AI

141 I A I

w (1 10)

4.4

Al

c u (1 00) c(2x2)

45

AR

BEF (eV)

40.8

I

21.2

1

1.5

3.1

4.3

5.9

1.0

3.0

4.0

5.8

4.0

6.2

1550 21.2

5.2

6.3

4.8

6.5

4.7

6.3

I

~

c u (100) c( 14x2)

48

AR

A1 (100)

34

Al

IA12Au

49

AR

21.2

lAuML

49

AR

21.2

IAuML(l2OK) 49

AR

21.2

3.5 (at 2) 1300

7

Al (1 11)

6.0 4.55

6.4

7.9

4.9

7.0

5.75

7.5

~

401

3d TRANSITION METALS Thin films of ferromagnetic materials epitaxially grown on non-magnetic substrates have been of interest for a long time (53-56). The electronic properties of such films are of great importance, although naturally the main impact is on in-situ studies of magnetization and spin-resolved ARUP spectra which are reported in another chapter of this monograph. Here we discuss the electronic properties with respect to the conduction bands of the non-magnetic thin films. Therefore we report briefly first results for Ni, Co, Fe and Mn. It seems to us that there will be great progress especially in this field in the next years. Thompson and Erskine (57) have studied Ni on Cu(OO1). F o r this system perfect epitaxy is known within the first few layers, which is not surprising in view of the small lattice mismatch of 3.2 %, by which amount the Ni NN distance is enlarged on Cu. The ARUP spectra of fig. 28 show Cu-substrate-derived peaks between -2 and -5 eV and very sharp Ni peaks between EF and -2 eV. In contrast to the Cu features the Ni features do not depend on hoproving the essentially 20 character of these features. The 2D band structure was evaluated as shown in fig. 29 both for even and odd symmetric states by appropriately chosen directions of the outgoing electrons and the vector potential of the incoming light. The magnetic exchange splitting is resolved at the M point for even symmetry as shown in fig. 29. Co/Cu(OOl) is studied rather extensively. Co grows pseudomorphically with a 2.3 % expanded lattice (58-61). For this system LEED intensity analysis is performed (60) for one ML and 8 ML films. For the monolayer film the interlayer spacings between the Co layer and the first Cu layer as well as between the first and second Cu layers are contracted by 6 % compared to bulk Cu. Co adsorbs in the fcc Cu site. This investigation yields the very reasonable result that the Co lattice is vertically contracted but it is laterally expanded. These findings show that pseudomorphy means only the same lateral lattice size and position, as it does in most cases, since the vertical distances are mostly unknown. The ARUP spectra for the ML Co/Cu(OOl) (59) system are not as sharp as those for Ni/Cu (57). Fig. 30 presents two examples. One reason for the rather broad features may lie in the large magnetic exchange splitting of 0.80 2 0.15 eV, which makes it more difficult to assign the related bands. Nevertheless, Miranda et al. (59) have been able to deduce a first 20 band structure for this system. Following their discussion the bands are slightly shifted to higher BE indicating a larger d-band filling. Continuing the path through the 3d transition metals from right to left in the periodic table we arrive at Fe. In principle it is not evident whether ARUP spectra can be measured to a better solution o r not for 3d metals. The magnetic 4

402

-7

-6

-5 -4 -3 -2 -1 BINDING E NERGY(eV)

E,

Fiq. 28 (left): ARUP spectra for a p(lx1) Ni film on Cu(100) along the Tfi direction of the 2D surface Brillouin zone. Features below -2 eV belong to the Cu substrate 3d states. From (57). Fiq. 29 (riqht): Dispersion of 20 energy bands for the p(lx1) Ni overlayer on Cu(100) along -i'x and %.Upper panel, even-symmetry states; lower panel, odd-symmetry states. From (57).

Fiq. 30: ARUP spectra taken at normal emission for: (a) 0.3 and (b) 1.2 f 0.2 monolayers of cobalt on Cu(100). The continuous line represents the fit of the experimental data at monolayer completion with the following contributions: Two pairs of Lorentzians for the exchange-split bands o f cobalt (dashed lines), the s-p band of Cu (dashed-dotted line) and a background of secondary electrons. Arrows indicate spin up and spin down assignment. From (59).

403

exchange s p l i t t i n g i s g r e a t l y increased up t o 2.6 eV f o r b u l k Fe. On t h e o t h e r hand,

t h e problem o f empty d states

enhanced.

Binns e t a l .

and l i f e t i m e broadening may even be

(62) p o i n t t o the d i f f i c u l t y o f separating 5 c l o s e l y

spaced Fe 3d bands. Also instrumental r e s o l u t i o n plays an important r o l e here, i f one wants t o measure a t ho= 120 eV i n order t o suppress t h e 4d i n t e n s i t y

from Ag or Pd substrates

against the adlayer 3d i n t e n s i t y v i a t h e Cooper

m i n i mum. Binns e t a l .

present one normal emission spectrum from a f c c Fe ML on

Ag(001) taken a t a photon energy o f 120 eV which e x h i b i t s only weak wiggles r a t h e r than w e l l resolved peaks (62). Nevertheless,

i n order t o e x t r a c t i n f o r -

mation on t h e magnetic order i n the t h i n - l a y e r Fe f i l m s they measured the Fe 3s core l e v e l . As shown i n f i g . 31 they measured a m u l t i p l e t s p l i t t i n g

of 4.4

5

0.1 eV, which i s s i m i l a r t o bulk Fe i n d i c a t i n g a s i m i l a r l o c a l moment i n t h e Fe ML. Furthermore, they compared Fe/Ag(001)

(63) and Fe/Pd( 111). The overlayer-

s u b s t r a t e i n t e r a c t i o n should be very d i f f e r e n t i n t h e two systems, since i n t h e former case t h e Fe 3d s t a t e s overlap w i t h t h e Ag 5sp band, w h i l e i n the l a t t e r case they overlap w i t h the Pd 4d states.

I n agreement w i t h these ideas they

found a ferromagnetic Fe l a y e r on Ag(001) b u t a "dead" l a y e r on P d ( l l 1 ) .

l n l FelAgllOOl

hr I 160eV

....

.

I 8

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

*

. -... . .

. ..

-..- ..::. *

Fiq. 31 Fe 3s photoelectron spectrum from a Fe ML L, Ag(001) a f t e r s u b t r a c t i o n o f t h e Ag 4s peak. BE i s measured r e l a t i v e t o t h e main Fe 3s peak. From (62).

I

! l l 4 0 Relohve Binding Energy IeVI

More r e c e n t l y , some e f f o r t was d i r e c t e d t o t h e Fe/Cu(001) system (64, 65). For t h i s system a l s o two LEE0 i n t e n s i t y analyses have been performed (66, 67), b o t h i n d i c a t i n g t h a t Fe on Cu(OO1) grows pseudomorphically,

i.e.

s t r u c t u r e w i t h t h e Cu i n t e r l a y e r separation e x a c t l y w i t h i n ? 0.05

i n an f c c

A.

Using

ARUPS, O n e l l i o n e t a l . (65) have analyzed the Fe ML. Some spectra o f t h i s study

404

a r e shown i n f i g .

32, and the evaluated 20 band s t r u c t u r e i s shown i n f i g . 33.

With respect t o t h e r e s u l t s o f Binns e t a l . (62) one c e r t a i n l y has t o take t h i s as a f i r s t step only, since the Fe s t a t e w i l l extend below 2 eV and t h e r e f o r e overlap s t r o n g l y w i t h the Cu substrate states. Mn i s a very i n t e r e s t i n g 3d element, since i t s atomic c o n f i g u r a t i o n i s 3d5, and according t o Hund's r u l e s i t should have i t s f i v e spins aligned. There are some reasons t o associate a l a r g e magnetic moment o f Mn w i t h a l o o s e l y bound Mn atom. I t i s t h e squeezing o f the Mn atom i n the bulk which causes i t t o disobey Hund's r u l e s . So t h e question a r i s e s as t o what happens i n Mn adlayer on metall i c substrates. Up t o now, there have been only very f e w i n v e s t i g a t i o n s o f t h i s problem (68-70).

On Cu(OO1) the Mn growth goes through the f o l l o w i n g stages:

l a t t i c e gas and ~ ( 2 x 2 ) i n t h e submonoalyer regime and a disordered l a y e r growth above 1 ML (68). The ~ ( 2 x 2 ) i s believed t o be t h e @ = 0.5-coverage

s t r u c t u r e on

t o p o f the Cu l a t t i c e instead o f a Cu3Mn(100) surface a l l o y (68). weak s t r u c t u r e s are found i n UPS. For coverages 0.18 5 0 2 0.25 resonance i s found a t -1.3

Only very

a weak surface

eV discussed as a v i r t u a l bound s t a t e (71, 72). The

work f u n c t i o n decreases from about 4.8 t o 4.2 eV w i t h i n one ML. For Mn on Ru(001) a d 3 s t r u c t u r e i s found f o r coverages up t o 8 ML, which transforms t o a (1x1)

pseudomorphic one upon annealing.

ARUPS i n d i c a t e s how

marginal t h e Mn adsorbate UPS p a t t e r n is against a 4d substrate l i k e Ru (70).

So f a r no 2D band mapping has been performed. Instead, t h e Mn 4s l e v e l s p l i t t i n g was measured i n d i c a t i n g a l a r g e a t o m i c - l i k e magnetic moment i n t h e ML

(69)

-

5

PALLADIUM AND PLATINUM Pd has been even more f r e q u e n t l y studied than the noble metals Cu, Ag, Au.

Among d i f f e r e n t substrates N b ( l l 0 ) was used by El-Batanouny e t a l . several reasons.

(73-79) f o r

For the Pd/Nb(llO) system the hydrogen-uptake r a t e was found

t o increase r a p i d l y and roughly l i n e a r l y w i t h Pd coverages i n excess o f one ML, w h i l e i t i s n e g l i g i b l e f o r clean N b ( l l 0 ) and N b ( l l 0 ) w i t h up t o one ML coverage o f Pd (80).

The f i r s t Pd l a y e r adsorbs i n a commensurate (1x1) arrangement,

which w i l l be r e f e r r e d t o as Pd*(llO)

A

(74).

I n t h i s l a y e r t h e NN distance i s

A

f o r P d ( l l 1 ) . As t h e second and t h e next f e w successive

Pd l a y e r s are deposited,

LEED shows the development o f a beat p a t t e r n charac-

2.86

instead o f 2.75

t e r i s t i c o f an incommensurate overlayer w i t h an atomic arrangement presumably being t h a t o f Pd i n P d ( l l 1 ) l a y e r (74, 79). F i n a l l y , the P d ( l l 1 ) LEED p a t t e r n i s observed. There i s a simple advance o f the Nb substrate since a t h i n (25 pm) Nb f o i l can be r e c r y s t a l l i z e d by annealing under vacuum w i t h t h e f i n a l r e s u l t t h a t t h e surface c o n s i s t s o f (110) f a c e t s e x h i b i t i n g a f a i r LEED p a t t e r n . Fig.

34 presents a s e t o f ARUP spectra f o r increasing Pd coverages.

For

coverages g r e a t e r than the ML ( y > 7) a peak a t 0.7 eV evolves and the o v e r a l l

405

p (IX I ) MONOLAYER Fe/Cu(IOOl

EVEN SYMMETRY

r

B 150 1.00 050

x

o

a50

100

E, 050 I00 150

200

ODD SYMMETRY

-X

r

e 1.50

ioo am

o

050

100

E, 050 I00

I50 2 00 2ML 0

D

-7

-6

-5 -4 -3 -2 -I BINDING ENERGY (OW

..

IYL

CILCULITEO h"

16Ra.V

21.22,"

IML

- YIJORITY ---- MINORITY

2ML

-.-

-..-.

E,

Fiq. 32 ( l e f t ) : ARUP spectra f o r one- and two-layer p ( l x 1 ) Fe f i l m on Cu(100). Values o f kll correspond t o t h e TR d i r e c t i o n . From (65). Fiq. 33 ( r i q h t ) : 20 band s t r u c t u r e o f p(lx1)Fe on Cu(100). The two broad curves i n d i c a t e t h e regions o f binding energy and k, where a prominent s t r u c t u r e r e s u l t i n g from t h e Cu sp band i s observed. L i g h t s o l i d and dashed curves represent c a l c u l a t e d surface Fe bands having over 50 % surface character. Data are represented by empty (two-monolayer f i l m s ) and s o l i d (one-monolayer f i l m s ) c i r c l e s ( h a = 16.85 eV) and rectangles ( h a = 21.22 eV). From (65).

spectrum changes t o become more s i m i l a r t o a Pd(l11) spectrum. The authors (79) do n o t take t h i s as a l a r g e change, but t a k i n g spectra a t other photon energies,

e.g.

a t ha= 90 eV as shown i n f i g .

35, o r other emission angles,

the

change i s q u i t e dramatic. Thus, t h e r e i s a c l e a r c o r r e l a t i o n between t h e change i n hydrogen uptake as i n d i c a t e d by the i n s e t i n f i g .

35,

and t h e e l e c t r o n i c

s t r u c t u r e as i n d i c a t e d by t h e ARUP spectra. The work f u n c t i o n changes w i t h coverage o f Pd. It goes through a minimum a t about 1 ML and reaches a f i n a l value a t 3 ML (73). strongly.

Figs.

34 and 35 i n d i c a t e t h a t the Pd and Nb 4d s t a t e s overlap

I n order t o suppress the c o n t r i b u t i o n s from t h e substrate one can

choose h w s o t h a t one works i n the Cooper minimum. The s i z e o f t h i s e f f e c t can be recognized from f i g . 35.

406

Fiq. 34: ARUP spectra for normal emission from a Nb(ll0) surface for various coverages o f Pd. At the Pd coverage of parameter y = 7, 1 ML Pd is deposited. Photon energy is 21.2 eV. From (79).

Fig. 36 presents the 20 band structure of the Pd 4d states in the pseudomorphic Pd*(llO) layer (77). The Ei states (i = 1...4) are numbered by their index. The two-dimensional Brillouin zone is shown in Fig. 36. The (110) face of a bcc crystal has CzV symmetry, so at the zone center (and at N) the states can be classified as Xi, We note that s. d,?, and dx2-y2 belong to Z1, dxy belongs to 22, dYZIXZ belongs to Z3,4. Along I'-N the only symmetry is a vertical reflection plane, so E l and Z4 can mix, as can Z2 and Z3. Similarly, along r-H, Z1 and Z3 mix, as do C 2 and Z4. States along these lines can be classified by even or odd symmetry under reflection. In the isolated monolayer there i s an additional symmetry, reflection in the plane (z * -z), which prevents these mixings. This fact is important in explaining the difference between the single-layer and the multi-layer systems. The authors performed a self-consistent linear augmented plane-wave calculation on a five-layer Nb film with a Pd layer on each side of the film. The Pd features overlap Nb bands and are resonances rather than surface states. How-

407

.:- 3 -4

'\

ICI

1. -0

-0

-6

-4

-2

0-E.

ENERGY OF INITIAL STATE lev1

N

r

H

Fiq. 35 (left): Normal-emission spectra at hw = 90 eV: Curve A, a Pd(ll1) overlayer on Nb(ll0); curve B, a Pd*(llO) overlayer on Nb(ll0); and curve C, Nb(ll0). The insets schematically show the hydrogen-uptake curves, where the change in resistance (AR) of the Nb foil is plotted against time. Hydrogen uptake is measured by the change in the resistance of the Nb f o i l with hydrogen bulk concentration. From (75).

Fiq. 36 (riqht): Experimental dispersion of Pd-induced states on Nb(ll0). Also shown is the surface Brillouin zone. Solid lines are states which are even and dashed lines states which are odd under reflection. Symmetry labels are explained in the text. From (37). ever, the Pd ML states overlap mainly s-like Nb bands and the coupling is not strong, which leads to sharp resonances. Finally and most importantly, the authors (77) stress that the Pd 4d-derived states lie below E F as in a noble metal. Comparison with the ML calculation shows that the noble-metal confiquration i s a consequence of the interaction with Nb. They point out that the isolated layer does not have a noble-meta1 configuration, because the large s component on the lowest state at ’ J implies that EF must fall below the top of the d complex. The center of gravity of the d states drops by 2 eV as a result of charge rearrangement. This noblemetal character then is in accordance with the missing interaction with H2. This argument is analogous to the observation that Ni does and Cu does not interact with Hp. The noble-metal character o f the Pd*(llO) layer is also in accordance with the missing Fano-type profile for the Pd 4p core-level emission in this system (76).

408

Now we turn to the noble-metal substrates. For Cu(ll1) fig. 37 exhibits the coverage dependence for normal emission (81). First of all, one recognizes the strong overlap of adlayer Pd 4d and substrate Cu 3d states. For thickness of 2 2.3 ML the spectra look bulk-like. Actually, Pessa and Jylha observed strong dependences from kl even for a 2 ML film. From LEED and AES it is concluded that, up to 1 ML, Pd grows pseudomorphically with a misfit o f 8 %. For 0 > 1 the LEED pattern relaxes into the Pd(ll1) one, and the growth mode is FM (layer by layer). The work function goes through a minimum at 0.3 ML and then rises linearly to the bulk-like value at 2.5 ML. From fig. 37 one may realize that the leading peak at 1.3 eV is resonantly enhanced, similar t o the Pd/Nb case (73). The 2D band structure o f the ML is not deduced by Pessa and Jylha. For Pd/Cu(001) a ~(2x2)structure is observed (82). It i s not clear at the moment whether this is an eventually buckled Pd ML or a Cu3Pd(100) surface alloy. The Auger curves tend to indicate a Pd layer. The electronic state of the ML is noble-metallike, in accordance with a chemisorptive behavior for CO which lies between Cu(OO1) and Pd(001) (82). Pd on both Ag(001) and (111) surfaces was studied in detail in the group of C. Norris (83,84) by using ARUPS, AES, LEED and work function measurements. At 300 K Pd grows in the layer mode. Retention of the p(lx1) pattern in the ML region indicates pseudomorphic growth giving rise to a 5.1 % expansion in the epitaxial Pd layer with respect to the bulk Pd. An increased background and reduced sharpness of the diffraction spots between 3 and 8 ML indicate a relaxation of the overlayer to the bulk Pd.

Fiq. 37: ARUP spectra obtained normal to the (111) surface o f the Pd overlayer on Cu system for various coverages R (in units of monolayer). Structures ST and S denote a satellite line in the incident radiation (no=21.22 eV) and the Shockley respectively. surface state of Cu(lll), From (81).

-M

-LD -20 E, I N I T I A L ENERGY ( e V )

-60

409

Fig.

38 presents normal emission spectra as a f u n c t i o n o f coverage which

e x h i b i t several

i n t e r e s t i n g aspects.

The overlap i n energy between t h e 4d

s t a t e s o f Ag and Pd i s small, rendering t h i s system w e l l s u i t e d t o the study of the e l e c t r o n i c s t r u c t u r e o f the Pd overlayer. This i s f u r t h e r supported by t h e observation t h a t t h e substrate emission decreases r a t h e r smoothly,

indicating

t h a t (1) no major charge t r a n s f e r takes place which would weaken a s p e c i f i c (bonding) band, and (2) no a d d i t i o n a l surface vectors are a v a i l a b l e f o r a r e d i s t r i b u t i o n o f emission i n space due t o the pseudomorphic growth. A t the ML, w e l l defined features are observed which have been used f o r t h e

I

I

i

I

1

I

1

-0

1

I

I

Fiq. 38: Normal-emission photoe l e c t r o n spectra f o r d i f f e r e n t coverages 0 ( i n monolayers) o f Pd on Ag(100). h w = 21.2 eV. The i n set shows i n more d e t a i l s p e c t r a f o r 0 < 1.0 ML i n t h e energy r e gion occupied by t h e Pd 4d band. The weak f e a t u r e a t -3.2 eV i n t h e spectra f o r O < 0.1 ML i s a s a t e l l i t e of the s i l v e r peak at -5.06 eV e x c i t e d by the He1 5 emission l i n e . From (83).

L -I

.I

.,

r,

I

t

-6 -4 -1 EF Energy of inihalrtate leVl

20 band mapping (see f i g . 39). A s i m i l a r r e s u l t i s found f o r t h e (111) surface: the main d i f f e r e n c e l i e s i n a smaller band width.

The authors c l a i m agreement

w i t h the band c a l c u l a t i o n f o r the free-standing ML o f Noffke and F r i t z s c h e (85) which i s remarkable i n view o f the 5 % expanded Pd l a t t i c e a t t h e Ag(001) surface. Although i t i s n o t easy t o recognize from t h e i r data, Smith e t a l .

(83)

argue t h a t t h e i r ML has noble-metal character s i m i l a r t o t h a t found f o r Pd on Nb (77).

Again, t h e bulk spectra evolve a t r a t h e r l a r g e thicknesses. T h i s cor-

r e l a t e s w i t h t h e development o f the work f u n c t i o n f o r which a minimum i s observed a t t h e (001) surface.

For (111) no minimum i s found,

which c o r r e l a t e s

w i t h t h e model o f t h e authors t h a t a t (111) 20 c r y s t a l l i t e s develop from the very beginning, whereas a t (001) a frozen Pd l a t t i c e gas i s expected due t o a higher d i f f u s i o n b a r r i e r p a r a l l e l t o the surface plane. For Pd on A u ( l l 1 ) l a y e r growth i s found (86). The angle-integrated UP spect r a (86) are much l e s s informative than the ARUPS data o f Pd/Ag(001) (83). Also angle-integrated

spectra from Pd/Ta( IIO), which was prepared by r e c r y s t a l -

l i z a t i o n o f Ta f o i l ,

i n d i c a t e the noble-metal

character o f the Pd ML (87).

4 10

Fiq. 39: The experimental 20 band structure (circles) for the Pd monolayer on silver (100). Open circles denote weak features. The full curves are the calculated energy bands of an isolated palladium (100) monolayer (85). From (83).

First results of Graham (88) for Pd on W(110) and (100) indicate similarities to the case o f Pd on Nb(ll0) (77). Finally, we turn to an s p substrate. Fig. 40 shows the normal emission spectrum for 0.7 ML of Pd on Al(111) (19). This result shows, better than any o f the d-metal substrate results discussed above, that the Pd ML has noblemetal character. This means that the atomic 4d10 5so configuration has not changed into the 4d9-6 550-4 configuration of bulk Pd; instead, a more atomiclike 4dlO-x 5sX (with x small) configuration is retained in the ML state. In all condensed states there is certainly also some admixture o f 5p states not noted in the formula above (87). From AES results, SK growth mode was concluded at 300 K (89). The 4d density of states develops as shown in fig. 41 over a rather long transition region up to about 10 ML. The center of gravity is shifted to EF by about 2 eV before the Pd 4d emission touches EF and the anticipated 4d + 5s redistribution can take place. At the same coverage empty 4d states evolve as shown in fig. 42 (90). It is interesting t o note that the work function changes (fig. 43) quite similarly to the case Pd/Ag(001). It seems that the development of the bulk work function and band structure are highly correlated. The development o f the 30 Pd band structure is connected with the 4d into 5s redistribution. This may explain the work function change also, since the 5s states leak considerably into the space i n front of the surface, while the localized d states do not, which may therefore increase the dipole barrier very effectively (89).

41 1

%

. . , . . . .

~

.

.. ,

0 7 ML Pd on AI(III)

. . . , 17

Fiq. 40: ARUP spectra f o r the clean Al(111) substrate and a 0.7 ML t h i c k Pd layer. The spectra are measured a t normal emission w i t h h w = 21.2 eV. From (19).

AI(II1). CLEAN

W/AI

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

-+ ..... vI

25 _..... ......................-.

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

3 .. m -3> ...... ..................1?............ ............... ............... t ................. 10 ......... : 5 ...... ............. .... ............... 0 ..... ............. ............................ vI

C..

..I.*

Pd/Alllll) hw = 9 5 eV .a.

,

-6

, . . 4 -2 E, BINDING ENERGY (eV)

I

0

I

,

2

.

,

l

,

L

l

l

,

l

6

F i q . 41 ( l e f t ) : Normal emission ARUP spectra from Pd f i l m s on A l ( 1 1 1 ) . The w i t h respect t o t h e e x c i t a t i o n was done w i t h He1 (21.22 eV) i n c i d e n t under 45 surface normal. A reference t a b l e f o r comparison o f the evaporation time, the Auger i n t e n s i t y r a t i o and t h e thickness i n ML i s given. From (89).

Fiq. 42 ( r i q h t ) : e l e c t r o n beam f o r Pd (330 eV) t o A1 1.0 i s e q u i v a l e n t From (90).

Inverse photoemission spectra a t normal incidence o f the t h e clean Al(111) surface and Pd deposits on t o p o f it. The (68 eV) Auger i n t e n s i t y r a t i o i s given as parameter. Pd/A1 = t o about 1 ML, Pd/Al = 5.9 = 5.4 ML, PD/Al = 25 = > 10 ML.

412

Fiq. 43: The work function of Pd deposited on Al(111) as a function of Pd evaporation time. The reference values from the literature are indicated by stars. The data have been taken simultaneously with the measurements in Fig. 41. From ( 89).

z u z U

7!!!LA L.0 0

EVAPORATION 10 20TIME bin)30

Interestingly, it was demonstrated recently by Rutherford backscattering that Pd interdiffuses into the bulk A1 at the Al(111) as well as at the Al(100) surfaces (130). The spectrum of fig. 40 is then more similar to a diluted alloy of Pd in Al. It is easy to verify that all other findings, i.e. the development of filled and empty bands and the chemisorption behavior, are well explainable under this assumption. We plan to recheck this for our own samples by inelastic ion scattering. Thin Pt films are studied only rarely. Recently it was found that Pt forms 2D commensurate islands on Nb(ll0) at sub ML coverage which become incommensurate prior to ML coverage (91). The Pt ML differs from Pt(ll1) which i s thought by the authors to be induced by the strong overlap between Pt and Nb and not by a change in electronic configuration, which is 5d9 6sl in the atom and not very much different in the metal. It is interesting to note that these authors therefore doubt the noble-metal interpretation for the Pd/Nb system. 6 sp METAL ADLAYERS 6.1 Hq, T1 and Pb The heavy sp metals Hg, T1 and Pb have some interesting properties and present their own problems in the evaluation of their electronic structure. Except for alkali and earth-alkaline metals, they are the only examples for this group o f metals. On the other hand, thin Pb films are well studied on many substrates, which is certainly due to the low melting point o f Pb which facilitates evaporation and the relatively large size of Pb which hinders interdiffusion for most systems. The problem in evaluating the electronic structure of a sp-metal adlayer is envisaged in fig. 44. For Pb on Ni(ll1) the SK growth mode has been found with several well ordered structures in the submonmolayer region (92). So, the full, densely packed ML is well characterized by AES as well as by photoemission from

413

-._...._.._.

........ ,...._..-'.'-

I

I

10

I

I

8

I

I

I

6

,

I

I L

I

I

I

2

,

10..ML ......

'-...

.......

,

I 0

clean

Fiq. 44: He1 (21.2 eV) excited photoelectron spectra for the bare and Pb-covered Ni(ll1) surface. The binding energy EgF is referred to the Fermi edge. The full curve is for bulk lead from (93). The spectra are taken in the angle-integrated mode using a double-pass cylindrical minor analyser (CMA). The surface normal is tilted by an angle of 42 ' with respect to the CMA axis so that the mormal emission spectra is fully transmitted. From (92).

-Ei/eV

the shallow Pd 5d core level. Nevertheless, the ML does not show up in photoemission from the Pb valence band. Only at coverages of about 10 ML i s a typical (93) Pb valence band spectrum observed. Pb possesses a 6s2 6p2 structure in the atom, which leads to a 6s-derived band around 6 eV and a 6p-derived band below EF. Also Sn layers on Ni(ll1) and Sn as well as Pb layers on Al(111) do not exhibit well resolvable valence-band peaks against the substrate emission (92). It seems that sp-derived adlayer states cannot be easily discriminated against substrate emission by ARUPS. There are only two exceptions concerning Tl/Cu(OOl) and Cs/Al(lll), which we will discuss below. In this section we will briefly report on few results known thus far for Hg, T1 and Pb. Recently, Hg adlayers have been studied by ARUPS on Ag(001) (94). Interestingly, the first two layers grow in fcc structure differently from the rhombohedral structure in the bulk. Nothing is seen from the s band expected for the Hg 6s2 configuration. Instead the shallow Hg 5d states are observed as shown in fig. 45. Besides the 5d3/2-5d5/2 spin-orbit split a third peak is observed which is marked by an arrow in fig. 45. This state is obviously not an interface state, since it is not weakened at higher Hg coverages. Instead, it is believed by the authors to be of itinerant character, i.e. a Hg 5d band is formed. It may be interesting to note that there is some similarity to the Au 5d emission found for the Au ML on Al(111). Furthermore, the Hg 5d states can be compared with Zn 3d at BE 9 to 11 eV below EF for which itinerant character was deduced from ARUPS for the bulk metal (95).

414

Fiq. 45: Normal emission ARUP spectra (hw= 50 eV) f o r various exposures o f Hg ( i n langmuirs) on Ag(100). Arrow denotes new feature. I n s e t shows spectrum for 20 L exposure (-7 monolayer) o f Hg. From (94).

1

-I

--

n

c

3

* =>

In

z

Y

c

z

12

10

8

6

4

BINDING ENERGY

2

E,

eV)

Recently, a l s o t h a l l i u m was studied on Cu(OO1) (96, 97).

I n the ML the T1

atoms are very l i k e l y t o be arranged i n long chains l y i n g i n t h e (110) furrows o f t h e Cu(OO1) substrate (see f i g .

5.12

A

46).

The spacing between t h e chains i s

and the mean atomic spacing along the chains i s 3.41

A.

The r e g i s t r y i s

t h r e e T1 atoms t o f o u r Cu atoms and the u n i t mesh is ~ ( 4 x 4 ) . Higher coverage i s achieved by t h e rows moving c l o s e r together, (96).

u n t i l a dense hcp ML i s formed

From the d i f f e r e n t distances along the rows and between t h e d i f f e r e n t

rows t h i s system was supposed t o be a v e r i f i c a t i o n o f a 1D e l e c t r o n i c system. This idea was substantiated by ARUPS as shown i n f i g . 46.From t h e deeper-lying T1 6s2 band one peak i s found t o disperse and one t o be f i x e d i n energy under v a r i a t i o n o f t h e emission angle

0. Following Binns e t a l .

(96)

both t h e

d i s p e r s i o n along the chains and the missing dispersion normal t o the chains are observed here, since two domains o f chains oriented along e i t h e r o f two perpend i c u l a r axes [ O l l ] and [Oll] are b u i l t up a t the surface. I n a f u r t h e r very det a i l e d i n v e s t i g a t i o n they looked f o r t h e 6p band near EF which i s expected according t o t h e atomic 6s2 6 p l c o n f i g u r a t i o n o f T1. They were able t o l o c a l i z e t h i s weak band as demonstrated i n f i g s .

47 and 48.

One phase o f t h e l i n e a r

chains undergoes a spontaneous ( P e i e r l s ) d i s t o r t i o n . As expected f o r a 10 elect r o n i c system, t h i s i s connected w i t h t h e opening o f a gap a t EF which was deduced here t o be about 0.3 eV. The d i s t o r t i o n along t h e chains has t h e p e r i o d o f 8 T1 atoms i n accordance w i t h LEED observation. example o f a 1D e l e c t r o n i c system a t a surface.

Up t o now, t h i s . i s t h e o n l y

415

I

i

E='

ioiii

4

10111

1

8

9 10 11 Bindingenergy lev1

12

F i q . 46 ( l e f t ) : The l i n e a r chain arrangement o f T1 atoms (shaded) adsorbed on t h e (100) surface o f copper (ppen c i r c l e s ) a t a coverage o f 0.6 ML. The separat i o n between chains i n 5.12 A and the mean atomic spacing along the chains i s 3.41 A. The ~ ( 4 x 4 ) u n i t mesh i s i n d i c a t e d by t h e square. The s t r u c t u r e i s i d e a l i s e d and does n o t show rumpling along the chains.

Fiq. 46 ( r i q h t ) : Photoelectron d i f f e r e n c e spectra (copper background subs t r a t e d ) i n the r e g i o n o f t h e T1 6s f e a t u r e from t h e ~ ( 4 x 4 ) l i n e a r chain s t r u c t u r e as a f u n c t i o n o f t a k e - o f f angle (analyzer r o t a t e d i n t h e (011) plane). From (96). F i n a l l y , t u r n i n g t o Pb, we have mentioned already t h e Pb on N i ( l l 1 ) Al(111)

systems (92).

and

Whereas UPS from t h e conduction s t a t e s d i d n o t p r o v i d e

any information, i n t e r e s t i n g r e s u l t s have been deduced from t h e a n a l y s i s o f t h e Pb 5d shallow-core state. The two substrates behave q u i t e d i f f e r e n t l y . Fig. 49 presents t h e Pb 5d emission from Pb l a y e r s o f d i f f e r e n t thickness on A l ( 1 1 1 ) . The BE stays constant w i t h i n the experimental accuracy o f about 50 meV. The P b / N i ( l l l ) looks very d i f f e r e n t as shown i n f i g . 50 i n which a continuous s h i f t o f t h e BE t o l a r g e r values can be seen. Both d i r e c t i o n and c o n t i n u i t y o f t h e s h i f t were explained i n a Born-Haber-Cycle model as shown i n f i g . 51. The e x c i t a t i o n energy !$(Z) tation i n t o different,

i s c a l c u l a t e d on a second p a t h by separating t h e e x c i otherwise known, energies.

For t h i s purpose, w i t h i n a

"gedanken experiment" the Z atom i s desorbed from the N i ( l l 1 ) surface by applyi n g EA(Z).

The gas phase Z-atom i s then photoionized by applying EBV(Z,gas)

which i s r e f e r r e d t o t h e vacuum l e v e l V. Then the so-called equivalent core approximation i s used t o set the core-ionized Z-atom (Z*) i o n i z e d Z+1-atom ((Z+l)+).

equal t o a valence-

The l a t t e r i s rendered n e u t r a l by f i l l i n g i n one

e l e c t r o n and gaining t h e i o n i z a t i o n energy for the Z+1 atom (11(2+1)), finally

the neutral

(Z+1)

atom is adsorbed again a t

the

Ni(ll1)

and

surface

416

-2.

--

;- 0 6 -

', .-..#-."'.. @.=Lo-

-

.-.......-.

,,

w

-12-

nlo

I

I

4 =O

J

c" - 1 0 -

*

-----....--.-... . . . . .

b.42.

TI 6p [second zanel

%

A.

.

k

5 -08-

'-1%.

I

,/

1

-2

10

12

1L

1 2n1o

k Ib"1

Energy of mktd state (eVl

Fiq. 47 ( l e f t ) : (a) Photoemission spectra around the Fermi l e v e l a t an e l e c t r o n from t h e clean substrate ( 0 ) and the T1 chains a t 0 c o l l e c t i o n angle o f 38 = 0.53 (.). (b) D i f f e r e n c e spectra showing the behavior o f the T1 6p feature and c l o s e t o t h e Fermi l e v e l . The sudden drop i n i n t e n s i t y between Oe = 40 Oe = 42 i s taken as an i n d i c a t i o n t h a t the 6p band has crossed t h e Fermi l e v e l . From (97). O

O

48 ( r i q h t ) : 6p band s t r u c t u r e o f the T1 chains ( @ = 0.53) a t T = 80 K. The i n s e t shows the i n t e n s i t y o f the T1 6p f e a t u r e close t o the Fermi l e v e l . The Fermi l e v e l crossing i s i n f e r r e d from the sudden drop i n i n t e n s i t y . From (97).

Fiq.

r e l e a s i n g E ~ ( 2 + 1 ) . W i t h i n t h i s BHC, EBV(Z,gas)

- Ii(Z+l)

-

EBF i s c a l c u l a t e d as EBF(Z)

= EA(Z)

+

E A ( Z + ~ ) . For t h i s w e l l defined system EA(Z) and E A ( Z + ~ )

were measured by a thermal desorption experiment (98). The gas phase

EBF value

was measured r e c e n t l y w i t h the important r e s u l t t h a t about 85 % o f t h e whole i n t e n s i t y was confined i n t o one l i n e which then could be used o u t o f a f i n a l s t a t e m u l t i p l e t , spreading over more than 2 eV. ments i s given i n f i g .

52,

The r e s u l t o f these measure-

i n d i c a t i n g a very good agreement w i t h the measured

values. D i f f e r e n t conclusions could be drawn from t h i s r e s u l t :

(1) The s h i e l d -

i n g o f t h e f i n a l - s t a t e hole i n Pb i s narrow i n space and complete, e l e c t r o n i s f i l l e d i n t o t h e valence s h e l l o f the (Z+1) s h i f t i n t h e case o f P b / N i ( l l l ) BE i n t h e

as if one

atom. (2) The continuous

i s caused by a continuous s h i f t o f the atomic

M L range both f o r Pb and B i . This continuous s h i f t i s b a s i c a l l y

caused by a l a t e r a l l y r e p u l s i v e i n t e r a c t i o n between the Pb and B i atoms.

(3)

The s h i f t t o higher BE i s caused by the higher atomic BE o f B i t o N i ( l l 1 ) g i v i n g t h e s i g n t o the EA difference.

It should be noted f i n a l l y t h a t t h e BE i s

considered here w i t h respect t o EF, so t h a t the Born-Haber-cycle i s independent

o f work-function changes.

417

49: The Pb 5d s p i n - o r b i t s p l i t doublet f o r Pb on A l ( 1 1 1 ) . The parameter i s t h e thickness o f the Pb layer. The b i n d i n g energy EgF i s r e f e r r e d t o t h e Fermi edge. Photon energy i s He11 r a d i a t i o n ( h w = 40.8 and 21.2 eV). The step a t 19.6 eV i s the Fermi edge from the 21.2 eV c o n t r i b u t i o n o f t h e r a d i a t i o n e x c i t e d by the He lamp i n the He11 mode. From (92). Fiq.

Fiq. 50: Pb 5d c o r e - l e v e l spectra f o r Pb on N i ( l l 1 ) . Other d e t a i l s as f o r f i g . 49. From (92).

21

20

19

18

17

-EkieV

Fiq. 51: Born-Haber c y c l e f o r t h e the core-1 eve1 calculation o f binding energy EgF referenced t o the F e r m i l e v e l . EA is t h e adsorpt i o n ( o r sublimation) energy, Egv the core-level b i n d i n g energy f o r t h e atom referenced t o the vacuum l e v e l and I 1 t h e f i r s t i o n i z a t i o n p o t e n t i a l . The a s t e r i s k i n Z* i n d i c a t e s a 2 atom w i t h a core hole. From (92). AOLAYER OF Z-ATOMS

418

1e.o.C

I

17.8

#

*

PblNilllll

52: Pb 5d5/2 binding energies referenced to the Fermi level as a function of coverage in units ML. (.) From the UPS experiment (hv.=.40.8 eV). (x) Calculated for the Born-Haber cycle model including the desorption energies from the TDS experiment. From Eg

Pb5d5i2

(98)*

11 4i x I

1

i

3

COVERAGE 6 / H L

6.2 Alkali metals Thin films of alkali metals on metals have been studied extensively. The interest in these systems arises from technological aspects such as photodetection or promotion in catalysis as well as from more fundamental considerations. Alkali atoms represent a simple adsorption system, the properties of which can be calculated self-consistently in the framework of the jellium model. Such calculations using the Kohn-Sham local-density approximation have been pioneered by Lang and Williams (99). A wealth of experimental data has been collected using mainly LEED, electron energy loss spectroscopy, contact potential and TDS (100). Not so much is known about the electronic structure, in part certainly due to the small cross section of the s electrons in photoemission. On the other hand, the difficulties in elaborating the electronic properties arise also from the high vapor pressures of these metals, which prevent the easy production of single crystals, and their high chemical reactivity. Due to their high vapor pressure the substrates have to be cooled below room temperature in order to stabilize more than the first ML. These difficulties are nicely represented in fig. 53 (101). Before the first very small 02 dose i s given to the Cs film, a contamination is already visible, which exceeds the 6s band emission below EF by a factor of four. One furthermore recognizes, how sensitive this surface is against very small amounts of 02. From the great number of studies (100) a consistent picture has emerged on alkali adsorption: the work function drops rapidly, reaches a minimum and increases slightly again at ML coverage approximately to reach the value of the alkali-metal surface. At full ML the alkali atoms form hcp structures. The

419

CS FILM NO I

hv: 30 eV

Fiq. 53: ARUP spectra of clean and oxygen-exposed Cs at ho = 30 eV. Some oxygen was incorporated into the Cs film prior to the intended exposure (bottom curve). Note that emission from the valence band of Cs is visible in all spectra. From (101).

0

10

BINDING ENERGY ( r V )

initial decrease of the work function arises, because the electronegativity of the alkali metals i s small compared to that of the substrate, and charge is transferred towards the substrate, as it i s well described in the jellium model by Lang (102). In this model it was shown that for increasing coverage the electronic charge, which is peaked at the adsorbate substrate interface, moves towards the adsorbate resulting in a depolarization of the adsorbate-induced dipole moment (103).

UI

-C

P

Fiq. 54: ARUP spectra of electrons emitted normally from a Cu(ll1) crystal at different Cs coverages. The peak labelled V i s due to electrons emitted from Cs valence states. @ = 0.25 is defined by the close-packed ~ ( 2 x 2 ) Cs overlayer as observed by LEED. From

c

U

% c

L

a + 0

(104).

I P,

P

5

2

-2

-1

0

Initial energy (ev)

420

I t seems t o be common b e l i e f a t the moment t h a t i n a q u a l i t a t i v e p i c t u r e

t h e bonding o f t h e a l k a l i atom i s more i o n i c a t small coverages and m e t a l l i c a t t h e ML. Therefore,

during the t r a n s i t i o n from atom t o ML the charge i n the

conduction band has t o reappear. This was f i r s t c l e a r l y observed by Lindgren and Wallden (104) as shown i n f i g . 54. Recently, t h i s was n i c e l y reproduced f o r Na on Cu(OO1) (105) and f o r a l k a l i metals on Al(111) even f o r l a r g e r photon energies (106,107). above EF

-

5 5 i n d i c a t e s t h a t i n the r e g i o n o f empty bands, i.e.

Fig.

as analyzed by inverse photoemission - also a s t r u c t u r e moves down

which i s assigned t o the empty p band by these authors. The idea t h a t t h e cond u c t i o n s e l e c t r o n i s l a r g e l y f i l l e d back i n the ML s t a t e i s confirmed

by an

experiment o f metastable 3s He* d e e x c i t a t i o n i n f r o n t o f a Cs ML on C u ( l l 0 ) (108).

This process involves o n l y the outermost atomic l a y e r and t h e r e also

mainly t h e most far-reaching o r b i t a l s .

56 t h e Cs 6s signal

fig.

orbitals,

The l a t t e r f a c t also explains why i n

i s much stronger than t h a t o f

t h e Cs 5 p - f i l l e d

which i s more l o c a l i z e d towards the center o f the atom.

Fig.

56

demonstrates again how s e n s i t i v e t h e surface i s w i t h respect t o oxygen. I t was only r e c e n t l y t h a t the shallow p-core states were a l s o investigated.

From these states the t r a n s i t i o n from ML t o m u l t i l a y e r can c l e a r l y be recognized. This was f i r s t observed by Rotermund and Jacobi (109) b u t not discussed

11.1 eV i n t h e It i s i n t e r e s t i n g t o

i n d e t a i l a t t h a t time. Fig. 57 i n d i c a t e s t h a t EgF (Cs 5p3/2) ML and i s then s h i f t e d t o 11.9 eV f o r the t h i c k Cs f i l m .

=

note t h a t the 5 ~ 3 1 2l e v e l i s composed from two s t r u c t u r e s separated by about

0.2 eV. I t was shown r e c e n t l y by Domke e t a l . (110) t h a t t h i s s p l i t t i n g , which has the exact value o f 0.23

eV,

i s due t o a surface core-level

shift.

This

s p l i t t i n g cannot be as w e l l observed f o r the 5p1/2 peak since l i f e t i m e e f f e c t s due t o a 5p 5p 6s Auger t r a n s i t i o n broaden i t considerably. I n t h e meantime t h e s h i f t i n BE f o r t h e t r a n s i t i o n from ML t o m u l t i l a y e r s has been observed by seve r a l groups (109-113). up t o 2 ML f o r

Fig. 58 shows the t r a n s i t i o n from submonolayer coverages

Cs on Al(111) (113). A t t h i s surface Cs b u i l d s w e l l ordered ad-

l a y e r s , from which t h e coverage can be determined exactly. I t i s i n t e r e s t i n g t o note t h a t there i s also a s h i f t i n BE i n the ML region. The i n t e r p r e t a t i o n o f these s h i f t s sial.

-

i n the ML as w e l l as from ML t o m u l t i l a y e r - i s s t i l l controver-

Hohlfeld e t al.

densities,

(113) a t t r i b u t e d the s h i f t s t o d i f f e r e n c e s i n e l e c t r o n

s h i e l d i n g t h e photoemission final. s t a t e hole, s i m i l a r l y t o Xe m u l t i -

l a y e r s on metals (15-17).

Contrary, Domke e t a l .

(110) discuss these s h i f t s i n

terms o f a Born-Haber c y c l e (see f i g . 51 f o r Pb on N i ( l l l ) ) ,

i.e.

i n terms o f

atomic BE d i f f e r e n c e s i n t h e i n i t i a l state. F i n a l l y , we b r i e f l y note t h a t there are recent attempts t o go beyond t h e j e l l i u m model (99) and include the atomic s t r u c t u r e o f the substrate, l i k e surface s t a t e s and also the Cs 5p states (115,116). found f o r Cs on W(OO1)

Wimmer e t al.

i t s d-

(115)

t h a t Cs forms a m e t a l l i c overlayer w i t h t h e valence

421

Fiq. 55: ARUP spectra (left side) and inverse photoemission spectra (right side) for K on Al(111) measured at different coverage as indicated. From (107).

AR

-2

-1

EF-O

EF=O

1

2

3

4

Energy /eV

Cs-65

S’ He'

Fiq. 56: Electron energy distribution

curves induced by deexcitation of metastable 35 He* from (a) a clean monolayer of Cs adsorbed on a Cu(ll0) surface, and after exposure to (b) 0.2 and (c) 0.5 L of 02. From (108).

422

hw=21.2 eV T =20K

..._......."... . .* . . . I .

I

1

I

-1L

-12

I

I

-10

"

-8

.."..-.__ 14

13 12 11 H) Energy below EF (eV)

Fiq. 57 ( l e f t ) : ARUP spectra i n t h e r e g i o n o f the 5p l e v e l s a t normal emission f o r (A) b u l k p o l y c r y s t a l l i n e Cs and (B) a Cs ML. From (109). F i q . 58 ( r i q h t ) : UP spectra o f Cs adsorbed on A l ( 1 1 1 ) i n t h e Cs 5p energy range. The ML spectrum i s compared w i t h the Cs gas phase spectrum from (114). From (113).

e l e c t r o n s p o l a r i z e d t o the also p o l a r i z e d Cs 5p shallow-core

electrons.

The

admixture o f t h e d i r e c t i o n a l character o f Cs d - l i k e charge and t h e p e r s i s t e n t dominance o f W d - l i k e covalent Cs(s,d)-W

surface states near EF i n d i c a t e a tendency towards a

(surface, d) band. Furthermore, f o l l o w i n g Wimmer (116) t h e

Cs 5p e l e c t r o n s are p o l a r i z e d even i n a Cs ML, as shown i n f i g .

59. Further-

more, the Cs NN distance i n the ML i s contracted by about 11 % compared t o t h e corresponding distance i n bulk Cs. This i s i n e x c e l l e n t agreement w i t h t h e experimental r e s u l t s (117,118)

f o r Cs adsorption on W.

Also a c o n t r a c t i o n b u t

423

r

Fiq. 59: Charge d e n s i t y o f t h e 5p-derived s t a t e s i n a hexagonal Cs monolayer i n a plane perpendicular t o the slap i n u n i t s o f 10-5 e/bohr3. I n s i d e t h e atomic spheres t h e s p h e r i c a l l y symmetr i c ( 1 = 0) components have ben subtracted and outside contours up t o a maximum value of 76x10-5 e/bohr3 are shown. From (116).

I

I

w i t h a smaller amount was observed f o r Cs on Al(111) (113) which should be even b e t t e r modelled by t h e ML. Thus, i t seems t h a t p a r t o f the compression observed on W i s due t o i n t e r a c t i o n w i t h the substrate, and t h i s e f f e c t seems somewhat t o o l a r g e i n the c i t e d c a l c u l a t i o n (116). The c o r r e l a t i o n w i t h the f i n d i n g s f o r t h e Ag ML on A l ( 1 1 1 ) 7

i s noteworthy.

CALCULATIONS OF ELECTRONIC STRUCTURE OF METAL MONOLAYERS

A r a t h e r l a r g e amount o f the t h e o r e t i c a l work i s already mentioned i n d i s cussing the case studies. We w i l l very b r i e f l y mention some o f these c o n t r i b u t i o n s i n c l u d i n g a d d i t i o n a l studies but without commenting on the various comput a t i o n a l methods. As a f i r s t guide, c a l c u l a t i o n s o f the band s t r u c t u r e f o r an unsupported ML are o f g r e a t value. Comparing b e t t e r t o t h e experimental r e s u l t s are s t u d i e s o f supported ML where the i n t e r a c t i o n o f the ML w i t h the substrate i s taken i n t o account. Most i n f o r m a t i v e would be a s e l f - c o n s i s t e n t band s t r u c t u r e c a l c u l a t i o n f o r a supported ML which takes i n t o account a l l s t r u c t u r a l parameters o f the adlayer, i.e. t h e substrate,

t h e NN distances w i t h i n the ML, the adlayer p o s i t i o n r e l a t i v e t o and the v e r t i c a l distance from the substrate. No such complete

calculation exists

so far,

mainly due t o the

fact

that

not

all

of

the

424

parameters are known e i t h e r from experimental work o r from t o t a l energy calcul a t i o n s which became f e a s i b l e more r e c e n t l y . It seems t o us t h a t also t h e vert i c a l distance between adlayer and substrate should be taken i n t o considerat i o n . This i s because o f recent i n s i g h t i n t o atomic rearrangement during reconstruction,

for instance a t the f c c (110) surfaces. For a l a t e r a l c o n t r a c t i o n

some release i n t h e v e r t i c a l distance i s t o be expected so t h a t the v e r t i c a l distance between adlayer and substrate should n o t be simply approximated by t a k i n g sums o f m e t a l l i c r a d i i . There were very e a r l y attempts t o non-self-consistently s t r u c t u r e o f a free-standing ML e.g. performed

a

self-consistent

o f Cu (119).

band-structure

c a l c u l a t e t h e band

Later Jepsen e t al.

calculation

for

(120)

free-standing

Cu(100) and (111) ML f i l m s . They found t h e d-band width W depending on NN i n t e r a c t i o n : W(100) = 2.0 eV, W(111)

=

2.7 eV and W(bu1k) = 3.4 eV. Such a reduc-

t i o n i n width i s expected from simple t i g h t - b i n d i n g theory. W(bu1k)

The r a t i o W ( l O O ) /

should be n e a r l y equal t o the square r o o t o f t h e r a t i o s between the

numbers o f nearest neighbors, i.e.

(4/12)1/2

=

0.58 and (6/12)1/2 = 0.71.

These

values compare q u i t e w e l l t o W(100)/W(bulk) = 0.59 and W(111)/W(bulk) = 0.79. Noffke and F r i t s c h e (86) have calculated s e l f - c o n s i s t e n t l y t h e band s t r u c t u r e of unsupported ML o f Fe, Co, N i and Pd using NN distances o f the b u l k meta l s . They c a l c u l a t e d spin-dependent d e n s i t i e s o f states and s p i n magnetic moments per atom which we do n o t discuss here. We f i n d it i n t e r e s t i n g t h a t they have g e n e r a l l y found an increased 3d and 4s occupancy a t t h e expense o f 4p occupancy f o r the ML. Wimmer (121) has performed a systematic study o f such k i n d f o r the a l k a l i , the a l k a l i n e - e a r t h and 3d t r a n s i t i o n metals. Much a t t e n t i o n was paid t o

self-consistent

calculation o f

the

surface

e l e c t r o n i c s t r u c t u r e f o r a great number o f surfaces, o f which we mention o n l y Cu(100) (24,122).

From these c a l c u l a t i o n s layer-resolved d e n s i t y o f s t a t e s and

band s t r u c t u r e were obtained,

i.e.

kll-resolved

states being h i g h l y l o c a l i z e d

i n the surface plane. Such c a l c u l a t i o n s mainly designed t o study surface s t a t e s

o f the bulk metal were also very h e l p f u l i n analyzing t h e e l e c t r o n i c s t r u c t u r e o f t h i n metal f i l m s . The features o f the f i r s t l a y e r are taken t o be i n d i c a t i v e f o r the e l e c t r o n i c p r o p e r t i e s o f the surface. For Cu(100) i t i s found t h a t i n the surface l a y e r t h e d e n s i t y o f s t a t e s i s r a t h e r increased i n the upper p a r t o f the d band (24). This seems t o be a Sene r a l t r e n d found f o r many other surfaces. What i s also i n t e r e s t i n g t o note i s t h a t the d band moves t o higher energies (away from EF) w i t h an increasing number o f layers. Considering the t r a n s i t i o n from atom t o bulk, which was b r i e f l y discussed i n reviewing t h e experimental r e s u l t s on Cu, the d i r e c t i o n o f t h i s s h i f t i s not understandable. I t was argued there t h a t t h i s s h i f t should be from t h e deep-lying atomic l i n e t o the h i g h - l y i n g bulk band. F i n a l l y , noted t h a t the f i n a l

i t should be

r e s u l t f o r the distance between d-band edge and EF i s

425

1.5 eV in (24), which is too small compared to the experimental result of 2.0 eV, which may be seen from the examples in section 3.1 above. These deficiencies seem t o be quite common to calculations of this kind at the moment, as one can realize comparing the references (119) and (123) with (24) for the Cu case. More recently several self-consistent calculations were performed for ordered ML on single-crystal surfaces. Some results for Cu on Ru have been presented in fig. 8 (25). Very elaborate calculations have been performed also for Ni on Cu(100) (123), Ag on Rh(100) and (111) (124), and Pd on Fe(100) (125). We are aware that this is not a complete list, but additional information can be found in the references of the given examples. The Ag on Rh study o f Feibelman and Hamann (124) is remarkable, since several physical entiti’es are calculated and discussed which can be evaluated in the experiment: not only the surfaceband dispersion but also surface core-level shifts and absolute work-function values are given. The same authors (126) performed calculations on the variation of work function with thickness of free-standing and adsorbed thin metal films. This work continued the jellium calculation of Schulte (127). They found that a strong surface state at EF, as for Cr(100), stabilizes the charge-density profile in the surface region and makes the work function independent of film thickness. Furthermore, they pointed out that metals with low state densities have low surface energies, and are thus not apt to be thermodynamically stable substrates for high-density-of-states metals. They finally remarked that there is no obvious candidate for a metal-on-a-metal system, for which strong thickness-dependent work-function variations can be expected. Interestingly, such a variation was recently reported for Li adlayers on W(0ll) and Mo(Ol1) (128). Finally, we would like to mention a calculation for Au, Pt, Ir and 0s overlayers on Cr(100) (129). It was found that neither Au nor Pt could remove the strong surface-state intensity near EF of the Cr(100) surface, whereas 0s was able to do so. This was explained by the different symmetries of the d bands near EF. For Au and Ir the top of the mostly filled d bands lies near EF. The wave functions are of anti-bonding character there, whereas, for Cr, EF intersects the d band in the lower half of the d band, where the symmetry of the wave function is bonding or non-bonding. This finding has strong implications on the adsorption test for surface states: only those adsorbates, whose valence orbitals have the right symmetry to interact with the surface-state band, can remove the surface states. 8

SUMMARY There i s no doubt that the investigation of metallic films on metallic substrates has a large impact on many fields of scientific as well as technologi-

426 c a l importance. A f i r s t glance a t the presented m a t e r i a l shows t h e impressive v a r i e t y o f systems which has been studied up t o now. Compared t o t h i s l a r g e number o f studied systems and the even l a r g e r number o f systems which are n o t investigated, the number o f papers, which are given reference t o ter,

i s r e l a t i v e l y small.

.11

t h i s chap-

This i n d i c a t e s t h a t t h e m e t a l l i c f i l m s on m e t a l l i c

substrates are j u s t s t a r t i n g t o be investigated. This becomes even more s t r i k i n g i n view o f t h e l a r g e number o f papers on a s i n g l e adsorbate l i k e CO. Therefore,

we are s t i l l

looking f o r c o r r e l a t i o n s between t h e e l e c t r o n i c

s t r u c t u r e - which i s the 30 band structure,

t h e 2D band s t r u c t u r e ,

surface s t a t e s and resonances, and the t r a n s i t i o n between them l i k e work function,

-

including

and q u a n t i t i e s

s-d e l e c t r o n t r a n s f e r or real-space bonding.

We have t o

l e a r n much more about t h e c o r r e l a t i o n between geometric and e l e c t r o n i c s t r u c t u r e , before we can t h i n k o f e l e c t r o n i c - i n t e r f a c e t a i l o r i n g . For each system several surface-analytical

techniques have t o be adopted,

before r e l i a b l e conclusions can be drawn. Even such a well-known technique as q u a n t i t a t i v e AES can be misleading, cate. Therefore,

as the case of Pd/A1(111)

tends t o i n d i -

i n f u t u r e studies, more s t r u c t u r a l methods have t o be used t o -

gether w i t h photoemission. There i s good hope t h a t t h i s may be f a c i l i t a t e d by t h e great progress which has been made i n Scanning Tunneling and LEED microsCOPY.

The question may be r a i s e d as t o whether or not the 20 band s t r u c t u r e i s a workable conception.

This i s c e r t a i n l y t r u e f o r c a l c u l a t i o n s b u t may n o t be

t r u e f o r experiments. I n the r e a l world o f experiments one needs a substrate as a support f o r t h e ML. To spread t h e M L on top of the substrate t h e adatom-subs t r a t e i n t e r a c t i o n needs t o be l a r g e r than the adatom-adatom i n t e r a c t i o n . Thus, a d e l i c a t e balance has t o be established t o have the adatom-substrate i n t e r a c t i o n l a r g e enough t o enable the spreading-out o f the ML and t o have i t as small as possible i n order not t o overlay the l a t e r a l i n t e r a c t i o n s . From t h e overview given above i t seems t h a t n e i t h e r system o f the d-metalon-d-metal

k i n d can serve as an example f o r a 2D-electronic system. The i n t e r -

a c t i o n w i t h the substrate i s t o o strong r e s u l t i n g i n a m i x t u r e o f i n t e r f a c e and 20-adlayer states. The only examples could be Ag or t h e a l k a l i - m e t a l adlaye r s on A l ,

i.e.

on an sp-metal substrate. We have given f u r t h e r arguments above

and have presented the Ag/A1(111) case i n d e t a i l . The a l k a l i - m e t a l adlayers are o n l y o f l i m i t e d value, since t h e i r conduction band i s h a r d l y t o be observed i n most cases due t o the small cross s e c t i o n i n photoemission f o r the s-derived states. The Ag/A1(111) case e x h i b i t s the i n t e r e s t i n g r e s u l t o f being compressed by 5.6 % i n t o a 20 l a t t i c e a t t h e f u l l ML coverage. This can be understood as one of t h e r a r e cases i n which a separate E D - l a t t i c e constant could be observed.

For the d-metal

substrates the adlayer-substrate

mostly t o determine the l a t t i c e constant,

i.e.

i n t e r a c t i o n seems

seems t o o v e r r i d e the l a t e r a l

427

i n t e r a c t i o n . Therefore,

c o n t r a c t i o n as w e l l as d i l a t i o n are observed.

A t the

moment t h e o v e r a l l impression i s t h a t the e l e c t r o n i c s t r u c t u r e seems r a t h e r i n dependent t o changes i n l a t t i c e parameter by about ?5 %.This s i t u a t i o n i s r a t h e r u n s a t i s f a c t o r y . It could w e l l be t h a t one has t o look f o r more s e n s i t i v e experimental parameters. We have elucidated one general d i s t i n c t i o n , i . e . a1 substrates.

t h a t between sp and d-met-

The sp-metal substrates seem t o be appropriate t o make t h e 2D

band s t r u c t u r e observable i n some cases. The d-metal substrates, on t h e o t h e r hand, a r e l a r g e l y dominated by a mixture o f adlayer and i n t e r f a c e states. I n t e r e s t i n g l y , t h e energy distance o f the d bands from EF move q u i t e d i f f e r e n t l y w i t h thickness f o r these two cases: f o r sp-metal

substrates i t moves

towards EF, f o r d-metal substates i t moves away from EF w i t h increasing t h i c k ness. I t i s a l s o n o t understood a t t h e moment. To deduce some general trends from t h e experiments i s r a t h e r d i f f i c u l t . This i s t r u e a l s o f o r most c a l c u l a t i o n s . We have somewhat enlightened t h a t f o r t h e Cu case. There are very few c o n t r i b u t i o n s , i n which shortcomings o f t h e own method and d i f f e r e n c e s w i t h recent r e s u l t s from other authors are discussed. From most work no g u i d e l i n e s f o r discussing experiments can be gained. For t h e d-metal

substrates the work f u n c t i o n seems t o go t o t h e new value

w i t h i n t h e f i r s t ML. This i s d i f f e r e n t on sp substrates, where a r a t h e r long t r a n s i t i o n o f up t o 10 ML i s found i n some cases. I n p a r t t h i s may be due t o a l l o y formation i n t h e f i r s t layer. Cu, Pd and Au on A1 and Au on Cu seem t o be such cases. I n f u t u r e work magnetic material, rare-earth metals and compounds w i l l g a i n some i n t e r e s t together w i t h a l k a l i and e a r t h - a l k a l i n e s i n g l e c r y s t a l s .

Photo-

emission should be c o r r e l a t e d more s t r o n g l y w i t h geometric s t r u c t u r e . Calculat i o n s should be performed f o r more r e a l i s t i c geometry i n c l u d i n g the v e r t i c a l distance o f t h e adlayer. The important parameters and c a l c u l a t i o n methods have t o be made more understandable.

ACKNOWLEDGEMENT

The author i s g r a t e f u l t o M. Reimers, J. R e i f f e l and I. Reinhardt f o r caref u l t y p e w r i t i n g , proofreading and composing o f t h e manuscript. Discussion w i t h K. Kambe and some comments o f S. D. Kevan are appreciated.

428

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70 3. Hrbek, I. K. Sham and M.-L. Shek, Electronic structure of Mn over ayers on the Ru(001) surface, Surf. Sci., 191 (1987) L772-L778. 71 J. Friedel, On some electrical and magnetic properties of metallic sol id solutions, Can. J. Phys., 34 (1956) 1190-1211. 72 P. W. Anderson, Localized magnetic states in metals, Phys. Rev., 124 1961) 41-53. 73 Shang-Lin Weng and M. El-Batanouny, Photoemission observtion of the formation of Pd(ll1) surface states (surface resonances) and resonant d levels for Pd overlayers on Nb, Phys. Rev. Lett., 44 (1980) 612-615. 74 M. Strongin, M. El-Batanouny and M. A. Pick, Structure of Pd overlayers on Nb and Ta and the relationship to hydrogen uptake, Phys. Rev. 5, 22 (1980) 3126-3129. 75 M. El-Batanouny, M. Strongin, G. P. Williams and J. Colbert, Relationship between electronic structure and hydrogen-uptake kinetics, Phys. Rev. Lett., 46 (1981) 269-272. 76 G. P. Williams, M. El-Batanouny, J. Colbert, E. Jensen and T. N. Rhodin, Qualitative determination of band occupancies and their correlation to chemisorption, Phys. Rev. 6, 25 (1982) 3658-3662. 77 M. El-Batanouny, 0. R. Hamann, S. R. Chubb and J. W. Davenport, Electronic structure of a Pd monolayer on Nb(llO), Phys. Rev. 8, 27 (1983) 2575-2578. 78 M. El-Batanouny. M. Stronqin and G. P. Williams, Site determination for palladium on niobium using angle-resolved photoemission, Phys. Rev. B, 27 11983) 4580-4585. 79 M. Sagurton, M. Strongin, J. Jona and J. Colbert, Observation of a firstorder structural phsae transition in a monolayer of Pd on Nb(ll0) and its relationship to electronic structure, Phys. Rev. B, 28 (1983) 4075-4979. 80 M. Pick, J. Davenport, M. Strongin and J. Dienes, Enhancement of hydrogen uptake rates for Nb and Ta by thin surface overlayers, Phys. Rev. Lett., 43 (1979) 286-289. 81 M. Pessa and 0. Jylha, Electronic structure evolution o f Pd overlayers on Cu, Sol. State Comun., 46 (1983) 419-422. 82 G. W. Graham, Carbon monoxide chemisorption on Cu(lOO)-c(2x2) Pd, Surf. Sci., 171 (1986) L432-L440. 83 G. C. Smith, C. Norris, C. Binns and H. A. Padmore, A photoemission study of ultra-thin palladium overlayers on low-index faces o f silver, J. Phys. C: Sol id State Phys., 15 (1982) 6481-6496. 84 C. Binns, C. Norris, G. C. Smith, H. A. Padmore, M. G. Barthes-Labrousse, Photoemission from low-dimensional systems, Surf. Sci., 126 (1983) 258-264. 85 J. Noffke and L. Fritsche, Spin polarised ultra-thin metallic films, J. Phys. C: Solid State Phys., 14 (1981) 89-95. 86 Shen Xinyin, 0 . J. Frankel, J. C. Hermanson, G. J. Lapeyre and R. J. Smith, Photoemission studies of ordered Pd overlayers on Au(ll1): Implications for CO chemisorption, Phys. Rev. 6, 32 (1985) 2120-2125. 87 M. W. Ruckman, P. 0. Johnson and M. Strongin, Photoemission studies of carbon monoxide on tantalum-supported palladium thin films, Phys. Rev. 6, 31 (1985) 3405-3408. 88 G. W. Graham, Summary abstract: electronic structure of palladium films on tungsten surfaces, J. Vac. Sci. Technol. A, 4 (1986) 760-761. 89 6. Frick and K. Jacobi, Growth and electronic structure of ultrathin palladium films on Al(111) and their interaction with oxygen and carbon monoxide, Phys. Rev. 8, 37 (1988) 4408-4414. 90 6. Frick, K. Jacobi, J. A. Wilder, H. J. Sagner and K. H. Frank, Inverse photoemission of Pd grown on Al(111), Surf. Sci., 193 (1988) 529-533. 91 Xiao-he Pan, M. W. Ruckman and M. Strongin, Electronic structure and chemical properties o f Pt overlayers on Nb(llO), Phys. Rev. 8, 35 (1987) 3734-3739. 92 K. Gurtler and K. Jacobi, Coverage and adsorption-site dependence of corelevel binding energies for tin and lead on Al(111) and Ni(lll), Surf. Sci., 134 (1983) 309-328.

432

0. Chadwick and A. B. C h r i s t i e , Oxidation o f p o l y c r y s t a l l i n e and (111) lead surfaces studied by e l e c t r o n spectroscopy, J. C. S. Faraday 11, 76 (1980) 267-275. 94 M. Onellion, J. C. Erskine, Y. J. Kime, S. Varma and P. A. Oowben, Structure-induced e l e c t r o n i c states f o r Hg overlayers on Ag(100), Phys. Rev. 8, 33 (1986) 8833-8836. 95 F. J. Himpsel, D. E. Eastman, E. E. Koch and A. R. Williams, Experimental E(k) dispersions f o r the Zn3d states: evidence f o r i t i n e r a n t character, Phys. Rev. B, 22 (1980) 4604-4609. 96 C. Binns, C. N o r r i s and S. J. Gurman, Observation o f the one-dimensional band s t r u c t u r e o f t h a l l i u m chains adsorbed on copper(100), J. Phys. C: S o l i d State Phys., 16 (1983) 417-422. 97 C. Binns, M. G. Barthes-Labrousse and C. Norris, Charge d e n s i t y waves i n quasi-one-dimensional t h a l l i u m overlayers, J. Phys. C: S o l i d State Phys., 17 (1984) 1465-1472. 98 K. G i j r t l e r and K. Jacobi, Coverage-dependence o f Pb5d core l e v e l b i n d i n g energies on A1 (111) and N i (ill), Surf. Sci., 152/153 (1985) 272-277. 99 N. 0. Lanq and A. R. Williams, Theory o f atomic chemisorption on simple metals, Phys. Rev. B. 18 (1978) 616-636. 100 A r a t h e r complete l i s t o f references i s given by: P. Soukiassian e t al., Phys. Rev. B, 31 (1985) 4911-4923. 101 S. Y. Su, I. Lindau, P. W. Chye, S.4. Oh and W. E. Spicer, Photoemission studies o f clean and oxidised Cs, J. E l e c t r . Spectrosc., 31 (1983) 221-259. 102 N. 0. Lang, Theory o f work-function changes induced by a l k a l i adsorption, Phys. Rev. B, 4 (1971) 4234-4244. 103 For a more extended discussion o f work f u n c t i o n the reader i s r e f e r r e d to: A. K i e j n a and K. F. Wojciechowski, Work f u n c t i o n o f metals: r e l a t i o n between theory and experiment, Prog. Surf. Sci., 11 (1981) 293-338. Lindgren and L. Wallden, Cu surface s t a t e and Cs valence e l e c t r o n s 104 S. A. i n photoelectron spectra from the C u ( l l l ) / C s adsorption system, S o l i d S t a t e Commun., 28 (1978) 283-286. 105 L. Wallden, Surface p h o t o e l e c t r i c e f f e c t f o r t h i n metal overlayers, Phys. Rev. Lett., 54 (1985) 943-946. 106 K. Horn, A. Hohlfeld, J. Somers, Th. Lindner, P. H o l l i n s , and A. M. Bradshaw, I d e n t i f i c a t i o n o f the s-derived valence-electron l e v e l i n photoemiss i o n from a l k a l i - m e t a l adlayers on aluminum. Phys. Rev. Lett., 61 (1988) 2488-2491. Frank, H . 4 . Sagner and 0. Heshett, Coverage-dependent s h i f t s of s 107 K.-H. and D resonances o f a l k a l i metals chemisorbed on Al(111), Phys. Rev. B, 40 (1989), i n press. 108 B. Woratschek. G . E r t l . J. KuDDers. W. Sesselmann and H. Haberland, Evidence f o r a quantum - s i z e e f f e c t -of t h e conduction e l e c t r o n s during o x i d a t i o n o f Cs, Phys. Rev. Lett., 57 (1986) 1484-1487. 109 H. H. Rotermund and K. Jacobi, Physisorption on a low work f u n c t i o n metal: ARUPS from xenon o r cesium, Surf. Sci., 126 (1983) 32-40. 110 M. Domke, T. Mandel, C. Laubschat, M. P r i e t s c h and G. Kaindl, Layerresolved photoemission study o f t h e C s / S i ( l l l ) 2 x l i n t e r f a c e , Surf. Sci., 189/190 (1987) 268-275. 111 G. Pirug, A. Winkler and H. P. Bonzel, M u l t i l a y e r growth o f potassium on a P t ( l l 1 ) surface, Surf. Sci., 163 (1985) 153-171. 112 3. Hrbek, Adsorption o f cesium on Ru(001), Surf. Sci., 164 (1985) 139-148. 113 A. Hohlfeld, M. S u n j i c and K. Horn, E l e c t r o n i c s t r u c t u r e o f cesium adsorbed on A l ( 1 1 1 ) , J. Vac. Sci. Technol. A, 5 (1987) 679-683. 114 S. Suzer, B. Breuckmann, W. Menzel, C. E. Theodosiou and W. Mehlhorn, Photoelectron spectra o f outer p s h e l l s o f a l k a l i metal atoms using t h e resonance r a d i a t i o n : m u l t i p l e t and s a t e l l i t e structure, J. Phys. B: Atom. Molec. Phys., 13 (1980) 2061-2070. 115 E. Wimmer, A. J. Freeman, M. Weinert, H. Krakauer, J. R. Hiskes and A. M. Karo, Cesiation o f W(OO1): Work f u n c t i o n lowering by m u l t i p l e d i p o l e formation, Phys. Rev. Lett., 48 (1982) 1128-1131. 93

433

116

E. Wimmer, Bond contraction in monolayers: 20-hexagonal Cs, Surf. Sci., 134

(1983) L487-L493. 117 A. G. Fedoros and

A. G. Naumovets, Cesium on tungsten (011) face; structure and work function, Surf. Sci., 21 (1970) 426-439. 118 P. Akhter and J. A. Venables, Observation of a registered phase in Cs/W( 110), Surf. Sci , 102 (1981) L51-L45. 119 N. Kar and P. Soven, Band structure of thin films, Phys. Rev. B, 11 (1975)

.

3761-3768. 120 0. Jepsen, J . Madsen and 0.

K. Andersen, Band structure of thin films by the linear augmented-plane-wave method, Phys. Rev. B, 18 (1978) 605-615. 121 E. Wimmer, All-electron local density functional study of metallic monolayers: I. Alkali metals, J. Phys. F: Met. Phys., 13 (1983) 2313-2321, 11. Alkaline-earth metals, ibid. 14 (1984) 681-690, 111. Transition metals Sc to Cu, ibid. 14 (1984) 2613-2624. 122 J. G. Gay, J. R. Smith and F. J. Arlinghaus, Self-consistent calculation of work function, charge densities and local densities of states for Cu(lOO), Phys. Rev. Lett., 38 (1977) 561-564. 123 Ding-sheng Wang, A. J. Freeman and H. Krakauer, Electronic structure and magnetism of Ni overlayers on a Cu(OO1) substrate, Phys. Rev. B, 26 (1982) 1340-1351.

P. J. Feibelman and

D. R. Hamann, Electronic structure of metal overlayers on rhodium, Phys. Rev. B, 28 (1983) 3092-3099. 125 Hong Huang, J. Hermanson, J. G. Gay, R. Richter and J . R. Smith, Electronic structure and magnetism of a Pd monolayer on Fe(100), Surf. Sci., 172

124

(1986) 363-371. 126 P. J. Feibelman and 0.

R. Hamann, Quantum-size effects in work functions of free-standing and adsorbed thin metal films, Phys. Rev. B, 29 (1984) 6463-

6467. 127 F. K. Schulte,

A theory of thin metal films: electron density, potentials and work function, Surf. Sci. 55, (1976) 427-444. 128 Yu. S . Vedula and V. V. Poplavskii, Layer-by-layer growth of lithium films on tungsten and molybdenum (011) faces: manifestations in the work function, J.E.T.P. Letter, 46 (1987) 230-233. 129 P. J. Feibelman and 0. R. Hamann, Surface states of clean and metaloverlayer-covered Cr(001) films, Phys. Rev. B, 31 (1985) 1154-1156. 130 R. J. Smith, A. W. Denier van der Gon, and J. F. van der Veen, Reaction of thin Pd films with Al(111) and Al(110) surfaces, Phys. Rev. B, 38 (1988) 12712-12715.


435

Chapter 11

THIN FILMS ON SEMICONDUCTORS R. D. BRINGANS

1. INTRODUCTION Angle resolved photoelectron spectroscopy (ARPES) is a particularly valuable tool for studying the electronic properties of thin films on semiconductors. The properties of the outer surface of the thin films, the interface states formed at the junction between the film and the semiconductor, and the thin films themselves can all be understood using ARPES. In particular, precise information about the atomic structure of the surface, interface or film can be revealed. This will be illustrated in this chapter by several examples in which the wavevector-dependent energy dispersions of occupied states, E(k), obtained with ARPES, are used to select which of several competing structural models is correct. Inversely, thin films on semiconductors can be engineered to give ideal semiconductor surfaces which can then be used to yield information about the ARPES technique itself. Sections 3 and 4 will examine examples of this use. A large portion of the chapter will deal with monolayer and sub-monolayer films. These systems are particularly well matched to ARPES experiments because they have good long range order, are stable and relatively passive against contamination. They are also particularly interesting for the light that they throw on bonding a t surfaces. For clean semiconductor surfaces, the directional covalent bonds typical of bulk Si, Ge, GaAs and related compounds, remain directional a t the surface. The broken or dangling bonds formed when the surface is created have high energies and so the surface atoms rearrange or rebond in a non-bulk-like topology to reduce the number of dangling bonds. When atoms interact with semiconductor surfaces, they can bond to the surface atoms in a variety of ways which alter the surface reconstruction, removing it completely in some instances. ARPES can then measure the dispersion of the overlayer-substrate bonds [as in Ge(lll):H, for example] or of surface orbitals which are fully occupied [as in Ge(lll):As, for example]. For films thicker than a few monolayers, the value of ARPES is much more limited because, in general, thick films of interest do not have surfaces with long range order. Alternative measurements such as core level photoemission spectroscopy, which are more sensitive to chemistry rather than to long range order, are often more informative in this case. Nevertheless, there are several examples where ARPES has provided valuable information and these will be discussed. Another class of interest is the production by heteroepitaxy of thick single crystal films which are not otherwise

436

stable. As a n example, ARPES measurements have been made on diamond-structure Sn produced heteroepitaxially on a n lnsb substrate. In all investigations of surfaces, interfaces and thin films, several techniques need to be used on the same system in order to obtain reliable results. Low energy electron diffraction (LEED), reflection high energy electron diffraction (RHEED), Auger spectroscopy (AES), angle-integrated ultra-violet photoemission (UPS), x-ray photoemission (XPS)and scanning tunnelling microscopy (STM) are all important adjuncts to ARPES measurements. In addition, theoretical calculations of minimum energy structural configurations and E(k) dispersions are of enormous value when coupled with ARPES measurements. The current chapter is concerned primarily with ARPES and the results of other measurements will be introduced only to expand on the information obtained with that technique. Systems for which ARPES provides only secondary information will also not be discussed in detail. The following section will deal with the methods commonly used to produce the thin films on semiconductors, the manner in which the ARPES measurements are carried out and the techniques used to interpret the results. Section 3 will describe results for a particular class of systems in which a single monolayer on a semiconductor surface provides a stable surface. I n many cases the resulting combination is close to an ideal bulk termination of the semiconductor. Ultrathin metal films will be discussed in section 4. These are also stable monolayer and submonolayer films with long range order. Their surface states will be compared to those expected for the bare semiconductor. Thicker films will be covered in section 5. In most cases, the atomic geometries are much more complicated for thicker films with effects such as island formation, lattice strain, and transitions from polar to non-polar material being important. 2. EXPERIMENTAL CONSIDERATIONS AND COMPARISON WITH THEORY 2.1 Use of molecular beam epitaxv techniques The increased availability of molecular beam epitaxy (MBE) techniques has opened up a significant new field of research for surface and interface states. MBE can be used to create atomically flat surfaces not attainable by cleavage. The polar GaAs surfaces, for example, cannot be formed by cleavage because of the enormous electrostatic cost that would be involved. Sputter-annealing is also not suitable because of the preferential sputtering of one of the atoms. Homoepitaxial growth onto polished surfaces, however, can produce atomically flat surfaces with a variety of surface Fompositions. The surface states on MBE produced GaAs(100) (see refs. 1,2, for example), GaAs(ll1) (refs. 2,3) and GaAs(-1-1-1) (refs. 2-4) have been studied with ARPES. For the current chapter we are interested in heteroepitaxial growth but the techniques used are very similar. In a typical MBE growth, separate effusion cells are used for the components of the thin film and the substrate is held a t a temperature for which atomic diffusion is high in

437

the plane of the surface but very low in the direction perpendicular to the surface. Because the growth takes place a t slow rates of around 1 monolayer per second (so that the atoms have sufficient time to find a low energy site on the surface), the growth system must have a very low base pressure in the 10-10to 10-11tom range. In the case of GaAs, cells with elemental As and Ga are used and substrate temperatures are kept in the range 550-650 "C(see ref 5 for a review of GaAs MBE). The growth can be thought of as a deposition of Ga in an overpressure of As4 (or in some cases, As2) molecules. The pressure of the group V molecules in 111-V MBE is typically around 10-6 torr and so there is a significant contamination of the vacuum system. As a result, ARPES systems with in-situ growth are usually dedicated to one type of material. A more optimal solution is the transfer of samples under ultra-high vacuum from a growth chamber to the ARPES chamber. Other techniques used to produce thin films on semiconductors involve evaporation from a single source and do not have the complication of the high partial pressures typical of MBE of 111-V compounds. These techniques have much in common with MBE, however, because they rely on the most important aspect of MBE, namely slow rates of evaporation in ultra-high vacuum onto reactive surfaces, to achieve ordered films. 2.2 ARPES measurements Once the system to be studied has been prepared, the requirements for ARPES measurements on thin films are similar to those for clean semiconductor surfaces. Thin films present few additional problems compared with clean semiconductor surfaces and in some cases are not as sensitive. In the case of monolayer films which passivate the surface, the film will not contaminate as rapidly in vacuum so that more time can be taken to make the measurements. Charging problems may occur for insulating films, but charging is not a problem for most of the examples cited here because the films are thin enough to allow easy conduction into the substrate.

2.3 Comparison of experimental and theoretical determinations of E(kld ARPES can be used to study the dispersion of bulk bands, surface states or interface states. In each case, the most powerful use of ARPES results occurs when a comparison between calculated and experimentally-determined E(k) plots is made. Theoretical band structure calculations can be made by a number of methods and comparison with bulk bands measured with ARPES has been used to determine the gccuracy of many of these methods. For diamond-structure Sn (a-Sn) grown on InSb(loo), normal-emission ARPES results were used to determine the bulk band structure of the a-Sn and then a comparison with various calculation methods could be made (ref. 6). In the case of surfaces, thin films and interfaces, the atomic structures are generally not known. Comparison between measured E(k) dispersions with those

438

calculated for models of the structure can then be used as a stringent test of the models proposed. Many of the results discussed in this chapter will deal with the surface properties of thin films on semiconductors because ARPES is a particularly powerful technique for examining the surface state dispersions Ei(kl1) of ordered surfaces. In order to obtain the experimental dispersions, measurements of the photoemitted intensity are made as a function of electron kinetic energy, Ek, and emission angle, 0. For a pure surface state, the initial state dispersion, Ei(kll),is then found directly from: Ei = hV-Ek kll = (sin@) . d{2 m Ek / h2) where Ei is the binding energy referred to the vacuum level, hv is the photon energy and m is the electron mass. The determination of surface state dispersions is complicated because ARPES spectra contain contributions from bulk initial states and so-called back bond states as well as surface states. A back bond usually represents a bond between a second layer atom in a bulk-like environment and a surface atom. The separation of spectral features between surface, bulk and back bond is difficult. Surface features have frequently been identified by their sensitivity to contamination. While this provides some evidence, it is often complicated by the fact that contamination can alter the electronic properties of the whole near-surface region and change the symmetry (e.g. alter reconstruction). Many of the monolayer films which we will be discussing are also insensitive to reactions with other atoms. An alternative approach is to predict theoretically the positions in E(kl1)of bulk derived features and compare them with the locations in E(kl1) of peaks found in the ARPES spectra. Remaining features can then be considered to be surface related. In the results shown in Fig. 1for Ge(lll)c(2x8) and Ge(1ll):AB 1x1 (refs. 7,8),the prediction of the bulk dispersion was accomplished by calculating the initial state band structure using a n empirical local pseudopotential method. Energies were calculated as a function of k l for fixed kll and i t was assumed that transitions were made into a final state with a free electron dispersion [Ef = hz ( k l z kllz ) / 2nd and with a n energy zero a t Vobelow the top of the valence band. The free electron final state is used because it selects the only final states with a high probability of reaching the energy detector in the experiment. Outside the crystal the electrons are in a plane wave state directed towards the detector. The free electron parabola used as a final state inside the crystal has a n identical form but is offset by the potential barrier E,. In the repeated zone pcheme, a single parabola in the k l direction is used, or in the reduced zone scheme only G-vectors parallel to k l are allowed. Other G-vectors give rise to so-called "secondary cone" contributions which generally have significantly lower intensity. Given known initial and final states a s a function of k l , possible transitions were found by searching for final and initial states separated by hv. The dispersion expected for each initial state could thus be found as a function of kit.

+

439

0 I

.m

1

>

\

.= =.

k

Y

F’

$ 2

w

3

a.

2 3 W

I

m >

g 4

W

z W

0 Ge ( 1 11) ~ ( 2 x 8 ) rn Ge (1 11) :As

5

a

/

hv = 2 5 e V

6

F

s

Figure 1: Peak positions in ARPES spectra from Ge(lll)c(2x8) and Ge(ll1):As 1x1 plotted as a function of energy and kll. The curves are the dispersions expected for direct bulk transitions. Surface states from Ge(l1l)c(Zx8) have been omitted for simplicity. From refs. 7,8. The comparison shown i n Fig. 1between the calculated bulk dispersions Ei(kll,hv) and the measured E(kl1,hv) data is very good indicating that this procedure is applicable. The zero of the final state parabola was taken to be Vo = 9.70eV below the top of the bulk valence band (Em).This was the value which was found to give the best overall agreement with the data. The process was checked by repeating the comparison for different values of h v and a similar agreement was found. The potential barrier a t the surface is given by E, = 9.70eV (EF-EvB) + Q where Q is the work function of the surface and EF is the Fermi enrergy. It is clear that there is a very good correspondence between the data and the calculation, showing that the free electron final state is the most appropriate final state to use for photon energies greater than about 15-20eV and that it is possible to reliably discriminate between bulk and surface derived spectral features. For the data in Fig. 1, the surface state band for Ge(ll1):As 1x1 disperses downwards from a binding energy of about 0.3eV a t the zone center and can be seen to be well removed from the bulk states. Once the surface or interface states have been identified, their dispersion can be compared with model calculations. In addition, the polarization of the incident photons is very useful for probing the character of different surface orbitals. For example, the photoemitted intensity from a pz type orbital directed normal to the surface will be greater for light with its polarization vector normal to the surface than for light with its polarization vector in the plane of the surface. This effect can be seen particularly well with linearly polarized synchrotron radiation, but also with unpolarized light. In the latter case, when the light is incident normal to the surface all of the polarization is in

+

440

the surface plane and pz-type orbitals will not be seen easily. As the sample is rotated with respect to the light beam, more and more intensity will be shown for pz orbitals. Various selection rules for some experimental geometries have been tabulated by Hermanson (ref. 9). 3. MONOLAYER FILMS TO CREATE IDEAL SURFACES In this section examples will be given for non-metallic overlayers on Si, Ge and GaAs substrates. The monolayers have been chosen so that the atoms in the overlayer saturate the dangling bonds at the semiconductor surface. This has several implications. The surfaces tend to become passivated if the overlayer atoms are also fully coordinated and the near-surface substrate atoms “feel” like atoms deep in the bulk of the substrate material. A surface structure in which the near-surface atoms are close to bulk crystal sites is essential for the determination of bulk band structure from angle-resolved photoemission measurements. 3.1 Hydrogen termination of Si and Ge surfaces The simplest case, in principle, is the saturation of dangling bonds with hydrogen atoms. Figure 2 shows this effect for the case of Si(ll1). Saturation of dangling bonds

Figure 2: Side view of a schematic structure of hydrogen terminated Si(ll1). H atoms are shown as open circles. with H has a theoretical counterpart in many cluster calculation techniques which use H atoms on the periphery of the cluster to simulate continuation into the bulk. Any method of removing or saturating dangling bonds will remove the electronic driving force for reconstruction. This is shown in the schematic density of states in Fig. 3. An unreconstructed bulk-terminated surface will have broken bonds and a surface state orbital which is partially occupied, leading in turn to a metallic surface. The surface can reduce its electronic energy if the surface state splits into a lower unoccupied and a higher occupied state. This can occur via reconstruction if the electronic energy reduction outweighs any energy increase due to the atomic strain involved. If we now saturate the dangling bonds with a hydrogen atom, for example, the surface state will

44 1

I

I

(a) Bulk Termination

I

(c) Saturation of Dangling Bonds

ENERGY

Figure 3: Schematic density of states for (a) a simple termination of a bulk semiconductor in which the broken bonds at the surface form a metallic band, (b) the same surface after reconstruction splits the surface band and (c) the same surface when each broken bonds is saturated by bonding to another atom. be fully occupied and no gain will be achieved by reconstructing the surface. In the case of hydrogen on Si surfaces, the Si-H bond strength is comparable to the Si-Si bond strength and so the surface state (or more accurately the Si-H bonding orbital) will be near the center of the bulk Si valence band. It has been found that hydrogen atoms bonding to Si and Ge surfaces do indeed remove the surface reconstruction. For the case of H on Si(ll1) and Ge(lll), early angle-integrated photoemission experiments and theoretical calculations were found to agree very well on the location of the Si-H and Ge-H orbitals (ref. 10,ll). Angleresolved photoemission measurements have been carried out (refs. 12,13) for the case of H on Ge(lll)c(2x8). After H adsorption, the Ge(lll)c(2x8) surface states disappear and a sharp peak corresponding to the Ge-H band can be seen clearly a t a binding energy of hbout 5eV. The ARPES spectra showing this effect in Fig. 4 correspond to the two symmetry directions on the Ge(ll1) surface. Bulk-derived peaks in the energy range 34.5eV are unchanged after interaction with H and were compared with calculations for bulk dispersions as described in section 2.3. This allowed an unambiguous identification of the Ge-H features in the spectra. The dispersion obtained in ref. 12 for

442

-

Ge (1 11)

.

... ....... Gelll1):H

e = 30’

8

6 L 2 BINDING ENERGY teVI

0

Figure 4 ARPES s ectra for the clean Ge(lll)c(2x8)surface and the same surface after termination with The removal of surface states and the addition of the Ge-H state near 5eV can be clearly seen. (After ref. 12.)

If

the Ge-H band is shown in Fig. 5 where it is compared with calculations from ref. 11for both Si(ll1):H and Ge(ll1):H. There is good qualitative agreement between the experimental and theoretical band shapes and the absolute binding energies are relatively close. The discrepancy which is observed between experimental and theoretical binding energies is a common problem, which will be discussed in more detail in section 3.3.1, and so the lack of precise agreement in the absolute binding energy is not serious. The removal of surface states and the achievement of bulk-like electronic states near the surface can also be seen with photoemission core level spectroscopy for the qases of Si(ll1):H and Ge(ll1):H (ref. 14). The surface shifts in the Si 2p and Ge 3d core levels are changed after the hydrogen termination. The shifts become much smaller than those seen on the clean surface and the overall width of the peak is considerably reduced. Hydrogen also bonds to the Si(100)2xl surface but the reconstruction is not removed completely. The Si-Si dimers on the clean surface cannot be fully broken by

443

O - ---Gellll):H

-Si (1ll):H

-

3 2.

0

-

Ge(ll1):H

Experiment Calculation Calculation

8-

-r I

I

[iiz]

-- I

k,,

I

I

[iio]

Figure 5: The measured and calculated dispersion of the Ge-H band in Ge(ll1):H. The peaks in the ARPES s ectra which were identified as being induced by H interaction are shown by the dashed i n e s and calculations from ref. 11are shown by the full curve and the symbols. (After ref. 12.) bonding to H atoms. A well-defined surface with a single monolayer of hydrogen bonded to the Si-Si dimers a t the surface has been studied with ARPES (ref. 15). The dispersion of the surface states for this Si(100)2xl+ H surface was found t o agree well with a band structure calculated for a symmetric dimer model in which the H atoms saturate the two dangling bonds on each Si-Si dimer (ref. 16). A 3x1 structure with Si-Si dimers bonded to one H atom per Si plus Si atoms bonded to two H atoms per Si atom has been observed (ref. 17) but there does not appear to be a stable surface in which the reconstruction is entirely removed so that all surface Si atoms are bonded to two H atoms. Core level and ARPES measurements have also been carried out for H bonded to GaAs(-1-1-1) (ref. 18) and GaAs(100) surfaces (refs. 18-20). For the GaAs surfaces, however, the H exposures used alter the Ga to As ratio of the surface layer and make the interpretation of surface state dispersions much more complicated than for the corresponding Si and Ge surfaces. Group VII-Terminated Si and Ge Surfaces Similar effects are seen on Si(l11) with group VII atoms for similar reasons. A partially covalent bond between the surface Si atoms and C1, for example, will also fully saturate the Si and C1 atoms. Several ARPES experiments have been carried out on this system (refs. 21-23) and yield some of the same qualitative results as those for H on Si(ll1) and Ge(ll1). The dispersion of the C1 induced states for a monolayer of C1 on Si(ll1) from ref. 23 is shown in Fig. 6. Polarization selection rules have been used to identify the orbital character of the states. There are two non dispersing bands labelled 3.2

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Figure 6: The measured dispersion of C1-inducedpeaks for Si(ll1):Cl (ref. 23) s and u, corresponding to Si-C1bonds, and two dispersing C1-Cl states labelled n+ and nwhich have a total bandwidth of l.OeV. These results compare well with band structures (refs. 22,241 calculated assuming a model of the surface in which each surface Si atom bonds to a single C1 atom in analogy to the H on Si(ll1)case in Fig. 2. Core level spectra show a single distinct chemical shift for C1 on Si(ll1) (ref. 23) and for C1 and Br on Ge(ll1) (ref. 25) which is also consistent with the C1 atoms being in the on-top site. Data also exist for C1 interaction with the Si(100) and Ge(100) surfaces (refs. 21, 25). The core level data for Ge(100)2xl+Cl (ref. 25) suggest that one C1 atom bonds to each surface Ge atom and that the Ge atoms are arranged in symmetric dimers [as was the case for the Si(100)2xl+ H results discussed above]. For fluorine atoms on Si(ll1) the situation is more complicated because the reaction can go beyond one monolayer. The F atoms can etch the Si surface via the formation of SiF4 molecules which then desorb. Core level spectroscopy (ref. 26) then shows that the surface Si atoms are bonded to one, two or three F atoms. A similar tendency to etch the surface has been suspected for H interaction with Si(ll1) (refs. 27,28) on the basis of electron energy loss results which show the presence of H-Si-H “scissor” vibrational modes. The effect, however, seems t o be much less severe than with F atoms.

3.3 Arsenic-Terminated Si and Ge Surfaces The hydrogen and group VII terminated surfaces remove the reconstruction on the (111)surface of Si or Ge by saturating the Si dangling bonds. An alternative method replaces Si atoms on the surface layer with As atoms as shown in Fig. 7. The extra

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valence electron on the As atom compared with a Si atom allows the formation of a doubly-occupied surface orbital instead of a singly-occupied orbital for the ideal clean surface. The substitution then makes all of the Si and As atoms fully coordinated.

'

3.3.1 Ge(ll1):As and Si(ll1):As The formation of a n ideal (111)surface with an As monolayer was first shown to occur for Ge(111)c(2x8)(ref. 7). Addition of As atoms to that surface using a molecular beam epitaxy type of technique removed the ~ ( 2 x 8reconstruction ) and replaced it with a (1x1) or unreconstructed surface. A similar result has been obtained for the addition of As atoms to the Si(111)7x7 surface (refs. 29,30). Angle resolved photoemission experiments were compared with surface band structures calculated for an energy-

Si(ll1):As 1 x 1

@

Si

0 As

Figure 7: Sideview of a schematic model for the Si(ll1):As 1x1 and Ge(ll1):As 1x1 surfaces is shown a t the left. Measured and calculated dispersions are shown at the right. Measured dispersions are shown b symbols and the LDA calculations are shown by the full lines (refs. 7,30 for the Ge an8Si surfaces respectively). Calculations using the quasi-particle method are shown by the dotted lines (refs. 31,32 for the Ge and Si surfaces respectively). The edge of the projected bulk band structure is shown by the shaded region.

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minimized atomic geometry of the structure in Fig 7 and the excellent qualitative agreement shown in Fig. 7 was found. The calculation, which was made with the local density approximation (LDA), does not correctly place the energy of the bulk bands relative to the surface bands. This is a well-known limitation of the LDA which arises because the surface electrons are more localized than those in the bulk. Recent calculations using the quasi-particle technique (refs. 31-33) have obtained the better agreement for the calculated and measured separation between the surface and bulk bands which is shown by the dotted lines in the figure. Subsequent measurements, including photoemission core level spectroscopy (refs. 29,341 scanning tunnelling microscopy (ref. 32,351, xray standing waves (ref. 36), medium energy ion scattering (refs. 37,381 and thermal desorption studies (ref. 39) have confiimed the model originally proposed. The Si(ll1):As surface has also been shown to be extremely passive against reaction with gas atoms. In particular, the stability of Si(ll1):As against oxygen and air was found to be very great (ref. 30) (a 5 minute air exposure only reduced the surface state intensity in ARPES spectra by 25%). Interaction of Si(ll1):As with atomic hydrogen did cause a change in the surface state, but after a n anneal the surface state was restored, showing that the H atoms adsorbed onto the Si(ll1):As surface rather than disrupting it. 3.3.2 Other group V atoms on SiClll) Other group V atoms do not seem to form a simple 1x1 structure on Si(ll1). Structures with symmetries of 6 d 3 x 6 d 3 and 4x4 (ref. 40) are seen for P layers, and with a symmetry of d 3 x d 3 for Sb and Bi layers (refs. 41,42, respectively). As discussed in ref. 7, the difference between the overlayer formed by As and by the other group V atoms is a result of the atomic sizes involved. Presumably, Sb and Bi atoms are too large to fit into a single layer with three bonds to Si. For P atoms, on the other hand, too much tensile strain would occur. For the case of Sb, ARPES and k-resolved inverse photoemission dispersion data (ref 41) have been interpreted in terms of a model of the surface in which three Sb atoms form a trimer or “milk stool” and bond t o three Si atoms. This leaves all Sb and Si atoms fully coordinated. There have been no calculations of surface bands for this model, and so no critical test of the model can be made. Nevertheless, the data in ref. 41 shows that there are a t least two occupied surface states and that there is a large gap between occupied and empty surface states. As with the Si(ll1):As case, the Si(ll1):Sb surface is considerably less reactive than the clean Si(111)7x7 surface. 3.3.3 Si(1OO):As A similar use of a n As monolayer as a passivating layer has been made on the Si(100) surface (ref. 43). The Si-Si dimers which form on the clean surface reduce the surface energy, but the Si atoms in the dimers are not fully coordinated. By replacing

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these dimers with As-As dimers (or more accurately breaking up the Si-Si dimers and adding As-& dimers on top), a fully coordinated surface with a 2x1 symmetry can be formed. Angle-resolved photoemission measurements of the surface state dispersion were made for As monolayers an on-axis Si(100)surface (ref. 43)and for a surface tilted around the [Oil] axis by 4 O from (100) (ref. 44). The latter surface consists of (100) terraces separated by steps which are two atomic layers high. The terraces then all have the As-As or Si-Si dimers aligned. For nominally on-axis (100) surfaces, single atom high steps predominate and this leads the presence of domains of different dimer alignment. Dispersions calculated for the structural model shown in Fig. 8 were compared with the measured dispersions and agreed well for both the double domain [on-axis Si(lOO)] and single domain [4" off axis] surfaces. The comparison is shown in Fig. 8 for the single domain case. As for the Si(ll1):As and Ge(ll1):As cases, the relative binding energies of the surface and bulk states were incorrect in the LDA calculation. The total energy calculation predicted that the lowest energy surface would have symmetric &-As dimers in contrast to the clean Si(100)2x1 surface which consists of asymmetric Si-Si dimers. The presence of symmetric rather than asymmetric As-As dimers was confirmed by the comparison between the calculated and

I

Si(100):As2 x 1

SINGLE-DOMAIN Si(100) 2x1

00

0

-

a

0

-2-

1-

m >

-

w

0

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-[oiil

5

s

UI

m

SINGLE-DOMAIN St(100):As 1x2

Fi re 8: Sideview of a schematic model for the Si(100):As 2x1 surface is shown at the l e p Measured dispersions (symbols) and calculated dispersions (lines) are shown at the right for single-domain Si(100) 2x1 and Si(100):As 1x2 surfaces (after ref. 44). Calculations for S1(100)2x1and Si(100):As 1x2 are from refs. 45 and 43 respectively.

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measured dispersions because asymmetry would cause a large splitting between the II and n* bands (0.95eV for a 4" tilt of the dimers), whereas no splitting was seen in the experiment. This is an example where ARPES dispersions have provided a critical test of a key aspect of a model structure. Core level spectroscopy data (ref. 34) were consistent with the model for Si(100):As 2x1. A single shift was seen for the Si 2p level and only one component was seen for the As 3d core level.

3.4 S, Se on Si(100)and Ge(100) A similar argument about fully coordinating the surface atoms holds for group VI atoms on Si(100). In this case a Se atom, for example, can form a bridge bond between two adjacent Si atoms. All of the Se and Si atoms can then be fully coordinated and a 1x1 surface symmetry will result. This is shown schematically in Fig 9(a). Core level spectroscopy investigations have been carried out for S on Si(100) (ref. 461, S on Ge(100) (ref. 47) and Se on Si(100) (ref. 48). Only the S on Ge(100) has been obtained in an ordered state and for this system, detailed core level photoemission measurements have shown that the S atoms are indeed in bridge sites and that the LEED pattern has a 1x1 symmetry. ARPES measurements (ref. 49) on this surface have shown the presence of a

Fi re 9: Sideview of a schematic model for the Ge(1OO):S 1x1 surface is shown a t the 1ePMeasured dispersions are shown a t the right (after ref. 49).

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strongly dispersing sulfur-induced band in the energy range 2-4 eV and two flat bands, one near 5eV and one near 7.5eV, as shown in Fig. 9(b). The dispersion of the uppermost state was identified as being due to the non-bonding lone pair states on the S atoms and the deeper lying states as being due to Ge-S bonding. Recent normal emission angleresolved photoemission fine structure measurements (ref. 50) are also consistent with the S atoms being in a bridge site on Ge(100). The results for S and Se on Si(100)both show that a range of oxidation states exist for the interface silicon atoms. The Si 2p core levels can be fit with shifts of 1 , 2 , 3 and 4 times 0.62eV for Si(1OO):S(ref. 46) and 1 , 2 , 3 and 4 times 0.53 eV for Si(100):Se(ref. 48). This is indicative of the formation of the compounds SiS2 and SiSe2 in which each Si atom is surrounded by four S or four Se atoms (in analogy with Si02). 3.5 Sb on GaAs(ll0) A stable monolayer of Sb was found to form on the GaAs(ll0) surface and, on the basis of photoemission, LEED and theoretical studies was interpreted by Skeath et a1 (ref. 51) to consist of zig-zag chains of Sb atoms. In the model, which is shown in Fig. 10, each Sb atom bonds to two other Sb atoms and to either a Ga or As atom. As is the case with the H, C1, As and Se terminated Si surfaces discussed above, all of the overlayer and substrate atoms are fully coordinated. Detailed core level measurements have been used to examine the interface quality and band bending as a function of preparation methods (ref. 52). ARPES measurements (refs. 53-56) have been compared with surface band structures calculated for the geometry shown in Fig. 10 (refs. 57,581, with an example of the comparison being shown in the figure. For the upper two bands there appears to be good qualitative agreement between the experimental and theoretical dispersions. The states St3 and S5 can be associated with Sb-Ga and Sb-As bonds respectively (ref. 58). Theory and experiment also agree that these two bands

(a) S I O E VIEW

@

(bJ TOP VIEW

b AS

o Ga

Figure 10: A schematic model for the GaAs(ll0):Sb 1x1 surface is shown a t the left. Measured dispersions (dotted lines) and calculated dispersions (full lines) (refs. 57,581 are shown a t the right. (Both figures are from ref. 56).

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should have some dangling-bond character. As discussed in ref. 56, the state labelled S probably corresponds to the SbSb band. ARPES measurements have also been carried out for InP(110):Sb (ref. 59) and GaP(110):Sb (ref. 55) with similar qualitative results being found. 4. ULTRATHIN METAL FILMS As was the case for the monolayer systems described above, metal atoms can also saturate dangling bonds a t semiconductor surfaces and lead to a relatively passive surface. In general the stable layers have larger unit cells than the ideal clean surfaces. It is also often found that surface state dispersions measured in AEtPES do not exhibit the full symmetry seen in LEED. This is one of the main contrasts with the results for the ideal surfaces discussed in Section 3, and some of the reasons for this observation will be addressed in this section.

4.1 Group 111atoms on Si(111)surfaces As an example of a stable metal film on a semiconductor, A1 atoms can bond to three Si surface atoms on the ideal Si(ll1) surface so that all of the A1 and Si atoms are fully coordinated. On the Si(ll1)surface, this occurs in an ordered one-third monolayer film which has 4 3 x 4 3 symmetry. The symmetry and coverage can be understood if the A1 atoms lie in threefold sites on the ideal Si(ll1) surface (ref. 60). The group ID atoms Al, Ga, and In on Si(ll1) have been known for a long time to show a 4 3 x d 3 LEED pattern (see ref. 60, for example). A recent RHEED study has shown that B atoms on Si(ll1) also form a 4 3 x d 3 reconstruction (ref. 61). It should be noted that reconstructions with other symmetries also occur for thin ( 5 one monolayer) films of the group III atoms on Si(ll1) (see the summary in ref. 62, for example). We will concentrate here on the 4 3 x 4 3 reconstruction, which is the one which has had the most attention. The first of these surfaces to be studied with ARPES was Si(ll1):Al 4 3 x 4 3 (ref. 63). The surface state dispersion found did not have the full d 3 x d 3 symmetry, but two bands were identified because the energy observed for the M point was different for two different symmetry directions. This observation was explained by Northrup (ref. 64) on the basis of band structure calculations. The A1 adatoms in a threefold site bond via their px and py orbitals to the pz (or dangling bond) orbitals on the surface Si atoms. As shown in Fig. 11, the coupling of occupied states will be strongest at the edge of the 1x1Brillouin zone. The ARPES measurement will therefore see strong A1 adatom states only at wave vectors near the edge of the 1x1Brillouin zone. With this in mind, it is possible to compare the theoretical and experimentally determined adatom-induced dispersions. The experimental results for the 4 3 x 4 3 surface formed by 1/3monolayers of A1 (refs. 62,63,65-671,Ga (ref.67) and In (ref. 68) are qualitatively the same. Theoretical dispersions have also been calculated for the Al, Ga and In-induced 4 3 x d 3 surfaces by Northrup and co-authors (refs. 64, 68 and 69 respectively). In the original calculation, total energies and surface electronic band

451

M

r

(30 0 0

Figure 11: (a) T4 and H3 models of the S i ( l l l ) : A l ~ 3 x surface, ~3 where the A1 atoms are shown b open circles and the outer layer Si atoms are shaded. (b) Orbitals taking lace in the &-A1 bonding are shown a t the M and r' points in the surface Brillouin zone. ft can be seen that the coupling is strongest near the edges of the zone. (From ref. 64) structures of Si(ll1):Al 4 3 x d 3 were calculated for two possible structural models in which the A1 atoms are each bonded to three Si atoms. The two models, which are shown in Fig ll(a), differ in the location of the A1 atoms with respect to the second layer Si atoms. The model with the lowest total energy has the A1 atom directly over the second layer Si atom and is labelled T4 (because the A1 atom is essentially four-fold coordinated). The calculated band structures have a very similar shape for Al, Ga and In overlayers and in each case agree well with those obtained experimentally with ARPES. This can be seen in Fig. 12 for Si(ll1):In 4 3 x 4 3 . In the figure, the calculated dispersions are shown with heavier lines where the calculation predicts strong emission (i.e. where the wave vector before folding is near the edge of the 1x1 Brilloun zone as described in ref. 64). An excellent agreement can be seen between the experimental and calculated band shapes. In none of the cases is it possible to distinguish experimentally between the H3 and T4 models. As discussed for the As-terminated surfaces, calculations such as these which are made within the local density approximation, are unable to accurately locate surface band energies with respect to the bulk bands. The preference for T4 comes primarily from its calculated total energy (ref. 64). A LEED I-V study of theSi(ll1):Ga 4 3 x 4 3 surface does show the T4 model to be the most consistent with the data (ref. 70). Recent STM measurements on surfaces with partial coverage of the d 3 x d 3 structure have allowed the registry between the Si substrate and Ga (refs. 71,72) and In (ref. 73) atoms to be determined. In both cases the T4 model fits the results. Another STM study of Si(ll1):Ald 3 x d 3 has found that Si adatoms can coexist as well separated defects with the A1 adatoms and the defect band seen in some ARPES data at low binding energies (around 0.4eV) was identified as coming from these Si adatoms (ref. 74).

452

A-1

- -k,, - [la71

~ziii

k’

Figure 12: Measured dispersions (full and open symbols for stronger and weaker features, esp ctively) and calculated dispersions (lines) are shown for S i ( l l l ) : I n J 3 x 3 3 . Calculations are shown for both the T4 (full and broken lines) and H3 (dotted and dash-dot lines) models of the surface. The heavier lines show where the angle- esolved photoemission is ex ected to have stron er intensity. The 1x1 and d 3 x d 3 surface Brillouin zones are &own in the inset. (A er ref. 68).

a

4.2 Group IV metal atoms on S i t l l l )

Both Sn and Pb form 113 monolayer d 3 x d 3 structures on Si(ll1) and Ge(ll1). It has been shown with surface xray diffraction measurements (ref. 75) that the Sn and Pb atoms on the Ge(ll1)surface occupy the T4 site as described above for the Si(ll1):Al surface. Surface state dispersions have been obtained from ARPES experiments for the 113 monolayer d 3 x d 3 structures formed by Sn on Si(ll1) (ref.76) and by Pb (ref. 77) on Ge(ll1). The data for the Sn case has two bands which have essentially the same dispersion as that for the Al, Ga and In d 3 x d 3 surfaces plus a third band close to the Fermi energy. The band structure calculations for A1 on Si (ref. 64) showed an unoccupied band which has a similar dispersion to this third band. The data for Si(lll):Snd3xd3 are thus consistent with Sn atoms bonding in the same three-fold sites as does Al. The extra valence electron on the Sn atom then occupies the third band. The data are also consistent with the idea that the “defect” band seen near the Fermi energy for the group III d 3 x d 3 surfaces arises from a small density of Si adatoms replacing group III adatoms. The bands seen for Ge(ll1):Pb d 3 x d 3 also seem to be similar to the other d 3 x d 3 surfaces (ref. 77) and total energy calculations for this surface also favor the T4 model (ref. 78). Sn on the Ge(ll1) surface can also form a 7x7 reconstruction. This has been examined with core level spectroscopy (ref. 79) and ARPES (ref. 80) in order to make comparisons with the Si(111)7x7 surface. The core level data show a t least two inequivalent sites for Ge atoms near the surface and two inequivalent sites for Sn

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atoms. The ARPES dispersions were found to be similar to those of the Si(111)7x7 surface except that the metallic state seen on the Si surface was found at greater binding energies for Ge(ll1):Sn 7x7. 4.3 A g and Au on Si(ll1) Thin films of Ag and Au on Si(ll1) also exist in a number of stable structures. The most studied of these has a 4 3 x 4 3 symmetry but the structure is not expected to be the same as for S i ( l l l ) : A l ~ 3 x because ~3 each Ag or Au atoms would not be able to bond t o three Si atoms. It has been shown that the 4 3 x 4 3 Ag and Au surfaces are significantly less reactive than the clean Si(ll1) surface (ref. 81) implying that few dangling bonds are left on the surface after the 4 3 x 4 3 structure has formed. There is still considerable controversy over what is the structure (and metal coverage) of the 4 3 x 4 3 Ag and Au surfaces. Many experimental techniques have been applied to the Si(ll1):Ag 4 3 x 4 3 surface in particular but a definitive conclusion cannot be made. STM images show that the surface layer consists of a honeycomb pattern of atoms (refs. 82-84) and this has been interpreted as a honeycomb of Ag atoms embedded in threefold hollow sites on the Si surface (refs. 82,84) based on the alignment between the honeycomb and the Si(111)7x7 unit cell and as a honeycomb of Si atoms above a single atomic layer of Ag atoms (ref. 83) on the basis of STM I-V measurements. Results from other techniques including core level spectroscopy (ref. 85) have not been able to fully resolve the conficting interpretations. This is a perfect opportunity for ARPES dispersions to provide an answer. Several angle resolved photoemission studies have been made of the surface state dispersions for the Si(ll1):Ag 4 3 x 4 3 surface (refs. 63,86,87) and the Si(ll1):Au 4 3 x 4 3 surface (ref. 88). The spectra show strong non-dispersing peaks near 6eV which arise from the Ag 4d (Au 5d) electrons and dispersing peaks a t lower binding energies. The data by Yokotsuka e t a1 (ref. 87) for Si(ll1):Ag 4 3 x d 3 show a nearly dispersionless band a t a binding energy of 0.9 eV and bands near 1.2 and 3.8 eV which have a strong dispersion with a clear 4 3 x 4 3 symmetry. This data should provide a critical test of structures for the Si(ll1):Ag 4 3 x 4 3 surface, but to our knowledge no band structure calculations have been compared with this dispersion. 4.4 Other metal overlavers A great deal of work has been carried out on metal films on III-V surfaces, but in almost all cases the metal does not form a stable thin film analagous to those discussed above nor does it form an epitaxial thick film. ARPES has thus been of limited use in most cases. An exception is Pb layers which form 1x2 and 1x3 reconstructions on GaAs(100). ARPES dispersions have been measured for these surfaces and compared with those for clean GaAs(100) surfaces, revealing three Pb-induced states (ref. 89). Several other metal overlayers have been examined with ARPES and determinations made of band dispersions. Most, however, have not been able to be

454

compared with calculated band structures. Among these are Si(ll1):Ni d l 9 x d l 9 (ref. 63) 5. THICKER FILMS AND INTERFACES This section deals with thick epitaxial films grown on semiconductor substrates. Because ARPES is most powerful when studying ordered systems, we will not consider disordered films. With this restriction in mind, the fabrication of thick films on semiconductors is of particular interest for two reasons. Firstly, the atomic structure and atomic and electronic properties of the interface formed between the film and the substrate can be examined. Secondly, a study can be made of any special characteristics (such as strain or metastable crystal structure) of the overlayer due to the presence of the substrate. I n addition, growth of epitaxial insulators (e.g. CaF2) and epitaxial metals (e.g. some of the metal-silicides) on Si opens the way to three-dimensional integrated circuits so that these films and their interfaces with Si have been studied in some detail. 5.1 Interface formation The interface between two different materials has many properties in common with surfaces or with the ultra-thin films discussed in the previous two sections. Interface electronic states are similar in character to surface states. The chemical bonding behavior which causes reconstruction on clean surfaces is also a dominant effect a t interfaces. In addition to their useful analogy with surfaces, interfaces are of vital importance in many electronic devices. The heterojunction between GaAs and Al,Gal-,As, for example, plays a central role in the high electron mobility transistor (HEMT). ARPES has been applied to the electronic and structural properties of interfaces, but only in a few cases. Because ARPES generally requires an ordered surface, its use has been limited. In most cases, films of a few monolayers in thickness do not have an atomically flat surface. In the AlAs-on-GaAs example, it is difficult to stop the AlAs growth after an integer number of AlAs layers. In many other cases, such as GaAs-on-Si the overlayer forms islands rather than growing layer by layer. Nevertheless, there are several cases in which ARPES has been used successfully to provide useful information about interface structure.

5.1.1 The GaAs-on-Si(ll1) interface The chemical nature and bonding topology at the interface between GaAs and Si is of particular interest because of the presence of a large (4%) lattice mismatch and because the interface forms a boundary between fully covalent and partially ionic materials. A third factor, the requirement that the Ga and As atoms find their appropriate sub-lattice sites during the heteroepitaxy, arises when GaAs is grown on Si. GaAs-on-Si is also promising technologically as it may allow the integration of the wellestablished Si device technology with the optical performance of the 111-Vcompounds.

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The strong bonding between As and the (100) and (111) Si surfaces that was described in section 3.3 suggests that Si may bond to GaAs via a layer of As atoms. Both the [lo01 and [1111directions in GaAs consist of a complete layer of As alternating with a complete layer of Ga. Core level photoemission (ref. 34) and x-ray standing wave (ref. 90) measurements have been made on the Si(ll1):GaAs interface. A comparison between core level results for Si(lll):As, Si(ll1):Ga and Si(ll1):GaAs indicated considerable Si-As bonding and possibly some Si-Ga bonding for the GaAs-on-Si interface. The x-ray standing wave measurements indicate that Ga and As occupy different (111)atomic planes with the Ga atoms located in the lower halves of the (111) double layers and the As atoms located in the upper halves. The simplest interpretation of these results is that a Ga-As double layer bonds on top of the As-terminated Si surface as shown in Fig 13(a). This interface structure would cause a divergence in the total energy of a thick film (ref. 91) and would also have

0 Ga 0 As 8 Si

(a)...SiSiAsGa As

(b)...SiGaAsSiAs

ENERGY BELOW ,E

(eV)

Figure 13: Side view of schematic models for very thin GaAs layers on Si(ll1) are shown at the left. Below each model is a corresponding band structure calculation. ARPES spectra measured a t the K oint of the surface zone are shown a t the right for Si(ll1):As and for Si(ll1):GaAs. T t e dashed spectra were taken from samples which were grown using a Ga prelayer. (After ref. 93). These results appear t o rule out structure (a).

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a high energy for thin overlayers. A model proposed by Northrup (ref. 92) on the basis of total energy calculations is shown in Fig. 13(b)and has a layer of Si atoms above one As layer and one Ga layer. A mixture of 1/4 x model (a) plus 3/4 x model (b) was found to give no divergence in the energy and is consistent with the core level photoemission (ref 34) and x-ray standing wave (ref 90) results. Recent ARPES results have been compared with band structure calculations for models (a) and (b) and has allowed model (a) to be ruled out for thin layers of GaAs on Si(ll1) (ref. 93). At the beginning of GaAs-on-Si(ll1) epitaxy, the GaAs does not completely cover the substrate and forms islands. The degree of island coverage is of the order of 50%, but depends on details of the growth method (ref. 34). To minimize the difficulty of interpretation of the data, thin GaAs layers were grown using As or Ga prelayers and a number of film thicknesses. The two band structures differ considerably at the K point of the 1x1 Brillouin zone and so spectra' for that point are compared with the calculations in Fig 13. The spectra for the K point show no states above E m and no peak until 1.5eV below EVB. The core level measurements showed that thick GaAs islands, regions with thin GaAs layers (one or two bilayers) and regions of Si(ll1):As all coexist on the surface (ref. 34), and the ARPES spectra will contain contributions from all of these regions. The fact that no peak is seen a t energies above EVBa t the K point in any of the spectra (which correspond to different GaAs equivalent thicknesses and different deposition methods) thus rules out the ...SiAsGaAs structure. The surface state which is observed a t K is has nearly the same energy as that for Si(ll1):As. This result indicates that the interface dipole is very small, and rules out the high dipole (2.6 eV) ...SiAsGaAs structure because the calculated lone pair state energy is 2 eV higher than on the Si(ll1):As surface. Interface structures which have smaller dipoles than ...GaAsSiAs, and which are equally low in total energy (ref. 92), can be constructed. In fact, the dipole for the structure ...(GaxSii.,)As(SixGai-x)As is zero when x = 3/4. The photoemission results may be indicative of an interface structure of this sort.

5.1.2 Ge on GaAs(ll0) Several ARPES studies have been made of the approximately lattice-matched Geon-GaAs(ll0) interface. Interface-related features were identified in ref. 94 and the effects of Ge-induced charge shifts on GaAs interband transitions were examined in ref. 95. Interdiffusion between Ge and GaAs appears to be an important effect and this is one of the reasons that most of the more recent work has concentrated on the Si-GaAs system.

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5.1.3 The CaFz-on-Si(ll1) interface One would expect that interfaces have states which are localized a t the interface in the same way that surface states are localized a t surfaces. There are very few examples, however, in which the dispersion of interface states has been measured. The interface between CaF2 and the Si(ll1) surface is well ordered and experimental evidence for interface dispersion appears to have been found. The interface between CaF2 and Si is a prototype for bonding between an ionic insulator and a covalent semiconductor. CaF2 is a large band gap insulator which has a similar crystal structure and similar lattice constant to those of Si. In addition to its interest for interface bonding, CaFz grown heteroepitaxially on Si represents a promising candidate as an insulating layer for three-dimensional Si integrated circuits. Several studies, most notably those using core level spectroscopy (refs. 96-loo), have sought to identify the nature of the bonding and the stoichiometry a t the interface. For the best-ordered interfaces, the results point to bonding between Ca and Si atoms with a missing layer of F a t the interface. Recent medium energy ion scattering measurements for a single monolayer of CaF2 evaporated on Si support this model (ref. 101). These measurements show that (i) the Ca:F ratio is approximately 1:1, confirming dissociation of the first layer of CaF2 molecules, and (ii) the Ca atoms sit in the threefold hollow site directly above the second layer Si atoms. Several attempts have been made to measure the interface dispersion for this system. A dispersion for a 3x1 submonolayer of pure Ca on Si(ll1) showed a state dispersing upwards from the zone center to the zone edge (ref. 971, as did the surface of a radiation damaged film of CaF2 (ref. 102). Recently an ARPES study has been carried out on CaF2 films which were one and two layers thick (ref. 103). By using low photon fluxes so that F atoms are not removed from the film and by reannealing after each measurement, ARPES spectra representative of the undamaged interface were

-M

-r

K

Figure 14: The measured dis ersion for the interface state of CaFz on Si(ll1) is shown by the filled circles and the fufi line. (From ref. 103).

458

obtained. The CaF2 valence band is around 7-8 eV below the Si valence band maximum and so the peaks found near the Fermi energy cannot be bulk CaFz in origin and were assigned to interface states. The dispersion of these states is shown in Fig. 14. The downwards dispersion is of opposite sign to those seen for Si(ll1):Ca 3x1 and radiation damaged CaFz and has a band width of around 0.6 eV. The dispersion compares favorably with that calculated (ref. 104) for the isoelectronic Na on Si(ll1) system when the Na atom is placed in the open hollow site. 5.1.4 Metals on semiconductors In general, ARPES has not been used a great deal to study the interface between metals and semiconductors. Several ARPES experiments have, however, been carried out for A1 layers on GaAs(ll0) and InP(110). Thin layers of A1 interact with the GaAs(ll0) surface in such a way that A1 and Ga atoms undergo a n exchange reaction (ref. 105). ARPES spectra at symmetry points have been taken before and after thin films of A1 were added to the GaAs(ll0) surface (ref. 106). It was found that the structure in the spectra disappeared as the A1 layer thickness increased beyond a fraction of a monolayer. Similar results have been seen for A1 on InP(110), where the peaks in the clean InP(110) spectra become attenuated with no new peaks appearing (ref. 107) and it was concluded that island formation disorders the surface after a coverage of 0.5 monolayers. ARPES measurements have also been carried out for Ag films on InP(110) (ref. 108). In contrast to Al, Ag is not expected to react strongly with the surface but McKinley et a1 (ref. 108) conclude from their data that the IriP(110):Ag interface is not abrupt. ARPES has been used in another mode in a study of Schottky barrier formation of A1 on the (100) surface of GaAs (ref. 109). The sharpness of the angle-resolved spectra allowed accurate measurement of band-bending changes as the metal layer was added. A comparison of the Schottky barrier height for A1 on the Asrich ~(4x4) and Ga-rich 4x6 GaAs(100)surfaces showed that the surface composition did not affect the height. 5.2 Artificially stabilized crystal structures Thin films can be formed under stress using strained-layer epitaxy techniques in which a thin film of lattice mismatched material is grown on a semiconductor substrate. Below a critical thickness the films will strain to match the lattice constant of the substrate and above this thickness, dislocations will form and the strain will reduce. This is an exciting area because it allows electron spectroscopy methods to be used to see the effects of stress on electronic properties. As a n example, the effect of strain on bulk energy bands has been examined with ARPES for GaAs and InxGal-,As. (ref. 110). The dispersion in the I?X direction was measured for strained and unstrained films and the deformation potentials were obtained as a function of k. In other circumstances, heteroepitaxy sometimes allows one to use a substrate to stress an overlayer in such a way that a crystal structure which does not occur naturally can be formed. In the

459

remainder of this section, examples of this type of artificially stabilized structure will be discussed. 5.2.1 a-Sn on InSb The diamond structure form of S n (labelled a-Sn) is not stable at temperatures above about 13 "C. Metallic Sn @-Sn) transforms spontaneously to a-Sn a t 13 "C,but undergoes a 26% volume increase which leaves only powder. It was shown by Farrow et a1 (ref. 111) that a-Sn could be grown to thicknesses of up to 500 nm on substrates of InSb or CdTe and that the transition to p-Sn did not occur until around 70 "C. Hochst and Hernandez-Calderon (ref. 6) used this growth technique to produce single crystal films of a-Sn(100) on InSb(100) and then carried out ARPES measurements on them. The results were important because so much is known about the other diamondstructure group IV elements. A comparison was made between the bulk band structure obtained in the experiment and band structure calculations. This comparison is shown in Fig. 15 with calculations by Chelikowsky and Cohen (ref. 112) using the non-local pseudopotential method. In order to locate spectral features as a function of the wave

+ ..

> W L

i 3 LL w

z W

r

-

X

Figure 15: Experimental band structure for a-Sn(100) for the I’ to X direction (full and open symbols for primary-cone and secondary-cone features, respectively) and calculated band structure from ref. 112. Figure is from ref. 6. vector perpendicular to the surface ( k l ) , a free-electron final state was used in a similar manner to that discussed in section 2.3. ARPES has also been used to characterize the interface formed by a-Sn on InSb(ll1) and InSb(-1-1-1) (ref. 113), CdTe(100) (ref. 114) and CdTe(ll0) (ref. 115). In all cases a sharp interface was observed.

460

5.2.2 Fe and Co on GaAs(ll0) Substrate stabilization has also been utilized in spin-polarized ARPES studies of thin magnetic films (refs. 116,117). A GaAs(ll0) substrate has been used to stabilize Co i n the bcc structure (ref. 116) and to provide single domain a-Fe(ll0) (ref. 117). Results were obtained which would not have been possible without the effect of the substrate. In the case of GaAs:Fe(llO), normal emission ARPES spectra for majority and minority spins were measured. The geometry of the samples gave single-domain magnetization with no external magnetic field applied and the strain caused by the substrate led to a thickness-dependent anisotropy in the magnetization (ref. 117). Results for bcc Co(ll0) films were compared with those for bcc Fe(ll0) in ref. 116 and it was found that the extra electron in Co went mainly into the minority spin band. These results are described in more detail in the chapter by Kisker and Carbone. 5.2.3 Si(ll1):Ge 7x7 and Si(ll1):Ge 5x5 The Si(1ll):Ge surface provides another example in which heteroepitaxy stabilizes a structure not seen in either Si or Ge alone. In this case, it is the surface structure which is stabilized in contrast to the stabilization of bulk crystal structures described in section 5.2.1. The reconstructions seen on clean, annealed Si and Ge (111) surfaces differ markedly, with Si(ll1) exhibiting 7x7 periodicity and Ge(ll1) having a ~(2x8) symmetry. In the case of Si(11117x7 there is strong evidence that the dimer-adatomstacking fault model (DAS model) is correct (ref. 118). The Ge(111)c(2x8)surface on the other hand only has the adatom component (ref. 119). In both cases the adatoms have a 2x2 local structure with a n adatom bonded to three out of four Si atoms in the layer below. The remaining atom in the second layer (the “rest atom”) has a dangling bond. In an attempt to further understand the driving force for these complicated reconstructions, experiments have been carried out on Si(ll1) surfaces with overlayers of Ge. At low coverages, a 7x7 pattern is seen and x-ray standing wave measurements seem to show that Ge atoms bond to the rest atoms and then on top of the adatoms (ref. 120). At both stages the underlying structure remains the same and gives rise to the 7x7 LEED pattern. At thicker coverages, a mixing between Si and Ge takes place, but a well ordered 5x5 LEED pattern is observed. A transmission electron diffraction study of Si(ll1):Ge 5x5 has shown that it has an atomic structure comparable to the DAS model. (ref. 121). In a recent ARPES and k-resolved inverse photoemission study, dispersions for both Si(ll1):Ge 7x7 and Si(ll1):Ge 5x5 have been compared with those for Si(lll)7x7 (ref. 122). In all cases, one unoccupied and three occupied surface states were seen and the dispersions for the different surfaces were all qualitatively similar. An example of the comparison between Si(111)7x7 and Si(ll1):Ge 5x5 is shown in Fig. 16. The surface states for Si(111)7x7have been correlated with the atomic structure on the basis of STM spectroscopy (ref. 123) and total energy calculations (ref. 124). The unoccupied S and occupied S1 state are assigned to dangling bonds on the adatoms , S2

46 1

,

I

x

D

x

kiil-

lXRx

F!

s,

r

R

-

l10il

WAVE VECTOR

Figure 1 6 Experimental band dispersions for Si(111)7x7 (crosses) and for Si(1ll):Ge 5x5 (squares). The figure is from ref. 122.

to the dangling bonds on the rest atoms and S3 t o back bond states. The equivalent states for Si(ll1):Ge 5x5 are labelled B, B1, B2 and B3 respectively in the figure. It was found that the Si(ll1)Ge 5x5 and Si(ll1):Ge 7x7 surfaces were more similar to one another than they were to the clean Si(111)7x7 surface, indicating that the Ge content of the surfaces is more important than the periodicity. 5.3 Thick metal films on semiconductors In general, there has not been much ARPES work on thick metal films on semiconductors because most do not grow epitaxially and thus do not have an ordered structure. Ag and Au films on Si(ll1) and the metal silicides appear to be exceptions to this rule and will be discussed in this section. 5.3.1 A ~ a n Auon d Si(ll1) Most of the work has been carried out for Ag films where it is found that the (111) plane of the Ag is parallel to the (111)plane of the Si substrate. The lattice constants of Ag and Si are different so this type of growth is referred to as “parallel epitaxy”. One of the earlier investigations by McKinley et a1 (ref. 125) found that the Ag grew in the Stranski-Krastanov mode as islands on top of a stable layer about one monolayer thick

462

until a thicker film formed as a single crystal with the alignment described above. They also found that there was little interdiffusion between Ag and Si atoms a t the interface. Finally. McKinley et a1 showed that the Fermi energy of the surface did not shift after the Ag deposition, suggesting that for n-type Si the Schottky barrier height is equal to the band bending of the clean Si(lll)2xl surface. It has also been found that the emission from the Ag film on Si(ll1) had 6-fold symmetry in contrast to the 3-fold symmetry seen for single crystal Ag samples (refs. 125,126). This was taken to indicate that the Ag film formed in domains which were rotated by 60" relative to one another. More recently, normal emission ARPES measurements have been camed out as a function of photon energy for a 1.6 nm film of Ag on Si(ll1) and the results obtained were compared with a band structure for Ag (ref. 127). A good qualitative agreement was found for the relatively flat bands in the band structure. Measurements for offnormal directions do not seem to show much dispersion (ref. 128)compared with results for Ag layers grown on Ni and Cu which are also incommensurate substrates for Ag. Core level spectroscopy measurements have also been carried out for thick Ag and Au films on S i ( l l l ) , Ge(ll1) (refs. 129) and it was found that intermixing between Au and the Ge substrate was stronger than in the Ag on Ge case. 5.3.2 Metal silicides Thick, metallic epitaxial films can be formed on Si by reacting some metal atoms with a clean Si substrate. These so-called metal silicides are of potential importance for Si integrated circuits, both as good metallization materials and because of their promise as a component of three-dimensional circuits. The silicides are typically grown by evaporating metals onto the Si surface and then annealing them so that the Si and metal atoms react to form the silicide compound. Co-evaporation of the metal and Si atoms is also used. In general there are several compositionspossible, with the final one in an annealing cycle being the most Si-rich. For Co on Si(lll), for example, CosSi, CoSi and CoSi2 are formed as the annealing of thin Co films proceeds, with CoSi2 being the stable structure after a long anneal. A significant amount of work has been carried out t o understand the growth mechanism of the silicides and a great variety of experimental techniques has been used. Normal emission ARPES has been utilized in several instances but usually not in a way which examines the band dispersion. For several silicides it has been found that there is little band dispersion in the bulk silicide material (see ref. 130 for PdzSi and ref. 131 for CoSia, for example). This has been attributed to incomplete epitaxy leading to a loss of long-range order and to the large unit cell in the case of Pd2Si (ref. 130). For float-zone grown single crystal VsSi, dispersing bands have been found and compare favorably with band structure calculations (ref. 132). Surface state dispersions have been observed for a Co-rich outer layer on CoSi2 (ref. 131). After the usual preparation technique, CoSi2 has a Si-rich outer layer with either one or two monolayers of Si atoms. An alternative bulk termination would have

463

a Co outer layer. To get a Co-rich surface, Pirri et a1 (ref. 131)evaporated a n extra Co layer onto a previously formed CoSi2 film and then annealed it at a lower temperature than that which is used to form the silicide. The normal-emission spectra for the Si-rich and Co-rich films were then found to be substantially different providing good evidence that the Co was not incorporated into the bulk of the silicide. In contrast to the Si-rich case, the Co-rich surface exhibited strongly dispersing surface bands.

6. SUMMARY ARPES is a powerful tool for understanding thin films and interfaces. In cases where a full angle-dependent series of spectra are compared with calculations of band dispersions, detailed structural determinations can be made. Many of these cases have been discussed in detail. The origins of the dispersing surface states, bonding states or interface states are summarized below for examples of the systems discussed. Examples have also been given i n which the use of heteroepitaxy has allowed ARPES to measure the bulk bands of otherwise unstable materials and to examine the effect of strain on bulk band properties. The variety of the information achievable is evident in the summary table.

System

Origin of dispersing band

Ge(ll1):H Si(ll1):Cl Ge(ll1):As Si(100):As Ge(100):S GaAs(ll0):Sb Si(ll1):Al Si(111):Sn Si(ll1):Ag Si(ll1):GaAs Si(ll1 ) : C a F ~ a-Sn GaAs(ll0):Fe Si(ll1):Ge Silicides

Ge-Hband

+

Cl-C1 band Si-C1band As lone pair band As dimer band S lone pair non-dispersing Ge-S band Sb-Ga band, Sb-As band and Sb-Sb band Si-A1band Si-Sn band non-bonding d electrons + unknown band As lone pair band Ca-Si interface band Bulk bands of a-Sn spin polarized Fe band structure strained surface band bulk and surface bands for silicides

+

Table 1: Examples of dispersing states seen in ARPES of thin films on semiconductors, and their origins.

464

7. ACKNOWJ-,EDGEMENTS I am grateful for discussions on the subject over the past few years with many collaborators. They include: H. Hochst, L. Ley, R. Z. Bachrach, J. E. Northrup, R. I. G. Uhrberg, M. A. Olmstead and D. J. Chadi. 8. REFERENCES 1 2

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S.-B-.DiCenzo, P. A. Bennett, D. Tribula, P. Thiry, G. K. Wertheim and J. E. Rowe, Phys. Rev. B, 31 (1985) 2330-2337. T. Yokotsuka, S.Kono, S. Suzuki and T. Sagawa, J. Phys. SOC. Jpn., 53 (1984) 696701. A.Cros, F. Houzay, G. M. Guichar and R. Pinchaux, Surf. Sci., 116 (1982) L232L236. R. J. Wilson and S. Chiang, P h s. Rev. Lett., 58 (1987) 369-372 E. J. van Loenen, J. E. Demuti, R. M. Tromp and R. J. Hamers, Phys. Rev. Lett., 58 (1988) 373-376. R. J. Wilson and S. Chiang, Phys. Rev. Lett., 59 (1987) 2329-2332. S. Kono, K. Higashi ama, T. Kinoshita, T. Miyahara, H. Kato, H. Ohsawa, Y. Enta, F. Maeda and $ Yaegashi, Phys. Rev. Lett., 58 (1988) 1555-1558. F. Houzay, G. M. Guichar, A. Cros, F. Salvan, R. Pinchaux and J. Derrien, Surf. Sci., 124 (1983) Ll-LS. T. Yokotsuka, S. Kono, S. Suzuki and T. Sagawa, Surf.Sci., 127 (1983) 35-47. F. Houzay, G. M. Guichar, A. Cros, F. Salvan, R. Pinchaux and J. Derrien, J. Phys. C, 15 (1982) 7065-7072. J. F. van der Veen, L. Smit, P.K. Larsen, J. H. Neave and B. A. Joyce, J. Vac. Sci. and Technol. 21 (1982) 375-379. J. R. Patel, P. E. Freeland, M. S. Hybertsen, D. C. Jacobson, and J. A. Golovchenko, Ph s. Rev. Lett. 59 (1987) 2180- 2183. W. A. Harrison, . A. Kraut, J. R. Waldrop and R. W. Grant, Phys. Rev. B, 18 (1978) 4402-4410. J. E. Northrup, Phys. Rev. B, 37 (1988) 8513-8515. J. E. Northrup, R. D. Bringans, R. I. G. Uhrberg, M. A. Olmstead and R. Z. Bachrach, Phys. Rev. Lett., 61 (1988) 2957-2960. P. Perfetti, D. Denley, K. A. Mills and D. A. Shirley, in B. L. H. Wilson (Editor), Proc. 14th Int. Conf. on the Physics of Semiconductors, Edinburgh, U.K., September 1978, Institute of Physics, Bristol, London, 1979, pp. 1081-1084. P. Zurcher, J. Anderson, D. Frankel and G. J. Lapeyre, Physica, 117B and 118B (1983) 857-859. F. J. Himpsel, F. U. Hillebrecht, G. Hughes, J. L. Jordan, U. 0. Karlsson, F. R. McFeely, J. F. Morar and D. Rieger, A pl. Phys. Lett., 48 (1986) 596-598. M. A. Olmstead, R. I. G. Uhrberg, R. $. Bringans and R. Z. Bachrach, J. Vac. Sci. and Technol., B4 (1986) 1123-1127. D. Rie er, F. J. Himpsel, U. 0. Karlsson, F. R. McFeely, J. F. Morar and J. A. YarmogPhys. Rev. B, 34 (1986) 7295-7305. M. A. Olmstead, R. I. G. Uhrberg, R. D. Bringans and R. Z. Bachrach, Phys. Rev. B, 35, (1986) 7526-7532. M. A. Olmstead, R. D. Bringans, R. I. G. Uhrberg and R. Z. Bachrach, Mat. Res. SOC.S mp. Proc. 94 (1987) 195-200. R. M. !r omp and M. C. Reuter, Phys. Rev. Lett., 61 (1988) 1756-1759. U. 0. Karlsson. F. J. HimDsel. J. F. Morar. F. R. McFeelv. D. Rieeer and J. A. ” Yarmoff Phys. Rev. Lett., 57 (1986) 1247-1250. A. B. McLean and F. J. Himpsel, Phys. Rev. B, 38 (1989) 1457-1460. J. E. Northru J. Vac. Sci. and Technol., A4 (1986) 1404-1406. R. Z. Bachrack, J. Vac. Sci. andTechnol.15 (1978) 1340-1343. A. Hui’ser, J. van Laar and T. L. van Roo ,Surf. Sci., 102 (1981) 264-270. A. Mcdinley, G. 3. Hughes and R. H. W i l h m s , J. Phys. C 15 (1982) 7049-7063.

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108 A. McKinley, A. W. Parke and R. H. Williams, J. Phys. C 13 (1980)6723-6736. 109 S. P. Svensson, J. Kanski, T. G. Andersson and P. 0. Nilsson, Surf. Sci., 124 (1983) L31-L34. 110 J. Hwang, P. Pianetta, G . D. Kubiak, R. H. Stulen, C. K. Shih, Y.-C. Pao, Z.-X. Shen, P. A. P. Lindberg and R. Chow, J. Vac. Sci. and Technol., B6 (1988) 12341239. 111 R. F. C. Farrow, D. S. Robertson, G. M. Williams, A. G. Cullis, I. M. Young and P. N. J. Dennis, J. Crystal Growth, 54 (1981) 507-518. 112 J. R. Chelikowsky and M. L. Cohen, Phys. Rev. B, 14 (1976) 556-587. 113 H. Hochst and I. Hernandez-Calderon, J. Vac. Sci. and Technol., A3 (1985) 911914. 114 M. Tang, D. W. Niles, I. Hernandez-Calderon and H. Hochst, Phys. Rev. B, 36 (1987) 3336-3343. 115 H. Hochst, D. W. Niles and I. Hernandez-Calderon, J. Vac. Sei. and Technol., B6 (1988) 1219-1223. 116 G. A. Prim, E. Kisker, K. B. Hathaway, K. Schroder and K.-H. Walker, J. Appl. Phys., 57 (1985) 3024-3026 117 K. Schroder, G. A. Prim, K.-H. Walker and E. Kisker J. Appl. Phys., 57 (1985) 3669-3671. 118 K. Takayanagi, Y. Tanishiro, M. Takahashi and S. Takahashi, J. Vac. Sci. and Technol., A3 (1985) 1502-1506. 119 R. S. Becker, J. A. Golovehenko and B. S. Swartzentruber, Phys. Rev. Lett., 54 (1985) 2678-2680. 120 B. N. Dev, G. Materlik, F. Grey, R. L. Johnson and M. Clausnitzer, Phys. Rev. Lett., 57 (1986) 3058-3061. 121 K. Takayanagi, Y. Tanishiro and K. Kajiyama, J. Vac. Sci. and Technol., B4 (1986) 1074-1078. 122 P. Mdrtensson, W.-X. Ni, G. V. Hansson, J. M. Nicholls and B. Reihl, Phys. Rev. B, 36 (1987) 5974-5981. 123 R. J. Hamers, R. M. Tromp and J. E. Demuth, Phys. Rev. Lett., 56 (1986) 19721975. 124 J. E. Northrup, Phys. Rev. Lett., 57 (1986) 154-157. 125 A. McKinley, R. H. Williams and A. W. Parke, J. P h s C 12 (1979) 2447-2463. 126 M. Hanbiicken, H. Neddermeyer and P. Rupieper, d k n Solid Films, 90 (1982) 3742. 127 A. L. Wachs, T. Miller and T.-C. Chiang, P h s. Rev. B, 29 (1984) 2286-2288. 128 A. P. Shapiro, T. C. Hsieh, A. L. Wachs, T. biller and T.-C. Chiang, Phys. Rev. B, 38 (1988) 73947407. 129 A. L. Wachs, T. Miller, A. P. Shapiro and T.-C. Chiang, Phys. Rev. B, 35 (1987) 5514-5523. 130 G. W. Rubloff, P. S. Ho, J. F. Freeoufand J. E. Lewis, Phys. Rev. B, 23 (1981) 41834196. 131 C. Pirri, J. C. Peruchetti, D. Bolmont and G. Gewinner, Phys. Rev. B, 33 (1986) 4108-4133. 132 M Aono, F. J. Himpsel and D. E. Eastman, Solid State Commun., 39 (1981) 225228.


469

Chapter 12 SPIN-AND ANGLE-RESOLVEDPHOTOEMISSIONFROM FERROMAGNETS E. KISKER AND C.CARBONE

1. INTRODUCTION Considerable progress has been achieved in recent years in the development of experimental techniques, based on electron spectroscopy and electron scattering, capable of explicitly detecting spin information. We review the recent developments of the technique of spin- and angle-resolved photoemission (SPARPES) from ferromagnets. SPARPES gives detailed information on the spin-split bulk and surface electronic structure of a ferromagnetic system. The electronic structure of a ferromagnet is characterised by a spinsplit density of states with an excess of electrons o f one spin direction. They are referred to as "majority-spin" ( t ) electrons, those of opposite spins as "minority-spin" (1) electrons. Fig.1 shows the Fe band structure as

Fig. 1. Calculated band structure o f Fe along high-symmetry directions (after Hathaway et al. / l / ) . Solid (broken) lines indicate majority- (minority-) spin bands.

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calculated by local spin density functional theory / l / . In the ferromagnetic state, bands for electrons with their magnetic moments parallel to the magnetization direction differ from those of electrons with opposite magnetic moments. In an approximative description, the two sets of bands are shifted rigidly in energy by the so-called exchange splitting A . For Fe, A 2: 2 eV (cf. Fig.1). To determine experimentally the electronic structure of magnetic materials, the spin information from the photoemitted electrons has to be determined. This has been done first in 1969 by Busch et al. /2/ in threshold photoemission from Gd. Spin- and anale-resolved photoemission on Fe and Ni was performed not earlier than 1983 /3-5/. Most of the work performed until now by SPARPES has been devoted to the study of the valence band structure of ferromagnetic 3d metals at temperatures well below their Curie temperature. However, a fundamental topic in ferromagnetism concerns the question how temperature affects the electronic structure when approaching the Curie temperature (Tc). The theoretical task to include thermal effects is complicated because of the lack of translation geometry in spin space. The models which have been developed so far are less generally accepted than those for the ground state electronic structure, and have been, in fact, matter of strong controversies. Also the core levels are of great interest for a detailed understanding of the electronic structure of solids. One of the most studied core levels by photoemission are the 3s levels of Fe and Mn. They exhibit a doublet structure in the case of metallic Fe, a-Mn and their compounds /6/. This feature has been interpreted as being related to multiplet terms originating from the direct exchange interaction between the 3s core hole and the 3d valence electrons. Within a simple atomic picture the two components would then be characterized by a strong spin polarization /6,7/ which should be opposite to each other. Use of the expected spin polarization of the Mn 3s multiplet components has been made in spin dependent photoelectron diffraction /8/. Genuine spin-resolved core level photoemission, however, has been performed only recently /9/, since the cross sections are small. Multi-electron effects such as resonances and Auger processes also show often a strong spin dependence. Near the core level excitation threshold resonant photoemi ssion and resonant Auger emission are observed when the core electron is excited into a fairly localized unoccupied state. Spin effects have been observed also in these cases since the empty states of a ferromagnetic material are spin split by the exchange interaction. Related to the resonant Auger electron emission are the valence band satellites,

471

with the well known example of the 6 eV satellite in Ni. Auger structures are often characterized by a complex polarization / l o / . The electronic and magnetic properties of the surface may significantly differ from those of the bulk. Because o f the high surface sensitivity and its energy dependence in VUV- and soft X-ray photoemission (20-100eV photon energy) both the surface and the bulk electronic structure can be studied. The small probing depth of the photoemitted electrons also allows study of the interplay between electronic and magnetic character of ultrathin films in the monolayer regime and of interface systems. In the following paragraph we summarize the basic principles of spin-resolved photoemission. The third paragraph presents a selection o f experimental results obtained by spin- and angle-resolved photoemission. The main aim there is to illustrate the rather wide range of application and the future perspectives of this experimental technique.

2. THE PRINCIPLES AND METHODS OF SPIN- AND ANGLE-RESOLVED PHOTOEMISSION Angle-resolved photoemission has been discussed in detail in chapters 1-3 o f this monograph. The most simple situation arises for normal emission. In this case the direction of the electron wave vector is the same inside and outside the solid. Most of the spin-resolved photoemission experiments have therefore been performed for normal emission.

2.1 Spin Detection

Either relativistic spin-orbit or quantum mechanical exchange interactions have to be used for spin analysis. The first of these methods has been most commonly applied and is called Mott scattering. Its physical principles are described i n detail elsewhere / l l / . The spin polarization P, is defined as P~=(N~-N~)/( N ~ + N J) N f are the numbers of electrons with their magnetic moments parallel or antiparallel to the quantization (z-) axis. In general, the spin polarization is a three dimensional vector (p). However, in many cases, one has deal with only one component of p by chosing the quantization axis parallel to the magnetization direction of a ferromagnetic sample. In scattering a polarized beam from a target, spin orbit interaction results in a left-right intensity asymmetry A(P) if the polarization vector has a component perpendicular to the scattering plane. The asymmetry i s detected by a pair of elec-

472

tron detectors which are placed symmetrically under suitable angles to the left and to the right side of the scattering target. The scattering asymmetry A(P) is defined as A(P)=(Nl-Nr)/(N1+Nr)

(2)

where N I , ~are the numbers of electrons detected in the detectors to the left and to the right side with respect to the incoming beam, respectivley. In so-called high-energy Mott scattering, a thin Au film of thickness d i s commonly used as a target on which the primary beam, accelerated to about 100 keV, is scattered to determine its spin polarization. The asymmetry in the intensity of the electron beam backscattered at angles of typically +1200 (where the spin sensitivity is largest near 100 keV energy) is measured by a pair of surface barrier detectors. The spin polarization is obtained from the asymmetry by the relation P=l/S(d) A (3) Here, S(d) is the so-called effective Sherman factor, which depends on the thickness of the scattering foil because of multiple scattering. S depends also on energy and on scattering angle. It is largest for scattering nuclei with large atomic number Z . For d=O only single scattering events have to be considered. For this case, the Sherman factor S has been calculated as S=0.39 at E=120 keV and 0=51200 /12/. Multiple scattering occuring in targets of finite thickness is difficult to take into account quantitatively. Therefore, S for a given scattering foil is determined experimentally by measuring the scattering asymmetry A with a beam of constant polarization for a set of films with different thickness, and extrapolating 1/A towards d=O. Since S(0) is known from calculations, the polarization P can be determined, and hence S(d) for each foil. The value of S is typically between 0.2 and 0.3 for gold f o i l s of about 1000 A thickness. With one pair of detectors, only one component of the spin polarization vector can be determined. A second pair of detectors with a scattering plane perpendicular to the first one can be installed easily for measuring the second transverse component of p. Measuring the third (longitudinal) component requires more effort. This component has to be rotated to a transverse one prior to Mott scattering. The low intensity of the scattered beams is the problem which has restricted the application of spin analysis to a limited number of experiments so far. The beams scattered into the collection angles of the electron detectors amount typically to some of the incoming electron beam. As a figure of merit of a spin polarimeter the quantity M=S2 I / I o , where I and I. respectively are the primary and the detected (scattered) beam intensities,

473

is commonly considered. M is only of the order of 10-4 for spin polarimeters know so far (for a recent improvement, see "Notes Added in Proof").

Mott detectors operating at about 100 keV scattering energy usually have the scattering chamber floated at the high voltage. Therefore, sufficiently large gaps to the surrounding electric shieldings have to be provided. With concentric cylindrical designs o f the scattering chamber and o f the shieldings, the dimensions of the spin detector are about 1 m in diameter and 1 m in length. Smaller Mott detectors are desirable and have been used. They operate generally at lower high voltages, i.e. several tens of keV. In some designs, a concentric arrangement of accelerating electrodes is used, and the scattered electrons are decelerated again prior to detection. Instead of surface barrier detectors, channeltrons can be used for electron detection in this case /13/. Spin-orbit interaction i s also observed in low-energy electron scattering at energies of the order 100 eV / l l / . A spin polarimeter based on spin polarised low energy diffraction from a W single crystal has been characterized by Kirschner and Feder /14/. Low energy scattering from polycrystalline Au has been characterized and by Unguris et al. /15/. A compilation of parameters on different spin detectors i s also given in ref.15. When the photoelectron spin is analysed in photoemission, two energy distribution curves (EDCs) are obtained for ferromagnets, one for the

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474

majority-spin electrons (If(EB)), and a second one for the minority-spin electrons ((It(EB)). Here EB is the binding energy. These two curves are referred to as the spin-resolved energy distribution curves (SREDCs). From the spin polarisation curve P(EB) as calculated with help of equ.3 together with the spin-averaged intensity curve the SREDCs can be calculated as I ? 1 4 ( EB)=O. 5 I(, EB) (l+P( EB) ) (4)

2.2. Experimental Systems

Various kinds of light sources have been employed: high pressure arclamps, rare gas resonant lamps and synchrotron radiation. Synchrotron radiation is now more widely accessible and has the advantage of producing intense, bright and continuously tunable light. Fig.2 shows a sketch of an experimental set- up for spin- and angle-resolved photoemission used in Berlin at the storage ring BESSY 116/. Monochromatized synchrotron radiation is reflected by a plane mirror onto the sample at normal incidence. The electrons emitted from the sample surface at a given angle are then analysed as a function of their kinetic energy by a multi-lens system with a 900 spherical condensor which acts as a dispersive element. The spectrometer is fixed in space, but the emission angle can be chosen by tilting the sample. Behind the exit slits of the analyser the electron beam is accelerated to 100 keV and enters the Mott scattering chamber for performing the spin analysis. With the experimental set-up shown above, a typical counting rate of lel/sec per mA of storage ring current was obtained in the backscattering electron counters from Fe 3d valence band states at 30-60 eV photon energy with a toroidal grating monochromator. A specific problem in spin- and angle-resolved photoemission concerns the magnetization of the samples. The size of the ligth spot and the analyzer acceptance area are typically larger than a single Weiss domain of a demagnetized sample. Accordingly, the samples have to be magnetically saturated within the sampled surface area to avoid (trivial) spin mixing due to electron emission from several macroscopic domains with different magnetization direction. To obtain magnetic saturation, in the earliest spin-resolved photoemission experiments /2/, the samples were immersed in an external magnetic field directed perpendicular to the electron emission direction ("longitudinal magnetization configuration"). The longitudinal magnetic fields however set limits to the attainable angle and energy resolutions 1171. It turned out that the most convenient way to bypass

475

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Fig. 3: (a) Spin-averaged, angle-resolved EDC from Fe(001) a h ~ 6 eV, 0 for normal emission and normal incident light. (b) Spin polarization curve measured simultaneously with the data of fig.3a. (c) Spin- and angle-resolved EDCs, corresponding to the data of fig.3a,b. the problem is to use the so called "transverse magnetization geometry", with the magnetization vector parallel to the sample surface and perpendicular to the electron emission direction /18/. Samples of suitable shapes, such as thin single crystal plates, picture frame shaped crystals or epitaxial films can be remanently magnetized in-plane, i.e. they remain magnetically saturated over a large enough surface area after the removal of the external magnetizing field and proved to be useful even for low-energy threshold photoemission /19/. The spin- and angle-resolved energy distribution curves are measured at a fixed photon energy for a given emission angle by recording simultaneously the signal from the two electron detectors in the spin polarimeter. The spin integrated signal from the electrons transmitted through the gold foil is

476

measured by a third detector placed directly behind the scattering foil. A voltage ramp is applied to the sample or to the spectrometer electrodes to scan the photoelectron energy. The results from the three measurement channels can be presented either in the set of data for the intensity and the spin polarization vs. energy, or as the two spin-resolved energy distribution curves (equ.4). As an example, Fig.3a shows a spin-integrated spectrum from Fe(100) at 60 eV photon energy, as recorded by the electron detector directly behind the scattering foil. Fig.3b in the same panel shows the spin polarization as a function of the electron initial state energy, for the data points of the EDC. Fig.3~ shows the SREDCs. These curves, for fully magnetized samples at low temperature, often allow a direct identification of the spin character of each feature which appears in the spin integrated EDC. The results shown in Fig.3~allow direct determination of the exchange splitting at the I",,t*J critical point as it will be discussed further in the section 3.1.lb.

3. SELECTED RESULTS 3.1 Fe(001) 3.1.1. Low Temperature Electronic Structure a) Photothreshold experiments Spin-resolved photothreshold measurements on Fe( 111) have been performed by Eib and Reihl /20/. The data are shown in Fig.4. The spin-polarization is positive at the photothreshold, decreasing at higher photon energies. The large positive threshold polarization is consistent with the Fe electronic structure along T-X. However, since both majority spin and minority spin bands are crossing the Fermi energy /1/ the quantitative interpretation of the experimental data is not straightforward.

b) Soin- and ansle-resolved experiments

Fig.5 is a collection of spin-resolved EDCs for normal emission from an Fe(001) surface, measured at various photon energies with s-polarised light /16/. In this geometry, the initial state wave vector is varied along the high symmetry direction T-H in the Brillouin zone. One sees that the relative weight of majority to minority-spin intensity near EF depends strongly

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Fig. 4: Spin-resolved threshold photoemission from Fe(ll1) (after ref. 20). on photon energy. At h ~ 6 0eV, the minority-spin peak is much larger than the majority-spin one (see also fig.3). At lower photon energy (~$30eV), the minority-spin peak vanishes, and a majority-spin peak dominates the spectrum at 20 eV. This is an indication for the observation of band dispersions in Fe. Dipole selection rules /21/ indicate that only transitions from the A5-symmmetry bands are allowed for s-polarized light and for normal emission, which are the conditions for the spectra in fig.5. The data can be understood by considering the change in initial state wave vector when the photon energy decreases from 60 to 20 eV. From the final state band dispersion which is shown in Fig.6 /22/ one would expect emission from initial states near r, at hv=60 eV. Then just the As- minority-spin band near Ep is excited. At 20 eV photon energy, the transition takes place near H. In this case, the 4 5 majority-spin band has reached EF, whereas the corresponding minority-spin band has already crossed through Ep. How well SREDCs taken at 60 eV photon energy compare with the band structure is seen best in Fig.7. Top of Fig.7 shows the valence band structure along P H . The binding energy of the peaks in the SREDCs (Fig.7, bottom)

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Fig. 5: Spin- and angle-resolved photoelectron energy distribution curves from Fe(100) with the photon energy varied between 20 and 60 eV. Top: Majority-spin EDCs. Bottom: Minority-spin EDCs. In each pair of majorityand minority-spin EDCs, the height of the larger ’peak,whichever is the largest, is normalized to 10 units. Indicated are also critical point energies of the sampled A5-symmetry bands (after ref. /16/). Fig. 6: Majority (---- and minority ( - - - - ) spin bulk band structure of Fe along A . The energy is referred to EF; the upper panel (for E>EF) shows only the A , symmetry bands, which are relevant for the final state in normal photoemission. Perpendicular arrows su gest direct transitions at the photon energies indicated next to the arrows ?after ref.22). agree quite well with the critical point energies at r. The majority-spin peak at 2.5 eV binding energy and the minority spin peak at 0.2 eV below EF are the pair of exchange split states at I"f25 and T’J25. The other peak in the majority spin EDC, at 2.1.2 eV below EF, corresponds to the emission from fl12which, though forbidden under ideal conditions, still contributes to the spectra. The reason for its occurence may be attributed t o experimental imperfections, e.g., incomplete 1 ight polarization and limited angular resolution. The minority-spin peak near EF is very narrow in energy. Also, its

479

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Fig. 7: Top: Part of the band structure of Fe along A in the vicinity of EF. Bottom: SREDCs from Fe(001) at 60 eV photon energy. The peaks are labeled with the critical point signatures. Fig. 8: Angle-dependent EDCs from Fe(001) at hv=60 eV for s-polarized light with the emission angle varied between 0 and 250. angular distribution is very sharp. Fig.8 shows spin-averaqed EDCs as a function of emission angle, for s-polarized light /23/. The sharp peak near EF vanishes already at 50 emission angle, and instead a peak near 1 eV becomes dominating. This is probably emission from T12fwhich becomes dipoleallowed for off-normal emission. The sharp feature for normal emission near EF is very useful for tuning the electron spectrometer for optimal angle and energy resolution. A1 1 the essential features of the experimental data have been reproduced by quantitative theoretical calculations using a non-relativistic Green’s function formalism on the basis of a one step model /22/. The observed exchange splitting at r is 2.4 eV. This value is considerably larger than predicted for bulk Fe(001) (2.0 eV) (see, e.g., ref.1). In view of the well-known strong surface sensitivity at energy around 60 eV (which has also been inferred directly from the measurement of the spin polarisation vs. temperature, see section 3.1.2 below), it could be expected that the data exhibit the predicted enhanced exchange splitting of surface resonances at f, the center of the 2D Brillouin zone /24/. Actually, the positions of the exchange-split states, considering the finite energy reso-

480

lution, agree quantitatively with calculated band energies at r of the first two layers /23/. It had also been suggested by Durham et al. /25/ that the large exchange splitting might be caused by an enhanced surface exchange splitting. 3.1.2. Finite temperature effects The effect of an increase in temperature is macroscopically evidenced in a decrease of the spontaneous magnetization M,=M(T)/M(O) which vanishes at the Curie temperature. I f the electronic structure would not change, it is expected that the spin polarization curve would be reduced uniformly as PT(E )=PT=o (E 1% (5) If the electronic structure would change also, e.g. with a decrease of the exchange splitting, the simple scaling behaviour (equ.6) would not apply and the PT(E) curve (T>O) might i n principle be of different shape as compared to the PT=o(E) curve. For the electronic structure of the 3d-metals at finite temperatures controversial models have been discussed /26/. The fundamental issue on itinerant ferromagnetism is: Is the reason for the decrease of long-range magnetic order a uniform decrease of magnetic moment (’Stoner model’) or is the magnetization reduced because local magnetic moments tend to fluctuate in direction? If the latter applies, a question is on the value of the local moments at elevated temperatures and on the spatial extent of the microscopic regions over which the magnetization direction is more or less constant. If the Stoner model is valid, the exchange splitting, as observed in photoemission, should decrease with temperature in proportion to the magnetization, and become zero at and above Tc. If a local moment model applies, the changes in the photoemission spectra would depend on the range of magnetic correlations. I n the limit of very large magnetic clusters it is expected that the electronic structure locally is similar to that in the ground state even at elevated temperatures. This limit i s referred to as the ’fluctuating band model’, as defined by Korenman, Murray, and Prange /27/. If there is no correlation between neighboring local magnetic moments, the ’disordered-local-moment’model would apply /28,29/. As a result of the strong spin disorder above Tc, an electronic structure quite different from that at low temperatures would result. In general, in the fluctuating band model and in the disordered local moment picture the behaviour of the band

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O = EF

BINDING ENERGY ( e V 1

Fi 9: The temperature dependence of the spin polarization curve from Feg001) at hv=60 eV. Fig.10: Spin polarization of photoelectrons from Fe(100) at fixed binding energy (2.6 eV) as a function of temperature at 60 eV photon energy and comparison with a layer-dependent meanfield calculation. splitting at elevated temperatures depends on their symmetry. Collapsing and non collapsing splittings at Tc might occur in the same material /27-29/. It is clear that by measuring the spin-resolved energy distribution curves as a function of temperature, one should be able to distinguish between the different models. Complications might arise due to the largely unknown influence o f phonon effects on the photoelectron spectra /30/. The exchange splitting at room temperature of Fe(001) is evidenced directly in the spin-resolved photoemission spectra in Fig.6b. For Fe, room temperature corresponds to T/Tc=0.28. The magnetization of the bulk has decreased from the T=O value only by about 5%. Therefore, the room temperature spectra correspond to a good approximation to the low-temperature electronic properties. The changes occurring in the spin polarization data at elevated temperatures are shown in Fig.9 /23/. It is seen that the spin polarization curve scales down with increasing temperature. The small hump in the curve for T=0.85 Tc at 4.5 eV binding energy is attributed to segregation of impurities to the surface during the measurements. Notably, the energy where the

482

r:s.

10 Fe 1100) hv = 60 eV ATr-0.3 A V r: 0.05

za

v)

2

0 4 2 ENERGY BELOW EF

0 (eV)

-

.

INITIAL STATE ENERGY lev)

Fig. 11: Spin- and angle-resolved photoelectron energy distribution curves from Fe(100) for emission centered around the surface normal and predominantly s-polarized light, at two temperatures (T=0.3 T, and T=0.85 T,). The photon energy is 60 eV and the initial states are near r /32/. Fig . 12: Calculated spin-resolved photoelectron energy-distribut ion curves obtained by a cluster-calculation for initial states near ’I and two different temperatures (T = 0.85 Tc and T>T ) . The short-range order parameter p is varied between 0 and 5.4 /36?. spin polarization crosses through zero does not change with temperature. This can be interpreted in terms of the decrease o f M, as explained above. The dependence of spin polarization on temperature measured at constant binding energy differs from the decrease of M, of the bulk, as shown in Fig.10 /16/. The data follow better a curve for the dependence of surface magnetization on temperature. The decrease of polarization fa1 1s in between the M,-curves for the the first and second layer, calculated in mean field approximation /31/. This fact is not surprising in view of the small probing depth of 60 eV-electrons. The complete information from the spin-resolved photoemission experiment is represented by the SREDCs which are displayed in Fig.11 for two temperatures, one taken at room temperature, and a second one at T/Tc=0.85 /32/. The most important information, not obtainable with spin-integrated photoemission, is the emergence of a new ("extraordinary") peak in the minorityThe latter is spin SREOC at the position of the majority-spin peak I''25f. simultaneously reduced in intensity by about the same amount as the minority-spin intensity increases at the same binding energy. The new peak has no

483

.

correspondence to the ground state electronic structure 133,'. This is evidence for the existence of regions which are magnetized in different directions than the remanent magnetization. If these regions were relatively large, the electronic structure in each o f them would resemble the lowtemperature electronic structure. Because of the spread of the magnetization directions, mixing of the SREDCs occurs with the result that for each primary peak an image is observed in the SREDC of opposite spin. A sum rule holds for the intensity at any binding binding energy in this simple picture. At the position of r’z5t, the sum rule is more or less fulfilled, but not at the position of TIz5( near EF. A reason for the strong decrease in intensity near EF at elevated temperatures is the broadening of the photoemission cone /16/. This indicates that the disorder at elevated temperatures influences the electronic structure. The data (Fig.10) evidently contradict the expectations from the Stoner model at elevated temperatures. They also contradict predictions from the Disordered-Local-Momentmodel /34/ that the splitting of A5-symmetry-bands collapses Stoner-like. The data resemble better the expectations from the local band model /35/. A more quantitative picture of the electronic structure at elevated temperatures was obtained by comparing the experimental data with the results of a theoretical model calculation /36/. The electronic structure is calculated in a tight-binding approximation within a model based on the existence of spin correlations with parametrized correlation length. Fig. 12 shows the photocurrent spectra calculated for a bcc lattice cluster of 2000 atoms for two temperatures, corresponding t o T/Tc=0.85 and T/Tc>l, for three values of the correlation length parameter A. For A=O, the "collapsing" peaks at T/Tc are nicely revealed, whereas for A=5.4 A, the exchange splitting remains almost constant up to T/Tc. The extraordinary peaks are visible only for d>4w. By comparing with the experimental data, it is concluded that the spin correlation length must be larger than 4 A /36/.

3.1.3 Core-level spectroscopy

A first principles theory of core level photoemission from magnetic 3d transition metals has to deal with the difficulty of describing the physical situation properly, taking into account the itinerant character of the 3d electrons. This is generally described in terms of the ratio U/W, where U is the intraatomic Coulomb interaction and W the bandwidth / 3 7 / . An electron energy distribution curve taken at hv=92 eV over an energy

484

.t 56

I1 58

L

I

56

1

1

I

I

1

I

SL 52 50 BINDING ENERGY (eV)

I

I 48

Binding Energy lev1

Fig. 13: Spin-averaged intensity distribution (a) and simultaneous1 measured spin polarization in the vicinity of the Fe 3p emission (by. Data are taken at 92 eV photon energy with normal-incident light and for normal emission. Dashed lines indicate the assumed background intensity and polarization of inelastically scattered electrons. In the spin-polarization curve, the statistical errors are indicated /9/. Fig. 14: Fe 3p core level spin-resolved energy distribution curves obtained after background subtraction /9/. region which includes the Fe 3p emission is shown in Fig.13a /9/. Because of the low cross section for Fe 3p photoionization the Fe 3p signal is superimposed on a large background of inelastically scattered electrons. No high binding energy satellites could be identified, not even in EDCs measured over a larger energy range than that covered in Fig.13a. The small Fe 3p signal to background ratio might, however, have obscured weak features. The photoelectron spin polarization in the kinetic energy region including the Fe 3p subshell emission is shown in Fig.13b. The magnitude o f the dip in the polarization implies that the net polarization of the 3p emission at the peak position is negative and that it amounts to about 20%. After background subtraction, the spin-resolved Fe 3p SREDCs are shown in Fig.14. The minority and majority spin SREDCs have full widths at half maximum of 1.750.3 eV and 2.720.4 eV, respectively. The majority spin EDC is more asymmetric than the minority spin curve. The difference, A , in binding energies between the peaks of the two Fe 3p SREDCs is smaller than their intrinsic width. Calculations within the local spin density functional formalism predict

485

an exchange splitting of 2.5 eV for the Fe 3p states 1381, similar in magnitude to the average valence band exchange splitting. Including the relaxation shift in an impurity-like calculation using the Slater transition state the splitting between the two spin components is reduced to 1.5 eV /38/. This value is still significantly larger than the measured value (~0.5eV). An alternative approach to the understanding of core level photoemission from 3d metals may start from the atomic model of coupling via the direct exchange interaction between the localised 3d electrons and the core hole. The coupling should produce in the photoemission spectra several stuctures corresponding to various final state multiplet terms /6/. A complex pattern would then be expected for the Fe 3p photoionisation. Although this model has been applied t o the interpretation of the 3s levels in ionic magnetic 3d compounds its extension to the present case is not straightforward. The multiplet pattern is not discernable in the Fe metal 3p spectra. It could be speculated that screening mechanisms of the core hole and d electron hopping tend to wash out spin-orbit related multiplet features in photoemission from metallic Fe. The different widths of the spin-resolved Fe 3p core level lines have been interpreted in terms of spin-dependent core-hole relaxation due to the larger number of majority-spin valence electrons as compared to those of opposite spin 191.

3.1.4. Resonant Auaer emission When a core-electron is photoexcited, recombination via Auger-decay might occur. The Auger-electron energy distribution curve can be observed in the photoelectron spectra. The intensity of the Auger-distribution depends on the cross section for exciting the photoemission hole. Since the cross section for excitation of a 3p electron is large when the 3p electron is excited into the empty 3d bands, the Auger intensity has a maximum at photon energies slightly above the 3p ionization threshold. This phenomenon is referred to as a "resonant" Auger process, and has been studied for Fe, Co, and Ni 139-421. As an example, Fig.15 shows the resonant Auger-distributions occuring in the vicinity o f the Fe-3p threshold (53 eV). In the top panel, the photoabsorption cross section i s shown, which exhibits a step at 53 eV due to the 3p excitation /42/. It has been shown /42/ that the resonant Auger-contribution exhibits a

486

r-

'

'

I

"

"

T

1 Pholon E n e r d e V I

-12 -10 -a -6 - L -2 Bmding Energy 1 e V )

o

Fig. 15: (a) Dependence on photon energy of total photo-current from Fe(100). (b) Series o f energy distribution curves from Fe(100) for 200 emission angle (19) and predominantly s-polarized light at photon energies in the vicinity o f the 3p resonance /42/. Fig. 16: (a) Majority-spin photoelectron EDCs from Fe(100) at hv=56 eV and 60 eV. (b) Minority-spin EDCs. Insets show convolutions o f the spin-split DOSs for comparison with the resonant intensities near 7 eV energy /43/. lineshape which is similar to the self-convolution of the Fe valence bands. From measured spin-resolved EDCs (see Fib.16) it is concluded that the resonant Auger structure reflects convolutions between the spin-spl it DOS. The majority-spin intensity can be reproduced by convolution o f the majority spin with the minority-spin partial DOS, whereas the minority-spin distribution resembles closely the autoconvolution o f the minority-spin OOS /43/.

487

3.2. Spin-resolved photoemission from Ni 3.2.1. Low-temperature electronic structure a) Photothreshold Experiments Band structure calculations indicate that Ni is a "strong" ferromagnet, the majority spin 3d bands being fully occupied with their top separated from the Fermi energy by the so-called "Stoner gap" (6). The Stoner gap has been estimated to be of the order of 0.1 eV in Ni /44/. It is determined by the position of X,t (see Fig.17). In threshold photoemission, the spin polarization from any Ni surface should have a negative sign at the photothreshold because of the Stoner gap /44/.It should then become positive at higher photon energies because of the predominant majority-spin character of the valence bands which contribute more and more at higher photon energies due to the opening o f the photoelectron escape cone. This behavior has been predicted by Wohlfarth /44,45/and was verified in a pioneering experiment by Eib and Alvarado /46/ (see Fig.18) on Ni(100). Similar data were obtained subsequently on Ni(ll1) /47/. In the experiments on Ni(100) and on Ni(ll1) the measured polarization at photothreshold was only about -50%,although the Stoner model predicts it to This . discrepancy has been attributed to the limited bandwidth of be ~ ~ 1 0 0 % the light. The expected high negative spin polarization was actually observed in an experiment on Ni(ll0) /19/. The results are shown in Fig.19. P+

-

EV I

M

3

za

2 10

% I

-

1

>r

ol

5

C

-1 -E

-2 -2c

-3

r

K

X

~-~110~-~-~001l-~

r

-x

Fig. 17: Band structure of Ni along r-K-X and X - r (after (after /49/). Fig. 18: The measured spin polarization vs. photon energy in a photothreshold experiment on Ni(lO0) (after Eib and Alvarado /46/). @ indicates the photothreshold.

488

Ni(1101

.

Fi 19: Spin-resolved threshold photoemission data from Ni(ll0). a: EllfllO], b: El1[OOl] /47/. Fig. 20: Comparision of the experimental data on Ni(100) from Fig. 18 with the results obtained from a "rigorous" photoemission calculation with the ferromagnetic exchange splitting A as a parameter (after Moore and Pendry 1481). That nearly -100% spin polarization was observed is understood because the energy separation between the top of the S4-Z4t- symmetry bands and the Fermi energy is large along T-K-X (see Fig.17). A l s o , the low work function of the Ni(ll0) surface causes a larger photocurrent than obtained from the two other surfaces, Therefore, the monochromator can be operated at better resolution. On Ni(llO), it depends on the direction of the light electric vector which symmetry of band states is sampled. With El1(llO), only initial states o f S4-E4 symmetry are dipole allowed while with El1(lOO), initial states of E3 are allowed /21/. A strong dependence of the spin polarisation on the light polarization direction (see Fig.19) is actually observed. Photoemission calculations have been performed by Moore and Pendry /48/ treating the exchange splitting as a parameter. It turned out that the data from Ni(ll1) and Ni(100) cannot be reconciled with the value of the exchange splitting for Ni as calculated by self-consistent band theory (0.6 to 0.8 eV /49/). Rather, a smaller value of only 0.3 eV i s necessary to yield agreement with the spin-resolved photothreshold data (see Fig.20). Such a small

489

I

TIT( =0.9

I

Energy below EF lev)

Fig. 21: (a) Spin- and angle-resolved energy distribution curves from Ni(ll0) at 16.8 eV photon energ (NeI) for normal emission and s-polarized light at three temperatures. (by Spin-averaged data /5/. value of the exchange splitting is also consistent with data from angleresolved /50/ and spin- and angle-resolved photoemission which are discussed below.

3.2.lb Spin- and ancrle resolved photoemission data from Ni The exchange splitting of Ni has been resolved for the first time expl icitely by spin- and angle-resolved photoemission /4,5/. Fig.21 shows data obtained on a ’picture-frame’single crystal of Ni(ll0) at room temperature. The exchange-split states ( X 2 f , X 2 1 , see Fig.17) are clearly resolved and their splitting is 0.18 eV, as has also been inferred from earlier spin integrated photoemission data /50/. The spin-resolved data show furthermore that X,l is very close to EF. It was suggested by Liebsch /51/ that the small value of the exchange splitting, its different value for states o f eg and tzg symmetry, the narrow 3d band width, and the occurence of the 6 eV valence band satellite (see section 3 . 2 . 3 ) are all consequences of the high Coulomb correlation among the 3d electrons. Oles and Stollhoff /52/ using a model Hamiltonian and nonspherical exchange and correlation terms were able to show that the exchange

490

splitting depends on the symmetry. Their calculated values for the exchange splitting are considerably smaller than those obtained by standard local spin density functional theory. It was speculated that the local approximation might be a reason for the discrepancies between the calculated electronic structure and the experi mental data. Wang /53/ showed that by introducing non-local corrections to the LSDF approximation, an exchange splitting o f only 0.4 eV is obtained, and X2J is found close to EF. However, the 3d band width is not reduced in this approach. Victora and Falicov /54/ have calculated an "exact density o f emitted states" by taking into account with equal importance bandstructure effects and electron-electron interactions. Very good agreement with the photoemission data is obtained in every respect.

3.2.2 Finite TemDerature effects in Ni The understanding of the electronic structure o f Ni at finite temperatures, and, in particular, near and above the Curie temperature, is the subject of a long standing dispute. The main question is whether or not above Tc there exist local magnetic moments. The angle resolved EDCs by Maetz et al. /55/ have been interpreted within a local moment picture, developed by Korenman and Prange /56/ ("three-peak-model"). However, since the EDCs vs. temperature have to be interpreted by comparison to model calculations employing many parameters, the analysis was not conclusive. Spin-resolved EDCs measured as a function of temperature could give a more distinct answer to the problem. Such an experiment was first performed by Hopster et al. /5/. The data are shown i n Fig.21. Obviously, the peaks in the SREDCs move closer to each other when the temperature is raised, which is shown in more detail in Fig.22a. Accordingly, the data might be interpreted within the Stoner model. However, the peaks in the SREDCs become gradually broader when the temperature is raised as shown in Fig.22b. This fact cannot be explained within the Stoner model. It was suggested /33/ that the broadening of the lines might be a consequence of spin-mixing due to thermal disorder of magnetic moments, similar to what has been observed more clearly in the case of Fe(001) (see above). The temperature dependence of the spin-polarization curves, shown in Fig.23 /57/, also resembles closely that of Fe(001) (Fig.8).

49 1

t

-

-

40’

tT/Tc=0.5 t 0.8

I

1 1 J

I

= t -80

0.5 O=EF Energy below E F (eV) OL 0.6 0.8

1.0 1.2 1 4

TlTc

Fig. 22: (a) Initial state energies of spin-resolved EDCs of Fig.21 as a function o f temperature. (b) Temperature dependence of the width of the exchange-split lines (after ref /57/). Fig. 23: Spin polarization curves from Ni(ll0) at different temperatures (after ref /57/).

3.2.3. Resonant Photoemission from Ni well known feature in energy distribution curves from Ni is the socalled 6 eV valence band satellite which has first been observed by Hiifner and Wertheim in X-ray photoelectron (XPS) EDCs /58/ and by Guillot et al. /39/ in ultraviolet photoemission (UPS). This structure has attracted a considerable amount o f attention also in connection with the above mentioned discrepancy between the photoemission data and the ground state electronic structure calculations for Ni. The 6 eV satellite structure is believed to originate from the 3d* configuration with two highly correlated holes in the 3d shell of a single Ni atom (see, e.g. Penn /59/). It has been found that the intensity of this structure in photoelectron EDCs increases strongly when the photon energy is tuned across the 3p-3d transition threshold around 65 eV (see Fig.24). Assuming a 3~639ground state configuration o f Ni, the configuration 3p53dlo is obtained at the excitation threshold. A SuperKoster-Kronig Auger transition (9) 3p5 3dlo + 3p6 3d8 +el A

492

with a final 3d8 configuration is likely to occur (see Fig.25 for an illustration). Because of the same final state (d8) these resonant Auger electrons should interfere with the 6 eV valence band satellite, and a Fano line shape for the excitation cross section as a function of photon energy should occur, as it is observed /39/. It was suggested by Feldkamp and Davis /60/ that the emitted electrons should be highly spin-polarised in an atomic picture because of the dominating 1G term in the 3d* multiplet and because only minority spin 3p electrons can be excited into the empty d-electron 00s above EP (see Fig.25), since Ni is a stronq ferromagnet. This prediction has been verified in a spin-resolved photoemission experiment by Clauberg et al. /61/ (see Fig.26). It was found that the resonant structure is spin-polarised in excess o f the average valence band polarisation (6%) in qualitative agreement with the predictions by Feldkamp and Davis.

3.3. Thin Film Magnetism

Fundamental questions regarding 2D ferromagetism theory have been raised a long time ago /62/. The band structure calculculations of the ground state electronic properties of supported monolayer films evidence the competition between the enhancement of the ground state magnetic moment, due to the reduced atomic coordination at the surface and its suppression by the hybridization with the substrate electronic states. Recently, advanced techniques i n the preparation and investigation of thin films and interfaces of ferromagnetic materials have allowed experimental tests of the theoretical predictions. Spin- and angle-resolved photoemission on well characterised ultrathin layers prepared in situ permits exploration o f the interplay between the electronic structure and the magnetic character of quasi PD-ultrathin films and interfaces. Study of those ultrathin magnetic films nevertheless is an experimental challenge. Problems to be encountered are: Segregation and intermixing of the substrate with the overlayer atoms, possibly low Curie temperatures of ultrathin films, and changes in the magnetic anisotropies with film thickness and with temperature.

493

Fig. 24: Photoelectron energy distribution curves from Ni (100) for photon energies between 63 and 85 eV (covering the 3p-3d transition treshold) (after Guillot et al. /39/). Fig. 25: Model for the resonant Auger transition in Ni (after ref. /61/). Fig. 26: Photoelectron spin polarization and energy distribution curves from Ni(ll0) at 67 eV photon energy /61/.

3.3.1. Fe/Aa(001) The interaction between the thin magnetic film and the supporting substrate i s expected to differ greatly from case to case. As a model for a weakly interacting system the growth of epitaxial Fe films on Ag (100) has

494

been studied. The spin-split electronic band structure of one and two epitaxial monolayers o f Fe on the Ag(001) surface has been calculated /64,65/. Both groups predict that the reduced atomic coordination and the weak interaction with the substrate cause a substantial enhancement of the Fe magnetic moment. However, these calculations are yet unable to specify the easy magnetization direction since spin-orbit effects are not included in the local spin density approximation. Fe films grow pseudomorphically on Ag(001), with a rotation of the surface nets by 450. The growth mode is layer by layer up to 3 ML /66/. The epitaxial growth proceeds via island formation at higher coverage. The epitaxial system of Fe on Ag is well suited for a detailed study o f the electronic structure of very thin films since Ag has only a very weak (sp) emission between the Fermi energy and 3.5 eV binding energy where the Fe d-bands are located. Fig.27 shows a series o f energy distribution curves for various Fe coverages deposited on the Ag(100) surface /67/. Fig.28 shows difference EDCs which give evidence for the Fe 3d emission and its development at very

Fe(001) on Ag(0011 hv=bOeV

8 6 4 2 Energy below E,(eVJ

1 4 1 2 1 0

.

0

Fi 27: Angle-resolved energy distribution curves for normal emission from AgYOOl), as a function o f Fe coverage /61/. Fig. 28: Difference EDCs for Fe on Ag(001) for the same experimental conditions as in Fig. 27 1671.

495 10

,

I

I

I

10

I

I

-1.0

f ln

ENERGY BELOW E,

(cV)

Fig. 29: (a) Spin-averaged EDC (closed circles) and spin-polarization data (0 en circles) for a 2.5-ML Fe film on Ag(001). (by SPin-resolved EDCs for a 5.2-ML Fe film; upward pointing triangles indicate major i ty-spin contribution (downward, minority spin) /67/.

low coverages. These data compare favourably with the overlayer calculated electronic band structure in the range from 0.95 to 2.5 ML /64,65/. The most striking result of this study is, however, that a net in-plane polarization is not observed up to 2.5 ML coverage. Although exchange-split states may be inferred from Fig.28 by comparison with the calculations, the absence of spin polarization indicates that these ultrathin films cannot be magnetized along the in-plane [loo] direction. Spin polarization is observed at 5 . 2 ML, the next coverage that has been studied, (Fig.29). Possible explanations for the delayed onset of the in-plane manetization are a strongly reduced Curie temperature or a strong surface magnetic anisotropy of the monolayer film. This second hypothesis has recently been strongly supported both from theoretical and experimental results /68-70/.

496

3.3.2. Fe/GaAs(llO) Thin ferromagnetic films on semiconductor substrates offer the possibility o f integrating magnetic elements in microelectronic circuits. For very small thicknesses (clOOA) their properties can be expected to be governed by specific interface effects. In particular, there is strong evidence that chemical interaction between the metal and the semiconductor substrate plays an important role in determining structure and morphology of the film. An unresolved question pertains to the microscopic reasons for the decrease of the magnetization, as measured by ferromagnetic resonance (FMR) for films less than 100 A thick /71/. A characterization by Auger, LEED and soft x-ray photoemission of valence band and core levels has been performed for Fe on GaAs(ll0) /72/. The formation of the interface region has been followed for incremental Fe coverages between 0.1 and 75 ML. The ordered growth of the overlayer is accompanied by reactive intermixing up to 15 ML coverage followed by further As outdiffusion, as evidenced from the observation of changes in the Ga and As 3d-lineshapes as a function of coverage, see Fig.30. Spin-resolved photo

-

r-

Fe/GhAslllO)

J L

21

20

F e / G o A s (110)

Go 3 d

19 I

18

-

A s 3d

17

Biridirig Energy ( e V I

Fig. 30: (a) Ga 3d and (b) As 3d core level spectra for sequential Fe deposition. Shifts induced by band bending have been substracted out. The spectra have been normalized t o comparable peak heights for showing clearly changes in line-shape and binding energy /72/.

497

emission indicates that the surface is ferromagnetically ordered at 5.2 ML Fe-film thickness /73/. The spin polarization increases with the Fe film thickness in a similar way as the magnetization in the FMR results /71/. The evolution of the valence band states in the spin-resolved EDCs as a function of metal coverage reflects the varying concentration of diluted Ga,As atoms in the Fe matrix. An enhanced occupation of bonding minority-spin states induced by hybridization of Fe 3d states is observed. It is inferred that the chemical interaction between interdiffused As, Ga and Fe effectively reduces the Fe net magnetic moment /73/.

Epitaxial growth of Fe on W(110) has been studied by Waller and Gradmann /74/. In view of the large lattice mismatch of (a~,-a~)/a,=-9.5%, only the first two monolayers grow layer-by-layerpseudomorphically with the same lattice constant as the substrate. With increasing film thickness, periodic lattice distortions compensate for the misfit. The electronic and magnetic properties of Fe films on W(110) have been investigated by spin-resolved photoemission by Kurzawa et al. /75/. Experimental data are shown in Fig.31. It was concluded from the spin polarization data that one ML of Fe on W(ll0) is ferromagnetic. At higher coverages, the SREDCs approach those as expected 0 % EF. At a for bulk Fe(llO), with a very high spin polarization of ~ ~ 8 near film thickness of .:65A, the easy magnetization direction switches from (110) to (OOl), similar as in the Fe/GaAs(llO) system. Gradmann, Korecki and Waller /76/ have explained this switching in terms of competition between surface and bulk anisotropies.

3.3.4. Gd/W(llO) Epitaxial Gd films offer the possibility of investigating the Gd electronic structure circumventing the difficulty o f preparing the clean surface of a single crystal. Surprisingly on the first sight, the expected high spin polarization of the Gd 4f electrons has not been observed using spin-resolved photoemission (see Fig.32) /77/. The data have been interpreted in terms o f a magnetic surface reconstruction such that the surface layer has a magnetization direction opposite to that o f the bulk.

498

0 201

1

1~21OK

Energy below E, IeVl

2 1 0 2 1 0 ENERGY BELOW EF ( e V )

Fig. 31: Energy distribution curves of clean W(110) and of epitaxial Fe layers on W(110) with thickness varying between 2 and 20 A /77/. Fig. 32: (a) Experimental Gd 4f photoemission intensity spectrum (circles) fitted with bulk and surface contributions and a smooth background for a Gd film on W(ll0) of thickness d=50 A thickness. (b) Experimental and calculated (sol id line) energy-resolved spin polarization curves. The calculated curve was obtained from the fit shown in (a).

Because of the short probing depths at 60 eV photon energy, a partial cancellation between bulk and surface polarization can explain the data.

3.3.5. Gd/Fe(1001 Gd monolayer films on Fe have been studied to investigate the interface electronic and magnetic coupling between two ferromagnetic materials. This system has also been characterized by Allenspach, Taborelli, and Landolt by spin-resolved Auger electron spectroscopy /78/. It was found that the Gd adatom magnetic moment i s aligned antiparallel to that of the Fe surface, the interface forming a ferrimagnetic system.

499

Synchrotron radiation from BESSY in the 30 to 70 eV photon energy range was used to observe directly the Gd 4f level and the Fe-derived valence bands at the interfacial region. Fig.33a shows SREDCs after evaporation of 1ML Gd onto the clean Fe(100) substrate 1791. The clean Fe(100) SREOCs taken before Gd deposition are shown in Fig.33b. The peaks at about 8 eV binding energy (EB) in Fig.33a are due to the Gd 4f emission. The Gd 4f (spin averaged) photoemission spectrum shows the 4f6 final state multiplet structure. The Gd (5d6s) valence states overlap the Fe valence bands, but, because of their very low cross section in comparison that of the Fe 3d states at 70 eV photon energy, they give a negligible contribution (*:I%)to the spectra. Since the largest contribution for the 4f-signal is superimposed on the Fe-minority- spin signal, it was concluded that the Gd 4f moment is aligned opposite to that of the Fe in agreement with the spin-resolved Auger-data 1781.

Fig. 34 shows a comparison of SREDCs for the clean Fe(001) and for the adsorbate covered substrate. It can be seen that also the Fe-derived valence band emission is affected by the Gd deposition. As compared to the clean

Energy below E F lev)

Fig. 33: (a) Spin-resolved energy distribution curves for a monolayer of Gd on Fe(001). (b) Spin-resolved energy distribution curves from clean Fe(100) before Gd evaporation 1791. Fig. 34: Comparison of measured SREDCs in the valence-band regime for 1ML Gd on Fe(100) (data points from Fig. 33(a)) with model SREDCs (solid lines). The model SREDCs are derived from those for the clean Fe(001) surface by assuming a reduction o f the long-range magnetic order by 60% (1791).

500

substrate spectra, the majority-spin SREDC increases near EF, whereas the peak at about E ~ = 2 . 6eV decrease relative to the peak at E,=l eV upon Gd adsorption. In the minority-spin EDC, a shoulder grows around EB=3 eV. These changes correspond to an overall decrease in spin polarization along the valence band region upon Gd adsorption which shows that the magnetization at the Gd/Fe interface is lower than that of the bulk Fe crystal. The data look similar as SREOCs from clean Fe(001) taken at elevated temperatures (cf. Fig. 10).

3.4. Spin-resolved photoemission from ferromametic allovs and comDounds 3.4.1. Fe3Pt(0011 -

The unusually small thermal expansion coefficient of a large class of materials in a rather broad temperature range around room temperature is referred to as "Invar" effect. It was first observed by Ch.E. Guillaume in 1897 in studies on Fe,Ni,-, alloys, with xe0.65. All the known Invar alloys are either ferromagnetic or antiferromagnetic, and their small thermal expansion coefficient is found in a temperature range around their Curie- or Nee1 temperatures, indicating the intimite relation of the effect to the magnetic phase transition. Typical Invar systems besides Fe65Ni35 are Fe,Ptl-,, or Cr,Fel-,, ~2~0.35. Several theoretical models have been proposed to explain the small thermal expansion, but no self-consistent theory exists since this has to deal with the complications to describe finite-temperature magnetism. Common to all of the models is the assumption that i n these materials the usual thermal expansion is reduced by the interplay between the value of the magnetic moment and the volume o f the unit cell. The probably oldest explanation of the Invar effect is the "2y-state"-modelproposed by Weiss /80/. He assumed that the thermal expansion is compensated by a thermally induced transition from a state with a large atomic volume and a large magnetic moment ("high-spin state") to a state with smaller atomic volume and small magnetic moment ("low-spin state"). Also modern theories predict a dramatic dependence of the magnetic moment o f Fe on its volume /81,82/. To test the hypothesis of Weiss, spin- and angle- resolved photoemission on ordered FesPt(001) has been performed /83,84/. Fig.35 shows the spin integrated spectrum, the spin polarization and the spin-resolved EDCs at 60

501

ai

Fig. 35: (a) Spin-integrated energy distribution curve (EDC) for normal emission and normal incident light from ordered Fe3Pt(001) at 60 eV photon energy; (b): spin polarization curve corresponding to fig. 35a; (c): spin-resolved energy distribution curves /83/.

eV photon energy, for normal emission and normal incident light. The dominating peaks in the spin-resolved EDC located at 2.6 eV and at 0.5 eV represent a couple of exchange split states. The exchange splitting is measured as 2.1 eV. Assuming a free-electron-like final state, the data can be interpreted semi-quantitatively by comparing with the band structure calculations of ordered Fe3Pt by Hasegawa /85/. Due to dipole selection rules, the allowed initial state wave function symmetry is A5 /Zl/. Thus,in the 60 eV data, the dominating peaks have been attributed to emission from the A5-symnetry bands near X (see Fig. 35). The weak structure near EF in the majority-spin EDC is presumably arising from the flat band of A2-symmetry just below E, which under perfect experimental conditions is not dipole allowed, but may contribute to the spectra, due to its high density-of-states and because of the finite angular resolution of the spectrometer and/or surface imperfections. The larger majority-spin intensity near EF in data taken at 90 eV photon energy is to be expected from the band structure and the final state

502

Fe,Pti001) h v = 60 eV -

$ -

-

-

+

lo' I

)r

5 0 a c

l

-" -10

A

c

c L al

2 L

.

-20-

Energy below

E, l e v )

Fig. 36: (a) Angle-resolved energy distribution curves from Fe3Pt(001) for normal emission and s-polarized light at 60 eV photon energy at 270 and 550 K (T,=450 K ) . The intensities are normalized to the photon flux; (b) difference between EOCs taken at 500 and 270 K. The dashed line is the difference between the 7-Fe DOSs at a=3.71 (high-spin state) and a=3.46 (low-spin state) /81/, convoluted with a 0.4 eV FWHM Gaussian-type resolution function after truncation by the temperature-dependentFermi function /84/. dispersions /83/. For hv=9OeV, the initial state wave vector i s near r, and therefore the increase in majority spin intensity near Ef is due to emission from the dipole-allowed A5-symmetry band closely below E, at r. The changes in EDCs as a function of temperature through the Curie temperature (Tc=450K) have also been studied /84/. Fig.36a shows spinintegrated energy distribution curves for T=270K (=0.6Tc) and 550K (=1.22Tc). The difference of these two EDCs is plotted in fig.36b. The difference spectrum exhibits a minimum at about 0.5 eV binding energy and a maximum slightly above the Fermi energy. The oberved temperature-induced changes are about 10 times larger than those expected from the Fermi function alone. Calculations on the electronic structure of Invar a1 loys at elevated temperatures are not yet available. Therefore, an attempt has been made to interpret the data within the 27-state model of Weiss /84/. The electronic structures of ordered Fe3Pt and of pure fcc Fe are closely related /83/. The dashed line in Fig.36b is the difference-DOS for fcc Fe in the low-spin (a=6.81a.u.) and the high-spin state (a=7.0a.u.). The DOS are shown in

503

I ;

f r r Fe

---

0

=70au

0

= 6 81 o u

I

I

-?

-1

1

05,

Bindlng Energy lev1

Fig. 37: Density-of-states of pure fcc Fe in the low-spin state and in the high-spin state (b). After ref. /81/. Fig. 37. The difference between the density-of-states curves compares we1 1 with the experimental difference curve. Thus, the coexistence of the 71 and the y2 states at elevated temperatures is consistent with the experimental data. Kakehashi has recently explained the Invar effect in terms of fluctuations of local magnetic moments / 8 6 / . Structures in the DOS which are sharp at low temperatures are washed out at higher temperatures because of fluctuations. This would result in similar changes in the EDCs as observed experimentally /86/.

3.4.2

A ferromagnetic compound which is used for magnetic data storage is Cr02. Nevertheless, its electronic structure is largely unknown. Recently, however, self-consi stent electronic structure calculation became avai 1 able /87/. The prediction was that Cr02 should be a half-metallic ferromagnet, i.e. that its majority-spin electrons behave metallic, but that there is a gap in the minority-spin DOS. First spin-resolved photoemission measurements on this compound have been performed recently by Kamper et al. /88/. Since bulk samples of sufficient size are not available, they used instead thin

504

films of Cr02 grown on substrates such as Ru02, Ti02, or A1203. The samples have been transfered to the photoemission chamber, and cleaned in situ by low-energy Ne-ion sputter cycles. Spin-resolved photoemission with 100 meV energy resolution was performed employing a He1 gas discharge lamp. In contrast to the predicted half-metallic behaviour, an extremely low photoemission intensity was observed at the Fermi energy as shown in Fig.38. Therefore, spin polarization measurements were only possible for binding energies larger than 1.5 eV. The spin polarization started at %+loo%at 1.5 eV binding energy, and decreased to about 20% at about 5 eV (see Fig.39). The peak in the EDC at 2.7 eV was explained as emission from d-states, and it was concluded from the data that the d-bands do not cut the Fermi level, in contrast to the predictions from band structure calculations. In this case, the magnetism must be due to localized magnetic moments.

Energy below EF l e v )

Fig. 38: EDC in the vicinty o f the Fermi energy of Cr02 (expanded by the factor of 40) as compared to the EDC of a polycrystalline Au foil. Fig. 39: Spin-polarization spectrum o f a polycrystalline Cr02 film at 300 K after 120 s of a sputter cleaning /88/.

505

4. OUTLOOK

The new technique o f spin- and angle-resolved photoemission allows to determine in the most direct way the spin-split electronic structure of magnetic materials. During the past five years measurements have been performed on a number o f prototype magnetic systems. Because o f the developments of more easy to handle spin detectors and the experience gained with those devices, and due to the progress in the development of energetic light sources, this technique will be applied to a wide variety o f more complicated magnetic systems which are found in many practical applications.

5. NOTES ADDED IN PROOF By spin- and angle-resolved photoemission with synchrotron radiation performed at Brookhaven National Laboratory, molecular adsorbates on Fe(001) have been investigated. Exchange-split adsorbate states of 0 p-orbitals have been observed by P.D. Johnson, A. Clarke, N.B. Brookes, S.L. Hulbert, B. Sincovic and N.V. Smith (Phys. Rev. Lett. 61, 2257 (1988)). See Fig.40. F.U. Hillebrecht, R. Jungblut and E. Kisker have demonstrated by measuring the Fe 3s core-level spin polarization that very-low-energyreflection on maqnetited Fe(001) provides a convenient spin polarimeter with an about 20 times larger efficiency than spin polarimeters based on spinorbit interaction (PRL 65, 2450 (1990)). r-

r

V

Fig. 40: Spin- and angleresolved EDCs from Fe(001)p(lx1) 0 at 60 eV photon energy

I

L

1

0

8

6

4

2

Binding Energy (eV)

EF

506

REFERENCES Work supported in part by Deutsche Forschungsgemeinschaft, SFB166 1 K.B. Hathaway, H.J.F. Jansen, and A.J. Freeman, Phys. Rev. B 31, 7603 119851 2

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3

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4 5 6

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(1985) 9 C. Carbone and E. Kisker, Sol. State Comm. 65, 1107 (1988) 10 see, e.g., M. Landolt in: Polarized Electrons in Surface Physics, World Scientific, edited by R. Feder, Singapore (1985) 11 J. Kessler, Pol. El., 2nd ed., Springer Ser. Atoms Plasmas, Berlin, Vol. 1 (1976) 12 J.W. Motz, H. Olsen, and H.W. Koch, Rev. Mod. Phys. 36, 881 (1964) 13 F.B. Dunning, F.-C. Tang, and G.K. Walters, Rev. Sci. Instr. 58, 2195 (1987); F.B. Dunning, L.G. Gray, J.M. Ratcliff, F.-C. Tang, and X. Zhang, and G.K. Walters, Rev. Sci. Instr. 58, 1706 (1987) 14 J. Kirschner and R. Feder, Phys. Rev. Lett. 42, 1008 (1979) 15 J. Unguris, D.T. Pierce, and R.J. Celotta, Rev. Sci. Instr. 57, 1314 (1986) 16 E. Kisker, K. Schroder, W. Gudat, and M. Campagna, Phys. Rev. B 31, 329 (1985) 17 E. Kisker, M. Campagna, W. Gudat, and E. Kuhlmann, in: Advances in Solid State Phys., ( J . Treusch, ed.) XIX, 259 (1979) 18 R.J. Celotta, D.T. Pierce, G.C. Wang, S.D. Bader, and G.P. Felcher, Phys. Rev. Lett. 43, 728 (1979) 19 E. Kisker, W. Gudat, E. Kuhlmann, R. Clauberg, and M. Campagna, Phys. Rev. Lett. 45, 2053 (1980) 20 W . Eib and B. Reihl, Phys. Rev. Lett. 40, 1674 (1978) 21 J. Hermanson, Sol. State Comm. 22, 9 (1977) 22 R. Feder, A. Rodriguez, E. Baier, and E. Kisker, Sol. State Comm. 52, 57 (1984) 23 E. Kisker and K. Schroder (unpublished) 24 S . Ohnishi, A.J. Freeman, and M. Weinert, Phys. Rev. B 28, 6741 (1983) 25 P.J. Durham, J. Staunton, and B.L. Gyorffy, Journ. Magn. Magn. Mat.45, 38 (1984) 26 see, e.g.: Panel discussion, Inst. Phys. Conf. Ser. 55 (1982) 27 V. Korenman, J. Murray, and R.E. Prange, Phys. Rev. B 16, 4032 (1977) 28 B.L. Gyorffy, J. Kollar, A.J. Pindor, J. Staunton, and G.M. Stocks, Proc. 3d metallic magnetism workshop, p. 121, Grenoble (1983) 29 B.L. Gyorffy, A.J. Pindor, J. Staunton, G.M. Stocks, and H. Winter, J. Phys. F. 15, 1337 (1985) 30 G. Jezequel, A. Barski, P. Steiner, F. Solal, P. Roubin, R. Pinchaux, and Y. Petroff, Phys. Rev B 30, 4833 (1984) 31 E. Kisker, J. Phys. Chem. 87, 3597 (1983) 32 E. Kisker, K. Schroder, M. Campagna, and W. Gudat, Phys. Rev. Lett. 52, 2285 (1984) 33 E. Kisker, Journ. Magn. Magn. Mat.45, 23 (1984) 34 J. Staunton, B.L. Gyorffy, A.J. Pindor, G.M. Stocks, and H. Winter, J. Phys. F15, 1387 (1985)

507

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V. Korenman,"The Local-Band Theory", in: Topics in Current Physics, Vol. 42 ("Metallic Magnetism"), edited by H. Capellmann, Springer, Berlin 1986 E. Haines, R. Clauberg, and R. Feder, Phys. Rev. Lett. 54, 932 (1985) Y. Kakehashi, K. Becker, and P. Fulde, Phys. Rev. B 29, 16 (1984) B. Drittler, M. Weinert, and P.H. Dederichs, priv. comm. C. Guillot, Y. Ballu, J. Paigne, J. Lecante, and K.P. Jain, P. Thiry, R. Pinchaux, Y . Petroff, and L.M. Falicov, Phys. Rev. Lett. 39, 1632 (1977) D. Chandesris, J. Lecante, and Y. Petroff, Phys. Rev. B 27, 2630 (1983) H. Kato, T. Ishii, S. Masuda, Y. Harada, T. Miyano, T. Komeda, M. Onchi, Y. Sakisaka, Phys. Rev. 632, 1992 (1985) K.-H. Walker. E. Kisker. C. Carbone. and R . Clauberq, - . Phvs. - Rev. B 35, 1616

43 44 45 46 47

K. Schroder, E. Kisker, and A. Bringer, Sol. State Comm. 55, 377 (1985) E.P. Wohlfarth, Phys. Lett. 36A, 131 (1971) E.P. Wohlfarth, Phys. Rev. Lett. 38, 524 (1977) W. Eib and S.F. Alvarado, Phys. Rev. Lett. 37, 444 (1976) E. Kisker, W. Gudat, M. Campagna, and E. Kuhlmann, Phys. Rev. Lett. 43, 966

35 36 37 38 39 40 41

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48 49 50 51 52 53 54 55

56 57 58 59 60 61 62 63 64 65 66 67 68 69

(1979) I.D. Moore and J.B. Pendry, J. Phys. C11, 4615 (1978) C.S.Wang and J. Callaway, Phys Rev. B 15, 298 (1977)

D.E. Eastman, F.J Himpsel, and J.A. Knapp, Phys. Rev. Lett. 44, 95 (1980) A. Liebsch, Phys. Rev. Lett. 43, 1431 (1979) P. Oles and G. Stollhoff, Phys. Rev. B 29, 314 (1984) C.S. Wang, Journ. Magn. Magn. Mat.31-34, 95 (1983) R.H. Victora and L.M. Falicov, Phys. Rev. B 31, 7335 (1985) C.J. Maetz, U. Gerhardt, E. Dietz, A. Ziegler, and R.J. Jelitto, Phys. Rev. Lett. 48, 1686 (1982) V. Korenman and R.E. Prange, Phys. Rev. Lett. 44, 1291 (1980) R. Raue, H. Hopster, and R. Clauberg, Z. Phys. 854, 121 (1984) S. Hiifner and G.K. Wertheim, Phys. Lett. 51A, 299 (1975) D.R. Penn, Phys. Rev. Lett. 42, 921 (1979) L.A. Feldkamp and L.C. Davis, Phys. Rev. Lett. 43, 151 (1979) R. Clauberg, W. Gudat, E. Kisker, E. Kuhlmann, and G.M. Rothberg, Phys. Rev. Lett. 47, 1314 (1981) N.D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966) N.C. Koon, B.T. Jonker, F.A. Volkening, J.J. Krebs, and G.A. Prinz, Phys. Rev. Lett. 59, 2463 (1987) C.L. Fu, A.J. Freeman, and T. Oguchi, Phys. Rev. Lett. 54, 2700 (1985) R. Richter, J.G. Gay, and J.R. Smith, Phys. Rev. Lett. 54, 2704 (1985) G.C. Smith, G.A. Padmore, and C. Norris, Surface Science 119, L287 (1982) B.T. Jonker, K.-H. Walker, E. Kisker, G.A. Prinz, and C. Carbone, Phys. Rev. Lett. 57, 142 (1986) J.G. Gay and R. Richter, Phys. Rev. Lett. 56, 2728 (1986) M. Stampanoni, A. Vaterlaus, M. Aeschlimann, and F. Meier, Phys. Rev. Lett. 59, 2483 (1987)

B. Heinrich, K.B. Urquhart, A.S. Arrot, J.J. Cochran, K. Myrtle and S.T. Purell, Phys. Rev. Lett. 59, 9309 (1987) 71 5.3. Krebs, F.3. Rachford, P. Lubitz, and G.A. Prinz, J. Appl. Phys. 53, 70

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unpublished 74 G. Waller and U . Gradmann, Phys. Rev. B 26, 6330 (1982) 75 R. Kurzawa, K.-P. Klmper, W. Schmitt, and G. Giintherodt, Sol. State Comm. 60, 777 (1986)

508

76 U. Gradmann, J. Korecki, and 6. Waller, Appl. Phys. A39, 1 (1986) 77 D. Weller, S.F. Alvarado, W. Gudat, K. Schroder, and M. Campagna, Phys. Rev. Lett. 54, 1555 (1985) 78 R. Allenspach, M. Taborelli, and M. Landolt, Phys. Rev. B 34, 6112 (1986) 79 C. Carbone and E. Kisker, Phys. Rev. B 36, 1280 (1987) 80 R.J. Weiss, Proc. Phys. SOC. (London) 82, 281 (1963) 8 1 0 . Bagayoko and J. Callaway, Phys...Rev. B 28, 5419 (1983) 82 V.L. Moruzzi, P.M. Marcus and J. KUbler, Phys. Rev. B 39, 6957 (1989) 83 C. Carbone, E. Kisker, K.-H. Walker, and E.F. Wassermann, Phys. Rev. B 35, 7760 (1987) 84 E. Kisker, E.F. Wassermann, and C. Carbone, Phys. Rev. Lett. 58, 1784 (1987) 85 A. Hasegawa, J. Phys. SOC. Japan 54, 1477 (1985) 86 Y. Kakehashi, 3. Phys. SOC. Japan (1984) 87 U.L. Moruzzi, P.M. Marcus, K.Schwarz and P. Mohn, Phys. Rev. B 34, 1784 (1986) 88 K.P Kamper, W. Schmitt, G. Guntherodt, R.J. Gambino, and R. Ruf, Phys. Rev. Lett. 59, 2788 (1987)

509

Chapter 13

INVERSE PHOTOEMISSION

P. D. JOHNSON

1.

INTRODUCTION

In this chapter we review Inverse Photoemission (IPES), the analogue of the parent technique Photoemission. Other chapters have demonstrated how the excitation of electrons by photons may be used to derive a variety of information on both the electronic and geometrical structure of different materials. With electrons being excited in photoemission, the primary requirement is that the initial state be an occupied state. In inverse photoemission an electron is added to the system and now the probed states or final states are unoccupied. Thus we review the extent to which the experience obtained in the development of photoemission may be carried over into studies of the unoccupied bands through the inverse photoemission experiment. Shown schematically in fig. 1, inverse photoemission is the process involving the emission of a photon during the radiative transition of an electron between two unoccupied states. In that the incident particle is an electron and the emitted particle a photon, inverse photoemission is generally considered as "time reversal" of the photoemission process. Such a time reversal would be strictly true only if the final states of inverse photoemission were located below the Fermi level. However considerable progress may be made if, neglecting for the moment the Fermi occupation of the electronic states, a direct comparison is made between the cross-section for the two "time-reversed transitions. Such a comparison has been made for the solid state by

'

*

Pendry and for adsorbed molecules by Johnson and Davenport. The interaction Harniltonian H' between the photons and electrons is given by

H' = (A.p+p.A)

'

+ -[ A f 2m2

where A is the vector potential of the electromagnetic radiation. In the Inverse Photoemission process photons are created and it becomes necessary to quantize the electromagnetic field. Thus the classical vector potential is replaced by a field operator A(x,t) defined by

where &(a)is the linear polarization vector whose direction depends on the photon propagation

510

f

Fig. 1. Comparison of the inverse and direct photoemission processes. (a) In IPES an electron which has coupled to an unoccupied state above E,, makes a radiative transition to an unfilled state above EF. (b) In PES an electron below EF is excited to a state above.,,E , direction q. The two operators atg,a and aq,.

either create or destroy a photon in the state q,a

respectively and V, is the normalization volume For the photon. From equations (1) and (2) it is possible, using first-order perturbation theory, to derive an expression for the differential cross-section for the emission of a photon such that

where the transition is between two electronic states I i > and I f > differing in energy by an amount f i w . The incident electron has a momentum n k and a represents the fine structure constant. A similar expression may be derived for the photoemission process and again assuming "time-reversal" it can be shown that the ratio R of the two cross-sections is given by

2

R=[?]

(4)

That is, the ratio of the inverse photoemission cross-section to the photoemission cross.

511

section is inversely related to the ratio of the square of the wavelength of the emitted particles, a reflection of the difference in available phase space for these final states. Equation (4) is derived with the assumption of complete time reversal, the matrix elements appearing in the equations describing the differential cross-section for inverse photoemission, eqn. (3),and the equivalent for photoemission being considered identical. For localized states this assumption may not be valid. In photoemission, the outgoing electron experiences a coulombic potential whereas in inverse photoemission the incoming electron is scattered by the short range potential characteristic of a "neutral" atom. Johnson and Davenport 2 have considered in detail the effect of using these different potentials in calculating the inverse photoemission crosssection into the localized level of an adsorbed molecule. Their conclusion was that the difference

Fig. 2. Comparison of the photoemission cross-section from a neutral hydrogen atom H ( dashed line ) and from a negative hydrogen ion H- ( solid line ). The cross-sections are normalized at v = 1.5~1 where v1 is the ionization potential of H-. ( Reproduced from ref. 3 ). between the two scattering potentials was most marked in the threshold region. A particularly illuminating example of this effect is provided by a comparison of the photoemission cross-

’. In fig. 2, these crosssections of the hydrogen atom, H, and the negative hydrogen ion, H sections are shown as a function of the photon energy, scaled to the threshold energy. The final state following photoionization of the atom is an outgoing electron in the coulombic potential of the positive ion, H+; from the negative ion, the photoelectron experiences the short range potential of the atom, H. Calculation of an inverse photoemission cross-section through the straightforward application of equation (4) to these different photoemission cross-sections will result in a threshold value of infinity for the coulombic polential and zero for the short range potential I In the UV energy range characteristic of inverse photoemission, the ratio R in equation ( 4 ) typically has a value of 10-5. It is precisely for this reason that the development of the technique as a viable spectroscopy has so lagged behind the development of photoemission. Indeed, it is only with electron sources operating in the space charge limited regime that inverse photoemission has developed into its modern momentum or K-resolved form (KRIPES). Detailed in the different

512

sections of this chapter IPES has now been applied to the study of bulk band structures, surface states and adsorbate induced features on both metals and semiconductor surfaces.

2.

INSTRUMEMATION

As has been reviewed extensively elsewhere, 5 the requirements of an inverse photoemission experiment divide into two elements, the electron source and the photon detector. In particular it is the properties of the former, the electron source, that determine the overall angular or momentum resolution. The ideal electron source would provide a large current into a well focussed spot with small angular divergence. Space charge effects will place limitations on the performance that can be achieved in practice but larger currents may be obtained where the spot size or angular convergence can be sacrificed. Stoffel and Johnson 6 have described an electron source whereby electrons are first accelerated in a simple diode extraction arrangement and then decelerated through a three element lens onto the sample. This gun, fig. 3, has been shown to operate successfully in a space charge limited mode, producing a 1mm. focussed spot with angular divergence of the order of 5O. Several authors have chosen to follow an alternative and earlier design due to Erdrnan and Zipf. 7 Here the extraction source is a triode rather than diode, but again, a lens is used to decelerate and focus the electrons on to the sample.

Fig. 3. Schematic diagram of the Stoffel-Johnson electron gun design. C and A represent the diode extraction source. A,F, and 0 ( ground potential ) represent the three element lens. L = D =16mm, Q = 2.5 D and P = 1.3 D. A development of IPES was the introduction of a spin polarized electron source into the experiment. This allowed studies of magnetic materials in the same style as spin polarized photoemission experiments. A typical source of spin polarized electrons has been described in considerable detail elsewhere. 9 Briefly electrons are photoemitted by circularly polarized light from a GaAs cathode that has been exposed to cesium and oxygen to lower its workfunction. Selection rules determine whether the photoemitted electrons are polarized either parallel or anti-parallel to the axis of rotation of the light. Experiments using such a source will be described in more detail later. However for now, we note that electron sources using the photocathode enjoy the advantage of a smaller energy spread, typically 0.1 eV rather than 0.27 eV for the BaO thermal source. The photon detectors used in IPES fall into two categories, those thal can be tuned to detect

*

513

.. .._ ._--____------________ .. . I . .

ZQ f J 0)

52

5z

< U k

I 9.2

I

9.6

10.0 ENERGY (eV)

10.4

Fig. 4. (a) A typical arrangement for the use of a Geiger Muller detector in IPES. The central electrode collects the electron cascade generated by the incident photon. (b) The bandpass are determined by the product of the transmission of the CaF window characteristics (-) (---) and the photoionization cross-section of the iodine vapor ( . , . . . ) . photons of different wavelengths and those that operate at a constant photon energy, 1.e. isochromat detectors. It is the latter, because of their ease of construction and operation, that have dominated the experiment to date. Indeed, it was with the introduction of the Geiger Muller counter, fig. 4(a), into the experiment by V. Dose, 10 that the recent surge of developments in IPES began. The first Geiger Muller counters used in IPES were band pass detectors centered at 9.7 eV with an energy window of approximately 0.8 eV. This resolution was determined by the transmission properties of a CaF entrance window and the photoionization properties of the iodine gas filling the detector, fig. 4(b). Whilst this arrangement is still widely used, several groups have replaced the CaF by a SrF window altering the detected photon energy to 9.5 eV and Because these detectors are insensitive to the direction of narrowing the bandwidth to 0.4 eV. travel of the detected photon they can be conveniently combined with large collection mirrors to enhance the signal rate. This advantage is not enjoyed so easily by detectors requiring a well defined source such as the spectrographs to be described later. Several different combinations of windows and gases have been used to generate other isochromat detectors for IPES studies. Another variant has been to replace the gas by the photo-

514

sensitive surface of an electron multiplier. Indeed, by coating the first dynode of an electron multiplier with another alkali-halide, KBr, Babbe et al. 1 2 have claimed both an increase in sensitivity and in resolution. The introduction of tunable spectrographs into Inverse Photoemission has allowed experiments to be performed in a similar style to Photoemission experiments using Synchrotron Radiation. Described in greater detail elsewhere, 5 three different spectrometer or spectrograph designs have been used to date. Two instruments are conventional in arrangement, one being based on a Toroidal grating l 3 and the second a normal incidence instrument l4 based on a spherical grating. The former allows photons to be detected in a higher energy range, 20-100 eV, the latter operates at lower energies 10-20 eV.

Grating sensitive detector

(b)

Detector

LiF

Fig. 5. (a) Off-Rowland circle normal incidence spectrograph with parallel detection. (b) Refractor with a lens as the dispersing element and single channel detection. The third spectrograph, 1 5 shown in fig. 5(a), is again of the normal incidence variety but here the authors recognize that the requirements of the experiment allow the focussing or optical properties to be relaxed in one dimension. This leads to a design in which the source of photons, the sample, is placed in one chamber and the photon detector placed in a separate chamber reducing the problem of shielding for the photon sensitive surface of the detector and allowing the full range of surface experiments to be carried out in the main chamber. With an instrument of this type the overall energy resolution that can be achieved at the lower energies is typically 0.3 eV. However this figure is essentially determined by the energy spread of the electron source, the 270 meV of the BaO cathode. A variant of the tunable detector was the replacement of the grating as the dispersive element by a lens manufactured from an alkali-halide. 1 k 1 7 The basic layout of such an instrument, a "Refractor", is shown in fig. 5(b). Because of the rapidly changing refractive index for wavelengths near the transmission cut-off of the alkali halide, different wavelengths

515

are focussed at different points along the axis of the lens. Tunability is therefore achieved simply by moving the photon sensitive surface with it's defining aperture along this axis. This simple detector can be operated with reasonably good resolution but over a more limited range than the large spectrographs, a typical range being 2.0 eV. Having discussed the various experimental details we now turn in the following sections to a discussion of the different range of experiments.

3.

METALS

3.1

Bulk States: The Direct Transition

As noted in the introduction to this chapter, the inverse photoemission process involves the emission of a photon during the radiative transition of an electron between two unoccupied states. As in photoemission, momentum conservation is maintained through the intervention of the crystal lattice. Thus the photon flux emitted at an energy nu for an incident electron beam energy E may be written 18

2. Here I Pf,i I ISthe square of the momentum matrix element between unoccupied bands i and f separated by nu and ci describes the coupling probability to the initial state. The first 6 function confines the transition to the same point in k space. In common with photoemission, kll is a good

quantum number but k l is indeterminate. Therefore most of the procedures already developed for bulk band mapping in photoemission will carry over into the study of the unoccupied bands. Indeed, in that this one to one correspondence exists, it cannot be said that anything new or unexpected has been learned about the bulk bands from IPES. However we briefly review some of the experimental methodology and discuss a few of the results. The type of data recorded in an experiment will be determined by the apparatus, and in particular, the type of photon detector used. With an isochromat detector of the Geiger Muller type, the emitted photon intensity is recorded as the incident electron beam energy is swept. For a given kll, determined by the angle of incidence of the electron beam and the incident beam energy, transitions are observed at some kl restricted through the 6 function in equation (5). Alternatively the photon detector may be of the spectrograph variety with the capability of detecting photons over a range of different energies. Now spectra will be recorded at some kll given by

516

_'X_

R=

d

2"

6"

I

=@

O

2

I

I

6 8 ENERGY ( e V ) 4

I

10

F=O

2

4

6

8

10

ENEEGY (eV)

Fig. 6. KRIPES data taken on Pd(ll0) as a function of 8 , the angle of incidence in the PP and E? azimuths. The incident electron beam energy was 22.5 eV relative to EF. Features labelled BB represent bulk transitions and those labelled S, are surface derived. where Ei is the incident energy with respect to the vacuum level and 0 is the angle of incidence. Ei is set to different energies and all allowed transitions are detected in parallel. Indeed, as an aside, we note that with the use of a spectrograph in IPES, it is far easier to map the unoccupied band structure at some kll # 0 than it is to do the equivalent experiment in photoemission. This reflects the fact that i n the latter experiment for a selected take-off angle each point in a spectrum corresponds to a different value of kll. As an example of bulk band mapping, we show in fig. 6,two sets of IPES spectra recorded moving away from the center of the zone in the PX and PB azimuths of a Pd (1 10) crystal. In both azimuths, transitions are observed into the unoccupied d band immediately above the Fermi level: little or no dispersion is observed ior this band. Transitions into dispersing sp bands, labelled BE, are also identified in both azimuths. We reserve our discussion of the unoccupied surface states, labelled S, until later. We show in fig. 7 a comparison between the experimentally observed peak positions and the bulk bands calculated with an interpolation scheme. 2o The latter scheme was fitted to the results of a first-principles calculation of Christensen 21 with minor adjustments to improve agreement with earlier photoemission data. 22 Aside from such studies there have also been several spin polarized inverse photoemission studies of the bulk ferromagnetic materials Ni and Fe. This latter type of experiment] reviewed

517

,OF-

8

I

\

6

v-

\

\

'

\

4

2

0X

-

r

Y

P A R A L L E L WAVE VECTOR

Fig. 7. Ef (kll) plot of the data of fig. 6 (solid circles) compared with the calculated dispersion for kinematically allowed direct transitions within the bulk band structure (solid lines). The projected bulk band gaps are indicated by shading. 2 ~ the introduction of a spin polarized electron source as extensively elsewhere, ~ - requires described earlier. The "spin resolved spectra N$ and NT are obtained from the raw spectra n, and nT ( photon counts with the incident spin aligned in opposite directions ) through

N = nu + (n l + pA ) T 2 and

(7)

(n, - nJ) I (nT + n,) and P is the projected component of the spin polarization of the incident beam on the sample. The first experiment of this type 8 was carried out on a N i ( l l 0 ) surface where as expected it was shown that the unoccupied bands are entirely of minority character. Figure 8 shows the spin resolved spectra, N, and NT, and the asymmetry A obtained in that experiment with the

A is the measured asymmetry

electron beam incident at different angles in the c110> azimuth. Further experiments on the bulk band structure of ferromagnetic materials have followed earlier photoemission work by

518

examining exchange splittings at different points in the zone on for instance F e ( l l 0 ) 26 and also the temperature dependence of the latter. 27 In agreement with the photoemission studies it was found that the exchange splittings showed a varying temperature dependence throughout the zone.

..

0.4

1 .

-0.6

0

I

'

N

T

-I

I

2

ENERGY ABOVE EF ( e V

1

Fig. 8. Spin polarized inverse photoemission spectra and spin asymmetry recorded from a Ni (110) surface in the el 10> azimuth for an angle of incidence of the electron beam of (a) Oo and (b) 20 .

3.2 Surface States 3.2.1. Shockley States and Image States Whilst nothing particularly new has emerged thus far from IPES studies of unoccupied bulk bands, a more significant contribution has been made through studies of the unoccupied surface slates. This stems from the observation by Johnson and Smith 28 that IPES is capable of observing a particular class of surface state derived from the long range image potential. These states are generally referred to as image stales. The observation of pre-emergent fine structure in low energy electron diffraction studies of surfaces 29 had previously lead to models invoking the existence of such states. It was postulated that at energies above the vacuum level the electrons might couple to these states causing sharp structure in the measured rdectivity of the electron beams. However more recently. the same fine structure has been interpreted in terms of interference effects between the incident and reflected beams, 30 rather than bound or stationary

519

states. The observation of image states in IPES therefore confirms the existence of bound states. Following on from the early observation of these states, their existence has repeatedly been confirmed through direct observation on a number of different surfaces. 31*32 A further development came, however, with the observation that the Rydberg series of image states display binding energies dependent on the particular crystallographic plane studied. l 7 It was shown that a simple one-dimensional potential model, the multiple reflection or phase model, 29.33 could be used to predict the binding energies of these states and further that the same model provided the link between the image states and the Shockley or crystal-derived surface states. These latter states have been the subject of a number of earlier photoemission studies 34 and more recently inverse photoemission studies. 31 The spectra in fig. 9 present an example of the observation of an image state in a KRIPES experiment. Here the spectra are recorded from a Cu(ll1)surface for various angles of incidence of the electron beam. Aside from transitions into bulk and surface states the image state is clearly seen approximately 0.8 eV below the vacuum level. Having given an introduction, we now present a more detailed description of the properties

Fig. 9. Spectra recorded from a Cu(ll1) surface as a function of the angle of incidence of the electron beam. BB represents an unoccupied bulk band, SS a Shockley surface state and IS an image state. The energy of the isochromat detector used was 11.O eV.

Energy obove EFleVI

520

of the image states before showing their relationship to the crystal-derived states through the multiple reflection model. An electron located outside of a substrate of dielectric constant c experiences a potential

V(z) =

eL (E---

I)

4z

1)

(E+

where z is the distance from the surface. This one dimensional potential is hydrogenic in form and the solution of Schrodinger's equation yields an infinite series of states converging on the vacuum level. For an infinitely repulsive metal surface ( E = 0 ) the binding energies Eb of this series have the form

0.85eV Eb = - 2 n

n = 1,2,3 ,.....

(9)

However if the condition of infinite repulsion is relaxed, wave function penetration of the substrate may be accounted for through the introduction of a "quantum defect" parameter a. Thus

If the reflectivity of the electron wave at the substrate is described by a phase change $c then for the limited energy range of the Rydberg series (eq. 9) the quantum defect parameter may be written 29

Given that $c changes from 0 to 7c on crossing a "Shockley inverted band gap, it may be anticipated from equations (10) and (11) that the binding energy of the image states will reflect the position of the vacuum level within the gap. It was the observation of this phenomena in a comparison of the n = 1 image states on the Cu (001) and Cu (111) surfaces that lead to a more detailed examination of the multiple reflection model of surface states. 2933In this model the electrons are considered to be trapped in the surface region through multiple reflection between the crystal barrier on the one hand and the surface barrier due to the image potential on the other. Using a scattering formulation Echenique and Pendry s3 demonstrated that the bound states or surface states would be given by singularities in the function

521

1

v=

1 - rcr be

x9,+

9,)

where rcei% and rbeigb are the reflectivities from the crystal and image barrier respectively. If one assumes that rc = rb = 1, then the requirement of a singularity in Y’ leads to a quantization condition for the existence of surface states $c

+

n = 1,2,3,

@b = 2x11

(13)

To quantify equation (13) further, we review the two band, nearly free electron description of the crystal band gap. Within this model the electron energies or bands are given by the solution of

I

n2k2 -E

I

2m

vP

n 2(k -

g)2

=

o

-E

2m

vg

where g is a bulk reciprocal lattice vector and Vg is the associated fourier component of the pseudopotential. At the zone boundary g/2. a band gap is opened up of width 21Vgl. Within this gap surface states may exist, characterized by a complex momentum, the imaginary component describing the decay of the states away from the surface. Goodwin 35 was the first to derive the surface state wavefunction within the nearly free electron model. If k = p + iq then the solution of eq.14 for p = 912 gives

ny 2m

=

where Eg =

(4EEg +

-1

v”,) * - (E + Eg)

n y . The corresponding wavefunction 8m

y~ = eq‘cos(pz+Q

with

n2

sin (26) = - 2rn

171

522

Matching logarithmic derivatives at the termination of the crystal zc and the image barrier leads to

Kt;lll

kt -

= p tan (pz,

+

.

6) - q

where K is the perpendicular component of the electron wavevector referenced to the crystal inner potential. The crystal termination is generally taken to be half a lattice spacing beyond the last row of atoms. The phase change Qc a 26 and thus from equation (17) spans the range from 0 to K on crossing the gap. A useful form for the phase change I$b on reflection from the asymptolic

377

0

FERMl LEVEL

( a ) cu (411)

FERMl LEVEL

0 0

s

2s

77

PHASE

Fig. 10. Energy variation of the phases (pc, Q~ and 9 = Qc + $B showing n = 1 image states IS and (a) the n = 0 crystal induced surface state (SS) for C u ( l l l ) , (b) the n = 0 surface resonance for Cu(OO1).

523

image barrier is provided by McRae and Kane, who using a expression 36

WKB approximation, derive the

with Ev - E referencing the binding energy to the vacuum level E., In fig.(lO) we show the result of applying the quantization condition, equation (12), to the copper (001) and (111) surfaces with the phases defined by equations (17) and (18). Not only is good agreement found for the binding energies of the image states but the figure shows that the condition n = 0 gives an excellent prediction for the binding energy of the Shockley type surface state at the bottom of the (111) bandgap 37 and also a surface resonance on the (001) surface. 38

Cu( I 1 1 )

7. ( n . 1 1 . )

Fig.11. Calculated charge densities of the n = 0 surface state and the n =1 image state for C u ( l l 1 ) from Ref. 39. Simple one dimensional models of the crystal-derived or Shockley states have traditionally employed a step potential at the termination of the crystal. Using wave function matching with appropriate Whittaker functions describing the electron states in the image region, Weinert et al 39 rederived the results of the multiple reflection model and from the form of the wavefunctions concluded that the quantum number n of the particular state is simply related to the number of extrerna in the wavefunction beyond the crystal boundary, fig. 11. Thus the one dimensional potential running perpendicular to the surface supports an infinite series of states in an identical fashion to the coulombic potential of the hydrogen atom. However for the latter coulombic potential n = 0 represents a non-physical solution, the wavefunction having a

524

singularity at the origin. The image potential on the other hand saturates in the surface region (see section 3.3) allowing an n = 0 lowest order solution which in the limit has an identical form to the wavefunction appropriate to the step potential. The step potential may therefore be viewed as a screened image potential and as with any short range potential the number of allowed states is finite. In a series of papers N.V. Smith and coworkers 19,40-4* have applied the phase model to a number of zone boundary surface states. Within the NFE model, the wavefunction inside the crystal for zone boundary states must now be described by four plane waves rather than two. The electron waves again make multiple reflections between the crystal potential and the one dimensional image potential. In each complete cycle, the surface barrier is approached twice and the quantization condition gives

If

is written as the average phase change on reflection from the surface barrier then (211

@ c + ~ @ b=> nn

showing that now the number of surface state solutions has doubled. The wavefunctions within the crystal may be expressed as even and odd combinations of the plane waves thus

X

-

r

-

Y

PARALLEL WAVE VECTOR

Fig. 12. E(kl1) dispersion relations for the surface features of P d ( i l 0 ) labelled Sn in fig. 6. The solid curves represent the predicted binding energies of surface states from the phase model. Shading indicates the projected bulk band gaps. The dashed curve (ET) is the electron escape threshold.

525

where at the zone boundary of the surface Brillouin zone kil = g11/2 and p, q, and 6 carry the same meaning as in equation (15). A complete analysis including detailed derivations of these different parameters has been presented by Chen and Smith. 42 As an example, we show in fig 12 the result of applying the quantization condition (eqn. 19) to the (110) surface of Pd. Several states, T azimuths, are observed experimentally (fig. 6 and ref. predicted by the model in the TX and i 19). We note that wavefunction matching with the same crystal wave functions, eqn. 21, but with a step potential rather than image potential description has also been applied by Bartynski et al. to the noble metal (110) surfaces. 43 The successes of the multi-reflection or phase model are demonstrated in Table 1 where the experimental observations and model predictions for the binding energies of surface states on different noble and transition metal surfaces are tabulated. The model predictions shown are restricted to those that have been derived using the straightforward application of equations (13) and (20) above with no attempt to adjust the form of surface potential as discussed in section 3.3 below. We now turn to a brief discussion of the effective masses observed for the image states. Because of their location well outside of the crystal potential, one assumes that these states will probably display a free electron like dispersion parallel to the surface with an effective mass of unity. However several experimental studies have suggested that in certain cases the effective mass may be considerably higher than this: m, = 1.6 for Ni(1l l ) , 5 5 Ag(001) 60 and Pt(001). 6 2 The earlier observations lead to theoretical models based on both surface corrugation 76 and on many body effects 77. However these ideas were quickly refuted in a series of papers. Several groups 58,7879 demonstrated that surface corrugation was not responsible for any observed enhancement. Indeed such a model requires an unrealisticly large corrugation potential. In several other studies, it was found that many body effects or a dynamic image ~ ~the potential lead to an enhancement of the effective mass of less than 3%. 3 9 ~ 7 9 ,On and experimental side, repetition of the original experiments on Ag (OOl), 6 1 N i ( l l 1 ) Pt(001) 6 3 has tended in all cases to reduce their experimental effective masses to values close to 1.Ome. However high resolution two-photon photoemission studies show that for certain image states located near the top of the NFE band gap, the effective mass can be higher than unity, 1.3me in the case of Ag(ll1). 6 1 The currently accepted explanation of this observation, is that the binding energy of the state represents the result of "competition" between, on the one hand, the crystal potential and on the other, the image potential. Near the edge of the bulk band gap, the surface state or image state may be expected to show a longer decay into the bulk and consequently the crystal potential will play a greater role. This is reflected in the image state displaying an effective mass similar to that of the nearby gap edge. In band gaps away from the center of the zone several of the crystal derived surface states have been found to have effective masses considerably larger than the 1.Ome. However by simply applying the phase analysis with gap edges determined from the combined interpolation scheme, N.V. Smith and coworkers 19.42,61 e e 3 have shown good agreement between predicted and experimentally observed effective masses for both image states and the crystal derived states on a number of different surfaces.

526

Table 1. Binding energies of surface states as determined experimentally and as predicted by the phase model for different critical points in the Erillouin Zone of noble and transition metal surfaces. The subscript refers to the phase model notation with 0 for crystal derived and 1 for image potential derived states. The former are referenced with respect to the Fermi level, the latter to the vacuum level (except for the c110> Y image states)

527

3.2.2

Tamm or d-type surface states.

There have been several studies of d-type unoccupied surface states on the (100) surfaces of Nb, Mo, Ta and W. Interest in these surfaces stems from the observation that the W 84 and Mo 85 surfaces undergo temperature dependent surface reconstructions. Several theories have suggested that surface states close to the Fermi level might well play a role in these reconstructions. 86 In a study of W(100) and Mo(l00) Drube et al. 8 7 identified a surface state of even symmetry, a dZ2 state, on both surfaces at the center of the zone, fig. 13. Interestingly an odd Z2 state predicted to cross the Fermi level at f FR on the W surface 88 was not observed even though a candidate for this state had previously been identified in an earlier photoemission study.

89

In

another IPES study Bartynski and Gustafsson have examined the unoccupied surface states on Ta(001). Ta has one less electron than W and thus it has been proposed that any occupied states

-

2

0

2

4

6

8

-

2

0

2

4

6

ENERGY (eV relative to E,I

Fig. 13. (a) Energy dependence of Inverse Photoemission spectra from W(OO1) at the zone center from ref. 76. The intrinsic surface state near EF and the image potential state at EF + 3.9 eV show no dispersion with k l . (b) Angular dependence along the [I101 direction (FR in the surface Brillouin zone). near the Ferrni level on W might be unoccupied on Ta. 91 In their experimental study Bartynski and Gustafsson identified a number of surface states and/or resonances on Ta but concluded that a simple rigid band shift did not result in complele overlap of the Ta and W surface features. They did however, identify a surface state at EF at the center of the zone which they associated with the "Swanson Hump" state previously observed in the photoemission study of W. 89

528 Pan et al. 92 have studied the unoccupied states on the Nb(001) surface. As in the other studies they identified an unoccupied surface state at the center of the zone of dZz character. Examining the photon energy dependence of this state, the authors found, in agreement with an earlier photoemission study of the same surface state, 93 that the wavelength dependence of the intensity closely followed the square of the amplitude of the external electric field, [E,12,,t. This observation, fig. 14, suggests that the state is highly localized in the surface region.

I

I

IE#

I

1

I

I

I

I

20

22

24

26

28

OUI

8 I

Id

I6

16

PHOTON ENERGY l e v 1

Fig. 14. The intensity of the dZz type surface state at the center of the zone on Nb(001) as a function of photon energy. The experimental points are compared with the calculated Fresnel fields inside and outside of the surface.

3.3

The Surface Barrier

The multiple reflection model provides a simple description relating the binding energies of both the image states and the crystal-derived or Shockley states. These binding energies reflect the local boundary condition, which in the surface region is determined by the response of the other electrons to the presence of the electron in the surface state. In the terminology of Lang and Kohn 94 an electron induces a local charge distribution in the surface region and the centroid of this induced distribution represents the classical image plane. In modelling the surface barrier it becomes necessary to use some form of saturated image potential. Whilst the form of the image potential given by eqn. (8) is appropriate at long range, close into the surface the potential has to flow smoothly over into a value characteristic of the inner potential of the metal. Weinert et al. 39 presented a systematic exploration of the relationship between the binding energies of the surface states and the position of the image plane. Using wavefunction matching with the image plane position as a variable they found that each position of the image plane defined a unique series of binding energies for the surface states. Within the limitations of their simple model they found that fitting to the experimental observations produced image plane positions

529

closer to the "jellium-edge" than calculated in the formal first principles theory of Lang and Kohn and further a crystallographic dependence. The same conclusions were arrived at by Ortuno and Echenique 95 using a similar one dimensional model. Interestingly, a more recent first principles calculation using a non-local exchange correlation potential has also placed the image plane closer to the jellium edge. 96 The exploration of the form of the surface barrier has continued in more sophisticated analyses. Using different surface barriers, Chen and Smith 42 attempted to fit the full range of surface states, both at the zone center and the zone boundary, on a number of different crystal planes. With a NFE description of the crystal potential they concluded that caution should be exercised when presenting quantitative information on the position of the image plane or shape of the surface potential. Still more sophisticated modelling relies on the use of fully self-consistent calculations of the crystal potential. This potential is matched to the so called JJJ potential, 97 which is thought to provide an adequate description of the saturated image potential. It takes the form (in hartrees)

Y

A exp [ - p ( z - za)]

+1

A and j3 are constants determined by matching V(z) and its derivative at the reference plane z = to. The parameter X determines the range over which the barrier saturates and UO represents the bulk inner potential. Using such a model Jennings et al. 98 have fitted both the planar average potential for a number of metals determined from density functional calculations and also the LEED fine structure observed for a number of different surfaces. Smith et al 99 have also used this same model to fit photoemission and inverse photoemission data from all of the noble metal and neighboring transition metal low index surfaces. In all of these models, there appears to be general agreement on the approximate position of the image plane, which ranges from 1.5 to 2.5 a.u. from the center of the last row of atoms depending on the crystal plane. Most of the density response occurs in the low density tails of the electron profile in the vacuum region. The simplest model for this density that would include the lattice, and hence any face dependence, would be the superposition of atomic like densities. Starting from this premise, Smith et al. 99 determine the planar averaged density for a single layer of atoms and extend this to the planar averaged density from a' series of layers < p(z) >. They show this to have the form

where zj represents the jellium edge position and ,€ determines the the decay length of the density profile. Within this model therefore the density profile reflects the jellium edge position, but only as a scaling factor, and the image plane position will show some face dependence. More recently Tamura and Feder 99a have considered the use of an energy-dependent "dynamical" rather than "static" surface potential barrier. For the Pd(ll0) surface, they found that the use of such a barrier avoided some of the problems encountered by Smith et al, 99 who found it difficult to define a single unique fit to all of the surface states on the (110) surfaces.

530

3.4

Interface states and Thin Films.

As a conclusion to our discussion of IPES studies of metallic surfaces we consider in this section the results obtained from interfaces or bimetallic systems. Described in greater detail elsewhere in this book, the study of thin films has been prompted by their unique properties compared to their bulk counterparts, in such areas as catalysis 100 and magnetism. lol To date IPES studies of thin films have been limited. Drube and Himpsel lo* have reported studies of monolayer coverages of Mn and V deposited on a Ag(l11) substrate. By comparing the spectra with those obtained in an earlier study of the Mn-in-Ag spin glass 103 and also with first-principles calculations of these thin films 1°4 the authors conclude that their films were ferromagnetic and that they were observing minority spin features. However more recent calculations Io5 suggest that, certainly in the case of a Ag(001) substrate, the early transition metals prefer an antiferromagnetic rather than a ferromagnetic configuration. The authors of the latter paper suggest that on the (111) surface the situation may be more complex. A spin polarized inverse photoemission study of such systems would be capable of determining whether

ENERGY ABOVE E, (eV)

Fig. 15. Inverse photoemission spectra recorded from the clean N b ( l l 0 ) surface (dashed spectra) and the Nb surface with a monolayer of Pd (solid line spectra). The normally incident electron beam energy with respect to the Fermi level is indicated.

531

the peaks above the Fermi level are polarized, evidence of ferromagnelism, or unpolarized, indicative of a paramagnetic or antiferromagnetic structure. Frank et al. lo6 have studied the growth of Ni films on a C u ( l l 1 ) substrate. In the region of one monolayer thickness they observe a well defined peak situated at the Fermi level, which they interpret as the appearance of an unoccupied nickel d band of minority character rather than the C u ( l l 1 ) Shockley state 37 pulled to lower binding energy. They support this argument by examining the adsorption characteristics of hydrogen on the thin film. The fact that hydrogen appears to adsorb on this surface leads the authors to suggest that as in the case of nickel surfaces lo7, it is the presence of d holes at the Fermi energy that mediates the adsorption. However they observe their "unoccupied nickel d band" at,the center of the zone in contrast to the results of a first-principles calculation by Tersoff and Falicov, lo8 who suggest that it should only be observed farther out in the zone. This therefore represents another system where SPIPES might well shed more light. Thin films of palladium grown on a N b ( l l 0 ) substrate have been extensively studied using photoemission, LEED,AES and a number of other techniques. This interest originally stemmed from the observation that the hydrogen absorption characteristics of the niobium are strongly modified by the presence of the thin films. lo9 Photoemission indicates that with the formation of the Pd monolayer the valence band has a form characteristic of a noble metal in that the d bands appear to be filled. l o Indeed the monolayer is inert to the adsorption of carbon monoxide at room temperature. Inverse photoemission studies of this system by Pan et al., 82 have revealed the presence of a well defined interface state with the formation of the first monolayer. Shown in fig. 15, the state displays little or no dispersion with .kl evidence of a two dimensional state. The interpretation of it being an interface state is confirmed by comparison with the results ofboth a FLAPW slab calculation and a Pd3Nb3 multilayer calculation. These calculations, fig. 16, indicate that with the formation of the interface, the state, which was previously a surface resonance on the clean niobium, now becomes more localized in the interface. Finally we consider alkali metal overlayers. Heskett et al. have studied the adsorption and growth of Na thin films on an Al(111) substrate. 113.114 .On the clean surface these authors identify an image state, 0.54 eV below the vacuum level. With the adsorption of Na they suggest that this state is quenched and that new features appearing in the spectra represent transitions into into the unoccupied 3p band and a hybridized s-d band. In support of this argument the authors find that the dispersion they observe for these states compares favorably with the dispersion calculated for a Rb thin film by Wimmer. 115 This interpretation of the spectra has however been disputed by Lindgren and Wallden. 116 The latter authors suggest that the peaks reflect the presence of bound state resonances in the thin film. In a series of papers 117-119 they have applied the phase model of surface states to the thin film situation. Thus the quantization condition, eqn. 13, would now give

where $c and $b are as defined in eqn (13) and ,@, = kd is the phase change through a film of thickness d. Applying this model to NdAI(111). Lindgren and Wallden demonstrated that the dominant peak in the spectra could be interpreted as a bound state resonance satisfying eqn (23). The latter interpretation is appealing in that the peak in the spectra of Heskett el al. does indeed appear to be tied to the vacuum level.

532

a

3.

sub-surface

3.

interface Nb

Fig. 16. Calculated local density of states at various sites (left to right) for the N b ( l l 0 ) surface, for the commensurate Pd/Nb(llO) surface and for the bulk PdaNba(l10) multilayer. The shaded regions delineate the positions of the surface and interface peaks in the various calculations.

4.

SEMICONDUCTOR STUDIES

Inverse Photoemission has been used to identity critical points and map out the dispersion of the conduction bands in a number of semiconductors. This exercise, identical to that for bulk band mapping in metals, has been carried out for Si and Ge, 12O GaAs, GaP l z 2 , CdTe, CdS, CdSe, 123 InP, lnAs and InSb. 124 In order to interpret the data, a free electron description has generally been used to describe the initial state and for the Ill-V compounds the dispersion obtained for the conduction bands in IPES experiments has nicely complemented the dispersion obtained from the final states in earlier ARPES experiments. 125 An example is given in Fig. 17 for the conduction bands of InP in the rZKX direction. l Z 4 Again, as in the case of metallic surfaces, the ability to vary the detected photon energy allows the clear identification of surface states and surface resonances. The termination of the bulk structure of the semiconductor results in the presence of broken or dangling bands in the surface layer. The surface atoms rearrange allowing bonding/antibonding pairs to form between these half-filled broken bonds and thereby producing both occupied and unoccupied surface states. States of the latter type have been identified on Si(lO0)ZXl and Si(ll1)7X7 126 and GaP(l1O)lXl. 122 On these particular surfaces, the unoccupied surface states fall within the gap. This is not always the case and on many other surfaces hybridization with bulk bands leads to surface resonances rather than surface states. Thus surface resonances have been observed on G e ( l l 1 ) Z X l 120 S i ( l l 1 ) Z X l 120.127 and G a A s ( l l 0 ) l X l . l2I

533

Momentum nlong Ill01

Fig. 17. Comparison of the experimentally determined conduction bands of InP in the rXKX direction from IPES studies, ref. 124 (filled symbols), with those obtained in PES studies (open symbols), ref 125. These are both compared with pseudopotential calculations for bands below 7 eV (ref. 125a) and free electron bands folded back into the reduced zone above 7 eV. Recently it has been demonstrated that information on both the occupied and the unoccupied surface electronic structure may also be obtained from the Scanning Tunneling Microscope. lZ8 In this technique a fine metal tip is brought up to the surface under investigation. By varying the bias voltage applied between the tip and surface, electrons are enabled to tunnel either into or out of the different surface states. The important and interesting characteristic of this spectroscopic technique is that it provides information on the real space location of these states and thus compliments the information obtained in PES and IPES experiments which locate the states in momentum space. A number of studies of semiconductor-metal interfaces have been carried out. These include Pd on Si(l1 1)7X7,126 Cu, Ag and Au on the same surface, 129 Ti on GaAs(l1O)lXl 130 and Sb overlayers on GaAs(l10) and InP(110). l 3 I In general, with the initial deposition of the metal, new unoccupied states are induced above the Fermi level. With the formation of an intermediate compound, the unoccupied density of slates is distinctly different from that characteristic of the metal overlayer formed at high coverage. For example, in the case of Pd2S.i formed when Pd is deposited on Si 126 the IPES study was characterized by a broad band of unoccupied states 4 eV in width as opposed to the narrow peak associated with the unoccupied d bands of Pd metal or the lower density of states of the conduction band of the Si substrate. It is possible to obtain a well-ordered (1x1) overlayers by thermal annealing after room temperature deposition of Sb onto freshly cleaved GaAs(l10) and InP(110) surfaces. The results of an inverse photoemission study of these ordered overlayers are shown in fig 18

534

I

,

1

, Sb/GaAs(llO) I

I

2

4

6

I

0

1

Sb/lnP(110)

1

E, = 15.6 eV

0

I

2

E, = 16.6 eV

0

(1x1)-Sb

A

clean

4

6

8

Energy (eV relative to E),

Fig. 18. Inverse photoemission spectra from clean cleavage (triangles) and an ordered (1XI) Sb overlayer (dots) for GaAs and InP. Sb induced states are marked by arrows. The peaks above 4 eV are derived from bulk states and are unaffected by the Sb adsorption. where it will be seen that the presence of the Sb produces a well defined surface resonance at 2.1 eV above the valence-band maximum for both substrates.

5.

ADSORF'TION SYSTEMS

Inverse photoemission has been applied to the study of atomic and molecular adsorption systems spanning bath chemisorption and physisorption. The full description of the bonding of atoms and molecules to surfaces involves the Identification of both bonding and antibonding orbitals. Whilst the division between bonding and antibonding does not necessarily represent a division between occupied and unoccupied, one may assume that the bonding orbitals, the more deeply bound states, have tended to be the subject of earlier photoemission studies. On the other hand the antibonding levels are more likely to be probed in inverse photoemission studies of adsorbates. Although limited, these studies have moved from the straight forward identification of the adsorbate induced levels to the examination of the two dimensional bandstructures associated with the adsorption. Discussion of the new features above the Fermi level ranges from their identification as the antibonding component of a surface molecule complex through to the possibility of standing wave resonances formed in a planar averaged cavity induced by Ihe adsorbate between the substrate and the surface barrier. 132.133 The latter model is identical to that used in the descriplion of thin films by Lindgren and Wallden (section 3.3). 1 1 6 In the following sections we discuss oxygen chemisorption, xenon physisorption, and Ihe adsorption of diatomic molecules, all on metal substrates.

535

5.1

Oxygen chemisorption

Oxygen represents the most extensively studied atomic adsorbate in inverse photoemission. Its chemisorption on all of the low index planes of nickel 134-137 and on the (110) and (111) surfaces of copper 138 has been studied. In Figure 19, the spectra recorded from a Ni(l10) surface as a function of oxygen exposure 137 shows the emergence of a peak 3eV above the Fermi level with the formation of the (2x1) overlayer structure. A similar adsorbate induced feature is observed on the Ni(11l) surface 136,where polarization of the emitted photons or symmetry selection rules have been used to determine that the new feature has A1 symmetry. The authors therefore associated it with the oxygen 2p, orbital. However this is in disagreement with the results of an earlier study of the same system 134 where it was concluded that the state was pxpy derived or A3 Symmetry.

L 3 w = 9.7eV

0

2

4

6

8

E - E , ( eV ) Fig. 19. Normal incidence IPES isochromat spectra (9.7 eV) recorded from N i ( l l 0 ) as a function of oxygen exposure as indicated. The different LEED patterns observed for the overlayer structures are also indicated. Using the surface molecule descrlption, Desinger et al. 137 have suggested that a correlation exists between the binding energies of the occupied bonding orbitals observed in photoemission studies and the energies of the unoccupied antibonding orbitals for the same system. They show that in progressing from Ni(l11) through Ni(001) to'Ni(l10) the bonding level moves further from the Fermi level to higher binding energy whilst the antibonding level moves away from the Fermi level in the opposite direction. The observation of the unoccupied level on the Ni(001)

536

surface is required to confirm such a picture but unfortunately the predicted position has In the first coincided with a substrate bulk band transition in all studies to date. 1 3 5 v 1 3 7 ~ 1 3 9 studies 135,137 it was suggested that an adsorbate induced state of A5 symmetry. i.e., 2pxpy character, leads to an increase in the density of states above the Fermi level. However, the later spin polarized study 139 found a decrease in the density of states rather than an increase and further, found no change in the spin polarization of the unoccupied d bands immediately above the Fermi level. This latter observation argues against the presence of an additional adsorbate induced feature. Interestingly, an adsorbate induced occupied feature, immediately above the d bands, was identified in earlier photoemission studies of oxygen adsorbed on the Cu(OO1) surface 140 However, the symmetry of the new state was not identified in those in a ~ ( 2 x 2 structure. ) studies. Donath et al. 14 have performed a SPIPES study of the 0 p(2xl)/Ni(llO) system and find that the adsorbate induced peak 3 eV above the Fermi level is exchange split by 80 meV. They interpret this as an indication that the oxygen atom is itself magnetized. We will return to a discussion of this observation below. On both Cu(ll1) and Cu(llO), an oxygen induced peak has been identified in IPES studies 13* at approximately 3.0 eV above the Fermi level, similar to that found on the nickel surfaces. On the Cu(l10) surface a number of other features were identified following the formation of an ordered overlayer. However, it was suggested that most of these features might well be associated with bulk and surface derived bands from the substrate. In particular a second adsorbate induced feature 6.3 eV above the Fermi level at the center of the zone is thought to reflect the folding of X ontoy via the 2x1 surface superlattice. Chen and Smith 133 have examined the adsorption of oxygen on these surfaces within the standing wave description. Using phase analysis they model the adsorbate layer by shifting the effective image plane position outward. Figure 20 shows the results of such an analysis for clean

8

“ 4

>-

W K

Y W

2

0 1.0

0.5

0

0.5

PARALLEL WAVE VECTOR

1.0

(i-‘)

Fig. 20. E(kl1) dispersion relations from ref 133 for clean C u ( l l 1 ) and for the adsorbate system Cu(l11)/02. Open circles are the inverse photoemission data of ref. 17 on clean Cu(ll1); the photoemission data of ref 37 on clean C u ( l l 1 ) are shown as the dots near F. Solid circles are the inverse-photoemission data of ref. 137 for Cu(l11)/02.

537

C u ( 1 f f ) and Cu(111)/0. With a displacement of the image plane of 1.4 A the band assigned to the pz derived antibonding orbital in the surface molecule model now appears in the standing wave resonance description as the clean surface "n=l" image state shifted towards the Fermi level. Interestingly, within this picture, the adsorbate induced peak identified in the SPIPES study of Ni(l1O)/O as an antibonding level 141 would now be associated with a modified surface state of the substrate. Thus any exchange splitting in the peak would reflect the surface magnetization of the substrate itself rather than the magnetization of the adsorbate. From the experimental data a picture emerges of oxygen bonding to the transition metals with the formation of a well defined bonding orbital approximately 6.0 eV below the Fermi level. Such an observation finds close agreement with a calculation of the electronic structure of the ~ ( 2 x 2 )oxygen structure on Ni(001) by Liebsch. 142 That calculation gave a splitting of 7.0 eV between the bonding and antibonding levels with the unoccupied 2pz orbital further from the Fermi level than the 2pxp, orbitals. It is not clear at this stage whether these unoccupied levels are to be associated with the new peaks observed in IPES studies, typically 3 eV above the Ferrni level, or whether they are in fact much closer to the unoccupied d bands. No candidate for such an orbital has been conclusively identified on any surface studied to date.

5.2 Xenon Physisorption Because of its weak interaction with the substrate, xenon physisorption has been thought to provide an ideal test of final state screening in electron spectroscopies such as photoemission and inverse photoemission. In photoemission studies, the occupied xenon levels are observed to move to higher binding energy with the growth of each new layer. Kaindl et al. 143 have suggested that these layer dependent binding energies reflect the distance-dependent image charge screening. Such a mechanism represents a final state effect with the photohole inducing the image or screening charge in the substrate. Wandelt and co-workers have proposed an alternative model in which the binding energies of the Xe levels are determined by the layer dependent workfunction. 1 4 4 t 1 4 5 In this latter model the mechanism is an initial state effect and the final state effects are thought to be negligible. In photoemission studies both of these models may be invoked in that they both result in binding energy shifts in the same direction. In inverse photoemission on the other hand the two models would result in binding energy shifts in opposite directions. The interpretation of the IPES data has relied on comparison with photoemission and EELS data, the latter representing transitions between the occupied and unoccupied states. In two separate 1PES studies of Xe physisorption, Horn et al. 146 and Wandelt et al. 147 interpreted their data in terms of the two different models. Horn et al. 146 studying the adsorption of Xe on A u ( l l 0 ) were able to identify peaks in the multilayer spectrum by comparison with atomic spectra and EELS data. With certain assumptions about the structure in the monolayer spectrum, they concluded that their results were consistent with the image charge screening model. In a later study, Wandelt e l at. 147 adsorbed Xe multilayers on the Ru(001) surface. They interpreted their multilayer spectrum, fig. 21, in a similar fashion to the earlier study. However they concluded that their observation, peaks moving closer to the Fermi level with increasing coverage, supported the local work function model. In that the spectra from the multilayers appeared similar it would seem that it is crucial to correctly establish the binding energies appropriate to the monolayer. Unfortunately the monolayer coverage displays the weakest signal.

538

0

2

.

4

6

8

E-EF l e v ) Fig. 21. Inverse photoemission spectra recorded from a clean Ru(001) surface and the same surface following exposure to xenon. The indicated exposures correspond to 1 ML (curve b), 2 ML (curve c) and 5 ML (curve d) of physisorbed xenon. B and S designate unoccupied bulk and surface bands of the Ru, respectively. We note however that in a later paper Bertel et al. 14* have suggested that interpretation of the data may be further complicated by whether or not wetting of the substrate occurs. In the following section we return to the subject of final state screening with our discussion of molecular adsorption.

5.3 Molecular Adsorption The most studied adsorption system in surface science has been and remains the adsorption of carbon monoxide on transition metal surfaces. It is now well established that in most systems the carbon monoxide is chemisorbed on the surface in an upright or near upright configuration with the carbon atom closest to the surface. The standard models of the adsorption propose that the bonding involves the molecular 50 and 2x: orbitals both centered on the carbon atom. The former is occupied in the gas phase and the latter unoccupied. In the Blyholder model 149 these molecular orbitals are thought to bond to the metallic occupied and unoccupied d orbitals as shown in fig. 22(a). Electrons are considered donated from the occupied 5a orbital to the d complex and this charge transfer is compensated by "back-donation'' into the unoccupied 2 r level. Avouris et al 150 have described an alternative model, the 2r resonance model, which favors a greater participation of the substrate sp continuum. In fig. 22(b) we show a molecular orbilal representation of this model. The interaction between the continuum and the unoccupied 271 orbital is thought to result in a considerable broadening of the latter and its concomitlanl partial

539

co

Metal

CO

2noo

Metal

Fig. 22. (a) The Blyholder model (ref. 149) of carbon monoxide adsorption with donation of electrons from the 50 orbital compensated for by back-donation of electrons into the molecular 271 level. (b) The 2x resonance model with increased interaction of the substrate continuum. occupancy. One essential difference that arises from these two possible bonding configurations is that with increased bonding strength the Blyholder model suggests that the unoccupied 2x orbital will move further from the Fermi level whilst the resonance model would predict the same level moving closer to the Fermi level. It is to be hoped therefore that IPES studies of the 2 x orbital will shed further light on the bonding mechanism. As we shall see however, a number of other factors potentially complicate the discussion. These include both adsorbate-adsorbate interactions and also final state effects where it is to be recognized that IPES represents, as does PES, an excited state spectroscopy. The first clear IPES observation of the unoccupied 2x orbital of CO adsorbed on a transition metal, namely the N i ( l l 1 ) surface, revealed a broad peak positioned 3 eV above the Fermi level. 1 5 1 Subsequent studies of numerous surfaces have revealed a similar but in general narrower feature. In Figure 23 we show the IPES spectrum recorded following CO adsorption on the Ni(001) surface. 152 Within the Blyholder model the carbon monoxide derived feature 4 eV above the Fermi level would correspond to the antibonding component of the metallic drr-2n band. We note in passing that to date no studies have found any structure identified as relating to the unoccupied or antibonding component of the do-5o bond. Several authors have attempted to correlate the observed energy of the 2x orbital with the bonding strength of the carbon monoxide. 77*152,153 Measured wilh respect to the Fermi level, there appear to be no obvious systematics in the observed position of the CO 2x orbital when either strongly chemisorbed on transition metals or weakly chernisorbed on the noble metal copper surfaces. However, in all cases of adsorption on metal surfaces, the 2x orbital is found below the vacuum level rather than above, as in the case of the gas phase molecule. This observation clearly contradicts the naive interpretation of the standard Blyholder model and has lead authors to look for correlations in terms of the binding energy with respect to the vacuum level. Figure 24 shows such a correlation by Johnson and Hulbert 152 where the binding energies

540

referenced with respect to the vacuum level are compared with the infra-red stretch frequencies of the different adsorption systems. 155 The latter being used as an indication of the relative bonding strength. The figure clearly shows that in moving from the gas phase GO 154 or the weak physisorption system CO/Ag, 156 through the weak chemisorption regime, GO on the copper surfaces, 77 to the stronger chernisorption systems, GO on the transition metal surfaces,l~l.152.157-159 the measured energy of the 2n orbital drops from above the vacuum level to below. As already noted, whilst bonding to the d orbitals alone will result in the 2rc orbital moving further from the Fermi level, increased interaction with the sp continuum is expected to result in the 2n moving to higher binding energy or closer to the Fermi level. Proponents of the surface resonance picture have therefore suggested that many of the observations favor their model. Indeed on one surface, namely Cu(OOl), two peaks were observed following GO adsorption and these were interpreted as the bonding-antibonding pair derived from the 2n-px interaction. 160

Fig. 23. Comparison of inverse-photoemission spectra recorded for an electron beam incident along the surface normal of (a) the clean Ni(001) surface and (b) the same surface following the adsorption of 20L of CO at 100K. The incident beam energy was 17 eV. Several authors 31.150.i5*t161,162 have noted that interpretation of the spectra may also be complicated by final state or relaxation effects. IPES is a probe of the excited state, an electron having been added to the system. For delocalized states, such as bulk bands, the perturbation introduced by this additional electron will be minimal. However in the case of molecular adsorbates, the more localized interaction will lead to relaxation effects which modify the measured final state energy. The coulombic interaction between the added electron and the other molecular electrons will lead to the affinity level or final state being at a lower binding energy

541

2

1

co

CO /Ag

I -4

I

I I

I

Fig. 24. Binding energies, with respect to Evac, of the CO 2x level plotted against the infrared stretch frequencies for the same adsorption systems. The vertical dashed lines represent from the left, the division into threefold, twofold and one fold adsorption sites. Reference sources are as follows: N2, CO (155), CO/Ag (156), C u ( l l l ) , Cu(OOl), Cu(ll0) (77),NdNi(001), P d ( l l l ) , Ni(001) (1521, Pd(001) (157), N i ( l l 0 ) (158), P t ( l l 0 ) (159). than the ground state. Indeed, as already noted, in the gas phase the measured affinity level of CO lies in the continuum above the vacuum level. When the CO molecule is brought into contact with a surface the screening provided by the metallic electrons reduces the separation between the affinity level and the ground state. It was this observation that lead Johnson and Hutbet? 152 to suggest that final state effects might well play a role in determining the observed positions of the CO 2 x orbital shown in Figure 24. Gumhalter and co-workers 162 have also discussed the role of such final state effects. They examine the effect of increased delocalization on the substrate image screening of the affinity level. Such a delocalization will result from a strengthening of the interaction between the molecule and the surface. They argue that CO adsorption on the noble metal surfaces such as copper, represents an upper limit to the image induced relaxation effects. On this basis they therefore conclude that CO adsorption on transition metal surfaces such as nickel must include initial state shifts reflecting the interaction of the 2 x orbital with the substrate sp continuum. In a recent study of CO adsorption on N i ( l l l ) , Frank et at. 163 reported the observation of a coverage dependent position for the CO 2 x level. At low coverage they identified a peak which they interpreted as the 2x level, only 1.3 eV above the Fermi level, closer than had previously been observed. At higher coverage with the formation of an ordered overlayer this peak moved further from the Fermi level and showed evidence of substructure or multiple peaks. Following an earlier study of CO on Ni(ll0) by Freund et al., 164 they suggested that the substructure reflected adsorbate-adsorbate interactions and that further it was this interaction rather than

542

final state effects that ultimately determined the observed position of the 2x level. Evidence for adsorbate-adsorbateinteractions is provided by a recent IPES study of CO on Ni(ll0). 165 Here the authors report the observation of a two dimensional bandstructure derived from the adsorbate 2~ orbitals. They suggest that their study combined with an earlier photoemission study 166 of adsorbate derived bands below E, represents the only complete study of all of the bands associated with the drr-2x interaction. Studies of the coadsorption of CO and potassium have consistently shown on all surfaces that the presence of the alkali metal results in the 2x level moving closer to the Fermi level. 77.152,167 Coadsorption is generally thought to result in increased back donation into the 2x level as evidenced by the considerable reduction in the infra red stretch frequency. 168 The shift of the 2 x level towards the Fermi level is therefore again inconsistent with the Blyholder model and implies that other interactions are taking place. Whether these interactions reflect a direct bonding between the CO and alkali metal 169 or long range electrostatic effects associated with the alkali atom 170 remains to be determined. There have been a few studies comparing the adsorption of NO and CO on different surfaces. 152.157 The two molecules differ in that gas phase NO already has an extra electron in the antibonding 2 x level. The question arises as to whether this extra electron will serve as a tag

1

I

1

1

I I 0.0

1

1

1

1

I I I ( 1.0 2.0

1

1

1

3.0

1

1

1

1

4.0

1

1

1

1

5.0

1

' 0

E N E R G Y ABOVE E,leV>

Fig. 25. Inverse photoemission spectra recorded from (a) Pd(ll1) and (b) Ni(001) following the adsorption of of NO at room temperature and 100K respectively. The incident electron beam energies were 17.0 eV with respect to the Fermi level. The 2rr orbitals are indicated by the vertical lines.

543 of the 2 x level and allow for a clearer identification of the interaction between the adsorbate and the substrate levels. To date all IPES studies of NO on transition metal surfaces have been consistent in placing the unoccupied 2 x level approximately 1.5 eV above EF. Examples are given in Figure 25 for NO adsorbed on a Ni(001) surface and a P d ( l l 1 ) surface. 152 Photoemission studies of these same adsorption systems have identified what is thought to be the occupied and 2.6 eV 172 below the Fermi level respectively. It is component of the 2~ complex 2.1 eV of interest to determine whether these latter levels are predominantly substrate drr or molecular 2 x in character ? Rogozik et al. 157 have suggested that in the ground state of the adsorbate complex, the NO 2rr level straddles the Fermi level. Interpreting the data within this framework, the peak observed in the photoemission spectra may be seen as the metallic dx component of the d n - 2 n bond. A similar picture has also been proposed in a discussion by Batra and Brundle 173 of an earlier photoemission study of NO adsorbed on Ni(001). The latter discussion was based on the results of a “ground-state’’ cluster calculation. Johnson and Hulbert 152 have presented an alternative view based on the excited state. They point out that the equivalent dx bonding component for CO adsorbed on transition metal surfaces has been identified in only a few systems 166,1748175and therefore suggest that the new feature observed in photoemission spectra may well represent emission from the predominantly molecular 2n orbital, in agreement with earlier studies. 171 By performing transition state calculations ( adding or subtracting 0.5 electron to or from the 2 1 level ) on a linear NiNO chain they find that the two final states are separated by an energy difference of the order of 5.0 eV. Thus in this picture, measurements from the two adsorbate induced features gives a measure of the effective electron - electron interaction Ueffin the presence of the metallic substrate. U,n therefore takes the values of 3.6 and 4.2 eV for Ni (001) and Pd (111) respectively. In the gas phase, an ionization potential of 9.26 eV has been measured for NO 176 and 0.024 eV for NO- li7 giving a U,ff of 9.28 eV The difference reflecting the increased screening in the presence of the substrate. It has been noted by several authors 151.152.16Z178.179that some measure of the screening provided by the metallic substrate may be obtained by comparing IPES spectra with the results of NEXAFS of Near Edge X-ray Absorption experiments. In the latter experiment an electron is promoted from a core level, [e.g . the C 1s level] to the unoccupied 2n level by absorption of a photon of the appropriate energy. The two spectroscopies differ through the presence of the core hole. Gumhalter et al. 162 have compared the CO/Cu (110) adsorption system with gas phase CO. They find that the presence of the metallic screening reduces the effective core hole potential U from 10 eV for the gas phase to approximately 2.2 eV in the adsorbed phase. A similar Comparison for the CO/Ni(001) chemisorption system produces a value of 3.75 eV. 1 5 2 Another measure of the level or effect of metallic screening may be obtained by comparing the observed binding energies of the molecular shape resonances or bound states in the continuum. These observations are described in the next section. 5.4

Molecular Shape Resonances.

Shape resonances are thought to arise through multiple scattering of the electron within the molecular potential l80 and have been observed in both valence l e l and core level photoionization. 182 By invoking dipole selection rules, the angular dependence of the shape

544 I

Fig. 26. Observations of the molecular shape resonance for CO adsorbed on Ni(001). (a) Cross-hatched peak shows the 2 x orbital above EF measured as the final state in IPES. The individual points 4 show the IPES cross-section for observation of this orbital as a function of the incident electron beam energy with respect to EF. (b) Photoionization cross section of the CO 4 0 molecular level from ref 183. (c) Near edge structure for carbon K-edae excitation from ref. 182.

10 20 ENERGY ABOVE EF ( e V 1

Ezl -

4

->

k z 5

I I I I

W

15

25

35

PHOTON ENERGY (eV1

I-

5

1

I I

i 0

E,

l

I

I

I

290 300 PHOTON ENERGY (eV1

I

I

I

I

310

resonance has been used. to determine the molecular orientation from both photoemission la3 and NEXAFS studies. la2 Johnson and Davenport 2 proposed that the shape resonance should be observable in Inverse Photoemission as an initial state effect rather than a final state effect as in photoemission. Thus the cross-section for observation-of the 2n level should peak at incident electron energies corresponding to coupling into the shape resonance as an initial state. The results of such a study for CO adsorbed on Ni(001) la4 are shown in fig. 26. The figure compares the intensity of the 2n level as a function of the incident beam energy in IPES studies with the shape resonances observed for the same system in valence level photoemission la3 and carbon K-edge NEXAFS studies. 182 The system is interesting in that it allows a comparison between the effective screening of a valence photohole and a core level photohole. For the valence levels the screening appears to be almost complete. Photoemission and inverse photoemission produce nearly identical values for the shape resonance position even though on the one hand the resonance is bound lo a positive ion and on the other the resonance is bound to a neutral atom. For the core level photoionization, the photohole is less well screened and the shape resource moves Closer to the Ferrni level. It would therefore appear that the level of screening or relaxation reflects the level of localization of the photohole. We note in passing that coupling of incident

545

electrons to the shape resonance as an initial channel has also now been reported in several EELS studies. 185 It has further been suggested that the position of the shape resonance may be used as an indication of the change in the interatomic bond length for molecules adsorbed on surfaces. 186 Whilst it has been clearly demonstrated that the resonance position reflects the bond length in the gas phase the above studies indicate that more caution should be exercised for the surface adsorbate where the quantitative effect of substrate screening will be difficult to determine.

6.

RESONANT INVERSE PHOTOEMISSION

The previous sections have covered a number of different experimental observations, all of which have been discussed and interpreted in terms of one electron transitions into well defined energy bands or levels. However it is well known that there is a variety of structure or peaks occurring within photoemission spectra that may be interpreted only within a framework of multi-electron excitations. 34 Such phenomena include, for instance, the observation of satellite structure or the observation of plasmon emission. It is only recently that multi-electron phenomena have been observed and identified in inverse photoemission and that as a result of the introduction of tunable photon detectors. Resonant enhancement of a radiative transition represents coupling between some discrete channel ( a plasmon or core level excitation ) and the continuum ( the direct transition ). Wendin has considered the theoretical aspects of resonant inverse photoemission. He finds that the emitted photon intensity I(E,o) given by

J

I @,w) = d% I k(w,E) ? 6(%+ 61- E)

where t&co,E) is the radiative scattering amplitude, reduces to an expression of the form

Here o(E) is the cross-section for the direct radiative transition, A(E-o) the lineshape or spectral function of the discrete excitation and R(o,E) describes the resonant enhancement of the radiative capture process. Probably the most striking example of the role of many electron effects was the observation by Drube and Himpsel lee that the intensity of the IPES transition or the cross-section shows a strong enhancement when the energy of the transition corresponds to the plasma frequency of the material. Their observation was made in a study of antimony thin films grown on different substrates. The spectra, reproduced in fig. 27, show peaks associated with transitions into the unoccupied levels of the antimony and also a peak remaining at fixed photon energy, irrespective of the incident electron energy. This latter peak they identified as a plasmon peak reflecting the decay of plasrnons either directly or indirectly into photons. More importantly however, their spectra clearly show that whenever the plasmon peak coincides in energy with a direct transition, then that transition shows a dramatic enhancement of its intensity. This same phenomenon has and of Nb(001) and Nb(ll0). 92 In a study of also been reported in IPES studies of graphite leg

546

8

10

12

14

16

18

20

22

Photon Energy (eV1

Fig. 27. Inverse photoemission spectra recorded from a thin film (20 A) of Sb grown on cleaved InP(110) for various energies Ei of the normally incident electrons.. The vertical arrow marks the photons of energy nwP emiited by decaying plasmons. Resonant enhancement occurs when the direct inverse photoemission channel coincides with the plasmon channel. AI(001) no such enhancement was observed. Indeed, on that surface an intensity minimum rather than maximum was observed at the plasma frequency. This observation was simply interpreted as the "time reversal" of the surface photoeffect. In the free electron gas the longitudinal plasmon will not couple directly to the transverse field of the photon. It is only in the surface region that bulk plasmons are able to decay into photons. Further, surface plasmons will decay into photons only through the intervention of surface roughness. In their study of niobium single crystals however, Pan et al. 92 were clearly able to show that the observed phenomenon was related to bulk properties and independent of the condition of the surface. Indeed they found that the resonant behavior did not occur for either surface or interface states. They suggested that scattering from the crystal lattice could be responsible for mediating the coupling between the photons and plasmons. Such scattering would be weak in free electron materials such as aluminum but strong for the transition metals. The spectral function for the plasmon will reflect the loss function Im(-I/&) for the material. Figure 28 presents a comparison between the intensity of the direct transition observed to resonate at the plasmon frequency of niobium and the loss function for that material derived from reflectivity measurements (ref. 191). Another example of such coupling is the so called "Giant Dipole Resonance". Here the excitation of a core to bound transition represents the discrete channel. Resonant enhancement of photoemission cross-sections at photon energies corresponding to the threshold for core to bound transitions is a well studied phenomenon. The equivalent resonance has been o b s e i e d in IPES by

547

I

I

I

I

'

I

I

I

I

L

Electron Beam Enerpy w r t E,(ev)

Fig. 28. Intensity of a direct transition (.) in inverse photoemission spectra recorded from a N b ( l l 0 ) crystal as a function of the electron beam energy from ref. 92. These are compared with the loss function I m ( l / [ q ) and the surface loss function I m ( l / [ & + l [ )for niobium from ref. 191. Drube and Himpsel in a study of lnSe Iz4 and in a number of studies of the rare earths in the High T, Superconductors by Weaver and coworkers. 192

7.

The Beginning of the End or the End of the Beginning ?

After a slower start the development of inverse photoemission has progressed to the point where the technique is providing relevant information on both the traditional and new electronic structure problems comparable to that obtained in PES. An example being the recent surge of activity in the field of High T, Superconductivity. Here PES and IPES have competed equally in the development of an understanding of the electronic structure. However it is the currently much higher energy resolution capability of the former technique that has ultimately provided data capturing the imagination of a wider audience. l g 3 The ability to achieve a high energy resolution thus presents one of the more immediate challenges in the further development of IPES. The

548

problem is one of reducing the energy spread in the source whilst maintaining sufficient incident flux to allow the experiment. The majority of this chapter has been devoted to the studies of metallic systems. This is partly a reflection of the bias of the author and partly a reflection of the bias in the field as a whole. Studies of the unoccupied surface states, both crystal derived and image potential derived, have lead to a renewed interest in the correct form of the surface barrier. This represents an important property of the surface and interest will obviously continue. Other metallic systems that will receive a growing interest are the newer areas relating to magnetic problems, both surfaces and thin films. However it may also be anticipated that more activity will be devoted to studies of the conduction bands of the technologically important semiconductors. Other areas of increased activity will be the more complex systems including alloys, bimetallic interfaces and different compounds. In these systems the possibility of using the site specific resonant behavior associated with core level excitation points to the development of IPES capabilities in a photon energy range higher than that currently accessible with the normal incidence spectrographs. This latter possibility represents another area with technological challenges which if solved may well prove rewarding.

Acknowledgements The author is extremely grateful for numerous discussions over the years with Jim Davenport, Steve Hulbert, Neville Smith and Mike Weinert.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

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553

Chapter 14 MLJLTIPHOTON PHOTOEMISSION J. BOKOR AND R. HAIGHT 1. INTRODUCTION

The other chapters of this monograph clearly display the wide scope of physical problems which can b e studied using angle-resolved photoemission spectroscopy (ARP). While the preponderance of work has examined the ground states of materials, inverse photoemission being one exception, an important area of study lies in the domain of excited-states. Nearly all applications of electronic materials involve excitations into conduction and interface states, and the dynamical evolution of such excitations is of obvious significance. Additionally, studies of chemical and structural dynamics, all of which may occur on extremely short time scales are of great interest. ARP represents an appealing probe since it affords the experimentalist a detailed view of the electronic states of the system. I n this chapter, excited-state spectroscopic studies as well as time-resolved studies of excited-state dynamics will be described. Such experiments involve the excitation (pump) of the sample under study with a pulse of light. The absorption of the light pulse results in excitation of normally unoccupied states of the system (e.g. the conduction bands of a semiconductor crystal or image states of a metal) and the state of excitation is then examined with a "probe," in this case by ARP. Thus at least two photons are involved in the photoemission process. The first approach to be considered involves using the nonlinear effects associated with a single intense laser pulse, i.e. two-photon photoemission. In these experiments laser photons carry energy greater than half of the material work function and photoemission is achieved when two photons are absorbed within the duration of the laser pulse. In such experiments nanosecond laser pulses have been used and the dynamics of the system have been inferred from detailed analysis of the energy spectrum. The basic principles underlying this type of experiment are shown in Fig. 1. In Fig. 1, process (A) involves direct two-photon photoemission with no intermediate state relaxation. Indeed, there need be no real intermediate state in this process. Process (B) involves excitation into a real excited state of the system by one laser photon, followed by some scattering or relaxation process to a different state with a second laser photon finally causing photoemission. These processes may be distinguished by the dependence of the energy of a feature in the electron energy spectrum on the photon energy. This class of experiments will be discussed in detail i n the second section of this chapter. A different approach involves the use of picosecond lasers to permit direct time-resolved measurements of excited state dynamics. In such experiments, a visible or infrared laser pulse is used to produce a transient excitation and a short wavelength laser pulse is used for ARP probing. The short wavelength probe radiation (25eV) can be generated by using non-linear frequency generation in both crystals and gases. By using short wavelength radiation for the probe source, the sequential pump and probe processes of interest may be readily distinguished in the photoemission spectrum from multiphoton photoemission arising from the pump source

554

Fig. 1: Schematic energy level diagram showing three different types of processes studied by multiphoton photoemission.

alone. Here, dynamics in the intermediate state can be directly studied by delaying the short wavelength probe pulse relative to the pump pulse by a time t, thus allowing investigation of the state of excitation with time. This type of experiment is shown as process (C) in Fig. 1. In this way, various contributions to the system relaxation can be studied. These include radiative and nonradiative recombination as well as diffusion away from the surface. This class of experiments will be described in the third section of this chapter. Inherent in these studies is the prolific use of lasers and non-linear optical techniques since such sources are at present the best way of producing sufficiently short, tunable, polarized pulses of light. Although discussion of the appropriate laser techniques will be brief, a large body of literature exists that provides a complete exposition of the details.''2 The chapter will conclude with a brief discussion of alternative source technologies that may also be used for multiphoton photoemission studies. 2. TWO-PHOTON PHOTOEMISSION

Absorption of a single photon results in the transition of an electron from its ground state to a higher lying excited state. Transitions of this type are well described by Fermi's golden rule and are linear in nature, i.e. the number of electrons promoted into excited states is linearly dependent on the number of photons in the excitation field. Until the advent of lasers, higher order processes were not considered because of the lack of sufficient photon intensities required to excite such nonlinear processes in materials. Pulsed lasers can easily produce enough intensity to excite higher order processes, resulting in the absorption of two or more photons in a single quantum-mechanical process. In such a higher order absorption, one or more intermediate states are considered. For example, a two-photon transition rate is written

555

where , q i and fig are dipole matrix elements between the final - intermediate states and intermediate - ground states respectively, Ei is the energy difference between the intermediate state and the photon energy, I is the laser intensity, and p(Ef) is the density of final states. Clearly, a strong enhancement in the transition rate can occur when the laser frequency is tuned to an intermediate state resonance. This enhancement forms the basis for spectroscopy of the intermediate states in two-photon photoemission. The earliest experiments that incorporated laser excitation with photoemission involved “double beam“ studies which involved a continuous UV source and a nanosecond laser. Wautelet and Laude3 applied the laser modulated photoemission technique to study Te as well as other semiconductors! They attributed their spectroscopic observations to absorption of two photons with real intermediate states as well as to surface photovoltage effects associated with carrier generation near the surface of Te. Such work represented a unique attempt to observe and study the unoccupied conduction bands of semiconductors with photoemission. Saile, et al? reported the first laser-synchrotron two-photon photoemission experiment. In that experiment, tunable vacuum-ultraviolet radiation from the DORIS synchrotron (10- 12 eV) was used to excite excitons in solid Kr. Pulsed laser radiation from a nitrogen laser (3.7 eV) was used to ionize the excitons yielding photoemitted electrons and the two-photon yield spectrum obtained by tuning the synchrotron radiation exhibited the excitonic series of solid Kr . Further work in two-photon photoemission concentrated on the dependence of the photoelectron emission on photon flux. A series of studies carried out by Bensoussan et a1.6 established the quadratic dependence of the photoelectron emission with laser intensity as expected from Eq. (1 . In one such investigation, well characterized Si (7x7) surfaces were prepared and studied. Excitation with a nitrogen laser or a dye laser clearly produced emission that varied as the square of the photon flux (see Fig. 2). Furthermore the constant of proportionality between the electron emission and the photon flux was determined as a function of photon wavelength.

?’

Once the essential two-photon nature of the electron emission was established, further attention was given to the features of the emission spectrum. Several spectroscopic features and their dependence on photon energy have been observed and studied. The relevant processes are displayed schematically in Fig. 1. If the photon energy is changed in a systematic manner, then process (A) will give rise to a feature in the emission spectrum that will shift with twice the fundamental photon energy. Here, a fixed initial state, e.g. a well defined occupied surface state, is observed by two-photon emission and its energy position within the spectrum will shift with 2hv. Process (B) corresponds to a fixed intermediate state that is an unoccupied state of the system. Here, we expect the emitted electron kinetic energy to shift with hu. In both cases, according to Eq. (1) we may expect the spectral emission features associated with the transition to exhibit a resonance behavior of the emission intensity with photon energy. Kasuya and Nishina’ applied two-photon photoemission spectroscopy to the study of GaSe. In their study, the polarization dependence of the photoemission process was exploited to

556

Fig. 2 Log-log plot of the photoelectron flux J, ys photon flux Jph from Si(ll1) (7x7) surfaces for hy = 3.68 eV. From Ref. 7 (reprinted by permission).

determine the symmetry assignment for the electronic transitions involved. Features observed in their spectra were explained by invoking direct optical transitions. Optically excited states of trans-polyacetylenewere studied by Salaneck, et al? They used a pulsed xenon lamp or a pulsed N2 laser to generate excited states and He I and He I1 angleintegrated photoemission spectra were taken from the excited material. Several sharp features were observed in the spectra above the valence band edge and these peaks were discussed in terms of polaron and soliton excitations of the trans-(CH,) chains. Bensoussan and Moison extended their earlier work on multiphoton hotoemission from by studying the energy spectrum of the photoemitted electrons.' Two regimes were identified. At low h e n c e and high photon energy, two- and three-photon processes were dominant, and the effects of the initial and intermediate states controlled the emission spectrum. At high fluence and lower photon energy, thermionic emission became dominant, and the emission spectrum fit a Maxwellian, giving an indication of the electron temperature.

f

Recently, studies of this type have been extended to the InP(100) surface." Two different distributions of photoexcited electrons within the conduction band were observed. The first distribution was associated with photoexcitation of electrons without energy relaxation at the intermediate level. This corresponds to process (A) in Fig. 1. A second distribution appeared for photon energies above 3.6 eV that showed the relaxation of electrons into a so-called "electron accumulation level" (see Fig. 3), analogous to process (B) in Fig. 1. This distribution was verified to display an energy dependence that varied only with hv and not 2 b . The intermediate state was found to lie 0.8 eV above the conduction band minimum and was

557

J-

VACUVM LEVEL

7 x

3

.

4

WTOELECTRON KINETIC ENERGVkV)

Fig. 3: Two-photon photoemission energy distribution curves for various photon energies on InF’(100), normalized to unit area. The arrows indicate the maximum kinetic energy allowed by a double photoexcitation process (twice the photon energy minus the work function). The inset shows the relation between the available DOS n(E) (solid curves: bulk st:tes; dotted curve: surface states), and the energy distribution in the intermediate state ni (E) (EDC‘s brought down by the photon energy); the DOS scale is only indicative. From Ref. 11(reprinted by permission).

tentatively assigned to the X secondary minimum. Multiphoton studies have also been carried out on Si12, as well as CdTe and ZnTe13 by

Williams et al. In these experiments, initial absorption produced carrier densities within the conduction bands of these materials that were subsequently photoemitted with a photon of higher energy. A sharp feature in the emission spectrum was identified as an intermediate state near the bottom of the conduction band. In their experiments the second (2.3 eV) and fourth (4.66 eV) harmonics of a continuously pumped, mode-locked and Q-switched Nd:YAG laser were used. By appropriate choice of the intensities of the two beams, the cooperative multiphoton process could be emphasized relative to two-photon effects from either the green or UV beams. In this way, states near the conduction band minimum of these materials could be investigated. For the case of silicon12, this method was used to measure the temperature of the hot conduction band distribution produced by 2.3 eV pulses at high fluences up to the melting threshold. Recently, an interesting application of two-photon photoemission has been the observation and detailed study of image states at the surfaces of metals. Electrons can be bound at a surface by the Coulomb field created via attraction to their image charges. Such states are characterized by a Rydberg-like series and were first studied using inverse photoemi~sion.’~ (See also chapter 15 of this monograph.) Using two-photon photoemission, Geisen et al. have studied image states on the (111) surfaces of Cu,Ag, and Ni,”*16 as well as the (100) surfaces of Cu and Ag.17 On the (111) surfaces, a sharp surface state that exists in the L2’- L1 band gap was used as the initial state, while for the (100) surfaces, there is no occupied surface state just below the Fermi level, and the bulk A1 band was used as the initial state. For (111) surfaces, when the photon energy was tuned to couple the initial surface state to the n = l intermediate image state, the photoemission spectrum exhibited a strong peak. Offresonance, emission was observed showing a peak shift proportional to 2 b as expected from our previous

558

discussion for process (A). Spectral features corresponding to process (B) were observed as well. Fmally, two electron cooperative processes, termed "energy pooling" by the authors, gave rise to a peak in the emission spectrum that was at twice the intermediate state energy, independent of the photon energy. Working in a photon energy regime where process (B) dominates, and measuring angle-dependent two-photon photoemission spectra from Ag( 1ll), Ag(loO), and Cu(lOO), this group has succeeded in determining effective masses for the n = 1 image potential (see Fig. 4) and have obtained good agreement between the experimentalresults and a phase shift analy~is.'~

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0 01 02 03

Final-State Energy IcV, re1 t o Vacuum1

Fig. 4 Angle dependent two-photon photoemission spectra and E vs k dispersions for the n= 1image-potential state on various surfaces. From Ref. 17 (reprinted by permission).

Similar experiments have been performed on Pd(ll1) by Kubiak'' Below hv = 4.9 eV, the spectra were dominated by process (A) and bulk states. Above hv = 4.9 eV, the n = 1image state was observed, and followed process (B) type behavior. An effective mass equal to the free electron mass was determined for this state.

As a final example, two-photon photoemission was used to observe an adsorbate induced state on the surface of Cu(ll1). Reiger et aL20 studied the intermediate state induced by the presence of 0 on Cu(ll1) with this technique. An unoccupied state at 2.79 eV above the Cu Fermi level was observed, in good agreement with that determined from inverse photoemission studies of the same system (see Fig. 5). Again, the kinetic energy dependence of the emission features on photon energy was used to determine the origin of fixed initial and intermediate

559

J 0

380 I

2

3

L

Fig. 5: Photon energy dependence of the two-photon photoemission spectra from O/Cu(lll).From Ref. 20 (reprinted by permission).

states of the system. Two-photon photoemission has provided a means to study excited states in a simple and straight-forward manner. In particular, exceptional energy resolution (-50 meV) was used in the last two studies described. The combination of the momentum resolving power of the technique with exceptional energy resolution results in a powerful means for studying a variety of systems. Extensions of this technique to the time resolved regime with the use of more energetic photons will be discussed in the next sections. 3. TIME-RESOLVED PHOTOEMISSION

The first successful efforts to directly time-resolve excited state dynamics using photoemission spectroscopy were those of the group of Williams and coworkers. In those experiments2' the second (2.35 ev) and fourth (4.7 ev) harmonics of a Nd phosphate glass laser were used to excite and probe single crystal ZnTe. The pulses produced by this laser were 5 picoseconds in duration and carrier relaxation times of several hundred picoseconds were measured (see Figs. 6 and 7). Although an inherent difficulty in the experiment was the discrimination of the sequential excitations of interest from multiphoton processes that resulted from the pump radiation puke alone, useful dynamics information was extracted from these studies. The technique was further advanced by the use of higher energy (10-15 eV) radiation and angle-resolved detection for ARP probing of the excited state dynamics. The probe radiation

560

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Fig. 6 Electron energy distriiution curves for ZnTe(ll0) under excitation by 5 psec pulses of radiation with photon energies of 2.35 eV (G) and 4.70 eV (U). Single-pulse energy densities are indicated. From Ref. 21 (reprinted by permission).

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Fig. 7: Photoelectron yield at 0.45 eV kinetic energy as a function of delay between excitation and probe pulses. From Ref. 21 (reprinted by permission).

was produced from intense pulses of visible laser light by using non-linear frequency generation in both crystals and gases. By using such short wavelength radiation for the probe source, the sequential pump and probe process of interest may be readily distinguished in the photoemission spectrum from multiphoton photoemission arising from the pum source alone. With this technique, experiments have been performed on the clean InP(IlO)* , G&4~(110)~, and Si(ll1)" surfaces cleaved in ultrahigh vacuum and states within the bandgap of some of these materials formed during deposition of various gases and metals have also been observed. Tbese studies were performed with 70 picosecond laser pulses and will now be described in greater detail.

P

56 1

The apparatus used in these experiments is unconventional and will be briefly described here. Greater detail may be found in Ref. 22. A single Nd:YAG laser system in combination with a variety of nonlinear optical techniques was used to produce both the pump and probe beams. W V radiation at 118.2 nm was produced by frequency tripling the 355 nm third harmonic radiation from the NdYAG laser. This was done using 5 Torr of Xe gas as a nonlinear medium (see Fig 8). The 355 nm beam was focused through the entrance slit of a 0.3m vacuum monochromator using f/10 optics and the monochromator was backfilled with Xe. The 118.2 nm probe was generated at the input focus, and was refocused by the monochromator optics at the exit slit. P W BEAM

f

INPUT 355 Nn

Fig. 8: Apparatus used for time- and angle-resolved photoemission experiments using 118.2 nm probe radiation.

Pump radiation was produced in either the visible or infrared regions. For visible pump excitation, the 532 nm second harmonic of the Nd:YAG laser was used. For infrared excitation, 2.8pm radiation' was produced by stimulated second-Stokes Raman scattering of the 1.06pm output from the NdYAG laser in high pressure methane gas. 3.1 InP(110)

The first application was to the study of electron dynamics on the cleaved InP(110) surface." The surface was pumped using the 532 nm second harmonic of the Nd:YAG laser. At a pump fluence of 0.5 mJ/cm2, a dense, degenerate electron-hole plasma was produced in the near-surface region. A series of pump-probe photoelectron spectra are shown in Fig. 9. A clear peak can be seen at 1.47 eV. This peak was attributed to a surface resonance lying 120 meV above the bulk conduction band minimum. This surface resonance has been designatedz C3. The population in the C3 surface resonance was presumed to be in equilibrium with the population in the bulk conduction band near the surface. By time-resolving both the width of the energy distribution as well as the angular distribution, it was possible to measure the dispersion of the C3 surface resonance, as well as the energy and momentum relaxation of the degenerate population of excited electrons. The time decay of the total integrated transient carrier signal is shown in Fig. 10, and the time dependent angular distributions are shown in Fig. 11.

562

Fig. 9 Pumpprobe ARP spectra from InP(110) for time delays of (a) t = -133 psec; (b) t = 0 psec; (c) t = 266 psec; (d) t = 0, where the surface was first exposed to hydrogen. The insets in (b) and (c) are magnified views of the 1.5 eV region. >From Ref. 22.

Since the transient population in the C3 surface resonance is produced only at the band minimum, the band dispersion could only be obtained for a small region in k-space near the

center of the surface Brillouin zone. Thus the dispersions were quoted in terms of effect& h : band was found to be anisotropic, with m'/m, = 0.2220.02 along the rX masses (m*). T direction, and m /me = 0.125?0.025 along the rX' direction, where me is the rest mass of a free electron The time decay behavior the population in the CJ surface resonance was controlled by the in turn controlled by carrier diffusion, two-body radiative recombination as well as Auger recombination. The model fit to the time decay data shown in Fig. 10 used accepted literature values for the bulk recombination parameters and neglected surface recombination

bulk conduction band dynamics, which were

3.2 Au/GaAs(llO) and O/GaAs(llO)Interfaces

During the InF' investigations, it was noticed that on certain "poor cleaves," signal from states apparently within the semiconductor band gap could be observed. This led to a more general investigation of band gap states at semiconductor surfaces and interfaces. The GA(1lO) surface was chosen for this study.23 Results obtained for clean GaAs surfaces were

563

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Fig. 10 Plot of the integrated transient carrier signal intensity from Id'( 110) as a function of time delay between the pump and probe pulses. From Ref. 22.

Fig. 11: Angular distributions of the transient carrier signal intensity for three cases. The open circles represent thedgnal intensity for scans in the I'X direction, and the open triangles for scans in t h e r X ' direction, at t = 0. The open boxes represent the signal intensity for a scan along rX and t = 150 psec. The dashed curves are a guide to the eye. From Ref. 22.

similar to those found on InP(110) surfaces. On "good cleaves," a peak due to electrons excited into the conduction band could be observed. This signal was enhanced by a surface resonance just as in Id'. Further, for "poor cleaves" additional signal was observed within the bandgap.

564

Studies were then made starting with "good cleaves" and then adsorbing sub-monolayer films of either gold or oxygen. These studies were aimed at determining the spectroscopy of gap states at metal/semiconductor and oxide/semiconductor interfaces. Such states had been postulated as being responsible for Fermi-level pinning at these interfaces.% Magnified views of the photoemission spectra obtained are shown in Fig. 12.

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Fig. 12: Left Magnified views of the band-gap region of photoemission spectra collected for (a) clean GaAs(ll0) photoexcited surface; (b) photoexcited surface, 0.1 ML Au coverage; (c) photoexcited surface, 0.35 ML coverage; (d) unexcited surface, 0.1 ML Au coverage. Right: (a) clean GaAs( 110) photoexcited surface; (b) photoexcited surface, 12600 L oxygen exposure; (c) unexcited surface, 12600 L oxygen exposure. From Ref. 23.

The spectra collected for the two optically excited interfaces show striking similarities in the band-gap electronic structure. In particular, the strongest peak within the gap for both cases is at 0.5 eV, which corresponds to the known eventual pinning position for these interfaces.% The spectra shown in Fig. 12 for the unexcited surfaces show that in both cases, complete pinning at 0.5 eV was not observed. This was attributed to the fact that the probing depth of 2 nm was comparable to the depletion width for the heavily doped p-type GaAs used.= These observations provided the first direct experimental evidence that a discrete state within the gap may be responsible for the final pinning position of the Fermi level, although such a connection

565

had been postulated. 3 3 Si(ll1) 2x1

A detailed study of gap state dynamics usin time-resolved photoemission s ectroscopy was carried out on the Si( 111)2x1cleaved surface! Previous optical absorption2'and reflectivity measurements= had identified a strong optical transition at 0.45 .eV, corresponding to excitation across the surface direct band-gap between the A and A surface states. This transition was pumped using a 2.8pm infrared laser source, and the photoemission spectrum was measured from the excited surface using the 118 nm probe beam. Fig. 13 shows typical results obtained on high quality cleaves. The spectra shown in Fig. 13 were taken at an emission angle corresponding to thejpoint in the surface Brillouin zone. I9

Fig. 13: Photoemission spectra from Si(ll1) (2x1) surface. (a) Unexcited surface; (b) Spectrum from surface taken with simultaneous 2.8 pm infrared excitation. From Ref. 24.

The additional peak at 0.5,eV seen in the spectrum from the excited surface arises from transient population in the A mid-gap surface state. The relaxation dynamics for the A* state were measured, with the results shown in Fig. 14. To understand this decay curve, it is necessary to consider both the surface electrons excited into the A state and the surface holes that are simultaneously pumped into the normally occupied ?r state. The decay dynamics are then determined by two mechanisms. At high densities, two-body radiative recombination of the surface electrons and holes dominates. This leads to the fast initial decay. At lower densities, the electrons non-radiatively decay into defect or step states. The holes can either scatter into such states or, since the energy position of the top of the normally occupied A state band lies somewhat below the top of the bulk valence band, the surface holes may also scatter into bulk valence band states. The abrupt end to the fast decay of the electron population is then explained by the escape of surface holes out of the A state, reducing the rate of radiative recombination.

566

500

lo00

1500

2ooo

DELAY TIME (psec)

Fig. 14: Time dependence of the T* (0.5 eV peak) signal intensity. The experimental data are shown as bold circles. The results of the model calculation for three values of Th are also shown. The values of the parameters B, and re were fixed at 0.004 cm2/sec and 2.5 nsec, respectively. Solid curve, r h = 300 psec; dotted curve, Th = 400 psec; dot-dashed curve, Th = 200 psec. >From Ref. 24.

Values for the two-body radiative recombination parameter, B,, and the surface electron and hole lifetimes, re and Th, respectively were obtained by fitting a numerical solution to two coupled differential equations to the data,. The fit was insensitive to the value of B,, with values of 0.002 cm2/sec < B, < 1.0 cm2/sec producing acceptable fits. An independent estimate of B, was obtained from the measured absorption spectrum using the van Roosbroeck and Shockley detailed-balance method. The value obtained in this way was B, = (2.7k 1.8)xl(r3 cm2/sec. The surface electron and hole lifetimes found were T , = 2.5 2 0.3 nsec and Th = 3002 100 psec. On a cleave that showed a high density of defects, the electron and hole lifetimes were significantly shorter: t, = 330230 psec and Th = 100250 psec. The cleavage dependence of these lifetimes strongly suggests that steps and defects play an important role in the dynamics. 4. FUTURE PROSPECTS AND ALTERNATIVE TECHNOLOGIES

Several improvements to the time-resolved ARUPS technique can be envisioned. Regarding the laser technology, it is possible to produce pulses with durations in the femtosecond regime with sufficient peak power to generate the W V radiation using nonlinear optical processes. This will enable the study of phenomena on a much shorter time scale. Using this same laser technology, it is also possible to tune the radiation over a limited range for the investigation of final state effects. Since the fluence of W V radiation per pulse must be limited due to space charge effects, improvement in count rate must be obtained by increasing the laser system repetition rate. New developments in laser technology will make possible repetition rates in the range of several hundred Hz to perhaps kHz. This will enable the study of dynamics at lower excitation densities or of weaker surface states. Another technology for extending the tunability of the probe radiation is the use of laser produced plasmas. The radiation produced by a laser plasma is broad-band and extends to the soft x-ray (E s lKeV ). Currently there is vigorous research on the question of how short the duration of the output of the laser-induced plasma can be made, but pulse durations of < 4

567

psec have recently been meas~red.2~ (Researchers hope to produce outputs with pulse widths less than 1 psec.) The production of x-rays from plasmas requires high temperatures and thus high intensity radiation. This restricts most laser-induced plasma schemes to low repetition rate lasers. The advantage here is that the probe light tunability is constrained only by the monochromators and choice of target material, not by the severely restricted availability of lasing materials. Yet another tantalizing technology on the horizon is that of soft X-ray free electron lasers?' Such lasers might produce tunable, intense, ultrashort pulses at energies as high as perhaps 1W200eV. It is also possible to consider performing two-photon photoemission as well as timeresolved ARP experiments at a suitable synchrotron radiation source. Clearly the advantage here is in the wide range of photon tunability and the availability of X-rays. Time resolved pump-probe experiments at a synchrotron will require synchronization of a pulsed laser to the time structure of the synchrotron and to exploit the high average photon flux available at synchrotrons, it is necessary to use a laser with a pulse repetition rate approaching that of the synchrotron (-1 MHz). One limitation of the current generation of synchrotron sources is that the bunch lengths are about 50-150 psec with many having bunch lengths above 500 psec. The technical difficulties in performing laser-synchrotron experiments have been overcome in an elegant set of studies of pulsed laser annealing by Larson, and coworkers?' In those experiments, time-resolved, high-resolution X-ray dfiaction was used as a probe of the lattice structure of Si just after recrystallization. The success of those experiments is a strong indication that time-resolved ARP and X-ray photoemission experiments can also be carried out using lasers synchronized to synchrotron radiation. 5. SUMMARY

The use of lasers and multiphoton techniques has made it possible to bring the powerful machinery of angle-resolved photoemission spectroscopy to bear on the next frontier in surface science, namely surface dynamics. Thusfar, effort in this area has concentrated on investigating the dynamics of electronic excitations at surfaces. Work of this kind will undoubtedly continue as the technique is extended into the picosecond time regime. However, it also seems possible that such phenomena as adsorbate vibrational excitation dynamics, chemical reaction dynamics, and ultrafast surface phase transitions will be amenable to study using these new techniques. As improvements in the technology make shorter wavelength photons available either via laser techniques or through laser-synchrotron techniques, an entire new array of time-resolved photoemission experiments will be possible involving the use of X-ray photoemission spectroscopy and its variations such as X-ray photoelectron diffraction?'

568

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2. Recent advances in the generation of short wavelength radiation using lasers are collected in D. T. Attwood and J. Bokor, eds. Short Wavelength Coherent Radiation.- Generation and Applications, (American Institute of Physics, New York, 1986). 3. M. Wautelet and L. D. Laude, Phys. Rev. Lett. 38,40(1976).

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12. J. P. Long, R. T. Williams, T. R. Royt, J. C . Rife, and M. N. Kabler, in her-Solid Interactions and Transient Thermal Processing of Materid, J. Narayan, W. L. Brown, and R. A. Lemons, eds. (North Holland, N. Y., 1983); J. P. Long, R. T. Williams, J. C. Rife, and M. N. Kabler, in Energy Beam-Solid Interactions and Transient Thermal Processing/l984, D. K. Biegelsen, G. A. Rozgonyi, and C. V. Shank, eds. (Materials Research Society, Pittsburgh, 1985). 13. R. T. Williams, J. C. Rife, T. R. Royt, and M. N. Kabler, J. Vac. Sci. Technol. 367(1981).

19,

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19. G. D. Kubiak, J. Vac. Sci. Technol. A 5,731( 1987). 20. D. Rieger, T. Wegehaupt, and W. Steinmann, Phys. Rev. Lett. 11,1135(1987). 21. R. T. Williams, T. R. Royt, J. C. Long, M. N. Kabler, J. Vac. Sci. Technol. 21, 509( 1982). 22. R. Haight, J. Bokor, J. Stark, R. H. Storz, R. R. Freeman, and P. H. Bucksbaum, Phys. Rev. Lett. 54, 1302(1985); J. Bokor, R. Haight, R. H. Storz, J. Stark, R. R. Freeman, and P. KBucksbaum, Phys. Rev. B 32,3669( 1985).

23. R. Haight and J. Bokor, Phys. Rev. Lett. 56,2846(1986). 24. J. Bokor, R. Storz, R. R. Freeman, and P. H. Bucksbaum, Phys. Rev. Lett. 881(1986). 25. J. R. Chelikowsky and M. L Cohen, Solid State Commun. 29,267( 1983).

26. W. E. Spicer, P. W. Chye, P. R. Skeath, C. Y. Su, and I Lindau, J. Vac. Sci. Technol. 16,1422(1979); W. E. Spicer, I. Lindau, P. Skeath, and C. Y. Su, J. Vac. Sci. Technol. 17, 1019(1980). 27. M. A. Olmstead and N. M. h e r , Phys. Rev. Lett. 52,1148(1984). 28. P. Chiaradia, A. Cricenti, S. Selci, and G . Chiarotti, Phys. Rev. B 32, -6959(1985). 29. R. Falcone, (private communication). 30. J. E. La Sala, D. A G. Deacon, and J. M. J. Madey, Nucl. Instr. and Methods in Phys. Res. m 2 6 2 (1986). 31. B. C. Larson, C. W. White, T. S. Noggle, and D. Mills, Phys. Rev. Lett. 48, 337(1982); B. C. Larson, C. W. White, T. S. Noggle, J. F. Barhorst, and D. M. Mills, Appl. Phys. Lett. 42,282(1983); and B. C. Larson, J. A. Tischler, and D. M. Mills, in Beam-Solid Interactions and Phase Transformations,H. Kurz, G. L. Olson, and J. M. Poate, eds. (Materials Research Society, Pittsburgh, 1986). 32. C. S. Fadley, in Progress in Surface Science, edited by S. G. Davison, ,&l (Pergamon, New York, 1984).

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571

Chapter 15

NEW FRONTIERS: HIGHLY-CORRELATED ELECTRONIC BEHAVIOR

R. F. WILLIS and S. D. KEVAN

1. INTRODUCTION Preceding chapters in this volume have explored the current status and reviewed various applications of angle-resolved photoemission. The emphasis has been on the solid state and what might loosely be termed "delocalized electronic phenomena within a (mostly) independent single-electron band approximation." That is, on phenomena associated largely with valence states describable by wide band (large kinetic energy) behavior. At the other extreme, there exists an equally voluminous literature on photoelectron spectroscopy of individual atoms and molecules in the gas phase (ref. I), with the emphasis on sharp energy levels and strongly localized states. Both fields have matured over the past fifty years to a level at which both the photoelectron spectra and the underlying physics is well understood. There exists, however, an intermediate regime in which the electronic behavior possesses the characteristics of both delocalized ("band-like") and localized ("bond-like") states. The properties of these "narrow band materials," as they have come to be called (ref. 2), are dominated by strong electron-electron interactions which force us to look beyond existing theories of electronic behavior based on the above extremes. We choose this to be our closing theme for two reasons. Firstly, photoelectron spectroscopy provides fundamental information on the electronic properties of solids, which is used to advance

our theoretical understanding. The physics of strongly correlated electronic behavior in narrow band solids represents a new frontier in our conceptual understanding. Indeed, the discovery of high temperature superconductivity in narrow-band transition metal oxide compounds is serving to underline severe limitations in the existing way we think about electronic transport mechanisms.

To quote P.W. Anderson in a recent review (ref. 3) of current thinking on this particular issue: "angle-resolved photoemission is, for this field, the experimental probe that tunneling spectroscopy played in unraveling the BCS mechanism responsible for conventional superconductivity in wide band materials." This brings us to our second reason: these new materials are pushing us beyond the instrumental limits of our existing experimental equipment. Higher resolution and increased intensity are demanded which will set new standards in the future.

572

In the following, we will attempt to summarize the ideas and methods which have evolved over the past few years concerning the theory of highly-correlated electronic states. In this, our own thinking has been advanced enormously by the papers and discussions published over the past ten years, represented by two NATO Advanced Study Institute proceedings - Moment Formation in Solids (1983) (ref. 4) and Narrow Band Phenomena (1987) (ref. 2). Our theme is the extent to which the various narrow-band phenomena show up in photoelectron spectroscopy, with specific

examples chosen to emphasize particular models and principles. Finally, we review the prospects for future high-resolution photoemission measurements.

2. HIGHLY-CORRELATED ELECTRONIC STATES IN SOLIDS The search for a good theoretical description of the electronic structure and related physical properties of narrow band materials has led us to two different approaches to describing the problem (ref. 5). namely: ab initio theories without any adjustable parameters; and model Hamiltonian theories with empirically determined parameters. In the ab initio methods (ref. 6), the usual approximation is either to limit the number of interacting electrons by considering only a small cluster of atoms - "large molecule approach" - or to replace the effect of the electron-electron interactions by some effective potential, as is done in density functional "band theory." The cluster calculations neglect long-range screening and lattice polarization effects. As a consequence, there is a tendency to predict band gaps which are too large and, due to the neglect of translational symmetry, they cannot describe different kinds of magnetic ordering. They are more successful in accounting for local excitations involving atomic multiplets, crystal, and ligand field level-splitting effects.

Density functional calculations (ref. 7) have been successful in

describing the cohesive energy, ground state charge-density distributions, types of magnetic order, and the F e d surfaces of many solids. They have failed to predict temperature dependent properties, give band gaps which are too small, and fail particularly badly in the present context of narrow band solids by predicting metallic behavior for known insulators - NiO, CuO, etc., being classic examples. The model Hamiltonian approaches have sought to give a more qualitative description, using highly simplified model-dependent many-body interactions.

They have been successful in

accounting for the physical interactions responsible for correlation gaps, mechanisms underlying magnetic exchange and superexchange, the Kondo effect, and thermal dependence of these properties. An important development in recent years has been the realization that careful analysis

of Auger and photoemission spectral lineshapes can provide values for and physical insights into the model-dependent key parameters (ref. 8). Two models in particular underline much of our present thinking - the Hubbard Hamiltonian

573

(ref. 9), which is usually applied to describe insulating systems, and coming from the opposite extreme, the Anderson Hamiltonian (ref. 10) used to describe metallic behavior.

2.1 The Hubbard Hamiltonian The Hubbard model (ref. 9) is based on a single s-band characterized by one-electron matrix elements,

qj, which describe electronic hopping between

sites i and j, and an on-site two-electron

Coulomb repulsion, U. When U>>tj, the half-filled s-band splits to form a "correlation gap" and insulating behavior. Mott had earlier argued (ref. 11) that the insulating behavior observed in many transition metal compounds was due to just such a mechanism: a large onsite d-d Coulomb interaction U suppressing charge polarity fluctuations. The electron-electron interaction energy U thus overcomes the kinetic energy, expressed in terms of the band width W. This Mott-Hubbard metal-to-insulator transition (ref. 12) was an important development in explaining why so many compounds (NiO, CuO, NiS, etc.) were insulating despite having partially filled Bloch bands. The Hubbard Hamiltonian expresses this competition between the lowering of the kinetic energy (by delocalization and band formation) and the Coulomb correlation energy U (localization):

in which the sums are over spin

(3

and wave vectors k or lattice sites i for a given band of index

P. Qo expresses the banding and U=EA+E, is the sum of the (negative) electron affinity and (positive) ionization potentials of a singly occupied ion screened by the polarizability of the solid. Hubbard (ref. 9) showed that such a model Hamiltonian yields an insulator for a half-filled band when U>W and a metal when U<W. Also, when U>W, the strong localization leaves the electron spin as the only low-energy-scale degree of freedom. These latter materials are magnetic insulators and the low-energy magnetic fluctuations can be described by spin-only Heisenberg-like Hamiltonians, generally expressing various "t-J models" in terms of the spin-spin exchange coupling parameter J. Because of their insulating character, Anderson (ref. 13) took U>>W, the d-band width for a transition metal compound, and showed that the interatomic cation exchange interactions occurred through the anion ligands via valance charge fluctuations (virtual excitations) involving both U and charge-transfer (superexchange interaction mechanism). The Mott-Hubbard model, together with Anderson's theory of superexchange has provided a framework for explaining much of the systematics of the magnetic, optical, and electronic properties of the insulting transition metal and rare earth compounds.

574

2.2 The Anderson Hamiltonian The Anderson model Hamiltonian is an attempt to express the problem of magnetic moment formation in solids (ref. 4). It draws on an idea first proposed by Friedel (ref. 14) that for 3d transition metal impurities embedded in a metallic host, the d-orbitals could still retain their localized character - and hence their magnetic moment - by forming virtual bound states, broadened and shifted in energy. Hund's rule would tend to split the minority and majority spin states such that a magnetic moment would be retained if this splitting was large compared with the width of the virtual "resonant" level. Anderson expressed this in the form:

As in the Hubbard model, all Coulomb interactions are neglected excepting that between two electrons in the impurity d (or f ) shell. The first term in this Hamiltonian describes the host metal valence band structure, E,,

while the second and third terms express the impurity atomic states,

Edm, and interactions U(ijPm), including multiplet structures.

The final term represents

hybridization of the impurity states, m, with valence states, k, of the host via the one-electron matrix elements, V,.

In the simplest case of a single localized d-orbital with onsite Coulomb

repulsion U hybridizing through V,

to a continuum band of width

W and Fermi energy EF, the

virtual bound state formed has a binding energy relative to EF denoted Ed (or Ef) and broadened by the hybridization interaction. For U >> Ed > pVh2, where p is the continuum density of states, the occupation of the virtual bound d-state is integer and a stable local moment is formed.

2.3 Metal-Insulator U vs A Phase Diauam The introduction of hybridization into the model produces a surprising richness of physical phenomena. The notion that all charge-transfer fluctuations are suppressed, due to high values of

U in the Mott-Hubbard picture, implies that all gaps are d-d type. However, the band gaps in many transition metal oxides, sulfides, etc. seem to reflect a dependence on the electronegativity of the anion. This underlines the importance of (a) hybridization of the d-orbitals with the anion ligand orbitals in these insulators, and (b) hole creation in the ligand valence band due to transfer of an electron into a localized, empty d-orbital. That is, there is another charge fluctuation energy which is different from U - namely an energy A corresponding to 4"

d?+'

L where

denotes

a hole in the anion valance band. A is called the "charge transfer energy" which can be defined as A = Ed + EL, in which case E(d"+') ~

- E(d")

=U

- Ed where E(d"-'),

E(d") are the total energies

of the localized d-orbital states (ref. 15). Even in the ionic case, the states

qn-'dy'

(i. j

correspond to different cation sites) will have a dispersional width (2w) because of translational

575

symmetry and overlap with the anion valence states of dispersional width (W). Also, the excited states, d""

L will have a dispersional width of (W+w).

Dependent on the relative values of U/A

and the band widths (a,W), various types of band gapping can occur. A simple total energy diagram (ref. 16), showing the relationship between these parameters for an ionic transition metal compound for which U >> 0, U > A and A > W, is sketched in Fig. 1.

: h E

Lu m c

0

I-

.

Increasing Bandwidth

Fig. 1. Total energy diagram depicting the various charge fluctuations in an ionic transition metal compound. U is the two-electron Coulomb repulsion energy and A is the charge transfer energy due to hybridization between d and ligand orbitals L, broadened into bands of width 2w and W+w (adapted from Ref. 16). For U > A, the gap is of the charge transfer type with a magnitude, A

U

-+

infinity, we can get a metallic ground state if A < W/2. Since

-

W/2. So, even for

w W/2, the size of the gap scales as the anion electronegativity for a given cation and crystal structure. For U < A we are in the Mott-Hubbard regime with a d-d gap for U > w and a d-band metal for U < w. The early transition metal oxides exhibit this behavior. NiS has a zero band gap. This approach has formed the basis for an elegant classification scheme (ref. 17) which provides a framework for bringing together a wide variety of behaviors observed in transition metal compounds. A "phase diagram" can be drawn, Fig. 2, which depicts various types of insulating and metallic properties in terms of the parameters U/r and

with T being defined

as the metal d-state to ligand p-state charge transfer matrix element in these compounds. If A > U,

576

the lowest lying hole/electron excitations are d-d fluctuations and a Mom-Hubbard metal-insulating gap is formed with E,,

= U. Both the electron and hole charge carriers move within a single

-

narrow d-band (width 2 0 ) with a large effective mass. At the opposite extreme, A < U, the lowest lying excitations are of the charge transfer type and Egap

A (related to the electronegativity of

the anion). The holes are now "light" particles in the anion valence band (width W+O) while the electrons remain "heavy" in the narrower d-band. The system is a charge-transfer semiconductor. The line A = U separates these two regimes.

I

1

W -

2

A

c

T

Fig. 2. U/T vs AfI' phase diagram depiciting various types of insulating and metallic behavior in transition metal compounds (Ref. 16). The stoichiometric compounds, La2Cu0, and YBa2Cu306.5, appear to fall into this latter charge-transfer semiconducting class.

Doping occurs by replacement of La2+ with S?'

or,

alternatively, introducing interstitial oxygen 02-defects (ref. 3) which produce charge compensation via light holes of primarily 0 (2p) character. A highly simplified density-of-states schematic representing the electronic properties of the undoped parent materials of these high-temperature superconductors is shown in Fig. 3 (ref. 18). As in the simpler oxides (CuO, NiO), the uppermost Cu 3d9 band is split into two "Hubbard bands,'' depending on whether an electron is extracted, d9+d8, (by photoemission) or injected, d9+d",

(by inverse photoemission).

The important parameters are the d-d Coulomb repulsion energy U of the localized two-hole state (d9+U+d8+d1O) and the charge transfer energy A required to excite an electron from the oxygen

577

p-band into the upper d-band, the gap depending on the band width W of the oxygen p-band to a first approximation. Again, the relative strengths of the dimensionless parameters U/W and &W serve to define a wide diversity of behavior, in this case dependent on the level of doping, ranging from metallic through semiconducting to insulating and magnetic behavior (ref. 3). We will return to this subject in a subsequent section.

t

9

cu d-d

8

9

10

Cu d-d

Fig. 3. Schematic of the density of states distribution in undoped high-temperature oxide superconductors, e.g., La2Cu0, and also, CuO, NiO. (Adapted from Ref. 18). The richness of behavior originates from the interplay between essentially an atomic effect (the Coulombic repulsion of two holes or two electrons on the same ion) and a solid state effect (hybridization and charge fluctuations dependent on the band widths, w and W). The important point in the context of photoelectron spectroscopy is that the measurement of both the occupied and unoccupied states energy distribution is necessary to determine U and A. An example of photoemission at two different photon energies (hu = 66 eV and 120 eV) and inverse photoemission @IS) at x-ray energies (hu = 1486 eV) from NiO is shown in Fig. 4 (ref. 15). The two spectroscopies provide different projections of the density of states features due to wavelength dependent cross-section effects. These results classify NiO as a charge transfer insulator with a

4.3 eV gap, and comparison with ionic cluster calculations suggest a d-d Coulombic repulsion U of between 7 and 9 eV (ref. 15). The charge transfer parameter A can also be incorporated into an Anderson-type Hamiltonian,

EQ. (2), in which the transition metal cation is treated as an impurity screened by hybridization with the delocalized anion L states. The problem reduces to one of highly localized and correlated

578

states, embedded in a semiconducting medium in which the long-range polarization effects of the solid (dielectric response) on the atomic ionization and affinity levels are accounted for. The Anderson Hamiltonian extends to other interesting phenomena. A notable case is the Kondo resonance effect associated with the low-temperature resistance minimum anomaly observed in dilute alloy systems containing d and f atoms (ref. 19).

PES

BIS 1486 eV

hv (eV)

1

'i t

Fig. 4.Photoemission and inverse photoemission (BIS) spectra from NiO which is classified as a charge transfer insulator with a 4.3 eV gap. Comparison with ionic cluster calculations suggests a d-d Coulomb interaction, U, of between 7 and 9 eV (Ref. 15). 2.4 The Kondo Hamiltonian Under circumstances in which the ground state is assumed to have n localized f (or d) electrons bound to a simple impurity atom, such that the Hubbard states separated by a large energy U, then for each virtual bound state

(r =

KP

(f"-' and f"")

are

E(P-') and E(f""+') much larger than the broadening of

IV,I2);

a localized moment exists in an otherwise

non-magnetic host. Schrieffer and Wolff (ref. 20) showed that if the impurity atom retains only its spin degrees of freedom (i.e., spin rather than charge fluctuations), then the Anderson Hamiltonian transforms into the Kondo Hamiltonian:

579

with S the impurity spin operator. All cerium intermetallics appear to lie in the Kondo regime of the impurity Anderson model in which the local moment due to the singly occupied 4f' shell has an antiferromagnetic exchange interaction J=(2V2U)/EAE&J) with each of N conduction electrons with energies E,. The ground state of this single local moment embedded in a spin-polarized conduction electron host is a singlet state. The result is a narrow many-body resonance located just above EF, shown schematically in Fig. 5, which is associated with the quenching of the Ce 4f magnetic moment. The position, width and intensity of this "Kondo resonance peak" is determined by the magnitude of TK, the Kondo temperature at which a resistance minimum is observed, which can vary from a few degrees Kelvin to hundreds of degrees Kelvin. An example is shown in Fig. 6, using the combined techniques of synchrotron photoemission and inverse photoemission @IS) (rzf. 21). Resonant photoemission from the 4d core level was employed to increase the 4f cross-section near the 4d absorption edge, near 120 eV. The experimental resolution employed in this case was 400 meV (PES) and 600 meV (BIS). The Kondo resonance temperatures for the two cases shown are of the order, TK-1-1OK in the case of CeAl and TK-900K for CeNi2, Tine linear coefficient of the specific heat y is proportional to TK-l reflecting the 4f spin entropy. Thus, the "heavy fermion" behavior of

CeAl can be understood as reflecting very small TK but extremely large y-values. No Kondo resonance peak is observed as a consequence in the spectrum of CeAl taken at 300K, Fig. 6.

I

Kondo \

Resonance

U

I

'

* Density of States

Fig. 5. Schematic of density of states spectral weight representing Kondo resonance effects in cerium intermetallics.

580

Ce 41 SPECTRAL WEIGHT --PES/BIS -THEORY

Al

(x 2.5)

-10

0

10

ENERGY AEOVEEF (eV)

Fig. 6. Experimental and calculated resonant photoemission and bremsstrahlung isochromat spectroscopy (BE)of the Kondo resonance in CeNiz (TK= 900K) and CeAl (TK = 1-1OK) taken at 300K (Ref. 21). 2.5 Remarks

The above model Hamiltonian approaches have provided a great deal of insight into the evolution of atomic-like to band-like electronic structure in narrow band materials. They have also revealed a surprising richness of physical phenomena. Unfortunately, although they are simple in form, they are proving remarkably difficult to solve for specific situations. They express strongly oversimplified descriptions of both the electron-electron interaction, as well as the one-electron dispersion relations and hybridization. For example, the electron-electron interaction is treated as an on-site interaction with the assumption that all other interactions are automatically incorporated

into renormalizations of the appropriate parameters in the Hamiltonian. The impurity model of the Kondo resonance effect, Fig. 5, ignores the lattice aspects of the cerium intermetallics and ducks the question of the competing role of long range RKKY exchange interactions mediating impurity-impurity atom coupling effects (ref. 22). For these cerium intermetallics which fail to order magnetically, even at the lowest-temperatures measured, or become superconductors, it is now common to refer to them as "Kondo lattice solids" to distinguish this unique and puzzling property. The translational symmetry is expected to produce fine structure in the Kondo peak (as

581

yet unresolved) due to narrow band dispersion effects. Indeed, it is speculated that the dispersion might be of the order of TK and produce some of the heavy fermion superconducting properties of the other actinides (such as UPt,). The picture we are left with is that despite the now strong body of spectroscopic evidence that very large Coulomb interactions are at work to stabilize the "atomic" behavior in these materials, the heavy particle transport properties are indicative of quasiparticles at E, which are highly sensitive to translational symmetry for which the crystal momentum remains a good quantum number. There is a growing appreciation (refs. 2-4) that this duality in behavior is responsible for the new and exciting ideas emerging from a more critical look at the Ferrni liquid theories as applied to these narrow band solids (ref. 3). For example, near ground state properties may satisfy Luttinger's theorem (ref. 23) over some scale of temperature and energy, the properties of this "Luttinger liquid" being a generalization of the Landau behavior of Fermi liquids in normal wide band metals. Above some critical temperature (e.g., TK in the Kondo case) bare or "undressed' atomic-like excitations at higher energy scales may dominate. Theoretically, it would be most satisfying to be able to calculate the electronic structure from

an ab initio calculation. A theoretical breakthrough to the problem of fluctuating valence in a more general Anderson Hamiltonian has been accomplished by Gunnarsson and Schonhammer (ref.

24) who have been able to calculate the spectral density of states distributions of d- and f-states resulting from an impurity model. Also, and surprisingly, density functional theory describes the Fermi surfaces of the heavy fermion systems, like UP$, very accurately (ref. 25). However, in general, the ab initio methods run into grave problems when it comes to describing excited states, temperature dependencies, band gaps, optical properties and phase transitions. The most likely future scenario will be one in which ab initio methods are used to calculate accurate ground state properties from which the appropriate parameters used in the model Hamiltonians can be derived. This can then, in turn, describe the properties of the excited states and their interactions. The resolution of spectral features indicative of this wide variety of phenomena has been one of the recent triumphs of photoelectron spectroscopy. Also the discovery of superconductivity with high critical temperatures in a range of oxides containing transition metal and rare earth ions (ref. 26) has provided an enormous impetus to this field. In the following section we review some of

the progress made with reference to selected examples of particular relevance in the present context.

3. HIGHLY-CORRELATED ELECTRONIC SYSTEMS 3.1 Strong-Correlation Effects in Chemisorption

The band width W is a function of the number of nearest-neighbor coordinating atoms and the

degree of interaction of their overlapping wave functions. Two-dimensional layers deposited onto single crystal substrates might be expected, therefore, to show these strong correlation effects - indeed, it is a surprise that they are not more prevalent than has been observed to date. The Cs/GaAs(l 10) has recently been shown to be an interesting example of a two-dimensional Schottky barrier system for which a delocalized one-electron description fails to describe the excitation spectra (ref. 27). The central problem is that one-electron theory predicts a partially filled gap, due to Cs(6s)-induced interface states, resulting in a higher density of states at the Fermi level (ref. 28). Experimentally, the surface is found to be insulating at all coverages up to a full monolayer of Cs (ref. 29). Another intriguing fact is that STM studies (ref. 30) show a tendency for the metal adatoms to form pairs, zigzag chains, and ordered clusters indicative of "surface molecule" rather than metallic behavior. Above one monolayer coverage, the surface becomes metallic. We note that in the case of Cs, the density of the bulk metal is near the Mott limit for

an insulator-metal transition (ref. 27). High-resolution ( 0.5 eV/A-') are further broadened. While these experimental resolutions are adequate to address relatively high energy issues such as bulk cohesion, lattice structure, and chemisorption, sensitivity to low energy phenomena is normally not available. Thus the signal/resolution trade-off provides a practical limit to the sensitivity and applicability of the technique.

4.

5.

Concluding Remarks The purpose of this monograph has been to explain the fundamentals issues involved in using ARP to study electronic phenomena in a variety of different of materials. Every chapter has indicated the technique's enormous breadth of application. The spectroscopy can now be considered to be "mature", in the sense that the fundamental details of interpretation have been (or are being) worked out, and we have indicated how it might be applied in emerging fields and technologies. A n evaluation of this sort is useful and timely. A technique like ARP needs to be applied in a variety of contexts lest experiments become purely technique-oriented, with little relation to condensed matter science in general. The most striking current example of how ARP is being applied to unusual materials is undoubtedly in the area of high Tc materials. Never before has so much attention been focused upon the technique. We envision a bright future with similar high-profile applications for some time to come.

599

REFERENCES 1. 2.

3. 4.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.

C. Kunz, Synchrotron Radiation (Springer, Berlin, 1979) E. Koch, ed., Handbook of Synchrotron Radiation (North-Holland, Amsterdam, 1983). G. Margaritondo, Introduction to Synchrotron Radiation, (Oxford University, New York, 1988). D.F. Alferof, Y,A. Bashmakov, and E.G. Bessonov, Sov. Phys. Tech. Phys. 18, 1336 (1974). B.M. Kincaid, J. Appl. Phys. 48,2864 (1977). C.T. Chen, Nucl. Inst and Meth. A 256, 595 (1987); C.T. Chen and F. Sette, Rev. Sci. Instr. 60, 1616 (1989). P.A. Heimann, et. al., Physica Scripta T31, 127 (1990). see, for example, Proceedings of the Sixth National Conference on Synchrotron Radiation Instrumentation, Nucl. Inst. and Meth. A291, 1 (1989). see, for example, Proceedings of the X-ray/EUV Optics for Astronomy and Microscopy Conference, SPIE 1160,2 (1989). J.W. Cooper, Phys. Rev. 128,681 (1962). M. El-Batanouny, M. Strongin, and G.P. Williams, Phys. Rev. B27,4580 (1983). for a review, see J. W. Allen, "Resonant Photoemission of Solids with Strongly Correlated Electron", in Synchrotron Radiation Research: Advances in Surface Science, R.Z. Bachrach, ed. (Plenum, New York, 1990). D.C. Koningsburger and R. Prins, eds., X-ray Absorption: Principles, Applications and Techniques of EXAFS, SEXAFS, and XANES (John Wiley, New York, 1988). C.L. Allen, T. Gustaffson, and E.W. Plummer, Chem. Phys. Lett. 47, 127 (1977).(?) C.T. Chen, R.A. Didio, W.K. Ford, and E.W. Plummer, Phys. Rev. B32, 8434 (1985); W. Eberhardt. E.W. Plummer. C.T. Chen. R. Carr. and W. Ford. Nuc. Inst. and Meth. A246,825 (1986). A. Szoke, in Short Wavelength Cohernet Radiation: Generation and Applications, AIP Conference Proceeding No. 147. D.T. Attwood and J. Bokor. eds. (American Inst. of Physics, New York, 1986). J.J. Barton, Phys. Rev. Lett. 61, 1356 (1988). G.R. Harp, D.K. Saldin, and B.P. Tonner, Phys. Rev. Lett. 65, 1012 (1990); S. Hardcastle, Z.-L. Han, J. Zhang, B.L. Chen, D.K. Saldin, and B.P. Tonner, Surface Science Letters, 245, L3 (1991).


601

INDEX

acetylene, 342 adiabatic approximation, 128 adsorbate dipole, 419 adsorbate surface Umklapp, 31 1 alkali metals, 95,96,42-48 alkali metal adsorption -CS/Al(lll), 420 -CS/CU(Oll), 420 -CS/CU(lll), 419 -CS/W(OOl), 420 -K/Al(lll), 420 -K/Cu(001), 346 -K/Ru(0001), 362 -Na/Al(lll), 531 -Na/Cu(001), 420 -Na/Pd( 11l), 330 alkali metal clusters, 94,95 alloy -surface, 393-397,408,410 -magnetic, 500-502 aluminum, 86,87 -(001), 18,39,105-107,111,113 -(ill), 107,116 aluminum, adsorption on -Ag/Al(001), 391-392 -Ag/Al( 11l), 379,380,392,393 -AU/Al(lll), 397 -CO/Al( 1ll), 332 -Cs/AI( 11l), 420 -CU/Al(lll), 386 -Na/Al(lll), 531 -Pb/Al(lll), 415 -Pd/Al(lll), 410 -Xe/Al( 11l), 297-8,324 aluminum films -Al/GaAs, 458 -A/InP, 458 -Al/Si(lll), 450

ammonia adsorption -Ir( 11l), 342 antibonding band, 131,305 antimony, adsorption -Si(11l), 447 -GaAs( 1lo), 449,534 -Inp( 110), 534 antimpny films, 546 APW, 225,231 arsenic adsorption -Si( 11l), 88-90,445-447 -Ge( 11l), 88-90,438,445-446 atomic effects, 6,571,590 Auger electron spectroscopy, 375-8 augmented plane wave, 225,231 back bonding, 156,438 backscattering, 246,260-262 band bending, 148-149 band gap problem, 64,78 band mapping, 4,32,215-221315-518 band width, 103,381-382,385,397,398 BCS theory, 586 beryllium(000 1), 18,32,36 bismuth -(ill), 118 bismuth adsorption -Si(lll), 446 Bi2Sr2CaCu208, 584-585 Blyholder model, 332,361,538 bond relaxation effect, 583 bonding state, 131 Born-Haber cycle, 45417,420 Born Oppenheimer approximation, 128 boron adsorption -Si, 450 bromine adsorption -CU(O01), 309-310

602

bulk photoeffect, 2,3 buried interface, 454 calcium floride adsorption -Si( 11I), 457 cadmium selenide, 532 cadmium sulfide, 532 cadmium telluride, 197-199,532 carbon dioxide adsorption -Ni(Oll), 339-340 carbon monoxide, solid, 321 carbon monoxide adsorption, 266,267, 3 19-334,343,344,349-358,360,362,540 cellular calculations, 292,296,298 cesium adsorption -Al(l11), 419,420 -GaAs(Oll), 581 -CU(OO1), 420 -Cu(Oll), 420 -Cu(lll), 419 -W(OOl), 420 charge density wave, 124,585 charge transfer energy, 573-577,584,585 charge transfer insuIator, 574-576,584 charge transfer, sp, 385,386,398 chemical shift, 282,283 chlorine adsorption -Ag(001), 310 -Cu(OO1), 306-310 -Ge(111), 443 -Si(111), 312-4,443-4 chromium (Oll), 336 chromium dioxide, 503-504 coadsorption, 324,330,343-348,362-3 cobalt, adsorption on -CO/CO(OOOl), 329,330,352 cobalt films -bee, 460 -Cu(OOl), 401 -GaAs, 460 cobalt disilicide, 462

coherent pseudopotential, 224 coincidence method, 4 Cooper minimum, 264,385,403,405,596 copper oxide superconductors, 583-587 core resonances, 234 correlation energy, 6,15-98,154,156-159, 489-490,572-577 CPA, 224 crud test, 110,130,167,211 copper -(001), 105,116,118,120,122,522-523,557, 558 -(111), 105114-116,120-121,138,519523,531,536,557,558 copper, adsorption on -Ag/Cu(001), 387-390 -Ag/Cu( 111), 390-391 -Au/CU(00 l), 394-396 -CO/Cu(OOl), 345,540 -CO/CU( 111), 266,267,321,324,332,358 -C0/Ch(001), 405 -Cs/CU(OOl), 420 -CS/cU(lll), 419 -Fe/Cu(OOl), 403 -formate/Cu(001), 272-275 -formate/Cu(Oll), 273,340 -K/Cu(001), 346 -methoxy/Cu(OOl), 272-275 -methoxy/Cu(Oll), 273 -Mn/Cu(001), 404 -Na/Cu(001), 420 -N2/Cu(001), 283 -Ni/Cu(001), 401 -O/CU(OOl), 259,260,272-275 -O/Cu(Oll), 272,303-6,536-536 -O/cU( 111), 559 -Pd/Cu(001), 408 -Tl/Cu(OOl), 414 -Xe/Cu(Ol l), 303-306 copper films -Cu/Ag(001), 380-382

603

-cU/Al( 11l), 386 -Cu/Pt( 11l), 385 -cU/Ru(0001), 382-384 -Cu/Si(lll), 533 -Cu/Zn(OOOl), 385 copper palladium alloys, 31 cupric oxide, 572 cupric sulfide, 574 Curie temperature, 470-472 curved wave, 252,271 cyanide, 338

dangling bonds, 438,440,441,532 DAS model, 141,460 dead layer, 403 defect band, 452 defect state, 147,172,177,178,181,184,185, 223,232,563,564 defects, surface, 120,121,296,562,565 degenerate semiconductors, 159,177 density functional theory, 29,46,47,64-67, 571 density of states features, 112 diamond, 82,83 dimers, surface, 171,175,178-180,192,193, 215-221,447 dipole velocity matrix elements, 19,52 direct transition, 17-20,29,31,32,215-221, 438,515-518 disordered local moment model, 480,483, 490 Doniach-Sunjic lineshape, 28 dynamical dielectric response, 40,72-74, 123 easy direction, 494,497 electron correlation, 6,154,489,490,573578,582-585 electron-electron interaction, 490 electron scattering, 246-247,252-255,259, 260,276

ellipsoidal mirror display analyzer, 11 empirical pseudopotential method, 66,82, 102,107,116 epitaxial growth, 180,191-196,436,457,494 ethylene, 319,342 EXAFS, 251 exchange splitting, 469-470,478-480,485, 488,489,517-518 excitonic effects, 92,555 extraordinary peak, 482,490 fcc/hcp site, 133,261-263,266,267 Fe3Pt, 500-503 Fermi golden rule, 5,15-17,109,113,326, 5 10,513 Fermi level pinning, 147-149 Fermi surface, 36,37,125-129,585-586 ferrimagnetic ordering, 498 ferromagnetic resonance, 496 final state damping, 6,19,21,28-30,33-36, 4 1,42,48,120,150,271 final state multiplet, 485 final state screening, 416,440,539 fluctuating band model, 480,483 formate adsorption -/Cu(OOl), 272-275 -/Cu(Oll), 273,340 forward scattering, 246,247,252-255,259, 260,276 Frank-van der Merwe growth, 376,378 free-standing monolayer, 25 1,262-264 gadolinium(0001), 470 gadolinium adsorption -Fe(001), 497,498 gallium adsorption -/Si(lll), 450 gallium aluminum arsenide, 459 gallium antimonide, 189-190 gallium arsenide,

604

-(01l), 4,47-5 1,92,93,185-190,532,560, 562,564 -(001), 191-194 -(lll) , 191,194-6 gallium arsenide, adsorption on -AI/GaAs(Oll), 458 -Au/GaAs(Oll), 582 -Co/GaAs(Oll), 460 -Cs/GaAs(Oll), 581 -Fe/GaAs(Oll), 460,496 -Ge/GaAs(Oll), 456 -Pb/GaAs(001), 453 -Sb/GaAs(llO), 449,534 -Ti/GaAs(Oll), 533 gallium arsenide films -Si(lll), 454-456 gallium phosphide(0l l), 185,450 gallium selenide, 555 2 gamma state model, 500 Geiger-Muller counter, 513 generalized susceptibility, 124 germanium -(001), 81,83,171,172,180-183 -(ill), 81,83,151,156-159,161,168-171, 438,532 germanium, adsorption on -As/Ge( 1ll) , 88-90,438,445,446 -CI/Ge( 1ll) , 444 -H/Ge( 11l), 441-443 germanium films -Ge/Si( 11l), 460 -Ge/GaAs(Oll), 456 gold -(ill), 115,116 -(Oil), 537 gold films, 393 -M(lll), 397 -CO/AU, 332 -CU(OOl), 394-396 -GaAs(Oll), 582 -Si(lll), 453,461,533

-W(Oll), 371 -W(OOl), 394 graphite, 298,545 Green function, 15,16,19,25,30,31,51,67 GW approximation, 47,48,72,73

H, structure, 451,452 halide adsorption -Br/Cu(001), 309-310 -Cl/Ag(001), 310 -Cl/cU(001), 306-310 -Cl/Ge(lll), 444 -Cl/Si( I l l ) , 443-444 -I/Ag(lll), 261-263 Hartree Fock method, 64,67,74 hcp/fcc site, 133,261-263,266,267 heavy Fermion, 578 heterojunction band offsets, 84 high T, materials, 583-587 Hubbard bands, 575,585 Hubbard Hamiltonian, 572,584 Huckel model, 102,103 Hunds’ rules, 404,577 hydrogen,H2, 334 hydrogen dissociation, 137,138 hydrogen adsorption -Ge(11l), 441-443 -Ni(Oll), 301-302 -Ni(lll), 131,132,302-303 -Pd( ill), 131,132,298-301 -Pt(lll), 131,132 -Ru(001), 134,136,137,301 -Si( 11l),(OOl), 440-443 -W(OO1), 129 iodine adsorption -Ag( 11l), 261-263 image plane, 529 image states, 103,518-520,524,557 indirect transitions, 295 indium adsorption

605

-Si(1ll), 450 indium antirnonide, adsorption on -a-Sn/InSb(OOl),(lll), 459 indium phosphide, 450,556,557,560,561 indium phosphide, adsorption on -Al/InP(Oll), 458 -Sb/InP(110), 534 interface state, 373,375,398,399,408,439 interpolation scheme, 525 invar effect, 500,502 inverse photoemission, 9,24,31,509-567 ion scattering, 375 iron, 469 -(001), 475-479,505 -(Oil), 518 -(ill), 476 iron, adsorption on -CO/Fe(Oll), 346 -Gd/Fe(001), 498 -O/Fe(001), 505 -N,/Fe( 11l), 336-337 iron films -Fe/Ag(001), 403,493-494 -Fe/Cu(001), 403 -Fe/GaAs(Ol l), 460,496 -Fe/W(Ol l), 497 jellium, 130 JJJ potential, 529 KKR, 224,233,309 KMNF,, 286 Kohn anomaly, 126 Kondo resonance, 577,578 Koopman’s theorem, 27 Kamers-Kronig relations, 33 krypton, 555

lanthanum cuprate, 575,584 LAPW, 309 lateral interactions, 292

lattice contraction, 397,398 lattice match, 372 LDOS, 17 lead adsorption -Al(lll), 415 -GaAs(001), 453 -Pb/Si( 11l), 452 lead sulfide, 200 lead selenide, 200 lead telluride, 200 LEED, 245,246,375 LiCl, 81,83 lifetime broadening, 19,21,28-30,33-36,41, 42,48,220 ligand holes, 573,574 Lindhard dielectric function, 47,133 lineshape, 28-30,36,48,49 local density approximation, 29,38,42,64, 66,75,84,88,89,446,451 local density of states, 17 local field effects, 76,78,86 local magentic moments, 495,573 low energy electron diffraction, 215,216, 375 Luttinger liquid, 580 magnesium (OOOl), 18 magnetic deflection, 12 magnetic scattering, 285 magnetic surface anisotropy, 495,497 magnetic surface reconstruction, 497 Mahan cone emission, 2,3,4 Mahan cone, secondary, 438 majority spin, 469,517-518 manganese, 470 manganese films -AS( 11l), 530 -CU(OOl), 404 many body effect, 17,23,24,26,50-52,54, 109,111,114,124,540,541,545 Many-body distortion of bands, 40

606

mean-free-path, 17,23,24 mean square vibrations, 250,271 mercury adsorption -Ag(OOl), 414,415 methoxy adsorption -CU(OOl), 272-275 -CU(Oll), 273 minority spin, 496 model Hamiltonians, 572-581 molecular beam epitaxy, 180,191-196,436, 494 molecular orientation, 248 molybdenum -(001), 127,527 -(Oil), 118,119,121 molybdenum, adsorption on -Ag/MO(Oll), 371 -Au/Mo(Oll), 371 -Pd/Mo(Oll), 371 molybdenum disulfide, 4 momentum broadening, 30 Mott scattering, detector, 471,475 Mott insulator, 573,575-578,582 muffin tin potential, 19 multidetection, 11 multiple reflection model, 520,525,526 multiple scattering, 246 multipole mode, 54-57 narrow band phenomena, 489,571,577 nearly free electron model, 102,107,521, 524 niobium carbide, 218,231,232 negative electron affinity, 5 12 negative U, 583 Newns-Anderson model, 130,361 nickel, 470 -(OOl), 105,487-491 -(Oil), 301,302,487-491,517,518,535 -(111), 487-491,525,539,541,557 nickel, adsorption on

-Ag/Ni( lll),(OOl), 390 -CO/Ni(001), 278,279,343-344,59,540 -CO/Ni(Oll), 278,278,333-4,345-356, 360,541,542 -CO/Ni(lll), 321,325 -C02/Ni(Oll), 339 -Cu/Ni(001), 281 -H/Ni(Oll), 301-302 -H/Ni(lll), 131,132,302,303 -N2/Ni(O11), 337,362 -NO/Ni(001), 543 -NO/Ni(lll), 338,362 -Pb/Ni(lll), 415 -S/Ni(001), 260,269-271 nickel films - C ~ ( l l l ) 531 , -Cu(OOl), 401 nickel oxide, 573,577,578 nickel sulfide, 573,575 niobium -(001), 528 -(Oil), 546 niobium, adsorption on -Pd/Nb(Ol l), 404-407,531 -Pt/Nb(Oll), 412 nitric oxide adsorption -Ni(001), 543-544 -Ni( ill), 338,362 -Pd( 11l), 543-544 nitrogen adsorption -CU(OOl), 283 -Fe( 11l), 336,337,348 -Ni(Oll), 337,362 nitrogen dioxide adsorption, 339 nitrous oxide adsorption, 339 noble gases -Kr, 555 -Xe, 537 -Xe/AI( 11l), 324-325 -Xe/Cu(Oll), 392-396 normal momentum, 4,17,33,44-46

607

nucleation, 372 one step model, 150,214,220,221 optical potential, 21 osmium (OOOl), 343 oxidation, 562 oxygen, 0, adsorption -Pt(lll), 337 -Ag(Ol l), 337 oxygen, 0 adsorption -Cu(OOl), 259,260,272-275 -Cu(Oll), 273,303-6,535,536 -cll(lll), 559 -Fe(001), 505 -Pd( 11I), 348,363 palladium, 558 -(001), 524,525,529 -(Oll), 516 -(ill), 104 palladium, adsorption on -Ag/Pd(001), 391 -C,H,/Pd( 11l), 343 -CO/Pd( 11 l), 321,325-329,362 -CO2/Pd(lll), 348 -Fe/Pd(lll), 403 -H/Pd(lll), 131,132,298-301 -NO/Pd( 11l), 543-544 -O/Pd( ill), 348,363 palladium films -Pd/Ag(OOl), 408,409 -Pd/Ag(ll l), 408-410 -Pd/Cu( 11l), 408 -Pd/Cu(001), 408 -Pd/Mo(Oll), 379 -Pd/Nb(Ol I), 404-407,531 -Pd/Si( 11l), 533 parallel detection, 11 paralleI momentum, 3,4,19 Peierls distortion, 124,127,414 phase model, 222,223,520,525,526

phosphorus adsorption -Si( 11l), 446 physisorption, 292-296,337,339,357 pi-bonds, 151 plasmon, 23,24,40,50-52 plasmon poll approximation, 76 platinum, adsorption on -benzene, 343 -CO/Pt( 111), 346 -cll/Pt( 1ll), 385 -H/Pt(lll), 131,132 -02/Pt(lll), 337 platinum films -Pt/Nb(Oll), 412 polar surface, 232 polarization effect, 8,9,109,111,166,167, 176,178,194,215,226,230,251,308, 309,313,325328,333,335,336,340, 342-346,439,440,488,528,535 polyacetylene, 556 projected gap, 106 pseudomorphic growth, 397,398,401 pseudopotential, 66,82,102,107,116,314 quantum chemistry, 130 quantum defect, 520 quantum Hall effect, 124 quasiparticles, 21,22,25-27,40-42,46,70,71, 77 radiation field, 220,225 random phase approx, 46-48 reconstruction, 124-128,145,146,1866,497 relativistic effects, 104,116-120,128,188190,199 resonance model, 538 resonant Auger, 485 resonant interaction , 309,491,574 resonant inverse photoemission, 546 resonant photoemission, 53 relaxation, 401

608

rhodium, -benzene adsorption, 343 RKKY, 580 ruthenium (OOOl), 537 ruthenium, adsorption on -CO/Ru(0001), 345 -Cu/Ru(0001), 382-384 -H/Ru(0001), 134,136,137 satellite, 50-52,470,484,491 scanning tunneling microscope, 533,584 Schottky barrier, 84,562-564 screening, 297 selenium adsorption -Si(OOl), 448-449 self-consistency, 103 self-energy, 21-24,34,36,40,44,46-48,70,71, 83 S E W S , 245,246 shake-up, 50-52332,337,345,346,350 shape resonance, 329,330,337,523,524 Sherman factor, 472 Shockley state, 102,103,105,518,519,222, 390,391 silicon, 80-83 -(001), 171-178,532-533 -(ill), 91,92,145,146,152-157,161-167, 532-533,555-557,560,565,566 silicon, adsorption on -Ag/Si( ill), 453,461,533 -AI/Si( 11l), 450 -As/Si( 11l), 88-90,445,446 -Au/Si( 11l), 453,461,533 -B/Si(lll), 450 -CaF2/Si( 11l), 457 -CI/Si(lll), 312-314,433-434 -Co/Si( l l l ) , 462 -Cu/Si(lll), 533 -Ga/Si(lll), 450 -GaAs/Si( 11l), 454-456 -Ge/Si(lll), 460

-H/Si( 1ll),(OOl), 440-443 -In/Si( 11l), 450 -Pb/Si( 1ll), 452 -Pd/Si( 1ll), 462,533 -S/Si(OOl), 448-449 -Se/Si(OOl), 448-449 -Sn/Si(lll), 452 silicides, 462 silver -(001), 19,20,116,119,525,557 -(ill), 115,530,557 silver, adsorption on -Cl/Ag(OOl), 310 -CO/Ag( l l l ) , 321,323,332,335,357 -Cu/Ag(001), 380-382 -Fe/Ag( 00 l), 403,493 -Hg/Ag( OOl), 4 14,415 -I/Ag( l l l ) , 261-263 -O/Ag(Oll), 306 -02/Ag(011), 337 -Pd/Ag( 11l), 408,409 -Pd/Ag(001), 408,409 silver films -Ag/Al( 00 l), 39 1,392 -Ag/Cu( 00 l), 387-390 -Ag/Cu( l l l ) , 390,391 -Ag/Si( l l l ) , 453,461,533 -Ag/W(O11), 371 single domain, 447 single step model, 5 sodium -(01I), 28-34,85,86 soft x-ray monochromator, 590 sp decompression, 385,386,398 space charge, 512 spectral function, 19,20,22,25-27,43 spectral weight, 69 spherical defelction analyzer, 9,lO spin asymmetry, 472 spin correlation length, 483 spin density wave, 124,586

609

spin-orbit interaction, 104,105,116-120, 128 spin polarization, 9,471 SPIPES, 517-518 step potential, surface, 103 Stoner model, 483,487,490 strain, 454-456,458,460 Stranski-Krastinov, 378,392,410,412,461 stress, 454-456,458,460 strong ferromagnet, 492 sulfur adsorption -Si(OOl), 448-449 superconducting gap, 587 superexchange, 583 surface barrier, 103,528,529 surface core level shift, 420,283 surface defects, 296 surface photoeffect, 2,4,53,546 surface plasmon, 57 surface reconstruction, 124-128,145,146, 186,497 surface relaxation, 184,401 surface resonance, 101,107,113,523 surface state, 16,30,99,145 surface stress, 454-456,458,460 surface strain, 454-456,458,460 surface Umklapp, 536 Swanson hump, 4,105,117,128,527 synchrotron radiation, 4,5,109,111,590591

thallium adsorption -Cu(OOl), 414 titanium, adsorption on -H/Ti(0001), 131-133,301 titanium adsorption -GaAs(Oll), 533 titanium carbide, 218,231,232 titanium nitride, 215-217,219,230,233 tight binding model, 102,103,309 time of flight analyzer, 13 time-reversed LEED state, 16,17,19,24 tin adsorption -InSb(lll),(OOl), 459 -CdTe (001),(0 1l), 459 torroidal analyzer, 12 transition matrix element, 219 tungsten -(001), 4,105117,127,128,283,527 -(01l), 118,121,125,283 tungsten, adsorption on -Ag/W(Oll), 371 -Au/W(O11), 371 -AU/W(OOl), 394 -CS/W(OOl), 422 -Fe/W(Oll), 497 -2H/W(001), 129 two-hole state, 576

T4 structure, 451,452 Tamm state, 103,116,117,119,217,222, 223,231,232 tantalum -(Oil), 118,122 -(001), 527 tantalum carbide, 218 tantalum disulfide, 4 tantalum diselenide, 4 tellurium. 555

vacancies, 223,323 vanadium carbide, 231,234 vanadium films -Ag( 1l l ) , 530 vanadium nitride, 215217,219,225 vertex correction, 50,67 vertical contraction, 401 virtual bound states, 574 Vollmer-Weber growth mode, 278

undulator, 591 UPt,, 579,581

610

water adsorption, 341 Weiss domain, 474 work function, 410,418 xenon adsorption -Al(1ll), 324-325 -Au(Ol I), 537 -Xe/Cu(Oll), 392-396 -graphite, 298 -Ru(001), 537

zinc, adsorption on -Cu/Zn(OOOl), 385 zinc selenide (01l), 196 zinc telluride (Oll), 196,557,559,560 zirconium carbide, 229 zirconium nitride, 218,230,231,233

611

STUDIES IN SURFACE SCIENCE AND CATALYSIS Advisory Editors: B. Delmon, Universitb Catholique de Louvain, Louvain-la-Neuve, Belgium J.T. Yates, University of Pittsburgh, Pittsburgh, PA, U.S.A.

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Preparation of Catalysts I.Scientific Bases for the Preparation of Heterogeneous Catalysts. Proceedings of the First International Symposium, Brussels, October 1417,1975 edited by B. Delmon, P.A. Jacobs and G. Poncelet The Control of the Reactivity of Solids. A Critical Survey of the Factors that Influence the Reactivity of Solids, with Special Emphasison the Control of the Chemical Processes in Relation to Practical Applications by V.V. Boldyrev, M. Bulens and B. Delmon Preparation of Catalysts II. Scientific Bases for the Preparation of Heterogeneous Catalysts. Proceedings of the Second International Symposium, Louvain-la-Neuve, September 4-7,1978 edited by 8. Delmon, P. Grange, P. Jacobs and G. Poncelet Growth and Properties of Metal Clusters. Applications to Catalysis and the Photographic Process. Proceedings of the 32nd International Meeting of the Socibtb de Chimie Physique, Villeurbanne, September 24-28, 1979 edited by J. Bourdon Catalysis by Zeolites. Proceedings of an International Symposium, Ecully (Lyon), September 9-1 1,1980 edited by B. Imelik, C. Naccache, Y. Ben Taarit, J.C. Vedrine, G. Coudurier and H. Praliaud Catalyst Deactivation. Proceedings of an International Symposium, Antwerp, October 13- 15,1980 edited by B. Delmon and G.F. Froment New Horizons in Catalysis. Proceedingsof the 7th InternationalCongress on Catalysis, Tokyo, June 30-July 4, 1980. Parts A and B edited by T. Seiyama and K. Tanabe Catalysis by Supported Complexes by Yu.1. Yermakov, B.N. Kuznetsov and V.A. Zakharov Physics of Solid Surfaces. Proceedings of a Symposium, Bechyiie, September 29-October 3, 1980 edited by M. UzniEka Adsorption at the Gas-Solid and Liquid-Solid Interface. Proceedings of an International Symposium, Aix-en-Provence, September 2 1-23, 198 1 edited by J. Rouqueroland K.S.W. Sing Metal-Support and Metal-Additive Effects in Catalysis. Proceedings of an International Symposium, Ecully (Lyon), September 14-16, 1982 edited by B. Imelik, C. Naccache, G. Coudurier, H. Praliaud, P. Meriaudeau, P. Gallezot, G.A. Martin and J.C. Vedrine Metal Microstructures in Zeolites. Preparation - Properties - Applications. Proceedings of a Workshop, Bremen, September 22-24, 1982 edited by P.A. Jacobs, N.I. Jaeger, P. Jirir and G. Schulz-Ekloff Adsorption on Metal Surfaces. An Integrated Approach edited by J. BCnard Vibrations at Surfaces. Proceedings of the Third InternationalConference, Asilomar, CA, September 1-4, 1982 edited by C.R. Brundle and H. Morawitz

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Heterogeneous Catalytic Reactions Involving Molecular Oxygen by G.I. Golodets Preparation of Catalysts 111. Scientific Bases for the Preparation of Heterogeneous Catalysts. Proceedings of the Third International Symposium, Louvain-la-Neuve, September 6-9, 1982 edited by G. Poncelet, P. Grange and P.A. Jacobs Spillover of Adsorbed Species. Proceedings of an International Symposium, LyonVilleurbanne, September 12-1 6, 1983 edited by G.M. Pajonk, S.J. Teichner and J.E. Germain Structure and Reactivity of Modified Zeolites. Proceedings of an International Conference, Prague, July 9-13, 1984 edited by P.A. Jacobs, N.I. Jaeger, P. Jirh, V.B. Kazansky and G. Schulz-Ekloff Catalysis on the Energy Scene. Proceedings of the 9th Canadian Symposium on Catalysis, Quebec, P.Q., September 30-October 3, 1984 edited by S. Kaliaguine and A. Mahay Catalysis by Acids and Bases. Proceedings of an International Symposium, Villeurbanne (Lyon), September 25-27, 1984 edited by 8. Imelik, C. Naccache, G. Coudurier, Y. Ben Taarit and J.C. Vedrine Adsorption and Catalysis on Oxide Surfaces. Proceedings of a Symposium, Uxbridge, June 28-29,1984 edited by M. Che and G.C. Bond Unsteady Processes in Catalytic Reactors by Yu.Sh. Matros Physics of Solid Surfaces 1984 edited by J. Koukal Zeolites: Synthesis, Structure, Technology and Application. Proceedings of an InternationalSymposium, Portoroi-Portorose, September 3-8, 1984 edited by B. Driaj, S. HoEevar and S. Pejovnik Catalytic Polymerization of Olefins. Proceedings of the InternationalSymposium on Future Aspects of Olefin Polymerization, Tokyo, July 4-6, 1985 edited by T. Keii and K. Soga Vibrations at Surfaces 1985. Proceedings of the Fourth InternationalConference, Bowness-on-Windermere, September 15-1 9, 1985 edited by D.A. King, N.V. Richardsonand S. Holloway Catalytic Hydrogenation edited by L. Cervenq New Developments in Zeolite Science and Technology. Proceedings of the 7th International Zeolite Conference, Tokyo, August 17-22, 1986 edited by Y. Murakami, A. lijima and J.W. Ward Metal Clusters in Catalysis edited by B.C. Gates, L. Guczi and H. Knozinger Catalysis and Automotive Pollution Control. Proceedings of the First InternationalSymposium, Brussels, September 8-1 1, 1986 edited by A. Crucq and A. Frennet Preparation of Catalysts IV. Scientific Bases for the Preparation of Heterogeneous Catalysts. Proceedings of the Fourth InternationalSymposium, Louvain-la-Neuve, September 1-4,1986 edited by B. Delmon. P. Grange, P.A. Jacobs and G. Poncelet Thin Metal Films and Gas Chemisorption edited by P. Wissmann Synthesis of High-silica Aluminosilicate Zeolites by P.A. Jacobs and J.A. Martens Catalyst Deactivation 1987. Proceedings of the 4th International Symposium, Antwerp, September 29-October 1, 1987 edited by B. Delmon and G.F. Froment

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Keynotes in Energy-Related Catalysis edited by S. Kaliaguine Methane Conversion. Proceedings of a Symposium on the Production of Fuels and Chemicalsfrom Natural Gas, Auckland, April 27-30, 1987 edited by D.M. Bibby, C.D. Chang, R.F. Howe and S. Yurchak Innovation in Zeolite Materials Science. Proceedings of an international Symposium, Nieuwpoort, September 13-1 7, 1987 edited by P.J. Grobet, W.J. Mortier, E.F. Vansant and G. Schulz-Ekloff Catalysis 1987. Proceedings of the 10th North American Meeting of the Catalysis Society, San Diego, CA, May 17-22, 1987 edited by J.W. Ward Characterization of Porous Solids. Proceedings of the IUPAC Symposium (COPS I), Bad Soden a. Ts., April 26-29, 1987 edited by K.K. Unger, J. Rouquerol, K.S.W. Sing and H. Kral Physics of Solid Surfaces 1987. Proceedings of the Fourth Symposium on Surface Physics, Bechyne Castle. September 7-1 1, 1987 edited by J. Koukal Heterogeneous Catalysis and Fine Chemicals. Proceedings of an International Symposium, Poitiers, March 15-1 7, 1988 edited by M. Guisnet, J. Barrault, C. Bouchoule, D. Duprez, C. Montassier and G. Perot Laboratory Studies of Heterogeneous Catalytic Processes by E.G. Christoffel, revised and edited by 2. Paal Catalytic Processes under Unsteady-State Conditions by Yu. Sh. Matros Successful Design of Catalysts. Future Requirements and Development. Proceedings of the Worldwide Catalysis Seminars, July, 1988, on the Occasion of the 30th Anniversary of the Catalysis Society of Japan edited by T. lnui Transition Metal Oxides. Surface Chemistry and Catalysis by H.H. Kung Zeolites as Catalysts, Sorbents and Detergent Builders. Applications and Innovations. Proceedings of an International Symposium, Wurzburg, September 48, 1988 edited by H.G. Karge and J. Weitkamp Photochemistry on Solid Surfaces edited by M. Anpo and T. Matsuura Structure and Reactivity of Surfaces. Proceedings of a European Conference, Trieste, September 13-16, 1988 edited by C. Morterra, A. Zecchina and G. Costa Zeolites: Facts, Figures, Future. Proceedings of the 8th International Zeolite Conference, Amsterdam, July 10-14, 1989. Parts A and B edited by P.A. Jacobs and R.A. van Santen Hydrotreating Catalysts. Preparation, Characterization and Performance. Proceedings of the Annual International AlChE Meeting, Washington, DC, November 27-December 2, 1988 edited by M.L. Occelli and R.G. Anthony N e w Solid Acids and Bases. Their Catalytic Properties by K. Tanabe, M. Misono, Y. Ono and H. Hattori Recent Advances in Zeolite Science. Proceedings of the 1989 Meeting of the British Zeolite Association, Cambridge, April 17-1 9. 1989 edited by J. Klinowski and P.J. Barrie Catalyst in Petroleum Refining 1989. Proceedings of the First International Conference on Catalysts in Petroleum Refining, Kuwait, March 5-8, 1989 edited by D.L. Trimm, S. Akashah. M. Absi-Halabi and A. Bishara

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Future Opportunities in Catalytic and Separation Technology edited by M. Misono, Y. Moro-aka and S. Kimura Volume 55 New Developments in Selective Oxidation. Proceedings of an International Symposium, Rimini, Italy, September 18-22, 1989 edited by G. Centi and F. Trifiro Volume 56 Olefin Polymerization Catalysts. Proceedings of the International Symposium on Recent Developments in Olefin PolymerizationCatalysts, Tokyo, October 23-25, 1989 edited by T. Keii and K. Soga Volume 57A Spectroscopic Analysis of Heterogeneous Catalysts. Part A: Methods of Surface Analysis edited by J.L.G. Fierro Volume 576 Spectroscopic Analysis of Heterogeneous Catalysts. Part B: Chemisorption of Probe Molecules edited by J.L.G. Fierro Volume 58 Introduction to Zeolite Science and Practice edited by H. van Bekkum, E.M. Flanigen and J.C. Jansen Volume 59 Heterogeneous Catalysis and Fine Chemicals II. Proceedings of the 2nd InternationalSymposium, Poitiers, October 2-6, 1990 edited by M. Guisnet, J. Barrault, C. Bouchoule, D. Duprez, G. Phrot, R. Maurel and C. Montassier Volume 60 Chemistry of Microporous Crystals. Proceedings of the InternationalSymposium on Chemistry of Microporous Crystals, Tokyo, June 26-29, 1990 edited by T. Inui, S. Namba and T. Tatsumi Volume 61 Natural Gas Conversion. Proceedings of the Symposium on Natural Gas Conversion, Oslo, August 12-17, 1990 edited by A. Holmen, K.-J. Jens and S. Kolboe Volume 62 Characterization of Porous Solids II. Proceedings of the IUPAC Symposium (COPS II), Alicante, May 6-9, 1990 edited by F. Rodriguez-Reinoso,J. Rouquerol, K.S.W. Sing and K.K. Unger Volume 63 Preparation of Catalysts V. Proceedings of the Fifth International Symposium on the Scientific Bases for the Preparation of Heterogeneous Catalysts, Louvain-laNeuve, September 3-6, 1990 edited by G. Poncelet, P.A. Jacobs, P. Grange and B. Delmon Volume 64 New Trends in CO Activation edited by L. Guczi Volume 65 Catalysis and Adsorption by Zeolites. Proceedings of ZEOCAT 90, Leipzig, August 20-23, 1990 edited by G. Ohlmann, H. Pfeifer and R. Fricke Volume 66 Dioxygen Activation and Homogeneous Catalytic Oxidation. Proceedings of the fourth International Symposium on Dioxygen Activation and Homogeneous Catalytic Oxidation, Balatonfured, September 10- 14, 1990 edited by L.I. Simandi Volume 67 Structure-Activity and Selectivity Relationships in HeterogeneousCatalysis. Proceedings of the ACS Symposium on Structure-Activity Relationships in Heterogeneous Catalysis, Boston, MA, April 22-27, 1990 edited by R.K. Grasselli and A.W. Sleight Volume 68 Catalyst Deactivation 1991. Proceedings of the fifth InternationalSymposium, Evanston, IL, June 24-26, 1991 edited by C.H. Bartholomew and J.B. Butt Volume 69 Zeolite Chemistry and Catalysis. Proceedings of an International Symposium, Prague, Czechoslovakia,September 8-13, 1991 edited by P.A. Jacobs, N.I. Jaeger, L. Kubelkovi and B. Wichterlovi

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Volume 7 1

Volume 72

Volume 73

Volume 7 4

Poisoning and Promotion in Catalysis based on Surface Science Concepts and Experiments by M. Kiskinova Catalysis and Automotive Pollution Control II. Proceedings of the 2nd International Symposium (CAPoC 2). Brussels, Belgium, September 10-1 3, 1990 edited by A. Crucq New Developments in Selective Oxidation by Heterogeneous Catalysis. Proceedings of the 3rd European Workshop Meeting on New Developments in Selective Oxidation by Heterogeneous Catalysis, Louvain-la-Neuve, Belgium, April 8-10,1991 edited by P. Ruiz and B. Delmon Progress in Catalysis. Proceedings of the 12th Canadian Symposium on Catalysis, Banff, Alberta, Canada, May 25-28,1992 edited by K.J. Smith and E.C. Sanford Angle-Resolved Photoemission.Theory and Current Applications edited by S.D. Kevan


Angle-Resolved Photoemission

Angle-resolved photoemission

Internal Photoemission Spectroscopy: Principles and Applications

Photoemission studies of high-temperature superconductors