Internal Photoemission Spectroscopy: Principles and Applications

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Internal Photoemission Spectroscopy Principles and Applications

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Internal Photoemission Spectroscopy Principles and Applications Valery V. Afanas’ev Laboratory of Semiconductor Physics Department of Physics and Astronomy University of Leuven Belgium

Amsterdam • Boston • Heidelberg • London • New York • Oxford • Paris San Diego • San Francisco • Sydney • Tokyo

Elsevier The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB,UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands First edition 2008 Copyright © 2008 Elsevier Ltd. 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 without the prior written permission of the publisher Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: [email protected]. Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notice No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress ISBN: 978-0-08-045145-9 For information on all Elsevier publications visit our web site at books.elsevier.com

Typeset by Charon Tec Ltd (A Macmillan Company), Chennai, India www.charontec.com Printed and bound in Great Britain 08 09 10

10 9 8 7 6 5 4 3 2 1

To My Father, to My Mother, to Olga


Contents

Preface List of Abbreviations

xi xiii

List of Symbols

xv

1

Preliminary Remarks and Historical Overview 1.1 General Concept of IPE 1.2 IPE and Materials Analysis Issues 1.3 Interfaces of Wide Bandgap Insulators 1.4 Metal–Semiconductor Barriers 1.5 Energy Barriers at Semiconductor Heterojunctions 1.6 Energy Barriers at Interfaces of Organic Solids and Molecular Layers 1.7 Energy Barriers at Interfaces of Solids with Electrolytes

1 1 2 5 8 12 14 18

2

Internal versus External Photoemission 2.1 Common Steps in Internal and External Photoemission 2.1.1 Optical excitation 2.1.2 Transport of excited electron to the surface of emitter 2.1.3 Escape from emitter: the Fowler model 2.2 IPE-Specific Features 2.2.1 Effects of the collector DOS 2.2.2 Effects associated with occupied electron states in the collector 2.2.3 Interface barrier shape 2.2.4 Electron scattering in the image-force potential well 2.2.5 Effects of fixed charge in the collector 2.2.6 Collector transport effects

23 23 24 25 29 32 32 34 35 39 42 45

3

Model Description and Experimental Realization of IPE 3.1 The Quantum Yield 3.2 Quantum Yield as a Function of Photon Energy 3.3 Quantum Yield as a Function of Electric Field 3.4 Conditions of IPE Observation 3.4.1 Injection-limited versus transport-limited current

48 48 50 53 57 57 vii

viii

Contents

3.5

3.4.2 Thermoionic emission versus photoemission 3.4.3 Photocurrents related to light-induced redistribution of electric field Experimental Approaches to IPE 3.5.1 IPE sample design 3.5.2 Optical input designs 3.5.3 IPE signal detection

59 60 62 62 64 65

4 Internal Photoemission Spectroscopy Methods 4.1 IPE Threshold Spectroscopy 4.1.1 Contributions of different bands to IPE 4.1.2 The Schottky plot analysis 4.1.3 Separation of different contributions to photocurrent 4.2 IPE Yield Spectroscopy 4.2.1 Mechanism of the yield modulation 4.2.2 Application of the IPE yield modulation to Si surface monitoring 4.2.3 Model for the optically induced yield modulation 4.3 Spectroscopy of Carrier Scattering 4.3.1 Scattering in emitter 4.3.2 Scattering in collector 4.4 PC and PI Spectroscopy 4.4.1 Intrinsic PC of collector 4.4.2 Spectroscopy of PI 4.4.3 PI of near-interface states in collector: the pseudo-IPE transitions

67 68 68 72 73 75 76 78 82 85 85 88 92 92 97 101

5 Injection Spectroscopy of Thin Layers of Solids: Internal Photoemission as Compared to Other Injection Methods 5.1 Basic Approaches in the Injection Spectroscopy 5.2 Charge Injection Using IPE 5.3 Carrier Injection by Tunnelling 5.4 Excitation of Carriers in Emitter Using Electric Field 5.5 Electron–Hole Plasma Generation in Collector 5.6 What Charge Injection Technique to Choose?

107 108 109 112 114 117 121

6 Trapped Charge Monitoring and Characterization 6.1 Injection Current Monitoring 6.2 Semiconductor Field-Effect Techniques 6.3 Charge Probing by Electron IPE 6.4 Charge Probing Using Trap Depopulation 6.5 Charge Probing Using Neutralization (Annihilation) 6.6 Monitoring the Injection-Induced Liberation of Hydrogen

124 124 127 133 137 141 145

7 Charge Trapping Kinetics in the Injection-Limited Current Regime 7.1 Necessity of the Injection-Limited Current Regime 7.2 First-Order Trapping Kinetics: Single Trap Model 7.3 First-Order Trapping Kinetics: Multiple Trap Model

148 148 150 152

Contents 7.4 7.5 7.6 7.7

Effects of Detrapping Carrier Recombination Effects Trap Generation During Injection Trapping Analysis in Practice

ix 154 158 160 161

8

Transport Effects in Charge Trapping 8.1 Strong Carrier Trapping Regime 8.2 Carrier Trapping Near the Injecting Interface 8.3 Inhibition of Trapping by Coulomb Repulsion 8.4 Carrier Redistribution by Coulomb Repulsion 8.5 Injection Blockage and Transition to Space-Charge-Limited Current

164 164 169 172 177 180

9

Semiconductor–Insulator Interface Barriers 9.1 Electron States at the Si/SiO2 Interface 9.1.1 Si/SiO2 band alignment 9.1.2 Si/SiO2 interface dipoles 9.1.3 Si/SiO2 barrier modification by trapped charges 9.1.4 Trapped ions at Si/SiO2 interface 9.2 High-Permittivity Insulators and Associated Issues 9.2.1 Application of high-permittivity insulators 9.2.2 Bandgap width in deposited oxide layers 9.3 Band Alignment at Interfaces of Silicon with High-Permittivity Insulators 9.3.1 Band alignment at interfaces of Si with elemental metal oxides 9.3.2 Interfaces of Si with complex metal oxides 9.3.3 Interfaces of Si with non-oxide insulators 9.4 Band Alignment between Other Semiconductors and Insulating Films 9.4.1 Ge/high-permittivity oxide interfaces 9.4.2 GaAs/insulator interfaces 9.4.3 SiC/insulator interfaces 9.5 Contributions to the Semiconductor–Insulator Interface Barriers

182 183 183 184 186 188 189 189 192 195 195 198 203 208 209 212 217 221

Electron Energy Barriers between Conducting and Insulating Materials 10.1 Interface Barriers between Elemental Metals and Oxide Insulators 10.1.1 Metal–SiO2 interfaces 10.1.2 Interfaces of elemental metals with high-permittivity oxides 10.2 Polycrystalline Si/Oxide Interfaces 10.3 Complex Metal Electrodes on Insulators 10.4 Modification of the Conductor/Insulator Barriers

224 225 225 227 231 237 242

10

11 Spectroscopy of Charge Traps in Thin Insulating SiO2 Layers 11.1 Trap Classification through Capture Cross-Section 11.2 Electron Traps in SiO2 11.2.1 Attractive Coulomb traps 11.2.2 Neutral electron traps in SiO2 11.2.3 Repulsive electron traps in SiO2

245 246 248 248 249 251

x

12

Contents 11.3 Hole Traps in SiO2 11.3.1 Attractive Coulomb hole traps 11.3.2 Neutral hole traps in SiO2 11.4 Proton Trapping in SiO2

251 252 252 256

Conclusions

260

References

263

Index

291

Preface It is well accepted nowadays that electron transport properties of heterogeneous material systems are to a large extent determined by energy barriers at the interfaces involved. In this way the necessity of the development of appropriate barrier characterization methods and, in more general sense, of the interface-sensitive spectroscopy techniques comes naturally. Moreover, with the size of the analysed objects reduced to the range of a few nanometres, the relative contribution of the surface or interface atoms to the density of states of a nano-layer or nano-particle increases accordingly. The latter makes the need for the characterization methods specifically sensitive to the properties of the interface region(s) even more acute. In the case of solid surfaces, the challenge of adequate characterization is met by electron spectroscopy methods, in particular by the photoemission techniques. Thanks to the sufficiently deep penetration of light into condensed phases, a similar way of experimental analysis appears also to be successfully applicable to interfaces. Considering that a charge carrier will be emitted into another solid, not to vacuum, one now speaks about the internal photoemission (IPE) process. The major goal of this book is to show how the IPE phenomenon can be applied as a spectroscopic tool to characterize interfaces between condensed phases. Despite the fact that IPE effects were first reported more than four decades ago, no systematic description of different IPE-based characterization methods is yet available. Williams (1970) has summarized his pioneering works in a rarely cited chapter of a book which was complemented more than two decades later by journal reviews by Adamchuk and the author of this book (Adamchuk and Afanas’ev 1992a; Afanas’ev and Adamchuk, 1994). To a large extent this situation arose because of the fact that only a limited spectrum of material systems had been analysed using IPE by that time. Though some of these results were of great importance for technological development like characterization of the Si/SiO2 system thus assisting the successful realization of silicon CMOS devices, perspectives of IPE as a useful spectroscopic method intended for wide application were unclear. The picture changed dramatically over the recent years thanks to the great expansion of the research concerning the non-silicon-based semiconductor and insulator materials, which evolved as the result of the forecasted evolution of semiconductor technology. This firmly established the IPE spectroscopy for further development and broad application in the analysis heterogeneous material systems. Therefore, this book has the purpose of not only filling a gap in the description of the experimental methodology of the IPE but, at the same time, also intends to provide the reader with reliable reference framework regarding interface barrier energies. After briefly overviewing the development of the IPE spectroscopy and its application to different materials in Chapter 1, the basic physical description of the method will be presented in Chapters 2 and 3 conducted in comparison with the classical external photoemission. The experimental approaches to interface characterization will be discussed in Chapter 4 and illustrated by experimental results obtained on interfaces of wide bandgap insulating layers. Next, as another example of the application of the IPE xi

xii

Preface

spectroscopy, the charge injection techniques will be described in Chapter 5. This is complemented by the comparison of charge characterization and monitoring methods in Chapter 6, followed, in Chapter 7, by a discussion of various aspects of trap spectroscopy based on trap capture cross-section parameter. Important extensions of the charge trapping analysis beyond the simple first-order kinetic model are presented in Chapter 8. Reaching the reference part of the book, this starts with addressing the high-permittivity (high-κ) insulating materials, where the available results regarding the interfaces of these materials with semiconductors and metals are discussed in Chapters 9 and 10, respectively. These are complemented in Chapter 11 by a survey of the trap analysis for the case of SiO2 , the ‘classical’ insulator in silicon electronics. The results obtained here over many years importantly demonstrate that charge trapping should not be considered solely as a purely electronic process but includes contributions of other sorts, such as ionic charges associated with protonic states in the oxides. This book should primarily serve as an introduction to the IPE spectroscopy which, depending on the aimed result, can be applied to different categories of researches. It may be useful for graduate and Ph.D. students entering the field of interface physics as well as for scientists and engineers interested in the most advanced characterization techniques. In addition, the current status of interface barrier characterization is presented and, in this respect the book can serve as reliable reference base needed in analysing electronic properties of heterostructures. It constitutes the first compilation of results concerning band alignment at the interfaces of high-κ insulating materials with semiconductors and metals. The author is thankful to many colleagues for their collaborations in the fields related to the physics of IPE and its spectroscopic applications. First of all, I would like to express my deepest gratitude to Prof. Vera. K. Adamchuk who introduced me to IPE nearly three decades ago and then greatly helped in my work in St.-Petersburg (Leningrad) University. Next, it is with pleasure that I acknowledge my debts of various sorts to Andre Stesmans arisen during years of research in the University of Leuven. Many other colleagues contributed significantly to the research results presented in this book. They include S. I. Fedoseenko of St.-Petersburg (Leningrad) University; J. M. M. deNijs and P. Balk, formerly with the Technical University of Delft; G. Pensl and M. J. Schulz of the University of Erlangen-Nurnberg. Special thanks are due to the colleagues at IMEC, Leuven, for their help in coping with the exploding research activity in the field of high-κ insulators: M. Houssa, M. Heyns, L. Pantisano, T. Schram, S. DeGendt, M. Caymax, M. Meuris, and to many others. Finally, the last but not least contribution of my wife, Olga Afanas’eva (Grishina), to IPE spectroscopy by patiently helping in preparation of this book as well as other numerous manuscripts during last 15 years is acknowledged with gratitude. V. V. Afanas’ev Leuven, Belgium March 2007

List of Abbreviations

ACI ALCVD BEEM CB CNL CV CVD ESR FN HOMO IL IPE IR LUMO MIGS MIS ML MOS PC PDA PI PST RE VB WF

Avalanche carrier injection Atomic layer CVD Ballistic electron emission microscopy Conduction band Charge neutrality level Capacitance–voltage Chemical vapour deposition Electron spin resonance Fowler-Nordheim Highest occupied molecular orbital InterLayer Internal photoemission Infrared Lowest unoccupied molecular orbital Metal-induced gap states Metal–insulator–semiconductor Monolayer Metal–oxide–semiconductor Photoconductivity Post-deposition anneal Photoionization Photon stimulated tunnelling Rare earth Valence band Work function

xiii


List of Symbols

a C D d E EC EF Eg EV F G h h hν I j k k LD m* m0 N n N(x) Ninj P p Q q R S T t x x¯

Inactivated area Capacitance Diffusion coefficient Thickness Energy Energy of the conduction band bottom edge Energy of the Fermi level Bandgap width Energy of the valence band top edge Strength of electric field Charge carrier generation rate Plank constant Inactivated volume Energy of a photon Electrical current Current density Boltzmann constant Wave vector Thermalization length Debye length Effective mass Free electron mass Density per unit area Refractive index Density per unit volume Injected carrier density Probability Carrier momentum Charge density per unit area Elemental charge Reflectivity Sample area Temperature Time Distance First centroid of a spatial distribution xv

xvi xm U V v vd VFB Vg VMG vth Y Z α ε ε0 κ λ μ ρ σ τ e h VAC φ ϕ χ

List of Symbols Spatial position of the potential barrier maximum Potential energy Volume Velocity Drift velocity Flatband voltage Gate voltage Midgap voltage Thermal velocity Quantum yield Centre charge expressed in elemental charge units Optical absorption coefficient Dielectric constant Dielectric permittivity of vacuum Relative dielectric permittivity Mean free path Mobility Volume concentration of charged centres Cross-section Time constant Barrier height Barrier height for electrons Barrier height for holes External photoemission energy threshold Work function difference Electrode potential Electron affinity

CHAPTER 1

Preliminary Remarks and Historical Overview

1.1 General Concept of IPE In most simple terms the internal photoemission (or IPE) can be defined as a process of optically induced transition of a mobile charge carrier, electron or hole, from one solid (the emitter) into another condensed phase (the collector) across the interface between these. The IPE is quite similar to the classical photoemission of electrons from a solid into vacuum (the external photoemission) because the optical excitation of a carrier in the emitter and its transport to the emitting surface or interface are the common steps. Differences between the external and internal photoemission processes are predominantly related to the different nature of the potential barriers at the surface and at an interface of a solid, respectively, to the differences in carrier transport associated with the barrier properties, and to the fact that the photon energy hν required for the IPE transition may be significantly (sometimes by one order in magnitude) lower than in the case of photoemission into vacuum, as it is illustrated in Fig. 1.1.1. This figure shows schematically the transitions corresponding to photoemission of electrons from a metal (Au) into vacuum, a wide bandgap insulator (SiO2 ), and a semiconductor (Si) in panels (a–c), respectively. The energy onsets of electron emission correspond to the experimentally determined photoemission threshold (work function) of the metal vac (Rhoderick, 1978), and the barrier heights SiO2 (Deal et al., 1966) and Si (Tung, 2001). Despite the close similarity between the IPE and the external photoemission the general understanding of the IPE process and related to its development of IPE-based spectroscopic methods came almost half a century after the classical photoemission picture was established. The most significant difficulty in the case of IPE consists in the need of sufficient understanding of the spectrum of electron states inside a solid to clarify the origin of the energy barriers at its interfaces. The latter are generically related to the occurrence of forbidden energy gaps (bandgaps) in a solid. Therefore, transport of charge carriers across the interface can only be adequately addressed when sufficient level of quantum theory of solids is attained. In fact, the concept of IPE was first introduced by Mott and Gurney to illustrate formation of conduction band in rock salt crystals by using comparison between the energy thresholds of electron photoemission from metallic sodium into the salt and to vacuum (Mott and Gurney, 1946) (cf. Fig. 1.1.1). Since then, thanks to the extremely rapid development (for review of early work see, e.g., Mead (1966) and Williams (1970)), the IPE spectroscopy emerged as the most physically sound and reliable tool to characterize energy barriers between condensed phases and to determine transport properties of excited charge carriers in the near-interface region. The ‘older sister’ of IPE, the external photoemission, gave 1

2

Internal Photoemission Spectroscopy: Principles and Applications

EVACUUM

5

EC

Energy (eV)

4 3

Vac SiO2

2 1 0

EC EF

EF Au

EF

Au SiO2 Vacuum

(a)

(b)

Si Au

n-Si EV

(c)

Fig. 1.1.1 Schematic of optically excited transitions corresponding to photoemission of electrons from the states near the Fermi level of a metal (EF ) into vacuum (a), insulator (b), and semiconductor (c). The shown threshold energies of transitions correspond to experimentally determined values for the surface of Au (the energy level of electron resting in vacuum is indicated as EVACUUM ), Au/SiO2 , and Au/n-type Si interfaces. The energies EC and EV correspond to the edges of the conduction and the valence bands, respectively. Zero of energy scale is placed to the Fermi level of the metal.

numerous hints to development of modern physics ranging from quantum theory of light to band theory of electronic states in condensed phases. In its turn, the IPE deals with intricate electron transfer interactions at interfaces of solids, which in many cases still cannot be adequately described even at the present level of quantum theory because detailed atomic structure of interfaces is unknown. Thus, when using this kind of spectroscopy one often addresses fundamentally novel elements in the condensed matter physics. 1.2 IPE and Materials Analysis Issues In addition to fundamental physics, great impetus to development of IPE spectroscopy came from the side of practical application of solid, primarily semiconductor-based heterostructures. Electron transport through and near semiconductor interfaces is crucial for operation of vast majority of solid state electronic and optoelectronic devices. Essential features of this transport are controlled by the density, relative energy, and quantum-mechanical coupling between electron states in the contacting materials and ultimately determine the rate of electron transition(s). Therefore, to understand the details of electron transport phenomena in device structures, spectrum of electron states at the interface requires quantitative characterization so one can control technologically and/or model numerically the electronic properties of the interfaces. The results of studies carried out over last 50 years strongly indicate that the spectrum of electron states at an interface cannot be immediately derived from the known bulk band structure of two contacting solids. Moreover, in many cases the properties of solid materials in vicinity of their interfaces appear to be very different from the bulk parameters. These differences indicate the significance of interface chemistry and bonding constraints on composition and structure of the near-interfacial layers of a solid (for recent review, see, e.g., Mönch (2004)). With the continuing trend to reduction of size and dimensionality of functional

Preliminary Remarks and Historical Overview

3

elements in solid state electronic devices, incorporation of new, often surface-stabilized materials in the device design, as well as the extension of the solid state electronics to new functionality areas, the need to understand interface properties of solid materials and related nanostructures is acute as never before. This need, in turn, raises question regarding reliable sources of information concerning electron states at interfaces of solids. More specifically, physical methods to probe the interface-relevant electron states appear to be in the focus of attention. As the physical picture of the observed process/phenomenon must be unambiguous and transparent to enable straightforward and reliable interpretation of the results, experimental characterization of electron states at the interfaces must go far beyond the conventional electrical characterization of the interface commonly applied in industry. This brings up the issue of designing the experimental physical methods suitable for detection and characterization of the interfacespecific portion of electron state density. When developing a characterization technique of this type one might follow two different paths to isolate interface-related contributions to the electron density of states (DOS). As the partial DOS is proportional to the number of atoms encountered in a particular bonding configuration, the bulk component(s) of DOS will be dominant (at least in the energy range outside the fundamental bandgap) unless the analysis is confined to a narrow near-interface layer of a solid. To enhance the sensitivity to electron states at the interface the studied volume of the sample can be limited to its very surface layer by using the surfacesensitive measurements. The most known example of this approach is provided by electron spectroscopy methods in which inelastic scattering of electrons in a solid limits the mean electron escape depth to values in the range of few nanometres (Feuerbacher et al., 1978; Briggs and Seah, 1985). By combining this surface-sensitive analysis with gradual increase of substrate coverage with the second component of the heterostructure, initial stages of interface formation and related evolution of electron DOS can be studied in detail. This kind of analysis is able to provide straightforwardly the information regarding atomic composition and chemical features of the interface as well as about electron DOS delivering in this way the most complete picture of the DOS development as a function of overlayer thickness. Moreover, electron spectroscopy analysis can be complimented by other surface characterization techniques ranging from optical spectroscopy to the scanning probe microscopy enabling reliable cross-checking of the results. Though the electron spectroscopy of surfaces represents the most successful approach to experimental DOS characterization, a small depth of analysis determined by inelastic mean free path of electrons (typically 3. These researchers introduced the algorithm to find the best fit of the IPE yield spectral curve using both the barrier height and the power factor p as fitting parameters. Remarkably, this effect is observed not only at the metal–electrolyte interfaces but, also, at the surfaces of metals in vacuum after adsorption of electronegative elements (e.g., oxygen on Mg(100) surface for which p = 3.5 is reported). It is also found that the work function of the metal with adsorbate determined using this ‘modified’ power fit is in much better agreement with the results of independent measurements (the Kelvin probe) than the work function value found using the Fowler plot Y 0.5 –hν. Interestingly, the photoemission from the clean Mg(100) surface obeys the Fowler law very well (see Fig. 1 in Lange et al., (1982)). The latter led the authors to suggestion that deviation from the free-electron type emission behaviour is caused by the energy-dependent scattering of electrons passing through the surface layer of the charged adsorbate species. Though in some cases the power factor fitting appears to be affected by the procedure of the fitting parameter choice (see, e.g., Vouagner et al., 2001) it has been successfully applied to describe the low-energy portion of the IPE spectra in Ag(100)–liquid NH3 system (Bennett et al., 1987). However, as the ‘normal’ Fowler behaviour is still observed at higher photon energies corresponding to the IPE of electrons into the conduction band of liquid NH3 , this ‘super-Fowler’ behaviour was considered to be a fingerprint of the NH3 final (tail) states below the conduction band bottom (Bennett and Thompson, 1986). The yet available experimental results suggest that deviation of IPE spectral curves from the Fowler (or Brodsky–Gurevich) behaviour is quite common and may bear additional physical information. The most important step in explaining the ‘super-Fowler’ increase of the yield with photon energy above the photoinjection threshold was done by Rotenberg et al. (1986) and Rotenberg and Gromova, (1986). They considered a non-ideal interface barrier with interfacial triangular portion of a non-negligible thickness δ and height U added to the conventional rectangular barrier between the Fermi level of a metal and the

22


bottom of the electrolyte (or solid insulator) conduction band as illustrated in Fig. 1.7.1. The electron photoemission over this barrier is again described in the framework of the free-electron model yielding the variable power exponent sensitive to the interlayer barrier parameters δ and U: Y (hν, ϕ) = A(δ, U)(hν − 0 + qϕ)p(δ, U) .

(1.7.2)

For small δ (δ ≈ 0.2 nm) p is found to be close to 2.3 with only a marginal sensitivity to the barrier height 0 which is in agreement with Fowler and Brodsky–Gurevich descriptions. However, as the width of the interlayer barrier δ increases to 0.6–0.7 nm, the power exponent becomes larger and may exceed p = 3.5. This result indicates that the value of p derived by using the Lange fit (Lange et al., 1981; 1982) or the differential method (Rotenberg et al., 1986) may be applied to determine the width of the polarization layer because the barrier reduction U with respect to the zero charge value 0 is determined directly by the observed spectral threshold as U = 0 − (cf. Fig. 1.7.1). This approach to the characterization of electrical double layer at the interfaces of metal–electrolyte solution systems may potentially encounter complications because, unlike the earlier suggestions (Neff et al., 1980; Sass, 1980), the electron thermalization length in H2 O was later found to be energy dependent and to affect the probability of electron detection in the electrolyte (Konovalov et al., 1988; 1990; Rips and Urbakh, 1991; Raitsimring, 1993; Benderskii and Yu, 1993; Kalugin et al., 1993). As the result, straightforward association of the exponent p observed in the photocurrent yield spectral dependence with that of the interface barrier transparency becomes impossible. Nevertheless, the results of Rotenberg et al. apparently are still applicable to the case of IPE into solid insulators and semiconductors over a non-ideal interface barrier, e.g., in the presence of an interlayer. One may notice, for instance, that the typical interlayer thickness of δ < 1 nm most of electrons will traverse it in ballistic regime because the electron–phonon scattering length is much larger (more than 3 nm in SiO2 , Berglund and Powell (1971), and Adamchuk and Afanas’ev (1992a)). Therefore, their scattering in the barrier region may be neglected, while nearly 100% collection efficiency of the excited carriers photoinjected into a solid insulator or semiconductor is ensured by electric field present far beyond the interface barrier region. Obviously, the above discussed model still use an oversimplified description of the electrostatic potential distribution which ignores the discrete nature of charged centres at the interface and, also, assumes perfect screening of image force potential by the conducting electrode. Nevertheless, evaluation of the charged (polarization) layer thickness using the near-threshold IPE spectroscopy seems to be feasible particularly when taking into account the absence of alternative characterization techniques.

CHAPTER 2

Internal versus External Photoemission

The overviewed results of internal photoemission (IPE) experiments in different material systems reveal a broad variety of approaches to observation and analysis of this phenomenon. The aim of this chapter is to sketch the way towards consistent description of the IPE process which can be applied more or less universally when interpreting the experimental data. In the core of this description is the multistep model of photoemission which describes this process as the sequence of quasi-independent stages sufficiently separated in time and in space. The applicability of this approximation is demonstrated by its successful application to the case of external photoemission, making now possible extension of this model to the case of IPE. The splitting of the photoemission process in several independent stages allows one to incorporate the additional effects associated with replacement of vacuum by a condensed phase by modifying only the pertinent stages accordingly. In turn, physical information can be extracted by analysing separate steps while keeping others unchanged. Obviously, this kind of description is highly simplified because it neglects mutual influence of the separate photoemission process steps. For instance, interference of electron waves in the barrier region would ‘mix’ the steps of barrier surmount and the transport in collector. Such interference is expected to cause oscillations in the barrier transparency (see, e.g., Kadlec, 1976; Kadlec and Gundlach, 1976), which may modulate the IPE yield in a similar way as it is observed in the case of conventional tunnelling current (Lewicki and Maserjian, 1975). It must be noticed, however, that such kind of effects is rarely noticed in the case of charge carriers excited to a sufficiently high energy coming above the barrier. This is also true in the case of ballistic electron emission microscopy (BEEM) experiments in which the primary electron flux seems to be perfectly suited to observe electron wave interference in the barrier region between the metal gate and the semiconductor or insulator collector material. Apparently, the already mentioned break of momentum conservation during electron transport across the interface prevents the electron interference by destroying phase of the reflected wave. Otherwise, the quantum oscillations would be easily observed even in the case of electron IPE from a metal as the theory predicts (Kadlec and Gundlach, 1976). With this feature in mind, we can now address the individual process stages aiming at revealing of common and dissimilar features of the external and internal photoemission processes. 2.1 Common Steps in Internal and External Photoemission It is evident from the above description of the multi-step photoemission model that the processes occurring inside the emitter are likely to be insensitive to the nature of the collector media and can be treated in the 23

24


same way both in the cases of photoemission into vacuum and photoemission into a media. This concerns two first stages of the photoemission: the optical excitation of charge carriers and their transport towards the surface (interface) of the emitter marked by arrows a and b, respectively, in Figs 1.3.2 and 1.7.2. 2.1.1 Optical excitation In the most simple way the optical excitation in emitter can be described as a transition (direct, indirect, non-direct) of an electron from the occupied initial states with energy distribution Ni (E) to the unoccupied final states with energy distribution Nf (E + hν). Assuming the momentum conservation to be unimportant (i.e., the non-direct transition scheme) the internal energy distribution of excited electrons in emitter can be expressed in a simple form (Powell, 1970): Nexcited (hν, E) = A(hν)Ni (E)Nf (E + hν)|Mif |2 ,

(2.1.1)

where A(hν) is determined by the intensity of light absorbed in the emitter, and Mif is the matrix element coupling the initial and final electron states. Would one limit the analysis to a narrow (> λph , at least in the kinetic energy range below 1 eV (Dalal, 1971; Schmidt et al., 1997), leading to c ≈ (λph )−1 and μ/c ≈ (λeh /λe )1/2 . Assuming that only a small portion of electrons excited in the near-threshold photon energy range is able to surmount the barrier (this argument is based on the escape cone considerations), one can use R ≈ 1, which leads to the inequality λph 1−R > λph may also be pertinent to description of photoemission of electrons from a moderately doped semiconductor if the kinetic energy of electrons in the conduction band of emitter Ek is smaller than the emitter bandgap width Eg . Under these circumstances the IPE may contain contribution stemming from electrons excited deep in the emitter (at an average escape depth of ≈(α + (λph )−1 )−1 , which makes it more sensitive to the bulk DOS of the emitter than to its surface. When considering photoemission of electrons from energetically the highest states of the emitter valence band, which is the case for most experiments using conventional optical excitation sources, the criterion of the ‘bulk’ IPE regime with large photoelectron escape depth can be formulated in simple terms as hν < 2Eg , where Eg refers to the bandgap width of semiconductor emitter. A very different picture emerges in the case of strong electron–electron scattering, i.e., λe

Ne = 0

if hν < .

(2.1.19)

Assuming that photoemission occurs due to excitation of electrons from a sufficiently wide occupied energy band, one may put (χm − hν) ≈ constant, which leads to the Fowler law (Fowler, 1931): Y (hν) ∝ Ne ∝ (hν − )2 .

(2.1.20)

Strictly speaking, this law is valid only at zero temperature. For any finite temperature one may fit the experimentally observed quantum yield dependence on the energy of photon using the Fowler function

1 2 π2 e−2μ e−3μ −μ + μ − e − 2 + 2 − ··· ln (Y/T ) = B + ln 6 2 2 3 2

(2.1.21)

32


to find the spectral threshold of photoemission under the condition that only a surface with one work function is contributing to photoemission. Would surfaces with several work function values contribute to photoemission, their spectral yield curves overlap and only application of Eq. (2.1.20) may give a chance to separate the corresponding thresholds (Okumura and Tu, 1983). The Fowler model uses a large number of simplifying assumptions. It is ignoring the complex band structure of the final electron states in the emitter and assumes the quasi-equilibrium shape (the Maxwell-type) of energy distribution of the excited electrons. The momentum conservation restrictions are neglected, and the classical barrier transparency formulation is used. The reader may find the further discussion on this subject in the article of Chen and Wronski (1995). Nevertheless, the ‘remarkable success’ (Chen and Wronski, 1995) of the Fowler model for several decades of its application provides strong experimental evidence in favour of this approximation when describing energy- and angle-integrated photoemission yield characteristics. The latter makes the Fowler model an ideal starting point for describing the IPE yield spectra. Now we will adapt this description to the case of IPE by using the corrections necessary to account for the replacement of vacuum by some condensed phase collector.

2.2 IPE-Specific Features Replacement of vacuum by a condensed phase collector material influences the photoemission process in a variety of ways. These include the effects caused by differences in the DOS of the final electron states between vacuum and a solid, by the presence of occupied electron states in the solid or liquid collector, by the application of electric field of considerable strength leading to the interface barrier shape modification, and by scattering of electrons in the barrier region as well as other collector transport effects. In this section the most important factors will be analysed to be later included into physical model of IPE described in Chapter 3.

2.2.1 Effects of the collector DOS The change of type of the electron states involved in the photoemission is the most obvious consequence of replacement of vacuum by a solid or liquid. The isotropic vacuum E(k) =2 k2/2 m dispersion curve which electron encounters in the classical photoemission picture is replaced by the conduction band states of insulator or semiconductor. The states in this band may have different quantum character because they are derived from the unoccupied electron states of different atoms. Along with relatively simple cases of s–p states which constitute the lowest conduction bands in oxides like SiO2 and Al2 O3 , rather complex band structures may be found in the oxides of transition metals due to the presence of d-states (see, e.g., Lucovsky, 2002). Additional complication of the picture is encountered in the complex metal oxides in which the unoccupied states originating from different cations give rise to quasi-independent sub-bands, each corresponding to the additional IPE threshold (Afanas’ev et al., 2005a). Finally, the solid layers as well as liquids used as collector media in the IPE experiments may contain a substantial structural disorder resulting in the well known band-tail states formation. These would obviously lead to a subthreshold photoemission with spectral characteristics strongly different from the regular IPE. An example of such behaviour is provided, for instance, by electron photoemission into liquid ammonia (Bennett, et al., 1987). As another example, the general character of the influence of the band-tail states on the IPE spectra is illustrated in Fig. 2.2.1 which compares the dependence of the quantum yield of electron photoemission from the valence band of Si into the conduction band of amorphous and crystalline (epitaxially grown)


33

a-Sc2O3/Si(100) 0.02

c-Sc2O3/Si(111) e

0.01

(IPE Yield)1/3 (relative units)

(a) 0.00

a-Lu2O3/Si(100) c-Lu2O3/Si(111)

0.02

e

0.01 (b) 0.00

a-LaLuO3 /Si(100) c-LaLuO3 /Si(111) e

0.02

0.01

(c) 0.00 2.0

2.5

3.0 3.5 Photon energy (eV)

4.0

Fig. 2.2.1 Spectral plots of the IPE yield in Y 1/3 –hν co-ordinates for electron photoemission from the valence band of silicon into conduction bands of different amorphous (a-) and crystalline (c-) oxide insulators, Sc2 O3 (a), Lu2 O3 , (b), and LaLuO3 (c). The scheme of the observed electron transitions is illustrated by the insert in the panel (a). The lines guide the eye and indicate the inferred electron IPE threshold e .

layers of several oxides: Sc2 O3 (a), Lu2 O3 (b), and LaLuO3 (c). The gross effect becomes clear when comparing the spectral characteristics of IPE in metal-oxide-semiconductor (MOS) structures with amorphous and crystalline insulators. It consists in smearing out of the near-threshold of the spectral curve in the samples with amorphous oxide material. As one can see from the (yield)1/3 versus hν spectral plots shown in Fig. 2.2.1, the amorphous oxides allow a much enhanced electron injection in the low-photon energy (sub-threshold) spectral range (hν < 3 eV) as compared to their crystalline counterparts. This difference cannot be accounted for by a simple change of the Si crystal surface orientation because both (100) and (111) faces of Si are known to have close photoemission thresholds at interfaces with SiO2 (Adamchuk and Afanas’ev, 1992a). Therefore, the observed difference in the IPE characteristics of the crystalline and amorphous oxide insulators rather refers to the differences in the energy distribution of their density of electron states near the conduction band edge. Namely, as indicated by the IPE data, the edge of the conduction band is smeared out in amorphous oxides suggesting a splitting down in energy of some cation-derived unoccupied band states.

34


Another important feature indicated by the data in all three oxides is that the IPE threshold e characteristic for crystalline oxides is still observed in the amorphous films at nearly the same energy of e = 3.1 ± 0.1 eV. Such insignificant sensitivity of the IPE threshold energy to the oxide crystallinity suggests that the momentum conservation condition is of little importance in the IPE transitions observed. Therefore, one may safely rely upon the indirect (or non-direct) transition model when describing the IPE characteristics (Powell, 1970; Williams, 1970). There are two other significant DOS parameters which may also have their impact on the photoemission characteristics. First, the density of electron states available in collector is not a constant but depends on the energy above the band edge. Would one assume the transition rate to be proportional to the density of final states (cf. Eq. (2.1.1)), the electron escape probability will be modulated by the DOS in the collector leading to additional dependence on the energy (Chen and Wronski, 1995). However, this effect is seen to be of marginal √ significance even in the case of photoemission into vacuum when the DOS is expected to increase as E − Evac and the escape probability might be expected to have the same dependence on electron energy. Nevertheless, the Fowler model which neglects the energy dependence of the escape probability is found to fit experimental data perfectly well. The possible explanation of this discrepancy stems from the detailed quantum-mechanical calculations of the barrier transparency (Kadlec, 1976; Kadlec and Gundlach, 1976) indicating that the barrier transparency rapidly saturates at nearly 100% when increasing the excess energy of electron above the barrier (within approximately 0.1 eV). Thus, the increase of DOS in the collector cannot lead to the proportional increase of the electron escape probability. In the light of this result the Fowler approximation of the stepwise barrier transparency function seems to have much better ground than it might be thought initially. Obviously, all these considerations are referring to sufficiently high DOS. When considering IPE into the band-tail states or to defects in the collector material their much lower density, as compared to the fundamental bands, may also influence the photoemission probability. The factor to be considered further is the difference between electron effective masses corresponding to the excited states in emitter and to the final state in the conduction band of the collector. The analysis performed in the framework of the parabolic band model and indirect optical transitions in the emitter suggests that the Fowler-type behaviour of the IPE quantum yield is still observed (Helman and SanchezSinencio, 1973). However, the ratio of the effective masses in the conduction bands of the emitter and the collector enters the energy-independent coefficient A in Eq. (1.3.1) making the IPE quantum yield (but not the energy threshold) sensitive to the effective mass difference. More severe distortion of the IPE yield spectral curves is predicted to occur would the momentum conservation be required in the IPE process (Chen et al., 1996). In particular, the power exponent p in Eq. (1.3.1) changes stepwise at certain photon energy. Nevertheless, as it appears now, the relaxed momentum conservation requirement seems to be the general case with the only possible exception of low-energy electron photoemission in lattice-matched heterojunctions. Keeping in mind the latter reservation, one still safely determine the IPE thresholds using the conventional power plot of the type given by Eq. (1.3.1).

2.2.2 Effects associated with occupied electron states in the collector In contrast to vacuum, the valence band of a collector material provides a continuum of the occupied electron states which may directly contribute to electron transport and, consequently, serve as final states in the IPE process. Obviously, the latter has no analogues in the conventional photoemission. This feature was recognized from the early days of IPE development and led to experimental observation of the IPE of holes (Williams, 1962; Williams and Dresner, 1967; Goodman, 1966b; 1970). Theoretical description of this process using the effective mass approximation yields the results similar to the IPE of electrons


35

(see, e.g., Helman and Sanchez-Sinencio, 1973), but now the relevant energy barrier h corresponds to the energy of the collector valence band top measured with respect to the bottom edge of the unoccupied states in the emitter as shown in Figs 1.4.1b and 1.5.1b. Combination of the energy thresholds of the hole and electron photoemission allows one to determine the collector bandgap width as (Goodman, 1966b): Eg (collector) = e + h − Eg (emitter),

(2.2.1)

where Eg (emitter) is the energy gap (if any) between the occupied and empty electron states in the emitter electrode. As the electron and hole IPE measurements are done in the monopolar injection regime, the bandgap width determined in this way is insensitive to the excitonic effects associated with Coulomb interaction between the charge carriers of opposite sign. By contrast, this interaction becomes important in the cases of fundamental optical absorption or intrinsic photoconductivity (PC) measurements because electron and hole are always generated at the same spatial location. The optical excitation of electrons from the occupied states in the collector to its conduction band represents another way for these states to contribute to the charge carrier generation. This effect is often referred to as the internal photoeffect or the photoconductivity but, despite similar name, this process is fundamentally different from the IPE because the energy distribution of the excited charge carriers is determined by the electron states of the same collector material. Nevertheless, it is still worth of considering the PC along with the IPE: The transport of the excited electron in the Coulomb potential well of the hole can be described in a way similar to the transport of electron in the image-force potential well (Knights and Davis, 1974; Weinberg et al., 1979; Adamchuk and Afanas’ev, 1992a). As a result, the transport parameters of excited electrons like the mean thermalization length can be evaluated from both the IPE and the PC data. At the same time, the onset of the intrinsic PC represents the most straightforward method to determine the bandgap width of the collector material. This is conventionally done by fitting the PC spectral dependence using the power law similar to that given by Eq. (1.3.1), though the exponent p in this case will be determined by the type of optical transitions dominating the PC excitation. Also, the PC spectral curves may provide information regarding electron states with energy levels within the collector bandgap (the impurity- or defect-related PC) which may later be compared to the results of IPE observations. Finally, the experimental arrangement of the PC measurements is in many cases identical to that one of the IPE. As a result, both experiments can be performed using the same samples, optical excitation scheme, and signal detection circuit by simply extending the photon energy range to hν > Eg (collector).

2.2.3 Interface barrier shape In the case of conventional photoemission the electric field outside the emitter is considered to be low and to have no measurable influence on the electron escape. Thus, the barrier shape at the surface is determined by the electrostatic potential distribution corresponding to the interaction of the photoelectron with the polarized conductor surface (the image-force potential) or, else, with the photohole it left behind (so-called dielectric limit). Replacement of vacuum by a condensed phase has two profound effects on the barrier shape. First, an electric field of considerable strength (up to several MV/cm) may be applied by using external biasing of the sample. Second, the collector material may contain fixed (in the case of a solid) or mobile (in the case of an electrolyte) charges which have additional direct impact on the barrier shape (see, e.g., Fig. 1.7.1 in which the polarization layer at the electrolyte–metal interface results in the interface dipole). To these features one must also add that the relative dielectric permittivity of the collector material εC may be much higher than one, leading to significant enhancement of the earlier discussed effects of the electric field penetration into the emitter. In the remaining part of this section

36


general approach to the interface barrier description will be discussed aiming at the extraction of relevant physical parameters from the IPE results. The description of the interface barrier one may start from the image-force model developed by Schottky to analyse the metal–vacuum barriers. In this model the potential of electrostatic forces acting on a point charge, e.g., an electron, located at a distance x from the surface plane of an ideal conductor (zero field penetration depth) is given by expression: U(x) = −

q , 8πεε0 x

(2.2.2)

where ε is the relative dielectric constant of the media accommodating the charge, and ε0 = 8.85 × 10−12 F/m the dielectric permittivity of vacuum. When applying this expression to describe the interaction between the photoelectron and the surface of emitter, one must account for the dynamic character of the photoemission process. Assuming that the transport of the excited electron can be described using the free-electron gas model of Fowler (Section 2.1.3), the time of ballistic flight across the barrier region of few nanometres in thickness can easily be estimated to be in the femtosecond range. This transit time determines the minimal frequency pertinent to description of the dielectric response of the emitter as well as of the collector material. As the frequency of 1015 Hz corresponds to the wavelength of light of about 300 nm, the dielectric constant of the collector must also be taken as the optical permittivity, i.e., ε ≈ n2 , where n is the refractive index of the collector material in the corresponding spectral range (Powell, 1970; Williams, 1970). In the first-order approximation, the time-dependent dielectric response of the emitter is determined by the characteristic time of the mobile charge carriers re-distribution. In metals the latter is expected to be in the order of the inverse plasma frequency: ωpl =

nq2 , εe ε0 m ∗

(2.2.3)

where n, εe , and me * are the free-electron concentration (not the refractive index), optical dielectric constant, and the electron effective mass in the emitter, respectively. For good metals the values of ωpl in the order of 10−16 s are expected which justifies direct application of Eq. (2.2.2) to the barrier description. In the case of photoemission from a semiconductor the transient of the majority carrier response is expected to be controlled by the Maxwell relaxation time τM = εε0 ρe , where ρe is the specific resistance of the emitter. For a silicon crystal with concentration of electrons of 1015 cm−2 at 300 K this time is about 5 ps, i.e., much longer than the expected electron transit time. This means that the majority charge carriers in semiconductor have no sufficient time to re-distribute in order to screen the hole left behind by the escaped photoelectron. Therefore, we should consider the electrostatic interaction of the unscreened hole in the semiconductor emitter with the electron entered the collector. The spatial displacement of a hole during the photoelectron transit time is negligibly small. Thus, in average, the hole will remain located at the point of its creation, i.e., at the mean photoelectron escape depth λe below the emitter surface plane. This charge distribution leads to the simple Coulomb potential: U(x) = −

q . 4πεe ε0 (x + λe )

(2.2.4)

This expression is still to be corrected for the difference in dielectric constants of the emitter and the collector, which will add some constant coefficient. Would the photoelectron escape depth still small


37

(few nanometres), λe becomes comparable to x and one can approximate both Eqs. (2.2.3) and (2.2.4) by one image-like potential as follows: U(x) = −

q , 8πεi ε0 x

(2.2.5)

in which εi is the effective image-force constant. This potential corresponds to the classical Schottky model, but εi represents now a phenomenological parameter accounting for different polarization processes at the interface. Experimental results accumulated over several decades suggest that this simplified barrier description is sufficient in most of the cases provided the density of uncompensated charges in the barrier region remains low. In this description it is usually assumed that Eq. (2.2.5) asymptotically approaches the real distribution of the electrostatic potential at sufficiently large distance from the interface, i.e., in the region x > δ, where δ is the image-force formation region with typical dimensions in the order of bond length in a solid. This model finds direct experimental support in the IPE observations indicating validity of the image-force model down to δ < 0.4 nm demonstrated at the Si/SiO2 interface (DiStefano, 1976). Within the image-force approximation one can describe the potential barrier profile at the interface by superposition of the step-like barrier 0 would be observed if no fields will affect the photoemission, with the image-force potential (2.2.5), and with the contribution of electric field F(x) to the potential energy variation at the interface (Berglund and Powell, 1971):

x (x) = 0 − q

F(z)dz −

q2 . 8πεi ε0 x

(2.2.6)

0

The second term in Eq. (2.2.6) includes the contributions of the electric field applied to the collector by biasing the sample, the possible contact potential difference, band bending in emitter, and the fixed charges encountered in the collector. In the most simple case of F = constant one obtains expression frequently used in analysing the field-dependent image-force energy barrier: (x) = 0 − qFx −

q2 . 8πεi ε0 x

(2.2.7)

The shape of this barrier is exemplified in Fig. 2.2.2 which shows the results obtained when using interface parameters typical for (100)Si/SiO2 structure, i.e., 0 = 4.25 eV with respect to the Si valence band top, and εi = 2.1 (Powell, 1970; Adamchuk and Afanas’ev, 1992a) and different strength of electric field in the insulator. The remarkable feature of this barrier is that its height appears to be field dependent: (F) = 0 − (F) = 0 − q

qF , 4πεi ε0

(2.2.8)

as well as the spatial location of the potential barrier maximum above the surface of the emitter: xm (F) =

q . 16πεi ε0 F

(2.2.9)

38

Internal Photoemission Spectroscopy: Principles and Applications (F )

e(F 0) 0 0.3 1.0

4

Energy (eV)

3

xm(F)

2 1

EC

0

EV

4.0 F(MV/cm)

1 2 0

1

2

3

4

5

Distance (nm)

Fig. 2.2.2 Calculated image-force potential barrier for electrons at the (100)Si/SiO2 interface for different strengths of the externally applied electric field in the oxide (in MV/cm).

The expressions (2.2.8) and (2.2.9) indicate that, with increasing strength of electric field F above the surface of the emitter, the barrier becomes lower and its top approaches the emitter surface plane as one also might notice from Fig. 2.2.2. The image-force barrier height reduction, often referred to as the Schottky barrier lowering, makes necessary the additional step in determination of the real barrier height at the interface 0 . The latter can be found from the field-dependent (F) values determined as the IPE threshold energies by extrapolation to F = 0. It is seen from Eq. (2.2.8) than convenient way to make such extrapolation is √to plot the spectral √ threshold values as functions of F, i.e., to use the Schottky co-ordinates (F)– F, and then apply linear fit to determine 0 (cf. Fig. 2.1.3b). Another important consequence of this barrier picture is that the interface barrier height determined as the energy of the image-force potential maximum. This energy corresponds to the position of an electron band in the collector at the distance xm from the surface of emitter. As illustrated in Fig. 2.2.2 case of Si/SiO2 interface, xm becomes less than 1 nm already at F = 2 MV/cm. Thus, the depth of interface probing in the IPE experiment is determined by two characteristic length values: on the side of emitter this is the mean photoelectron escape depth λe , and, on the side of collector, this is the barrier top location point xm . Both λe and xm are in the nanometre range thus making the IPE barrier measurements mostly sensitive to the electronic structure of the interface rather than to the bulk of the solid components. Before concluding this section one needs to mention two additional issues which may appear of importance when analysing the interface barrier shape in relationship with the field-dependent photoemission data. First, in the case of IPE it is possible that the transport of the injected charge carrier across the interface region 0 < x < xm will occur much more slowly that it is predicted by the free-electron model. For instance, a hopping of charge carrier between polaronic or defect states may require thermal activation and, therefore, will occur with typical frequencies well below the lattice vibration ones (0.1–1 ps).


39

This slow transport would make no difference in the case of metal emitter, but if the IPE from a semiconductor is considered, the transport time should be compared to the Maxwell relaxation time. If the carrier transit time appears to be larger than τM , semiconductor will have a sufficient time to become polarized and the centroid of the corresponding space charge will be located as a distance comparable to the Debye screening length LD given by Eq. (2.1.10). For moderately and low-doped semiconductors the Debye length by far exceeds the range of the image-force action, i.e., when replacing λe in Eq. (2.2.4) by a much larger than x value LD /2 one obtains vanishing contribution to the electron energy. Therefore, the image-force effects will become negligible leading to approximately rectangular (or triangular if electric field is applied) barrier with the field-independent barrier height. An example of this behaviour is provided by hole photoemission experiments at the Si/SiO2 interface (Adamchuk and Afanas’ev, 1984; 1985; 1992a). Second, it was attempted by Hartstein and Weinberg to re-formulate the classical image-force model to the quantum-mechanical case by scaling the potential value given by Eq. (2.2.5) using the interface barrier transparency coefficient. The latter would account for the absence of measurable barrier lowering in their photo-stimulated tunnelling experiments (Hartstein and Weinberg, 1978; 1979; Hartstein et al., 1982). This approach suggests that the image charge is proportional to the average portion of the electron density encountered beyond the barrier. Though this intuitive suggestion has a certain logic, more elaborate theoretical treatments of the quantum-mechanical electron transport across the interface found this hypothesis unsubstantiated (Johnson, 1980; Puri and Schaich, 1983). Also from the experimental point of view, it appeared that, as far as concerns the photon-stimulated tunnelling of electrons from Si into SiO2 , the rate of electron transitions is uncorrelated with the concentration of electrons in the conduction band of silicon (Afanas’ev and Stesmans, 1997a, b). Such behaviour indicates the source of electrons to be decoupled from Si and, therefore, is likely associated with some near-interfacial defects in the oxide optically excited to a state from which electrons tunnel into the conduction band of SiO2 . This suggestion is supported by observation of similar photon-stimulated tunnelling transitions at the interfaces of SiO2 with other semiconductors (6H and 4H polytypes of SiC) (Afanas’ev and Stesmans, 1997b). Obviously, in the case of defect excitation inside the insulator no additional charge transfer across the interface occurs and no image potential appears. Therefore, there is no experimental ground yet to deny the classical image-force picture in favour of more sophisticated quantum-mechanical description.

2.2.4 Electron scattering in the image-force potential well One of the most important differences between the photoemission into vacuum and the IPE consists in charge carrier scattering in the collector after it escapes the emitter electrode. This scattering may occur through elastic (only momentum re-distribution) and/or inelastic (momentum re-distribution and the energy loss) mechanisms, which have considerable impact on the interface barrier transparency. As one might notice from Fig. 2.2.2, electron scattering in the space region between the emitter surface and the maximum of the image-force barrier (0 < x < xm ) might prevent its escape even when the initial, prior to the scattering, momentum along the normal to the surface of emitter was sufficient to surmount the barrier (Berglund and Powell, 1971; Silver and Smejtek, 1972). This process can be taken into account by introducing the additional barrier transparency factor T associated with the probability of scattering. In several independent works it was found that attenuation of electron flux passing over the image-force barrier by scattering can be described as (Silver et al., 1967; Onn and Silver, 1969; 1971; Berglund and Powell, 1971; Powell and Beairsto, 1973):

xm (F) T = exp − ,

(2.2.10)

40


where the field-dependent distance between the surface of emitter and the geometric plane of the imageforce barrier maximum xm is given by Eq. (2.2.9), and represents the mean free path of electron, assumed to be energy independent. The exact physical mechanism of electron flux attenuation is likely to depend on the collector material investigated, but it was argued that the exponential form of Eq. (2.2.10) can only be accounted for by considering electron energy losses (Silver and Smejtek, 1972), quite in contrast to the original model of Berglund and Powell (1971) in which only the momentum re-distribution was taken into account. In this sense the parameter appears to represent the mean electron thermalization length rather than the mean free path with respect to the electron–phonon scattering. In the electron energy range close to the IPE spectral threshold one may neglect the electron–electron scattering in the collector because its kinetic energy is smaller than the collector bandgap width. In this case the major contribution to the energy losses will be provided by high-energy phonons. Validity of this assumption is proven at least for SiO2 in which the onsets of longitudal optical (LO) phonon scattering were directly revealed by the IPE experiments (Afanas’ev, 1991; Adamchuk and Afanas’ev, 1992a). This mechanism of scattering leads to considerable energy dependence of in the low-energy range because electrons with kinetic energy lower than the phonon energy have much longer thermalization length and, therefore, a higher chance to surmount the barrier. In addition to phonons, charges present in the barrier region of the collector may also contribute to elastic scattering of electrons escaping the emitter. In the case of energy-independent electron mean free path, the effect of elastic scattering can be analysed using model developed by Young and Bradbury (1933) to describe electron current flow in a gas. In this model the transparency of the barrier layer of total thickness d is given as ⎛ x ⎞

d

w(x)dx w(z)dz ⎠, T =1− exp ⎝ (2.2.11) cos θ cos θ 0

0

where w(x) is the probability for an electron with energy (hν − 0 ) above the barrier to return to emitter given for the regions x < xm and x > xm by following expressions: ⎡ w(x) =

and

1⎢ ⎣1 − 2

⎡ w(x) =

1⎢ ⎣1 + 2

⎤ (F) − (x) ⎥ ⎦ (hν − 0 ) + (F) − (x)

for x > xm ,

⎤ (F) − (x) ⎥ ⎦, (hν − 0 ) + (F) − (x)

for x < xm ,

where (F) is the barrier height at electric field strength F and the electrostatic potential at point x. These are given by Eqs. (2.2.8) and (2.2.7), respectively. In Eq. (2.2.11), represents the electron mean free path and θ is the polar angle of scattering. This approximation yields the barrier transparency only weakly dependent on the applied electric field which is also consistent with results of electron diffusion analysis in the near-interface barrier region (Silver and Smejtek, 1972). Therefore, elastic scattering by itself cannot account for strong field dependences of the IPE yield often observed experimentally. Rather, one should now address the field and energy dependence of the scattering probability.


41

Interaction of an injected electron with a non-screened Coulomb potential centre in the near-interfacial layer of collector can be described using the Rutherford scattering approach and neglecting the electron– phonon scattering. The differential scattering cross-section can be integrated over the whole scattering solid angle with the integration limits restricted by half of the mean distance between the charges rm , leading to the classical expression for the integral scattering cross-section (Smith, 1959): 2 rm σc = 2πR ln 1 + 2 , R

2

(2.2.12)

with the effective scattering radius R given by

R=

Zq2 , 8πεi ε0 E

where Zq is the charge of the scattering centre and E is the kinetic energy of electron far enough from the Coulomb potential well. This expression is still to be corrected for the influence of external electric field of strength F because the scattering radius of the centre R will effectively decrease when the Coulomb potential Zq2 /4πεi ε0 r is replaced by Zq2 /4πεi ε0 r – qFx. The results of numerical simulations of this effect for electrons with energy close to thermal one indicate that this type of scattering inhibits carrier transport across the area with cross-section decreasing with electric field strength approximately as F −0.7 (Adamchuk and Afanas’ev, 1992a). Important feature of the scattering cross-section given by Eq. (2.2.12) is its rapid increase with decreasing electron energy E. Thus, in contrast to the case of electron–phonon scattering, the scattering by the Coulomb potential (in general, by any static potential) will lead to a decrease of the scattering rate with increasing kinetic energy of a carrier. From this comparison it is clear that by analysing the dependence of the scattering parameter on electron energy one may obtain information regarding dominant scattering mechanisms affecting the IPE. At the same time, an increase of in the range of low-electron energies (in order of the maximal phonon energy in the collector) may cause distortion of the IPE spectra curves in the immediate vicinity of the threshold energy. Therefore, this portion of the yield spectra cannot be used in the linear extrapolation when determining the spectral threshold value. The final comment concerning the carrier scattering effects in IPE is related to the fact that no reliable IPE observations can be made in the absence of the electric field of sufficient strength. As Eq. (2.2.10) indicates, the low field leads to low barrier transparency because xm becomes much larger than . Physically this would mean that the carrier will lose its energy before reaching the barrier top and then will return to the emitting electrode driven by the attractive image force. This effect has several consequences:

• The need to apply sufficient electric field to the collector makes difficult observation of IPE into narrow bandgap materials. • In the case of collector thickness d much larger than , the carriers of one sign will be emitted only from the electrode at which they encounter electric field of the appropriate orientation. • The double-interface injection is possible in sample structures with the collector layer sandwiched between two electrodes (cf. Fig. 1.3.1) if ≥ d, or, else, if the electric field attracting charge carrier if present at both interfaces because of built-in charge of the opposite sign.

42


2.2.5 Effects of fixed charge in the collector Charges of different origin may potentially be embedded into atomic network of a solid collector material giving rise to distortion of electrostatic potential encountered at the interface with emitter. Influence of charge on IPE characteristics may be described by modifying the interface barrier shape by additional component of electric field introduced to the second term in Eq. (2.2.6). As the starting approach one may assume that the charge is fixed in time and distributed uniformly in a plane parallel to the emitter– collector interface (Powell and Berglund, 1971; Brews, 1973a; DiMaria, 1976; Przewlocki, 1985). In other words, the discrete nature of the charge and its possible lateral non-uniformity are neglected. Under these assumptions the charge is characterized by the in-depth concentration profile ρ(x) and gives following contribution to the strength of electric field at a distance x from the surface of conducting emitter (Powell and Berglund, 1971): 1 F1 (x) = − ε0 εD d

d

1 (d − x)ρ(x)dx + ε0 εD

0

x ρ(x)dx,

(2.2.13)

0

where d is the thickness of the collector layer sandwiched between two conductors, and εD the static dielectric constant of the collector material. The barrier height at the interface in the presence of build-in charge can be then expressed as: q2 q = 0 − − 8πε0 εi xm ε0 εD

xm ρ(x)dx,

(2.2.14)

0

where the second term corresponds to the conventional image-force barrier lowering, and the third term stems from the charge distributed within the interface barrier region 0 < x < xm . The charge located outside of this region contributes to the electric field through Eq. (2.2.13) causing variation of xm . The contribution of charges located outside the barrier region to the strength of electric field at the surface of d emitter can be expressed in even more simple way by using the total charge density Q ≡ 0 ρ(x)dx and d the centroid x ≡ Q1 0 xρ(x)dx of its in-depth distribution in the collector layer (DiMaria, 1976): F1 =

Q d−x . ε0 εD d

(2.2.15)

In the case d >> xm one may simply correct the externally applied electric field by using the above expression. The centroid approximation is basically equivalent to the replacement of the real charge distribution across the thickness of a collector by a single charged plane with total charge Q at a distance x from the surface of emitter, as illustrated by schematic band diagram of metal–collector–metal structure shown in Fig. 2.2.3. Though this representation looks perfectly justified from the electrostatic point of view, the important limitation of the centriod approximation, namely the absence of charges of opposite sign, must be kept in mind. The latter essentially requires from the collector to be free of any substantial mobile charge carrier density, i.e., to be of a dielectric nature. The hypothesis regarding the laterally uniform charge distribution used in the presented analysis may be considered realistic if the mean distance between the individual charged centres is small as compared to the distance from the charged area to the emitter surface. Powell and Berglund (1971) explicitly indicated the problem associated with discrete nature of charges located close to the emitter/collector interface. Indeed, with the characteristic probing depth in the IPE experiment in the order of λe or xm , both in the

Internal versus External Photoemission Q0

Q>0

43

Q xc . The highest of two barriers will determine the energy threshold for electron photoemission in vicinity of the charged centre. Similarly to the ideal image-force barrier height, the barriers 1 and 2 are field-dependent which is illustrated in Fig. 2.2.5 by plotting their values using the Schottky co-ordinates. The sensitivity of 4.4 4.2

Barrier height (eV)

4.0

Schottky model

3.8 3.6 1

3.4 3.2 2

3.0

2

1

2.8 2.6 0.0

0.5

1.0

1.5

2.0

(Field)1/2 (MV/cm)1/2

Fig. 2.2.5 The Schottky plot of the minimal barriers 1 and 2 in Si/SiO2 structure caused by a Coulomb attractive centre located at xc = 1 nm (solid lines) and xc = 3 nm (dashed lines) above the silicon emitter surface as compared to the ideal image-force model (the Schottky model, dotted line).


45

these field dependences to the location of the charged centre potentially allows one to evaluate the mean surface-centre distance. This can be done by comparing the experimentally observed field dependence of the lowest spectral threshold observed in the IPE experiment to the calculated barrier dependences of 1 and 2 type. There is a special case in which an analytical result using Eq. (2.2.16) can be obtained: for a centre located exactly in the geometrical plane of the emitter/collector interface xc = 0 (Afanas’ev and Stesmans, 1999a), which leads to the image-force like potential with a reduced effective image-force constant εeff = εi /(1 + 2εi /εD ). In this case the presence of interface charge may even lead to the effective imageforce constant values less than one which can hardly be interpreted if using the conventional image-force barrier model. It must be added in conclusion that the presented picture refers to the case of attractive potential, which enables observation of IPE in immediate vicinity of the charged centre. Would the potential be repulsive, it will hinder the photoemission of carriers in its vicinity by scattering them. The lowest IPE spectral threshold in this case will correspond to the charge-free collector regions and, therefore, will bear little information on the charge location. 2.2.6 Collector transport effects While in the case of photoemission into vacuum every electron which left the emitter is collected thus generating the photocurrent, in the case of IPE there is a finite probability that electron will be trapped along its path across the collector towards the anode by some defect or impurity. The trapping results in reduction of the current flowing in the external measurement circuit by a factor of xt /d, where xt is the emitter-trap distance and d is the collector thickness (Powell, 1977; DeVisschere, 1990). In order to analyse the trapping quantitatively, let us consider the case of deep traps in the collector, i.e., neglect the possibility of carrier emission after trapping. These traps can be characterized by a field-dependent capture cross-section σ(F) and by the in-depth distribution N(x) with the origin of x-axis placed to the plane of the injection emitter/collector interface as shown in Fig. 2.2.6. Further, we assume that the trapping of the photoinjected carriers is a sole mechanism of the collector charging, and the trap density is high enough to ensure that N(x) is not changing significantly during

N(x)

x

0 Emitter

d Collector

Metal

Fig. 2.2.6 Idealized scheme of an injection experiment in the case of collector containing trap with in-depth distribution N(x) and characterized by the centroid of trap distribution x.

46


the IPE experiment. The latter condition also means a low flux of the injected carriers to the traps which during the measurement time t does not affect the trap concentration in any substantial degree or influences significantly the strength of electric field F in the collector layer. Under these conditions the gradient of injected carrier flux can be written in simple form as (Adamchuk and Afanas’ev 1985; 1992a): ∂n(x) = −σ(F)N(x)n(x). (2.2.17) ∂x Using the fact that the carrier flux at the surface of emitter is entirely determined by the IPE quantum yield and by the photon flux, the value n(x = 0) may be considered as a known leading to solution of Eq. (2.2.17) ⎡ ⎤

x n(x) = n(x = 0) exp⎣−σ(F) N(x )dx ⎦. (2.2.18) 0

By using x = d one finds the portion of carriers passed through the layer: ⎤

d n(d)/n(x = 0) = exp⎣−σ(F) N(x )dx ⎦ = exp [−σ(F)N], ⎡

(2.2.19)

0

d where N = 0 N(x)dx is the total trap density in the collector layer. In its turn, the rate of carrier trapping in the collector layer of a thickness dx at a distance x from the emitter can be expressed using Eq. (2.2.17). The captured carriers will also contribute to the current measured in the external circuit with a weight factor of qx/d. Therefore, the total IPE current will be equal to the sum of contributions of the carriers passed the whole collector without being trapped and the displacement current generated by carriers immobilized in the collector (Adamchuk and Afanas’ev, 1992a,b):

d I = qn(d) + q

x n(x)N(x)σ(F)dx d

0

x = qn(x = 0) exp [−σ(F)N] + {1 − exp [−σ(F)]N} d

(2.2.20)

where x represents the centroid of trapped carriers distribution in the collector. Experimental methods of determination of the centroid will be discussed in more detail in Chapter 8. Equation (2.2.20) importantly indicates that the correct measurements of the current proportional to the IPE yield qn(x = 0) are still possible if the assumptions of the quasi-stationary photo-injection are valid. In fact, even in the case σN >> 1 the second term in Eq. (2.2.20) allows one to determine the spectral dependence of the IPE yield on the basis of displacement current observation which the true IPE current scaled down by a factor x¯ /d. Moreover, by using the charging rate measurements (the photocharging technique) one may also obtain the same information as from the current detection. All these options will be considered in more detail in the next chapter when discussing on the experimental realization of the IPE spectroscopy. The most important factors which might lead to distortion of the IPE characteristics due to trapping in the collector is the field dependence of the capture cross-section and the injection-induced variation of electric field at the surface of emitter. The latter effect can easily be minimized by performing measurements at relatively high strength of the externally applied electric field which would make the


47

1.0 0.1 0.3 1 0.8

Transparency

3

0.6

10

0.4 30

Trap density (1012 cm2):

0.2

100 0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Field (MV/cm)

Fig. 2.2.7 Transparency of the trap-containing collector layer as a function of electric field for the distribution of Coulomb attractive traps located close to the surface of emitter (x/d 1, the shape of the IPE spectral curves will remain unchanged and allows correct determination of the spectral threshold.

CHAPTER 3

Model Description and Experimental Realization of IPE

3.1 The Quantum Yield The photoemission of charge carriers requires quantification, which would allow one to relate the theoretical models discussed in the previous chapter to experimentally measurable quantities like electric current or charge. The physically most simple way to quantify the number of photoemitted carriers is to introduce the quantum yield of photoemission, which is defined as an average number of electrons or other carriers emitted per one photon absorbed in the emitter (see, e.g., Spitzer et al., 1962). The quantum yield defined in this way is often referred to as the internal quantum yield (or the internal quantum efficiency) because its value is determined entirely by the processes inside the analysed sample and at its surface. The internal yield Yint can be expressed by integrating the energy distribution of the excited carriers at the surface of emitter N*(E, hν) and the barrier transmission probability P(E): ∞ Yint (hν) =

N ∗ (E, hν)P(E)dE.

(3.1.1a)

0

By assuming that only the electrons optically excited to the energy states above the interface barrier height have a non-zero chance to surmount the barrier, the expression can be simplified by placing the origin of the energy scale to the uppermost occupied state in the emitter as shown in Fig. 3.1.1. The maximal energy of photoelectron in the distribution N ∗ (E, hν) becomes equal to hν leading to the integral (Powell, 1970): hν Yint (hν) =

N ∗ (E, hν)P(E)dE.

(3.1.1b)

The presence of the energy-dependent escape probability P(E) in Eqs (3.1.1a) and (3.1.1b) represents a significant factor which makes the quantum yield behaviour different from that of the optical absorption coefficient α(hν). The latter includes only the convolution of the initial and final density of states (DOS) weighted by the appropriate matrix element(s) of transition(s). For this reason attempts to analyse the internal photoemission (IPE) yield spectra in the same way as it is done in the case of optical absorption, 48

49

Energy


N*(E hn)

hn

Emitter

Ni(E)

0

Collector

Valence band

Density of states

Distance

Fig. 3.1.1 Schematic energy band diagram illustrating the internal photoemission (IPE) of electrons from the valence band of a semiconductor. Zero of energy scale is placed to the top of the valence band. In the classical barrier transparency approximation only electrons in the energy interval (, hν) are capable of escaping the emitter.

i.e., independently on the absolute energy of the final state (Winer and Ley, 1987; Ristein et al., 1995), would lead to an oversimplified picture unsuitable for reliable extraction of the electron state density. From the point of view of physics, the use of the internal quantum yield is perfectly justified, but faces a difficulty in experimental determination of the photon flux absorbed in the emitter. To resolve this problem one might consider measuring the flux of photons incident on the sample nph (hν) as well as of those reflected from its surface nph (hν)R(hν), where R(hν) is the optical reflection coefficient. Thus, the absorbed photon flux can be calculated as the difference between two measured values equal to nph (hν)[1 − R(hν)]. However, the need to measure two photon fluxes simultaneously adds to the complexity of the experiment, while in certain geometries of the photoemission experiment, e.g., when using the normal to the surface of emitter light incidence, it becomes hardly possible. One might attempt to calculate the absorbed flux from the incident one by using tabulated values of R(hν), but the latter is known to be sensitive to the samples’ surface structure and roughness leading to additional complications. The experimentally most simple way of the yield determination consists in normalization of the photoemission current to the incident photon flux nph (hν), which is called the external quantum yield (or the external quantum efficiency) because it may contain contributions of the sample or even equipment parts located outside the emitter. The relationship of the external yield to the internal one may be expressed as: Yext (hν) = Yint (hν)[1 − R(hν)].

(3.1.2)

In the case of electron photoemission into vacuum from a material with known optical reflectivity spectral distribution the internal yield can be found easily using Eq. (3.1.2). However, much more complicated situation may appear in the case of IPE because of optical interference in the emitter/collector/ambient structure and possible light absorption on its way towards the active surface zone of the emitter. Moreover,

50


in widely used experimental arrangement with a thin conducting (metal) layer over the collector shown in Fig. 1.3.1a the incident light enters an analogue of the Fabri–Perot interferometer resulting in deep modulation of the light intensity at the surface of emitter (Goodman, 1966a; Powell, 1969). Together with light absorption, the interference makes necessary a sophisticated simulation of the in-depth distribution of the electromagnetic wave power (DiMaria and Arnett, 1977). This simulation requires sufficient knowledge of the optical constants of all the materials involved in the sample structure. In certain cases one still can use the known bulk parameters of the corresponding stoichiometric compounds, but in many material systems, e.g., in thin layers of complex composition, the optical constants themselves remain unknown. This would prompt the optical analysis on the same sample as that used in the IPE experiment by means, for instance, of spectroscopic ellipsometry adding to the overall complexity of the experiment. Thus, the determination of the internal quantum yield appears to be not so easy task in the IPE experiments as it was in the classical photoemission. For the above reasons the internal yield is rarely used in the IPE spectroscopy. Instead, the spectral curves of IPE are obtained by analysing the external quantum yield (or the external photoresponse) calculated as (DiMaria and Arnett, 1977): Y (hν) ≡

ne (hν) I(hν) × hν = , nph (hν) S(hν)T (hν)A

(3.1.3)

where ne (hν) is the flux of emitted charge carriers which give rise to the photocurrent I(hν), S(hν) is the incident light power corresponding to the incident photon flux nph (hν), A is the sample surface area, and T (hν) is the transparency of the optical input of the sample. In the case of a thin-film collector (i.e., with the thickness L (3.2.3) 2 E + E0 2 E + E0 1/2 E + E0 + + E0 P(E, ) = 0 if E ≤ , where E0 represents the energy of the bottom of the emitter conduction band in the free-electron model which accounts for the real value of the group velocity of the excited electrons. In the Fowler model (cf. Fig. 2.1.4) this energy is equal to χm if measured with respect to the vacuum level. With the present choice of zero energy at the upper edge of the occupied electron states in the emitter E0 corresponds to the energy width of the filled conduction band in a metal, i.e., E0 = χm − . In a semiconductor emitter E0 corresponds to an effective energy describing the group velocity of an electron excited to a state in the conduction band well above its bottom. Importantly, typical values of E0 are close to 10 eV (Powell, 1970; Williams, 1970) which makes the denominator in Eq. (3.2.3) a much weaker function of the electron energy E than the numerator (E − ), particularly when considering the near-threshold energy range, i.e., E ≈ . Therefore, the largest relative variation of the barrier transparency with increasing

52


electron energy will be proportional to (E − ) and can be approximated by the linear function: P(E, ) ≈ C(E − ),

(3.2.4)

where C is a constant. Using this expression for P(E) in Eq. (3.1.1b) together with N*(E, hν) = N*(E − hν) one obtains the following expression for the quantum yield (Powell, 1970): hν Y (hν − ) ≈ C

N ∗ (E − hν)(E − )dE = C

hν−

N ∗ (−y)(hν − − y)dy,

(3.2.5)

0

where the integration variable is changed to y = hν − E. In the case of a simple N*(E − hν) functional dependence the integral (3.2.5) can be taken analytically leading to the model dependences of the quantum yield which are summarized in Table 3.2.1 following the original result of Powell (1970). Though the presented quantum yield model uses large number of simplifying assumptions, in particular, by neglecting entirely the carrier momentum conservation requirement, it accounts very well for a large number of experimental observations (for review, see, e.g., Williams (1970) and Adamchuk and Afanas’ev (1992a)). Moreover, the predicted quantum yield behaviour appears to be in good agreement with results of more elaborate theoretical descriptions. For instance, the yield spectral dependence of electron IPE from the semiconductor valence band is predicted to follow Y ∝ (hν − )3 law, as indicated in Table 3.2.1. This result is based on the triangular shape of the N*(hν − E) distribution observed experimentally through the electron energy distribution curves of electron photoemission from a Si crystal into vacuum (see, e.g., Rowe and Ibach (1974)). The same cube spectral dependence is theoretically predicted in the case of indirect optical excitation in emitter by Ballantyne (cf. Table II in Ballantyne, 1972). Later, also in the case of optical excitation with relaxed k-conservations requirements, this result was affirmed by Chen, Jackson, and Wronski (cf. Eq. (21) in Chen et al., 1996). This wide agreement allows one to use the spectral dependences of the quantum yield listed in Table 3.2.1 to fit the IPE data and to determine the spectral threshold provided the energy distribution of excited charge carriers in the particular emitter material is known. The latter can be evaluated, for instance, from the vacuum photoemission experiments (for electrons only) or from the IPE spectra obtained from the same emitter in combination with different collector material (for both electron and hole IPE). Alternatively, one may use the exponent power p in Eq. (1.3.1) as independent fitting parameter together with the spectral threshold . This approach allows one to evaluate the unknown shape of the excited carrier energy distribution in emitter which, in its turn, may be considered as a close replica of the initial DOS (cf. Eq. (2.1.2)). There are two methods to determine p from the experimental Y (hν) datasets. First, Table 3.2.1 Functional form of quantum yield spectral dependence for various energy distributions of excited charge carriers at the surface of emitter (after Powell, 1970). N ∗ (−E)

Y (hν, )

Impulse Step Ramp

δ(E) θ(E) C•E

A(hν)(hν − ) A(hν)(hν − )2 A(hν)(hν − )3

Power Exponent

C•E q C•exp(E/kT )

A(hν)(hν − )q+2 A(hν)(kT )2 exp[(hν − )/kT ]

Emitter type IPE from a narrow band IPE from a metal IPE from a semiconductor valence band Thermally broadened DOS


53

one may plot the normalized integral of the quantum yield as a function of photon energy (Lange et al., 1981; 1982): 1 Y (hν)

hν

Y (hν )d(hν ) =

hν − , p+1

(3.2.6)

which linear fit allows determination of both p and . The problem with this kind of analysis is related to the necessity to choose some lowest integration limit prior to determination because of ‘spurious background photoemission currents, . . . which give rise to severe distortions due to the accumulative nature of the integration procedure’ (Lange et al., 1981; 1982). Second, one may also calculate numerically the derivative of natural logarithm of Y on photon energy which leads to: hν − ∂[ ln Y (hν)] −1 , (3.2.7) = ∂(hν) p yielding the result similar to that of Lange et al. but free of somewhat arbitrary choice of the integration limit. The differential IPE analysis offers an additional advantage because it may also be used to isolate contributions to the IPE yield from the interface regions with different barrier heights (Okumura and Tu, 1983). It is worth of reminding here, however, that all the above results are obtained when assuming an ideal rectangular interface energy barrier and the DOS of the final electron states in the collector sufficiently high to ensure rapid saturation of the electron escape probability when pn becomes larger than pc in Eq. (3.2.2). Any deviation of the barrier shape from the ideal one caused by interface charges, dipoles, band edge shift, etc., would lead, in general, to additional energy dependence of barrier transparency as suggested, for instance, by the IPE results obtained at interfaces of metals with an electrolyte (Rotenberg and Gromova, 1986).

3.3 Quantum Yield as a Function of Electric Field As it is discussed in Chapter 2, there are several physical factors making the IPE quantum yield sensitive to the strength of electric field at the interface. If one would neglect the influence of the electric field penetration into the emitter, which is only significant in heavily doped semiconductors under depletion or inversion, three field-related factors are to be considered: (1) the field-induced barrier lowering (the Schottky effect); (2) the field-dependent scattering probability of charge carrier in the image-force barrier region; (3) the field-dependent transport of carriers in the collector. The influence of the first factor becomes obvious when considering the interface barrier in the framework of the image-force model as illustrated in Fig. 2.2.2. With increasing strength of electric field the top of the barrier shifts closer to the surface of emitter and its energy becomes lower according to Eq. (2.2.8). This effect can easily be incorporated into the quantum yield analysis by using in Eq. (3.2.5) and in Table 3.2.1 the field-dependent barrier height given by Eq. (2.2.8). The physical mechanism of the IPE enhancement by electric field-induced barrier lowering is illustrated in Fig. 3.3.1 showing the convolution of initial ramp-type energy distribution of excited electrons with the field-dependent barrier transparency P(E, F) ∝ (E − (F)) (Powell, 1970). The field-induced barrier lowering not only allows the electrons

54


N*(E h)

Density of states

P(E, ) C(E ) 2

1

hn Energy

0

N*(E h)P(E )

Fig. 3.3.1 Convolution of the ramp-type energy distribution N ∗ (E − hν) with the Fowler barrier surmount probability for two values of the interface barrier height 1 and 2 .

with a lower energy enter the collector but, in addition, increases chance of more energetic electrons to surmount the barrier by decreasing the value of the critical momentum pc . The impact of electron–phonon scattering on the quantum yield can also be described using the imageforce potential well model. Assuming the energy-independent mean free path of the injected carriers in the collector , the IPE yield will be modulated by the field-dependent factor given by Eq. (2.2.10) which corresponds to the probability of passing the space interval [0, xm ] without interaction with a phonon. Incorporation of the field-induced barrier lowering and the electron–phonon scattering led us to a more general expression which can be used to analyse the IPE yield as a function of both photon energy and electric field (Powell, 1970):

xm (F) Y (hν, F) ≈ C(hν)[hν − 0 + (F)] exp − ,

p

(3.3.1)

where C(hν) includes the contributions of the optical effects in the emitter and in the experimental system if Y is measured as the external quantum yield. It is worth of adding here that expression similar to Eq. (3.3.1) can also be applied to analyse the field dependence of intrinsic photoconductivity in the collector (Adamchuk and Afanas’ev, 1992a) because this process has several common features with the IPE over the image-force barrier. The similarity of the image-force barrier and the Coulomb potential well was already noticed by Weinberg et al. (1979), and illustrated in Fig. 3.3.2. An electron attempting to escape from the attractive field of a hole in the valence band must overcome the barrier with top located at some distance xm from the point of electron-hole pair creation. The position of the barrier maximum can be easily calculated using zero electric field condition to be equal to: q xm (F) = , (3.3.2) 4πεi ε0 F


55

EC qFx xm

Distance

Fig. 3.3.2 Potential energy distribution in the case of intrinsic photogeneration of charge carriers in an insulator of semiconductor in a uniform externally applied electric field of strength F.

where the optical dielectric constant of the collector εi is to be used to account for dynamic character of the electron-hole pair dissociation. However, the photoconductivity has one significant difference from IPE: There is a negligibly low density of allowed electron states inside the bandgap of collector. Therefore, instead of continuous distribution of excited carriers in energy encountered in emitter during IPE, the photoconductivity provides all electrons already above the field-lowered barrier at xm because photoexcitation to states with energies lower than the conduction band edge is nearly impossible. The minimal energy of an electron at point xm in the absence of inelastic scattering will be in this case: (F) = 2Fxm (F) = q

qF , 4πεi ε0

(3.3.3)

which would allow all the electrons to escape in the ideal case of no scattering. Thus, no photocurrent increase caused by the ‘barrier-height lowering’ can be observed in the case of photoconductivity. In the presence of electron–phonon scattering the electrons which lost their excessive energy in the spatial region x < xm will be unable to dissociate from the hole thus forming an exciton followed by the geminate recombination. The probability of this event can be evaluated in the same way as it is done for electrons surmounting the image-force potential (Berglund and Powell, 1971) with functionally the same result given by Eq. (2.2.10). This leads to a simple expression for the field-dependent photoconductivity current (Adamchuk and Afanas’ev, 1992a):

xm (F) I(hν, F) ≈ I0 (hν) exp − ,

(3.3.4)

where I0 (hν) is determined by the optical properties of collector and the sample and xm (F) is given now by Eq. (3.3.2). This expression appears to fit quite well in the field-dependent photoconductivity of an insulator with low trap density, e.g., the thermally grown SiO2 on Si (Afanas’ev, 1991; Adamchuk and Afanas’ev, 1992a).

56


F

y q xc

Emitter

e lan ep c a erf Int Collector

Fig. 3.3.3 Scheme of the backscattering cross-section evaluation for a charged scatterer located at a distance xc above the surface of emitter.

While the influence of electron–phonon scattering still can be described in simple terms (assuming the energy-independent mean free path of electron), the scattering by a charged defect represents much more difficult case. This is caused by strong sensitivity of the scattering angle both to the kinetic energy of electron (cf. Eq. (2.2.12)) and to the position of the centre with respect to the interface plane. To illustrate the latter point one might consider a Coulomb centre with a charge q located in collector at distance xc above the emitter surface as shown in Fig. 3.3.3. The maximal kinetic energy of electron escaping in the direction along the normal to the interface plane can be evaluated as (hν − − qFx) in the presence of electric field of strength F, also oriented along the normal to the interface plane. This energy can now be compared to the energy of electron interaction with the Coulomb potential at a distance y in the plane parallel to the interface and placed at distance xc above it:

(hν − + qFx) x=xc =

q2 , 4πε0 εD y

(3.3.5)

where the static dielectric constant of the collector is used to describe the potential of the fixed charge scatterer. Very approximately, one may assume that all the electrons entering collector within the circle of radius y around the Coulomb centre will be backscattered towards emitter and, therefore, will be lost for the IPE process (both for the repulsive and attractive centre potentials). Accordingly, the cross-section of backscattering can be expressed as:

q2 σC = πy = π 4πε0 εD (E − + qFxC ) 2

2 .

(3.3.6)


57

This approximation is rather rude as it neglects several factors, in particular the distortion of the imageforce barrier at the interface (cf. Fig. 2.2.4 for the Coulomb attractive centre) and the mutual influence of the neighbouring charged scatterers. Nevertheless, Eq. (3.3.6) importantly indicates a strong dependence of the backscattering cross-section on the electron energy, electric field strength, and the location of the Coulomb potential. The cross-section remains to be integrated over the energy distribution of electrons leaving the emitter, and over the in-depth distribution of the charged centres, which cannot be done analytically because of considerable non-linearity. One might expect the energy dependence to be close to σC ∝ (E − )−2 , in agreement with the standard expression of type Eq. (2.2.12) and the field dependence of σC ∝ (FxC )−2 for the near-threshold energy range (small E − ). As in most of the practical cases the in-depth centre distribution function is unknown, reliable quantification of the backscattering probability becomes extremely difficult. The unknown in-depth distribution of traps makes also difficult quantification of the field-dependent transport of charge carriers in collector. As can be seen from Eq. (2.2.20), the current modulation by carrier trapping is proportional to the centroid of trap distribution in the collector. Further complication can be expected in the high trapping probability case, i.e., if σ(F)N ≥ 1. The results obtained for the idealized model of interfacial trapping as shown in Fig. 2.2.7 indicate the large density of charged traps introduces strong (superlinear) dependence of the collector transparency on electric field. Obviously, in this case analysis of the field-dependent IPE current can deliver little if any reliable information regarding the interface barrier. As discussed in this section, simultaneous contribution of several effects in the IPE yield dependence on electric field makes extraction of physical information from these curves much less reliable as compared to the analysis of the spectral curves. As a result, the field dependences of IPE can be used to determine interface barrier height (Powell, 1970) in only few cases of nearly ideal interfaces with negligible density of interface charges and low collector trapping probability. The situation may be somewhat easier would the potentials of imperfections be screened by a high density of electrons in the nearby metal electrode or ions in the electrolyte. However, the barrier in this case is unlikely to remain the ideal one. Dipole contributions may have a profound effect on the barrier leading to quite different field dependences. For instance, in contact with electrolytes the variation of electrode potential appears to be equivalent to the photon energy variation (cf. Eqs. (1.7.1) and (1.7.2)) because of complete screening of electric field inside the narrow polarization layer. 3.4 Conditions of IPE Observation The experimental realization of IPE spectroscopy requires reliable determination of the quantum yield which depends on our ability to separate the optically stimulated electron transitions at the interface from the electron injection processes of different origin. When considering detection by using electrical measurements, the IPE must be the rate-limiting injection process otherwise the measured current will be determined by other factor(s) and becomes insensitive to the photoinjection rate. In this section we will analyse the requirements to the interface barrier and the collector properties ensuring IPE detection as well as the artefacts caused by the light-induced sample heating and re-distribution of electric field in the semiconductor heterostructures.

3.4.1 Injection-limited versus transport-limited current As already discussed, inelastic scattering of a charge carrier injected into collector leads it to thermalization within few nanometres above the surface of emitter (Berglund and Powell, 1971; Neff et al., 1980).

58


Therefore, the carrier escape from the barrier region requires the presence of a non-zero attractive electric field at the interface to overcompensate the action of the attractive image potential driving carriers back to the emitter. Would the field be absent or be repulsive in the collector layer with a thickness exceeding the mean thermalization length , the IPE becomes impossible. This situation requires analysis of an influence of the space charge of the injected carriers, which obviously create some repulsive field, on the injection rate at the interface. If this influence is considerable, the current flow in the emitter–collector system will be determined by the transport properties of the collector rather by the rate of (photo)injection at the studied interface. On the basis of this kind of arguments Williams indicated that the condition to observe IPE is the presence of a blocking contact at the emitter–collector interface which ensures that the carrier supply rate remains much lower than the current carrying capability of the collector (Williams, 1970). In the opposite case (the Ohmic contact) the current is limited by the flow of carriers across the collector while the interface can always supply more carriers than the collector material can carry under given applied field. The necessary but not sufficient condition to have a blocking contact at the interface is >> kT (Williams, 1970). Next, one must ensure that the injected carriers drift away at least as fast as they arrive to the interface from the emitter side. Thus, in the most simple case of a metal-semiconductor contact (Williams, 1970), for the carrier concentration n, assumed to be equal at both sides of the interface, and their thermal velocity vth in the conduction band, one must equilibrate the current of electrons from the side of the metal emitter qnvth /4 by the current on the semiconductor side of the interface qnμF, leading to the strength of electric field needed to saturate the current: Fsat =

vth , 4μ

(3.4.1)

where μ is the drift mobility of carriers in the collector. In typical crystalline semiconductors the mobility is high and leads to the saturation field in the range of 0.01–0.1 MV/cm (Williams, 1970). Thus, in the Schottky contacts the impurity concentration above 1014 cm−3 will be sufficient to ensure the injectionlimited current. However, the situation may become entirely different in the case of insulating collector in which the field must be applied externally. Moreover, in the presence of deep traps the mobility μ in Eq. (3.4.1) must be replaced by the effective mobility μeff = θμ, where θ < 1 is the average fraction of charge carriers remaining in the transport band of the collector (Lampert and Mark, 1970). In this case one may find the critical value of electric field corresponding to transition to the space charge limited, i.e., insensitive to the rate of injection at the interface, current mode. This can be done by using requirement that the charge of carriers trapped in the collector with a volume concentration Ntrapped (cf. Fig. 2.2.6) by uniformly distributed traps would screen the externally applied field of strength F completely at the surface of emitter (Afanas’ev and Adamchuk, 1994): qNtrapped = 2Fε0 εD ,

(3.4.2)

which, in turn, can be used to calculate the steady-state current density under assumption that every trapped carrier is emitted back to the transport band after an average time τ: The mean path of the carrier across the collector of thickness d will be approximately equal to d(vth /μF), which corresponds to the average number of trapping events (vth /μF)σN, where N is the total trap density across the thickness of the collector material per unit area (cf. Eq. (2.2.19)). Therefore, the average transport time for Ntrapped carriers uniformly distributed across the collector thickness will be in the order of ttransport =

1 vth τ σN, 2 μF


59

resulting in the current density equal to: j=

qNtrapped 4F 2 με0 εD 2Fε0 εD . = = 1 vth τvth σN ttransport 2 τ μF σN

(3.4.3)

Thus, for a given current density j, the critical field strength at which the trapped carriers are capable of screening emitter entirely will be equal to: jvth σNτ . 4με0 εD

Fc =

(3.4.4)

Therefore, to keep the current injected at the emitter–collector interface the sole factor determining the current measured across the whole sample, the average field in the collector must be kept well above the indicated Fc value. For a typical amorphous insulator values vth = 106 cm/s, σ = 10−15 cm2 , N = 1016 cm−2 , τ = 10−2 s, μ = 1 cm2 /Vs, εD = 3.9, to keep current of 1 nA the critical field can be calculated to be equal to approximately 104 V/cm. Would the trap density be higher or traps be deeper leading to a longer de-trapping time τ, the critical field becomes higher which might lead to problems associated with dielectric breakdown of the collector and leakage currents. Therefore, the requirements to the collector suitable for IPE current detection may be formulated in most simple terms as follows:

• to have low trapping probability of injected charge carriers; • to be of a small thickness; • the present traps must have a short occupancy time, i.e., they must be shallow at the temperature of the measurements.

3.4.2 Thermoionic emission versus photoemission In the case of relatively low interface barrier height (less than 1 eV) often encountered in Schottky contacts or in semiconductor heterostructures, the photoemission is always observed against a background of thermoionic emission of carriers from the tail of their equilibrium energy distribution (Williams, 1970). In metal-semiconductor contacts the current of thermoionic emission is well described by the Richardson equation for thermoionic emission of electrons into vacuum:

jth = AT exp − kT 2

,

(3.4.5)

where A is a constant and T is the emitter temperature. During illumination not only the IPE related to optical excitation of carriers in emitter is occurring but, at the same time, the sample is heated due to the light absorption. The carriers injected into the collector by IPE or from the thermal distribution in the emitter as illustrated in Fig. 3.4.1 are indistinguishable and both will contribute to the photocurrent measured as a difference between current flowing across the sample under illumination and the current observed in darkness. Two components of the photocurrent may be compared by first differentiating

60


hn EFkT EF

Emitter

Collector

Fig. 3.4.1 Injection at a metal-semiconductor contact of electrons from the optically and thermally excited states.

Eq. (3.4.5) (Williams, 1970):

2 jth ∂jth exp − = AT 2 + = 2 + . ∂T T kT 2 kT T kT

(3.4.6)

If the photon flux reaching the metal emitter is 1015 photons/cm2 s then, since the quantum yield of IPE is usually in the range 10−3 electron/photon (see, e.g., Schmidt et al., 1996; 1997), the expected IPE current will be in the order of 10−7 A/cm2 . The small increase of the temperature of the sample, say 1◦ C at room temperature, will lead to the increase of jth by 10−11 A/cm2 if = 1 eV is taken (Williams, 1970). This allows reliable detection of the IPE current. However, would one take = 0.41 eV and jth = 1 A/cm2 , the increase of temperature by as little as 10−4◦ C leads to the increase of jth by 0.6 × 10−5 A/cm2 making the IPE current a negligible contribution to the total photocurrent. Thus, there will be no way to distinguish the IPE signal on the background of the light-induced thermoionic current unless additional experiments are conducted, e.g., analysis of the current kinetics or the spectral response curves. According to Williams, for /kT > 40 the photoemission can easily be distinguished from the thermoionic emission effects, while for /kT < 20 this becomes problematic (Williams, 1970). 3.4.3 Photocurrents related to light-induced redistribution of electric field There is another physical mechanism leading to generation of photocurrent unrelated to IPE but interfering with it. The origin of this contribution is clarified in Fig. 3.4.2 showing the energy band diagram of semiconductor–insulator–conductor sample biased by a positive voltage which turns the p-type semiconductor surface to inversion (Sze, 1981). Panel (a) corresponds to the band diagram in darkness, with the applied bias voltage divided between the space charge layer of semiconductor and the potential drop on the insulator. Panel (b) shows evolution of the band diagram, under the same voltage applied, when the sample is illuminated by a high intensity light with photon energy exceeding the semiconductor bandgap width, i.e., hν > Eg (sc). Under illumination the band bending in semiconductor decreases (the photovoltage effect) because of high density of electrons and holes photo-generated across the space charge layer. Accordingly, the externally applied voltage is re-distributed leading to an increase of the potential drop on the insulator. Would the insulator be a non-ideal one, with some level of leakage current caused


(a)

61

(b)

Fig. 3.4.2 Energy band diagram of a semiconductor–insulator–conductor structure in darkness (a) and under intense illumination (b) illustrating the light-induced re-distribution of electric field: The smaller band bending in semiconductor electrode results, for the same voltage applied to the sample, in a larger voltage drop across the insulator leading to the corresponding enhancement of the leakage current which is measured as a photocurrent.

by, for instance, trap-assisted tunnelling, the increase of the voltage applied to this layer will lead to an enhancement of the illumination-induced leakage current which would add to the IPE current aimed to be detected. The same is true if the insulating layer is thin enough to allow direct tunnelling of electron from the conduction band of semiconductor to the anode. Taking into account that the quantum yield of photogeneration at hν > Eg (sc) may approach 100%, this kind of photocurrent significantly reduces chances to observe the ‘true IPE’. In general, the measurements of IPE current in samples with large band bending in semiconductor and non-zero dark current are to be avoided. The experimental practice suggests that even in the absence of measurable leakage current across the insulating layer, the IPE current detection in samples with semiconductor electrode biased to depletion or inversion leads to an enhanced noise. The latter is caused by time-dependent variation of the semiconductor band bending due to instability of the light source intensity. Variation of the band bending leads to time-dependent re-charging current in the external circuit adding to the real IPE photocurrent signal. The remedy in this case may be illumination of the sample with additional stable source of low-energy photons (but still with hν > Eg (sc)) to make the variations of the semiconductor band bending induced by the primary light beam negligible. An example of such experimental arrangement is shown in Fig. 3.4.3 intended to study IPE and photoconductivity in the silicon–insulator–metal structures with wide bandgap oxide insulator. The use of He–Ne laser emitting at 632 nm wavelength as the secondary beam allows one to saturate the photoresponse of Si surface in depletion. Obviously, one may use the difference in the spectral response to distinguish between the photogeneration in semiconductor electrode and the IPE process, the first having the spectral threshold equal to Eg (sc). In this case the IPE current is to be detected on the background of the signal stemming to the light-induced leakage current enhancement. The potential danger of this approach consists in spectral distribution of the non-IPE current reflecting not only the variations in the semiconductor absorption and reflection coefficients but, also, the variations in the surface recombination rate caused by different in-depth

62


Photodetector He–Ne laser, 632 nm Photocurrent Sample Light source

Monochromator Beam splitter

Fig. 3.4.3 Optical scheme of a two-beam experimental IPE setup used to suppress the band bending effects in a semiconductor electrode of the sample.

photogeneration profile at different photon energies. In addition, the illumination-induced band bending is not a linear function of the incident light intensity, which might cause additional dependence of the effect on the photon energy because of spectral distribution of the light source used. 3.5 Experimental Approaches to IPE 3.5.1 IPE sample design In the above discussion the most frequently used configurations of IPE experiments are already mentioned. Basically, they may be divided into three groups which will be discussed below in some more detail: (1) the thin-collector configuration; (2) the thick collector structure; (3) the electrolyte collector. The thin-collector sample represents a capacitor in which a (semi)-insulating collector layer of thickness ranging from nanometres to microns is sandwiched between the emitter and the opposite (field) electrodes. The latter is used to apply the electric filed of desirable strength to the collector by biasing the sample structure with corresponding voltage (cf. Fig. 1.3.1a). This configuration is the one most used in practice because it allows great flexibility in variation of electric field, including its orientation, and enables use of collector materials with considerable trap density which, however, has only a limited direct impact on measurements because the layer involved in the experiment is thin. The most significant disadvantage of this arrangement is the high dielectric quality of the collector layer needed to guarantee a sufficiently low background leakage current to allow the IPE current detection. Only insulators of sufficient purity with low density of imperfections can be used as collector media which strongly limits the range of IPE applications. Next, in this configuration both the emitter and the field electrode are exposed to light at the same time which may potentially lead to simultaneous photoinjection of charge carriers of opposite sign at opposite interfaces of the collector layer, as it is illustrated in Fig. 3.5.1. The contributions of electron and hole IPE to the measured photocurrent may potentially be separated by using measurements of the sign of charge trapped in the collector (Adamchuk and Afanas’ev, 1992a) or, else, by applying the metal electrodes with different work function to observe (un)correlation between the IPE yield spectra and the Fermi energy of the particular electrode (DiMaria and Arnett, 1975; 1977). In any event, additional measurements appear to be necessary. Next, in the


63

Collector IPE IPE PC

PC

Field electrode

Emitter

IPE IPE

(a)

(b)

Fig. 3.5.1 Photon–excited electron transitions in emitter/collector/field electrode sandwich structure with positive (a) and negative (b) voltage bias applied to the field electrode. The transitions related to the internal photoemission (IPE) and oxide photo-conductivity (PC) are indicated.

case of a collector thickness comparable to the mean thermalization length of a carrier , the ballistic injection of carriers of the same sign but in opposite direction is also possible, which complicates the analysis of IPE spectra unless the spectral thresholds of IPE at two interfaces of the collector are strongly different. In practice this means that collectors which are less than 3–4 nm in thickness are unsuitable for IPE analysis in the sandwich structure (Dressendorfer and Barker, 1980). Next sort of problems in sandwich capacitors concerns uncertainty in electric field strength because the work function difference between the emitter and the field electrode adds to the externally applied voltage. Due to formation of charged (polarized) layers at many interfaces, the tabulated vacuum work function values cannot be used to estimate this difference (see, e.g., Afanas’ev et al., 2002a; Afanas’ev and Stesmans, 2004a) causing difficulties when analysing the field-induced barrier lowering in the framework of the image-force model. One may use the current zero-point on the IPE current–voltage curve to determine the emitter-field electrode work function difference in situ (cf. Fig. 24 in Adamchuk and Afanas’ev, 1992a), but this method gives meaningful results only in the laterally uniform capacitors with a charge-free collector layer. Finally, the thin-film sandwich samples configuration often results in a high capacitance (in excess of 10−6 F/cm2 ), which limits application of the AC current IPE detection techniques because of a high input impedance of the current measurement circuit. As a result the conventional AC measurement scheme with a chopped light beam appears to be limited to low-frequency range, e.g., 13 Hz (DiMaria, 1974), and offers little advantage over the DC current measurements with a long integration time (Dressendorfer and Barker, 1980). In both IPE current measurement modes the issue of leakage current appears to be critical. In the thick collector samples configuration the electric field at the interface with emitter is produced by the charge of ionized impurities (cf. Fig. 1.1.1c), so this kind of samples are mostly semiconductor heterojunctions and Schottky diodes (Williams, 1970). The strength of electric field can be varied in some range by changing the collector doping level, but the reversal of the field in the same sample becomes impossible. The charge carriers leaving the emitter pass through the high-field region and then diffuse to the opposite electrode which can be placed at any position in the sample ensuring an Ohmic contact. This flexibility allows illumination of the interface through the backside of the semiconductor substrate in the range of its optical transparency. The latter is particularly important when using a pulsed laser excitation because the free-electron light absorption makes metals intransparent for light pulses of high power. The problems with the thick collector samples are usually associated with need to suppress the background current caused by thermal generation inside the interface field region which can be achieved by lowering

64


the temperature of the measurements. Also, the capacitance of such semiconductor barrier structure becomes high with increasing dopant concentration. Finally, the spectral range of the measurements is generally limited by the optical transparency of the substrate material making it difficult to apply to a narrow-band collector materials. In the latter case illumination through a semitransparent metal emitter might be an option. The electrolyte collector may be considered as a sort of the thick collector sample but with a very thin ( 2 correspond to the final state spatially located in the SiO2 collector in which case no image-force is acting. Therefore, these states can be associated with some imperfections at the interface of SiC with SiO2 or inside the oxide. As no measurable decay of the photocurrent is observed after prolonged illumination with hν > 2 , it was concluded that these electron states can communicate electronically with SiC substrate by tunnelling, which limits their location to a tunnelling distance in SiO2 from the surface of emitter, i.e., to few nanometres. The origin of these states can be traced down to clusters of carbon created during oxidation of SiC because of incomplete removal of carbon in the form of volatile oxide species (Afanas’ev et al., 1997a). The latter conclusion is based on the similarity observed between the trap-related component of the SiC/SiO2 IPE spectra and the IPE observed from thin a-C:H layers deposited onto SiO2 (Afanas’ev et al., 1996a, b; 1997a). The example of the electron IPE spectra from the a-C:H into SiO2 is shown in Fig. 4.1.5 for the carbon films of three compositions characterized by different optical bandgap width. The graphitic carbon appears to give spectral thresholds of IPE at around 3 eV, while sp2 -bonded carbon clusters of smaller size give the zero-filed threshold at around 4.5 eV, i.e., close to the value observed as ¯ the threshold 2 in SiC/SiO2 structures. In turn, on the C-rich interfaces formed by oxidation of (000 1) faces of hexagonal SiC polytypes the IPE spectra appear to resemble those of the IPE from graphitic carbon (Afanas’ev et al., 1996a; 1997a). This example of IPE study indicates the importance of the field-dependent barrier analysis in identification of electron transitions contributing to the photocurrent.

12 10 8 6

a-C:H SiO2

4 2 0 3

4 5 Photon energy (eV)

6

Fig. 4.1.5 Electron IPE yield as a function of photon energy for the as-deposited a-C:H layers of different bandgap, 3.0 (), 1.74 (), and 0.70 () eV, measured at the strength of electric field in SiO2 collector layer of 4 MV/cm. The scheme of the observed electron transitions is shown in the insert.

72


4.1.2 The Schottky plot analysis The field-dependent IPE threshold measurements can also be used to reveal the character of the interface barrier perturbation would it deviate from the ideal image-force behaviour. For instance, it is found that incorporation of protons or Li+ ions to the Si/SiO2 interface by annealing at an elevated temperature results in formation of a positive charge (Afanas’ev and Stesmans, 1998a, b; 1999a). This charge causes significant lowering of the potential barrier for electron IPE from the Si valence band into the conduction band of the oxide suggesting location of the ionic charges close to the interface. The latter is exemplified by the IPE yield spectral plots shown in Fig. 4.1.6 for the control (uncharged) sample ( ) and the samples containing the annealing-induced H+ or Li+ charges (, ). To obtain more information regarding character of the barrier perturbation the field-dependent spectral thresholds 0 (control samples) and Q (charged samples) were compared using the Schottky plot shown in the insert. In the case of positive charge present (, ) the lowest IPE threshold Q is seen to follow the Schottky law but with significantly increased slope. This effect can be understood in the framework of the model considering the imageforce barrier modification by the Coulomb potential of individual charge centre discussed in Section 2.2.5. In particular, the case of the charge location close to the surface of emitter appears to be in a good agreement with the observed barrier lowering values (Afanas’ev and Stesmans, 1999a). Numerical fit of the shown Schottky plots allows one to evaluate the average distance between the ion and the Si surface to be 0.2 ± 0.1 nm for both H+ and Li+ suggesting these ions to be attached to the first layer of oxygen atoms bonded to the Si crystal surface (the Si–O bond length is approximately 0.154 nm in SiO2 ). Interestingly, in the earlier studied case of Na+ ions diffused from the outer SiO2 surface through the oxide towards its interface with Si (DiStefano and Lewis, 1974) even larger barrier reduction is observed as also shown by triangles in the insert in Fig. 4.1.6. A weaker dependence of the spectral threshold on

•

106

0

104 103

(eV)

IPE yield (relative units)

4.0

105

3.5

Q

3.0 0 1 2 (F )1/2(MV/cm)1/2

102

Q 0

101 100 3.0

3.5

4.0

4.5

5.0

Photon energy (eV)

•

Fig. 4.1.6 Spectral curves of the IPE quantum yield from (100)Si into SiO2 in the control sample ( ), a H2 -annealed sample () exhibiting a positive charge density of 5 × 1012 q/cm2 , and in a Li-diffused sample () exhibiting a positive charge density of 4 × 1012 q/cm2 . All the curves are measured using an externally applied electric field of 2 MV/cm, with the metal biased positively. The arrows indicate the spectral thresholds of IPE at 2 MV/cm in the control (0 ) and charged (Q ) samples. The insert shows the Schottky plot of the IPE spectral thresholds in the control sample ( ), a H2 -annealed sample () exhibiting a positive charge density of 5 × 1012 q/cm2 , a Li-diffused samples exhibiting a positive charge density of 4 × 1012 q/cm2 () and ∼2 × 1013 q/cm2 (), and in a sample-containing 1.3 × 1015 Na+ /cm2 () according to (DiStefano and Lewis, 1974). The lines result from fitting of the ideal image-force barrier behaviour (0 ), and the barrier lowering in the presence of a Coulomb attractive centre in SiO2 at 2 Å above the Si surface plane (Q ).

•

Internal Photoemission Spectroscopy Methods

73

electric field suggests that considerable portion of these ions remains in SiO2 and produces attractive potential for electrons. The latter adds to the externally applied field and weakens the barrier lowering measured as a function of external electric field. This effect can also be seen as related to the overlap of long-range Coulomb potentials of ions in an insulator with a low dielectric constant (εD = 3.9 for SiO2 , Sze (1981)). To summarize, the IPE threshold spectroscopy appears to be a unique experimental tool in characterization of the interface barrier behaviour not only in the case of ideal image-force barriers but also in the presence of perturbing charges.

4.1.3 Separation of different contributions to photocurrent The given so far IPE threshold determination examples make use of knowledge that the observed IPE current is related to photoinjection of electrons into SiO2 . This is possible because the barriers for electron injection at the interfaces of silicon dioxide with metals and semiconductors are usually significantly lower than the barriers for hole injection. This conclusion was reached on the basis of several experiments including the optical interference analysis (Powell, 1969), insensitivity of the IPE current measured under positive bias to the anode material (Williams, 1965), and the negative charge trapping in the oxide observed after a prolonged photoinjection. Direct determination of the electron and hole IPE barriers at the Si/SiO2 interface gives values of 4.3 and 5.7 eV, respectively, if oxidation of Si is carried out in pure O2 (Adamchuk and Afanas’ev, 1984). However, in a general case, one must address identification of the injected charge carrier type corresponding to the particular spectral threshold because several processes may contribute to the photocurrent (cf. Fig. 3.5.1). An example of several approaches to separation of the IPE and PC contributions to the photocurrent as well as of the electron and hole IPE can be given using IPE/PC results for Si – thin film HfO2 structures with a thin (1 nm) SiON or Si3 N4 interlayer and semitransparent Al or Au field electrodes shown in Fig. 4.1.7 (Afanas’ev et al., 2002b). First, in the high photon energy range (hν > 5.9 eV) the photocurrent yield is seen to be insensitive to the orientation of electric field, to the type of interlayer between Si and HfO2 (SiON or Si3 N4 ), and to the metal used as the field electrode material (Au or Al). This behaviour suggests (Williams, 1965) relationship of this current to photogeneration of charge carriers inside the HfO2 collector layer. Taking into account a high quantum efficiency of this generation process it can be reliably associated with intrinsic photogeneration of electron–hole pairs in HfO2 with the spectral threshold corresponding to the (lowest) HfO2 bandgap indicated by arrows in all four panels in Fig. 4.1.7. Next, as the low-energy portions (hν < 5 eV) of the spectra taken under the positive metal bias appear to be insensitive to the metal electrode material and, at the same time, different from those taken at negative bias, they can be associated with IPE of electrons from Si substrate into HfO2 (Williams, 1965). This interpretation is supported by kinks in the spectral curves seen to occur at photon energies around 3.4 and 4.4 eV which correspond to the already mentioned optical singularities E1 and E2 of Si crystal (indicated by dashed lines in Fig. 4.1.7). Therefore, the energy barrier between the top of the Si valence band and the bottom of HfO2 conduction band can be determined from the spectral onset of photocurrent measured when applying a positive bias to the metal electrode. Further, when addressing the spectra obtained with metal field electrodes biased negatively, panels (c) and (d), it becomes noticeable that replacement of Au field electrode with Al one leads to a large ‘red shift’ of the photocurrent threshold. This trend can immediately be associated with an up-shift of the Fermi level in Al indicating the metal to be the source of carriers (electrons). However, this logic is valid only for Al. As one may notice, an increase of the quantum yield in the Au-gated samples at hν > 3.6 eV is also visible in the structures with Al electrodes on the background of electron IPE from the metal. As no such photoemission is seen to occur when Au is biased positively (panels (a) and (b)), the corresponding current must be related to IPE of holes from Si into HfO2 . The spectral threshold of hole IPE is equal to the

74

Internal Photoemission Spectroscopy: Principles and Applications 106 105

(100)Si/SiON/HfO2

(100)Si/SiON/HfO2/Au V>0

V 5.5 eV shown in Fig. 4.1.5 is likely to be caused by π → π* excitations in the chains or rings of π-bonded carbon atoms (Afanas’ev et al., 1996a, b). Remarkably, in the graphite-rich layers (, ) this feature is seen to be shifted to a lower energy (4.5–5 eV) which is consistent with the expected decrease of the π–π* splitting with increasing the size of the π-bonded carbon cluster (Lee et al., 1994). On the other hand, example of very similar to Si pattern is provided by the IPE experiments on Ge interfaces with HfO2 shown in Fig. 4.2.3 for the samples with interlayers of different chemical composition (Afanas’ev and Stesmans, 2006). The quantum yield of electron IPE is

IPE/PC yield (relative units)

106

(100)Ge/Si/SiOx /HfO2

105 104 (100)Ge/GeN O /HfO x y 2 103 Eg(HfO2) 5.6 eV

102 101 100

E1

101 2

3

E2

4 5 Photon energy (eV)

6

Fig. 4.2.3 IPE yield as a function of photon energy measured with +1 V bias on the Au electrode in n-Ge/HfO2 (10 nm)/Au capacitors with interlayers of different composition indicated in the figure. Arrows indicate the spectral threshold of intrinsic oxide PC Eg (HfO2 ) and the energies of direct optical transitions in the Brillouin zone of Ge crystal, E1 and E2 , respectively.

78


seen to exhibit features at photon energies of 3.3 and 4.4 eV, which are consistent with energies of direct optical transitions in Ge (Cardona and Pollak, 1966). Interestingly, the depth of the IPE yield modulation is seen to be different in the Ge/HfO2 samples with GeNx Oy and Si/SiOx interlayer. The weaker impact of the E1 and E2 transitions on the yield in the latter case may be associated with a symmetry lowering of the Ge crystal lattice at the surface caused by the strain induced by the over-growth of the 1.2-nm thick Si capping layer. This observation would be consistent with the high sensitivity of the IPE to the very surface layer of the emitting material because only the optical transitions occurring within the IPE signal formation depth (i.e., mean photoelectron escape length) will contribute to the spectral features observed on the IPE spectra shown in Fig. 4.2.3. 4.2.2 Application of the IPE yield modulation to Si surface monitoring The sensitivity of the IPE yield to the intensity of the optical transitions in the very surface layer of an emitter makes its analysis a promising technique to evaluate the crystalline quality of semiconductor surfaces. An example of such application can be given for silicon interfaces with different oxide insulators, which represents a highly relevant issue for a number of practical microelectronic applications of this semiconductor (Wilk et al., 2001). Upon Si disordering, peak in the optical reflectivity and optical absorption spectra at hν = 4.3–4.4 eV (the E2 singularity) typical of the single-crystal silicon disappears, leading to featureless spectra of Si optical parameters in the photon energy range from 4 to 4.7 eV (Philipp, 1971; Jan et al., 1982). Potentially, the conventional optical absorption spectroscopy also allows one to monitor the electron transitions in the vicinity of the E2 point. However, direct optical measurements have poor sensitivity to the surface/interface layer of semiconductor because the light absorption occurs at a depth of about 1/α (α is the optical absorption coefficient of a solid) yielding a probing depth of 10–100 nm of Si. By contrast, monitoring of the E2 singularity related feature in the IPE spectra allows one to trace the processing-induced distortion of the lattice with the probing depth in order of only few nanometres (Adamchuk and Afanas’ev, 1992a). The principle of using IPE for monitoring the Si surface optical properties is already discussed (cf. Fig. 4.2.2 showing the electron energy band diagram of Si at its interface with SiO2 ). The X4 → X1 excitation indicated by the arrow provides the exited electron in a final state well below the oxide conduction band edge, which makes it emission into SiO2 impossible. The corresponding distortion of the IPE spectra is expected to be proportional to the partial optical absorption coefficient of electron transitions in the E2 peak. The character of the of IPE spectra distortion in the photon energy range corresponding to emission of an electron from the valence band of (100)Si into a 5-nm thick thermal oxide is illustrated in Fig. 4.2.4. As predicted by the theory (cf. Table 3.2.1, Powell (1970)), in the vicinity of the spectral threshold the IPE spectral curves must obey the cubic law Y ≈ A(hν − )3 , where A is a constant and is the IPE spectral threshold. The shift of the threshold towards lower energy is caused by the Schottky lowering of the Si/SiO2 potential barrier consistent with that predicted by Eq. (2.2.8). At around hν ≈ 4.2 eV the spectral curves begin to deviate from the theoretical dependence. The spectral position of this feature is seen to be insensitive to the electric field-induced shift of the IPE spectral threshold. The latter importantly indicates that the distortion of IPE yield curves originates from the field-independent optical excitation which can be associated with the E2 feature in the optical characteristics of the Si crystal substrate on the basis of coinciding spectral position. To ensure the correct assignment of the feature observed in the IPE spectra to the peak in the optical constants of Si crystal, it was attempted to reduce the intensity of dominant X4 → X1 transition by high-dose implantation of a donor impurity (phosphorus). As can be seen from Fig. 4.2.2, the final state of the optical transition at point X1 of the Si Brillouin zone is very close to the bottom of the Si conduction band, and, in the case of heavily doped n-type Si formed by P doping, it will be occupied with a high


79

(IPE yield)1/3 (relative units)

(100)Si/SiO2 (5 nm) 10 E2

5

0 3.5

4.0 4.5 Photon energy (eV)

5.0

Fig. 4.2.4 Spectral dependences of electron IPE from the valence band of (100)Si into 5-nm thick thermal SiO2 measured in Si/SiO2 /Au structures with different positive bias applied to the metal (in V): 1 (), 1.5 (), 2 (), 2.5 (), and 3 (3). The arrow indicates the energy of the E2 transition in silicon.

density of electrons. The latter will reduce the oscillator strength of the optical transitions because they become impossible between the points of high symmetry and, therefore, must occur at different wave vector values. The IPE spectra shown in Fig. 4.2.5 indicate that for the P-implanted Si(100)/SiO2 sample a high density of electrons is present in the Si conduction band (they account for the IPE from the Si conduction band at low photon energies similarly to the case discussed in the beginning of the previous section, cf. Fig. 4.1.1) and the feature at hν = 4.4 eV is greatly reduced in comparison to the control

104

IPE yield (relative units)

No implantation 103

E2

11016 P/cm2

102 101 100 101 102 3

4

5

Photon energy (eV)

Fig. 4.2.5 Spectral dependences of electron IPE yield from the valence band of (100)Si into 85-nm thick thermally grown SiO2 for the low-doped n-type Si substrate () and for the phosphorus-implanted (D = 1 × 1016 P/cm2 at E = 80 keV) one (). The arrow indicates the energy of the E2 transition in Si crystal.

80


(unimplanted) sample. Therefore, the observed modulation of the IPE spectra can be firmly associated with excitation of X4 → X1 transitions not only on the basis of the same photon energy position but, also, on the basis of the exposed sensitivity to the conduction electron density in Si. Further, the remarkable sensitivity of the IPE spectra to the Si surface processing is illustrated by the IPE spectra shown in Fig. 4.2.6a for (100)Si oxidized in dry O2 at 1000◦ C for various times resulting in the oxide layer of different thickness. It is clearly seen that, with increasing oxide thickness, the depth of the yield curve modulation in vicinity of the E2 singularity decreases approaching nearly zero value similar to that attained in the phosphorous-implanted samples (curve (4) in Fig. 4.2.6a). In order to make a meaningful comparison between the intensities of the direct optical transitions at the interfaces of silicon with differently prepared insulators, one must find a way to characterize the distortion of the IPE spectral curves in a quantitative way. Assuming that the dependence of the IPE


Si(100)/SiO2

4 32

1

10

5

(a) 0

S

0.2

0.1

(b) 0.0 4.0

4.2 4.4 4.6 Photon energy (eV)

4.8

Fig. 4.2.6 (a) Cube root plot of the spectral dependences of electron IPE from the valence band of (100)Si into thermally grown SiO2 layers of different thickness obtained by oxidation of the crystal in dry O2 at 1000◦ C (in nm): 55 (1), 100 (2), and 160 (3) as compared to the samples with a 100-nm thick oxide implanted with high dose of phosphorous prior to oxidation (4). The curves are measured using Si/SiO2 /Au structures with the average strength of electric field in the oxide 1 MV/cm with the metal biased positively. (b) The relative deviation of the quantum yield from the cube law S(hν) as a function of photon energy for (100)Si/SiO2 samples with different oxide thickness (in nm): 23.5 (), 46 (), 55 (), 84 (), 100 (3), and 148 ( ).


81

yield on photon energy Y0 (hν) is a monotone function of the photon energy, one may define the relative deviation function S(hν) characterizing the normalized spectrum distortion (Adamchuk and Afanas’ev, 1992a): S(hν) =

Y0 (hν) − Y (hν) , Y0 (hν)

(4.2.1)

where Y (hν) is the experimentally observed IPE yield, and Y0 (hν) is obtained by extrapolation of the yield measured at hν < E2 to the higher photon energies. In a simplest case, when E2 lies slightly above the spectral threshold from the semiconductor valence band, one may approximate Y0 as a power function (Powell, 1970), obtaining: S(hν) = 1 −

Y (hν) , C(hν − )3

(4.2.2)

where the constant C is determined from the slope of the near-threshold part of the linear Y 1/3 –hν plot or, else, may be taken from a reference sample. The S(hν) curves derived for (100)Si/SiO2 interfaces with different thickness of the thermal oxide layer are compared in Fig. 4.2.6b. Their shape is very similar to the E2 optical absorption peak of Si crystal due to the X4 → X1 and 4 → 1 transitions which is gradually attenuated with increasing the oxidation time. Importantly, this optical feature appears to be much less pronounced at the oxidized Si surfaces than at the atomically clean ones (see, e.g., Allen and Gobeli, 1966), suggesting that the oxidation of the Si surface leads to some kind of crystal symmetry reduction leading to a decrease of the oscillator strength of the X4 → X1 and 4 → 1 direct optical transitions (Adamchuk and Afanas’ev, 1992a). As a most simple way to compare different surfaces of Si, the maximum modulation depth of the IPE spectrum can be determined as the peak value Smax of the S(hν) function. For the sake of comparison, the IPE results for the Al2 O3 grown on (100)Si using the atomic-layer deposition at 300◦ C are shown in Fig. 4.2.7. For the as-deposited alumina layer () the E2 feature


15

(100)Si/Al2O3 (50 nm)

E2

As-deposited 950C 10 min 10

E1 5

0 2.5

3.0

3.5

4.0

4.5

5.0

Photon energy (eV)

Fig. 4.2.7 Spectral dependences of electron IPE from the valence band of (100)Si into 50-nm thick as-deposited Al2 O3 layer () and after 10-min post-deposition oxidation in pure O2 at 950◦ C (). The arrows indicate the energies of transitions E1 and E2 .

82

Internal Photoemission Spectroscopy: Principles and Applications 0.6 MeOx 0.4

(111)Si

Smax

Cleaved SiO2

0.2

0.0 1

10 Oxide thickness (nm)

100

Fig. 4.2.8 Maximum modulation depth of the IPE spectrum at the E2 point versus insulator thickness for SiO2 layers (circles) thermally grown on (100) () and (111) ( ) Si, and for low-temperature deposited Al2 O3 (), ZrO2 (), and HfO2 () layers on Si(100). Arrow indicates the Smax value evaluated from the external photoemission yield spectra of the clean cleaved (111)Si (Allen and Gobeli, 1966). Lines guide the eye.

•

is much more pronounced than in thermal SiO2 /Si structures, which is also consistent with the IPE spectra shown in Figs. 4.1.7 and 4.2.1 for other metal oxides deposited at relatively low temperature (300–350◦ C). However, there is a observed substantial increase of the IPE spectral threshold energy after 10 min oxidation of the Al2 O3 /Si sample in O2 at 950◦ C (), which suggests formation of an aluminosilicate layer at the interface. Most importantly, the modulation depth of the IPE spectrum at point E2 drops drastically after this oxidation indicating a substantial perturbation of the Si crystal surface structure. The results of the IPE yield analysis in the vicinity of E2 optical singularity are illustrated in Fig. 4.2.8 by comparing values Smax for different insulating layers on (100)- and (111)-oriented Si crystals. As the reference S value, one may use the value S ≈ 0.35 determined from the external photoemission spectra of a clean cleaved (111)Si crystal (Allen and Gobeli, 1966), and S = 0 for amorphous Si (Jan et al., 1982). It is well seen that in the case of thermal SiO2 growth, the silicon surface crystallinity degrades with increasing oxide thickness (oxidation time). By contrast, the crystallinity of the (100) Si surface with deposited Al2 O3 , ZrO2 , or HfO2 is approximately independent of the overlayer thickness and, at least for the same deposition method (results for the atomic-layer deposition are shown in Fig. 4.2.8), on the composition of the deposited oxide. The corresponding Smax values are even higher than the value Smax = 0.35 obtained after (111)Si crystal cleavage (Allen and Gobeli, 1966), pointing towards the presence of atomic steps on the clean surface as a possible symmetry reduction factor.

4.2.3 Model for the optically induced yield modulation The results presented above demonstrate the origin of the mechanism of the IPE spectral distortion by optical features of the emitter crystal. However, they provide no immediate link to the measurable values of the optical absorption coefficient or the optical reflectivity. In order to quantify the influence of optical singularities one may use a simple model describing attenuation of incident light at a depth comparable to the mean photoelectron escape depth λe (Adamchuk and Afanas’ev, 1992a). In this case the internal


83

quantum yield is related to the optical absorption coefficient α(hν) and the escape depth λe , assumed to be energy independent, by the relationship (Berglund and Spicer, 1964b): Y ∗ (hν) = Y (hν, )

α(hν)λe , 1 + α(hν)λe

(4.2.3)

where Y ∗ (hν) is the spectral dependence of the quantum yield obtained neglecting the optical effects, e.g., given in Table 3.2.1. In the limiting case of strong electron scattering α(hν)λe an excitation of additional interband electron transitions occurs leading to an increase of the optical absorption coefficient by a value of α∗ (hν), which adds to the energy-independent optical absorption α0 . Would the conventional procedure of the quantum yield determination by normalizing the current to the incident photon flux still be used, this additional optical absorption will modify the yield curves because the variation of the optical constants is neglected when calculating Y . Two cases are possible, depending on the energy of the final electron state Ef in the additional interband transitions (Adamchuk and Afanas’ev, 1992a). If Ef > the additionally excited electrons will contribute to the IPE and the real quantum yield will be determined by the total optical absorption [α0 + α∗ (hν)]: Y1 (hν) = [1 − R]Y (hν, )

[α0 + α∗ (hν)]λe . 1 + [α0 + α∗ (hν)]λe

(4.2.5)

Therefore, there will be the photon-energy-dependent enhancement of the quantum yield as compared to the predicted Y (hν, ) function which can be characterized by the relative deviation function S(hν) constructed in a similar way as that given by Eq. (4.2.1). This function can now be expressed as assuming that the contribution of the optical reflectivity [1−R] remains unchanged: α∗ (hν) Y1 (hν) − Y0 (hν) α0 = S(hν) = . Y0 (hν) 1 + [α0 + α∗ (hν)]λe

(4.2.6)

If Ef < the additionally excited electrons will contribute only to the light attenuation but not to the IPE. The real quantum yield is still be determined by the optical absorption α0 : Y1 (hν) = [1 − R]Y (hν, )

α 0 λe , 1 + [α0 + α∗ (hν)]λe

(4.2.7)

suggesting a decrease of the quantum yield as compared to the ‘no-singularity’ case. For the spectral deviation function (4.2.1) one obtains now the following expression: S(hν) =

Y0 (hν) − Y1 (hν) α∗ (hν)λe = . Y0 (hν) 1 + [α0 + α∗ (hν)]λe

(4.2.8)

84


hn0

4

Ef >

Yield1/p

nt

ta

3 a

2

s on

c

Ef <

1 0 Photon energy

Fig. 4.2.9 Simulation of the IPE yield changes caused by the Lorentz absorption peak centred at photon energy hν0 [α*(max) = α0 ; α0 λe = 0.2] with the energy of the final electron state above and below the interface barrier height .

The character of the expected IPE spectral plot distortion is illustrated in Fig. 4.2.9 by simulation of the influence of the Lorentz-type absorption peak on the Y 1/p –hν plot. Two possible cases are shown with the final states of additional transitions contributing to the IPE (Ef > ) and providing no charge carriers at an energy sufficient for the interface barrier surmount (Ef < ). It is obvious that both the enhancement and attenuation of the external IPE yield can be observed. It must be added, however, that construction of the spectral deviation function S(hν) seems to be more appropriate method because Eqs (4.2.6) and (4.2.8) indicate that the spectral shape of this function closely resembles that of the partial absorption coefficient α∗ (hν) of the additionally excited interband transitions (cf. Fig. 4.2.6b).


It is worth now to illustrate the just predicted enlargement and reduction of the quantum yield with respect to the idealized power law by experimental IPE spectrum of electron IPE from the valence band of GaAs(111)B into the epitaxially grown SrF2 collector (Afanas’ev et al., 1991b) layer shown in Fig. 4.2.10. GaAs(111)B/SrF2

X7 X6

4 3 2 1 8 7 0 3.0

3.5

4.0

4.5

5.0

5.5

Photon energy (eV)

Fig. 4.2.10 Cube root of the electron IPE quantum yield as a function of photon energy measured at the interface of GaAs(111)B with 120-nm thick epitaxially grown layer of SrF2 . The strength of electric field in the fluoride during measurements 0.4 MV/cm, with the Au field electrode biased positively. The arrows indicate the energy position of direct optical electron transitions in GaAs crystal.


85

As can easily be noticed, the quantum yield obeys cube behaviour predicted by the Powell’s theory over the energy range of ≈1 eV above the spectral threshold. When the photon energy increases further, the yield increases faster than the expected yielding a ‘hump’ on the spectral curve at hν ≈ 4.4 eV. Further increase of the photon energy leads to a rapid decrease of the quantum yield at around hν ≈ 4.8 eV below the line obtained by extrapolating the initial nearly ideal portion of the spectral curve. The insensitivity of the spectral positions of these features to the strength of electric field in the fluoride layer (Afanas’ev et al., 1991b) indicates their optical origin. Accordingly, they may be associated with direct optical excitation of 8 → 7 transitions in GaAs yielding electrons with energies above the conduction band edge of SrF2 , and with X7 → X6 excitations, which give no contribution to IPE because their final state appears to lie below the interfacial barrier top. Potentially, would the photoelectron escape depth be known from an independent experiment, this kind of measurements is capable of providing quantitative information regarding strength of direct optical transitions at the surface of the emitter.

4.3 Spectroscopy of Carrier Scattering In the process of IPE the excited charge carrier must travel from the point of its optical excitation in an emitter to some point behind the maximum of potential barrier in a collector without experiencing any substantial energy loss. Therefore, variations in the inelastic scattering rate in emitter or in collector will affect the probability of carrier to escape and, therefore, the IPE quantum yield value. Would this change in the scattering rate occur in the carrier energy range above the spectral threshold of IPE, this transportinduced variation of the quantum yield will be reflected in the IPE spectral characteristics enabling one to determine energy onset(s) of the inelastic scattering process(es). In this way, one may attempt to identify the dominant scattering mechanisms. Obviously, the transport properties of emitter and collector affect different steps of the IPE process and scattering in these materials is to be analysed separately. 4.3.1 Scattering in emitter The scattering of charge carriers on their way from the point of excitation to the surface of emitter affects the quantum yield by modulating the photoelectron escape depth λe which is largely determined by the rate of inelastic electron–electron scattering. In the most simple case of a large, as compared to λe , light penetration depth α−1 , the quantum yield is proportional to λe (cf. Eq. (2.1.9)). The principle of observing the energy loss mechanism during electron IPE from a wide bandgap emitter like SiC is illustrated in Fig. 4.3.1 (Afanas’ev and Stesmans, 2003a). For a photon of energy hν < Eg (SiC) exciting

B

A

EC Eg EV SiC

SiO2

Fig. 4.3.1 Electron energy band diagram of a SiC/SiO2 interface with the schemes of electron transitions contributing to the IPE in the spectral range hν < Eg (SiC) (process A) and hν > Eg (SiC) with the additional electron–electron scattering process B shown.

86


an electron in the SiC conduction band by transition indicated by arrow A, the excited carrier can experience only the quasi-elastic scattering by phonons because its energy remains insufficient to excite a valence electron to the SiC conduction band. When the photon energy exceeds Eg (transition B), the generation of new electron–hole pairs during transport of excited electrons towards the emitter surface becomes possible. As the result of a pair generation, the initially excited electron loses its energy and cannot anymore be injected into SiO2 . Therefore, the rate of inelastic scattering of the excited electrons sharply increases when hν becomes larger than Eg , which, in its turn, reduces the photoelectron escape probability and the rate of the IPE yield increase with photon energy. Then the energy position of the loss feature observed in the IPE spectra can be directly associated with the onset of electron–hole pair generation process, i.e., with the bandgap of emitter Eg representative of the SiC surface layer of thickness comparable to the mean photoelectron escape depth (few nanometres). The essential condition to observe such kind of effects in the case of IPE from a semiconductor conduction band can be expressed as < Eg (emitter) 3 eV. The IPE allows a high degree of experimental flexibility in terms of materials properties and fast technological turnaround because of simplicity of field electrode formation on the blanket films of collector material on top of the substrate. However, the need for optical input might preclude one from direct analysis of the device-relevant structures. As the major drawbacks of the method one should indicate a low injection current levels resulting from the requirement to minimize the sample heating effects, and the photodepopulation effects potentially preventing defects with large PI cross-section from being observed as charge traps. In the latter case other injection techniques are to be recommended.

EC a

b

c

hn

EC Et EV Emitter

Collector

Fig. 5.2.1 Photodepopulation of traps during IPE injection: illumination by photons of energy hν not only photoinjects electrons from a semiconductor emitter (process a) which then can be trapped in the collector by traps with energy level Et (process b) but, also, can empty these traps if hν > EC (collector) − Et (process c).

112


5.3 Carrier Injection by Tunnelling The tunnelling of charge carriers from emitter into collector when a high electric field is applied to the interface apparently represents technically the simplest method of charge injection. The corresponding transitions are schematically shown in Fig. 5.3.1 for the cases of electron (a) and hole (b) tunnelling from a semiconductor field emitter. These require no external excitation of charge carriers, and can be realized simply by applying a sufficient bias voltage to the electrodes of a capacitor sample. The current density is determined by the strength of electric field at the injecting interface, and can be expressed as (see, e.g., (Weinberg, 1982): β J(F) = CF 2 exp − , F

(5.3.1)

where the pre-exponent coefficient C and the slope of the exponent are given by: C=

q 3 m0 = 1.54 × 10−6 16π2 mc∗

4 (2mc∗ )1/2 3/2 = 6.83 × 107 β= 3 q

m0 mc∗ mc∗ m0

1 (A/V2 ),

(5.3.2a)

3/2 (V/cm),

(5.3.2b)

where m0 is the mass of electron in free space, mc∗ is the effective mass of electron in the collector, and the barrier height is expressed in electron Volt. Though the original expressions of the FN type (5.3.1) were derived for the case of electron tunnelling from a metal into vacuum (Fowler and Nordheim, 1928) they still well applicable to electron tunnelling at interfaces of solids (Snow, 1967; Lenzlinger and Snow, 1969). Moreover, tunnelling of holes, which is impossible in a solid/vacuum system, can also be described by using the FN model and the free carrier mass equal to m0 (Waters and Van Zeghbroeck, 1998; Chanana et al., 2000). The simplicity of experimental arrangement and a high current density attainable in the FN injection made the tunnelling one of the most widely used carrier injection techniques. However, several factors preclude this injection method from being considered a suitable one for the trap spectroscopy (Afanas’ev and Adamchuk, 1994). First, when a high electric field is applied to the collector layer, the injected charge carriers are significantly accelerated and their energy distribution deviates from the thermal one. These

(a)

(b)

Fig. 5.3.1 Schemes of electron transition corresponding to tunnelling injection of electrons (a) and holes (b) from a semiconductor into insulator.

Injection Spectroscopy of Thin Layers of Solids

113

a b

d

c

Fig. 5.3.2 Schemes of secondary effects influencing charge accumulation in the course of tunnel carrier injection: depopulation of traps caused by high field or electron impact (a), generation of new traps (b), secondary emission of carriers of opposite sign from field electrode (c), and the impact ionization in collector (d).

‘hot’ carriers may lead to additional effects schematically illustrated in Fig. 5.3.2, which complicate the description of charge accumulation kinetics using a simple carrier-trap interaction picture. To start with, the high electric field may promote the detrapping (process a) leading to a decrease of trap occupancy with increase of the applied field (DiMaria et al., 1975, Eitan et al., 1982; Nissan-Cohen et al., 1986). Next, the ‘hot’ carriers may acquire from the electric field energy sufficient to generate new traps in the course of injection experiment (process b) (Badihi et al., 1982; Nissan-Cohen et al., 1986; DiMaria and Stasiak, 1989; Heyns et al., 1989; DiMaria 1999; 2000; Vogel et al., 2001). In this case, the measurement procedure by itself affects the trap ensemble (Nissan-Cohen et al., 1986). Next set of problems is associated with monopolarity of the carrier injection under high strength of the applied electric field. This question concerns primarily the possibility of tunnelling of the carriers of opposite charge sign at the opposite interfaces of collector which is highly relevant issue if the corresponding barrier heights have close values. Additionally, the arrival of ‘hot’ carriers to the opposite electrode may lead to the secondary emission phenomena, including injection of carriers of opposite sign (process c in Fig. 5.3.2), liberation of hydrogenic species, or impact ionization (process d). In some cases, these processes may cause even inversion of the trapped charge sign with the progressing injection time (Knoll et al., 1982; Maserjian and Zamani, 1982; Weinberg et al., 1986). As a result, the charge trapping kinetics will include contributions of compensating charges making its reliable analysis hardly possible because the ratio between the electron and hole injection rate cannot be found from the simple tunnelling current measurements. Finally, lateral uniformity of the carrier flux is also highly questionable when FN tunnelling is used to inject the charge. This is related to two physical issues: first, as one might notice from Eqs (5.3.1) and (5.3.2) the tunnelling current depends exponentially on electric field. As a result, any lateral inhomogeneity of electric field including that caused by the trapped charge carriers will lead to a laterally non-uniform rate of tunnelling transitions. Second, tunnelling may occur not only in a way shown in Fig. 5.3.1 but, also, via some intermediate electron state in the collector would the corresponding defect or impurity level be available in the energy range of interest. This process, often referred to as the trap-assisted tunnelling, results in a current hardly distinguishable from the conventional tunnelling one except of a lower effective barrier height. However, as the trap-mediated transitions are always spatially

114


correlated with the location of imperfection providing the intermediate electron level, the corresponding tunnelling rate map will be peaked at a certain number of injecting ‘spots’ resulting in inhomogeneous carrier profile. One might attempt to improve the homogeneity of the trap-assisted tunnelling by using an overlayer containing a high concentration of intermediate electron states aiming at a lower strength of electric field needed to attain a desired current density (Ron and DiMaria, 1984). For instance, Si-rich SiO2 films enable highly efficient electron injection into SiO2 which can be used both in the experimental research and in the charge-storage memory devices (DiMaria and Dong, 1980; DiMaria et al., 1980; DiMaria et al., 1981). A similar result can also be obtained when using granular metal films as electron injector (Falcony et al., 1982). Nevertheless, the need of additional sample processing makes this approach less attractive when material characterization is needed. Deposition of the special injecting material not only adds to the processing time and complexity but, also, may potentially introduce significant artefacts related to the exposure of the collector surface to elevated temperature and/or to reactive species. As a result, this injection method has not received much attention in research. 5.4 Excitation of Carriers in Emitter Using Electric Field The effect of carrier ‘heating’ in the presence of a high electric field described in the previous section may also be applied to increase the carrier energy in the emitter in order to enable them to overcome the potential barrier. Obviously, the electric field must penetrate into the emitter to a sufficient depth to allow a carrier to gain energy comparable to the interface barrier height. For this reason the field-induced ‘heating’ of carriers is possible only when using a semiconducting emitter material. If the electric field oriented along the normal to the emitter–collector interface plane allows a charge carrier to accelerate and to acquire the energy sufficient to meet the Fowler barrier surmount condition, the carrier gets a chance to overcome the barrier and to contribute to the injection current. There are two most important techniques which employ this principle of injection: the avalanche carrier injection (ACI) and the injection from a p–n junction. ACI occurs when a high-frequency AC bias is applied to the field electrode of the sample with the polarity required to switch the surface of semiconductor from accumulation to inequilibrium depletion (see Nicollian and Brews (1982) for a review). Due to the electron energy band bending in the emitter which can be much larger than its bandgap width, charge carriers are accelerated across the inequilibrium depletion layer during each voltage pulse and some of them become able to surmount the barrier at the interface and enter the collector (Nicollian et al., 1969; Nicollian and Berglund, 1970). Injection of ‘hot’ carriers from the p–n junction occurs in a similar way but, in order to create a sufficiently large potential variation across the surface layer of semiconductor emitter, the appropriate biasing of the sub-surface junction is used (Verwey, 1973). As already indicated, the necessary condition of the field-stimulated carrier heating is the presence of high electric field at the surface of semiconducting emitter. To attain the avalanche breakdown, the minority charge carriers entering the inequilibrium depletion layer must be accelerated by this high field and cause electron–hole pair generation through impact ionization in the emitter. In its turn, each newly generated carrier will also be accelerated to energies allowing next impact ionization event leading to the development of the electron avalanche (Nicollian et al., 1969; Nicollian and Berglund, 1970). A simple analysis of the impact ionization process in the space-charge surface layer predicts the avalanche breakdown threshold voltage to be related to the concentration of the ionized doping impurity as Va ∝ [n]−2/3 (Goetzberger and Nicollian, 1967). Therefore, the onset of the avalanche breakdown will mostly be determined by the properties of the emitter surface (doping impurity concentration, impact ionization efficiency …). In experiment the ACI occurs when the externally applied voltage rapidly switches the semiconductor substrate surface from accumulation to inequilibrium (deep) depletion. Therefore, the corresponding


115

30 Va

Voltage

20 10 0 10 t1

t2 t3

Time (a)

(b)

(c)

(d)

(e)

Fig. 5.4.1 Time diagram of voltage pulse sequence during avalanche injection of electrons from a p-type semiconductor when applying a sawtooth pulse ACI excitation (a). The band diagrams of the semiconductor/insulator interface at various times are illustrated in the following panels: t < t1 (b), t1 < t < t2 (c), t2 < t < t3 (d) and t = t3 (e). Time t1 corresponds to the beginning of the ramp pulse, t2 to the threshold of ACI, and t3 to the end of the pulse followed by switching of the semiconductor surface to accumulation (b).

voltage represents a sequence of sinusoidal, triangular, or rectangular pulses (Nicollian and Berglund, 1970; Young et al., 1979; Ang et al., 1994). The detailed description of the ACI technicalities can be found in the literature (see, e.g., Nicollian and Brews, 1982; Barbottin and Vapaille, 1989) and here only the most important physical features of this injection mechanism will be overviewed. In Fig. 5.4.1 are shown the triangular voltage pulse series (a) and the energy band diagram of the semiconductor– insulator–metal structure corresponding to different time intervals (b–e) for the case of electron ACI from a p-type emitter. At t = 0 the surface of the p-type semiconductor is in accumulation (b) and holes give the dominant contribution to the space charge. As the voltage ramp starts at t2 , it turns the semiconductor to deep depletion as illustrated in panel (c), and, at a voltage above the avalanche breakdown threshold Va reached at t2 , to the avalanche breakdown (panel (d)). During this stage the band bending in semiconductor appears to be so large that some electrons acquire energy sufficient for injection over the interface barrier into the insulating collector. As avalanche develops, the electrons remaining in the emitter start to form an inversion layer leading to decrease of the voltage drop across the space-charge layer at surface of emitter and to the corresponding increase of the potential variation across the insulating layer (e). To prevent the dielectric breakdown of the collector, the voltage is switched back to accumulation at time t3 . Then, the avalanche electron injection (AEI) can be started again during the next voltage pulse. If one assumes that the high-energy portion of electron energy distribution at the interface still can be described by a Maxwell–Boltzmann distribution with the effective temperature Tc , the ACI can be described using Eq. (3.4.5) with Tc in place of the emitter temperature. The hot carrier temperature is controlled by the strength of electric field near the surface and by the carrier scattering rate. Typical values of Tc in the case of electron ACI from silicon into silicon oxide are lying in the range 5000–6000 K (Nicollian and Brews, 1982; Ang et al., 1994). The strong dependence of the ACI current on the strength of electric field at the interface allows to use its density to monitor the trapping-induced variations of the field at the surface of emitter. In order to keep the injection current at a preset value, one must adjust

116


the gate voltage to compensate the field induced by charge carriers trapped in the collector. Thus, the variation of the ACI voltage directly corresponds to the trapped charge-induced electric field. The ACI appears to be practical only in a relatively narrow range of the emitter doping (see Nicollian and Brews, 1982, pp. 495–508): The upper emitter doping range is about 1018 cm−3 and is limited by the increasing rate of interband electron tunnelling (Zener breakdown) with increasing impurity concentration. The lower limit of the doping range is governed by two factors: (1) The avalanche breakdown at the edge of the gate contact caused by an enhanced, as compared to the plane capacitor structure, strength of electric field. (2) The dielectric breakdown of the collector layer which may occur when the semiconductor emitter surface is turned into accumulation and all the applied voltage appears across the collector film. In practice these limitations dictate use of specially fabricated samples for ACI in which the desired emitter doping level is attained through custom processing. As a result, the application of ACI appears to be very limited. So far the only material system to which it was applied with success is the thermally grown oxide on silicon. Further, the significant sample requirements are combined with other problems of ACI. First, as ACI of only minority charge carriers from a semiconductor is possible, p-type emitter is needed to inject electrons and n-type one to inject holes. Therefore, it is impossible to inject carriers of opposite charge signs in the same sample. This forces one to combine ACI with other injection methods (tunnelling, IPE, or photogeneration of carriers) adding to the complexity of experimental arrangement. Next, the ACI current density and the strength of electric field at the emitter–collector interface are uniquely related. Therefore, the current cannot be changed without varying the strength of electric field unless the ACI voltage pulse frequency is varied. Moreover, the strength of electric field in the collector is not kept constant but varies during the injection pulse as it is discussed just above. As a result, one cannot use ACI to obtain information regarding the field-dependent charge trapping process. Some of these problems may be resolved when using a non-avalanche injection from a sub-surface p–n junction in the emitter. There are several geometry configurations for this kind of injection based on the metal–insulator–semiconductor transistor or the gate-controlled diode structures. The discussion here will be limited to those providing a laterally uniform injection flux because in the case of nonuniform injection reliable determination of capture cross-section becomes impossible. The major feature of the non-avalanche injection methods consists in creation of a stationary large band bending at the surface of semiconductor by using a p–n junction under a reverse bias as schematically illustrated in Fig. 5.4.2. The source of minority carriers ensuring sufficiently high injection rate may be the n–p junction under forward bias right below the space–charge layer (Verwey, 1973; Schwerin et al., 1990) or the optically generated electron hole pairs in the bulk of semiconductor crystal (Ning and Yu, 1974). In the latter case an optical input is required but the range of its transparency may be more narrow that for IPE. For instance, polycrystalline Si electrodes appear to be suitable for this kind of excitation at least for the Si crystal emitter (Ning and Yu, 1974). The minority carriers diffuse into the p–n junction region and are accelerated there by electric field to energy sufficient to surmount the potential barrier as illustrated in Fig. 5.4.2b. This process can also be described as thermoionic (or Schottky) emission from the inequilibrium charge carrier energy distribution (Ning and Yu, 1974). The current density can easily be varied in the range from 10−9 to 10−4 A through different minority carrier generation rate irrespectively of the strength of electric field at the injecting interface. Therefore, analysis of the field-dependent charge trapping becomes possible as well as independent control of the injection rate. However, the non-avalanche method allows injection of only one type of charge carriers in one device and requires much more elaborate sample processing than any other injection technique. Nevertheless,


117

Drain Gate Source

n p

Collector p n

n

n n –p well Substrate (a)

(b)

Fig. 5.4.2 (a) Schematic cross-section of metal–insulator–semiconductor transistor-type device used for non-avalanche substrate hot-electron injection and (b) the electrostatic potential distribution across the emitter/ collector interface in the constant current injection mode.

the possibility to study metal–insulator–semiconductor transistor structures made the injection from p–n junction a popular technique for analysis of the processed devices (Bright and Reisman, 1993). 5.5 Electron–Hole Plasma Generation in Collector Most straightforward way of charge carrier injection in the collector consists in their direct optical excitation across the bandgap as was earlier discussed in Section 4.4.1 in relationship with the photoconductivity (PC) spectroscopy. Electron–hole pairs generated by photons of sufficient energy or by high-energy particles, e.g., electrons, may be separated by the applied electric field making the free carriers available for trapping by defects in collector. The latter process leads to build-up of the collector-trapped charge as illustrated in Fig. 5.5.1. Therefore, the response (in terms of charging) of the collector to the irradiation will be determined by the spectrum of the present imperfections and, in its turn, can be used for characterization of the trapping centres (Powell and Derbenwick, 1971). In the case of high-energy radiation like X-rays or γ-radiation, all the components of the emitter–collector–field electrode sample structure are sufficiently transparent allowing one to avoid fabrication of samples with a specially designed optical input. The last feature makes radiation response measurements a convenient tool to evaluate the integral trapping behaviour of materials imbedded in device structures with a complex architecture.

hn > Eg

Fig. 5.5.1 Scheme of electron–hole pair generation by high-energy photons (or particles) followed by carrier separation in electric field externally applied to the collector material layer sandwiched between two conducting electrodes.

118


Obviously, the use of PC as injection method to characterize traps in the collector faces several problems mostly related to the quantification of the charge accumulation process. First, the total absorbed radiation dose cannot be directly used to determine the density of injected charge carriers because of the dose enhancement effect caused by internal conversion of high-energy photons in the emitter or field electrode. At the same time, measurement of photo- or radiation-induced current requires fabrication of guard rings around electrodes as well as protection from ionic currents caused by ionization of the ambient. These problems result in much more complex sample design would some degree of quantification be required. Second group of problems arises from the bipolar nature of the PC carrier generation. Simultaneous generation of electrons and holes in the collector may not only lead to accumulation of mutually compensating charges but, also, to significant influence of recombination on the charge-trapping kinetics adding extra complexity to its analysis (Williams, 1992). Moreover, though the initial spatial distribution of generated electrons and holes may be considered uniform throughout the collector layer, in the presence of electric field the charge carriers will be re-distributed leading to the depth-dependent electron/hole concentration ratio. Under these conditions a simple form of the first-order trapping kinetics (Nicollian et al., 1971; Ning, 1978) becomes inapplicable leading to a more complex and, therefore, less accurate data fitting procedures. In many cases the quantitative description of the radiation-induced charge build-up kinetics requires trap parameters determined from an independent experiment (see, e.g., Oldham et al., 1986; Boesh et al., 1986). Finally, another principal complication of the radiation method of charge injection needs to be mentioned: this concerns generation of additional trapping sites by high-energy photons in the collector and at its interfaces. This factor is most important when γ-radiation is used because its energy is sufficient for generation of high-energy electrons through the Compton effect. Practically, the trap generation phenomenon sets the upper limit of the irradiation dose and, therefore, the lower limit of the trap capture cross-section detectable in the experiment because further increase of the dose would lead to artefacts. For instance, generation of additional electron traps in SiO2 insulating layers thermally grown on Si is reported to become significant for doses above 1 Mrad (Si) (Aitken and Young, 1976; Schmitz and Young, 1983). This absorbed dose corresponds to generation of ≈1014 electron–hole pairs/cm2 in the oxide layer of 100 nm thickness assuming the mean energy per pair creation of 18 eV. Therefore, only the traps with capture cross larger than 10−14 cm2 can be detected in the experiment of this kind. To this should be added that irradiation may also induce significant side effects like release of radiolytic hydrogen which may have additional significant impact on trap generation (see, e.g., Afanas’ev et al., 1995a). Nevertheless, one modification of the PC-based electron–hole pair generation technique appears to overcome some general shortcomings and become more suitable for the trap spectroscopy experiments. This method is based on use for the PC excitation of photons from the range of strong optical absorption of the collector material. The photons, usually from the vacuum ultraviolet spectral range (λ < 180 nm), penetrate through a semitransparent metal electrode and absorbed in a thin surface layer of the collector as illustrated in Fig. 5.5.2 (Afanas’ev and Adamchuk, 1994). The depth of the electron–hole plasma generation layer is determined by the optical absorption coefficient α and is in the order of 1/α. If this penetration depth is much smaller than the thickness of collector layer, one may extract charge carriers of only one sign into the remaining volume of collector as illustrated in Fig. 5.5.2 enabling a quasimonopolar charge photoinjection (Stivers and Sah, 1980). In this case the conditions of the first-order trapping kinetics application are met enabling extraction of the capture cross-section and the trap density values. It also needs to be added that the major portion of the collector volume remains unexposed to the light because the latter is absorbed in the outer collector layer. Therefore, analysis of photoactive traps becomes possible when using this kind of photoinjection in combination with sufficiently thick collector layer (d >> 1/α) (Afanas’ev and Stesmans, 1999b).


119

hn > Eg

1/

1/

(a)

(b)

Fig. 5.5.2 Scheme of spatially limited photogeneration of charge carriers in collector using the strongly absorbed radiation. From the electron–hole pair generation region with thickness in the order of 1/a in the remaining volume of the collector are extracted exclusively holes (a) or electrons (b) as determined by the orientation of electric field.

The current density of photogeneration in sufficiently high electric field at the surface of collector is primarily determined by the intensity of the used light source. In the photon energy region of around 10 eV a resonant light source easily delivers a flux of 1015 photons/cm2 s, which is sufficient to generate electron current exceeding 10−5 A/cm2 because the probability of pair generation per one absorbed photon approaches one. In this way the densities of injected carriers up to 1019 cm−2 may be in reach enabling detection of traps with capture cross-section as small as 10−18 cm−2 . However, this is possible only if the collector is thick enough to absorb the incident photon flux entirely. In the case of a thinner layer monopolarity of injection becomes an important issue as will be discussed below. One might consider (Afanas’ev and Adamchuk, 1994) traps with a (macroscopic) capture cross-section σ located at a distance xc from the substrate in the collector layer of thickness d. In the experiment the collector is covered with semitransparent field electrode through which the structure is illuminated by a light with absorption coefficient α in the collector as illustrated in Fig. 5.5.3. Upon filling, the traps may also be neutralized (annihilated) by charge carriers of the opposite sign with the recombination cross-section σr . Neglecting the IPE of charge carriers from the electrodes as well as the influence of the trapped charge on electric-field-dependent PC and trapping processes, one may compare the time constants of trap filling (τf ) and recombination (τr ). Would the traps be filled by holes, one may write for these time constants: τf =

q jh σ

and

τr =

q , j e σr

(5.5.1)

where jh and je are the hole and electron currents at the point of trap observation, respectively. The condition of negligible influence of recombination on the hole capture kinetics can be expressed as τf σr

exp[−α(d − xc )] − exp [−αd] . 1 − exp [−α(d − xc )]

(5.5.5)

In most cases the recombination corresponds to the carrier trapping by the attractive Coulomb potential which is characterized by far larger capture cross-section than the trapping by a neutral centre leading to inequality σr >> σ. For instance, in the thermally grown SiO2 on Si, σr is typically in the range between 10−12 and 10−14 cm2 while the neutral traps are characterized by the section comparable to the atomic


121

radius of the trapping site, i.e., σ < 10−15 cm2 (DiMaria, 1978; Buchanan et al., 1991). Therefore, the condition (5.5.5) can be met only if e−α(d−xc ) − e−αd = e−αd (eαxc − 1) > 1. Next, the trap distance xc from the substrate surface (cf. Fig. 5.5.3) must remain sufficiently small as compared to the light penetration depth α−1 . By using Eq. (5.5.5) with parameters typical for SiO2 collector, i.e., α = 106 cm−1 (Powell and Morad, 1978; Weinberg et al., 1979), d = 100 nm, xc = d/2, and σr = 10−13 cm2 , the minimal detectable crosssection appears to be around 10−15 cm2 . This example demonstrates that the possibility of correct determination of the trapping centre parameters depends on several factors including the spatial location of traps in the collector. The latter requires characterization of the in-depth charge location adding to the complexity of the trapping measurements (Afanas’ev and Adamchuk, 1994).

5.6 What Charge Injection Technique to Choose? Depending on ultimate goal of the charge trapping experiment, different requirements to the optimal injection method can be formulated. For instance, the on-line device testing requires compatibility with the used fabrication technology and large throughput of the analysis. At the same time, the type of material systems experiences only little changes associated with gradual evolution of the production process. However, as we will mostly be interested in the spectroscopic characterization of electron states in different collector materials, other demands like universality of the technique, high degree of injection monopolarity, wide range of injected carrier density, and possibility of independent control of electric field gain more significance. Therefore, it seems useful to compare the properties of different injection techniques discussed earlier in this chapter. For collector materials with low interface barriers the thermoionic (the Schottky) emission represents the most simple, universal, and, therefore, widely used injection method. Other techniques become of interest only when the barrier height is so large that thermoionic current appears to be below the necessary level. Table 5.6.1 summarizes properties of different injection methods relevant to the last case, i.e., to the samples with a wide bandgap collector material and large interface barrier heights. These methods are compared on basis of several empiric criteria which will be briefly discussed below. Table 5.6.1 Comparison of different charge injection techniques suitable for trapping spectroscopy. Injection method

IPE

Tunnelling

ACI

Injection from p–n junction

Photo generation

Range of applications Technical simplicity Sample processing Current control Current range Current uniformity Monopolarity Charge sign change

+ − −/+ + − + + −

+ + + − + − − −

− −/+ − − + − + −

− + − + + + + −

+ − −/+ + −/+ + − +

122


First, the range of applications refers to the potential of using the particular injection technique in samples of different sort, e.g., with metallic or semiconductor electrodes, different collector films, etc. Obviously, the methods employing optical excitation (IPE, PC) and tunnelling can be applied in all the cases. By contrast, only semiconductor emitters of sufficient quality can be used to enable ACI or non-avalanche injection from a sub-surface p–n junction. Moreover, ACI also requires a high-quality dielectric collector layer because a leakage current might prevent application of electric field of the strength sufficient for development of avalanche breakdown in semiconductor. In practice, only high-quality SiO2 layers have the quality sufficient for ACI, while its application to prospect other insulating materials remains questionable. Second, the criterion of technical simplicity refers to the experimental arrangement of the injection. The use of optical excitation (IPE, PC) requires additional optical instrumentation and, therefore, makes these methods more laborious and costly. By contrast, injection from p–n junction and tunnelling can be realized by simple biasing of the sample with simultaneous current monitoring which makes them most suited for a rapid evaluation of the material properties. In the case of ACI a special generator system with a feedback loop is required to maintain the constant injection current (Nicollian and Brews, 1982). Though this equipment is usually custom-designed, the measurements remain 100% in an electrical domain and do not require any expensive optical elements. Next, the sample processing criterium indicates the complexity of preparation procedure needed to fabricate the structure enabling the application of desired injection technique. Obviously, the tunnelling needs just a conducting contacts which can be fabricated in great variety of ways with minimal requirements to area, thickness uniformity, etc. The optical techniques (IPE, PC) set an additional requirement of sufficiently transparent optical input but experience shows that it adds only a little to the complexity of fabrication. The ACI faces much larger challenges because the semiconductor emitter with doping range in a narrow region must be used (Nicollian and Brews, 1982). The latter precludes, for instance, use of the technique at temperatures below the dopant frees-out point. Finally, injection from p–n junction requires formation of the corresponding doping profile and lateral isolation of the injecting areas making the methods strongly bounded to the microelectronic processing facilities. The current control refers to the possibility of the carrier injection rate variation while keeping the strength of electric field in the collector constant. The methods in which the carriers with energy sufficient to overcome the interface barrier are supplied by photons (IPE, PC) or from the reverse biased p–n junction have an external experimental parameters which allow such a current variation (light energy or intensity, p–n junction bias). In the case of tunnelling, FN expression (5.3.1) indicates the voltage as the only external parameter affecting the injection rate. Moreover, injection in this case is limited to the high-field range which is not necessarily the best choice for analysing trapping properties. The avalanche injection potentially allows the current adjustment by varying the voltage pulse frequency but, as discussed in Section 5.4, the electric field cannot be considered constant during the ACI. Therefore, the strength of electric field remains actually uncontrolled in this case and, similarly to the case of tunnelling, is limited to the range of high fields. The range of the injected current density directly affects the possibility to detect carrier trapping by centres with different capture cross-sections. In the case of IPE, the low value of quantum yield makes impossible reaching high current densities because of sample heating. This method suites well the investigation of traps with large cross-sections, but defects with σ < 10−17 cm2 can hardly be characterized. Potentially, PC allows one to overcome the heating issue because of much larger quantum efficiency of electron– hole pair generation than the IPE from an electrode, but a light source of high brightness in the photon energy range hν > Eg (collector) is required. All the electrically stimulated injection techniques easily outperform the optical methods in this sense and allow one to reach the injected charge densities in excess of 1 C/cm2 .


123

The current uniformity requirement is essential when the trapping analysis is supposed to deliver information regarding the capture cross-section values. As will be discussed in Chapter 7, the correct extraction of the cross-section is possible only if the free carrier concentration can be considered as a constant over the entire studied volume of the collector. Thanks to the relatively weak (power) dependence of the barrier transparency on the barrier height in the case of the over-barrier IPE, the latter method provides injection with good lateral uniformity. The same is also true for the PC and injection from p–n junction. By contrast, in the case of tunnelling any local reduction of the interface barrier height would lead to greatly (exponentially) enhanced local current density. Therefore, the average current density may significantly deviate from the real local one. Also, the tunnelling occurring via some intermediate electron level of a defect or impurity will also add to the current density uncertainty because it will always be correlated with the spatial location of the defect. In the case of ACI, the effective temperature of charge carries will be strongly affected by the local non-uniformities of electric field which might be caused by trapped charges. This would lead to laterally non-uniform injection profile and, in turn, to problems with calculation of the injected carrier concentration. The monopolarity of injection refers to the possible presence of charge carriers of opposite signs in the collector. Would this happen, the trapping kinetics will be affected by recombination (annihilation) effects precluding a simple and, therefore, reliable first-order kinetics description. Obviously, the PC results in incorporation of carriers of both signs in an equal amount and cannot be considered as truly monopolar as discussed in Section 5.5. In the case of tunnelling the monopolarity is also an issue because of possible hot-electron-induced hole emission from anode (Vargheze et al., 2005) and impact ionization in the collector (Knoll et al., 1982). Three other methods still can be considered to deliver a monopolar carrier flux as long as regime of injection from only one interface is realized. The latter can be achieved, for instance, by using emitter and field electrode materials with substantially different barrier heights at their interfaces with collector. In some cases investigation of recombination effects is of particular interest by itself because comparison of the capture and annihilation cross-section allows to make a judgement regarding charge state of the trapping site (Rose, 1963; DiMaria, 1978). This makes important the possibility to inject charge carriers of opposite sign into the collector layer in the same sample. The only technique which enables this is photogeneration in the strong optical absorption range discussed in the previous section which places this method to a somewhat special position. All the other techniques are either do not allow second type carriers to be injected or, else, this injection cannot be reliably quantified. With an unknown je /jh ratio no quantitative information regarding recombination characteristics of the defects can be obtained. When summarizing the features of the considered charge carrier injection techniques one easily recognizes that none of the methods alone is able to provide an experimentalist with a universal tool suitable for all the purposes. For this reason several methods are combined in one sample, e.g., when ACI of holes is combined with electron IPE or tunnelling electron injection. However, as can be noticed from Table 5.6.1, the optically assisted injection methods are most suitable for spectroscopic applications if not considering traps with very small capture cross-section and the device-like sample structures. Taking into account that the sample and instrumentation requirements are basically identical for IPE and photogeneration of carriers, their combination seems to be the best suited for the spectroscopic purposes. To this must be added that the use of very low (the picoampere level) photocurrents as probes for trapped charges allows one to obtain, in the same experimental arrangement, the information regarding the trapped charge density and spatial location. This probe mode can be realized by simple attenuation of the exciting light to the level at which the photocurrent is not affecting the trap occupancy in any measurable way. With this charge quantification technique discussed in the next chapter, the IPE/PC photoinjection emerges as the most valuable source of spectroscopic information concerning trapping sites in the collector material.

CHAPTER 6

Trapped Charge Monitoring and Characterization

The determination of a trap capture cross-section requires calculation of the trapping probability as a function of the injected charge carrier density (see, e.g., Ning and Yu, 1974). Therefore, in addition to the injected carrier density that can be directly determined by integrating the current over the time of injection, one must find a way to quantify the density of carriers trapped in the collector material. The trapped carrier density is to be determined during the injection or, would the injection be interrupted, after each injection step. The principal requirement here is that the trapped charge must remain unperturbed by the experimental method used to measure its density. The latter limits the methods to those sensing the charge-induced electric field, which would be referred in the following discussion as the charge monitoring methods. Unfortunately, these methods are able to provide only limited information regarding the charge. At best, the charge density and the centroid of its spatial distribution can be evaluated. More complete characterization of the trapped charges is usually based on removal of the trapped carriers from collector or even employs the sample destruction when it is done using the etch-back charge profiling methods (Nicollian and Brews, 1982). Nevertheless, these charge characterization techniques are still can be applied to provide more detailed information on the trap properties. They can even be used to determine properties of several types of traps provided they can be selectively filled during injection to enable reliable separation of their contributions. The latter can be ensured by combining the charge injection and the trapped charge monitoring to pre-set the injected carrier density corresponding to filling of the centres with a particular capture cross-section. Obviously, in the latter case different traps will be characterized by using injection experiments in different samples. In this chapter several approaches to the charge characterization and monitoring will be overviewed. In addition, the last section will be devoted to the detection of atomic hydrogen liberation which frequently appears to be a concomitant effect of the charge injection and in some cases may also influence the charging process.

6.1 Injection Current Monitoring The charge carrier injection processes overviewed in the previous chapter have a common feature, which consists in significant dependence of the injection current on the strength of electric field applied to the emitter/collector interface. Would the charge carrier trapping in the collector during the injection lead to a variation of the field, the injection rate will change accordingly. When limiting consideration to the case of monopolar injection, the trapped charge will always cause a partial compensation of the externally applied electric field resulting in a decrease of the current under constant injection bias conditions. In order 124

Trapped Charge Monitoring and Characterization Q0

125

Q Q

V

F V/d

(a)

x

x

V

V V

F V/d (V V)/d F1

F V/d F1

(b)

(c)

Fig. 6.1.1 Band diagram of emitter/collector/field electrode sandwich structure biased by a voltage V without charge in the collector layer (a), after tapping a negative charge Q at distance x from the emitter (b), and after application of additional bias V to the field electrode in order to maintain the same strength of electric field at the emitter/collector interface (c).

to maintain the injection rate at the same initial level (the constant-current injection mode), the externally applied bias has to be adjusted (increased) to compensate for the electric field of the trapped charge. Therefore, the increase of external field is approximately equal to the field produced at the injecting interface by the trapped carriers and can be used to monitor the density of trapped charge during injection. To illustrate this approach to charge monitoring let us assume that the collector of thickness d is sandwiched between the emitter and the field electrodes as illustrated in the band diagrams shown in Fig. 6.1.1. Would the carrier trapping occur in one plane at a distance x from the surface of emitter and the trapped charge density will be equal to Q(x), the corresponding variation of electric field at the emitter/collector interface will be given by expression similar to Eq. (2.2.15), i.e., F(x) =

Q(x) d − x . ε 0 εD d

(6.1.1)

This field will be subtracted from the strength of the field initially applied to the interface through the external bias of the field electrode F = V /d (cf. Fig. 6.2.1a). To compensate this field variation, the voltage V is to be increased by: V (x) = −Fd =

−Q(x) (d − x). ε 0 εD

(6.1.2)

Would the trapped charge be distributed inside the collector with the volume density ρ(x), by using Q(x) = ρ(x)dx and integrating across the whole thickness of the collector layer, one obtains following expression for the voltage adjustment needed to compensate the influence of the trapped charge (Powell and Berglund, 1971): −1 V = ε0 εD

d ρ(x)(d − x)dx, 0

(6.1.3)

126


or, when applying the charge centroid formulation (cf. Eqs (2.2.14) and (2.2.15)): V =

−Q (d − x). ε 0 εD

(6.1.4)

Eqs (6.1.3) and (6.1.4) indicate that the adjustment voltage V is proportional to the trapped charge density Q which makes possible its direct use when determining the capture cross-section of a trap. Indeed, the derivative of Q on the injected carrier density will be equal to that of V plus/minus a constant making the correct extraction of capture cross-section possible (Ning and Yu, 1974). Thus, monitoring of the bias voltage in the course of the constant-current injection experiment is justified if only the capture cross-section spectrum is of interest. The determination of real trap densities is more complicated because of necessity to know the centroid of the trapped charge distribution x¯ . Would the charge traps of several varieties be present in the collector, the centroids of their in-depth distributions remain to be determined separately. This makes the trap characterization a multi-step procedure. First, the V kinetics is monitored and analysed to separate contributions of traps with different (distinguishable) cross-sections. Next, the injection experiment is repeated with interruptions corresponding to the sequential filling of the observed traps. For each trap the spatial location (centroid x¯ ) and the corresponding total V shift should be determined to make possible evaluation of the trap density by using Eq. (6.1.4). So far the field produced by the trapped charge carriers is assumed to be laterally uniform at least in the plane of the injection emitter/collector interface. In reality, however, this may not be the case because of possible lateral non-uniformity of the trap spatial distribution and the discrete nature of the trapped charges. To remain negligible, the spatial scale of the non-uniformities and/or the mean distance between the trapped carriers (related to their volume concentration nt as rmean = (nt )−3 ) must be much smaller than the distance from the charge trapping volume to the point of observation. The latter corresponds to the surface of emitter and is given by the charge centroid value x¯ . Therefore, monitoring of the charge trapping near the injecting interface using the current measurements is unreliable in general because the charge-induced distortion of potential barrier at the emitter/collector interface will automatically lead to the lateral non-uniformity of injection. In this case the adjustment of the applied bias will predominantly increase the injection rate across the charge-free areas of the interface while the current through areas close to trapped carriers will nearly be blocked by the Coulomb repulsion. In fact, this problem was pointed out already by Powell and Berglund (1971), but there still no satisfactory solution yet. The only way to assess the charge density near the injection interface is to interrupt the injection and apply other, less sensitive to the charge discreetness, monitoring technique. Thus, the injection current monitoring methods cannot reliably evaluate the trapping process close to the interface, which also makes questionable their applicability to structures with ultrathin (in the order of few nanometers) collector layers sandwiched between the emitter and field electrodes. Another possible source of problems in the charge monitoring through current is related to artefacts caused by mutually compensating charges located in spatially different parts (layers) of the collector. According to Eqs (6.1.3) and (6.1.4), charges located far from the injecting interface have only a minor effect on the injection rate. Therefore, a relatively small charge of opposite sign located (trapped) closer to the emitter/collector interface might be able to overcompensate the field of remote charges. For instance, in the case of Fowler–Nordheim FN tunnelling injection the impact ionization in the collector (process d in Fig. 5.3.2) would result in generation of carriers of opposite sign and their drift towards the emitter. The latter may cause accumulation of a compensating charge (positive charge of trapped holes for the case shown in Fig. 5.3.2). In general, only a highly monopolar injection current can be used to monitor the trapping.


127

As a final remark, it is also worth mentioning here that the distortions of potential barrier at the interface of an ideally conducting (metal) emitter and a dielectric collector are predicted to depend on the spatial location of the charge (Powell and Berglund, 1971; Brews, 1973a): Charges located in the plane of the interface are expected to give no effect as their contribution to the electric field at the plane corresponding to the maximum of the image-force interface barrier at x = xm (cf. Fig. 2.2.2) is zero. According to this description, only charges located at a distance x > xm from the surface of emitter will affect the barrier and the corresponding rate of injection. Therefore, the current will be almost insensitive to the charges located in the region 0 < x < xm prompting application of an alternative charge measurement method(s).

6.2 Semiconductor Field-Effect Techniques The electric field created by the charge of trapped carriers can also be observed through its effect outside of the collector layer if the latter is non-conductive, i.e., no charge screening occurs. In a most simple way, one might detect the field of trapped charges using the Kelvin probe with oscillating capacitor though this technique is prone to adsorption-induced instabilities and require large sample area (Lagowski and Edelman, 1998). Alternatively, a semiconductor space–charge layer can be used as the field-sensing element (Sze, 1981; Nicollian and Brews, 1982). Once the band bending at the surface of semiconductor is measured as a function of applied electric field, the additional contribution of trapped charge to the field would lead to a voltage shift of this dependence in a way similar to the described in previous section for the voltage dependence of the injection current. Equations (6.1.3) and (6.1.4) remain valid in this case but the measured voltage now refers not to some constant current point but to a pre-selected value of the semiconductor surface potential. The reference points are usually selected in accordance with the technique applied to measure the surface potential (band bending) in semiconductor. In the cease of capacitance–voltage (CV) measurements, it is often referred to zero band bending (the flatband point VFB ) or to the Fermi level position in the middle of semiconductor bandgap (the midgap point VMG ), which meaning is illustrated in Fig. 6.2.1. The capacitance values corresponding to these band bending values can easily be calculated for the known semiconductor doping, collector specific capacitance, and temperature (Sze, 1981; Nicollian and Brews, 1982). The measurements of flatband and midgap voltage variations give identical results as long as influence of the interface states with energy levels between the midgap and the Fermi energy in the bulk of semiconductor remains negligible. The same would be true for the flatband voltages measured using Q EC

EC

EF

VMG

EV

EF

(a)

Q

EF VFB EF

EV

(b)

Fig. 6.2.1 Energy band diagrams of semiconductor (the emitter)–insulator (collector)–metal (the field electrode) structure at midgap (a) and flatband (b) points in the presence of a negative charge in the insulator.

128


n- and p-type semiconductor sensors if there are no semiconductor–collector interface traps present. However, the latter is rarely the case, and the possible influence of interface states always remains an issue when semiconductor band bending is used to monitor the charge trapping in collector. To account for this effect, the contribution of interface states to the observed CV curve shift can be directly quantified when comparing the charge accumulation kinetics measured in samples with n- and p-type doping (see, e.g., de Nijs et al., 1994; Druijf et al., 1995). The application of the latter approach is illustrated in Fig. 6.2.2 in the case of electron–hole pair generation in ultrathin layers of several insulators on (100)Si (Afanas’ev and Stesmans, 2002; 2004b). The charge is seen to be marginally sensitive to the conductivity type of silicon substrate indicating relationship of the observed positive charges to the holes trapped in the insulating collector oxide. This is, however, not a general rule. In other material systems, e.g., in the oxidized SiC, the interface state charges may 4 3 2 1

Al2O3

VFBCOX/q (1012 cm2)

0

(a)

3

2

1

SiOx /ZrO2 (b)

0 4 3 2 1

SiO2 (c) 0 0

5

10

15

20

Electron–hole pairs (1014 cm2)

Fig. 6.2.2 Normalized flatband voltage shift as a function of the electron–hole pair density generated by 10-eV photons in mental–oxide–semiconductor (MOS) capacitors with different insulators: (a) Al2 O3 of 15 (•), 5 () and 3 () nm thickness; (b) 0.5 nm SiOx /ZrO2 stack with ZrO2 thickness of 20 () and 5 (, ) nm; (c) thermal SiO2 with thicknesses of 3.0 () and 2.9 () nm. The filled and empty symbols correspond to MOS capacitors fabricated on n- and p-type (100)Si substrates, respectively. The last point on each curve shows the neutralizing effect of 3 × 1015 electrons/cm2 , photoinjected from Si.


129

provide dominant contribution to the CV curve shift observed upon electron injection (Afanas’ev et al., 1999). In any case, comparison between the CV curves measured in n- and p-type semiconductor samples appears to be the only reliable method to evaluate the contribution of interface traps to the total charge. Particularly, when the measurement temperature is lowered, the integral of the interface trap charge across the entire semiconductor gap can be determined from the difference of flatband voltages of n- and p-type samples (Stesmans and Afanas’ev, 1998). Application of the midgap voltage measurements instead of flatband one was also suggested to exclude the interface state charge effects (Scoggan and Ma, 1977). This technique is based on the assumption that the midgap point, at least in the case of silicon, is close to the point of electroneutrality of semiconductor surface. Therefore, the shift of the midgap voltage point of the CV curve (naturally, identical in the n- and p-type semiconductor samples) was thought to provide the net density of the charge trapped in the insulating collector. However, direct comparison of charges deduced from the midgap voltage shift measurements to those derived from the trapped charge thermal depopulation curves revealed substantial contribution of interface traps to VMG variation (Shanfield and Morivaki, 1987). Therefore, there still no alternative technique to determine the net trapped charge except of evaluating the interface trap contribution to the CV curve shift independently. Other techniques enabling determination of the band bending in semiconductor as a function of applied electric field may also be used to monitor charge trapping in the insulating material above semiconductor surface. One may use for this purpose the value of photovoltage which, if the intensity of exciting light is sufficient to make the bands at the surface of semiconductor flat, yields the band bending value directly (cf. Fig. 6.2.3) (Lam, 1970; 1971; Schroder, 2001). By tracing the photovoltage dependence on the externally applied electric field, the contribution of trapped charges can be quantified in the same way as when using the CV curve measurements. However, problems related to the carriers trapped by interface states remain unresolved. In addition, one must also check the data for negligible contribution of the diffusion component of the photovoltage (sometimes referred to as the Dember photovoltage) because of high intensity of the exciting light needed to attain the flat bands. If the collector material layer is embedded as gate insulator in metal–insulator–semiconductor transistor structure, the transistor threshold voltage VTH can also be used to monitor the charge trapping. This technique is similar to the CV measurements but uses the density of charge carriers in the inversion channel to measure the strength of electric field at the semiconductor/insulator interfaces. An advantageous feature of this method is its technical simplicity and immediate applicability to the real device structures. However, the contribution of interface traps to VTH shift remains to be evaluated separately (McWhorter and Winokur, 1986). As one interesting modification of this technique one should mention here the Q

Q VPH

EC

EF

EV

In darkness

EC EF

EV

Illumination

Fig. 6.2.3 Light-induced changes in the energy band diagram of metal–insulator–semiconductor structure with photovoltage (VPH ) value indicated for the case of saturation photovoltage (an intense illumination).

130


‘pseudo-MOS’ transistor which can be activated in a thin semiconductor layer on insulating collector film by applying bias to the backside of a sufficiently conducting substrate (Cristoloveanu and Williams, 1992). In this case no transistor processing is required because a high lateral resistance of thin semiconductor film appears to be sufficient to isolate the ‘pseudo-transistor’ formed by a four-head point resistance probe from the leaky edges of the sample. Among the methods described, the CV measurements represent the most widespread ones because of their technical simplicity and fast sample turn-around. By using this kind of charge monitoring one may also address the charge characterization issue in terms of the in-depth distribution profile. The profiling procedure consists in a stepwise etching of the collector layer followed by repetitive application of field electrode after each etch-off step and recording of the CV curve. By writing the contributions of the interface state charge and of the charge trapped in the collector in separate terms, the flatband voltage measured with respect to an ideal (zero) value can be expressed as follows (Woods and Williams, 1976):

VFB

Qss d 1 = ms − − ε 0 εD ε0 ε D

d ρ(x)(d − x)dx,

(6.2.1)

0

where ms is the work function difference between the applied field electrode and the semiconductor substrate, and Qss the density of charge per unit area trapped by semiconductor interface states at flatband point. It is reasonable to assume that, as the etching affects the collector layer only, ms and Qss will remain unchanged upon the collector thinning. Therefore, all the changes in VFB will be associated with decreasing insulator thickness and the density of charge it contains (see, e.g., Afanas’ev and Adamchuk, 1994): VFB = VFB (di ) − VFB (di−1 ) Qss (di−1 − di ) Q(di−1 )di−1 Q(di )di 1 = + − − ε0 εD ε0 ε D ε0 εD ε0 εD

di−1 xρ(x)dx,

(6.2.2)

di

where, di Q(di ) =

ρ(x)dx; i = 1, 2, 3, . . . . 0

If in the removed layer of the collector no charge was present, i.e., ρ = 0, the last term in Eq. (6.2.2) vanishes and Q(di−1 ) = Q(di ). In this case VFB represents a linear function of the remaining collector layer thickness until the etching reaches the charge-containing layer. The latter will manifest itself by deviation of the VFB (d) dependence from the straight line. If the collector thickness variation per etching step d = di−1 − di is small enough to neglect variation of the charge density ρ over the removed layer, one can evaluate the corresponding removed charge density as: Q(di ) = Q(di−1 ) − ρ(di∗ )di , where, di−1 (di )2 di + di−1 xρ(x)dx = ρ(di∗ ) ; di∗ = . 2 2 di

(6.2.3)


131

Then expression (6.2.2) can be re-written as follows: ε0 εD VFB (di ) = Qss d + Q(di )d

+ ρ(di∗ )d

d di + 2

.

(6.2.4)

If the values of the intermediate layer thickness di (i = 1, 2, 3 . . .) are determined by some independent technique (ellipsometry, accumulation capacitance value, etc.), the second derivative of Eq. (6.2.4) provides one with the local charge density averaged over the etch step thickness interval. Would the collector etching be combined with the capacitance-voltage measurements in the same electrolyte cell (Nabok et al., 1984), the trapped charge profiling can potentially be attained by simultaneous recording of the flatband voltage and of the accumulation capacitance in electrolyte–insulator–semiconductor structure. However, a low density of measured current severely limits accuracy of this technique. A simplified version of the etch-back technique can be applied if only the trapped charge centroid value is of interest which is pertinent to the most of the trap spectroscopy studies (Woods and Williams, 1976). As can be seen from Eq. (6.2.1), the removal of the charge-free collector layer will lead to a linear decrease of VFB (or VMG ) with decreasing thickness of the collector. Next, one can determine contribution of the interface charges by performing the etch-back measurements in the control, not subjected to any charge injection sample (line 1 in Fig. 6.2.4). This line can be used as the reference when the etching experiment is repeated in the sample subjected to injection and, therefore, containing some trapped charge (line 2 in Fig. 6.2.4). The latter will also result, at least in the first etching steps, in a linear decrease of VFB but with different slope. The lines obtained by extrapolation of VFB (d) dependences will intersect at a point d* corresponding to zero value of integral in the right-hand part of Eq. (6.2.1). Being re-written in the charge distribution centroid notations (cf. Eq. (6.1.4)) this condition immediately yields d ∗ = x¯ enabling direct readout of the centroid value. The weak points of this method consist in a limited accuracy caused by need of the extrapolation procedure. Also the assumption of only minor changes of the interface state charge in the course of the injection experiment may add to the uncertainty. The described etch-back techniques of the trapped charge characterization have obvious problem that the collector sample layer is damaged (etched off) during the analysis. As an alternative method one might consider possibility of a non-destructive charge characterization by using the measurements of electric 10

Midgap voltage (V)

2 8 6 1 x

4 2 0

0

50

100

150

200

Remaining thickness (nm)

Fig. 6.2.4 Variation of the midgap voltage upon removal (etching) of the insulating collector layer in the control (curve 1) and charge-injected (curve 2) samples illustrating determination of the charge centroid position x¯ .

132

Internal Photoemission Spectroscopy: Principles and Applications F1

F2 x

Q

Fig. 6.2.5 Illustration of electric fields created by a negative charge trapped in one plane distance x¯ from the surface of emitter. F1 and F2 are the additional fields at interfaces of collector with emitter (left) and field (right) electrodes.

field the charge induces at both interfaces of the collector layer. The idea of this methods is illustrated in Fig. 6.2.5 using an idealized charge location model in one plane at a distance x¯ from the surface of emitter. For the total thickness of the collector layer d the trapped charge of density Q will induce the electric field at the left (F1 ) and right (F2 ) interfaces of the collector equal to (DiMaria, 1976; DiMaria et al., 1977a): F1 =

Q d − x¯ ; ε0 εD d

F2 =

Q x¯ , ε0 εD d

(6.2.5)

which then can be used to determine charge parameters Q and x¯ : Q = ε0 εD (F1 + F2 );

x¯ = d

F1 . F1 + F 2

(6.2.6)

Measurements of the charge-induced electric fields F1 and F2 can be performed using a number of methods. For instance, if the shifts of the current–voltage curves of electron tunnelling are measured for both interfaces of the collector layer (V1 and V2 ), they provide the field variation directly: F1 = V1 /d and F2 = V2 /d, respectively. Another possibility is to use semiconductor material for both the emitter and the field electrodes. In such semiconductor–insulator–semiconductor structure the depletion can be observed using the CV curve measurements for both electrodes enabling fast characterization of the trapped charge. As suitable materials for semiconductor field electrodes one may consider un-doped (or low-doped) poly-crystalline semiconductor films, like Si. Another possibility is opened when analysing buried field insulator layers in semiconductor–on-insulator structures obtained by epitaxial overgrowth, ion implantation (Separation by IMplanting OXygen, SIMOX technology, see for a short review, Revesz (1997)), wafer bonding (Mazara, 1993), zone melting re-crystallization of the deposited over-layer (Zavracki et al., 1991), etc. By applying the ‘double-CV’ (Nagai et al., 1985) or ‘pseudo-MOS’ transistor measurements (Cristoloveanu and Williams, 1992) to these structures the charge density and its centroid can be evaluated. However, the charge centroid determination is not always relevant to characterization of the real in-depth distribution of the trapped charge carriers. This is related to two basic aspects of the charge centroid approach. First, there should be no charge compensation in the collector layer. Would two charges of opposite sign be located at two interfaces of the collector layer, Eq. (6.2.6) may result in a negative charge centroid value which has no physical meaning. Second, in the charge centroid formulation (cf. integral before Eq. (2.2.15)) any symmetric in-depth charge distribution across the collector layer would


133

result in x¯ = d/2, even if two charges are located in the planes of interfaces between the collector and two electrodes. Therefore, the location of charge centroid in the bulk of the collector cannot be immediately used as an argument indicative of the ‘bulk’ nature of the observed trapped sites. One might perform centroid determination measurements in samples with different thickness of the collector layer to observe possible relationship between the volume of the material and the density of traps. Another way to exclude uncertainties caused by interface charges is to apply photoinjection current probing methods which are believed to be marginally sensitive to the interface charges (Powell and Berglund, 1971; Brews, 1973a). These techniques will be discussed in the next section.

6.3 Charge Probing by Electron IPE When attempting to use injection of charge carriers to monitor trapping-induced variations of electric field in the collector, one must ensure that the measurement procedure by itself has no substantial effect on the charge density. For this reason, in the ‘probe’ mode the injected current density must be low enough, i.e., the density of the injected per unit area carriers must be much smaller that σ −1 , where σ is the capture cross-section of the dominant trap. Next, as the net current measured in an external circuit is equal to the sum of all the current flowing through the collector layer, the monopolarity of injection must also be ensured in order to extract the electric field variation value only at one selected interface. In practice, these requirements exclude application of the field-induced currents as well as of the photo-conductivity (PC) from the list of reliable charge monitoring methods. Only the monopolar internal photoemission (IPE) meets the above conditions which, from the early days on, made IPE the method of choice for charge characterization despite its technical complexity as compared to purely electrical measurements (Powell and Berglund, 1971; Brews, 1973a; DiMaria, 1976; DiMaria et al., 1977a). The idea of this measurement method is illustrated in Fig. 6.3.1 for the case of sensing of a negative charge in the collector using the IPE of electrons from both emitter and field electrodes. As compared to the charge-free sample (panels (a–c)), the repulsive field of the charge prevents IPE at low fields (panels (d–f)). Therefore, to attain the same value of the IPE current, the bias applied to the charged sample must be increased by voltages V + (for positive bias, cf. panel (e) in Fig. 6.3.1) or V − (for negative bias, cf. panel (f) in Fig. 6.3.1) causing the corresponding shifts in the voltage dependences of the photoinjected current along the voltage axis. The voltage shifts V + and V − are related to the charge-induced fields F1 and F2 given by Eq. (6.2.5) (DiMaria, 1976a; 1977b): V + = F1 d =

Q (d − x¯ ), ε0 εD

(6.3.1a)

Q x¯ ε0 εD

(6.3.1b)

V − = F2 d =

enabling one to determine both the charge density and its centroid using Eq. (6.2.6). Examples of the charge-induced variation of the IPE current–voltage characteristics are shown in Fig. 6.3.2 for the case of electron trapping in SiO2 layer on (100)Si emitter crystal with a semitransparent Au field electrode (Afanas’ev and Adamchuk, 1994). The oxide layers were fabricated using two different methods, namely, the thermal oxidation in dry O2 at 1000◦ C to the oxide thickness of 66 nm (panel (a)) (for details see Afanas’ev et al. (1995a)), or by implantation of a high dose of O+ ions into Si and followed by high-temperature (1350◦ C) annealing (SIMOX, technology) resulting in a 400 nm thick oxide (for details see Afanas’ev and Stesmans, 1999). The oxides was charged by injecting ≈2 × 1016 electrons/cm2

134


(a)

(b)

(c)

V Q

(d)

V

(e)

(f)

Fig. 6.3.1 Energy band diagrams of emitter–collector–field electrode sample without (a–c) and with a negative charge trapped in the insulating collector layer (d–f). Panels show the cases of zero bias (assuming equal work functions of emitter and field electrode materials) (a, d), the onsets of electron IPE from emitter (e), and from field electrode (f). To reach the strength of electric field at the interface of emitter or field electrode sufficient to inject electrons into the collector layer, the bias applied to the charged sample must be increased by V + and V − , respectively.

using IPE from Si substrate (a) or by generating electron–hole pairs by 10-eV photons in the surface oxide layers (b). Upon this injection the IPE current–voltage curves corresponding to electron emission from Si (positive bias) or Au (negative bias) are seen to be shifted with respect to the control (uncharged) sample curves by V + and V − , respectively. In the first case close values of V + and V − suggest x¯ = d/2 indicative of a symmetric in-depth distribution of trapped electrons in the thermal oxide. By contrast, the oxide of SIMOX structure exhibits a much larger V + than V − which corresponds to predominant electron trapping close to Si substrate (¯x ≈ d/10) associated with the presence of silicon clusters in the insulating layer (Afanas’ev and Stesmans, 1999). It should be reminded at this point that Eqs. (6.2.5) and (6.3.1) are applicable only to the case of laterally uniform charge distribution. This conduction requires from the charges to be of sufficiently high density and located at a distance from the injecting interface exceeding the typical distance between the trapped electrons. For not too thin insulating collector layer (d > 20 nm) these conditions can be met for the charges located in the bulk of the collector material. However, the charges close to the interface cannot be considered as uniform ones because of their discrete nature (Powell and Berglund, 1971). As a result, the IPE-based charge profiling methods proposed by many authors (Powell and Berglund, 1971; Lynch, 1972; Shousha, 1980; Przewlocki, 1985) should be used with great degree of scepticism because the lateral variations of the charge density may lead to significant artefacts and erroneous interpretations.


135

0.3 IPE from Si Photocurrent (pA)

0.2 0.1

V

0.0 0.0

V

0.2 0.3 0.4 15

IPE from metal 10

5

0

5

10

15

Voltage (V) (a) 1.5 IPE from Si Photocurrent (pA)

1.0 0.5

V

0.0 V

0.5

IPE from metal 1.0 40

30

20

10

0

10

20

30

40

Voltage (V) (b)

Fig. 6.3.2 Charge-induced variation of the electron IPE current–voltage characteristics measured at photon energy of hν = 5.0 eV in Si/SiO2 /Au samples with thermally grown (a) and O+ -implantation produced (b) oxide layers; show the curves for uncharged sample, correspond to the curves observed after injection ≈2 × 1016 electrons/cm2 . The shifts of the curves to be used for charge characterization, V + and V − , are indicated by arrows.

Now we can consider the possibility of applying the electron photoinjection probe to analyse the trapped charge of the opposite sign, e.g., that of trapped holes. Attractive potential between the injected and trapped charge carriers leads to significant complications in the analysis because the impact of trapping must be taken into account. First, the density of the probing IPE current must be limited to a level at which annihilation of the trapped charge will lead only to a small (less, say, than 10%) variation in its density during charge characterization. Second, in the low field region the presence of positive charge in the bulk of the collector results in formation of a ‘giant potential well’ acting as a trap with 100% capture probability (DeKeersmaecker and DiMaria, 1980). This case is illustrated in Fig. 6.3.3 indicating two important consequences: (1) Not a single injected electron will be able to cross the entire collector layer. Therefore, the photocurrent measured in the external circuit will be the displacement one.

136


qV

Fig. 6.3.3 Band diagram of the emitter–collector–field electrode structure with a positive charge trapped in the bulk of the insulating collector layer. At zero and low externally applied bias IPE of electrons is possible from both interfaces of the collector.

(2) Electrons can now be injected simultaneously from both electrodes into the collector leading to mutual compensation of the displacement currents. To overcome these complications one might consider two options. First, one may apply the field electrode made of material with work function strongly different from the IPE threshold energy of the emitter. In this case, in a limited range of photon energies, the one-interface IPE can be ensured (DeKeersmaecker and DiMaria, 1980). The current measured in the external circuit in this case will be equal to the net displacement current: x¯ dQ , d dt

(6.3.2a)

d − x¯ dQ , d dt

(6.3.2b)

I+ = if electrons are injected from emitter, and I− =

if electrons are injected from the field electrode. However, analysis of these currents might be complicated if one of the collector electrodes is semiconducting. In this case one must also add to the external current the component related to semiconductor (de)polarization due to the changes in the surface potential (Aitken and Young, 1976): Isc = −

ε0 εD d , d dt

(6.3.3)

as well as the term corresponding to the displacement current (DiMaria et al., 1977b): d ID = − dt

xm ∂ρ x¯ 1− Q + dx, d ∂t

(6.3.4)

0

describing the contribution to the current of charge carriers which have not reached the opposite electrode because of trapping. These two contributions to the photocurrent may cause significant distortion of the


137

Photocurrent (pA)

1.5

1.0

VCO

0.5

0.0

0.5 30

20

10

0

10

20

30

Voltage (V)

Fig. 6.3.4 Charge-induced variation of the electron IPE current–voltage characteristics measured at photon energy of hν = 5.0 eV in Si/SiO2 /Au samples with a 100-nm thick thermally grown oxide. show the curves for the uncharged control sample, indicate the curve observed after injection ≈1 × 1015 holes/cm2 using generation of electron–hole pairs in the surface oxide layer by 10-eV photons.

current–voltage curve if the semiconductor surface appears to be in the condition prone to large band bending variation, e.g., in depletion. To avoid problems caused by the double-interface injection and the semiconductor space–charge layer response, both relevant to the range of low electric fields, one might limit the measurements to a highfield range (DiMaria et al., 1977b) aiming at determination of the so-called cross-over voltage (VCO ) corresponding to the onsets of the one-interface injection (DeKeersmaecker and DiMaria, 1980). The value of this voltage corresponds to the depth of the electrostatic potential well qV created by the positive charge as illustrated in Fig. 6.3.3 and depends of the charge distribution centroid. Once found, the cross-over voltages can be used instead of V + and V − values to characterize the trapped charge density and spatial location. The problem here consists in low accuracy of the method caused by low current density in vicinity of the cross-over point and a significantly distorted shape of the current–voltage curve, which makes extrapolation of current to zero less accurate. The distortion of the IPE current–voltage curves might be caused not only by the double-interface injection but, also, by the field-dependent trapping of the injected carriers inside the collector. The last point is illustrated in Fig. 6.3.4 which compares the electron IPE current–voltage curves in (100)Si/SiO2 /Au sample with a 100-nm thick thermally grown oxide prior () and after hole trapping (). Despite the additional attractive electric field introduced by the positive charge, the electron current after hole trapping is seen to become considerably lower after hole injection than in the control sample. This effect is caused by the field-dependent attenuation of electron current by trapping as discussed in Section 2.2.6. Potentially, the attenuation coefficient can also be used to estimate the positive charge density (cf. Fig. 2.2.7), but this would require pre-knowledge of the Coulomb attractive capture cross-section. 6.4 Charge Probing Using Trap Depopulation The measurements of the current or the charge passed the external circuit during removal of the trapped charge carriers from the collector layer may offer another way to charge characterization. This technique allows one to evaluate the charge density, spatial location, and, in some cases, other important parameters of the trapping site like thermal or optical energy depth, photoionization cross-section, etc. The experiment consists in monitoring the trapped charge outflow under conditions enabling depopulation of

138


(a)

(b)

Fig. 6.4.1 Illustration of two approaches to depopulation of traps in the insulating collector material: (a) by means of carrier excitation from the energy level of the trapping site into the transport band(s) of the collector and (b) by using injection of carriers of the opposite charge sign from the electrodes to neutralize the filled traps.

trapping sites filled during the preceeding injection step. Another option is to monitor the charge remaining in the collector after applying some depopulation excitation to the sample. There are several ways to empty the traps which can be divided in two groups schematically illustrated in Fig. 6.4.1 (Afanas’ev and Adamchuk, 1994). The first one includes techniques based on excitation of trapped charge carriers into the collector band states and their removal by the applied electric field (cf. Fig. 6.4.1a). The second option is to use neutralization (annihilation) of the trapped charge by injecting the carriers of the opposite sign from emitter or field electrodes (cf. Fig. 6.4.1b). The mechanisms of carrier detrapping are numerous (Jacobs and Dorda, 1977a, b; DiMaria, 1978; Barbottin and Vapaille, 1989; Bourcerie et al., 1989; Sah, 1990; Vuillaume and Bravaix, 1993; Wrana et al., 1997), and include thermally, optically, or field-stimulated carrier emission from the traps. Some of the most frequently encountered electron transitions are schematically illustrated in Fig. 6.4.2 for the case of depopulation of the filled electron traps. Among these mechanisms the thermal (a) and optical (b) detrapping are of particular interest because the analysis of detrapping rate dependence on the temperature and the photon energy, respectively, enables determination of the trapping level energy. In addition, these two depopulation techniques require no application of a high electric field to the collector enabling one to conduct measurements without complications associated with the background leakage current caused by injection from electrodes or by the defect-assisted charge transport across the collector. Therefore, it becomes possible to monitor the displacement current (or integral of it over time) related to the spatial location of the trapped charge with respect to the conducting electrodes applied to the collector (cf. Eqs (6.3.2a) and (6.3.2b)). When a trapped carrier is liberated and allowed to drift towards one of the collector electrodes without being re-trapped, it induces the displacement current in the external circuit of the emitter–collector–field electrode structure. The total charge induced by removal of one charge carrier can be evaluated using the Ramo’s theorem as (see, e.g., DeVisschere, 1990): q∗ =

x q, d

(6.4.1)

where q is the carrier charge, x is the distance it travelled, and d is the thickness of the collector. One has two options in collecting the liberated charges: By applying the bias of appropriate value and polarity


hv

139

hn

b

(c)

(b)

(a)

Et

(d)

(e)

(f)

Fig. 6.4.2 Schemes of carrier transitions contributing to depopulation of electron traps: (a) thermally induced (phonon-assisted) detrapping, (b) optical depopulation, field-induced detrapping via tunnelling to the collector band (c) or to the nearby electrode (d), (e) impact ionization by a ‘hot’ electron, and (f) the trap-assisted tunnelling.

(a)

(b)

Fig. 6.4.3 Removal of charge carriers from the trapped sites with the opposite electrodes of the collector used to collect and count them. The voltage applied to the field electrode is positive (a) or negative (b).

the carriers may be forced to drift towards the emitter or, else, towards the field electrode, as illustrated in Fig. 6.4.3. The requirement here is that all the carriers must be collected at one electrode (Mehta et al., 1972; Kapoor et al., 1977a). To ensure the latter, the charge collected in the external circuit during depopulation can be measured as a function of the applied bias. Once all the carriers are collected at only one electrode, further increase in the bias voltage would not lead to any charge variation as illustrated in Fig. 6.4.4. Therefore, the saturation charge values, Q+ and Q− , will be equal to (Mehta et al., 1972; Kapoor et al., 1977a; Powell, 1977): Q+ =

d − x¯ Q, d

(6.4.2a)

140

Internal Photoemission Spectroscopy: Principles and Applications Q

Collected charge (arb. units)

1

V

0

1 40

V

Q

30

20

10

0

10

20

30

40

Voltage (V)

Fig. 6.4.4 Schematic shape of the depopulation charge–voltage curve illustrating the charge saturation levels Q+ and Q− used to characterize the depopulated charge and the saturation onset voltages V + and V − used to characterize the fixed (i.e., not available for depopulation) component of the trapped charge.

Q− =

x¯ Q, d

(6.4.2b)

where Q is the real density of detrapped charge and x¯ is the centroid of its spatial distribution. The superscripts refer to the polarity of bias applied to the field electrode with respect to the potential of the emitter. From Eqs (6.4.2a) and (6.4.2b) immediately follows: Q = Q+ + Q− ,

x¯ = d

Q− . + Q−

Q+

(6.4.3)

Potentially, the observation of the field-dependent depopulation enables characterization of not only the emptied traps but, also, of the built-in electric field in the collector associated with traps which are not available for depopulation under given experimental conditions. To demonstrate this one might separate the trapped charge in two portions. The first one which can be released, Qr , and the second component which remains unchanged during the experiment, often referred to as a fixed charge, Qf . The latter can be characterized through the observed voltages V + and V − at which the collected charge saturates (cf. Fig. 6.4.4) in a similar manner as it is done using voltage shifts of the IPE current–voltage curves. These voltages exactly correspond to the bias level needed to compensate the field of the trapped charge, both fixed Qf and that available for release Qr , at one of the collector interfaces (Mehta et al., 1972; Barbottin and Vapaille, 1989): d − x¯ r d − x¯ f d V+ = Qr + Qf , (6.4.4a) ε0 εD d d and V

−

x¯ r x¯ f d Qr + Q f , = ε0 εD d d

(6.4.4b)


141

where x¯ r and x¯ f are the centroids of the released and the fixed charges in the collector, respectively. The Eqs (6.4.4a) and (6.4.4b) correspond to the flatband conditions at the surface of the emitter and at the surface of field electrode (cf. Fig. 6.4.3) and are equivalent to Eqs (6.3.1a) and (6.3.1b). Next, would the depopulated charge density Qr and its centroid x¯ r be determined from the saturation values of the detrapped charge using Eq. (6.4.3), the density of the fixed charge remaining in the collector and its centroid can be found using following expressions: Qf =

ε0 εD + (V + |V − |) − Qr d

Qr x¯ r − ε0 εD V − x¯ f = ε ε . 0 D (V + + |V − |) − Qr d

(6.4.5a) (6.4.5b)

Though the accuracy of this approach might not always be great, it is sufficient to get an impression regarding the character of the fixed charge distribution in the bulk of the collector (with all the limitations of the centroid concept kept in mind). In the experiment of this kind the liberated charge carriers are used in a way similar to that of the monopolar IPE probing, but the carriers just move in the opposite direction (from the bulk towards the interfaces of the collector layer). Therefore, similarly to the case of the IPE probe current, one should address the conditions of applicability of this method (Afanas’ev and Adamchuk, 1994). First, as the depopulation of available traps must be studied at different biases, there should be possibility to repeat the experiments by re-filling the traps after each step without affecting the fixed charges. Else, one should to perform the depopulation analysis on the series of identical samples containing traps filled under the same conditions to attain equal densities of charges Qf and Qr . Though the latter would result in great sophistication of the experiment, apparently this is still the only method to investigate trapping centres of different type (e.g., photo-active versus photo-inactive) or the defects characterized by different depth of the trapped carrier energy level (see, e.g., Wrana et al., 1997). Second, the charge sign of the carriers liberated in the depopulation step and of those contributing to the fixed charge must be the same to ensure mutual repulsion. In the case of mutually compensating fixed charge and that available for release the already mentioned effect of the ‘giant potential well’ (DeKeersmaecker and DiMaria, 1980) (cf. Fig. 6.3.3) would prevent drift of the released carriers to the electrodes leading to their re-trapping. Unfortunately, the co-presence of mutually compensating charges is often encountered in metal oxide insulators (see, e.g., Afanas’ev and Stesmans, 2004b) and the only feasible way to ensure that the charges of only one sign are present is to ensure the monopolar character of the filling injection step. It is also potentially possible to neutralize the trapped carriers of one sign by using the additional annihilating injection step that employs a large value of the Coulomb attractive cross-section typical for this process (DiMaria, 1978). However, the knowledge of the neutralization process kinetics in the chosen range of electric field is required to ensure the complete removal of the compensating charges. 6.5 Charge Probing Using Neutralization (Annihilation) From the above discussion regarding the charge-probing techniques employing analysis of the injected or liberated charge carriers transport it becomes obvious that substantial influence of carrier trapping in the charge neutralization (annihilation) event leads to significant complications in interpretation of the results. Nevertheless, one might attempt to use the neutralization by itself to obtain information on the charge density and its in-depth distribution. The basic idea of this approach consists in observation of the charge annihilation using the charge-sensitive monitoring method like CV measurements while

142


supplying the carriers of the opposite sign to a limited volume (layer) of the collector material. The observed decrease of the trapped charge density caused by this spatially limited injection can be associated with the charge density in the layer which is made accessible to the neutralizing charge carriers enabling one to perform the in-depth charge profiling (Chang and Lyon, 1986; Adamchuk and Afanas’ev, 1992a; Afanas’ev and Adamchuk, 1994). In its most simple version the charge-annihilation profiling method uses the fact that electron tunnelling across a triangular barrier shown in Fig. 6.5.1 supplies electrons to the collector region x > x0 where x0 is the point in space at which an electron enters the conduction band of the collector (Chang and Lyon, 1986). For the known interface barrier height and the strength of electric field F the value of x0 can easily be calculated: . (6.5.1) F This procedure enables one to obtain a histogram of the trapped charge in-depth distribution near the emitting interface as illustrated in Fig. 6.5.1 by observing the charge density annihilated by tunnelling injections performed at incremental strengths of electric field. However, despite its apparent simplicity, this charge profiling method uses assumption that the trapped positive charge has no effect on the local barrier height or on the local strength of electric field. Only in this case the distance x0 can be calculated using the known value of the applied external bias. This is obviously an oversimplification because the x0 =

EF EC

EF EC

EF

EC x3

x2 x1

Fig. 6.5.1 Schematic representation of the layer-by-layer trapped charge annihilation process using electron tunnelling from the Fermi level of the emitter under incremental bias voltage applied to the field electrode opposite to emitter.


143

discrete charge would have a strong effect on the interface barrier shape (cf. Fig. 2.2.4) (Adamchuk and Afanas’ev, 1992a). Therefore, the results of this kind of experiments would require numerical simulation to determine the real x0 values which, in turn, is possible only when the barrier height and dielectric constant of collector in the near-interface region are independently and reliably determined by using, for instance, the field-dependent IPE spectral measurements described in Chapter 4. In addition, the region of in-depth sensitivity of the tunnelling-based technique is limited to the values of x0 corresponding to the electron tunnelling rate sufficient to ensure complete annihilation of the charge which makes the profiling of bulk charge (large x0 ) impossible. On the other hand, small x0 values are also out of reach because of dielectric breakdown of the collector layer, when attempting to apply a high electric field. In an attempt to resolve the indicated problems associated with tunnelling-induced charge neutralization profiling method it was proposed to use, in a similar spirit, the IPE of electrons under retarding external bias (Adamchuk and Afanas’ev, 1992a; Afanas’ev and Adamchuk, 1994). The retarding bias is used to confine the layer of collector attainable to photoinjected electrons as illustrated in Fig. 6.5.2. By starting neutralization at some high negative bias and then decreasing it in a stepwise manner one can observe the decrease in the positive charge density by using CV curve shift while, at the same time, the charge passed in an external circuit Q can also be measured. These two measurements are related to the annihilated charge density and to its centroid as: d − x¯ VFB = Q, (6.5.2a) ε0 εD Q =

x¯ , d

(6.5.2b)

allowing straightforward determination of the density and centroid of the trapped charge annihilated per each neutralization step. After completing the measurements and obtaining a set of (Qi , x¯ i ) data pairs, one may further assume that, after each neutralization step, all the charges available for neutralization are annihilated (i.e., saturation is reached). Then we can spread each Qi charge over a layer of thickness 2(¯xi−1 , x¯ i ) centred at spatial plane xi in order to evaluate the volume density of the charge. In fact, there is even no need in performing CV measurements because the injection current would fall to zero once the electric field vanishes at the injecting interface with decreasing density of the attractive positive charge. The latter means that the variation of the flatband voltage must be always equal to the

VR

x1

x2 x3 x4

Fig. 6.5.2 Schematic representation of the layer-by-layer trapped charge annihilation process using electron IPE under decreasing values of retarding voltage applied to the field electrode opposite to emitter (not shown).

144

Internal Photoemission Spectroscopy: Principles and Applications 10

VMG(V)

8 6 4 2 0 0

2

4

6

8

10

VR(V)

Fig. 6.5.3 Variation of the midgap voltage determined using CV measurements in (100)Si/SiO2 (80 nm)/a-C/Au capacitors with the value of retarding voltage VR in the course of trapped hole annihilation measurements using IPE of electrons from silicon. The straight line indicates the ideal case VR = VMG .

decrease of the retarding potential applied to the field electrode. Validity of this picture can directly be proven by experimental results on annihilation of holes trapped in a 80-nm thick SiO2 layer on (100)Si shown in Fig. 6.5.3 (Afanas’ev and Adamchuk, 1994). The observed one-to-one correspondence between Vmg and the variation of the retarding voltage VR indicates that VR can be used instead of Vmg (or VFB ) in Eq. (6.5.2). Therefore, the IPE-based annihilation technique appears to be well suited for analysis of collector interfaces not only with semiconductors enabling CV measurements but, also, with other conducting materials. The just described IPE partial neutralization method also has an advantage of charge sensing in the bulk of the collector because the IPE can be performed under a low electric filed. However, there is important technical aspect which might potentially limit the accuracy of the charge characterization. One may notice from scheme shown in Fig. 6.5.2 that the strength of electric field at the interface between collector layer and the field electrode is much higher than that at the emitter–collector interface. The importance of the one-interface IPE condition becomes obvious when considering Eq. (6.5.2b) and subtracting the contribution of a current flowing from the field electrode in the opposite direction. Would the IPE quantum yields of the emitter and the field electrode be equal to Ye and Yf , respectively, the relative systematic variation of the charge centroid will be equal to (Afanas’ev and Adamchuk, 1994): ¯x Yf = x¯ Ye

d −1 , x¯

(6.5.3)

which allows us to evaluate the allowed quantum yields ratio: To attain a 10% accuracy for x¯ = 10 nm and d = 100 nm (Yf /Ye ) must be below 1%. Therefore, to ensure a negligible impact of IPE from the collector/field electrode interface on the charge measurements, the barrier height for electrons in the field electrode should be significantly higher than that of the emitter. Then it is possible to obtain the one-interface IPE regime by properly choosing the photon energy range. Transparent electrolyte electrodes as well as thin layers of semi-metals with low density of electron states near the Fermi level (e.g., amorphous carbon, a-C) can be used to block IPE from the field electrode. The typical result for the in-depth profiling of positive charges induced by injection


145

4 Charge concentration (1018 q/cm2)

Si/SiO2 (80 nm)

3

2

1

0

0

10

20 30 40 50 60 Distance from silicon (nm)

70

80

Fig. 6.5.4 Concentration profiles of positive charges observed after photogeneration of holes in a 80-nm thick oxides thermally grown on (100)Si in dry O2 at 1000◦ C (solid line) or in O2 + 1% HCl at 1150◦ C (dashed line). The partial charge neutralization measurements were performed using IPE of electrons from the silicon substrate when applying a 10-nm thick a-C injection-blocking interlayer between SiO2 and the semitransparent Au field electrode.

of holes at the interfaces of (100)Si with SiO2 layers grown using two different oxidation methods is exemplified in Fig. 6.5.4 as measured using a 10-nm thick a-C interlayer between the SiO2 collector and the Au field electrode. Substantially more deep distribution of trapped charges in the oxide grown in the presence of HCl becomes evident from this analysis.

6.6 Monitoring the Injection-Induced Liberation of Hydrogen The charge trapping properties of the collector material addressed so far were treated as purely electronic processes involving only two types of mobile charge carriers: electrons and holes. It is long known, however, that considerable contributions to charge transport and accumulation in insulators may stem from ionic species (Woods and Williams, 1973; DiStefano and Lewis, 1974; Williams, 1974; Hickmott, 1980; Greeuw and Verwey, 1984). While contributions of obvious ionic contaminants like alkali metals can successfully be minimized nowadays, there is one component of charge which is hardly avoidable in solid-state technology, namely, hydrogen. Hydrogen is easily transported in solid systems, it is also often used in chemical processes to deposit semiconducting or insulating compounds (Ritala, 2004; Campbell and Smith, 2004) or in the post-deposition annealing ambient (e.g., the forming gas). H is easily dissolved in metals making them an internal hydrogen source in metal-covered systems, it can be easily uptaken from an ambient through water or hydrocarbon molecules adsorption (Halbritter, 1999), thus becoming hardly avoidable component of any multi-layered solid-state structure. At the same time, characterization of chemical and physical states hydrogen occupies appears to be complicated by the absence of Auger transitions and by a low binding energy of 1s electron in the bonded H atoms (

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