Internal Photoemission Spectroscopy Principles and Applications
This page intentionally left blank
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
This page intentionally left blank
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
This page intentionally left blank
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 <5 nm) leaves open the question concerning the relevance of the results obtained at the initial stages of interface formation to the device-type heterostructures prepared by other technological methods. The latter may not only have a much larger thickness of the contacting solid layers causing significant structural and (or) thermo-mechanical mismatch but, also, are subjected to a number of technological treatments resulting in chemical reaction or inter-diffusion of components at the interfaces, changing their phase, etc. For instance, when fabricating an electronic device structure on semiconductor one must activate doping impurity using a high-temperature annealing (900–1000◦ C in the case of silicon (Sze, 1981)). This process unavoidably leads to structural and chemical modifications of interfaces accompanied by corresponding changes of the electron DOS, in particular defects. As chemical and structural conditions encountered at the annealed ‘buried’ interface cannot be reproduced when treating an ‘open’ surface structure, the electronic structure of the former should be characterized in a separate experiment(s). Obviously, one might attempt to bring the ‘buried’ interface to the depth range accessible to the surface-sensitive electron spectroscopy methods by using ion sputtering or selective etching. However, the structural damage associated with this sample preparation procedure will definitely be non-negligible and might lead to significant methodological problems and complications. As an alternative to the surface analysis, investigation of an interface may be carried out by studying electron transport properties provided the electron transition across the interface represents the
4
Internal Photoemission Spectroscopy: Principles and Applications
rate-limiting step (Williams, 1970). In this case the experimentally measured current across the heterostructure will carry information about rate of electron transitions across this barrier. Other approaches to isolation of the interface-related electron transitions make use of measurements of capacitance or admittance associated with a semiconductor space–charge layer (Nicollian and Brews, 1982), formation of a built-in electric field, etc. Obviously, the common denominator of all these methods is the energy barrier at the interface, whose height characterizes energy offset between electron states involved in the current transport (cf. Fig. 1.1.1). By applying appropriate electron transport model (the thermoionic emission, the Fowler–Nordheim or direct tunnelling, etc.) one can find the relevant barrier height from relatively simple electrical measurements if other transport parameters (e.g., the electron effective mass if considering the tunnelling) are known. Though being widely used to characterize interfaces of different semiconductors with metals and insulators (Rhoderick, 1978; Sze, 1981; Nicollian and Brews, 1982; Rhoderick and Williams, 1988; Tung, 2001), this analysis of transport of thermalized charge carriers appears to have significant limitations at least in two aspects. First, the lateral non-uniformity of interface barrier leads to dramatic complication of the data analysis as compared to the idealized uniform barrier case (Tung, 2001). To avoid systematic errors, measurements need to be extended to a sufficiently broad temperature range and then results are numerically simulated (see, e.g., Lonergan and Jones, 2001). Besides losing an ability to extract barrier height through a universal and straightforward analytical procedure, this complication also rises questions concerning reliability and physical meaning of the extracted barrier values because the uniqueness of the parameter set used to fit experimental curves can hardly be proven. Second, in the case of wide-gap semiconductors and insulators, the rate of thermoionic transitions appears to be too low to produce a measurable electric current. At the same time, analysis of electron tunnelling rate in sufficiently high electric field faces not only above mentioned barrier non-uniformity problem but, also, the unknown effective mass value in the near-interfacial region as well as possibly field-dependent initial DOS distribution (see, e.g., Weinberg, 1977; 1982; Waters and Zeghbroeck, 1999). Moreover, it is not always evident that one can directly calculate the correct strength of electric field at the interface simply from the applied voltage value because of charge trapping effects and non-equilibrium charge carrier concentration in vicinity of the interface barrier. Finally, in the case of trap-assisted electron transitions, the microscopic origin and properties of the involved defects or impurities are generally unknown which precludes extraction of any meaningful barrier height. As a result, in most of the wide-gap materials the fitting of the measured tunnelling current–voltage characteristics using an idealized laterally uniform barrier model with assumed values (in most of the cases the bulk ones) of the carrier transport parameters yields only an ‘effective’ (or ‘apparent’) barrier height. Obviously, these values cannot be considered as the reliable ones prompting one to consider alternative approaches to the interface barrier characterization. As it appears now, the most productive technique to characterize the interface barriers at ‘buried’ interfaces (i.e., those separated from the sample surface by a layer of a solid) is closely related to photoelectron emission spectroscopy, more specifically, to the photoemission quantum yield technique (Fowler, 1931; Hughes and Dubridge, 1932; Dubridge, 1935). In this method the electron barrier height at the surface (interface) of a solid is found by determining the minimal energy of a photon needed to excite photoemission (photoinjection). The latter is done by extrapolating to zero the spectral dependence of the photoemission quantum yield, i.e., the number of electrons which escape emitter normalized to the number of absorbed photons of a given energy hν. This ‘critical’ photon energy found is this way is called ‘the spectral threshold of photoemission’, in Fig 1.1.1, and corresponds to the minimal energy offset between the occupied electron states of the emitter and the empty states of the second solid in a contact. The physical picture of the photoemission will be addressed in the forthcoming chapters in more detail. The important feature of this technique worth of mentioning here is the sufficient physical transparency of the process which excludes most of the doubtful interpretation(s), and practically direct ‘readout’ of the spectral threshold from the experimental spectral dependences of the quantum yield. No pre-knowledge of transport parameters of the studied solids is required, and the lateral barrier non-uniformity can be
Preliminary Remarks and Historical Overview
5
quantitatively analysed from the near-threshold IPE data (Okumura and Tu, 1983). Taking into account that the theory of external photoemission in vicinity of its spectral threshold is well developed (Kane, 1962; 1966; Ballantyne, 1972), it comes as no surprise that the same kind of formalism was applied to the description of IPE (or photoinjection) with remarkable success (Williams, 1970). In the remaining part of this chapter the development of most important areas of IPE spectroscopy application will be overviewed in order to provide the reader with the current status of the research.
1.3 Interfaces of Wide Bandgap Insulators Wide bandgap insulators play decisive role in realization of functional metal–insulator–semiconductor (MIS) devices and developed on the MIS basis integrated circuits in which these materials serve as gate or field insulators, as well as tunnelling layers in non-volatile memory devices and insulators of capacitors in dynamic memory integrated circuits (Sze, 1981; Nicollian and Brews, 1982). As the functionality of insulating layer is directly determined by the height of energy barriers at its interfaces with semiconductors and metals, the importance of barrier characterization was recognized from the very early days of MIS technology development. Most of the efforts have been concentrated on investigation of electronic structure of interfaces of silicon and its thermally grown oxide in the metal–oxide–semiconductor (MOS) structures. In the pioneering works of Williams (1965) and Goodman (1966a) the experimental arrangement employing illumination of MIS or MOS capacitor by monochromatic light through a semitransparent metal electrode (cf. Fig. 1.3.1a) was introduced which remains the mostly used configuration nowadays. Goodman also suggested application of a transparent electrolyte solution contact to suppress IPE from the gate electrode and allow reliable measurements of the net substrate injection current (cf. Fig. 1.3.1b) (Goodman, 1966b). Interpretation of the IPE spectra was essentially based on the classical photoemission model but one might already notice that different authors use different power exponent p of the quantum yield spectral dependence: Y = A(hν − )p ,
(1.3.1)
where is the barrier height at the interface, hν the photon energy, and A a constant. Most often, the spectral curves are linearized using Y 1/2 –hν co-ordinates (the so-called Fowler plot) following simplest description of the electron photoemission process (Fowler, 1931; Allen and Gobeli, 1966; Helman and Sanchez-Sinencio, 1973). Application of more advanced theoretical treatments (Kane, 1962; Berglund hn Electrolyte
hn
Thin metal Insulator
Insulator
Substrate
Substrate
(a)
(b)
Fig. 1.3.1 Schemes of IPE experiments employing excitation with light penetrating through a semitransparent metal electrode (a) or passing through an optically transparent electrolyte solution contact (b).
6
Internal Photoemission Spectroscopy: Principles and Applications
and Spicer, 1964a) leads to a different exponent, e.g., Y 1/3 –hν (Deal et al., 1966). In the case of IPE from an energetically narrow band (e.g., the bottom of conduction band in the degenerately doped n − Si), when the Fowler model clearly becomes inadequate, Goodman found the spectral yield to follow other law (Goodman, 1966c): 1 2 Y =C 1− , (1.3.2) hν where C is a constant. In vicinity of the IPE spectral threshold, i.e., when (hν − )/ < 0.1, this expression can be approximated by a linear function Y = C(hν − )/2 importantly indicating relationship between the exponent p of photoemission yield spectral dependence Y = A(hν − )p and the shape of the initial DOS in the emitter. By using these simple models the barrier heights at interfaces of SiO2 with Si and several metals were determined by number of researchers with a high degree of confidence (Williams, 1970). The results concern mostly electron energy barriers between the top of Si valence band eV (Si) or bottom edge of the Si conduction band eC (Si) measured by using electron IPE with respect to the bottom of the SiO2 conduction band, and the barriers e (Me) between the Fermi level of different metals and the oxide conduction band. Using a hole IPE from Si into SiO2 , Goodman (1966b) also measured the energy barrier h (Si) between the bottom of the Si conduction band and the uppermost occupied electron state in SiO2 . The measured electron barriers were later used to evaluate the electron effective mass from the tunnelling experiments (Snow, 1967; Lenzlinger and Snow, 1969) and paved way to the consistent description of tunnelling effects in MIS structures (Weinberg, 1977; 1982). Despite predominant description of the IPE as a kind of conventional photoemission process, several additional effects were reported:
• considerable impact of optical interference in thin insulating layer on the spectral dependences of the IPE quantum yield (Goodman, 1966a; Powell, 1969; DiMaria and Arnett, 1977); • non-negligible influence of the image–force barrier reduction at the interface (the Schottky effect) on the measured barrier height (Deal et al., 1966; Goodman, 1966a; Powell, 1970; DiStefano, 1977); • additional photocurrent related to optical excitation of defects in the insulating layer (Williams, 1965; Korzo et al., 1968; Thomas and Feigl, 1970); • saturation of IPE current at high applied voltages (Goodman, 1966a) later explained by effects of electron scattering in the barrier region (Berglund and Powell, 1971); • decay of the photoinjection current with time caused by trapping of charge carriers in the insulating layer (Williams, 1965; Goodman, 1966b; Powell and Berglund, 1971). These effects clearly indicate influence of additional, not observed in the case of conventional external photoemission processes on spectral and field characteristics of IPE prompting more elaborate description of the phenomenon. To some extent this task was fulfilled by Powel and Berglund by incorporation into the analysis of the image force interaction (Powell, 1970), the effects of electron–phonon scattering (Berglund and Powell, 1971), and the barrier distortion by near-interface built-in charges (Powell and Berglund 1971). The important feature of this analysis consists in ascribing the additional effects to the very last stage of the photoemission process – the escape over the potential barrier – while the optical excitation and transport in the emitter are believed to be the same as in the case of external photoemission. Moreover, Fowler’s condition of electron escape into vacuum (Fowler, 1931) is also supposed to remain
Preliminary Remarks and Historical Overview
7
valid in the case of photoemission into a solid (Powell, 1970). As a result, the procedure of determination of the spectral threshold and interface barrier height is still the same in the case of IPE as in the case of external photoemission with the only image force correction necessary. Basically this result stems from assumption that momentum conservation condition has little effect on the barrier transparency, i.e., the band structure of the second solid (collector) is of minor significance. This supposition seems to be justified at least in the case of amorphous insulators studied in those days. In the case of relaxation of the momentum conservation requirements (which is in fact assumed in the early Fowler’s model, see the later analysis by Chen and Wronski (1995)) the photoemission spectral distribution is determined exclusively by the properties of emitter electrode resulting in identical behaviour of IPE and external photoemission from semiconductor and metal electrodes (cf. Table I in Powell (1970) and Table II in Ballantyne (1972)). This photoemission-type model, applied with great success to many material systems over past decades will be discussed in detail in Chapter 3. As further developments of Powell’s model of IPE several important results need to be mentioned. First, the validity of the image force model of the interface barrier reduction was demonstrated down to a distance of about 0.4 nm from the geometric plane of interface (DiStefano, 1976). Second, several studies indicated the spectroscopy of IPE quantum yield as a technique of optical characterization of semiconductor/insulator interfaces (DiStefano and Lewis, 1974; Adamchuk et al., 1988; Afanas’ev et al., 1992a). Though this approach addresses the conventional optical transitions between high-symmetry points in the Brillouin zone of the emitter, being detected through photoemission of electrons it becomes a surface (interface)-sensitive method (Adamchuk and Afanas’ev, 1992a). It appears also possible to isolate in the IPE spectra effects related to electron scattering by phonons in the near-interface SiO2 layer including the energy thresholds of single-phonon scattering (Afanas’ev, 1991a). Further, the energy onset of electron–electron scattering in the oxidized SiC is observed in close correlation with the bandgap width of the particular polytype of this semiconductor (Afanas’ev and Stesmans, 2003a). These features provide strong support to the multi-step model of photoemission (Berglund and Spicer, 1964a; Stuart et al., 1964; Powell, 1970; Williams, 1970) in which this process is described as a sequence of relatively independent steps illustrated in Fig. 1.3.2: the optical excitation in emitter (a), transport of excited carrier to the emitting surface or interface (b), surmounting the surface/interface potential barrier (c), and transport in the collector material towards the current-collecting electrode (anode) (d). This splitting in steps allows b
c d EC
a EC
EV Emitter
Collector
Fig. 1.3.2 Multi-step model of IPE process illustrated for the case of electron photoemission from a valence band of semiconductor emitter to the conduction band of insulating collector. The stages of optical excitation (a), transport of electron to the surface of the emitter (b), surmounting of the potential barrier (c), and further transport in the collector (d) are indicated by arrows.
8
Internal Photoemission Spectroscopy: Principles and Applications
one to conduct a much simpler analysis of experimental results than the complex descriptions treating the photoemission process as a single-quantum-mechanical process. The possibility of reliable barrier height determination at interfaces of wide bandgap insulators with metals and semiconductors demonstrated on SiO2 -based systems prompted extension of the IPE analysis to other insulators. Most of the early studies were concentrated on amorphous alumina (Goodman, 1970; Szydlo and Poirier, 1971; Gundlach and Kadlec, 1972; DiMaria, 1974; Powell, 1976) and silicon nitride (Goodman, 1968; DiMaria and Arnett, 1975; 1977). Interfaces of other insulators were studied sporadically which was mostly related to insufficient level of technology of the insulator growth. High leakage current obviously limits sensitivity to the optically induced electron transitions. The interface barriers were evaluated for native oxides on Ge (Kasumov and Kozlov, 1988; Oishi and Matsuo, 1996) and GaAs (Yokoyama et al., 1981; Kashkarov et al., 1983), Y2 O3 (Riemann and Young, 1973), AlN (Morita et al., 1982), P3 N5 (Hirota and Mikami, 1988), CaF2 and SrF2 (Afanas’ev et al., 1991b; 1992a). Also, IPE analysis was extended to interfaces of carbon-based materials with SiO2 (Afanas’ev et al., 1996a, b). In recent years the increasing importance of the interface barrier and band offset measurements was recognized in relationship with development of new material systems for advanced microelectronic devices. In particular, the need to replace standard SiO2 gate insulation in MIS devices by a dielectric with higher permittivity (κ) led to development of numerous technologies of metal oxide growth on semiconductor substrates (for review, see Wilk et al. (2001), Houssa (2004), and Huff and Gilmer (2005)). The achievements in high-κ insulator growth methods made possible application of the IPE to large number of interfaces. The results available up to the date will be overviewed in Chapters 9 and 10, though, without doubt, the list of investigated systems will increase further in the very near future. As a final remark concerning application of IPE to studies of electron states in wide bandgap insulating materials one must add that injection of charge carriers can be used to fill the trapping centres in the insulators associated with intrinsic defects of impurities (Williams, 1970). Moreover, the field-dependent IPE enables not only charging the traps but, when used in a probe mode, to quantify the trapped charges and characterize their in-depth profile. This approach was earlier overviewed using examples of SiO2 trapping studies (Afanas’ev and Adamchuk, 1994). However, great importance of the trapping issues in the novel high-κ insulating materials makes necessary detailed consideration of the potentials and limitations of IPE in the charge trapping experiments as compared to other charge injection methods. These problems will be addressed in Chapters 5–7 of this book, while the available information concerning atomic nature and electronic properties of defects in thin insulating films of SiO2 is discussed in Chapter 11. 1.4 Metal–Semiconductor Barriers Photoinjection of charge carriers in metal–semiconductor interface barrier structures (often referred to as the Schottky contacts) is a long known phenomenon used for investigation of electron transport properties (see, e.g., Williams, 1962; 1970 and references therein). This technique is seen as the most straightforward way to provide information regarding barrier height between the Fermi level of a metal and the conduction band of semiconductor electrode through observation of electron photoinjection (see, e.g., Rhoderick 1978; Rhoderick and Williams, 1988). Moreover, as illustrated in Fig. 1.4.1, it is also possible to detect IPE of holes from the optically excited states deep in the metal conduction band into the semiconductor valence states enabling determination of the energy barrier between the metal Fermi level and the top of the valence states in semiconductor. The spectral dependences of both electron and hole IPE yield from metal to semiconductor can easily be analysed in the framework of the single-band model neglecting the carrier momentum conservation requirement (e.g., by assuming that ‘The surface barrier provides the missing momentum’, Helman and
Preliminary Remarks and Historical Overview
9
EC EC
EF
EF
EV EV (a)
(b)
Fig. 1.4.1 Optically excited electron transitions corresponding to photoemission of electrons (a) and holes (b) at the metal–semiconductor interface.
Sanchez-Sinencio (1973)) leading to the Fowler-type spectral dependence of the yield Eq. (1.3.1) with the exponent p = 2. This simple expression is widely used to fit the IPE yield spectra (see, e.g., reviews in Williams (1970), Rhoderick (1978), Rhoderick and Williams (1988), and Tung (2001)) despite the fact that its applicability formally requires the sample temperature to be zero. Nevertheless, deviations from the parabolic yield spectral dependence related to thermal broadening of the Fermi–Dirac electron energy distribution were claimed to be insignificant allowing reliable barrier determination at room temperature if the experimental points in immediate vicinity of the spectral threshold are simply discarded (Derry, 1986). Alternatively, one might use the complete Fowler function (Fowler, 1931; Dubridge, 1935) to simulate the experimental IPE yield curves at an arbitrary temperature (de Sousa Pires et al., 1984; Rhoderick and Williams, 1988) or, else, to simulate the effect of thermal excitation on IPE numerically (Shigiltchoff et al., 2002). Despite wide application of Fowler’s formalism in interpreting experimental data, limitations of this approach are well recognized. Among others, three effects attracted the attention. First, the Fowler electron escape condition stating that for any electron ‘whose kinetic energy normal to the surface augmented by hν is sufficient to overcome the potential step at the surface’ (Fowler, 1931), obviously neglects both the momentum conservation and the energy distribution of final electron states in the collector. The latter factor is found to result in an enhanced exponent of the IPE yield spectral dependence (Chen and Wronski, 1995): Y = A(hν − )2+c ,
(1.4.1)
provided the density of delocalized states in the conduction band of the collector may be written in the form NC (E) ∝ (E − EC )c , where EC is the conduction band edge in the collector. Therefore, in the case of parabolic extended band states, c = ½ and the yield exponent is 5/2 in place of 2 in the Fowler model. Second, as compared to IPE into wide bandgap insulators or to photoemission in vacuum, in the case of Schottky contacts one might notice a considerably lower kinetic energy of electrons which might meet the escape condition (about 0.5 eV in the latter case as compared to 4–6 eV in the former two cases, see the energy scale in Fig. 1.1.1). This lower kinetic energy of electron in emitter results in a much larger mean free path with respect to electron–electron (inelastic) scattering potentially making the momentum
10
Internal Photoemission Spectroscopy: Principles and Applications
a ‘good’ quantum number. When calculating the quantum-mechanical interface barrier transparency under assumption of momentum conservation, several authors reported on significant deviations from the Fowler law just above the IPE spectral threshold (Anderson et al., 1975; Kadlec 1976; Kadlec and Gundlach, 1976; Kao et al., 1980) leading to a shift of the ‘apparent’ spectral threshold with respect to the real value. The use of conventional Fowler analysis may lead to an error in excess of 50 meV in determination of the Schottky barrier height (Anderson et al., 1975). Nevertheless, in most of the practical cases the Schottky contacts are formed by deposition of a polycrystalline metal layer on the surface of semiconductor. The polycrystalline structure of the metal layer results in averaging of contributions stemming from different metal faces ultimately leading to the Fowler-type spectral response curve. The barrier height determined from IPE spectra appears in this case in good agreement with results of independent barrier measurements (see, e.g., Blauärmel et al., 2000) for Au/n-Si structures characterized both by IPE and the ballistic electron emission microscopy (BEEM). Third, in the range of low kinetic energies of photoexcited electrons in metals relevant to the Schottky barrier measurements, the inelastic mean free path λe becomes strongly energy dependent. The latter is neglected in Fowler’s description in which the analysis of electron transport to the emitting surface is omitted entirely. The characteristic feature of λe is dependence on kinetic energy Ek with main term proportional to Ek−2 (Quinn, 1962). As the first result, this decrease λe with electron energy leads to a slower increase in the photoemission quantum yield with increasing photon energy than predicted by the Fowler model (Dalal, 1971; Engstrom et al., 1986; Myrtveit, 1993). Further, in the case of large λe (e.g., λe = 340 nm in Au at Ek = 0.6 eV, Schmidt et al., 1996), there is an increasing effect of the quasi-elastic electron–phonon scattering (Kane, 1966) characterized by the corresponding mean free path λph . The effect of phonon scattering consists in re-direction of the photoexcited electrons leading to considerable enhancement of the photoemission yield for large λe /λph ratios (Dalal, 1971) and in the case of photoemission from thin metal films (Schmidt et al., 1996; 1997). The importance of these physical effects is obvious not only for the IPE spectroscopy techniques under consideration but, also, has a practical aspect caused by application of IPE in Si-based Schottky diodes in infrared sensors (see, e.g., Elabd and Kosonocky, 1982; Pohlack, 1986; Wu et al., 2004). The influence of scattering and of the final electron state density distribution on the total IPE yield naturally leads to questions concerning accuracy of the results obtained when interpreting IPE spectra using the simple Fowler-type approach. In the particular case of the Schottky contact discussed in the present section one has unique opportunity to compare the barrier height determined in an IPE experiment to the results obtained using other techniques, like analysis of current–voltage and capacitance–voltage characteristics of Schottky diodes (Rhoderick 1978; Rhoderick and Williams, 1988), photoelectron spectroscopy at the initial stages of interface formation (Ludeke, 1986), and the BEEM (Kaiser and Bell 1988a, b). The common conclusion from the works in which this direct comparison was made is that the independent barrier measurement techniques give consistent results (within accuracy limit of at most 0.05 eV) even when the IPE spectral dependence are analysed using the ‘standard’ Fowler spectral plot Eq. (1.3.1) with p = 2 to determine the spectral threshold (see, e.g., van Otterloo and Gerritsen, 1978; Kao et al., 1980; Ishida and Ikoma, 1993; Blauärmel et al., 2000; Shigiltchoff et al., 2002) as well as many other reports. This consistency allows one to suggest that, at least in the vicinity of the spectral threshold, the basic assumptions of the Fowler model remain sufficiently correct to ensure accuracy of the method of about 50 meV. Moreover, in this way the proven validity of the physical description also applies to the cases of IPE at interfaces of other materials like wide bandgap insulators or organic films. In the latter two cases the IPE appears to be in an exclusive position to characterize interface barriers as the alternative methods are not applicable because of large barrier height (e.g., current–voltage measurements or BEEM) while others, like photoelectron spectroscopy, suffer from artefacts caused by insulator charging (Nohira et al., 2002; Toyoda et al., 2005) or decomposition of the sample as it is observed to happen in the case of organic films (Koch et al., 2001).
Preliminary Remarks and Historical Overview
11
Worth of mentioning here is another advantage of IPE and BEEM as injection techniques which probe the interfacial barrier in the most straightforward way. These methods allow direct characterization of the barrier height non-uniformity which in other measurement approaches (like current–voltage or capacitance–voltage characteristics analysis or photoelectron spectroscopy) is usually neglected. In the case of non-uniform barrier the IPE yield curve may exhibit Fowler plot with several linear segments, each of them may be used to identify the individual barrier heights (Tung, 2001) as demonstrated in a number of experimental studies (Okumura and Tu, 1983; Tanabe et al., 1991; Chang et al., 1992; Shalish et al., 2000; Bradley et al., 2004). The IPE or BEEM experiments are capable of revealing not only the lateral non-uniformity of the barrier but, also, provide its quantification in terms of barrier height and the interface coverage (on the basis of quantum yields ratio). This is contrast to the current–voltage measurements which interpretation requires numerical simulation to fit the results (Lonergan and Jones, 2001), leaving open the question regarding uniqueness of the found set of transport parameters (for the recent review, see Tung (2001)). As mentioned above sensitivity of the IPE current to the local barrier height also opens a way to the scanning IPE microscopy aimed at lateral analysis of the interface barriers realized by measuring the IPE current as a function of co-ordinate when exciting with sharply focussed UV laser beam. Though this method was initially used to study sodium contamination of Si/SiO2 and metal/SiO2 interfaces (DiStefano, 1971; Williams and Woods, 1972; Bouthillier et al., 1983), most of the efforts were later shifted to analysis of Schottky contacts (Okumura and Shiojima, 1989; Miyazaki et al., 1994) and semiconductor heterojunctions because of availability of tunable laser light sources in the near-IR spectral range (Coluzza et al., 1996; Almeida et al., 1998; Margaritondo, 1997; 1999). As compared to BEEM (Kaiser and Bell, 1988a, b), the scanning IPE clearly has a lower lateral resolution (100–200 nm even in the near-field photocurrent mode, Margaritondo (1997)) but it is by far more flexible because samples with metal overlayer of 10–30 nm in thickness can easily be analysed. Moreover, the local current density in the case of scanning IPE is considerably lower than that one in BEEM, which helps to avoid an injection-related damage associated with electrochemical reactions at the interface. From the brief overview of the metal–semiconductor interface studies one can make very important conclusion concerning the interface barrier height determination using IPE. The results obtained in the framework of a simple Fowler-type model appear to be in excellent agreement with the data provided by alternative measurement techniques employing different physical principles. The major source of uncertainty in the IPE analysis is related to the choice of appropriate model describing the dependence of the spectral yield on the photon energy. As it appears now, several properties of materials and the interface itself, including the energy-dependent densities of states in electrodes, the mean free paths of charge carrier, the optical absorption behaviour, and the interface barrier lateral non-uniformity. However, instead of attempting to find the optimal model for each case, one may evaluate the ‘model-related uncertainty’ of the interface barrier determination using the Fowler plots with different exponent values. The difference between thresholds obtained by using extrapolation in Y 1/2 –hν and Y 1/3 –hν co-ordinates was found to range from 0.1 to 0.2 eV for 3–3.5 eV barriers at the metal/Si3 N4 interfaces (DiMaria and Arnett, 1977), i.e., the ‘model-related uncertainty’ does not exceed ±0.1 eV, i.e., 3% of the measured barrier. Similar evaluation in the case of Schottky barriers on a Si:H from Y 1/2 –hν and Y 2/5 –hν plots ±0.05 eV for approximately 2-eV high barrier (Chen and Wronski, 1995). In the case of BEEM the change of the power law used leads to a 0.03 eV Schottky barrier height change at (111)Si/Au interface (Cuberes et al., 1994) which is in agreement with 0.04–0.08 eV model-related differences reported for Schottky barriers on other semiconductors (Prietsch and Ludeke, 1991; Prietsch, 1995). Therefore, if avoiding more system-specific analysis, one must accept a 2–3% ‘model-related uncertainty’ in the absolute value of barrier height derived from the IPE threshold measurements. Obviously, the relative measurements are of much better accuracy. One of the possible ways to improve the absolute accuracy is to allow variation of the exponent in (1.3.1), i.e., to make p the experimental fit parameter. This approach will be discussed later in this chapter in relationship to the IPE into electrolyte solutions (Section 1.7).
12
Internal Photoemission Spectroscopy: Principles and Applications
1.5 Energy Barriers at Semiconductor Heterojunctions The determination of band offsets at semiconductor heterojunctions looks quite similar to the characterization of semiconductor–insulator interfaces. The schemes of optically excited electron transitions shown in Fig. 1.5.1a and b are quite similar to that in Fig. 1.3.2, and include both electron and hole photoemission transitions, which may occur from the valence or conduction band. In addition, the IPE analysis of interfaces between relatively narrow-gap semiconductors enjoys availability of high intensity light sources like the free-electron laser enabling the outmost sensitivity, energy resolution, and possibility of photoemission microscopy (Coluzza et al., 1992; McKinley et al., 1993; Margaritondo, 1997; 1999; Nishi et al., 1998). As a result, from the very beginning the IPE was labelled as ‘a suitable method for determining band offsets in semiconductor heterostructures’ (Abstreiter et al., 1985; 1986), and applied to studies of a wide range of systems. There are, however, several aspects making the IPE at semiconductor heterojunctions very special case requiring great care in analytical description. To start with, most of the heterojunctions studied so far represent epitaxial structures in which the translational symmetry is preserved across the interface. Therefore, there is no more fundamental reason to discard the electron or hole momentum as a ‘good’ quantum number as it is done in the Fowler’s description. Moreover, adding to this argument, the kinetic energy of a charge carrier in the band contributing to the IPE process is usually smaller than the bandgap width of the emitter (cf. Fig. 1.5.1) resulting in a low inelastic scattering rate as compared to the IPE over a higher barrier or the IPE from a metal electrode. This, in turn, leads to a large excited carrier escape depth which has two important consequences. First, the momentum relaxation time may appear to be large enough to ensure momentum conservation during the IPE process. Second, would the mean carrier escape depth become comparable to the width of the space charge layer in the emitter, additional broadening of the excited carrier distribution at the interface may occur as illustrated in Fig. 1.5.2. In the latter case, the excited carrier distribution cannot anymore be considered as a replica of the initial state DOS in the emitter. The energy distribution of excited electrons (holes) also appears to become affected by the transport properties of the emitter and the electric field distribution near its surface. These factors exclude the straightforward application of the yield power fit based on the initial state DOS energy dependence. Numerical simulation of the yield curves measured in the samples with different emitter
EC
EC EC
EV
EV
EC
EV (a)
EV (b)
Fig. 1.5.1 Schemes of electron (a) and hole (b) IPE transitions in semiconductor heterojunction involving both the valence and conduction band state excitation in a more narrow bandgap emitter material.
Preliminary Remarks and Historical Overview
13
EC
le
qFle
EV
Fig. 1.5.2 Effect of electric field penetration into the emitter electrode. electrons excited with the same photon energy from the same initial state but at different distance for the heterojunction will have different energies when reaching the surface of the emitter.
doping level becomes necessary (see, e.g., similar approach in the case of external photoemission of electrons from Si(111) in Sebenne et al. (1975)). Even if the field-penetration-related effects remain insignificant, the requirement of momentum conservation in the IPE process brings important modification to the predicted shape of the quantum yield dependence on the photon energy. In particular, in the case of different effective masses of charge carriers in the emitter and collector, the simple power law like that given by Eq. (1.3.1) becomes inadequate (Chen et al., 1996; Aslan et al., 2005) and might lead to substantial error in the spectral threshold determination. Importance of the momentum conservation issues is supported by the recent analysis of BEEM results at Au/Si(111) and Au/Si(100) interfaces (Prietsch, 1995; De Andres et al., 2001) indicating ‘a predominant conservation of lateral momentum at the interface’ (Dähne-Prietsch and Kalka, 2000). Taking into account these considerations the corresponding model will be described in Chapter 3. Nevertheless, despite the mounting evidence for the momentum conservation importance, it still remains a common practice to analyse experimental IPE yield spectra using Eq. (1.3.1) without taking into account DOS energy distribution in the emitter or the collector. Remarkably, different authors use largely differing exponents p in Eq. (1.3.1) to fit the experimental curves for the same type of initial electron states. The Fowler plot, i.e., p = 2 is the most popular one (Heiblum et al., 1985; Haase et al., 1987; Coluzza et al., 1988; 1992; Almeida et al., 1995; Chang et al., 1998; Nishi et al., 1998; H.B. Zhao et al., 2003), but one can also find analysis with p = 1 (Abstreiter et al., 1985; 1986), p = 5/2 (Cuniot and Marfaing, 1985; Mimura and Hatanaka, 1987), and p = 3 (Haase et al., 1991; Seidel et al., 1997). This inconsistency in a way of describing the yield spectral curves prompted more elaborate treatment of the IPE in semiconductor heterojunctions with proper treatment of electron DOS in both solids and quantum-mechanical description of electron transition of the interfacial barrier (Chen et al., 1996). As the general conclusion it emerges from this study that an enhanced exponent in Eq. (1.3.1) is required. Its value can be obtained by adding 0.5 to the p value predicted by the Kane’s model (Kane, 1962). Interestingly, for indirect transitions which are of much relevance in the case of electron IPE from the valence band of cubic semiconductors (the valence band top is located in the centre of the Brillouin zone,
14
Internal Photoemission Spectroscopy: Principles and Applications
i.e., at k = 0), this modified model yields p = 3, i.e., the same as predicted by the Powell’s model which neglects the influence of the carrier momentum conservation on the IPE process as well as the energy distribution of DOS in the collector (Powell, 1970). From the point of view of material studies, most of the IPE spectroscopy studies of semiconductor epitaxial heterojunctions were concentrated so far on interfaces of AIII BV group semiconductors. The primary source of interest here comes from practical applications though important fundamental issues are also addressed, e.g., non-commutativity of the interface band discontinuities (Seidel, 1997). There is still only limited number of works on other systems like Si/SiGe (Renard et al., 1995; Chang and Lyon, 1998; Aslan et al., 2005) or AII BVI heterojunctions (Nishi et al., 1998; H.B. Zhao et al., 2003). Another field of IPE application is related to interfaces between amorphous and crystalline semiconductors (Cuniot and Marfaing, 1985; Mimura and Hatanaka, 1987; Coluzza et al., 1988). In this case, in addition to the disorder-induced variations in the band structure, the important issue consists in the determination of mobility edge energies for electrons and holes and associated with this energy range electron states (Wronski et al., 1989; Wronski, 1992).
1.6 Energy Barriers at Interfaces of Organic Solids and Molecular Layers As compared to the above discussed IPE into inorganic semiconductor and insulator solids, photoemission into organic of molecular materials brings up several novel aspects primarily associated with molecular, i.e., localized nature of the involved electron states. There are several fundamental issues which concern the electron transport across the interfaces of molecular solids (see, e.g., Cahen et al., 2005):
• The nature of electron energy levels relevant to carrier injection and transport, i.e., their association with particular molecular fragments. • Band alignment at the interface as influenced by interaction, both chemical and electrostatic, between the molecule and the substrate surface. • The role of molecular structure, e.g., orientation and conformation. • The size effects associated with transition from 3- or 2-dimensional molecular array to a singlemolecule structure, and with variation of the molecular chain length. • The origin and energetics of elemental excitations in organic and molecular materials, e.g., excitons, polarons, etc. In fact these fundamental physical issues are closely related to practical materials science problems. The latter arise when applying molecular systems as electrically conducting, semiconducting, or insulating elements in electron devices. For instance, in an electroluminescent polymer device the charge carriers of opposite sign must be injected into the active area to create an exciton via Coulomb capture. The radiative decay of the excitonic state would then provide the desirable light emission (Bradley, 1996). For the twolayer device architecture the energy band diagram is shown in Fig. 1.6.1 in which are indicated the work functions of the metallic anode and cathode electrodes as well as the energy barriers for electrons and holes at the injecting interfaces e and h , respectively. Obviously, in order to attain an acceptable device performance in terms of the operation voltage and the emission efficiency, the injecting interfaces should be engineered in a way enabling maximal injection current density. The latter requires the proper material selection, which, in turn, needs good understanding of the energetics of electron states involved in the carrier injection at the interface. As a result, this practical issue prompts experimental determination of the band offsets and barriers at the molecular interfaces.
Preliminary Remarks and Historical Overview
15
EVACUUM qV fCA
xII
Cathode
xI
e Anode
Cathode
Anode
h I
II
Fig. 1.6.1 Schematic energy diagram of a two-layer device with electron (I) and hole (II) transporting polymers characterized by electron affinities χI and χII , respectively. The shift in the energy of the vacuum level EVACUUM is caused by the applied voltage V and the contact potential φCA between the cathode and anode electrodes stemming from the difference in their work functions Cathode and Anode . The potential barriers for electrons (e ) and holes (h ) and the polymer junction are also indicated.
From the early days of research in the field of organic and molecular interfaces the IPE spectroscopy emerged as the most straightforward and reliable method of interface band diagram characterization. As compared to other spectroscopic methods like the external photoemission or the inverse photoemission (Dose, 1983) the IPE addresses electron states directly involved in the electron or hole current flow, i.e., relevant to the device operation. Moreover, a low density of electric current excited in the organic material during IPE experiment and the presence of two conducting electrodes allow one to minimize the impact of the material charging which may lead to important artefacts in the vacuum electron spectroscopy techniques (Cahen et al., 2005). Finally, the damage of the organic or molecular material in the IPE experiment is also much reduced because the excitation is performed by using photons of much lower energy (usually the sub-bandgap one) than in the case of external photoemission known to cause significant sample modification (see, e.g., Koch et al., 2001). To this list of advantages of IPE measurements should also be added that many devices like, for instance, the electroluminescent structures, have both electrical contacts and an optically transparent output area which can be used as an optical input in the IPE experiment (Jonda et al., 1999). All these features make IPE spectroscopy the most relevant technique for analysis of energetics of the molecular and organic interfaces. In the initial experiments on the IPE into organic materials (Williams and Dresner, 1967; Bässler and Vaubel, 1968; Lakatos and Mort, 1968; Binks et al., 1970; Williams, 1970) their energy band structure has been presented in a way similar to that in inorganic semiconductors and insulators, i.e., using the conventional valence and conduction band concepts (see, e.g., Giro and Marco, 1979; Rikken et al., 1994a, b). However, it has been later realized that the electron states responsible for current transport in organic systems are predominantly of molecular origin leading to considerable localization of the charge carrier caused by polarization of the surrounding network (the polaron formation) (Conwell, 1996). The resulting from the molecular picture band diagram of the metal/organics interface is exemplified in Fig. 1.6.2, which indicates the highest occupied molecular orbital (HOMO) representing the analogue of the upper states in the valence band, and the lowest unoccupied molecular orbital (LUMO) (the analogue of the lowest states in the conduction band). In addition are shown the polaron levels of an electron P− and a hole P+ split from the LUMO and HOMO states, respectively, by the network polarization. It is generally believed that the IPE process occurs much faster that the polaron formation. Therefore, analysis of hole and electron IPE spectra allows determination of the true HOMO and LUMO state energies,
16
Internal Photoemission Spectroscopy: Principles and Applications EVACUUM U
EVACUUM
EF
x LUMO
e Et
h
P I P
Eg HOMO
d
Fig. 1.6.2 Energy diagram of an interface between a metal and a molecular material. The energy of LUMO and HOMO states with respect to the vacuum level correspond to the electron affinity χ and the ionization potential I of a molecular material, respectively. The barriers for electron and hole injection to these states, e and h , depend also on the metal work function and the interface dipole U. The energy of the polaron states P− , P+ and the corresponding transport gap Et are also indicated.
respectively, as measured with respect to the metal Fermi level (cf. Fig. 1.6.2). The energy difference between these two states (the HOMO–LUMO gap) yields the real bandgap of the molecular material Eg , which is different from or transport gap (also referred to as the single-particle gap) Et determined by the polaron levels (Cahen et al., 2005). The barrier heights for injection of charge carriers (e and h for electrons and holes, respectively) will generally be determined by the work function of the metal used in the contact, the HOMO–LUMO gap determining the band offset at the interface, the energy position of the gap relative to the Fermi level determined by the ionization potential of the molecular material I (i.e., the energy of HOMO state with respect to the electron level in vacuum), and the interface dipole U, all shown in Fig. 1.6.2. By contrast, the transport of the injected carriers after their thermalization, formation of an exciton and its decay will be controlled by the electron P− and hole P+ polaron states and by the transport gap Et = Eg − (P− + P+ ) = I − χ − (P− + P+ ), where χ is the electron affinity of the molecular system (i.e., the energy of LUMO state measured with respect to the vacuum level). The localized nature of molecular electron states in organic solids is obvious including the HOMO and LUMO states controlling the current injection. Nevertheless, interpretation of the IPE spectra in nearly all the published studies is done using the free-electron type Fowler model with a remarkable success. It is worth of reminding here that the Fowler’s approach neglects both the carrier momentum conservation in the photoemission process and the energy dependence of DOS both in the emitter (the free-electron gas is assumed) and in the collector (Fowler, 1931). Relaxation of the momentum conservation condition seems, indeed, to be justified by a disordered nature of most of the molecular materials. However, the reason for energy independence of the DOS in the organic collector is unclear because these states are derived from highly localized (Campbell et al., 1996a) molecular orbitals. The latter is expected to give rise to a narrow band of electron states acting as the energy band-pass filter (Williams, 1970). The spectral distribution of the IPE quantum yield in this case is predicted to be a replica of the DOS of the initial electron states in the emitter electrode, i.e., give a step-like function in the case of IPE from a metal (Williams, 1970). At the same time, available literature results overwhelmingly suggest that the Fowler’s description accounts very well for the experimental data on IPE at the metal/organic material interfaces (Giro and Marco, 1979; Rikken et al., 1994a, b; Campbell et al., 1996a; Vuillaume et al., 1998; Campbell and Smith, 1999; Jonda et al., 1999; Huang et al., 2001; Sigaud et al., 2001; 2002; Haik et al., 2004; 2006; Kampen et al., 2004). To explain these experimental observations one must assume that at the interfaces of organic materials with metals and semiconductors the LUMO/HOMO states are energetically broadened to the extent at
Preliminary Remarks and Historical Overview
17
which the DOS can be considered as continuum. Several physical mechanisms may potentially account for such broadening. First, it is already suggested by Williams that narrow DOS bands might be split by vibrational modes of molecular fragments into several sub-bands (Williams, 1970). Second, there is an interface dipole U (cf. Fig. 1.6.2), which extends to some depth δ into the collector material and, therefore, will smear out the DOS in the latter by electrostatic interaction. This kind of interface dipoles is usually associated with interaction between the adsorbed molecules and a conducting substrate (see, e.g., Witte et al., 2005), or, else, with some adsorbate-related charges (Blyth et al., 2000). Third, there are significant image–force interactions at the interfaces of organic materials with metals which may lead to additional 0.1–0.2 eV broadening of the collector DOS (Rikken et al., 1994a, b; Campbell et al., 1996a; Tutis et al., 1999; Sigaud et al., 2001). Finally, the presence of uncompensated defect- or impurity-related charges in the near-interface layer of organic or molecular material might add to the LUMO/HOMO level broadening (Halbritter, 1999). Whatever the exact mechanism is, the experimental data indicate that the level broadening is sufficiently large to allow application of the Fowler (or Powell) model to describe the IPE into molecular materials. As an additional remark concerning the IPE at the interfaces of organic or molecular materials, it is worth of mentioning that low sample processing temperatures of these compounds and the presence of foreign molecules (remnants of solvents or precursors, by-products of chemical reactions, adsorbates, impurities, etc.) leave the possibility of photocurrent excitation by optical ionization of the defect/impurity electron energy level in the collector as illustrated in Fig. 1.6.3. Would these ‘extrinsic’ states in the gap be easily re-filled by the charge carriers supplied from the emitter, e.g., by electron tunnelling, these optical transitions will result in a steady-state photocurrent quite similar to the IPE current. However, as no optical excitation of charge carriers on the emitter is involved in this injection process, the indicated mechanism cannot be considered are the IPE-type process. Rather, this is an optical excitation of the near-interface defects (Adamchuk and Afanas’ev, 1992a) to which we will further refer as to ‘pseudoIPE’ excitation. There are recent experimental indications that this mechanism may be involved in the photocurrent excitation in the GaAs Schottky contacts modified by a molecular interlayer (Hsu et al., 2003; 2005) and may probably be encountered in other material systems as well. The spectral dependences of the quantum yield of the pseudo-IPE are expected to be determined by the energy distribution of the gap states involved in the photoexcitation in the collector and by the energydependent photoionization cross-section (Lucovsky, 1965; Landsberg, 1991). Thus, the corresponding spectra are likely to be only marginally sensitive to the DOS of the emitter electrode, e.g., to its Fermi
A LUMO (EC) EF
B Defect level HOMO (EV)
Fig. 1.6.3 Optically induced electron transitions corresponding to the IPE of electrons from metal into semiconductor/insulator conduction band (A) and to the ionization of near-interface defect level filled by electron tunnelling from the conducting electrode (the pseudo-IPE process, B).
18
Internal Photoemission Spectroscopy: Principles and Applications
energy. The latter allows one to distinguish the IPE current from the pseudo-IPE signal by comparing spectral response of structures fabricated by applying metal electrodes with different work function (Giro and Marco, 1979; Campbell et al., 1996a; 1999; Jonda et al., 1999). The sensitivity of the photocurrent spectral threshold to the work function of the emitter electrode would be consistent with the ‘true’ IPE photoinjection process. If this is not the case, the pseudo-IPE transitions are likely to dominate the observed photocurrent. The determination of the spectral threshold and its interpretation in the case of pseudo-IPE become problematic. Clearly, no meaningful threshold value can be derived when fitting the spectral curves with an exponent (Hsu et al., 2003; 2005), but immediate association of the photocurrent spectrum with the DOS of the gap states in a molecular layer seems also to be unreliable because the dependence of the photoionization cross-section on photon energy remains unknown. One might apply the method of the best power fit (Lange et al., 1981; 1982) which will be discussed in more detail in the next section. The lowest spectral threshold derived in this way for the pseudo-IPE process can be associated with the energy needed to photoionize the uppermost occupied electron state measured with respect to the corresponding bulk band edge of the collector material (cf. Fig. 1.6.3). Next, if one assumes that the gap states have a continuous distribution both in space and in energy, in the low-electric field regime (when the variation of electrostatic potential across the layer of a thickness comparable to the carrier tunnelling length is negligible) the energy of the uppermost occupied electron state at the interface can be sensitive to the Fermi energy in the emitter. In this way one can still obtain information regarding the band alignment at the interface even in the case when only the pseudo-IPE transitions are observed. However, the accuracy of this analysis is likely to be limited taking into account possible electrostatic potential drop between the conducting electrode and a trap in the insulating collector.
1.7 Energy Barriers at Interfaces of Solids with Electrolytes The photoemission of electrons into electrolyte is usually considered to belong to the field of photoelectrochemistry rather than constitute a part of solid state physics because it directly involves interaction of the injected charge carriers with molecules of a solvant and dissolved substances in electrolyte. Nevertheless, it is still worth of considering this phenomenon here along with other IPE processes because of several significant achievements in describing the photoemission process in general and a number of unique applications of the IPE developed when applying electrolytic contact to a metal or semiconductor. Apparently, the first report on photo-stimulated electron transfer at a metal–electrolyte interface dates back to 1839 when E. Becquerel reported observation of light-induced current in electrochemical cell which later became known as the Swensson–Becquerel effect (for a brief review, see, e.g., Honda, 2004). The broad research area of photoelectrochemistry developed since then is primarily related to the practical applications in the fields of photo-induced reactions in electrolytes, corrosion science, etc. However, as it appeared later, nearly all the electronic processes known to occur at the surfaces of solids (i.e., at their interface with vacuum) have found their analogues in the solid–electrolyte systems. These include not only the already mentioned photoemission of electrons from a metal or semiconductor (see, e.g., reviews in Brodsky et al. (1970), Brodsky and Pleskov (1972), Pleskov and Rotenberg (1972), Benderskii and Brodsky (1977), Sass (1980), and Benderskii and Benderskii (1995)) but also the inverse photoemission measurements (see McIntyre and Sass, 1986) and the tunnel injection similar to BEEM approach (Diesing et al., 2003). The remarkable feature of all these phenomena in the solid–electrolyte system is that they involve electron transitions from or to the states of the emitter energetically located well below the energy level of electron in vacuum. Thus, the application of an electrolyte contact allows one to address the electronic structure of solids in the energy range between the Fermi level and the vacuum level which
Preliminary Remarks and Historical Overview
19
is hardly accessible when using the conventional electron spectroscopy methods (Sass et al., 1975; Sass, 1980). The detection of electron states below the vacuum level made possible characterization of low-lying energy bands in metals (Sass, 1975; 1980; Sass et al., 1975; Neff et al., 1984; 1985) as well as studies of photoemission related to decay of multi-electron excitations (surface plasmons) (Sass, 1980; Kostecki and Augustynski, 1995; Fedurco et al., 1997; Fedurco and Augustynski, 1998). As the additional advantages of the electrolyte contact one should also mention its optical transparency and low sensitivity of the interface barrier to the crystallographic orientation of the emitter. The latter allows direct observation of crystallographic effects in the electron IPE by rotating a single-crystal sample of cylindrical shape in the electrochemical cell under narrow optical beam (Sass, 1975; 1980; Sass et al., 1975; Neff et al., 1984; 1985). In order to understand the mechanism of interface barrier reduction in the conductor–electrolyte structure one should consider two factors: the DOS in a liquid and the spatial distribution of electrostatic potential at the interface. The DOS of a polar liquid can be considered in similar way as that of a molecular amorphous solid and characterized by conventional bandgap with considerable density of band tail states. In the case of H2 O the energy range of the latter may reach 2 eV (Goulet et al., 1990; Bernas et al., 1997). In addition, the charge of electron injected into a polar liquid will lead to re-orientation of the surrounding molecules leading to the state with somewhat lower energy analogous to a polaron state in solids. The energy of this salvated electron appears to be below the tail states of the solvant resulting in electron localization. Transition of the injected electron to the salvated state is suggested to occur in two ways: First, the injected electron can be inelastically scattered and then salvated upon thermalization (Bard et al., 1980; Neff et al., 1980; Krebs, 1984). Second, electron can directly be injected into the salvated state(s) formed ‘by solvent dipole fluctuations’, i.e., breaking the Franck–Condon principle (Krohn et al., 1980). Therefore, the DOS of the electrolyte states accepting the photoemitted electron can be represented as a combination of delocalized band-type states and a wide tail of localized ‘tail’ states. The in-depth distribution of electrostatic potential at the interface between a conducting electrode and electrolyte is determined by the presence of mobile ionic species which create the double electrical layer (the dense portion of it with dimensions in the order of molecular size is called the Helmholtz layer, and the diffuse portion is usually referred to as the Gouy–Chapman layer). There is no electric field present beyond the polarization layer. The latter accommodates entirely the potential drop between the metal (emitter) and the electrolyte, as schematically shown in Fig. 1.7.1. In a concentrated electrolyte the potential variation is confined to the few-Ångstrom thick Helmholtz layer, so electrons optically excited in the emitter are injected directly to the states of the electrolyte shifted by the applied electrode potential
EC (w 0) U qw 0
EC e 0 qw
EF Metal
Electrolyte
d < 1 nm
Fig. 1.7.1 Energy diagram of a metal–electrolyte solution contact illustrating direct contribution of the electrode potential ϕ to the electron measured barrier height e .
20
Internal Photoemission Spectroscopy: Principles and Applications
(Brodsky and Pleskov, 1972). As the result the observed barrier height for IPE into electrolyte appears to be linearly dependent on the electrode potential which makes it an equivalent variable parameter to the photon energy. In other words, the variation of the electrode potential is equivalent to variation of the exciting photon energy. Therefore, spectral curves of the electron IPE into electrolyte can be obtained at fixed photon energy by varying the electrode potential which has a number of experimental advantages. For instance, the conditions of the constant excitation rate and the absence of the optical parameters variation are met automatically. The above described potential barrier shape is significantly different from the conductor–solid insulator barriers in which the electrostatic potential is distributed over the entire dielectric layer. Nevertheless, assuming that the transparency of the narrow double electronic layer for excited electrons is only a weak function of the electron energy (Brodsky et al., 1970; Brodsky and Pleskov, 1972) one may consider the IPE into electrolyte as IPE under nearly zero-field conditions. The absence of electric field beyond the double electric layer makes necessary special efforts to prevent diffusion of the injected electron back into emitter. The latter is attained by introducing electron scavenger molecules into the electrolyte solution which would trap the photoinjected electron after its thermalization and salvation (Barker, 1971; Barker et al., 1973). As the result, generation of the photocurrent resulting from the electron photoemission from a metal (or semiconductor) into electrolyte includes a number of steps inside the electrolyte solution illustrated in Fig. 1.7.2: the electron thermalization (process d) which brings it to the bottom of the conduction band of the electrolyte EC , the salvation (process e), which may be followed by capture by a scavenger molecule (g) or, else, by return to the nearby emitter electrode (f). These additional, as compared to the IPE into a solid steps have considerable effect on the photocurrent density. However, as the only parameter which might be sensitive to the energy of electron entering the liquid – the thermalization length – seems to vary only slightly with the kinetic energy electron in the conduction band (at least in H2 O, see, Neff et al. (1980) and Sass (1980)), the spectral distribution of the photocurrent can still be used to determine the spectral threshold of the IPE. Analysis of the spectral curves of IPE current (measured as a function of the electrode potential while keeping the photon energy constant) is typically done using the free-electron-type model. By considering electron propagation across the barrier region Brodsky et al. (1970), and Brodsky and Pleskov (1972) affirmed the Fowler’s result (1.3.1) with p = 2 for the case of IPE from a metal into media with low b
c
d a e EC
EC g A e [eA]
f ESALVATED
Metal Electrolyte
Fig. 1.7.2 Multi-step model of electron IPE at a metal-electrolyte interface including stages of optical excitation (a), transport of electron to the surface of the emitter (b), surmounting of the potential barrier (c), thermalization in the electrolyte (d), salvation (e), diffusion back to the emitter (e), and capture by a scavenger ion A+ .
Preliminary Remarks and Historical Overview
21
dielectric constant, but found p = 5/2 for emission over rectangular barrier (which was actually assumed by Fowler (1931). Accordingly, the electron IPE yield into electrolyte is described by them using the Brodsky–Gurevich law (or 5/2 law) as: 5
Y (hν, ϕ) = A(hν − 0 + qϕ) 2 ,
(1.7.1)
where ϕ is the electrode potential, and the barrier height 0 between the Fermi level of the metal emitter and the conduction band of the electrolyte solution refers to zero density of ions in the Helmholtz layer. In some cases, e.g., for diluted electrolytes, this expression can be modified to account for the additional variation of electrostatic potential across the Gouy–Chapman layer if the width of this layer exceeds the photoelectron thermalization length (Brodsky and Pleskov, 1972). In any event, the determination of the IPE threshold in the case of electrolyte or other highly polarizable media is suggested to be performed by using linear extrapolation of the yield (or the photocurrent) to zero value using the Y 0.4 –ϕ or Y 0.4 –hν plots in place of Fowler’s Y 0.5 –hν extrapolation method. Numerous attempts were made to demonstrate a better correspondence of the experimental results to the Brodsky–Gurevich law than to the Fowler’ one (Brodsky and Pleskov, 1972; Benderskii et al., 1974). Nevertheless, the independent comparison of IPE yield behaviour from Ag into ultra-pure NH3 indicates that ‘neither model of the photoyield has consistent superiority over the other’ (Bennett and Thompson 1986; Bennett et al., 1987). Actually, the difference in the power factor arises in the Brodsky’s model from the additional electron momentum dependence of the incident electron flux at the interface that corresponds to the idealized case of negligible electron– electron scattering rate in the emitter. The Fowler’s approach in which the momentum conservation condition is neglected seems to be more pertinent to electrons excited to a higher energy. In any event, both the Y 0.4 –hν and Y 0.5 –hν extrapolations yield very close results in terms of the barrier height in the metal–electrolyte system (cf. Fig. 5 in Brodsky and Pleskov (1972)). More interesting effect in terms of the spectral threshold determination was reported by Lange et al. (1981; 1982) and consists in observation of the spectral dependences of type (1.3.1) with p > 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
Internal Photoemission Spectroscopy: Principles and Applications
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
Internal Photoemission Spectroscopy: Principles and Applications
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 (<1 eV) energy range in vicinity of the photoemission threshold, for the final states far enough from the conduction band minima Nf and Mif can be considered as weak functions of the electron energy E + hν (Powell, 1970; Williams, 1970). In this case the energy distribution of excited electrons Nexcited (hν, E) will be a replica of the initial density of states (DOS) Ni (E) translated upward in the energy scale by the photon energy hν (Powell, 1970): Nexcited (hν, E) = B(hν)Ni (E − hν)
(2.1.2)
where the coefficient B(hν) is less than 1 and assumed to be independent on the energy of initial electron state. One might also consider more realistic models taking into account the carrier momentum conservation and using a detailed description of band structure of particular emitter (see, e.g., Kane, 1962; Ballantyne, 1972; Helman and Sanchez-Sinencio, 1973; Chen and Wronski, 1995). However, the complex multi-band final state structure involved in the excitation of electron to energies sufficient to escape the emitter appears to be reasonably well approximated by the energy-independent Nf (E + hν): at least the final conclusions regarding functional dependence of the photoemission yield on (hν − ) difference (cf. Eq. (1.3.1)) are practically the same in the simple non-direct transition model (cf. Table I in Powell (1970)) and according to the analysis of the complete band structure of several semiconductors (cf. Table II in Ballantyne (1972)). This result suggests that the internal energy distribution of the excited charge carriers (at least its energetically highest portion) is predominantly determined by the DOS of initial electron states Ni (E). This simple result is essentially based on the assumption of insignificance of the momentum conservation requirement in the case of transition contributing to photoemission. Though this hypothesis might look as to have little to do with reality, in most of the cases one may find its reasonable justification. For instance, in most of the cubic semiconductor crystals the top of the valence band is positioned in point of the Brillouin zone, i.e., at k = 0, as shown in Fig. 2.1.1. To observe any photoemission from these states, one must provide the excited electron with momentum sufficient to reach the surface of emitter and overcome the barrier. This is possible only in the case of indirect or non-direct transitions. Electrons directly excited from other portions of the valence band may also contribute to photoemission but with different (a higher) value of the threshold photon energy (Ballantyne, 1972). Potentially, each type of optical transition in emitter will provide photoemission with its specific energy threshold as can be deduced from the schematic E(k) diagram shown in Fig. 2.1.1 for a model solid
Internal versus External Photoemission
25
Conduction band Escape surface
Energy
Vacuum level
direct
indirect
ds
non-direct
Valence band kindirect kdirect kds
Momentum
Fig. 2.1.1 Schematic energy dispersion diagram for electron photoemission from a parabolic band which illustrates different spectral thresholds corresponding to direct electron transitions in emitter (direct ), the direct transitions followed by elastic scattering (d+s ), and to the indirect or non-direct transitions (indirect and non-direct , respectively). The escape of electrons is determined by the ‘escape surface’ (Ballantyne, 1972) determined by the requirement of the tangential momentum conservation.
with two parabolic bands, from which photoelectrons are emitted into vacuum or into another substance with a parabolic conduction band. The minimal photon energy sufficient for electron emission indirect = non-direct corresponds to excitation of an electron from the top of the valence band to the energy level in emitter corresponding to the minimum of the conduction band of the collector (or to the vacuum level). Interaction with the lattice would provide the electron with the momentum it needs to surmount the barrier. In the case of direct transition a somewhat higher threshold value direct is expected because the final state must lie at the ‘escape surface’ (Ballantyne, 1972), which is only possible if the initial state has E < EV as shown in Fig. 2.1.1. It is also possible that, upon direct excitation, the electron will experience an elastic scattering. This process may lead to additional threshold d+s , also shown in Fig. 2.1.1. Would the electron transitions indicated in this figure contribute to the photoemission with comparable strength, different thresholds might be resolved. However, the difference between the thresholds corresponding to different types of optical transitions may not be large, because it is determined by the E(k) dispersion of the electron bands in the emitter and in the collector. The splitting between the thresholds becomes insignificant if the energy dispersion is small which corresponds to a high effective mass case. In any event, the lowest spectral threshold will always correspond to the indirect or nondirect transitions guaranteeing determination of the minimal energy separation between the uppermost occupied electron states in the emitter and the lowest available unoccupied states in the collector. 2.1.2 Transport of excited electron to the surface of emitter The described scheme of optical excitation results in the energy distribution of the excited electrons Nexcited (hν, E). The initial spatial distribution of these electrons correspond to the in-depth profile of
26
Internal Photoemission Spectroscopy: Principles and Applications
light absorption, i.e., follows the conventional Buger’s law: Nexcited (x) = Nexcited (x = 0) exp [−α(hν)x],
(2.1.3)
where α(hν) is the optical absorption coefficient of the emitter. In order to escape the emitter, an excited electron must reach the surface without losing its energy. The escape can be prevented by any inelastic electron–electron scattering leading to the energy loss or, else, by a quasi-elastic electron–phonon scattering which re-distributes the electrons in the momentum space. These scattering processes affect probability of the excited electrons to reach the surface and attenuate their flux from the optically excited region of the emitter towards the barrier at its surface or interface. The impact of scattering on the photoemissive yield can be described using so-called ‘random walk model’ illustrated in Fig. 2.1.2. This model assumes that, in the near-threshold range of electron energies, an electron can suffer any number of phonon scattering events, but the first electron–electron collision leads to the energy loss so large that electron escape becomes impossible (Kane, 1966; Dalal, 1971; Schmidt et al., 1997). Being described under these assumptions the scattering was shown to modulate the quantum yield of photoemission by the function (Kane, 1966): S(hν, E) =
Bα(hν) , α(hν) + μ
(2.1.4)
where B=
1 − R(E) , 1 − R(E) + μc [1 + R(E)]
(2.1.5)
refers to the probability of electron escape from the emitter, and R(E) is the electron reflection coefficient at the surface (interface). The scattering of electrons is characterized by coefficients μ and c related to the electron mean free path with respect to the electron–electron (λe ) and the electron–phonon scattering ph
ph
ph
(1R)/2
1/2R/2 e
Fig. 2.1.2 Major components of the ‘random walk model’: the elastic electron–phonon scattering characterized by the electron mean free path λph , the inelastic electron–electron scattering with the corresponding mean free path λe , and the electron reflection coefficient at the interface R which divides the flux of randomly scattered electrons into two portions.
Internal versus External Photoemission (λph ) as follows: c=
1 1 + ; μ= λe λph
c c2 − . λph
27
(2.1.6)
In the case of metal–semiconductor interfaces (the Schottky contacts) the inelastic electron mean free path in the metal is usually much larger that the elastic one, i.e., λe >> 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 << , (2.1.7) 1+R λe and, accordingly, to 1−R S≈ 2
λe , λph
(2.1.8)
From Eq. (2.1.8) one may notice that the elastic electron–phonon scattering is in fact enhancing the photoemission yield by a factor λe /λph as compared to the ‘no-scattering’ case S = (1 − R)/2. The latter expression actually describes the barrier transparency unrelated to the transport properties of the emitter. It is worth of adding here that the above analysed case λe >> 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 << λph . Here the chance of an electron to reach the emitter surface without losing its energy decreases exponentially with the depth of its excitation inside the emitter x. This yields (assuming λe << 1/α): S(hν, E) =
1−R λe α. 2
(2.1.9)
This is a common situation if photoemission occurs over a sufficiently high energy barrier, e.g., into vacuum or a wide bandgap insulator. The probing depth of photoemission in this case is determined by λe (1.3 nm in Si near the spectral threshold of photoemission into vacuum (Sebenne et al., 1975)). The above discussion on the impact of electron scattering on photoemission yield and the related estimate of the probing depth in this kind of experiment aims at the analysis of the electric field penetration effects on the spectral threshold determination briefly mentioned in Section 1.5 (cf. Fig. 1.5.2). Penetration of electric field into the emitter is of little importance in the case of metal, but in a semiconductor the depth
28
Internal Photoemission Spectroscopy: Principles and Applications
of electric field screening may be quite large and associated with considerable variation of electrostatic potential across the surface space charge layer. The characteristic field penetration depth can be evaluated as the Debye length (Sze, 1981): εsc kT , (2.1.10) LD = nq2 where εsc is the static dielectric constant of semiconductor emitter, k is the Boltzmann constant, T is the temperature, n is the concentration of majority charge carriers in the bulk of semiconductor, and q is the elemental charge. Would the semiconductor surface be depleted, the maximal width of the depletion layer in thermodynamic equilibrium can be calculated as (Sze, 1981): Wmax =
4εsc kT ln (n/ni ) , nq2
(2.1.11)
where ni refers to the intrinsic charge carrier concentration in the semiconductor. If the photoelectron escape depth is much smaller than the electric field penetration depth, i.e., λe << (LD , Wmax ), the effect of the photoemission spectral threshold in the order of ≈ qFλe
(2.1.12)
may be expected, where F is the strength of electric field at the surface of semiconductor. In the strong electron–electron scattering limit (hν > 2Eg ) this effect seems to be of minor significance ( ≈ 0.01 eV for F = 0.1 MV/cm, and λe = 1 nm). However, in the case of a heavily doped semiconductor a much higher electric field might be encountered when turning its surface to depletion or inversion. This effect leads to significant barrier lowering as illustrated in Fig. 2.1.3a for the case of electron photoemission from a heavily doped p-type semiconductor. The strength of electric field in the semiconductor surface layer increases with the concentration of the ionized doping impurity atoms (acceptors) NA as (Sze, 1981): Fmax ≈ qNA Wmax /εsc .
(2.1.13)
In the case of silicon, already at NA = 1018 cm−3 , Fmax reaches 0.5 MV/cm at room temperature. Higher dopant concentrations would lead to even higher fields and are found to have considerable effect on the photoemission threshold. This case is illustrated in Fig. 2.1.3b which shows the threshold of electron IPE from the valence band of (100)Si crystal into the conduction band of thermally grown SiO2 measured in the samples with low (1 × 1015 cm−3 , ) and high (6 × 1019 cm−3 , ) concentration of boron acceptors in Si (Adamchuk and Afanas’ev, 1992a). The experimentally determined barrier values are plotted as functions of square root of the externally applied electric field (the Schottky co-ordinates) to account for the image-force barrier lowering which will be discussed in Section 2.2.3 in detail. The primary effect consists in the large (approaching 1 eV) additional barrier lowering in the case of heavily doped p+ -Si substrate indicative of the electrostatic potential variation in the Si surface layer within the photoelectron escape depth. The significance of such effects is expected to increase with increasing the photoelectron escape depth, e.g., in the above discussed cases of reduced inelastic scattering in emitter. Therefore, when aiming at reliable determination of the photoemission spectral threshold, the depletion of highly doped semiconductor substrates must be avoided to exclude the artefacts related to the electron field penetration effects. It is advisable then to keep the surface of semiconductor emitter in the state of accumulation.
Internal versus External Photoemission
EC
4.4
29
Si(100)/SiO2 Ideal image-force lowering
e
Barrier height (eV)
4.2 qF
e
4.0 3.8 3.6
qF
e
3.4 3.2
EV (a)
3.0 0.0
0.5
1.0
0.5
2.0
(Oxide field)1/2 (MV/cm)1/2 (b)
Fig. 2.1.3 (a) Schematic energy band diagram illustrating the effect of electric field in the emitter on the photoemission spectral threshold. (b) Field-induced variation of the barrier height for electrons photo-injected from the valence band of Si into the conduction band of SiO2 determined from IPE measurements using p-type Si(100) crystals of different doping concentration: 1 × 1015 () and 6 × 1019 cm−3 (). The data shown in the Schottky co-ordinates √ – F which allow linearization of the dependence predicted by the ideal image-force barrier model.
As the final note here one may address the potential impact of the scattering on the energy of electrons arriving at the surface of the photoemitter. Their energy distribution N*(E, hν) will ultimately determine the photoemission quantum yield. Obviously, the elastic scattering has little effect on Nexcited (E, hν) in the framework of Kane’s model (Kane, 1966). This appears to be reasonable approximation in the case of photoemission into vacuum because the average energy losses due to phonon scattering are still much smaller than in the electron–electron scattering event (Kane, 1966; Ballantyne, 1972). The electron– electron scattering is not so benign in terms of its effect on the electron energy distribution. In metals, the inelastic mean free path of electrons is found to decrease with increasing the kinetic energy Ek of electrons (measured with respect to the Fermi level) as λe ∝ 1/Ek (Quinn, 1962). The influence of this effect on the spectral distribution of the IPE quantum yield is expected to be considerable in structures with low interface barriers, e.g., in the Schottky contacts (Dalal, 1971). Nevertheless, in the case of high interface barriers (of several electron volt in height) the relative difference in the scattering rate between an electron with the energy just sufficient to surmount the barrier, and another one, 0.5 eV more energetic, is expected to be marginal. For this reason one may assume, at least within the simple scattering models described in this chapter, that the internal energy distribution Nexcited (E, hν) will be nearly the same as the distribution of excited carriers at the surface of emitter N*(E, hν). In other words, the scattering in emitter would affect the number of photoexcited electrons reaching the emitter surface but not their energy distribution. The inelastically scattered carriers will give no contribution to the photoemission and may be ignored in this experiment.
2.1.3 Escape from emitter: the Fowler model At first sight it may appear that the escape of electron from emitter into another phase (the collector) will mostly be sensitive to the properties of the latter. Nevertheless, using the assumption that the ‘role’ of
30
Internal Photoemission Spectroscopy: Principles and Applications
Metal
Vacuum
Vacuum level
Energy
Conduction band
m
EF
E h 2k2/2m kFermi Momentum
Distance
Fig. 2.1.4 Energy band diagram of the metal surface used by Fowler (1931) to describe electron photoemission into vacuum.
the collector DOS is simply limited to setting the surface or interface barrier of height , the probability of escape will be governed by the electron energy and momentum distribution at the surface of emitter. This approach was pioneered by Fowler (1931) and later gained considerable support not only because of its physical transparency but, to a large extent, because it allows to analyse different photoemission phenomena in the same framework of description. This model was also successfully applied to a broad range of material systems providing strong experimental evidence that the peculiarities of the electronic structure of the collector material and the coupling of the collector DOS to the electron states in the emitter do not affect the energy threshold of photoemission. Rather, their influence may be described by introducing some weakly dependent on electron energy barrier transparency coefficient. As a result, the Fowler approximation may also be considered as the starting stage in analysis of electron escape from the emitter common for all the photoemission processes. Fowler formulated his hypothesis by suggesting that the ‘. . . number of electrons emitted per quantum of light absorbed is to a first approximation proportional to the number of electrons per unit volume of the metal whose kinetic energy normal to the surface augmented by hν is sufficient to overcome the potential step at the surface’ (Fowler, 1931). Now the task consists in calculating the number of electrons for which this condition is met. The model of DOS at the metal surface considered by Fowler is illustrated in Fig. 2.1.4 in which, using the Fowler’s notation, the energy of the metal conduction band bottom with respect to the level of vacuum is indicated as χm (see also Appendix in Chen and Wronski (1995)). The distribution of electron’s velocity components in the ranges (u, u + du), (v, v + dv), (w, w + dw) with u normal to the sample surface is assumed to obey the Fermi–Dirac statistics:
m∗ n(u, v, w)du dv dw = 2 h
3
1 + exp
−1
m∗ 2 2 2 du dv dw, (2.1.14) u + v + w − EF /kT 2
Internal versus External Photoemission
31
where m* is the effective mass of electron, and EF the Fermi level of the metal. The number per unit volume of electrons with velocity component normal to the surface in the range (u, u + du) can be calculated as:
m∗ ñ(u)du = 2 h
3
−1 ∗
∞ 2π m 2 (u + ρ2 ) − EF /kT du ρ 1 + exp dρ dθ. 2 0
(2.1.15)
0
Now one may calculate the density of electrons which meet the Fowler condition by integrating the electron distribution over the normal velocity range corresponding to the energy above the barrier height reduced by the photon energy hν:
∞ Ne = u2 m∗/2=χm −hν
2πkT ñ(u)du = m∗
2kT m∗
1 2
m∗ h
3 ∞ 0
ln{1 + exp [−y + (hν − )/kT ]} dy. [y + (χm − hν)/kT ]1/2 (2.1.16)
In the photon energy range close to the spectral threshold of photoemission one may neglect y as compared to (χm − hν)/kT in the denominator under integral in Eq. (2.1.16), which leads to √
∞ k2T 2 2 2π(m∗ )3/2 Ne = ln{1 + exp [−y + (hν − )/kT ]}dy. h3 (χm − hν)1/2
(2.1.17)
0
When (hν − )/kT ≡ μ ≥ 0, i.e., hν > the logarithm may be expanded and integrated term by term giving √ 2 π k2T 2 2 2π(m∗ )3/2 e−2μ e−3μ 1 2 −μ Ne = − e − + − · · · . + μ h3 (χm − hν)1/2 6 2 22 32
(2.1.18)
When T → 0 Ne ∝
(hν − )2 (χm − hν)1/2
if hν >
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
Internal Photoemission Spectroscopy: Principles and Applications
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)
Internal versus External Photoemission
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
Internal Photoemission Spectroscopy: Principles and Applications
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
Internal versus External Photoemission
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
Internal Photoemission Spectroscopy: Principles and Applications
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
Internal versus External Photoemission
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).
Internal versus External Photoemission
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
Internal Photoemission Spectroscopy: Principles and Applications
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.
Internal versus External Photoemission
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
Internal Photoemission Spectroscopy: Principles and Applications
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<0
x
x (a)
(b)
(c)
Fig. 2.2.3 Schematic energy band diagram of the emitter–collector–metal structure (a) without and (b) with a positive, and (c) with a negative charges Q present in the collector at a distance x = d/3 from the emitting surface (the left interface of the collector).
range of few nanometres, the fixed charges must be of high density (above 1013 cm−2 ) to be treated as the laterally uniform distribution. Otherwise the injected electron will encounter an array of discrete charges of single-electron magnitude surrounded by uncharged collector regions. When considering the influence of the discrete charged centres at the interfacial barrier one must also account for the polarization of emitter surface these charge cause. In the case of an ideally conducting emitter the polarization would lead to a dipole-like potential, also sensitive to the distance between the charge and the emitter in which the distribution is usually unknown. An additional complication here is associated with partial overlap of the electrostatic potentials of the individual charges when they are located at some distance from the emitter surface. Taken together, these features make analytical description of the barrier and the associated IPE characteristics too sophisticated to be used for unambiguous interpretation of the experimental data. Nevertheless, there is a regime in which certain information regarding the spatial location of discrete charges can be obtained from analysis of the IPE spectral thresholds. This approach uses the fact that the screening depth of a charge located just above the surface of a moderately doped semiconductor is given by the Debye length LD expressed by Eq. (2.1.9), which is much larger than the charge–surface distance. In this case, for a photoelectron escaping emitter from a small depth λe , the charged centre will exhibit an unscreened Coulomb potential (Adamchuk and Afanas’ev, 1988b; 1992a). Thus, for a positively charged attractive centre located at a distance xc above the emitter the one-dimensional potential energy may be written as: (x) = 0 −
q2 qq∗ − qFx − , 8πε0 εi x 4πε0 εD |xc − x|
(2.2.16)
where q* is the charge of the centre. The shape of such barrier is illustrated in Fig. 2.2.4 for two different positions of the centre xc above the Si/SiO2 interface plane as compared to the ideal image-force barrier shown by dashed line. The charge-perturbed barrier exhibits two maxima 1 and 2 , one located at
44
Internal Photoemission Spectroscopy: Principles and Applications 0
0 4
4 1
3 Energy (eV)
2
1
3
2
2
1
1
0
0
1
2
1 xc 3 nm
xc1 nm 1
0
1
2
3
1
4
0
1
2
3
Distance (nm)
Distance (nm)
(a)
(b)
4
Fig. 2.2.4 Distortion of the image-force potential barrier for electrons at the Si/SiO2 interface (cf. Fig. 2.2.2) by a centre with attractive Coulomb potential located at xc = 1 nm (a) and xc = 3 nm (b) above the emitter surface. The lowest spectral thresholds 1 and 2 are indicated for clarity.
xm1 < xc and another at xm2 > 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).
Internal versus External Photoemission
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
Internal Photoemission Spectroscopy: Principles and Applications
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
Internal versus External Photoemission
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) for different trap densities (in units of 1012 cm−2 ). The field-dependent capture cross-section from (Adamchuk and Afanas’ev, 1992a) is used.
trapped charge-induced field a factor of minor relative significance. Because of this, the measurements in the gateless structures cannot generally be considered as reliable ones. The field dependence of the capture cross-section is typical for the Coulomb attractive traps (Ning, 1976a; DiMaria, 1978; Buchanan et al., 1991). Obviously, the field-induced variation of the trapping probability will affect the field dependence of the IPE yield as observed experimentally in low-permittivity insulating materials like SiO2 (Adamchuk and Afanas’ev, 1992a). The character of the curve distortion is obvious from the n(d)/n(0) ratio (transparency) calculations using Eq. (2.2.19) and parameters characteristic for SiO2 . These curves are shown in Fig. 2.2.7 for different concentrations of the attractive Coulomb traps characterized by the field-dependent capture cross-section σ ∝ F −3/2 (DiMaria, 1978) and located close to the emitting surface, i.e., x/d << 1 (DiMaria et al., 1977b). Significant distortion of the low-field region is obvious, and this effect should be kept in mind when attempting to extract some physical parameters from the field dependences of the IPE yield. At the same time, as long as the trapping probability remains independent on the energy of the incoming electrons, i.e., x/ >> 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
Model Description and Experimental Realization of IPE
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
Internal Photoemission Spectroscopy: Principles and Applications
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 << λ/n, where λ is the wavelength of light and n is the refractive index of the material) one may neglect optical interference effects and use T (hν) = const. This appears to be a reasonable approach when considering a narrow spectral range (<1 eV in photon energy) typically used to determine the IPE spectral thresholds provided the optical singularities of the materials (the metal plasma frequencies, the onsets of direct transitions in semiconductors, etc.) do not enter the spectral range of interest. Thus, the relative quantum yield values, which are sufficient for determining the spectral thresholds, can be found directly by normalizing the photocurrent or some quantity proportional to it to the incident photon flux. This most simple (from the point of view of experiment) approach is used with great success in the practical IPE measurements, but one must keep in mind that different optical effects may have significant influence of the IPE spectral curves particularly if a broad spectral range is addressed (DiStefano and Lewis, 1974).
3.2 Quantum Yield as a Function of Photon Energy Using Eq. (3.1.1a) or (3.1.1b) one can find analytical expression for the IPE quantum yield as a function of photon energy and of the interface barrier height by approximating the energy distribution of the excited charge carriers in emitter by some simple model function (Powell, 1970). Assuming that all the energy-conserving transitions are allowed, while the energy dependences of the final DOS the emitter, of the matrix elements of optical transitions, and of the electron scattering parameters in emitter (λe , λph ) are weak at least in a narrow electron energy range in vicinity of the IPE threshold, both N*(E, hν) and P(E, ) can be expressed through the differences between the energy of electron and hν or , respectively (Powell, 1970). The electron transmission probability over the barrier can be calculated by using the Fowler escape condition under assumption of isotropic momentum distribution of the excited charge carrier (Hughes
Model Description and Experimental Realization of IPE
51
p [2m*(E0 hn)]1/2 pc
Escape surface: pn > pc
Fig. 3.2.1 Illustration of the carrier escape condition in the case of isotropic momentum distribution in the photoexcited state.
and Dubridge, 1932; Goodman, 1966c; Powell, 1970; Williams, 1970) illustrated in Fig. 3.2.1. The barrier height at the interface defines the critical value pc of the momentum component normal to the interface plane which must be exceeded to allow an excited electron to enter the collector. From the obvious relationship: p2c = 2m∗ ( + E0 ),
(3.2.1)
and the probability that the normal component of the momentum of an electron pn will be larger than pc (the latter defines the ‘escape cone’): f (p) =
1 pc , 1− 2 pn
(3.2.2)
one arrives to the barrier transparency expressed in terms of the total carrier energy as follows (Powell, 1970): 1 1 0 + E0 1/2 E− P(E, ) = = 1− if E > (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
Internal Photoemission Spectroscopy: Principles and Applications
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
Model Description and Experimental Realization of IPE
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
Internal Photoemission Spectroscopy: Principles and Applications
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
Model Description and Experimental Realization of IPE
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
Internal Photoemission Spectroscopy: Principles and Applications
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)
Model Description and Experimental Realization of IPE
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
Internal Photoemission Spectroscopy: Principles and Applications
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
Model Description and Experimental Realization of IPE
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
Internal Photoemission Spectroscopy: Principles and Applications
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
Model Description and Experimental Realization of IPE
(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
Internal Photoemission Spectroscopy: Principles and Applications
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
Model Description and Experimental Realization of IPE
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
Internal Photoemission Spectroscopy: Principles and Applications
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 (<1 nm) non-zero field region determined by the polarization layer, which cannot prevent tunnelling of a photoinjected electron back to emitter. Therefore, to enable the IPE observation, one introduces scavenger ions into the solution, which trap and stabilize the electrons in the salvated state as illustrated in Fig. 1.7.2. The obvious advantages of the electrolyte electrodes are the easy application, good optical transparency over broad spectral range, absence of optical interference effects typical for the thin-film collector samples, and the possibility to deposit desirable ions to the interface in situ. However, electrochemical reactions at the interfaces with electrolytes may introduce significant uncertainty related to the roughening of the emitter surface (Kostecki and Augustynski, 1995) or its chemical modification (oxidation or reduction) limiting the spectrum of emitters available for investigation in an emitter-electrolyte system. The temperature range of these measurements is also limited.
3.5.2 Optical input designs The light introduced into the system used for IPE experiment unavoidably passes through one of the (semi)transparent components. The latter must ensure sufficient range of optical transparency combined with good electric conductivity which is not always an easy task to achieve. Only electrolytes in which absorption edge of the solvent lies typically at a high energy (around 6 eV for H2 O, Williams et al., 1976; Goulet et al., 1990) while the concentration of dissolved species may be kept at a relatively low level combine these two properties successfully. Moreover, the electrolyte collector contact offers a unique possibility of simultaneous analysis of different crystal faces at the surface of emitter by using, for instance, the samples of cylinder shape (Sass, 1980). Alternatively, the electrolyte contact may also be used as the field electrode as shown in Fig. 1.3.1b which allows to improve the spectral characteristics of the optical input and, in some cases, to block electron or hole injection from the field electrode (Goodman, 1966b; 1970). One may also use the optical transparency of semiconductor materials to transmit the light towards their interfaces by using backside illumination scheme. This primarily concerns wide bandgap semiconductor crystal substrate (Coluzza et al., 1992; Ishida and Ikoma, 1993; Nishi et al., 1998). In the visible and near-infrared spectral ranges transparent field electrode materials like In oxide (Pan and Ma, 1980a, b) may also be applied. The common problem of transparent electrodes of this type is a narrow optical transparency window limited by the bandgap width of the material. In addition, large thickness of the electrode may require correction for the impurity- or defect-related optical absorption, but this can easily be achieved by using complementary optical transparency measurements. Finally, mainly aiming at the extension of the spectral range of the measurements to the ultraviolet region, one may use semitransparent metal layer as the field electrode on top of a thin or thick collector layer. The optical transparency of 0.3–0.35 can easily be achieved (Mehta et al., 1972), while the optical range of the measurements is limited only by the plasma frequency of the metal used. The major challenge in applying semitransparent metal electrodes comes from the technological side because only the films of sufficiently small thickness (10–20 nm) are transparent. There is a broad range of elemental metals which can be used in this way (see, e.g., Deal et al., 1966), as well as thermally stable conductive compounds (nitrides, carbides of refractory metals) characterized by excellent adhesion to most of the substrate or collector layer materials. Also, availability of metal electrodes with different work function offers
Model Description and Experimental Realization of IPE
65
significant advantages in identification of the injecting interface in a sandwich structure. The spectral threshold and the quantum yield of IPE may be correlated to the emitter–collector interface injection would the replacement of the field electrode by a metal with different work function result in the same IPE spectra.
3.5.3 IPE signal detection In a most straightforward manner the photoinjection of charge carriers in the collector layer can be detected by measuring the photocurrent generated on their way to the field electrode. This photocurrent technique is most widely used in the IPE spectroscopy applications due to its relative simplicity and universality. As already briefly mentioned, there are several experimental problems in photocurrent measurements related to a large capacitance of the current source and to the photocurrents not related to IPE which may arise in the samples with one or more semiconducting electrodes. In general, these complications limit the frequency range of the AC current measurements to few tens of Hz, and make application of the DC measurement scheme more practical, at least in samples with low leakage current density. With the sensitivity of a standard electrometer of 1 fA or even better, the factor limiting accuracy of the photocurrent measurements is the stability in time of the base dark signal. In the absence of substantial dark current drift, the averaging of the dark current and the current under illumination allows to reach the sensitivity to the photocurrent readout of about few fA in Si/SiO2 /metal structures. As an alternative one may consider option to detect the carrier injection through the measurements of the charge density trapped in the insulating collector. In the small-signal regime this is shown to be equivalent to the photocurrent measurements (Adamchuk and Afanas’ev, 1985, 1992b). This photocharging technique employs detection of the trapped charge through repetitive capacitance–voltage (CV) measurements in metal-oxide–semiconductor capacitor structures after exposure to a monochromatic light pulse. The injection-induced shift of the flat band point ( VFB ) on the CV curve (Sze, 1981) can be calculated assuming the constant trapping probability given by (1 − n(d)/n(x = 0)) and using Eqs. (2.2.19) and (2.2.20):
VFB
q = − t CD
d
d−x n(x)N(x)σ(F)dx d
0
= −n(x = 0) t
q d−x {1 − exp[−σ(F)]N}, CD d
(3.5.1)
where t is the duration of the illumination pulse, and CD = ε0 εD /d is the specific low-frequency capacitance of the collector layer. Therefore, by normalizing the rate of the VFB variation to the photon flux (cf. Eq. (3.1.3)) one obtains the value proportional to the IPE quantum yield as long as the trapping probability remains constant. The latter condition is easily met when conducting measurements in a sample with high trap density under a constant external electric field of a sufficient strength (Adamchuk and Afanas’ev, 1992a, b). Though the photocharging detection of IPE is possible only in the thin-collector samples with a highquality semiconductor–collector interface to allow CV charge monitoring, this technique offers several important advantages. First of all, the charge of the injected carriers is directly determined from the direction of VFB variation (Adamchuk and Afanas’ev, 1985; 1992a, b). Second, one may preferentially detect the carriers of one charge sign by intentionally introducing one or other type of the trapping centres. Third, the sensitivity of the measurements can be enhanced by increasing the exposure time t, i.e., by
66
Internal Photoemission Spectroscopy: Principles and Applications Measuring capacitor h
Floating field electrode
S Vmeas
Collector Vg Emitter
Fig. 3.5.2 Electrical connection enabling the floating field electrode to be used as the charge trapping one (the floating gate): After the initial voltage Vg is set, the switch S is set open. The high-quality (low-leak) measuring capacitor enables readout of charge variation at the floating gate through CV measurements using the measurement bias source Vmeas and the capacitive voltage divider.
integrating the measured IPE current. Finally, the CV measurements are much less sensitive to leakage current than low-level DC current ones because the former can be performed at a high probing signal frequency, e.g., at 1 MHz. The sensitivity of the photocharging measurements is directly related to the probability of charge carrier to be trapped in the emitter. As the high defect density in the collector may be undesirable, one may use the floating-gate configuration illustrated in Fig. 3.5.2, in which the filed electrode is disconnected from the bias source during measurements and acts as a trap with 100% efficiency. Recording of the CV curve is still possible without connecting to the gate again by biasing the substrate of the sensing capacitor. The advantage of this method is that samples of very small area, like metal–insulator–semiconductor transistors, can be analysed because the sensitivity is not scaled down with the sample area as in the case of photocurrent detection. However, the floating-gate configuration is highly sensitive to the lowlevel leakages which are integrated over the whole time needed to record the spectral curve or the photocharging kinetics. For this reason this method can be recommended only for the highly insulating collector materials like thermal SiO2 on silicon. To conclude, the experimental arrangement of the IPE spectroscopy appears to be dramatically different from the conventional photoemission spectrometer design with no ultrahigh vacuum environment needed. Instead, the high electric quality of the emitter–collector interface appears the pre-requisite of the successful IPE experiment. This brings up the technology of the interface fabrication as the key element in the realization of the IPE spectroscopy. Fortunately enough, the same issues dominate the development of technology of advanced microelectronic devices, so the IPE greatly profits from the achievements in this field. With the suitable sample in hand, the experimental set-up consists of the illumination and signal detection parts which in most of the cases can well be used at room temperature and ambient. Thus, the most of the experimental efforts in the case of IPE are related not to the measurements per se, but to the analysis of the results. First of all, the identification of the dominant contribution to the measured photocurrent is needed to obtain meaningful interpretation of the IPE spectra.
CHAPTER 4
Internal Photoemission Spectroscopy Methods
As already discussed, inelastic scattering of photoinjected charge carriers in collector material results in their thermalization at a distance of few nanometres from the surface of emitter. This feature effectively erases any information regarding the initial energy distribution of the injected carriers making most of the electron spectroscopy approaches used in the case of external photoemission inapplicable. Therefore, information regarding electron states involved in the internal photoemission (IPE) process can be obtained only from the quantum yield value, which corresponds to the total number of carriers escaped the emitter. Nevertheless, as the carriers contributing to the IPE are transported in a ballistic regime from the point of their excitation to the surface of emitter and further, towards the image force barrier top, their energy distribution is reflected in the escape probability value which, in its turn, determines the quantum yield. As a result, not only the IPE threshold energy can be found from the yield spectra but, also, all the other processes potentially affecting the quantum yield (optical singularities, scattering thresholds, etc.) can be characterized in their relationship with the energy of exciting photon or with the average energy of the photoinjected carriers. In addition, optical excitation of the occupied electron states in the collector allows one to obtain information about the bandgap width of the materials as well as concerning irregular electron states with energy levels inside the gap. By combining these approaches, one can extract vast amount of information concerning the uppermost occupied and lowest unoccupied electron states in the emitter–collector system. Worth of adding here is that these portions of the electron state spectrum of the interface determine the most important electron transport properties of heterostructures. The latter makes the IPE spectroscopy the most relevant tool of their analysis. In this chapter four major IPE spectroscopy methods will be discussed: (1) The spectral threshold determination which allows quantification of energy band offsets at the emitter–collector interface. (2) The total yield spectroscopy enabling observation of the optical transitions in the surface layer of the emitter. (3) The scattering spectroscopy revealing onsets of electron energy-loss processes both in the emitter and in the collector. (4) The photoconductivity (PC) and photoionization (PI) spectroscopy addressing the band-type states and localized states in the collector, respectively. 67
68
Internal Photoemission Spectroscopy: Principles and Applications
4.1 IPE Threshold Spectroscopy 4.1.1 Contributions of different bands to IPE
105
103 102
C
0.8 0.4
0.0 2.6 2.8 3.0 3.2 3.4 hn (eV)
101
20 Y 1/3 (relative units)
IPE yield (relative units)
104
Y (relative units)
Determination of the spectral thresholds of different photoinjection processes represents the most widely used application of the IPE to characterization of interfaces. In this method, the energy band offset at the interface is associated with the spectral threshold determined as the minimal photon energy necessary for injection of a charge carrier. The basic idea of this technique is related to the description of the IPE yield dependence on the photon energy as a fingerprint of the initial state density of states (DOS) in the emitter weighted by the escape probability and integrated over all the carrier energies exceeding the interface barrier height (cf. Eq. (3.1.1b)). Application of this description is illustrated by the IPE yield dependencies on photon energy shown in Fig. 4.1.1 for n+ -Si(100)/SiO2 interface as measured under different strength of electric field in the collector. The field was controlled externally by applying the corresponding bias voltage to the semitransparent field electrode (13-nm thick Au) on top of a 124-nm thick oxide layer. The IPE spectra are seen to contain two contributions (usually referred to as ‘bands’, in similarity with conventional optical absorption or photoemission spectroscopy), the one with a low yield and spectral threshold at around 3 eV, and another one, with much higher quantum yield and the spectral onset at around 4 eV. The former IPE band is associated with optical excitation of electrons from the occupied states in the conduction band of heavily phosphorus-doped (nD ∼ 1019 cm−3 ) silicon to energies sufficient to be injected into the unoccupied states of the SiO2 conduction band. In the case of Si crystals with a lower donor concentration this IPE becomes less and less pronounced (see, e.g., the yield dependence on the n-type Si doping level in Afanas’ev and Stesmans (1997b)). At approximately 1 eV higher photon energy starts the second IPE band associated with photoemission of electrons from the valence band of silicon into the oxide conduction band. To determine the exact band offsets at the interface, one should first find the corresponding spectral thresholds at different field strength and
100 101 102
n-Si(100)/SiO2
103 3
V
C
E2 E1
10 0
3
4
4 hn (eV) 5
5 6
Photon energy (eV)
Fig. 4.1.1 IPE quantum yield as a function of the photon energy for the heavily doped n-type (100)Si/SiO2 (124 nm)/Au(15 nm) structures at different strength of electric field in the oxide (in MV/cm): 0.2 (), 0.36 (), 0.55 (), 0.77 (), 1.17 (3), and 1.57 ( ). Determination of the spectral thresholds of electron IPE from the conduction (C ) and valence band (V ) of silicon into the oxide conduction band using Y –hν and Y 1/3 –hν plots is illustrated in the left top and right bottom inserts, respectively. The arrows indicate the spectral thresholds as well as energies of optical singularities E1 and E2 of Si crystal.
Internal Photoemission Spectroscopy Methods
IPE threshold (eV)
4.5
69
V(F 0) 4.3 eV
4.0
V
3.5 C(F 0) 3.2 eV 3.0
C
0.0
0.2
0.4
0.6
(Field)1/2
0.8
1.0
1.2
1.4
(MV/cm)1/2
Fig. 4.1.2 The Schottky plot of spectral thresholds electron IPE from the conduction (C ) and valence band (V ) of silicon into the oxide conduction band as functions of the electric field strength in the oxide of n+ -(100)Si/SiO2 (124 nm)/Au(15 nm) structures. Lines illustrate the determination of zero-filed barrier heights corresponding to the fundamental band offsets at the interface.
then obtain their zero-field value using extrapolation in the Schottky co-ordinates. According to the Table 3.2.1, the quantum yield of IPE from an energetically narrow distribution of electron states should increase linearly above the spectral threshold as, indeed, is observed in the linear plot of the IPE yield shown in the upper left insert in Fig. 4.1.1. Then, the corresponding spectral threshold C can be analysed using the Schottky plot shown in Fig. 4.1.2 (the bottom line). In its turn, the yield of IPE from the semiconductor valence band is expected to follow the cube spectral dependence (Powell, 1970). Determination of its spectral threshold V requires linear extrapolation of the Y 1/3 –hν plot which is exemplified in the lower right insert in Fig. 4.4.1. However, the spectra are seen not to be perfectly linear but exhibit a dip at around hν = 4.3–4.4 eV. This behaviour is related to a significant variation of optical properties of the silicon emitter in vicinity of E2 singularity (hν = 4.4 eV) associated with excitation of direct optical transitions between points of high symmetry in the Brillouin zone of Si crystal. Variation of the optical parameters, entirely neglected in the simple IPE description, modulates the IPE yield spectrum. Therefore, only a limited portion of the spectral curve can be used to determine the IPE threshold greatly impairing accuracy of the procedure. In fact, the linear fit of the IPE spectra shown in the upper left insert in Fig. 4.4.1 is also limited to the photon energy range hν < 3.4 eV because of E1 optical singularity occurring at this energy. Powell suggested to analyse voltage dependences of IPE current measured at different photon energies by using linear extrapolation in the Y 1/3 –V 1/2 co-ordinates (Powell, 1970). This method potentially allows one to exclude the influence of optical effects because only the shape of the Y 1/3 –V 1/2 curve is analysed. However, this method suffers from the influence of scattering effects in the low field range and, therefore, requires application of a high electric field. In addition, the ideal image-force barrier behaviour is assumed for the field-dependent barrier height, which greatly limits the applicability of the Powell’s approach. Instead, while keeping in mind the limited accuracy of threshold determination, we can find the thresholds by extrapolating yield in the photon energy range below 4.4 eV. The corresponding values of V are also indicated in Fig. 4.1.2. Now, by using the linear extrapolation to zero electric field one can estimate the barrier heights between the conduction/valence bands of Si and the conduction band of SiO2 to be C (F = 0) = 3.20 ± 0.05 eV and V (F = 0) = 4.30 ± 0.05 eV, respectively.
70
Internal Photoemission Spectroscopy: Principles and Applications
The observed 1.1-eV difference between the barriers for electron IPE from the valence and conduction band states of silicon accounts well for the bandgap width in this semiconductor (1.12 eV at room temperature). From the slope of the Schottky plots using Eq. (2.2.8) one may estimate the effective imageforce constant εi to be close to 2, which is consistent with the expected value εi ≈ n2 = 2.1. This example clearly shows the way how different components of the emitter DOS can be traced both on the basis of their energy thresholds and using the relative quantum yield which is proportional to the initial DOS. It should be added, however, that the observed IPE thresholds are not necessarily associated with DOS of the emitter electrode but may also contain contributions of other states located near the interface or in the collector layer itself. For instance, the electron IPE yield spectra of 6H–SiC/SiO2 interface shown in Fig. 4.1.3 as Y 1/3 –hν plots exhibit three spectral thresholds indicated by arrows. Only the lowest threshold 1 and the upper one 3 are field dependent, as illustrated by the Schottky plots shown in Fig. 4.1.4. Observation of the Schottky barrier lowering suggests the relationship of these thresholds to excitation of the occupied electron states of the SiC emitter. The change of SiC polytype from 6H–SiC F (MV/cm): 1.0 2.0 3.0 4.0 5.0 6.4 3
(IPE yield)1/3 (relative units)
12 1
1
10 8
0 6
3
4 2
4
6H–SiC/SiO2 1
2 0
2
2
3
4
5
6
Photon energy (eV)
Fig. 4.1.3 IPE quantum yield as a function of the photon energy for the n-type 6H–SiC/SiO2 (22 nm)/Au(15 nm) capacitor at different strength of electric field in the oxide indicated in the figure. The spectral thresholds of three observed IPE bands are indicated for clarity. The lines represent a guide for eye, not the curve fitting.
IPE threshold (eV)
6
3
5
2
4
SiC/SiO2
1
3
4H 6H,15R 3C
2 0
1
2
(Field)1/2 (MV/cm)1/2
Fig. 4.1.4 The Schottky plot of IPE spectral thresholds as functions of the electric field strength in the oxide at the interfaces of different SiC polytypes (3C, 6H, 15R, 4H) with thermally grown SiO2 layers. Lines illustrate the determination of zero-filed barrier heights.
Internal Photoemission Spectroscopy Methods
71
to other (3C , 15R , 4H ) is found to affect the lower IPE threshold in accordance with the polytypespecific value of the SiC bandgap width (Afanas’ev et al., 1996a) varying from 2.38 eV in 3C SiC to 3.25 eV in 4H–SiC (Choyke, 1990). This effect and the observed difference in the relative quantum yield value allows interpretation of the SiC/SiO2 IPE spectra as the electron IPE from the valence band with the threshold 3 and the electron emission from the conduction band of SiC with the polytype-sensitive threshold 1 (Afanas’ev et al., 1996a). The remarkable feature here is considerable conduction band IPE even from a moderately doped (nD = 4 × 1016 cm−3 ) SiC indicative of a large photoelectron escape depth. Indeed, as the maximal kinetic energy of electron in the conduction band is equal in this case to hν, it appears to be below the bandgap width of the semiconductor (3.02 eV for 6H–SiC) resulting in a reduced rate of electron–electron scattering in the emitter.
(IPE yield)1/3 (relative units)
As far as it concerns the spectral threshold 2 which is also clearly seen in the IPE spectra in Fig. 4.1.3, its field dependence appears to be below the spectral resolution limit in all the studied samples (cf. Fig. 4.1.4). This behaviour would indicate that the electron excitations at hν > 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
Internal Photoemission Spectroscopy: Principles and Applications
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<0
104 103 102
e(Si)
e(Al)
Yield (relative units)
101 Eg(HfO2)
100 101
(a)
106 105
Al
Eg(HfO2) (c)
Au
(100)Si/Si3N4/HfO2
(100)Si/Si3N4/HfO2/Au V<0
V>0
104
h(Si)
103 102
e(Si)
e(Al)
101 Eg(HfO2)
100 101 3
4
Eg(HfO2)
E2
E2
E1
(b) 5
Al
Au
6 2 3 Photon energy (eV)
(d) 4
5
6
Fig. 4.1.7 IPE yield as a function of photon energy in n-Si/SiON/HfO2 (10 nm)/Au (a) and n-Si/Si3 N4 / HfO2 (10 nm)/Au (b) capacitors measured under positive voltage on the Au electrode of 1.0 (), 1.5 (), 2.0 (), and 2.5 () V; Filled symbols correspond to the samples additionally oxidized for 30 min in O2 at 500 () and 650 ()◦ C, measured with a metal bias of +2.0 V. Panels (c) and (d) show IPE yield as a function of photon energy in the as-deposited p-Si/SiON/HfO2 (9 nm) and p-Si/Si3 N4 /HfO2 (10 nm) MOS capacitors with Au () and Al () electrodes measured under negative voltages of −2.0 and −2.5 V, respectively; Filled symbols correspond to the samples additionally oxidized for 30 min in O2 at 500 () and 650 ()◦ C, measured under −2.0 V bias on Au electrodes. Arrows and dashed lines indicate the spectral thresholds and the energies of optical singularities of the Si substrate crystal, respectively.
energy barrier between the top of HfO2 valence band and the bottom of Si conduction band as shown in Fig. 3.5.1. The association of the IPE band with spectral threshold of 3.6 eV with the hole injection from Si gains further ground from the observation of its modulation at the energy corresponding to E2 singularity of Si, and from the significant attenuation of this current in samples subjected to supplemental thermal oxidation (filled symbols in Fig. 4.1.7). In the last case the oxidation of silicon leads to formation of SiO2 -like interlayer which, as already mentioned, represents a barrier of large height for holes in Si. Thus, there is a possibility to separate contributions of different IPE transitions by combining measurements in samples with different field electrode materials, different emitter–collector combinations, and two opposite orientations of electric field in the collector. Additionally, in the case of collector PC or bulk defect PI, one may also consider analysis of the photocurrent as a function of the collector thickness because, for photon energies below or in the vicinity of the intrinsic optical absorption edge of the collector, this signal must scale up linearly with the photoexcited material volume (Williams, 1965).
IPE yield (relative units)
4
3
2
Y 1/2 (relative units)
Internal Photoemission Spectroscopy Methods
75
h(Si/SiO2)
1.5
Si(111)/SiO2
F(MV/cm):
1.0
2.0
0.5
1.35 1.0
0.0 4.5
5.0
5.5 hn (eV)
6.0
1
0 4.5
5.0
5.5
6.0
Photon energy (eV)
Fig. 4.1.8 Hole IPE quantum yield as a function of the photon energy in (111)Si/SiO2 /Au structures measured using photocharging technique under different strength of electric field in the oxide (in MV/cm): 1.0 (), 1.35 (), and 2.0 (). Determination of the spectral threshold h corresponding to the energy barrier between the top of the oxide valence band and the bottom of the conduction band of silicon in the insert. Lines guide the eye.
In an ideal case one may try to find experimental configuration(s) enabling IPE only at one interface. In this case the sign of the injected charge carriers will be uniquely determined by the orientation of the electric field which must be attractive to make IPE possible. This can be realized in samples with a thick collector when electric field needed for IPE is present only in the barrier region, or in the case of electrolyte contact because its conductivity is determined by ions rather than by electrons. This kind of approach was used, for instance, to observe IPE of holes from Si into SiO2 (Goodman, 1966b). Alternatively, the problem of hole IPE from Si into SiO2 can be addressed using observation of positive photocharging which employs a much higher probability of a hole trapping in SiO2 than that of an electron (Adamchuk and Afanas’ev, 1985; 1992b). The hole IPE spectra obtained using the photocharging method are exemplified in Fig. 4.1.8. Insert illustrates the spectral threshold determination. One can directly see now that a much higher photon energy is required for the hole IPE than for the electron one (cf. Fig. 4.1.1). One of the important effects revealed by combined electron and hole IPE measurements in Si/SiO2 structures consists in observation of interface dipoles (up to 0.3 eV) associated with incorporation of Cl to the interface in the case of Si oxidation in the presence of Cl-containing molecules (HCl, Cl2 ) (Adamchuk and Afanas’ev, 1984; 1992a, b). The bandgap width of the SiO2 collector layer found from the IPE barriers using Eq. (2.2.1) remains constant Eg = 8.9 eV and coincides with that obtained from the PC measurements (DiStefano and Eastman, 1971; Adamchuk and Afanas’ev, 1992a, b). This result exemplifies the ability of IPE threshold spectroscopy in revealing dipole components of the interface energy barriers.
4.2 IPE Yield Spectroscopy The IPE spectra discussed in the previous section are often seen to exhibit modulation of the quantum yield at the photon energies corresponding to excitation of direct optical transitions specific to the particular crystal emitter (cf. Figs 4.1.1 and 4.1.7 for a silicon crystal, see also DiStefano and Lewis (1974)). Association of these features with the properties of electron states of the emitter is easily proven
Internal Photoemission Spectroscopy: Principles and Applications
(IPE yield)1/3 (relative units)
76
4
(100)Si/ZrO2
(100)Si/Al2O3 d(hn) 0.02 eV E2
E2
e
E1 Si Ox Me
2
e(ZrO2)
e(Al2O3)
e(SiO2) 0
3
4
E1 3
4
5
Photon energy (eV)
Fig. 4.2.1 Cube root of the IPE yield as a function of photon energy for MOS structures with different dielectrics. Left panel shows results for as-deposited 5-nm thick Al2 O3 () or supplementally oxidized at 650◦ C for 30 min () as compared to a 4.1-nm thick thermal SiO2 (). Right panel shows IPE spectra of electrons from Si into as-deposited 7.4 nm ZrO2 () or additionally oxidized at 650◦ C for 30 min (). All curves are measured under an applied electric field of 2 MV/cm in the insulating layer closest to Si. The arrows E1 and E2 indicate onsets of direct optical transition in the Si crystal. The spectral thresholds e are indicated for different oxides. The error in the IPE yield determination is smaller than the symbol size.
by observation of their same spectral position in samples with different collector material. One may compare the IPE results for Si/SiO2 (Fig. 4.1.1) and Si/HfO2 (Fig. 4.1.7) interface to the spectra obtained when using Al2 O3 or ZrO2 collector layers as illustrated in Fig. 4.2.1. In all the cases the IPE yield increase deviates from the cube law with photon energy at around hν = 3.4 eV (E1 feature) while at around hν = 4.4 eV (E2 feature) the quantum yield is decreasing in its absolute value which cannot be explained using the simple IPE theory: Integrals (3.1.1) or (3.1.1a) can never have a negative first derivative on the photon energy. Therefore, some additional physical process has to be invoked to explain the observations.
4.2.1 Mechanism of the yield modulation The explanation of the IPE yield decrease with increasing photon energy in vicinity of hν = 4.4 eV is easily found when comparing absolute energies of the final excited electron states in the X4 → X1 and, somewhat weaker, 4 → 1 direct optical transitions (the E2 feature) to the energy electron needs to be injected into SiO2 or a wide bandgap metal oxide as illustrated in Fig. 4.2.2. From the band diagram of Si crystal (Cardona and Pollak, 1966) it is seen that the final states are close to the bottom of Si conduction band (see the bold arrow in Fig. 4.2.2), i.e., the photogenerated electrons are ∼3 and ∼2 eV below in energy than the bottom of the conduction band of SiO2 and HfO2 , respectively. As the result, the X4 → X1 and 4 → 1 transitions strongly contribute to optical absorption but give no corresponding contribution to the electron IPE (Adamchuk and Afanas’ev, 1992a). Therefore, the decrease in the observed quantum yield is caused by combination of two factors. First, the reflectivity of silicon strongly increases when photon energy approaches the energy of the E2 feature causing reduction in the external quantum yield (cf. Eq. (3.1.2)). Second, the direct transitions account for very large value of optical absorption coefficient of silicon (α ≈ 2.5 × 106 cm−1 ) leading to substantial light attenuation at a depth comparable to the mean photoelectron escape depth. In other words, the high oscillator strength of X4 → X1 and 4 → 1 direct optical transitions allows them to effectively ‘screen’ the electron excitations to the energetically higher states which may potentially contribute to the IPE. In a similar way, the transitions between 3 and 1 E-k branches responsible for the E1 feature in the optical spectra of Si at hν = 3.4 eV (Pollak and
Internal Photoemission Spectroscopy Methods
Energy (eV)
10
77
Eg(Si)
5
EC
X1
0 5 10
X4
L
EV Si
X
SiO2
Fig. 4.2.2 Electron energy band structure of silicon crystal (Cardona and Pollak, 1966) with the energy band diagram of Si/SiO2 interface shown in the same energy scale. Bold arrow indicates X4 → X1 direct optical transitions occurring at photon energy of 4.4 eV responsible for the E2 feature in the optical spectra of Si. The final electron state in this transition (X1 ) is seen to be energetically well below the oxide conduction band bottom making photoinjection of electrons impossible.
Rubloff, 1972), also give no contribution to the electron IPE because of insufficient energy of electrons in the final state. Modulation of the IPE spectral curves by optical features of the emitter can be observed not only for silicon but also for other materials. For instance, ‘saturation’ of the electron IPE yield from amorphous carbon to SiO2 in the spectral range hν > 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
Internal Photoemission Spectroscopy: Principles and Applications
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
Internal Photoemission Spectroscopy Methods
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
Internal Photoemission Spectroscopy: Principles and Applications
(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
(IPE yield)1/3 (relative units)
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 ( ).
Internal Photoemission Spectroscopy Methods
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
(IPE yield)1/3 (relative units)
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
Internal Photoemission Spectroscopy Methods
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 << 1, Eq. (4.2.3) leads to expression (2.1.9) for the external quantum yield. In the absence of any optical singularities, the light absorption at the surface of emitter may be characterized by the energy-independent coefficient α0 which would scale the internal quantum yield by a constant factor: α 0 λe Y0 (hν) = Y (hν, ) . (4.2.4) 1 + α 0 λe The external quantum yield can be calculated from Eq. (4.2.4) by multiplying by a factor [1 − R], where R is the optical reflectivity of the sample (cf. Eq. (3.1.2)). Next, let us assume that at certain photon energy hν0 > 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
Internal Photoemission Spectroscopy: Principles and Applications
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).
(IPE yield)1/3 (relative units)
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.
Internal Photoemission Spectroscopy Methods
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
Internal Photoemission Spectroscopy: Principles and Applications
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) << Eg (collector). This would enable detection of the scattering-modulated IPE signal well below the spectral threshold of PC which has much higher quantum yield than the IPE. In the case of IPE from the valence band of a semiconductor the largest kinetic energy of an electron will be equal to hν − Eg (emitter) leading a different condition for observation of inelastic scattering effects in IPE: < 2Eg (emitter) << Eg (collector). The experimental evidence for quantum yield reduction when the excited carrier energy exceeds the inelastic scattering energy onset is provided by the electron IPE spectral curves shown using the logarithmic yield scale in Fig. 4.3.2 for 6H–SiC/SiO2 interface. One might notice that the quantum yield above the threshold of electron IPE from the conduction band of SiC indicated as 1 shows a drop at around hν ≈ 3.1 eV indicated by the arrow Eloss . For the photons with the energy higher than this value the rate of the further yield increase appears to be much reduced suggesting a reduced IPE probability. As the energy point at which the IPE yield decrease is observed appears to be insensitive to the strength of electric field in the oxide (which is seen to cause a shift of the spectral threshold to a lower photon energy due to the Schottky effect) this feature is clearly related to the processes occurring inside the SiC emitter and unaffected by the image force. At the same time, the optical absorption and reflectivity of 6H–SiC in the spectral range around hν = 3 eV do not exhibit variation strong enough to explain the yield decrease by the influence of direct optical transitions discussed in previous section because of indirect
IPE yield (relative units)
103
3
6HSiC Eloss
102
2
101 F(MV/cm) 1.0 2.0 3.0 4.0 5.0 6.4
100 101 1 102
2
3
4
5
6
Photon energy (eV)
Fig. 4.3.2 IPE yield as a function of photon energy for a 6H–SiC MOS structure at different strengths of the electric field in the oxide (in MV/cm): 1.0 (), 2.0 (), 3.0 (), 4.0 (), 5.0 (3), and 6.4 ( ). The arrow Eloss indicates the position of the electron energy loss peak.
Internal Photoemission Spectroscopy Methods
87
4HSiC
102
Eloss
101 100 101 IPE yield (relative units)
(a) 102 102
15RSiC Eloss
101 100 101
(b)
102 102
3CSiC
101 100 101 (c)
102 2
3
4 5 Photon energy (eV)
6
Fig. 4.3.3 IPE yield as a function of photon energy for the 4H SiC (a), 15R SiC (b), and 3C SiC (c) MOS structure at different strengths of the electric field in the oxide (in MV/cm): 0.3 (), 0.5 (), 1.0 (), 2.0 (), and 3.0 (3). The arrow, marked Eloss , indicates the position of the electron energy loss peak.
nature of the SiC bandgap. Therefore, the onset of inelastic electron–electron scattering in the SiC crystal represents the only feasible explanation of the observed yield behaviour. Further support to this interpretation is provided by the results presented in Fig. 4.3.3(a–c) which shows the spectra of electron IPE into SiO2 from other three SiC polytypes, 4H, 15R, and 3C, respectively. For the first two polytypes the spectra exhibit the feature similar to than the 6H–SiC data (cf. Fig. 4.3.2) also indicated by arrows as Eloss . Though it is less pronounced in the 4H–SiC sample than in 6H–SiC, its energy position seems also to be insensitive to the strength of the applied electric field. In the case of 3C– SiC (Fig. 4.3.3c) no modulation of the IPE spectrum is observed. The latter is consistent with the earlier discussed mechanism of the excited electron scattering through excitation of another electron across the SiC bandgap. For 3C–SiC, the bandgap width (2.38 eV according to Choyke (1990)) is considerably lower than the threshold of IPE from the conduction band. Therefore, for any electron contributing to the IPE process, the inelastic scattering is possible and its energy threshold remains unobservable. In Fig. 4.3.4 the energy position of the scattering feature Eloss is shown as a function of the optical bandgap width of the corresponding SiC polytype (Choyke, 1990). The loss is seen to occur at the energy slightly (≈0.1 eV) above the SiC bandgap value, but, apart from this, the correlation between two energies is clear. The value of the shift of the loss peak to higher energy is close to the energy of the LO (970 cm−1 ) and TO (790 cm−1 ) optical phonons ω in SiC (Engelbrecht and Helbig, 1993). Apparently, the phonon
88
Internal Photoemission Spectroscopy: Principles and Applications
Electron energy loss (eV)
3.4
4H–
3.3 Eloss Eg hv 15R–
3.2
Eloss Eg
6H–
3.1
3.0
2.9 2.9
3.0
3.1
3.2
3.3
3.4
SiC bandgap width (eV)
Fig. 4.3.4 Spectral position of the electron energy loss peak in the IPE spectra as a function of the optical bandgap width of the corresponding SiC polytype (according to Choyke (1990)). Lines guide the eye.
emission helps to excite transition of the secondary electron from the top of the SiC valence band to the SiC conduction band bottom. 4.3.2 Scattering in collector As already discussed in Chapter 2, scattering of charge carriers in the image-force potential well, i.e., in the spatial region between the surface of emitter and the top of the potential barrier xm shown in Fig. 2.2.2, modulates the quantum yield by a term exp[−xm / ] (cf. Eq. (2.2.10)). Using the field dependence of xm given by Eq. (2.2.9) one can determine the mean electron thermalization length by fitting the lowfield portion of the IPE yield versus field curve with Eq. (3.3.1) while keeping the photon energy hν constant. An example of results obtained using this approach is presented in Fig. 4.3.5 which shows
Mean free path (nm)
15
Si(100)/SiO2
10
5
MC simulation Experiment
0 0.0
0.5 1.0 hn (eV)
1.5
Fig. 4.3.5 Mean free path of an electron at Si/SiO2 interface as a function of difference between exciting phonon energy hν and the interface barrier height . The points show the experimental data, the dashed line – the Monte–Carlo (MC) simulation results obtained under assumption of LO phonon scattering.
Internal Photoemission Spectroscopy Methods
89
the mean electron thremalization length as a function of excess photon energy over the Si(100)/SiO2 interface barrier (Afanas’ev, 1991a). Experimental points are obtained by fitting of the IPE current– voltage characteristics using Eq. (2.2.9) with p = 3 corresponding to the case of electron IPE from the valence band of semiconductor (Powell, 1970). In the range of small excess energy of electrons, i.e., (hν − ) < 0.3 eV, the thermalization length strongly increases indicating a lower electron scattering rate. The constant thermalization length model (Berglund and Powell, 1971) is seen to be a realistic approximation in the excess electron energy range from 0.3 to 1 eV. At excess energies higher than 1 eV increases as approximately ∼ (hν − )1/2 (Afanas’ev, 1991a). These experimental results can be compared to the results of the Monte–Carlo (MC) simulation of electron transport across the image-force barrier region assuming electron interaction with to LO phonon modes (ω1 = 0.063 eV and ω2 = 0.15 eV) which are also shown in Fig. 4.3.5 by a dashed line (Afanas’ev, 1991a). The MC simulations performed using the electron–phonon scattering parameters of bulk SiO2 (Fitting and Friemann, 1982; Fitting and Boyde, 1983) are seen to reproduce the experimental data on electron scattering quite well. Importantly, they also reveal a reduction of scattering rate in the low electron energy range which can now be explained in some more detail. Analysis of electron trajectories indicates that most of the electron–phonon interactions occur in the immediate vicinity of the potential barrier top because electrons are travelling there with a minimal normal velocity and, therefore, are dwelling for the longest time in this spatial region. When the energy of electron is smaller than the phonon energy ω, no scattering with phonon emission is possible resulting in the nearly no-energy-loss transport. This effect appears to be particularly pronounced in the case of emission from the silicon valence band because of triangular shape of the excited electron distribution in the case of IPE from the valence band (cf. Table 3.2.1) with large portion of the low-energy charge carriers. These carriers provide most significant contribution to the increase of because the latter is averaged over the whole energy spectrum of the electrons entering the oxide. These results on electron scattering indicate the inelastic interaction with LO phonons, primarily with ω2 = 0.15 eV mode, to be the dominant mechanism of electron thermalization at the Si/SiO2 interface. At the same time the MC simulations predict that the energy onsets of this scattering process can also be observed. This would naturally lead to determination of the scattering mode energy, i.e., will allow one to determine the energy spectrum of phonons in the near-interface layer of the collector. However, analysis of current–voltage curves of electron IPE from the valence band is unsuitable for this purpose because, in addition to the broad energy distribution of electrons passing through the barrier region, the barrier height at the interface is also a function of electric field (cf. Eq. (2.2.8)) and it changes in the course of the IPE current–voltage curve recording at a constant hν. The way to the phonon mode spectroscopy was paved by IPE experiments using degenerately doped n-type Si in which electrons occupy a narrow energy range of states close to the bottom of the semiconductor conduction band (Afanas’ev, 1991a). Optical excitation of these electrons results in a nearly mono-energetic flux of charge carriers arriving to the Si/SiO2 interface as illustrated in the insert in Fig. 4.3.6a. The spectral curves of electron IPE presented in this figure using linear yield plot (cf. Table 3.2.1) exhibit non-monotonous yield increase with increasing energy of the photons. This might look similar to the scattering-related features observed in the electron IPE spectra of SiC/SiO2 interface shown in Figs 4.3.2 and 4.3.3. However, in contrast to the SiC/SiO2 case, in n+ -Si/SiO2 structures the spectral position of the yield deviations from the linear increase is seen to be affected by the strength of electric field in the oxide. This behaviour is consistent with the prediction that electron scattering occurs in the vicinity of the field-dependent potential barrier maximum. Moreover, for the spectral curve measured at the highest strength of electric field in the oxide of F = 2.2 MV/cm (3) deviations from linearity are seen to be weak. The latter is, again, in agreement with the reduction of the scattering probability caused by a progressive shift of the barrier maximum towards the emitter surface with increasing electric field.
90
Internal Photoemission Spectroscopy: Principles and Applications
1.0
1.0
n-Si 0.5
0.0 2.7
SiO2
0.5
Scattering probability
IPE yield (relative units)
0.063 eV 0.15 eV
0.0 2.8
2.9 3.0 3.1 3.2 Photon energy (eV)
0.0
(a)
0.1 0.2 0.3 Electron energy (eV) (b)
Fig. 4.3.6 (a) The quantum yield of electron IPE from the conduction band of n+ -Si(100) into SiO2 as a function of photon energy as measured under different strength of electric field in the oxide (in MV/cm): 0.3 (), 0.5 (), 1.0 (), 1.5 (), and 2.2 (3). The insert shows the scheme of the observed electron transitions. (b) The electron scattering probability as a function of its kinetic energy above the potential barrier top obtained from the corresponding spectral curves shown on panel (a). Three upper curves are shifted along the vertical axis for clarity. Dashed lines indicate the energy of SiO2 LO phonon modes.
The electron scattering probability may be quantified by constructing the spectral deviation function of type given by Eq. (4.2.1) (Afanas’ev, 1991; Adamchuk and Afanas’ev, 1992a): P[hν − (F), F] = 1 −
Y (hν, F) , C[hν − (F)]
(4.3.1)
in which the constant C is determined by the slope of the spectral curve less affected by the scattering (curve (3) in Fig. 4.3.6a). The results of scattering probability calculations are illustrated in Fig. 4.3.6b in which the energies of the dominant LO phonon modes in SiO2 are indicated for comparison. The onset of scattering is seen to be well correlated with the lowest LO mode (ω1 = 0.063 eV) while the contribution of the higher phonon mode (ω2 = 0.15 eV) can also be distinguished on curves corresponding to IPE spectra taken at relatively high electric field strength () and () in Fig. 4.3.6. One may significantly improve the spectral resolution in the measurements of this type by using laser excitation. This point is illustrated in Fig. 4.3.7 which shows the electric field dependence of the electron IPE current from n+ -Si into SiO2 excited by Cd-vapour laser (hν = 2.84 eV). The increase in the IPE current under constant hν with increasing field is associated with the barrier lowering (the Schottky effect) and with the shift of its maximum closer to the injecting interface. The curves are shown for two dopant concentrations and exhibit undulations associated with onsets of inelastic electron scattering. These onsets are more clearly seen in Fig. 4.3.7(b) which shows the first derivative of the photocurrent on voltage for the sample with nD = 2 × 1019 cm−3 as a function of the applied field. The peaks are observed at the strength of electric field corresponding to the excessive energy of electrons of 0.03 and 0.06 eV, which is close to the energy of acoustic and optical phonons in SiO2 , respectively. In this measurement mode the IPE scattering spectroscopy closely resembles the inelastic tunnelling spectroscopy in which the impact of
Internal Photoemission Spectroscopy Methods
Photocurrent (pA)
10
91
hn 2.84 eV
5
(a)
dI/dV (relative units)
0 40
30
20
10 (b) 0 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Electric field (MV/cm)
Fig. 4.3.7 (a) Photocurrent as a function of electric field as measured in n+ -Si(100)/SiO2 /Au structures using 2.84-eV laser excitation. The current originates from the electron IPE from the conduction band of Si doped with phosphorous with concentration nD = 5 ×1018 cm−3 () and nD = 2 × 1019 cm−3 (). (b) First derivative of the IPE current–voltage curve versus strength of applied electric field. The arrows indicate the position of electron scattering-related features.
scattering on the electron tunnelling current is analysed. Similar to the tunnelling spectroscopy technique, further improvement of the energy resolution may be attained when the temperature of measurements is lowered because of reduction of thermal width of the energy distribution of initial electron states in the conduction band of n+ -doped semiconductor. By analysing electron scattering probability in the barrier region one may also obtain information about influence of static scattering impurities on the thermalization length. This is exemplified in Fig. 4.3.8 which shows (hν − ) curves obtained from the electron IPE experiments in Si/SiO2 structures prepared by thermal oxidation of Ge-doped Si crystals (Afanas’ev et al., 1992b). The overall shape of the curves remains approximately the same suggesting that LO phonon scattering dominates the electron energy dissipation process. At the same time, a considerable reduction of the thermalization length is seen to occur progressively with increasing Ge concentration in the samples as illustrated in the insert. Apparently, elastic scattering of electrons by Ge ions in the near-interface oxide layer results in effectively longer time the electrons dwell in the potential barrier region. This eventually would lead to a higher probability of energy loss through electron–phonon scattering.
92
Internal Photoemission Spectroscopy: Principles and Applications
1 nm
Mean free path (nm)
4
10
3 2 1 0
1
5
0 0.0
0
0.2
2
(1020 cm3)
0.4 0.6 hn (eV)
0.8
Fig. 4.3.8 Mean free path of an electron at Si/SiO2 interface as a function of difference between exciting phonon energy hν and the interface barrier height derived from the IPE measurements in the samples with different Ge content in the starting Si crystal (in cm−3 ): 0 (), 8 × 1018 (), and 2.5 × 1020 (). The insert shows the dependence of in the plateau region on Ge concentration.
The described spectroscopy of energy losses in the IPE spectroscopy is somewhat similar to the conventional energy loss spectroscopy used in the external photo- and secondary electron spectroscopy methods. However, at least in the case of spectroscopy of carrier scattering in the collector, one observes predominantly the scattering events in the spatial region close to the top of the image-force barrier maximum. This feature makes the IPE scattering spectroscopy mostly sensitive to the interfacial layers of the contacting materials, once again indicating the interface-sensitive nature of the IPE spectroscopy in general.
4.4 PC and PI Spectroscopy Both PC and PI processes in the collector provide photocurrent (or photocharging) signal which can be detected in the same way as the current (or charge) originating from the IPE-type electron transitions. This kind of measurements enables additional characterization of electron states in collector, which is of particular importance when characterizing thin layers of solids and their interfaces. In this section the description of the PI/PC methods will be split in two parts depending on type of electron states participating in the primary optical excitation. The electron transitions between fundamental band states of collector leading to PC will be considered first, and then the processes involving localized states in the collector resulting in PI will be addressed. In its turn, the discussion on PI will also be separated in two parts. The ‘real’ PI of electron states well isolated electrically from the collector contacts represents the most simple case. In the case of electron exchange between localized states and the contact, i.e., when the gap states are spatially located in the immediate vicinity of the interface, the already mentioned ‘pseudo-IPE’ excitations will be analysed. 4.4.1 Intrinsic PC of collector In contrast to IPE, the intrinsic PC is expected to be insensitive to the orientation of electric field in the collector or to the material of the metal electrode. In its turn, for the same strength of electric field, the IPE current is expected to be insensitive to the insulator thickness if the carrier trapping probability is low and has no measurable influence on the current density. The PC current is likely to increase with the thickness
Internal Photoemission Spectroscopy Methods
93
(PC yield)1/2 (relative units)
1500 ZrO2
HfO2
1000 Nb2O5 Si Ox
Au
Ta2O5 TiO2
500 Al2O3 0 3
4
5 6 Photon energy (eV)
7
Fig. 4.4.1 PC spectra of (100)Si/oxide/Au samples with various high-permittivity oxide insulators: atomic-layer chemical vapour deposited (CVD) Al2 O3 , ZrO2 , HfO2 , Ta2 O5 , and TiO2 , and for Nb2 O5 grown using liquid-source mist deposition measured at a strength of electric field in the oxide of 1 MV/cm with metal biased negatively. Lines illustrate the procedure of PC threshold determination. Insert shows electronic transitions in the oxide responsible for PC.
of collector (d) in the range d < 1/α, where α is the optical absorption coefficient in the analysed spectral range. Therefore, analysis of the photocurrent dependence on insulator thickness, electrode material, and orientation of the electric field are the experimental criteria to be considered when attributing the observed photocurrent to the IPE or to the PC process. Assuming the mean free-path of photogenerated charge carriers to be larger than the thickness of the collector layer, the PC current will be proportional to the joint density of states (J-DOS) for optical transitions. In amorphous insulators this dependence is experimentally observed to be close to Iph ∼ (hν − Eg )2 (DiStefano and Eastman, 1971; Afanas’ev and Stesmans, 2004a) which allows determination of Eg by extrapolation of the current normalized to the incident photon flux nph to zero using (Iph /nph )1/2 –hν plot. The applicability of this procedure is illustrated in Fig. 4.4.1 in which the PC spectra of samples with six different high-permittivity oxide insulators of 6–20 nm thickness deposited on (100)Si are compared (Afanas’ev and Stesmans, 2004a). Being plotted in the (Iph /nph )1/2 –hν co-ordinates, the spectra show well-defined linear portion, which allows determination of the oxide bandgap as the intrinsic PC threshold. One of the remarkable features to be mentioned here is significant bandgap narrowing observed in low-temperature deposited alumina, in which the bandgap width appears to be approximately 30% smaller than in the Al2 O3 crystal (8.7 eV, Bortz and French (1989) and French (1990)). These results indicate that the fundamental electronic structure of the deposited oxides is not necessary identical to that of the bulk crystal of chemically the same oxide. Again, similarly to the case of IPE, the exponent of the PC spectral dependence can be considered as an independent parameter corresponding to the energy dependence of J-DOS (intrinsic PC) or to the energy dependence of PI cross-section. By using the found exponent one can associate the observed PC with particular type of optical transitions in the same way as it is done for optical absorption edge spectra (see, e.g., Pankove, 1975). The important portion of the PC spectra is the sub-threshold region, which potentially might reveal intrinsic or extrinsic band-tail states of the amorphous (or liquid) collector material. In Fig. 4.4.2 are
94
Internal Photoemission Spectroscopy: Principles and Applications
(PC yield)1/2 (relative units)
4000
Si(100)/ZrO2/Au
3000
2000
1000
100 nm 50 nm
0 4.5
5.0
5.5
10 nm
6.0
6.5
Photon energy (eV)
Fig. 4.4.2 PC spectra of (100)Si/ZrO2 /Au samples with different thickness of the oxide (in nm): 10 (), 50 (), and 100 () measured at a strength of electric field in the oxide of 1 MV/cm with metal biased negatively.
shown the PC spectra of the deposited at 300◦ C ZrO2 layers of different thickness, all exhibiting the same spectral threshold at 5.5 eV (Afanas’ev and Stesmans, 2004a). With increasing the oxide thickness, a progressively intense subthreshold PC is observed, suggesting excitation of some states in the bulk of the oxide. As the annealing at 800◦ C is found to have no measurable effect on the relative intensity of the subthreshold PC, one can exclude possible presence of different crystalline phases in the zirconia film as the origin of the complex PC spectrum because the phase composition of the film is strongly affected by the high-temperature treatments (Houssa et al., 2001). This result would rather suggest the relationship of the subthreshold PC to some defect or impurity incorporated into the film during the deposition process. Sub-threshold PC may also originate from excitation of some electron states concentrated predominantly near one interface. In this case the spectra of photocurrent obtained with different orientation of electric field in the collector may also differ because the transport of electrons and holes will not be identical. The carriers of one type will be transported more easily than other if the latter are left in some state within the collector bandgap. An example of such behaviour is provided by near-threshold PC spectra of SiO2 thermally grown on Si(100) (Adamchuk and Afanas’ev, 1992a, b). While the spectra obtained with positive bias of the flied electrode of Au/SiO2 /Si capacitor exhibit clear shoulder at around hν = 8.5–9 eV shown in Fig. 4.4.3, no such sub-threshold PC is seen if the measurements are repeated in the same sample when the metal electrode is biased negatively. In the last case the PC yield increases as (hν − Eg )2 leading to the intrinsic PC threshold of 8.9 eV in good agreement with the earlier observation (DiStefano and Eastman, 1971). The inference that the PC signal measured at hν < 9 eV originates not from the intrinsic PC but from excitations of some other type is supported by comparison of photocurrent to the photocharging exemplified by the data shown in Fig. 4.4.4. The spectral dependence of the positive photocharging rate () is observed to follow that of the photocurrent () only for hν > 9.3 eV which can logically be associated with generation of holes in SiO2 , their transport towards Si substrate and trapping by the ‘detecting’ defects (hole traps). It is likely that these processes occur in the same way if photons of different energy are absorbed in the bulk of the SiO2 collector layer. At lower photon energies a reduced value of the photocharging/photocurrent ratio is observed as shown in the insert. The latter indicates a lower efficiency of the positive charge trapping suggesting that the photogeneration in the spectral range below 9 eV occurs not into the bulk states of the SiO2 layer but in somewhat different way. A large photocurrent signal
Internal Photoemission Spectroscopy Methods
PC yield (relative units)
F (MV/cm)
Si(100)/SiO2
4
95
6.80
3
5.50 3.70 2.27
2
1.36 0.63
1
0.18 0 7
8
9
10
Photon energy (eV)
Yield (relative units)
2
Q/I (relative units)
Fig. 4.4.3 PC yield (photocurrent per incident photon) as a function of photon energy as measured in Au/SiO2 (55 nm)/Si(100) structure under negative bias on the metal electrode corresponding to the strength of electric field in the oxide indicated in the figure. 1.0 0.5 0.0 8
1
9 hn (eV)
10
Si(100)/SiO2 0 8.0
8.5
9.0
9.5
10.0
Photon energy (eV)
Fig. 4.4.4 Spectral curves of quantum yield of photocurrent () and positive photocharging () measured in vicinity of intrinsic PC threshold of SiO2 in Au/SiO2 (160 nm)/Si(100) structures with positive bias on the metal field electrode. The latter corresponds to the average strength of electric field in the oxide of 1.1 MV/cm. The insert shows the photocharging/photocurrent ratio as a function of the photon energy.
without corresponding hole trapping rate suggests that most of the current is carried by electrons while the holes are apparently left close to Si substrate and neutralized there by electron tunnelling (Adamchuk and Afanas’ev, 1992b). Thus, the sub-threshold PC in Si/thermal oxide structures is associated with excitation of near-interface defects with energy levels close to the top of the oxide valence band presence of which is also supported by hole IPE results shown in Fig. 4.1.8 suggesting a significant density of SiO2 gap states above the valence band top. The example of the collector PC analysis in Si/SiO2 structures demonstrates the most complex problem of the method which consists in association of the observed PC threshold with the oxide bandgap or, alternatively, with ionisation energy of some imperfection-related state. As a general way of reasoning one may argue that the imperfection-related states must be much more sensitive to the peculiarities of
96
Internal Photoemission Spectroscopy: Principles and Applications
the collector (and of the whole sample) processing as compared to the intrinsic (fundamental) properties. Indeed, in the discussed case of Si oxidation the change of technological parameters is seen to affect the sub-threshold PC drastically (cf. Fig. 41 in Adamchuk and Afanas’ev (1992a)). In this way the criterion of reproducibility between different material technologies can be used to separate fundamental excitations from the imperfection- or impurity-related ones. One may also try to analyse the field-dependent PC to obtain additional information regarding origin of the final electron state in the corresponding optical transition. For instance, the simple model of electron escape from the potential well of a hole it leaves behind (cf. Fig. 3.3.2) predicts the exponential behaviour of the photocurrent on inverse square root of the electric field given by Eq. (3.3.4) (Adamchuk and Afanas’ev, 1992a). By using this model one can extract the mean free path of a carrier with respect to thermalization as a function of photon energy. For the discussed example of SiO2 PC the procedure of determination is illustrated in Fig. 4.4.5a, which shows the logarithmic plot of photocurrent as a function of F −1/2 as observed at different energies of the exciting photons. The corresponding plot of as a function of photon energy shown in Fig. 4.4.5b reveals a remarkable feature, namely, a much larger mean free path of electron at hν < 9.3 eV than at a higher photon energy. This behaviour would indicate that the average kinetic energy of electrons excited in the former spectral range is higher than of electrons dominating the photocurrent at, say, hν ≈ 10 eV. Such a ‘decrease’ in the average energy of electrons with increasing photon energy is only possible if optical excitation in the low photon energy range is dominated by transitions from some electron state in the oxide bandgap supporting the above analysis of the sub-threshold PC in the Si/SiO2 structures.
/2
SiO2
8
~
(h
)1 Eg
6 5
6 4
Eg(SiO2) 4
3
hn (eV) 8.86 9.16 2 9.23 9.68 10.18 10.81 0 0.0 0.5
2
Mean free path (nm)
log (photocurrent) (relative units)
Interestingly, if assuming the electron mean free path to be determined by energy losses caused by interaction with LO phonons in SiO2 as it happens in the case of electron IPE from a contact, one may determine the threshold of the fundamental PC from analysis of the current-voltage curves using a constant LO phonon emission rate above the threshold of their excitation (Fitting and Friemann, 1982).
1
1.0
1.5
2.0
8.5
9.0
0 9.5 10.0 10.5 11.0 11.5
(Field)1/2 (MV/cm)1/2
Photon energy (eV)
(a)
(b)
Fig. 4.4.5 (a) PC current per incident photon as a function of inverse square root of electric field in the oxide of Au/SiO2 (160 nm)/Si(100) structures measured under excitation by photons of different energy hν. Lines indicate linear fit used to determine the mean free path of an electron . (b) The mean free path of an electron as a function of photon energy in vicinity of spectral threshold of SiO2 PC. The solid line shows approximation of the intrinsic PC portion of the curve by the function ∼ (hν − Eg )1/2 . This fit yields the oxide bandgap width Eg (SiO2 ) = 8.9 eV indicated by the arrow.
Internal Photoemission Spectroscopy Methods
97
In this case the probability of phonon emission will be proportional to the time electron remains in the potential well of a hole, which would decrease with electron energy as the first power of its velocity in the conduction band of SiO2 . Therefore, one may write ∼ (hν − Eg )1/2 which expression fits well the high-energy portion of the curve shown in Fig. 4.4.5 yielding Eg = 8.9 eV. The advantage of this method consists in insensitivity of the results to the substantial variation of optical constants of SiO2 in the used photon energy range. However, the proposed simple description of electron–hole dissociation relays on the ballistic character of electron transport after optical excitation and may not necessarily be valid in an arbitrary collector material. 4.4.2 Spectroscopy of PI The optical ionization of localized electron states in the collector with energy levels corresponding to the collector bandgap may lead to generation of photocurrent which bears information regarding defects or impurities present in the collector material. This kind of measurements may be of particular value if the research is focussed on the properties of collector itself because the energies of the found states can be directly compared to the band diagram of the emitter–collector–field electrode structure found from the IPE and PC experiments. The major difficulty here consists in identification of electron transition involved in the PI, or, in other words, in the determination of charge sign of the carrier photoexcited from the localized state into the transport band of the collector. In the most straightforward way this problem can be resolved by directly observing variation of electric charge in the collector caused by the PI transitions by measuring shift of the capacitance–voltage curves of metal–insulator–semiconductor structures (Mehta et al., 1972; Jacobs and Dorda, 1977a, b; DiMaria et al., 1978a). One may apply more sophisticated tools aimed at the collector surface potential monitoring ranging from the conventional Kelvin probe to techniques enabling lateral resolution like scanning tunnelling microscope (Im et al., 1999) or photoelectron emission microscope (Siegrist et al., 2004). In the core of PI analysis lies the assumption of linear dependence of the process rate on the photon flux nph (hν) and on the number of localized states (traps) Nt (hν) available for optical excitation at a given photon energy hν: ∂Nt = σph (hν)nph (hν)Nt (hν), ∂t
(4.4.1)
where σph (hν) represents the cross-section of PI. The problem with direct application of Eq. (4.4.1) is related to the fact that σph (hν) is also a function of the electron level energy Et and usually expressed as a function (hν − Et ) (see, e.g., Eqs (5.2.40)–(5.2.42) in Landsberg (1991) or Figs 1 and 2 in Lucovsky (1965)). Therefore, would a trap distribution Nt (Et ) be present in the sample, the PI rate normalized to the photon flux (i.e., the PI quantum yield) will be proportional to the integral over distribution of traps lying within energy of hν from the edge of the band to which charge carrier are excited (see, e.g., DeKeersmaecker and DiMaria, 1980): hν Yph ((hν) ∝
Nt (Et )σph (hν − Et )dEt ,
(4.4.2)
0
where zero energy corresponds to the edge of the band. From Eq. (4.4.2) one can easily see that the PI signal is actually proportional to the convolution of the trap energy distribution and the energy-dependent PI cross-section which excludes simple analysis and makes necessary additional experimental efforts. Potentially, one may consider two modes when measuring PI as a function of photon energy: the ‘fast’ and ‘slow’ spectral sweep (Kapoor et al., 1977a, b). In the ‘fast’ hν sweep mode the occupancy of initial states
98
Internal Photoemission Spectroscopy: Principles and Applications 105
Yield (relative units)
104
Si(100)/SiO2
103 102 0
101 100
1
1 2
101
Et 2
102 3
0 4 5 Photon energy (eV)
6
Fig. 4.4.6 Photocurrent quantum yield as a function of photon energy measured at the electric field strength in the oxide of 4 MV/cm under positive metal bias in the control Si/SiO2 (66 nm)/Al structure () and in those exposed to 1 × 1019 10 eV photons/cm2 without () and with subsequent H2 anneal at 400◦ C () followed by injection of 1018 electrons/cm2 from Si. The arrows indicate the observed IPE and PI spectral thresholds which schemes are clarified in the insert.
of the PI process is assumed to remain unchanged during the whole measurement time. The resulting PI yield in this case, both in current and charge, can be expressed using the integral given by Eq. (4.4.2). The only information available in this case is the energy onset of the PI process which can be considered either as the energy level of the localized state (if a well-defined state structure is discussed) or, else, as the upper edge of the localized state distribution. An example of experimental results corresponding to the former case is shown in Fig. 4.4.6 in which the photocurrent yield is shown for the Si(100)/SiO2 structure prior () and after incorporation () of large density of H-passivated Si dangling bond defects (O3 ≡Si–H entities) into the oxide by exposing it to 10-eV photons (Afanas’ev and Stesmans, 1997c). The control (pre-irradiation) spectrum shows two spectral thresholds 1 and 0 corresponding to excitation of electrons from the near-interface defects generated during oxide growth and from the valence band of Si crystal, respectively. Incorporation of defects to the oxide and filling them by electrons using avalanche injection from Si results in considerable negative charge accumulation. Subsequent exposure to a monochromatic light reveals additional photocurrent with spectral threshold 2 which may be correlated with decrease of the negative charge. As the latter is observed to occur at both bias polarities and irrespectively of strength of electric field in the oxide, the excitation of electrons from the negatively charged centres to the SiO2 conduction band represents the most logical way to describe the process. Assuming that the defects of the same atomic structure, i.e., O3 ≡Si–H, have the same energy level of the trapped electron, one may simply determine the energy of this level with respect to the SiO2 conduction 1/2 band by extrapolating the PI current to zero in the YPI –hν co-ordinates, which appear to fit experimental data reasonably well as shown in Fig. 4.4.7. However, in addition to the threshold 2 = 3.1 eV one also finds there a significant increase of the PI signal at photon energy above 4 eV indicative of the second transition threshold from the same (O3 ≡Si–H)− or, else, from an additional defect bath. The same trend is observed both in the PI current and charge measurements (cf. Fig. 4.4.7b), and all the trapped electrons can be removed during extended illumination by photons with hν < 4 eV. Then the excitation of second transition, possibly from a Si–H bond in the negatively charged O3 ≡Si–H entity appears to be the likely explanation of the second PI threshold. What is important here, is that the PI spectrum recorded in the ‘fast’ hν sweep mode cannot be seen as a replica of the localized states energy distribution in the collector bandgap. In this sense PI differs from the IPE significantly.
(Yield)1/2 (relative units)
Internal Photoemission Spectroscopy Methods
99
4
3 Charge
3 2
Si
1
2
Traps SiO2
1 Current
0
0 3
4
5
3
4
5
Photon energy (eV) (a)
(b)
Fig. 4.4.7 (a) Photocurrent quantum yield as a function of photon energy in the Si/SiO2 (66 nm)/Al structure exposed to 1 × 1019 10-eV photons/cm2 , annealed in H2 (400◦ C, 30 min) and subjected to the avalanche electron injection from Si to the dose of 1018 electrons/cm2 . The points are taken at the electric field strength in the SiO2 of 0.5 (), 1.0 () and 2.0 MV/cm () with the metal biased positively. (b) Photocurrent quantum yield as a function of photon energy in the same structure measured for an oxide field of 1 MV/cm with metal biased positively () or negatively () and the PI (the photo-discharging) yield measured with F = 3 MV/cm () under positive metal bias.
To obtain information regarding energy distribution of the ionized localized states, not weighted by their energy-dependent σph , Thomas and Feigl introduced the ‘slow’ photon energy sweep mode in which the measurement time t at each spectral point is postulated to exceed by far the time constant of the (quasi-) exponential PI current decay (Thomas and Feigl, 1970). This condition actually means integration of the PI response over the time t which allows one to collect at every measurement point a significant portion of charge available for PI at a given photon energy. The problem with this kind of measurements consists in the necessity to detect a low photocurrent over extended period of time which makes them highly sensitive to the dark (leakage) current and to the drift of the measurement equipment. As an extreme case of the ‘slow’ sweep method it was proposed to perform the optical (dis)charging measurements not in the small-signal mode as described in Chapter 3 (cf Eq. (3.5.1)) but by tracing the charge kinetics to its saturation at incremental photon energies (Afanas’ev and Stesmans, 1999b). An example of such a trace obtained in SiO2 sample containing charged Si clusters is presented in Fig. 4.4.8, which shows the kinetics of flatband voltage shift measured in Si/SiO2 /Au capacitor under condition of hν increment once less than 20% relative variation of the detrapped charge is attained. The latter would mean that nearly all the traps depopulated at the selected photon energy are energetically located in a narrow spectral window equal to the increment of the photon energy with respect to the preceding PI step. This allows immediate determination of the trap spectral density per unit sample area providing most straightforward DOS results (Afanas’ev and Stesmans, 1999b). Moreover, from the PI kinetics at each hν one directly extracts the PI cross-section which is now also relevant to the narrow ‘slice’ of the localized state energy distribution. In this way a complete characterization of electron state through its PI parameters can be achieved. Another advantage of direct charge monitoring consists in the possibility to separate the PI transitions originating from electron states with different sign or value of the initial charge. This possibility is exemplified in Fig. 4.4.9 by DOS histograms of Si clusters determined in the course of the just discussed exhaustive PI measurements (Afanas’ev and Stesmans, 1999b). Panels (a–d) correspond to the SiO2 layers containing clusters of different effective radius as was characterized trough their electron capture cross-section. The dashed distributions correspond to the PI of clusters resulting in the generation of a
100
Internal Photoemission Spectroscopy: Principles and Applications
VFB (V)
10
Clusters Si SiO2 hn (eV): 3.25 3.33
5
3.42
3.52
0 0
100
200
300
400
Illumination time (min)
Fig. 4.4.8 Shift of the flatband voltage VFB on the capacitance–voltage curve in Si/SiO2 /Au sample with the oxide-containing Si clusters as a function of the illumination time (Afanas’ev and Stesmans, 1999b). The photon energy hν increases from 3.25 to 3.52 eV in ∼0.1 eV steps.
60
/0
(a)
40 0/
20
DOS (1011 cm2 eV1)
0 60
/0
40
(b)
0/
20 0
/0
(c)
20
0/ x5
10 x1 0 6 0/
4
0
x1
/0
2 2
(d) x 50
3
4
5
E EC(SiO2) (eV)
Fig. 4.4.9 Density of oxide gap states in Si/SiO2 /Au samples with SiO2 layers-containing clusters of different size as determined from PI measurements using 0/+ (dashed line) and −/0 (dotted line) transitions as a function of energy below the SiO2 conduction band. The cluster size is characterized by electron capture radius of 2, 3, 1, and 0.5 nm in samples (a–d), respectively (see Afanas’ev and Stesmans (1999b) for details).
Internal Photoemission Spectroscopy Methods
101
positive charge in the initially electrically neutral oxide, i.e., to the 0/+ transition of the cluster. The dotted curves correspond to the neutralization of negative charge trapped on the clusters in the course of the pre-PI electron injection. These excitations correspond to −/0 cluster transition or to the compensation of its charge by the positive charge of neighbouring cluster. The results reveal nearly the same energy onsets of the 0/+ and −/0 transitions in all the cases except the sample (d) with the smallest clusters suggesting the transitions to be dominated by some common electron state likely to be associated with some defect at the cluster/oxide interface (Afanas’ev and Stesmans, 1999b). Remarkably, the energy onset of the PI transitions is seen to be close to the earlier discussed threshold (2 = 3.1 eV) of trapped electron emission from the negatively charge O3 ≡Si–H fragment in SiO2 . Only in the case of smallest clusters in sample (d) the shallow electron states expected from the quantum confinement considerations are observable in −/0 transitions suggesting that small cluster surface area makes only few O3 ≡Si–H states available. Though the above results indicate great potential of the PI spectroscopy of electron states in the collector material, the applicability of this method depends on the possibility to preserve the desired charge of the analysed electron state without significant changes during the time needed for PI spectral measurements. This limits the possible collector materials to the wide bandgap insulating layers of sufficient quality. Nevertheless, as the time constant of PI process is inversely proportional to the flux of incident photons (cf. Eq. (4.4.1)) one may appear to be in more favourable conditions when using advanced high-brightness light sources like a free-electron laser. Taking into account that absolute DOS determination becomes now possible as demonstrated in Fig. 4.4.9, this kind of spectroscopy is definitely set for further development. 4.4.3 PI of near-interface states in collector: the pseudo-IPE transitions In the previous section the PI process was described when assuming that the excited localized electron states with energy levels in the bandgap of collector cannot communicate electrically with emitter or with a conducting field electrode. This approximation is likely to be valid in the case of emitter/collector and the filed/electrode collector interfaces of high quality and when a high defect or impurity density is located in the bulk of the insulating collector. It is possible, however, that chemical interactions at the interfaces of collector or their contamination in the process of fabrication will lead to an enhanced density of electron energy levels within the collector bandgap. These states will be constantly re-filled by electron tunnelling from an electrode and, at the same time, may contribute to the PI transitions without, however, being exhausted by a prolonged PI (cf. Fig. 1.6.3). An important feature of this kind of PI process is that it leads to injection of one type of charge carriers, possibly at one interface only which makes it very similar to IPE. However, neither the optical excitation nor the transport of the excited carrier are relevant to the electron states of the emitter. For this reason this process was denoted in Section 1.6 as the pseudo-IPE. As one can see from the scheme of this process shown in Fig. 1.6.3, optical excitation in this case occurs entirely inside the collector material leading to a greatly enhanced effective carrier escape cone (close to 2π at all the excitation energies) as compared to the narrow and energy-dependent electron escape cone in the Fowler model of photoemission given by Eq. (3.2.2) and illustrated in Fig. 3.2.1. In addition, the energy of excited state in the PI process is still smaller than the collector bandgap width, which means that the only mechanism of its relaxation in energy is interaction with phonons. The latter is much less efficient than the inelastic electron–electron scattering in the case of IPE from metals or narrow-gap semiconductors. Thus, the lifetime of the excited state in the process of PI, including the pseudo-IPE excitations, will probably much exceed the lifetime of excited charge carriers in the case of IPE from an emitter. These two features, the larger escape cone and the longer lifetime of the excited state, make the escape of a carrier from the excited state of the PI in the collector much more probable than that from the state optically excited inside the emitter. For this reason the quantum yield of the pseudo-IPE may be large even if the density of the contributing initial states in the bandgap of collector remains by far lower than the density of occupied electron states in the emitter in the same energy range (cf. processes B and
102
Internal Photoemission Spectroscopy: Principles and Applications
A in Fig. 1.6.3). In some cases the photocurrent originating from the pseudo-IPE may bury the real IPE signal entirely. There are two crucial questions concerning the pseudo-IPE photocurrent. First, how this signal can be separated from the conventional IPE, or, in other words, how to identify the source of the photocurrent observed? Second, what kind of physical information can be possibly extracted from the pseudo-IPE current spectra?
F (MV/cm) 2.7 3.1 3.4 3.8 4.2 4.6 5.0 5.4 5.7 6.5
102
101
100
101 2.3
2.4
(a)
2.5
2.6
2.7
2.8
2.9
3.0
Photon energy (eV) 150
2
100
EB (eV)
3
EB
1
50
A (relative units)
Yield/F 2 (relative units)
A simple way to address the first question is to check the correlation between the observed photocurrent and the variations of DOS in the emitter electrode. In the case of IPE the current is directly correlated with the density of initial states while the PI/pseudo-IPE current will be sensitive to the density of initial gap states in the collector. A good example of such approach is given by identification of the photon-stimulated tunnelling (PST) current in Si/SiO2 structures (Afanas’ev and Stesmans, 1997a, b) in which the signal was traced as a function of electron density in the conduction band of Si varied through intentional doping with phosphorous donors. From the data obtained on the sample with just one donor concentration and shown in Fig. 4.4.10 it appears that the current at different photon energies and fields can well be described if assuming the rate-limiting step to be the electron tunnelling from
hn
0 (b)
0
1
2
3 4 F (MV/cm)
5
6
0
Fig. 4.4.10 (a) Relative yield of PST at the (111)Si/SiO2 interface as a function photon energy at different strengths of the electric field in the oxide, denoted in MV/cm. The lines represent fitting results. (b) Binding energy EB of the initial state of the PST transition (cf. insert) and the pre-exponential factor A as functions of the electric field as obtained from the data fitting. Curves are guides to the eye.
Internal Photoemission Spectroscopy Methods
103
some optically excited state. By using model of electron tunnelling from Si conduction band into SiO2 (Weinberg, 1977; 1982), one can fit the data as indicated by lines in panel (a) and determine the energy of initial electron state and the density of electron in this state as functions of electric field (panel (b)). What is unusual in the latter plot is that the density of electrons contributing to the photoexcitation and subsequent tunnelling from the excited state into the oxide has the field onset at about 2 MV/cm which is inconsistent with assumption that photoexcitation occurs inside the silicon emitter. The most straightforward way to resolve this discrepancy is to change the Si doping level and then to trace the PST current together with the current of conventional IPE of electrons from the silicon conduction band which can be observed at somewhat higher photon energy as shown in Fig. 4.4.1. The results for Si crystals with different concentration of electrons in the conduction band are summarized in Fig. 4.4.11 which compares behaviour of the quantum yield of both IPE and PST. In the case of IPE (filled squares), the linear relationship between the yield and the electron density is evident. However, no correlation between the PST transition rate and the electron density in the Si conduction band is seen (filled circles). The latter result clearly indicates a different source of electrons in the PST process than the conduction band of silicon. The data shown in Fig. 4.4.11 may also be used to illustrate another approach to identification of the initial electron state (Afanas’ev and Stesmans, 1997b). Would the same collector material (SiO2 ) be applied to different emitter materials (Si or different polytypes of SiC), the variation of the supposed initial state energy (the bottom of the semiconductor conduction band) will directly affect the energy derived from the PST analysis. The energy positions of the conduction band for several emitter crystals measured with respect to the collector conduction band (which represents the final electron state in PST) are indicated in Fig. 4.4.11 by arrows (Afanas’ev et al., 1996a). The open symbols show the energy of initial state EB the PST transitions observed at the relevant interfaces as determined from the PST current analysis. It is clearly seen that the energy of this initial state is uncorrelated with the band structure of semiconductor which would mean that it belongs to SiO2 collector rather than to an emitter (Afanas’ev and Stesmans, 1997b). The latter conclusion has found an independent support from observation that the method of SiO2 fabrication (thermal oxidation of Si, chemical vapour deposition, implantation of O+ ions) has dramatic impact of the PST quantum yield while the electron band structure of Si crystal and the oxide itself remains largely unaffected (Afanas’ev and Stesmans, 1997d, e). IPE
101
Energy (eV)
n, p-(100)Si 100 3.0
(0001)6HSiC 101
2.8
PST
Yield (relative units)
3.2
n-(100)Si
(0001)4HSiC 102 2.6 1014 1015 1016 1017 1018 1019 1020 1021 1022 Conduction electron concentration (cm3)
Fig. 4.4.11 Energy EB of the initial state of PST transitions measured relative the conduction band of SiO2 at the interfaces with (100)Si (), (111)Si (), (0001) 6H–SiC () and (0001) 4H–SiC () for different nominal concentration of electrons in the substrate. The solid arrows indicate the conduction band offsets at the corresponding interfaces as determined from IPE spectroscopy. The relative yield of PST ( ) and IPE () at the interfaces of SiO2 with (100)Si are also shown. Lines are guides to the eye.
•
104
Internal Photoemission Spectroscopy: Principles and Applications
Yield (relative units)
1.5
d(hn) 0.05 eV
1.0 h 0.5
0.0
2.8
3.0 3.2 Photon energy (eV)
3.4
Fig. 4.4.12 Quantum yield of defects PI at the Si(111)/SiO2 interface as a function of photon energy for electric field strengths (in MV/cm): 2.3 (), 2.85 (), 3.46 (), 4.0 (), 4.6 (3), and 5.7 ( ). The insert shows the scheme of the observed pseudo-IPE electron transitions. Arrows indicate the energy width of the monochromator slit.
One may further refine the model of the process by observing PI of the same state when the strength of field in SiO2 is kept above the 2 MV/cm onset value needed to provide electrons to the oxide gap states as revealed by the PST analysis. These PI results are shown in Fig. 4.4.12 for several filed strength values rewardingly yielding the same energy of the initial electron state as the PST current data analysis. The scheme of the corresponding electron transition is shown in the insert indicating the two-step process of the pseudo-IPE in which the PI of the oxide gap states represents the rate-limiting step. From the discussed results one may sketch two general approaches to identification of the photocurrent generation mechanism. First, one might attempt to trace the sensitivity of the photocurrent spectra to the known features of electron DOS in the emitter. To variation of the carrier concentration and the energy of the bands (by varying the emitter material), it is also possible to associate the optical singularities and onsets of electron scattering processes with the IPE from the states excited inside the emitter material. One can see, for instance, that the optical singularities of Si crystal at points E1 ≈ 3.4 eV and E2 ≈ 4.4 eV are universally observed in the IPE spectra from this semiconductor into different collector materials (cf. Figs 2.2.1, 4.1.6, 4.1.7, 4.2.1, 4.2.4, and 4.2.7) provided the IPE threshold energy is lower than that of the optical feature. Second, it is also seems possible to affect the properties of the near-interface layer of the collector to track possible pseudo-IPE excitations. The marginal sensitivity of the spectral thresholds to the type of interlayer would in this case indicate the IPE from emitter. One may see that at the interfaces of Si with HfO2 the chemical composition of the interlayer (SiON or O-free Si3 N4 ) has only little influence on the spectral curves (cf. Fig. 4.1.7). Analysis of the low-energy of photocurrent spectra for the Si(100)/ZrO2 interface delivers just opposite result. The photocurrent yield is seen in Fig. 4.4.13 to decrease dramatically after oxidation of the sample in O2 at 650◦ C. This treatment results in growth of a SiOx -like interlayer which apparently affects the electron occupancy of gap state in zirconia responsible for the photocurrent which excitation can be identified as the pseudo-IPE process. Now one may address the second question regarding the kind of physical information, which still can be extracted from the analysis of the pseudo-IPE photocurrents. The threshold of the PI transition is determined by the barrier height between the upper occupied electron state in the collector and the
IPE yield (relative units)
Internal Photoemission Spectroscopy Methods
105
Si(100)/SiOx/ZrO2 F 3 MV/cm 1.0
0.5
0.0
2.4
2.6
2.8
Photon energy (eV)
Fig. 4.4.13 IPE yield as a function of photon energy for n-Si/7.4 nm ZrO2 /Au MOS structures in as-deposited state () and after oxidation at 500◦ C for 60 min (), 650◦ C for 30 min (), and at 800◦ C for 10 min (). The measurements are done with applied field strength in ZrO2 layer of 3 MV/cm, metal biased positively. The error in the yield determination is smaller than the symbol size.
lowest unoccupied energy band. (One may, in a similar way, define the barrier for the case of hole photoexcitation). While the band edge energy remains the fundamental property of the collector, the energy distribution of electrons in states within the collector bandgap will be determined by the energy distribution of the available levels and by their occupancy function. The latter, in its turn, is determined by the Fermi energy in the nearby electrode as well as by the distribution of electrostatic potential at the interface. Would one consider an ensemble of states with identical and well reproducible atomic structure, the levels of these states are expected to be close in energy. Therefore, their PI will occur with the spectral threshold corresponding to this energy provided the electrons can be supplied to these levels from an electrode. As a result, the pseudo-IPE threshold, if observed, is expected to be marginally sensitive to the electron structure of the ‘emitter’ which serves only as the source of electrons needed to re-fill the gap states. Another scenario concerns strongly disordered systems with continuous energy spectrum of gap states: the upper edge of the occupied levels will likely be determined by the Fermi level of the nearby (semi-)conducting electrode. In addition, it might also be affected by the variation of the electrostatic potential across the depth of electron exchange between this electrode and the collector gap states. In this case one may expect certain sensitivity of the pseudo-IPE threshold to the Fermi energy of the ‘emitter’ accompanied with a strong sensitivity of this threshold to the applied electron field. The latter is related to the tunnelling mechanism of electron exchange between the gap states and the electrode which supplies the carriers to traps located at a larger depth in the collector away from the interface with increasing strength of electric field. The last scenario is most difficult to analyse because the pseudo-IPE photocurrent behaviour closely resembles that of the conventional IPE. Some modification of the collector material DOS seems to be the only reliable way enabling identification of the relevant photoinjection mechanism. Some of the outlined problems in identification of the dominant photocurrent excitation mechanism are exemplified by the electron IPE spectra from different metallic conductors shown in Fig. 4.4.14 using the Fowler co-ordinates for two insulating collector materials: (a) a CVD SiO2 and (b) a spin-on deposited porous methyl-silesesquioxane (p-MSQ) (Shamuilia et al., 2006). In the former case the thresholds of IPE from the same metal into thermal SiO2 on Si are shown by arrows for comparison. One may notice two effects: first, the thresholds of photoexcitation are considerably higher for the deposited oxide collector and, second, the sensitivity to the metal type nearly disappears (cf. data for Al and Au). This insensitivity
106
Internal Photoemission Spectroscopy: Principles and Applications 9
Ta CVD SiO2
8
Ox -
7 6 5
Al TaNx ~1 eV Au
Me TaNx
4
Yield1/2 (relative units)
2
Al
Thermal SiO2
3 Al
TaNx
Au
Au
1 0
(a) p-MSQ ( 2.3)
6 5
Au Al TaNx
4 3
0.2 eV 2 1 (b) 0 2.5
3.0
3.5
4.0
4.5
5.0
5.5
Photon energy (eV)
Fig. 4.4.14 (a) Fowler plots of the electron IPE yield at interfaces of 100-nm thick chemical vapour deposited SiO2 with Ta (), TaNx (), Al (), and Au (3) electrodes measured at the same bias of −10 V on the metal. Lines illustrate determination of the spectral threshold. The spectral thresholds of IPE from these metals into thermally grown SiO2 on Si are indicated by bold arrows for comparison. The insert shows the metal/insulator interface band diagram in the ideal case (solid lines) and in the presence of a negative polarization layer (dashed curve). (b) Fowler plots of electron IPE yield at interfaces of 190-nm thick p-MSQ with Au (), Al (), and TaNx () layers as compared to the interfaces of Al () and Au (3) with the deposited SiO2 .
to the Fermi energy of the conducting electrode suggests the dominance of the pseudo-IPE process involving some states with a well-defined energy level. The fact that these states are observed at close energies in both CVD SiO2 and p-MSQ matrices suggests that they do not constitute an element of the collector material network but, more likely, are related to some extrinsic species, for instance, adsorbate molecules. As additional complication to the picture one might notice the spectral threshold variation in the case of interface of Ta and TaNx with CVD SiO2 which appears in correlation with application of a plasma-assisted interface formation process. The latter is likely to affect the charge density in the near-interface collector layer thus causing the electrostatic potential variation schematically illustrated in the insert in Fig. 4.4.14a.
CHAPTER 5
Injection Spectroscopy of Thin Layers of Solids: Internal Photoemission as Compared to Other Injection Methods
The spectroscopic internal photoemission (IPE) approaches discussed in the previous chapters were primarily aimed at characterization of electron states in emitter, collector, and at their interfaces through the density of states (DOS) properties characteristics, i.e., the energy of the states and their density. This way of electron state characterization is by far not the only possible one. The following chapters will discuss the description of localized states in the collector material as charge carrier traps, characterized by their specific capture cross-section, density, and spatial distribution. The issue of traps is highly pertinent to many material problems related to electrical properties of thin semiconducting or insulating layers. In particular, charge trapping behaviour of thin insulating films largely determines reliability of electronic devices, radiation response, and most important performance characteristics of some of them (non-volatile memory cells). At the same time, solid layers of several nanometres in thickness frequently exhibit striking differences in their properties from the known properties of bulk materials as well as remarkable sensitivity to the conditions of the layer preparation and growth. This makes the issue of trap characterization highly relevant when, for instance, selecting one or another material for the particular microelectronic device application. Addressing the fundamental material properties, it is well recognized now that the initial stages of solidto-solid heterojunction formation influence not only the properties of interface and narrow near-interface region but, also, influence the properties of the growing overlayer, most significantly, the spectrum of imperfections it accommodates. There are numerous factors affecting formation and behaviour of intrinsic defects and impurities despite the stoichiometry of the grown phase may remain perfect within the resolution of the available composition analysis methods (typically 0.1–1%). For instance, an energy released upon reaction of the chemical precursors and inequilibrium character of the overlayer growth may supply extra energy needed to create imperfections with density by far exceeding that expected from the thermodynamic equilibrium considerations. This is complemented by structural stress caused by the atomic mismatch at the interface, variations of the molar volume during chemical reactions, and differences in the thermal expansion coefficients of the contacting solids. Finally, the interface itself represents a source of defect generation as well as the preferable place of segregation of impurities. As a result of combined action of these factors, a growing overlayer experiences influence of the interface far beyond its first monolayers. In addition, application of particular growth methods, e.g., different chemical 107
108
Internal Photoemission Spectroscopy: Principles and Applications
precursors and/or different growth temperatures, may also modify the spectrum of imperfections in a thin film of a material making it strongly dissimilar to that known for the bulk phase(s).
5.1 Basic Approaches in the Injection Spectroscopy To understand the nature and mechanism(s) of defect generation in some material the corresponding electron states have to be identified and characterized through their amount (concentration, density) and their spatial location. Unfortunately, sensitivity of the electron spectroscopy techniques routinely used in materials analysis to identify electron states at atomic level is still by far insufficient to trace the behaviour of defects. Another obstacle in applying these methods to solids consists in the already discussed small electron escape depth (<5 nm), making problematic analysis of layers of a larger thickness. Application of optical spectroscopy techniques is also difficult because they require a substantial volume of material to analyse. At the same time, one is rarely interested in the properties of bulk material in a heterojunction structure. Moreover, the relevance of the optical results to the electronic properties of the defects represents a separate problem. Apparently, only the electron spin resonance (ESR) spectroscopy approaches the desirable sensitivity (1011 –1012 states/cm2 ) but it is capable of detecting of only the states which belong to unpaired electrons and requires highly sophisticated experimental equipment and special sample preparation (see, e.g., Griscom, 1990; Stesmans and Afanas’ev, 2004). In this chapter and in the following chapters the possible solution of the defect monitoring problem will be discussed which is applicable to insulating or semi-insulating solids. It is based on the observation of interactions of the injected mobile charge carriers with defects in the collector layer which leads to formation of a trapped charge which can be detected with high sensitivity through its influence on electric field. The basic idea of the method is that the imperfections, at least those relevant to the electrical behaviour of the collector material, will capture some of the injected carriers (cf. Fig. 5.1.1). Would these carriers remain on the trapping site for some time after injection, the density and spatial location of the trapped charge can be determined providing a way to characterize the number and spatial distribution of the charge trapping defects (Nicollian et al., 1969; 1971; Powell and Derbenwick, 1971; Ning and Yu, 1974; Nicollian and Brews, 1982). The density and spatial location of trapped charge provide one only with total amount of the occupied trapping sites but cannot distinguish between the traps of different sort. To separate traps in different groups one may use defect classification based on the value of the capture crosssection which can be found from analysis of the charge trapping kinetics (Rose, 1963). The capture cross-section is related to the spatial span of the electrostatic potential of an imperfection and to the type of the potential (attractive of repulsive) (Rose, 1963; DiMaria et al., 1976). In this way, the cross-section bears an important information regarding the electron states pertinent to the observed defect. Therefore,
Emitter
Collector
Field electrode
Fig. 5.1.1 Scheme of injection experiment aimed at probing of the trapping centres in the collector material. The injected charge carriers trapped inside the collector are symbolized by filled circles ( ).
•
Injection Spectroscopy of Thin Layers of Solids
109
by using the capture cross-section value, one can separate contributions of different centres to the charge trapping, i.e., to realize spectroscopic measurements. This approach to the defect characterization is clearly phenomenological in its nature and does not provide direct information regarding atomic origin of the observed states. This aspect makes the issue of the defect density quantification particularly important because any progress in understanding of the nature of the traps will be based on the correlative comparison between the results of charge trapping experiments and complementary methods sensitive to the atomic structure (optical absorption or luminescence spectroscopy, ESR, etc.). The same requirement to quantification of the trap density is applicable when associating the trapping centres with the presence of a particular impurity. In the latter case the concentration of the intentionally introduced impurity may be correlated with the observed trap density in a direct way. Once identified atomically through the correlative analysis, the traps with specific capture cross-section may further be used to monitor generation of the corresponding defect- or impurity-related imperfections (see, e.g., Afanas’ev et al., 1995a). The properties of charge trapping centres attract not only the fundamental interest from the point of view of the solid state physics but, also, have a number of practical points in device applications of materials. The latter are predominantly related to use of insulating layers in microelectronic devices in which the trapped charge would directly affect the electrical conductivity of the transistor channel. The spectrum of traps is mostly determined by the device processing technology, but additional defects may also be introduced in the course of device operation by application of a high electric field (Nissan-Cohen et al., 1986) or during the hot-carrier injection (DiMaria and Stasiak, 1989; Heyns et al., 1989), exposure to ionizing radiation (Aitken and Young, 1976; Aitken et al., 1978a, b; Aitken, 1980; Adamchuk et al., 1990; Afanas’ev et al., 1995a), and by other factors. Taking into account a small area of the modern electronic devices, the injection spectroscopy of defects in many cases appears to be the only tool suitable for characterization of imperfections in the insulating layers (Afanas’ev et al., 1994a). At the same time, the charge injection represents relatively simple experiment enabling rapid feedback to the device processing technology. In the forthcoming sections several important aspects of IPE application in the charge trapping spectroscopy will be discussed and illustrated. In the rest of this chapter the IPE will be described as the carrier injection method and compared with alternative charge injection techniques to demonstrate the modes of their optimal application. In the next chapter the IPE and photoionization (PI) will be considered as the charge monitoring methods and, again, compared to the alternative charge measurement techniques. As it appears, the IPE emerges as the only non-destructive charge-sensing technique capable of providing the information regarding in-depth charge distribution in thin insulating films. Finally, the methodology of the capture cross-section determination will be addressed to show how the combination of charge-injection and charge-detection measurements can be used to assess the spectrum of charge-trapping defects.
5.2 Charge Injection Using IPE To control the carrier injection rate one should ensure that only one injection mechanism provides the dominant contribution to the current. As already discussed in Section 3.4.2, the thermoionic emission of carriers is always an important factor when considering interface barriers of relatively low height, i.e., /kT < 40 (Williams, 1970). In fact, this emission by itself can be used to fill the trap states in structures with low barriers like Schottky contacts or heterojunctions of narrow-gap semiconductors. In this case the injection rate is determined by the strength of electric field at the injecting interface. However, with increasing the barrier height to the range > 1 eV at room temperature, the rate of electron emission from
110
Internal Photoemission Spectroscopy: Principles and Applications
the equilibrium thermal energy distribution strongly decreases. This makes the time of injection needed to attain a certain injected carrier density prohibitively long. In addition, the parallel, e.g., trap-assisted, injection mechanisms start to provide a non-negligible contribution to the current. In the latter case the injection occurs locally in space (at the points corresponding to location of the relevant mediating traps) compromising the trapping kinetics analysis which requires a uniform injected carrier distribution as will be discussed in Chapter 7. In order to increase the injection rate from the equilibrium carrier distribution in an emitter electrode, one might consider two ways. The first one is to increase the strength of electric field to enable carrier tunnelling. This emission, conventionally referred to as the Fowler–Nordheim (FN) emission (Fowler and Nordheim 1928; Snow, 1967), will be considered later in this chapter. The alternative solution is to increase the temperature of the measurements in order to enhance the injection rate (the bias-temperature stress application). Unfortunately, this simple excitation appears to enhance not only the carrier injection but, at the same time, the rate of electrochemical reactions potentially leading to significant variation in the density and energy spectrum of defect states at the interface (the so-called bias-temperature instability) (Blat et al., 1991; Gerardi et al., 1991; Bassler et al., 1999). Nevertheless, thanks to its technical simplicity, this approach is still used as an integral indicator of the interface resistance against injection-induced damage. However, no direct information regarding trapping properties of the defects accommodated by collector material can be extracted in this case. The obvious solution of problems related to the insufficient carrier injection rate over high barriers consists in the carrier excitation by some external field. In this sense the optical excitation, i.e., the IPE injection (photoinjection), provides the most straightforward way to control the carrier supply across the interface. This kind of experiment requires no exciting light monochromatization because now, in contrast to the IPE spectroscopy discussed in Chapter 4, one is interested exclusively in the total number of charge carriers which surmount the barrier at the interface per unit time. Even if the carriers have different energies when entering the collector, at a distance in the order of mean free path (few nanometres) all of them will be thermalized and, therefore, become indistinguishable. When applying IPE as the source of injected charge carriers three externally variable parameters can be used to adjust the current density to a desirable value: the photon energy spectrum, the light intensity, and the strength of electric field at the emitter–collector interface. Usually, while keeping the spectral composition of the exciting light unchanged, one uses the incident photon flux to attain the same injection rate at a fixed field strength enabling analysis of the field-dependent trapping parameters in a wide range of electric field strength (DiMaria, 1978; Buchanan et al., 1991; Afanas’ev and Adamchuk, 1994). This is one of the important advantages of the IPE injection over other techniques like tunnelling or avalanche injection in which the injection current density is uniquely determined by the strength of electric field at the interface. Another important feature of the injection by IPE is that it has minimal requirement to the properties of the photoemitter (metal type or semiconductor doping level) making this method universally applicable to different material systems. Also advantageous is a relatively weak sensitivity of the IPE current excited by a polychromatic light flux to the non-uniformities of the interface barrier. This is related to a generally weaker (power) dependence of the IPE quantum yield on the difference between the photon energy and the (local) barrier height (cf. Table 3.2.1) than in the case of thermoionic, tunnel, or avalanche injection currents, all exponentially depending on the barrier height. Finally, as will be discussed in the next chapter in some more detail, the IPE measurements performed in the unperturbing probe mode (when the current density remains so low that it has no effect on the trap occupancy) enable one to obtain unique information regarding density and character of the spatial distribution of the trapped charge carriers. As less beneficial aspects of the IPE application as the carrier injection technique one should indicate several issues. First of all, the need to have an optical input into the emitter/collector system generally requires a custom sample design. The latter usually concerns fabrication of a semitransparent emitter or
Injection Spectroscopy of Thin Layers of Solids
111
field electrode which is not always compatible with the fabrication technology conventionally used in the microelectronic industry. However, when using a simple evaporation of metal electrodes through a shadow mask or the electrolytic contact, the IPE appears to be advantageous for physical characterization because no complete lithographic processing is required. Second, the IPE typically has a low quantum yield, usually in the range 10−6 –10−4 (see, e.g., (DiStefano and Lewis, 1974)). This means that, to obtain a high injection current density, the sample must be exposed to a high radiation flux most of which will be absorbed in electrodes without providing any contribution to the IPE. This could lead to the sample heating and cause secondary effects (detrapping, increase in the background leakage current, photochemical reactions, etc.), potentially compromising the trapping measurements. As a result, the IPE current density is to be limited, usually to the range below 10−6 A/cm2 . This leads to a long time of injection needed to reach a desirable injected charge density, e.g., 1 C/cm2 . Besides the simple experiment time limit issue, the high integral exposure of the collector to photons brings up an additional problem. The traps filled by injection are exposed to intense illumination which in certain cases may lead to their depopulation by PI as illustrated in Fig. 5.2.1. The photoactive electron traps are well known to be present in a number of insulating materials like SiO2 , Al2 O3 , Si3 N4 , and their study requires either use of a wavelength-selected IPE injection or application of other injection method. Also, when using the sandwich sample structure for IPE experiments, the double-interface injection, i.e., simultaneous IPE of charge carriers of opposite sign from the opposite interfaces of the collector, may become a problem. The solution lies in the proper choice of the field electrode material enabling effective blockage of IPE at one of the interfaces under photon energy and electric field orientation used (Afanas’ev and Adamchuk, 1994a). To summarize, the application of IPE as the charge-injection method is justified in the case of samples with sufficiently high energy barriers at the collector interfaces with emitter and/or field electrodes. This basically means that the collector must be a wide-bandgap solid (semi-)insulator with Eg > 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
Internal Photoemission Spectroscopy: Principles and Applications
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
Internal Photoemission Spectroscopy: Principles and Applications
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
Injection Spectroscopy of Thin Layers of Solids
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
Internal Photoemission Spectroscopy: Principles and Applications
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,
Injection Spectroscopy of Thin Layers of Solids
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
Internal Photoemission Spectroscopy: Principles and Applications
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).
Injection Spectroscopy of Thin Layers of Solids
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 << τr , or, in terms of local electron and hole current densities: τf je σr = << 1. τr jh σ
(5.5.2)
120
Internal Photoemission Spectroscopy: Principles and Applications
hn > Eg
exp(ax)
xc
0
d Distance
Fig. 5.5.3 In-depth profile of electron–hole pair generation in collector layer by light with large absorption coefficient α illustrating collection of charge carriers of opposite sign at trapping sites located in a plane parallel to the emitter surface and located at a distance xc from it: holes will be collected from the region xc < x < d, while electrons will be accumulated from the region 0 < x <xc .
For the chosen experimental configuration (cf. Fig. 5.5.3) the currents of electrons and holes can be calculated directly by integrating the absorbed light profiles over the ranges [d, xc ] and [xc , 0], respectively: je exp [−α(d − xc )] − exp [−αd] . = jh 1 − exp[−α(d − xc )]
(5.5.3)
Next, Eq. (5.5.2) will result in the following inequality: exp[−α(d − xc )] − exp[−αd] σr × << 1, 1 − exp[−α(d − xc )] σ
(5.5.4)
which sets the lower limit of the trap capture cross-section which might be studied without substantial influence of recombination: σ >> 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
Injection Spectroscopy of Thin Layers of Solids
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.
(5.5.6)
To meet the inequality condition (5.5.6) the exciting light must be strongly attenuated by the collector layer to ensure αd >> 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
Internal Photoemission Spectroscopy: Principles and Applications
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 .
Injection Spectroscopy of Thin Layers of Solids
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
Internal Photoemission Spectroscopy: Principles and Applications
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.
Trapped Charge Monitoring and Characterization
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
Internal Photoemission Spectroscopy: Principles and Applications
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.
Trapped Charge Monitoring and Characterization
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
Internal Photoemission Spectroscopy: Principles and Applications
‘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)
Trapped Charge Monitoring and Characterization
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
Trapped Charge Monitoring and Characterization
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
Internal Photoemission Spectroscopy: Principles and Applications
(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.
Trapped Charge Monitoring and Characterization
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
Internal Photoemission Spectroscopy: Principles and Applications
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
Trapped Charge Monitoring and Characterization
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
Internal Photoemission Spectroscopy: Principles and Applications
(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
Trapped Charge Monitoring and Characterization
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)
Trapped Charge Monitoring and Characterization
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
Internal Photoemission Spectroscopy: Principles and Applications
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.
Trapped Charge Monitoring and Characterization
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
Trapped Charge Monitoring and Characterization
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 (<10 eV) usually overlapping with the valence states of the host solid. Alternative approaches like the nuclear magnetic resonance and the optical absorption in the infrared photon energy range have a limited sensitivity and require bulk samples to provide the desirable information. The time-of-flight mass spectroscopy and nuclear reaction analysis can quantify hydrogen content down to approximately 1 atom.%, but provide no information
146
Internal Photoemission Spectroscopy: Principles and Applications
regarding its chemical state and, therefore, regarding the possible involvement in the charge transport or trapping. At the same time there is plenty of experimental evidence indicating H as important factor of charging, for instance, of SiO2 insulating films and their interfaces (Nicollian et al., 1971; Feigl et al., 1981; Gale et al., 1983; Stahlbush et al., 1993; de Nijs et al., 1994; Afanas’ev et al., 1995a, b; Cartier and Stathis, 1995; Vanheusden et al., 1995; 1997; Afanas’ev and Stesmans, 1998a, b; 1999a; 2000a; 2001a, b; Rivera et al., 2002). Therefore, identification of the H-related charge transport and trapping interaction is gaining more and more importance as novel oxide-based insulators attract an increasing attention (see, e.g., Afanas’ev and Stesmans, 2002; 2004b, for some insulating metal oxides). In this section the technique for in situ detection of atomic hydrogen released in a solid-state structure is addressed which uses the effect of deactivation of doping impurities in semiconductor crystals, in particular, deactivation of B acceptors in silicon (Sah et al., 1983a, b; Pankove et al., 1983). The scheme of this interaction revealed by infrared optical absorption studies and theoretical calculations consists in bonding of H to Si atom of the Si3 ≡B Si acceptor complex resulting in saturation of the unpaired electron state (DeLeo and Fowler, 1985; Johnson, 1985; Watkins et al., 1990). Therefore, once atomic H is liberated inside the collector or at its interface(s), some of the released hydrogen atoms may enter the surface layer of the B-doped silicon and cause partial passivation (deactivation) of acceptors. The latter can easily be detected using CV measurements (Sah et al., 1983a, b) enabling one to monitor concentration of the liberated atomic H by applying the very same technique as used for the trapped charge monitoring (Afanas’ev et al., 1994a; 1995a; 2001a, b; de Nijs et al., 1994; Druijf et al., 1995; Vasconcelos et al., 1997; 1998; 2000; Afanas’ev and Stesmans, 2004b). In the simple case of insulating collector the concentration of acceptors in the near-interface layer of semiconductor can be monitored by using the value of capacitance in the inversion flat portion of the high-frequency CV curve. This capacitance is directly related to the maximal width of the depletion layer in equilibrium Wmax (cf. Fig. 9 in Chapter 7 of Sze (1981)): Cinv =
ε0 εD , d + εεscD Wmax
(6.6.1)
where εD and εsc are the relative dielectric permittivities of the collector and semiconductor, respectively, and Wmax is given by Eq. (2.1.11). In the case of a thin collector layer one may assume that the minimal capacitance is mostly determined by the width of the depletion layer in semiconductor, which yields: Cinv ≈
ε0 εsc 1 ∝√ , Wmax na
(6.6.2)
where na is the concentration of acceptors at the surface of semiconductor. Therefore, by analysing the variations of the relative capacitance in inversion δC inv ≡ Cinv /Cinv as a function of the injected charge density one may trace possible correlation(s) between the charge trapping and the liberation of atomic H in the collector. The revealing power of such correlative analysis is illustrated by the experimental results shown in Fig. 6.6.1 for the case of trapping holes in thermally grown SiO2 layers on Si with cooling down in O2 (sample type A) or subjected to the post-oxidation annealing in Ar + 10% H2 (sample type B, for details see Afanas’ev and Stesmans (2001a)). Variations of the relative inversion capacitance shown in the panel (b) correlate with the hole trapping and, most importantly, with subsequent neutralization of the trapped positive charge whose kinetics are shown in the upper panel (a). This correlation indicates
Q/q, [E] (1012 cm2)
Trapped Charge Monitoring and Characterization 8 (a) 6 4 2
E centers
0.00
(b)
0.01 dCinv
147
0.02
Electron injection
0.03 0.04 0.05
Hole injection 0
1
2
Injected charge carriers (1015 cm2)
Fig. 6.6.1 Density of positively charged centres (a) and relative variation of inversion capacitance (b) as functions of injected electron/hole density in MOS structures of type A () and B (). The data for samples subjected to 30 min post-metallization anneal in forming gas (N2 + 10% H2 ) at 400◦ C are shown by filled symbols for comparison. The E centre density is shown for samples A () and B ( ) on panel (a).
the direct involvement of H-containing centres in SiO2 in the charging/annihilation process ultimately revealing the protonic nature of the positive charge trapped in silicon dioxide upon injection of holes (Afanas’ev and Stesmans, 2001a; Afanas’ev et al., 2001a; 2002c). Once the high-frequency regime is reached in the CV measurements (Nicollian and Brews, 1982), the important advantage of the inversion capacitance determination consists in the insensitivity of this capacitance value to the density of interface defects or oxide charges. However, the interface traps might affect the semiconductor doping determination if the depletion portion of the CV curve is used for analysis (Brews, 1973b; Nicollian et al., 1973). Obviously, there are other possibilities to evaluate the doping impurity concentration which must be used if inversion cannot be observed on the CV plots. The problem with alternative methods, like the spreading resistance measurements (Pankove et al., 1983) or the infrared optical absorption spectra (Johnson, 1985), is mostly related to the detection of the acceptors distributed over substantial portion of the semiconductor crystal. By contrast, CV measurements are specifically sensitive to the doping of semiconductor interface (or surface) layer of thickness Wmax , which makes them the preferred monitoring technique.
CHAPTER 7
Charge Trapping Kinetics in Injection-Limited Current Regime
7.1 Necessity of the Injection-Limited Current Regime Using the known density of the injected carries (Ninj ) and that of the trapped ones (Nt ) in the collector we can start considering possible ways to determine the properties of the capturing sites (cross-section and density). The derivative of the trapped charge density on the injected one has an obvious physical meaning of the charge carrier trapping probability averaged over the whole available volume of collector material and, therefore, contains contributions of all the traps present there. The question now concerns the conditions when the contributions of different centres to the charge trapping can be separated and quantified when knowing just two measured values, i.e., Ninj and Nt . The very first simplification in describing the carrier trapping process comes from the assumption that the carrier concentration is constant over the whole analysed volume of collector, i.e., the average of the concentration is equal to its microscopic value which can be found from the injection current density j and known value of electric field F (Rose, 1963): j = q(nμe + pμh )F,
(7.1.1)
where n, p are the concentrations and μe , μh are the field mobilities of electrons and holes injected into the collector, respectively. In the case of monopolar injection discussed in Chapter 5, Eq. (7.1.1) can be directly used to calculate the concentration of free carriers and, in this way, determine the value of the trapping probability. When writing Eq. (7.1.1) one assumes that the electric field in the collector is constant, i.e., it is unaffected by the injected and trapped charges. The latter is true only if the carrier concentrations remain small. If this condition is not met the Coulomb interaction between the charges will affect both the injection of carriers and their drift in the collector. In a limiting case of strong trapping the captured charges are able to screen the externally applied electric field leading to the space–charge-limited current with its steady-state value controlled by the trapping–detrapping balance rather than by the rate of injection at the contact (Lampert and Mark, 1970). The issue of the carrier injection rate affected by the space charge in the collector has already been briefly addressed in Section 3.4.1 when discussing the conditions of the internal photoemission (IPE) current observation. In that case the transport across the collector is of minor interest because the same injection current will be measured as long as most of the carriers 148
Charge Trapping Kinetics in Injection-Limited Current Regime
149
reach the field electrode, i.e., irrespectively of the electric field distribution across the collector layer. However, when analysing the charge trapping rate determined by the local concentration of carriers, the impact of internal fields may be substantial because, for the same current density, Eq. (7.1.1) (or its simple version for the monopolar injection regime) predicts the concentration to depend inversely on the strength of locally applied electric field. Therefore, it is useful to evaluate the limits of the constant carrier concentration approximation for the case of a charge-containing collector. The transition from the injection-limited to the space–charge-limited regime may be expected to occur when the density of charge carriers in the collector becomes sufficient to compensate the external electric field applied to the interface. Assuming that the density of carriers immobilized on deep traps is still low (the initial state of injection into a charge-free collector), the areal density of injected charge Q can be estimated as: Q = qGτ,
(7.1.2)
where G is the carrier injection rate and τ is the mean transport time across the collector layer. The latter can be evaluated using the drift velocity vd of the carriers and assuming that they are injected at one contact and drift through the whole collector of thickness d as follows: τ≈
d d d2 = = , vd μF μV
(7.1.3)
where V is the voltage applied across the collector layer. To compensate the applied voltage the charge Q has to create a comparable variation of electrostatic potential: V≈
d Q =Q , C ε 0 εD
(7.1.4)
where C is the specific capacitance of collector layer of thickness d and relative dielectric permittivity εD . Using the above equations the transition to the space-charge-limited regime is expected to occur when qG d 3 ≈ 1. με0 εD V 2
(7.1.5)
The latter condition is equivalent to the requirement that the injection current must be low enough to ensure the absence of space-charge effects, i.e., the injection-limited current mode discussed in Section 3.4.1. Further, one can use it to evaluate the upper limit of the injection rate G that enables experiments with negligible influence of the space charge. In a thin collector layer with sufficiently high mobility one almost always remains in the safe interface-injection-limited current mode. For a 100-nm thick layer of SiO2 (εD = 3.8) and applied voltage of 10 V the condition (7.1.5) is met for electrons (μe ≈ 20 cm2 /V s (Goodman, 1967; Hughes, 1973; 1975a)) when G reaches 1025 cm−2 s−1 and for holes (μh ≈ 10−9 cm2 /V s (Hughes, 1975b; 1977)) when G approaches 1016 cm2 s−1 , both values hardly be observed in a real experiment taking into account large bandgap of SiO2 (≈9 eV) and high interface barriers. However, with increasing thickness of the collector, the situation rapidly deteriorates. When SiO2 thickness is increased to 1 μm under the same bias, the hole space–charge effects are expected to become important when G approaches 1013 cm−2 s−1 , i.e., the injection current density about 1 μA/cm2 . The latter can easily be provided by a number of injection techniques discussed in Chapter 5. Therefore, in the case of materials with low mobility, the correct analysis of trapping is possible only if the samples with thin-film collector are used.
150
Internal Photoemission Spectroscopy: Principles and Applications
7.2 First-Order Trapping Kinetics: Single Trap Model Now, when assuming that the injection-controlled current regime is maintained, one might analyse interaction of the injected carriers with trapped centres. We will assume that the charge carrier trapping probability remains low enough to ensure a negligible gradient of their concentration across the collector (cf. Eq. (2.2.17)), and that the traps with the same capture cross-section σ have no mutual influence. Then the probability of one carrier to be trapped in a layer (x, x + dx) from the surface of emitter can be expressed as a multiple of the available trap concentration and of a cylinder volume of collector with cross-section σ and length equal to the path of a carrier moving with thermal velocity vth for the time it drifts across the layer of thickness dx with drift velocity vd as schematically illustrated in Fig. 7.2.1. The corresponding analytical expression for the trapping probability is well known (Rose, 1963; Nicollian et al., 1971): p(x, x + dx) = [N(x) − Nt (x)]σ
vth dx, vd
(7.2.1)
where N(x) and Nt (x) are the total concentration of traps and that of traps already occupied by charge carriers, respectively. Integration over the whole collector thickness allows one to express the trapping probability in terms of real densities of the traps and their occupied portion (Nicollian et al., 1971; Ning and Yu, 1974): p = [N − Nt ]σ
vth , vd
(7.2.2)
which is valid as long as p is small (<0.2 to ensure the sufficient accuracy of linear expansion of the term given by Eq. (2.2.19): e−σN ≈ 1 − σN). The trapping probability can also be expressed as the first vth
vth
vth
vth v th
x
dt dx/vd
x dx
Fig. 7.2.1 Schematic illustration of the trapping process in the framework of the first-order trapping model. The electron dwells in the layer (x, x + dx) for a time dt = dx/vd which allows interaction (capture) with all traps with capture cross-section σ located within a cylinder with a section σ and length equal to dtvth .
Charge Trapping Kinetics in Injection-Limited Current Regime
151
derivative of the trapped carrier density on the density of injected carriers: p=
dNt (Ninj ) , dNinj
(7.2.3)
where t Ninj =
n(t )dt = q
−1
0
t
j(t )dt
(7.2.4)
0
and t is the injection time. Then one can write the first-order trapping equation as: dNt (Ninj ) vth = [N − Nt ]σ , dNinj vd
(7.2.5)
which has a well-known solution (Nicollian et al., 1971; Ning and Yu, 1974; DiMaria, 1978; Williams, 1992) in the following form: v ∗ −σ th N Nt (Ninj ) = N 1 − e vd inj = N 1 − e−σ Ninj ,
(7.2.6a)
where σ ∗ = σ vvthd is usually referred to as the macroscopic capture cross-section. In the case of a constant injection current, j, Eq. (7.2.6a) can be rewritten in terms of the trap filling time constant τ (Williams, 1992): t Nt (t) = N 1 − e− τ , (7.2.6b) where τ=
q . jσvth
It is seen now that in general the analysis of charge trapping kinetics provides only the value of the macroscopic cross-section σ* which differs from the microscopic one σ by the field-dependent factor vth /vd ∝ 1/F. The effect of electric field consists in variation of the total (microscopic) path the carrier travels when drifting from the emitter to the field electrode. One observes directly from the numerically simulated electron trajectories that this path is much larger in low fields than in high ones (see, e.g., (Fitting and Friemann, 1982). As an example how important this influence might be, one can evaluate the effective cross-section for the case of a carrier diffusing around its drift trajectory within radius equal to the diffusion length d D ∝ D , vd where D is the diffusion coefficient. By using Einstein’s relationship between the drift mobility and the diffusion coefficient D/μ = kT/q one obtains the following estimate of the apparent (effective) cross-section: d kT d σeff ∝ 2D = D = . (7.2.7) vd q F In a low field and in a thick collector layer this apparent cross-section may by far exceed the microscopic cross-section σ. This effect reflects the fact that charge carrier is free to diffuse over large volume on
152
Internal Photoemission Spectroscopy: Principles and Applications
its way across the collector. Therefore, to obtain a meaningful result one should look at the high-field region in which the carrier drift velocity becomes comparable to the thermal one bringing σ* value close to that of σ. In some cases one may reach the regime of saturation of the drift velocity which would mean that the latter becomes equal to the thermal velocity, i.e., vd = vth . For instance, in amorphous silicon dioxide the electron drift velocity saturation is reported to happen in the range of electric fields between 0.5 and 3 MV/cm in which vd ≈ vth ≈ 107 cm/s (Hughes, 1978). Using this result DiMaria directly associated the experimental values of capture cross-sections of traps encountered in SiO2 films with their real microscopic values (DiMaria, 1978). Worth adding here is that one also should average the capture crosssection over the energy distribution of carriers in the collector (Lax, 1960; Ning, 1976a; 1978; Williams, 1992). This effect of excessive electron energy on the cross-section might appear to be significant as indicated by the additional decrease of the Coulomb attractive cross-section for electrons in SiO2 measured at strength of electric field exceeding 1 MV/cm (Buchanan et al., 1991). With electrons gaining more and more energy in the increasing electric field, the field-dependent Coulomb cross-section decreases more rapidly (approximately as F −3 ) as compared to the case of thermalized electrons (σ ∝ F −3/2 ) (see, e.g., Dussel and Böer, 1970). Nevertheless, as long as one type of collector material is analysed, most significant differences in the macroscopic cross-section σ* of various traps are expected to arise from the differences in their microscopic σ values if the measurements are performed in the same, sufficiently high electric field. Influence of the vth /vd ratio in this case can be considered simply as a scaling factor which has the same value for all the traps, irrespective of their capture cross-section. The most important problem now consists in finding a way to separate contributions of different centres to the charge trapping kinetics making necessary the multiple trap analysis.
7.3 First-Order Trapping Kinetics: Multiple Trap Model Within the approximation that each trap interacts with injected charge carriers independently, the firstorder kinetics can easily be extended to the case of multiple traps by simple summation of their contribution to the density of trapped carriers. Would several types of traps with density N i and capture cross-section σi (i = 1, 2, 3, . . .) be present in the collector, the total density of trapped carriers may be written as a sum of their independent contributions (Ning and Yu, 1974): Nt (Ninj ) =
i
Nti (Ninj ) =
i
∗
N (1 − e−σi Ninj ),
(7.3.1)
i
where the macroscopic capture cross-sections are related to the microscopic ones as σi∗ = σi vvthd . Potentially one may directly use Eq. (7.3.1) to fit the experimentally measured Nt (Ninj ) curve in order to determine trap parameters Ni and σi∗ . However, it was noticed by Williams (1992) that the ‘perfect’ fit of the experimental charge trapping kinetics often requires larger number of trap types that can be expected on the basis of physical reasoning. The second problem with direct fitting consists in a mutual influence of the densities and cross-sections of different traps caused by the cross-correlation of the fitting parameters. It is, therefore, highly desirable to know at least the number of different trapping centres before applying the fitting procedure (Stivers and Sah, 1980; Sah et al., 1983c; Williams, 1992). In some cases the plot of the trapped carrier density versus logarithm of the injected charge exhibits clear kinks indicative of filling the traps of one type (Stivers and Sah, 1980; Sune et al., 1990; Williams, 1992). The only disadvantage of this approach is that the cross-sections of the traps should be different by more than one order in magnitude to be distinguished using the log plot.
Charge Trapping Kinetics in Injection-Limited Current Regime
153
Another way to determine the number of available trap types and their cross-sections was proposed by Ning and Yu (1974) and consists in numerical differentiation of the trapping kinetics. If calculating the trapping probability using Eq. (7.2.3) and expression for Nt (Ninj ) given by Eq. (7.3.1) one obtains the sum of independent contributions to the carrier trapping probability in the form of sum of several exponential terms: i dNt ∗ = N σi∗ e−σi Ninj , dNinj
(7.3.2)
i
This expression would yield several linear portions if plotted using log (dNt /dNinj ) ∝ Ninj co-ordinates. The slope of each linear portion can be used to determine the cross-section of the corresponding trap (Ning and Yu, 1974; Buchanan et al., 1991; Afanas’ev and Adamchuk, 1994; Afanas’ev et al., 1997b). Though the need of numerical differentiation makes this procedure somewhat less accurate than the direct fitting, experience shows that it can resolve traps with cross-sections differing by a factor of approximately 5. Practical application of this method is illustrated in Fig. 7.3.1 for the case of electron IPE from Si into SiO2 collector layer containing both the positive charges and neutral electron traps generated by photogeneration of electron–hole pairs using 10-eV photons (Adamchuk and Afanas’ev, 1992b; Afanas’ev and
Nt (1012 cm2)
3
2
1
(a) 0 9 s21 1015 cm2
log(dNt/dNinj)
8 7 6 5 4
s17 1014 cm2
3 2 1
(b)
0 0
20
40
60
Injected electrons
80
100
120
(1013 cm2)
Fig. 7.3.1 Electron trapping kinetics (a) and the logarithm of the trapping probability (b) observed when photoinjecting the carriers from Si into SiO2 layer previously irradiated by 10-eV photons. The strength of electric field in the oxide during injection is 1 MV/cm. Capture cross-sections of the found traps are indicated. These correspond to electron trapping by the Coulomb attractive centres related to positive charges in silicon dioxide (σ1 ) and to the irradiation-induced neutral electron traps (σ2 ).
154
Internal Photoemission Spectroscopy: Principles and Applications
Trapped holes (1012 cm2)
5 2 4 1 3 2 3
1 0 0
20 40 60 80 Injected holes (1013 cm2)
100
Fig. 7.3.2 Kinetics of hole trapping in (100)Si/SiO2 (100 nm)/Au capacitors measured using electron–hole pair generation in the oxide surface layer by 10-eV photons when applying +10 V bias to Au field electrode, and CV-curve-based trapped charge monitoring. Curve 1 corresponds to hole trapping in the control sample, curve 2 shows the hole trapping curve measured in sample pre-injected by 1017 electrons/cm2 using avalanche electron injection (AEI) from Si, and curve 3 represents the difference kinetics numerically calculated from the previous two trapping curves.
Adamchuk, 1994). The top panel shows charge trapping kinetics measured by recording a capacitance– voltage (CV) curve after each photoinjection pulse, the bottom one represent the logarithmic plot of the trapping probability numerically calculated from the trapping kinetics. Contributions of two traps with different capture cross-section are evident from the latter graph. As the final step one may fit the trapping curve using two trap contributions and the evaluated cross-section values to find the traps densities. Another way to separate contributions of different centres to charge trapping consists in subtraction from the measured trapping curve of the contribution of background trapping determined in the control sample. In this way one extracts the net contribution of traps introduced by some additional treatment of the collector material. This way of trap separation is exemplified in Fig. 7.3.2 which shows the kinetics of hole trapping in a 100-nm thick SiO2 layer on Si in the control sample (curve 1), in the sample pre-injected with 1 × 1017 electrons/cm2 (curve 2) and their difference (curve 3) corresponding to the trapping of holes by negatively charged centres (electrons captured by neutral traps in SiO2 ). The latter curve can easily be fit by the first-order trapping kinetics by using a single trap cross-section which appears to be equal to 1 × 10−13 cm2 at F = 1 MV/cm. Remarkably, this cross-section corresponding to the hole trapping by the Coulomb attractive potential appears to be close to that for the attractive Coulomb trapping of electrons in SiO2 (σ1 in Fig. 7.3.1). This coincidence suggests that the spatial span of the Coulomb potential predominantly determines the cross-section value while the details of carrier scattering inside the potential well are of minor importance. The latter conclusion is based on the observed nearly 10 orders in magnitude difference between electron (Goodman, 1967; Hughes, 1973; 1975a) and hole mobilities in SiO2 (Hughes, 1975b; 1977) indicative of huge differences in interaction of these two types of charge carriers with the oxide network during their transport. Despite these differences the attractive Coulomb trapping of electrons and holes occurs with the same cross-section. 7.4 Effects of Detrapping The first-order trapping kinetics discussed just above represents a highly idealized description which is ignoring several important physical factors. Among others, to be addressed further, the assumption is
Charge Trapping Kinetics in Injection-Limited Current Regime
155
made that the trapped charge carrier remains at the same trap for the whole time of experiment. Would this not be the case and the carrier be allowed to escape the trap (detrapping process) one must add to Eqs (7.6.6) and (7.3.1) term(s) describing the loss of charge. Potentially, all the processes of detrapping discussed in Section 6.4 and schematically indicated in Fig. 6.4.2 may be relevant. In the most simple formulation the carrier liberation process is characterized by the detrapping time τ which corresponds to the mean time the captured carrier dwells on a trap before it emitted back to the transport band or recombined with the charge carrier of opposite sign (DiMaria, 1978; Yamabe and Miura, 1980). Though this approach does not address the physics of the detrapping, it allows one to express the charge trapping kinetics in analytical form by avoiding complicated expressions appearing when contributions of different emission mechanisms are written explicitly (see, e.g., Eq. 16 in Williams (1992)). The rate of detrapping can be written as Nt /τ and subtracted from the charge trapping rate for a single trap given by Eq. (7.2.5):
dNt (Ninj ) 1 Nt vth (7.4.1) = (N − Nt )σ − = N − Nt 1 + ∗ σ ∗ , τσ dNinj vd τ which has functionally the same solution as Eq. (7.2.5) but with different coefficients corresponding to the effective (apparent) trap density and their cross-section (see, e.g., Afanas’ev and Adamchuk, 1994a): ⎛ ⎞ σ ∗ Ninj − q N ⎝1 − e 1+ jτσ ∗ ⎠ = Neff (1 − e−σeff Ninj ), (7.4.2) Nt (Ninj ) = q 1+ jτσ ∗ where j is the injection current density, Neff =
N 1+
q , jτσ ∗
(7.4.3a)
and σeff =
σ∗ 1+
(7.4.3b)
q . jτσ ∗
The denominator in the right-hand part of Eqs (7.4.3a) and (7.4.3b) corresponds to the ratio between the time constant of trap filling given in the constant current injection mode by jσq∗ and the time constant of emptying by detrapping equal to τ. This result indicates that the constant current injection in absolutely necessary to keep constant the parameters describing the trapping kinetics Neff and σeff when the influence of detrapping is substantial. In turn, any experimentally observed dependence of the trapping parameters on the carrier injection rate can be considered as clear evidence of non-negligible influence of detrapping effects on the charge accumulation. Another, rather obvious consequence of the detrapping consists in a decrease of the charge density after injection is stopped. If the injected carriers by themselves are not the primary detrapping factor (the case of impact ionization, scheme e in Fig. 6.4.2), one may expect the detrapping time constant τ to remain unchanged when stopping the injection. Therefore, the trapped charge is expected to decrease from its value reached during the injection as: Nt (t) = N(t = 0)e− τ , t
(7.4.4)
where the beginning of observation (t = 0) corresponds to some time after injection is terminated. Also, as the detrapped carriers drift across the collector, they will cause the corresponding displacement current
156
Internal Photoemission Spectroscopy: Principles and Applications
in the external circuit with the same exponential decay (see, e.g., Afanas’ev et al., 1994b). Analysis of the detrapping kinetics after terminating the injection, monitored using the charge or current measurements, represents the most reliable method of the detrapping time constant determination, including possible separation of different contributing carrier emission processes. The identification of the detrapping mechanism(s) is usually based on observation of the carrier liberation rate as influenced by some external physical parameter. For instance, in the case of thermal emission (transition a in Fig. 6.4.2) one obtains (DiMaria, 1978; Yamabe and Miura, 1980; Williams, 1992): Et 1 ∝ e− kT , τ
(7.4.5)
which enables determination of the (thermal) trap energy Et by using the slope of the log(τ)–1/T line (the Arrhenius plot). For more extensive discussion on this subject the reader may address works of other authors (see, e.g., Simmons and Tam, 1973; Gupta and Van Overstraeten, 1976). In some cases the thermally activated detrapping can be accompanied by influence of electric field assisting the carrier liberation by reducing the height of the potential barrier the carrier has to overcome (the Poole–Frenkel mechanism, see e.g., (Arnett and Klein, (1975)). The purely thermal (the Schottky emission) and field-assisted mechanisms can be distinguished by using the field and temperature dependences of the detrapping rate though the definite conclusion is not always easy to reach (Bourcerie et al., 1989). The optical radiation can also be a factor of depopulation (transition b in Fig. 6.4.2) (Mehta et al., 1972; Kapoor et al., 1977a,b; Jacobs and Dorda, 1977a, b; DiMaria, 1978) and can be characterized by the energy-dependent photoionization (PI) cross-section σph (hν), which relates PI probability per unit time to the exciting photon flux nph (hν): 1 = σph (hν)nph (hν). (7.4.6) τ This expression can be generalized to the case of light intensity variation across the excited layer (potentially caused by optical interference effects, absorption, etc.) by integrating the light intensity and the filled trap distribution across the collector thickness (DiMaria and Arnett, 1977; DiMaria, 1978): τ=
Nt d
,
(7.4.7)
σph (hν) nt (x)nph (hν, x)dx 0
where it is still reasonable to assume that the PI cross-section is spatially independent. As already discussed in Section 4.4.2 the spectral dependence of σph is determined by the energy of trapped carriers measured with respect to the band they are excited to. Thus, by analysing dependence of the inverse depopulation time constant on photon energy the optical energy depth of trapping site can be found. The liberation of carriers by electron impact (impact ionization) represents more complicated case because it can be observed only if the carriers are present in the conduction band of the collector, but not after the injection is terminated. Analysis of the field-dependent charge trapping dynamics appears to be the only way to characterize this kind of detrapping (Nissan-Cohen et al., 1986). In addition, the emission rate will depend not only on the concentration of electrons moving in the collector but, also, on the strength of electric field which determines their energy distribution: only sufficiently ‘hot’ carriers may cause the impact ionization of traps (process e in Fig. 6.4.2). Analysis of the high-field electron trapping in SiO2
Charge Trapping Kinetics in Injection-Limited Current Regime
157
indicates sharp field dependence of the impact ionization rate (DiMaria et al., 1974; 1975; Porod and Kamocsai, 1990): b 1 ∝ e− F , (7.4.8) τ where b is a constant and F is the strength of electric field in SiO2 . So far, there is no evidence that this mechanism of detrapping is of importance in other materials than silicon dioxide. The removal of a charge carrier from a trapping site by its tunnelling to the neighbouring defect (the hopping detrapping, transition f in Fig. 6.4.2) is most relevant to the case of thin-film collector structures in which eventual removal of the carrier is enabled by spatial proximity of electrodes. According to Mott, the hopping rate can be expressed using two exponential terms, one in energy and another in space describing the thermal activation of transition rate and the spatial decay of the trapped carrier wave function, respectively (Mott and Davis, 1979): 2x E 1 ∝ W0 e− α(E) e− kT , τ
(7.4.9)
where W0 is determined by the electron band structure and electron–phonon interaction parameters of the collector, α(E) is the attenuation length of the wave function of electron on trapping site, x is the mean hopping distance and E corresponds to the energy splitting between the neighbour trap levels. For deep levels (Et > 2 eV) the electron wave is highly localized on the trapping site and its spatial extent is expected to be in the range of few angstroms. Thus, the detrapping becomes possible only if defects are present in high concentration (above 1020 cm−3 ). The latter may well be the case in the near-interface regions of insulating materials contaminated by adsorbate molecules making the trap-assisted transport mechanism also relevant to the case of thin collectors. In addition to the thermally assisted transitions, detrapping may also occur via electron tunnelling from the trap level to band states of collector if electric field of sufficient strength is applied (transition c in Fig. 6.4.2). The functional form of the tunnelling transition rate is given by expression similar to that in the Fowler–Nordhein (FN) theory despite localized type of the trapped carrier wave function (see, e.g., Balk, 1988): B 1 (7.4.10) = AF 2 e− F , τ where A and B are constants. Characteristic to this detrapping mechanism are strong field-induced changes in the effective trap density and their cross-section (Nissan-Cohen et al., 1986; Scharf et al., 1996). The detrapping by tunnelling is of particular importance when traps located in collector close to conducting electrodes are investigated (transition d in Fig. 6.4.2). In this case the final state may belong to the electrode making easy removal of carriers (or vice versa) even from energetically deep traps (Lundstrom and Svensson, 1972). The major feature of this detrapping mechanism consists in relationship between the tunnelling rate and the trap–electrode distance which in some cases makes possible determination of the detrapped charge in-depth profiles (Benedetto et al., 1985; Oldham et al., 1986; Schmidt and Köster, 1992; Scharf et al., 1996). The basic relationship between the carrier tunnelling rate and the trap–electrode distance x is assumed to remain exponential (Schmidt and Köster, 1992): 1 1 = e−2kx , τ τ0 (E)
(7.4.11)
where the normal to the collector–electrode interface component of the electron wave vector k and τ0 are determined according to the band diagram of the interface. Examples of such calculations as well
158
Internal Photoemission Spectroscopy: Principles and Applications
as the detrapped charge profile examples at Si/SiO2 interface can be found, for instance, in Schmidt and Köster (1992). As a note of caution in relationship with the tunnelling rate-based charge profiling method here must be added that discharging of defects may also occur via intermediate electron levels of interface traps (Druijf et al., 1993). To exclude the possible influence of such process the application of tunnelling charge profiling should be limited to samples with low density of interface imperfections. 7.5 Carrier Recombination Effects Removal of trapped charge carriers is possible not only via liberation to the transport band of the emitter but, also, through annihilation with carriers of the opposite charge sign. This may happen in the case of non-monopolar injection when both electrons and holes are injected from the opposite electrodes into the collector or, else, generated across the collector layer by high-energy photons of particles as illustrated in Fig. 7.5.1. As it appears, recombination of trapped carriers has strong effect of the effective trap parameters one derives from charging kinetics analysis. Let us assume that carriers of one type are preferentially trapped in the collector while the carriers of the opposite sign interact mostly with the trapped carriers of first type (Boesh et al., 1986). This happens, for instance, in thermally grown oxide layers on Si in which the probability of hole trapping is by orders in magnitude higher than that of electrons (see, e.g., Adamchuk et al., 1990). As a result, the charge trapping kinetics can be described as capture of holes characterized by macroscopic capture cross-section σh∗ partially compensated by recombination of trapped holes with the co-injected electrons with macroscopic cross-section σr∗ . Would the holes and electrons be injected with constant current densities jh and je , respectively, the occupancy of hole traps will follow the rate equation similar to Eq. (7.4.1): dNt (t) je jh = (N − Nt )σh∗ − Nt σr∗ . dt q q
(7.5.1)
In general, one needs to know the currents stemming from both injected carrier to extract meaningful trapping parameters. In some cases (uniform pair generation across the collector by a weakly absorbed
(a)
(b)
Fig. 7.5.1 Recombination of charge carriers in collector caused by injection of two types of carriers from the opposite electrodes applied (a) or by generation of electron–hole pairs across the collector layer (b).
Charge Trapping Kinetics in Injection-Limited Current Regime
159
radiation) it is possible to use je = jh . However, as the carriers will be collected over the entire volume of the sample, integration over collector thickness still to be performed. In the latter case the spatial location of traps plays an important role as discussed in Section 5.5. There is, however, one particular case when the neutralizing charge carriers are injected at much higher rate than the carriers mostly trapped in the collector, i.e., jh << je and jh σh << je σr . The latter inequality comes as the consequence of the former one because charge recombination always corresponds to carrier trapping by the attractive Coulomb potential which is expected to have much larger capture cross-section than any neutral trap in the same material (Rose, 1963; DiMaria, 1978). Then Eq. (7.5.1) can be re-written as (Afanas’ev and Adamchuk, 1994): dNt (t) je jh = Nσh∗ − Nt σr∗ , q q dt
(7.5.2)
and, taking into account that Ninj ≈ je t/q, one obtains dNt (Ninj ) jh = Nσh∗ − Nt σr∗ . dNinj je
(7.5.3)
The initial slope of this kinetic curve corresponds to the first term in the right-hand part of Eq. (7.5.3):
dNt (Ninj ) jh = Nσh∗ . (7.5.4) dNinj je Ninj →0 In its turn, the saturation of the trapping kinetics will occur at the trapped charge density equal to: Nt (saturation) =
jh σh∗ N je σr∗
(7.5.5)
Therefore, the ratio between the initial slope and the saturation level of trapping kinetics measured in the regime of strong recombination will provide one with the value of recombination cross-section σr∗ as illustrated in Fig. 7.5.2. 6
N t (sat) (jh /je)(sh*/s*r)N
Trapped carriers
5 4 3
s*r [dNt /dNinj]/Nt(sat)
2 1
(dNt /dNinj) (jh/je)sh*N
0 0
20
40
60
80
100
120
Injected carriers
Fig. 7.5.2 Schematic representation of the carrier trapping kinetics in the strong recombination regime indicating portions of the curve used to determine the recombination cross-section σr∗ .
160
Internal Photoemission Spectroscopy: Principles and Applications
7.6 Trap Generation During Injection It was so far assumed in the analysis that the density of trapping centres in collector remains unchanged over the whole time the injection experiment is conducted. However, this is not always the case. Thin SiO2 layers on silicon subjected to high-field electron injection or to irradiation provide clear example that the injection by itself may lead to production of new, additional charge traps (Badihi et al., 1982; Nissan-Cohen et al., 1986; DiMaria and Stasiak, 1989; Adamchuk et al., 1990; Heyns et al., 1989; Afanas’ev et al., 1995b). One might attempt to analyse the impact of trap generation on the trapping kinetics using the simple formulation of the first-order model for one trap given by Eq. (7.2.5) and assuming that the density of the injection-induced traps is proportional to the density of injected charge carriers Nt = RNinj (Afanas’ev and Adamchuk, 1994): dNt (Ninj ) = (RNinj − Nt )σ ∗, dNinj
(7.6.1)
which has solution in the following form: Nt (Ninj ) = RNinj −
R −σ ∗ Ninj 1 − e . σ∗
(7.6.2)
Two limiting cases can be considered now which are also illustrated by calculated kinetic curves shown in Fig. 7.6.1. First, if the trap generation occurs slowly, i.e., it is observed in the range of injected carrier densities by far exceeding the inverse cross-section of these defects σ ∗ , second term in Eq. (7.6.2) can be neglected and one obtains Nt (Ninj ) ≈ RNinj . Thus, the charge trapping kinetics reproduces the trap generation one which reflects the more rapid filling of the generated traps than their production. This conclusion is also valid for other laws describing trap generation as a function of injected carrier density. Note that no information regarding the capture cross-section of generated traps can be extracted from the charging kinetics in this case.
Trapped carriers
2
1 Nt
in RN
N
0
0
10
20
t
30
j
s*
in RN
j
R/
40
50
60
70
Injected carriers
Fig. 7.6.1 Carrier trapping curves for the constant trap generation probability Nt = RNinj and large (upper curve) and small (bottom curve) capture cross-section of the generated defects.
Charge Trapping Kinetics in Injection-Limited Current Regime
161
In the case (σ ∗ )−1 >> Ninj one encounters an unusual trapping kinetics shape which is super-linear in its initial part and follows kinetics of trap generation for larger Ninj as can be seen from Eq. (7.6.2): Nt (Ninj ) = RNinj −
R , σ∗
(7.6.3)
i.e., the trapped carrier density, again, follows the trap generation kinetics but shifted along the trapped charge density scale by amount of charge equal to R/σ ∗ . As the slope of the trapping kinetics at large Ninj is uniquely defined by R, in the case of the assumed linear trap generation law their capture cross-section can also be found from the mentioned trapped carrier density shift. There is, however, potential problem in using the above simplified picture of trap generation related to the need of sufficient energy to generate a defect in the collector material. The latter would require a ‘hot’ charge carrier to acquire sufficient energy in the applied electric field lading to sharp a field dependence of the trap generation rate R. In the case of high-field stressing of silicon dioxide the generation rate was shown to be close to exponential function of the average electric field in the collector (Badihi et al., 1982): F
R ∝ e F0 ,
(7.6.4)
where F0 is a constant. Such strong field dependence might lead to the non-uniform profile of the trap generation if the electric field non-uniformity is present, including that associated with the trapped charge. The non-uniform trap profile complicates the data analysis making necessary numerical simulation of the results. As the common feature of trapping in the presence of defect generation one obviously notices the absence of saturation on the charge accumulation kinetics. This was always seen as evidence of the injectioninduced trap generation (Badihi et al., 1982; Nissan-Cohen et al., 1986). In addition, a super-linear increase of the trapped carrier density with increasing the density of injected ones may also serve as indicator of additional trap formation. In these cases the physical meaning of the apparent cross-section might be extracted by fitting the experimental kinetics with the first-order trapping curve remains to be addressed separately.
7.7 Trapping Analysis in Practice With the basic features of the first-order trapping kinetics and its simple extensions discussed, one may now consider practical aspects of the trapping kinetics analysis. Let us assume that the density of trapped carriers and the density of injected ones are determined yielding the experimental Nt (Ninj ) dependence, and the goal now is to extract trap parameters from this curve. The first question to be addressed concerns the applicability of the first-order model to the studied trapping process. This model assumes that each trap interacts independently with the same concentration of injected charge carriers. Therefore, the trapping probability must remain small enough to ensure negligible gradient of the carrier concentration across the studied layer of collector material. If considering 20% accuracy sufficient, this requirement limits the initial carrier probability determined as slope of Nt (Ninj ) curve at Ninj → 0 to 0.2. Trapping kinetics exhibiting a higher initial slope are to be analysed taking into account in-depth variation of the available carrier concentration which will be discussed in the next chapter. Next, as more and more traps become occupied (charged), the injected carriers will experience increasing influence of repulsive potentials of these traps. In fact, the first-order kinetics of charge carrier trapping
162
Internal Photoemission Spectroscopy: Principles and Applications
is written in the form of chemical reaction kinetics between neutral particles (Nicollian et al., 1971), i.e., ignoring entirely the long-range Coulomb interactions between the trapped and the still free charges. The latter effect is expected to become important when the spatial range of Coulomb potential in the collector material rc becomes comparable to the mean distance between the traps rc ≈ (nt )−1/3. The Coulomb potential can be expected to affect the motion of the free charge when it becomes comparable to the thermal energy (Rose, 1963): 2kT =
q2 , 4πε0 εD rc
(7.7.1)
which yields the upper limit of trap concentration available for analysis without considering the Coulomb interaction (correlation) effects: nt <
q2 8πε0 εD kT
−3 .
(7.7.2)
At the temperature of 300 K and using the dielectric constant of 3.9 characteristic for amorphous SiO2 (Sze, 1981) one obtains nt < 1 × 1017 cm−3 . In the case of high-permittivity insulators with εD ≈ 15–20 (Wilk et al., 2001) or the most widespread semiconductors (Si, Ge, GaAs, SiC) with εD ≈ 10–16 (Sze, 1981) the first-order kinetics can be applied to the samples with a higher trap concentration. The trap concentration can be evaluated from the trapped charge density by simply normalizing it to the collector layer thickness which would give exact result in the case of uniform in-depth trap distribution. Next stage in the trapping kinetics analysis consists in checking whether or not additional processes affect the trapped charge density. In the most simple way this can be done by monitoring the charge density for a time comparable to the typical time of the experiment after carrier injection is terminated. Note, in order to isolate the effect of photodepopulation one needs to illuminate the sample with light of the same spectral composition as one used for the injection but without applying bias. In some cases dependence of the trapped charge density on the carrier injection rate must be measured to quantify detrapping (Scharf et al., 1996). Once the time constant of detrapping τ is estimated, one can analyse the trap filling kinetics at time t < τ using the first-order model. Finally, the saturation of the trapped charge with injection charge (time) can be used to evaluate the importance of the trap-generation effects. Now the trapping curve can be replotted using log (dNt /dNinj ) ∝ Ninj co-ordinates to determine the number of different trap types which can be distinguished using the available dataset. Straight portions of this plot would immediately indicate an ensemble of traps with well-defined capture cross-section which can be found from the slope of the graph. In some cases portions of the kinetic curves controlled by the traps with strongly different cross-sections can also be distinguished using Nt –log(Ninj ) plot in which these are seen as separate ledges (Stivers and Sah, 1980; Sune et al., 1990; Williams, 1992). To refine the analysis, it may be advised to fit the kinetics numerically using the found number of different trap types and their approximate capture cross-sections as the initial parameter set. The quality of this fit can be evaluated using the residuals plotted as function of the injected carrier density (Williams, 1992) which are indicative of the cross-sections of traps not described adequately in the framework of the first-order trapping model. If significant, these deviations from the expected trapping behaviour would indicate additional physical processes affecting the accumulation of charge carriers on the trapping sites (recombination, redistribution of injection current flow, etc.). In this case additional analysis becomes necessary to exclude or quantify the factor(s) causing deviation of the trapping curve from the expected shape.
Charge Trapping Kinetics in Injection-Limited Current Regime
163
As a final short note it is worth addressing here the question how uniquely the values of the capture crosssection are defined in a real solid. Apparently, a little site-to-site variation of the electrostatic potential and the polarizability of the trap-related imperfections can be expected to occur in crystalline materials. However, in irregular matrices of amorphous solids or at the interfaces of crystals with such matrices random variations of local surrounding may have significant effect on the carrier trap interactions. Relevant to the case of a carrier trapping is that the value of cross-section is determined by the local vibrionic modes as evidenced by numerous experiments with use of hydrogen–deuterium replacement techniques (Kiselev et al., 1981; Gale et al., 1988; Hess et al., 1998; 1999). One of the important conclusions reached in these studies consists in significant spread of hydrogen binding energy in Si H bonds (Hess et al., 1999) which is in qualitative agreement with earlier reported spread in the activation energy of thermal detachment of H from Si atom at the Si/SiO2 interface (Stesmans, 1996; 2002). It is therefore reasonable to expect a similar spread in the capture cross-section values for compositionally identical defects with disorder-induced variations in their configuration and/or surrounding. In an unpublished report, Nicollian suggested the local strain to be also affected by charge state of a trap resulting in variation in the cross-section of neighbouring, still unoccupied defects (see discussion on this subject in Williams, (1992)). To account for the latter effect, Williams developed a phenomenological model assuming that the section decreases with the number of injected carriers, which will be discussed in more details in the next chapter. Analysis in the framework of this, stress-sensitive model and that done using the simple first-order trapping kinetics given by Eq. (7.2.6a) yield results on cross-section differing by a factor of up to two (see Table 1 in Sune et al. (1990)). Thus, as a first rough estimate of the strain-induced variation in the cross-section in disordered surrounding one should accept an uncertainty of this order. Under these circumstances there is little sense to target separate contributions from the traps differing in their cross-sections by factor of less than 5.
CHAPTER 8
Transport Effects in Charge Trapping
As already mentioned earlier, the first-order trapping kinetics is relevant to the case of trapping of uniformly injected charge carriers by an ensemble of non-interacting trapping centres. These simplifying assumptions limit applicability of this kinetic model to the samples with the collector of low trapping probability as well as of low volume trap concentration. The indicated suppositions are necessary to ensure the same concentration of the carriers over the studied volume of a solid, and the insensitivity of the capture probability on an arbitrary trap to the occupancy of the other traps. Once the above conditions are not met, gradients in the free carrier concentration and the associated with its spatial inhomogeneity of trap occupancy must be taken into account. In most of the cases, the trapping kinetics under these circumstances cannot be described analytically and requires numerical simulation. Reliable determination of trap parameters becomes in this case problematic because a smooth, featureless kinetic curve is to be fitted using a multi-parameter model leading to significant cross-correlation effects. Nevertheless, it will be attempted in this chapter to go beyond the simple first-order description by considering several model cases which still can be treated analytically. These would indicate the most significant variations of the trapping kinetics associated with carrier transport effects. 8.1 Strong Carrier Trapping Regime The case of strong carrier trapping represents one of the most difficult situations because the concentrations of the free and the trapped charges become coordinate dependent. In addition, there is a problem with determination of the injected carrier density because a significant portion of the injected charge is trapped in the collector and does not provide an adequate contribution to the current measured in an external circuit. Finally, the carrier trapping probability is not anymore a linear function of the trap density because of the probability normalization requirement (Afanas’ev and Adamchuk, 1994). In the case of one type of traps with σ ∗ N > 1, the latter leads to the replacement of right-hand part in Eq. (7.2.5) by a term normalized to the unity: v dNt (Ninj ) ∗ −σ th (N−Nt ) = 1 − e vd = 1 − e−σ (N−Nt ) , dNinj
(8.1.1)
in which the solution can easily be written in an indirect but still analytical form as (Afanas’ev and Adamchuk, 1994): ∗ 1 1 − e−σ (N−Nt ) Ninj = Nt − ∗ log (8.1.2) ∗ σ 1 − e−σ N 164
Transport Effects in Charge Trapping
sN
Trapped carriers
20
20
165
N 10
2 1
15
0.4 0.2
10 5 0
0
50 100 Injected carriers
150
Fig. 8.1.1 Trapping curve shape variation with transition to the regime of strong trapping. The curves numerically calculated using Eq. (8.1.2) are shown for the same N but different σN parameter values indicated in the figure.
As it is clearly seen from the kinetic curves shown for different values of σN parameter in Fig. 8.1.1, the kinetics observed at large σN are almost linear but very rapidly saturate when approaching the trap density N (same in all the cases). This curvature of the kinetic curve cannot be adequately fit by the first-order model and may potentially lead to significant artefacts if the latter is attempted to be applied. As one might notice from Fig. 8.1.1, the initial trapping probability for the cases with large σN is always close to unity and becomes barely sensitive to the capture cross-section value. Thus, the apparent crosssection which may be derived by normalizing the trapping probability to the trapped carrier density observed in saturation (N in Fig. 8.1.1) will become dependent on the trap density and actually bears no information regarding the microscopic capture cross-section. This is seen even more easily when applying a simplified expression for the carrier trapping probability using the trap occupancy fraction f (Nt ): dNt (Ninj ) Nt , = P0 [1 − f (Nt )] = P0 1 − N dNinj
(8.1.3)
where P0 represent the initial trapping probability. Solution of this equation is P0 Ninj N t = N 1 − e− N ,
(8.1.4)
and corresponds to the apparent capture cross-section value of P0 /N. This type of cross-section dependence on the trap density and large P0 are the reliable indicators of transition to the strong trapping regime. The important feature of this trapping regime is that contributions of different traps potentially present in the collector cannot be distinguished anymore. The traps just contribute to the total trapping probability P0 , roughly as: P 0 = 1 − e−
Ni σi∗
.
(8.1.5)
Yet, the considered deviation of the trapping curve from the first-order kinetics stems solely from the trapping probability normalization to unity. The charge carriers are assumed to be uniformly generated in the collector layer and supplied to all the available traps. However, in the case of strong trapping the free carrier concentration is also expected to decrease when going deeper into the collector away from the injecting interface. To describe the carrier concentration n(x) decay one may use Eq. (2.2.17) with
166
Internal Photoemission Spectroscopy: Principles and Applications
the concentration of unoccupied traps equal to [N − Nt (x)] and assuming the initially uniform in-depth profile of trapping sites in the collector: ∂n(x, t) = −σ ∗ n(x, t)[N − Nt (x, t)], ∂x
(8.1.6)
in which the dependence on the injection time is also written explicitly. This expression is valid under condition that the carrier distribution in a layer of collector material of thickness dx still can be considered to remain uniform. The latter condition is met if the relative ‘trapping volume’ remains much smaller than the analysed volume of a solid, i.e., (σ*)3/2 N(x) << 1. Under these conditions the gradient of the injected currier flux can be expressed in the following way (Arnett and Yun, 1975): ∂j(x, t) = −σ ∗ j(x, t)[N − Nt (x, t)]. ∂x
(8.1.7)
At the initial stages of injection the decrease in the available trap density due to their filling can be neglected resulting in exponential attenuation of the injected carrier flux: j(x, t → 0) = j(x = 0) e−σ
∗ Nx
− xx
= j(x = 0) e
t
,
(8.1.8)
where xt = (σ ∗ N)−1 corresponds to the mean path of the injected carrier before trapping and, at the same time, gives the centroid of the trapped carrier in-depth distribution. The current observed in the external circuit will contain contributions of the carriers passed through the whole collector layer of thickness d without trapping (the conduction component) and of those captured by defects (the displacement current): ∗ xt ∗ I ∝ j(x = 0) e−σ Nd + 1 − e−σ Nd . d
(8.1.9)
In the case of a thick collector, i.e., when xt << d, only the displacement component will be of most importance resulting in the current density scaled proportionally to the inverse thickness of the collector layer: xt j(x = 0) ∗ ∗ I ∝ j(x = 0) (1 − e−σ Nd ) = (1 − e−σ Nd ). ∗ d σ Nd
(8.1.10)
This current behaviour, sometimes termed a ‘quasi-stationary current’ (Lampert and Mark, 1970), is observed in the range of very low injected current densities in highly trapping collector materials corresponding to a negligible decrease in the density of available traps during the injection. Note that these results can easily be generalized to the case of an arbitrary in-depth distribution of traps N(x) by replacing x the multiple Nx in Eq. (8.1.7) by the integral 0 N(x)dx. When the fraction of the occupied traps cannot be neglected in the expression for the trapping probability (8.1.6) a more complicated treatment becomes necessary. Assuming the absence of the carrier detrapping, the rate of electron trapping must exactly correspond to the decrease of the injected carrier flux: dNt (x, t) j(x, t) = σ∗ [N − Nt (x, t)]. dt q
(8.1.11)
Transport Effects in Charge Trapping
167
Then, by using 1 ∂j(x, t) ∂Nt (x, t) , = q ∂x ∂t
(8.1.12)
one obtains following expression for the time-dependent profile of trapped carriers in the collector (Arnett and Yun, 1975; Ning, 1976b): −1
x eσNinj − 1 e xt Nt (x, t) = N σN , = N 1 + σ∗N e inj − 1 e inj − 1 + eσNx
(8.1.13)
where distance x is measured with respect to the injecting interface. Typical trapped carrier profiles given by Eq. (8.1.13) are exemplified in Fig. 8.1.2 for different densities of the injected carriers Ninj . It can be noticed that the charge builds up rapidly near the surface of emitter with centroid x¯ = xt = (σ ∗ N)−1 , but, with progressing injection, x¯ shifts away from the surface of emitter. For large Ninj the front of the charge distribution is shown to move with velocity equal to j(x = 0)/N (Arnett and Yun, 1975). Because the trapped charge profile measurements lack sufficient accuracy, the charge evolution in most cases is characterized using the measurements of charge centroid (Yun, 1973; Arnett and Yun, 1975). Corresponding values are usually calculated numerically (see, e.g., Yun, 1974) for different σ ∗ and N enabling extraction of trap parameters using this kind of fitting. However, there is still no satisfactory solution of the problem of separating contributions of different traps to the accumulated carrier density because, in the presence of the trapping-induced carrier concentration gradient, the capture events involving traps of different types cannot be considered as independent processes anymore. To enable experimental determination of the charge centroid x¯ as a function of the injected carrier (or the charge) density a combination of the displacement current measurements (or the measurements of the corresponding charge) with capacitance–voltage (CV) curves was developed. These methods use the fact that, when injecting the charge carriers from semiconductor substrate, the trapped charge-induced
Trap occupancy
1.0
1
0.5
2
5
10
15
sNinj
0.5 0.2 0.0
0
5
10
15
20
x/xt
Fig. 8.1.2 In-depth distributions of the trap occupancy function N(x, Ninj )/N at different injected carrier densities corresponding to different values of σ ∗ Ninj parameter. The spatial depth of the distribution is indicated in relative units x/xt = xσ ∗ N.
168
Internal Photoemission Spectroscopy: Principles and Applications
shift of the CV curve is proportional to qNt (d − x¯ ) while the charge measured in the external circuit will be equal to qNt x¯ /d. Then, by using the variable injected charge values (Yun, 1974; 1975) or by applying the staircase voltage sequence to inject the charge (Lehovec et al., 1978) x¯ can be obtained as a function of Ninj . Let us assume that injection of charge carriers occurs at the interface between an insulating collector and a semiconducting emitter as a result of some pulsed excitation (gate voltage, channel current, light pulse, etc.). The pulse starts at time t0 when the surface potential of the semiconductor has value (t0 ). During this pulse a charge qNt is introduced to the collector while a charge Q∗ (t) is registered to pass through the external measurement circuit. After the pulse ends at time t1 the semiconductor surface is switched towards the initial surface potential value (t1 ) = (t0 ). In this case the charge Q(t1 ) yields the value of the charge remaining in the collector after the injection pulse (Yun, 1975): Q(t1 ) = −qNt S,
(8.1.14)
where S is the capacitor area. The conditions of applicability of this simple description are the absence of conduction current through the collector layer and zero injection current from the opposite (field) electrode. The properties of semiconductor surface (interface trap density, dopant concentration) are also assumed to remain unaffected by the charge carrier injection. The increment of the field electrode bias needed to attain the same surface potential value of the semiconductor emitter is essentially the same as the shift of the flatband (midgap, threshold) voltage which is proportional to qNt (d − x¯ ). In combination with Eq. (8.1.14) it allows determination of Nt and x¯ . Therefore, an array of Nt (¯x ) data points can be generated by applying to the sample injection pulses of different duration. However, to be performed on the same capacitor, this type of measurements would require complete removal of trapped carriers from the collector prior to subsequent charge injection pulse. The necessity of restoring the initial charge-free state of the collector represents the most significant constraint of the Yun’s trap profiling method. This requirement makes the measurements time consuming but, even more important, an additional problem is related to the absence of clear criteria for the zero charge state restoration. Possible compensation of charged traps by defects captured carriers of the opposite sign makes simple monitoring of the charge-induced field unsatisfactory. To avoid the need of charge elimination, Lehovec et al. suggested to fill the traps by repeating the injection pulses (Lehovec et al., 1978). The measurement procedure as well as the monitored quantities – the charge passed in the external circuit and the voltage needed to compensate the field of the trapped charge – remain the same but they are now increasing in a staircase manner. The trapped charge density and its centroid are now calculated after each charging pulse (Fig. 8.1.3). Remarkably, despite the seeming similarity of the measurement procedures, the Yun and Lehovec methods of charge profiling are found to give significantly different results (Lehovec et al., 1978). The latter suggests that different sequences of charging pulses result in different in-depth distributions of the trapped charge once again indicating strong influence of the transport properties of the collector on its charging behaviour in the strong trapping regime. The above considered limit of P0 = 1 is rarely encountered in the thin-film collector layers. Rather, an intermediate case when strong trapping is accompanied with some conduction appears to be practically relevant. Unfortunately, the contribution of the conduction current cannot be easily taken into account because its value also depends on the voltage pulse amplitude and the density of trapped charge which affects the strength of electric field at the injecting interface. At the same time, large P0 value means that the carrier retrapping neglected in Eq. (7.4.1) might become a non-negligible factor. When taking these effects into account the analytical solution of the charge trapping problem appears to be impossible. One may simulate the results numerically by separating the collector into several regions (see, e.g., (Bibyk and Kapoor, 1984)) or by using the Monte-Carlo simulations (Travkov et al., 1987). These studies importantly
Transport Effects in Charge Trapping Q0
Q qNt
VFB(t0)
169
Q qNt Q* Qx/d
x
VFB(t0)
VFB(t1) VFB(t0) V V qNt(d x)/d (a)
(b)
(c)
Fig. 8.1.3 Schematic of trapped charge density and centroid determination in the case of 100% trapping in the collector layer using a charging voltage pulse (Yun, 1975; Lehovec et al., 1978). The band diagram of the semiconductor– collector–field electrode structure at flatband point prior to charge injection (a), at the same bias voltage after charge injection (b), and at flatband point after charge injection (c). The relationship of the measured values to the trapped charge density Q = qNt and centroid x¯ is clarified.
demonstrate the significance of the current lateral redistribution effects caused by repulsive potentials of filled traps. With the progressing charge build-up, this current flow non-uniformity increases to a level when carriers are almost exclusively transported along percolation paths formed by trap-free regions of an insulator. Under these conditions extraction of any meaningful information regarding trap properties becomes hardly possible. To conclude the discussion concerning the strong carrier trapping case it is worth of summarizing its most essential features. First, the injection conditions have substantial effect on the spatial distribution of trapped charge which is not anymore a replica of the in-depth distribution of the trapping centres. Second, even the centroid of the charge distribution appears to be more sensitive to the injection process than to the spatial distribution of traps. As a result, the extraction of trap parameters becomes very problematic particularly if a non-uniform trap distribution is suspected in the collector volume. Finally, in the case of random distribution of traps, the effect of lateral redistribution of current flow may become important. In the next section the impact of local fields of filled traps on the trapping kinetics caused by non-uniform injection probability will be considered in more detail. 8.2 Carrier Trapping Near the Injecting Interface The influence of trapped charge carriers on the lateral profile of the injected current can be most easily exemplified in the case when the trapped carriers are located right above the surface of emitter. Repulsive Coulomb field of the filled traps will locally inhibit injection leading to the effective decrease of the current-emitting area as illustrated in the insert in Fig. 8.2.1. In particular, in the case of injection mechanisms characterized by strong dependence of the injection rate on strength of electric field like Fowler–Nordheim (FN) tunnelling or Avalanche Carrier Injection (ACI) (cf. Sections 5.3 and 5.4, respectively) the current will be blocked in vicinity of the filled traps. This sensitivity to the field induced by trapped charges makes these injection techniques particularly vulnerable to the artefacts caused by the lateral current redistribution. At the same time, as was already discussed in the previous chapter, the constant current injection mode is preferred in the experiment to ensure the constant ratio between the time
170
Internal Photoemission Spectroscopy: Principles and Applications 13 2 1.0 a 5 10 cm
Trapped carriers
a0
0.5 a
Collector a
a
Emitter 0.0
0
1
2 s*Ninj
3
Fig. 8.2.1 Effect of the local blockage of injection on the shape of charge trapping kinetics. The solid trapping curve is shown for the case a = 3 × 10−13 cm2 and N = 1 × 1012 cm2 as compared to the classical case a = 0 (dashed curve). The insert illustrates geometry of the model used to describe the local injection inhibition effect.
constants of trap filling and depopulation. Therefore, would the filling of one trap lead to inhibition of injection from the emitter surface region of area a (cf. Fig. 8.2.1), in the presence of Nt filled traps current of the same density j will be injected from a portion of sample area (1 − aNt ) when neglecting the trap-to-trap potential overlap. This current redistribution will lead to an increase of the local current density by a factor of (1 − aNt )−1 in the areas where no filled traps are found. The trapping equation in this case can be written in the following form (Afanas’ev and Adamchuk, 1994): dNt (t) N − Nt (t) j , = σ∗ dj q 1 − aNt (t)
(8.2.1)
which yields the solution N − Nt . (8.2.2) N Obviously, the condition aN < 1 should be fulfilled to ensure the possibility of maintaining a non-zero injection current. The charge trapping curve obtained using Eq. (8.2.2) is compared in Fig. 8.2.1 to the conventional first-order trapping kinetics given by Eq. (7.2.6) which corresponds to a = 0. One immediately sees an increase of the trapping kinetics curvature when the injection current redistribution becomes noticeable. Therefore, would the capture cross-section still be calculated using the conventional first-order kinetics (7.2.6) it will deviate from the real (macroscopic) value. σ ∗ Ninj = aNt − (aN − 1) log
To determine the cross-section correctly in the case of local inhibition of the injection current one needs to know the screening parameter a. Potentially, the latter can easily be calculated for a given energy of charge carrier, the strength of the applied electric field, and the dielectric constant of the collector. Unfortunately, under real experimental conditions, one deals with rather broad energy distribution of the optically or field-excited carriers which move quasi-ballistically across the interface region. In this case one has to consider the energy-dependent a value as well as the energy distribution of the excited charge carriers. Apparently, the only exception is the FN tunnelling of carriers in which case the area screened by a filled trap can be calculated for a given trap-emitter distance because the energy of the initial state is well defined. In the latter case the influence of electrostatic polarization of emitter should also be taken into account, particularly for the case of electron tunnelling from a metal electrode.
Transport Effects in Charge Trapping
171
The trapping of carriers close to the injecting interface may also lead to a problem with determination of the injected carrier density and with the monitoring of the trapped charge using the injection current. Once trapped inside the collector, the injected charge carrier will not provide an adequate contribution to the electric current measured in the external circuit. To account for these carriers, the lost contribution to the external current can be calculated from the flatband, midgap or threshold voltage shift V proportional to qNt (d − x¯ ) (cf. Fig. 8.1.3) (Ning, 1976b; Williams, 1992): Ninj (t) =
1 ε0 εD V (t) 1 + q q d
t
j(t )dt ,
(8.2.3)
0
where the second term corresponds to the charge measured in the external circuit. Unfortunately the use of this method to correct the injected charge for trapped carriers is limited to high-quality semiconductor– insulator interfaces which is required to measure CV curve or to determine the transistor threshold voltage. The variation of the field electrode voltage needed to maintain the same injection current, which is often used as the method of trapped charge monitoring (cf. Section 6.1), cannot be applied to trace the interfacial charges. The inhibition of the injected current is expected to occur, in first-order approximation, in linear proportion to the trapped charge density. At the same time, the variation of electric field needed to compensate for the injecting area decrease will be governed by the first derivative of the current– voltage characteristics of the particular injection mechanism in the remaining charge-free regions at the emitter–collector interface. Therefore, in the case of FN tunnelling or ACI with the current exponentially depending on the applied electric field, the additional voltage needed to compensate for charging will increase logarithmically with the density of charge trapped near the injecting interface. This will obviously preclude one from extracting the relevant trap parameters. Worth of reminding here that the inhibition of injection by interfacial trapping may be expected if the filled trap is located at a distance comparable to the range of Coulomb potential rc in the collector material defined by Eq. (7.7.1). For the case of SiO2 (εD = 3.9), rc exceeds 10 nm at room temperature and, even in a material with εD = 10–20 it appears to be in the range of several nanometres. Therefore, in the case of nanometre-thin collector layers the monitoring of the injection voltage in the constant current injection experiment cannot be used to evaluate the trapped charge. Another issue in investigating the trapping of charge close to the injecting interface consists in significant concentration of carriers with an excessive kinetic energy. All the considerations of the capture processes discussed so far refer to the carriers with energy in the order of kT which move slow enough to interact electrostatically with a trapping centre (Rose, 1963). This would require from a carrier to reside at the distance in order of rc from the trap for a time sufficient for atomic displacement which should be in the order of the inverse phonon frequency (10−12 –10−13 s). For the estimate of rc mentioned just above, this condition would correspond to the velocities of carriers of 107 cm/s or below. This value is in the range of thermal charge carrier velocities in most of solids, but an excessive kinetic energy of few tens of electron Volt would make the trapping event highly unprobable. Therefore, one might expect a lower capture cross-section for the non-thermalized charge carriers transported across the near-interface layer of collector ballistically (Afanas’ev and Adamchuk, 1994). To account for this effect one may use the exponential thermalization law which predicts that the chance for a carrier to reach a plane at distance x from the surface of emitter decreases with x as (Berglund and Powell, 1971): x n∗ (x) = e− , n(0)
(8.2.4)
172
Internal Photoemission Spectroscopy: Principles and Applications
which is previously used to describe scattering of excited electrons in the image-force potential well (cf. Section 2.2.4). Then, as only the thermalized (inelastically scattered) carriers will interact with traps while all the carriers contribute to the measured injection current, the distance-dependent variation of the apparent capture cross-section can be expected as: x σ(x) = σ 1 − e− ,
(8.2.5)
where σ corresponds to the trapping of a thermalized charge carrier by the same trap. This dependence of the cross-section on the distance between a trap and the emitter makes analysis of interface trapping particularly complicated. While in a thick collector layer one still able to get a flux of thermalized charge carriers by injecting them from the opposite interface (all carriers will lose their excess energy during transport through the bulk of a solid), no satisfactory solution is currently seen for layers with thickness smaller than except of studying charge trapping as a function of energy of the injected charge carriers. From this point of view, the injection using internal photoemission (IPE) offers the best possible solution because the maximal energy of carriers is directly controlled by the highest photon energy present in the spectrum of the exciting light.
8.3 Inhibition of Trapping by Coulomb Repulsion As already mentioned, one of the deficiencies of the simple first-order kinetic description consists in neglecting the charged origin of the captured particles (charge carriers). In fact one might expect the repulsive Coulomb potential to act between two carriers irrespectively them being free or trapped by a defect. Therefore, at a finite temperature and external field, it is unlikely that two carriers of the same charge sign will be separated by a distance smaller by the effective radius of Coulomb potential given by Eq. (7.7.1). Along with this idea Wolters and van der Schoot (1985) and Wolters and Zegers van Duinhoven (1989) suggested that some volume h will be inactivated for further trapping around any centre that captured a charge as illustrated in Fig. 8.3.1. Would other, still empty traps be located within this volume h, their filling becomes impossible because not a single charge carrier will be able to drift to them. In this way the Coulomb repulsion between the trapped and free charge carriers would lead to a reduction of the ‘trapping volume’ of the collector by a factor of (1 − h/V ) (V is the volume of collector) per each filled trap. When Nt traps are filled, the volume still available for charge flow will decrease by a factor (1 − h/V )N t . Assuming that h << V , one can approximate the volume change by an exponent as (Wolters and van der Schoot, 1985): h Nt ∼ −Nt h 1− (8.3.1) =e V. V Collector h
h
h h
h
h h
Emitter
Fig. 8.3.1 Inactivation of traps by Coulomb repulsion of the filled (charged) traps. Each trap captured a carrier makes volume h around it inaccessible to other mobile carriers and, therefore, inhibits filling of other, still empty traps located within this volume.
Transport Effects in Charge Trapping
173
As the probability of trapping a carrier is expected to be proportional to the collector volume that contains traps, the factor given by Eq. (8.3.1) will lead to the lower charge density variation derivative. Using the first-order kinetic Eq. (6.2.5) this effect can be described by the following differential equation: h −Nt V dNt = σ ∗ (N − Nt )e , dNinj
(8.3.2)
which can be further simplified by assuming Nt << N thus yielding h −Nt V dNt = σ ∗ Ne . dNinj
(8.3.3)
The latter equation has a simple solution (Walters, 1985): Nh V Nt = log 1 + Ninj σ ∗ . h V
(8.3.4)
The kinetics of charge trapping described by Eq. (8.3.4) is compared in Fig. 8.3.2 to the simple firstorder model described by Eq. (6.2.5) plotted as functions of the injected carrier density normalized to the capture cross-section. For the low injected carrier densities two models give similar results, but diverge as injection continues. The kinetics calculated taking into account the additional factor of Coulomb screening results in a faster trapping than the first-order kinetics. The latter is just opposite to expectations and indicates significant inaccuracy of the made supposition Nt << N under model parameters used. In addition, the kinetics given by Eq. (8.3.4) has no saturation which is also the consequence of the accepted condition Nt << N. Therefore, application of Walters model is possible only in the case of very high trap density when the parameter hN/d is much larger than one (Williams, 1992; Afanas’ev and Adamchuk, 1994). Actually, the observed sensitivity to the conditions of SiO2 collector fabrication of the effective trap concentration V /h (Wolters and van der Schoot, 1985), which is expected to be determined by the ‘universal’ volume h, points towards significant incompleteness of this model. One might attempt to obtain more physically relevant description when considering a simpler model when the traps are located in one plane normal to the direction of carrier flow. The model of this kind
Trapped carriers
10
h 1018 cm3
h0
8 6 4 2 0
0
1
2 s*Ninj
3
Fig. 8.3.2 Carrier trapping kinetics predicted in the case of inhibition of trapping in vicinity of a filled trap (solid line) as compared to the first-order trapping curve (dashed line). The curves correspond to N = 1013 cm−2 , h = 10−18 cm3 and d = 100 nm.
174
Internal Photoemission Spectroscopy: Principles and Applications
was considered for the case of hole trapping near Si/SiO2 interface which was studied as a function of externally applied electric field to isolate the Coulomb effects (Adamchuk and Afanas’ev, 1988a; Afanas’ev and Adamchuk, 1994). When holes are coming as a uniform flux from the bulk of SiO2 collector after being generated by photons of sufficient energy, some of them get captured in the trapaccommodating layer of the oxide. The repulsive Coulomb potentials of these trapped holes will affect the drift of the incoming free holes deviating them towards the still charge-free regions as illustrated in Fig. 8.3.3. This carrier flow redistribution leads to the formation of ‘forbidden’ regions of a certain area a surrounding each charged (i.e., filled) trap. All the unoccupied traps within this area will be prevented from capturing charge carriers because the latter are deviated away by the repulsive field of neighbouring occupied trap. To analyse this trapping inhibition mechanism, let us assume that all empty traps within the area a around each of Nt trapped carriers are excluded from the capture process. If the local trap density around the occupied trap is equal to the average trap density per unit area N, then the number of traps available for trapping will be equal to (Adamchuk and Afanas’ev, 1988a): N(Nt ) = N − Nt − NaNt ,
(8.3.5)
dNt 1 + aN ∗ ∗ . = σ (N − Nt − aNNt ) = σ N 1 − Nt N dNinj
(8.3.6)
which results in the trapping equation
Collector
a
a
a
a
a
a
a
Emitter
Fig. 8.3.3 Spatial scheme of trapping inhibition in the case of a planar trap distribution. Trajectories of carriers arriving as a uniform flux from the bulk of the collector are sketched. The in-plane view shows how the charged traps (filled symbols) prevent filling of empty ones (open symbols) in the regions they electrostatically screen (shadowed areas). Note, the filled traps may inactivate multiple of their number of the empty traps.
Transport Effects in Charge Trapping
175
This equation can be generalized to the case of strong trapping when replacing σ ∗ N by the trapping probability given by Eq. (8.1.5) (Afanas’ev and Adamchuk, 1994): 1 + aN dNt , = P0 1 − N t dNinj N
(8.3.7)
which solution can be written in the form Nt =
P0 N 1 − e N (1+aN)Ninj , 1 + aN
(8.3.8)
i.e., the same as the conventional first-order kinetics but with ‘new’ effective values of the total trap density Neff and the cross-section σeff : Neff =
N ; 1 + aN
σeff =
P0 (1 + aN). N
(8.3.9)
These expressions physically mean that the Coulomb screening of empty traps reduces the density of trapped charge and accelerates the saturation of trapping curve. In the case of a high trap density (the strong trapping limit) one may assume P0 ≈ 1 and obtains: σeff ≈
1 (1 + aN) ≈ a. N
(8.3.10)
This expression indicates that, by fitting the charge trapping kinetics using the first-order model, one can determine from the initial portion of the charge trapping curve (when aNt << 1) the area inhibited by the Coulomb repulsion. The value of a is expected to be determined exclusively by the dielectric constant of the collector and be the strength of externally applied electric field. Therefore, it is expected to exhibit a universal dependence on electric field for the same collector material. The latter type of behaviour is affirmed by the comparison of experimental values of the effective crosssection determined in the initial stages of hole trapping in three differently prepared Si/SiO2 structures (Afanas’ev and Adamchuk, 1994) shown as a function of the strength of externally applied electric field in Fig. 8.3.4. The data points appear to be insensitive to the initial trap density which differs between these samples by the factor of almost 10. At the same time, it is relatively easy to simulate the carrier transport numerically to determine the value of a from the known bulk parameters of SiO2 . These results are also shown in Fig. 8.3.4 by dashed line. One can see now that the experimental values of a are perfectly consistent with results of modelling, both predicting σeff ≈ a ∝ F 0.7 . This agreement greatly reassures the correctness of the trap inhibition description presented above. Another feature predicted for the case of Coulomb inhibition of charge trapping consists in the fielddependent saturation charge density. As it can be seen from Eq. (8.3.9), in the case of high trap density one can easily meet condition aN >>1 which leads to a field-dependent Coulomb-limited trap density: Neff =
1 N ≈ . 1 + aN a(F)
(8.3.11)
Again, the kinetics of hole trapping at interfaces between Si and SiO2 provide experimental support to such description as illustrated in Fig. 8.3.5 which shows the saturation positive charge densities as a function of
176
Internal Photoemission Spectroscopy: Principles and Applications
Effective cross-section (cm2)
1012
1013
1014
a(F )
105
106 Electric field (MV/cm)
107
Fig. 8.3.4 Field dependence of the effective cross-section of hole capture at the interfaces of (100)Si with 80–100-nm thick SiO2 collector layers thermally grown using different silicon oxidation conditions. Experimental data are shown by symbols of different shape. The dashed line represents result of numerical simulation of the carrier drift in the field of a repulsive Coulomb centre in SiO2 at 300 K (Afanas’ev and Adamchuk, 1994).
) F a( sa
t
1/
15 N
Saturation density (1012 cm2)
20
10
5
0 0
5
10
15
20
1/a(F ) (1012 cm2)
Fig. 8.3.5 Comparison between the experimentally observed values of saturation level of hole trapping kinetics at the interface between (100)Si and thermally 100-nm grown oxide (O2 + 1% HCl, 1150◦ C) as measured at different strengths of electric field in the oxide and the inverse field-dependent Coulomb screening area a obtained by numerical modelling.
the inverse a(F) value at given strength of electric field in the oxide (Afanas’ev and Adamchuck, 1994). In the low field region which corresponds to large values of a, the relationship (8.3.11) is seen to hold perfectly. A lower than predicted trapped charge density observed at a higher field is probably caused by annihilation of trapped holes by electrons tunnelling from the silicon substrate (Schmidt and Köster, 1992).
Transport Effects in Charge Trapping
177
The important feature of the trapping process governed by the Coulomb screening is that the apparent cross-section σeff appears to be close to the capture cross-section of Coulomb attractive trapping centre (DiMaria, 1978) despite the fact that in the former case the carrier is trapped by a neutral centre. This result reflects symmetry between the physics of attraction and repulsion of a charge by electrostatic potential of the same shape and comes, therefore, as little surprise. Would one compare in the framework of the first-order kinetics the trapping of holes occurring in SiO2 with the cross-section ≈10−13 cm2 at F = 1 MV/cm (Woods and Williams, 1976) to their annihilation by subsequently injected electrons which has approximately the same cross-section value (Ning, 1976a; DiMaria, 1978; Buchanan et al., 1991), one would end up with contradiction in interpreting these cross-section values. For both types of carriers the Coulomb attractive potential is observed. The answer to this puzzle is provided by the results shown in Fig. 8.3 4 indicating that the hole trapping is governed by the effective rather than by macroscopic value of the cross-section. Therefore, correct interpretation of the trapping data would require knowledge of the charge state of a centre after it captures a carrier to evaluate the importance of Coulomb effect on trapping kinetics.
8.4 Carrier Redistribution by Coulomb Repulsion Despite the successful application to the experimental data interpretation, the model picture described in the previous section remains physically incomplete because the Coulomb repulsion of the injected carriers by filled traps would also lead to a spatial redistribution of the current flow evident from Fig. 8.3.3. It is intuitively expected that the current in charge-free portion of the collector will gradually increase when the density of trapped charge increases with progressing injection. Unfortunately, for the threedimensional (3D) case the analysis of the current flow redistribution cannot be performed in analytical form because, at large trapped charge densities, the type of the spatial distribution of traps appears to be important. For a random distribution one might expect the current to be confined to some trap-free percolation paths, while the uniform or the equidistant distribution will ultimately result in the injection blockage. In addition, the long spatial range of Coulomb potential will result in a larger inactivation volumes in the case of traps separated by a distance slightly exceeding rc than simply 2h. For instance, in the 2D trap distribution case, numerical simulation of carrier transport shows that two charges separated by a distance 2(a/π)1/2 will screen the area approximately equal to 3a. Nevertheless, it appears possible to sketch a general approach to the solution of the problem at least in 2D-case by using expressions of the available trap density and the current densities modified by the Coulomb repulsion. If going beyond the linear trap-screening model given by Eq. (8.3.5), one should normalize the screened portion of the area to 1, which, in the same spirit as in Eq. (8.1.1), leads to the density of trap accessible to drifting carriers N(Nt ) = N − Nt − N(1 − e−aNt ).
(8.4.1)
In a similar way, assuming that the same macroscopic current density j0 is redistributed over the unscreened portion of the collector layer area, the local current density which governs the trapping rate can be expressed as: j0 = j0 eaNt . (8.4.2) e−aNt By combining these two equations in the trapping rate expression one obtains the following equation: j(Nt ) =
dNt = σ ∗ (N − Nt eaNt ). dNinj
(8.4.3a)
178
Internal Photoemission Spectroscopy: Principles and Applications
Generalization of the above equation to the 3D case can be done if assuming that N traps are uniformly distributed over the collector layer of thickness d with concentration N/d. Then, once each of the Nt filled traps inhibits further captures in a volume h, the volume still available for trapping will decrease with h increasing Nt as (1 − e− d Nt ) while the volume over which the injected carriers are distributed will vary h as e− d Nt leading to the increase of their local flux similar to the case given by Eq. (8.4.2). Combination of the trap-screening factors and the current enhancement one in the rate equation results is expression similar to Eq. (8.4.3a): h dNt (8.4.3b) = σ ∗ N − Nt e d Nt dNinj in which the ratio h/d can now be associated with the screened area a in Eq. (8.4.3a). This simple consideration also demonstrates the problem associated with the analysis of 3D-trap screening case. The screened volume h appears to correspond to ad, i.e., the filled trap ‘shadows’ a cylinder of area a across the whole collector thickness. This is obviously an overestimation of h, one would rather expect the inhibited volume in the order of (a)3/2 . This overestimation is caused by normalization of the current density to the available volume of the collector, rather than to the area through which carriers are free to drift in each sub-layer of a thickness in the order of (a)1/2 . At the same time, the issue of connectivity between the current-carrying channels arises when attempting to transfer 2D-analysis result to 3D case. The solution of Eq. (8.4.3a) written for the 2D trap distribution leads to the integral: Ninj Nt σ dNinj = ∗
0
0
dNt
N − Nt eaNt
,
(8.4.4)
which cannot be expressed in analytical functions. Nevertheless, one can either evaluate it numerically, or, else, to consider limiting cases of the initial portion of the trapping curve and its saturation region. The saturation corresponds to zero value of the denominator in the function under integral in Eq. (8.4.4) resulting in the following equation for the saturation density of trapped charge Nts : Nts = Ne−aNt . s
(8.4.5)
This expression predicts a strong (exponential) dependence of the trapped charge on the average area of the region inhibited by the Coulomb screening. With lowering the strength of applied electric field in the collector, the increasing area a (cf. Fig. 8.3.4) will lead to a progressive decrease in the density of occupied traps. In the range of low injected carrier densities, the initial trapping probability remains the same as in the ∗ case of the first-order kinetics, i.e., σ ∗ N in the linear regime and −e−σ N in the case of strong trapping. However, as the accumulated charge will saturate at a much lower density as predicted by Eq. (8.4.5), the apparent cross-section may become significantly larger than σ ∗ approaching, in the limiting case of ∗ = a (cf. Eq. (8.3.10). The problem here is that the apparent capture cross-section will strong trapping, σeff decrease with increasing the injected carrier density making impossible isolation of traps with small crosssections. In this sense the influence of Coulomb potentials of the occupied traps represents significant obstacle for trap spectroscopy because the charging kinetics is more significantly affected by variations of carrier transport than by the trapping properties of the defects with small capture cross-sections. Taking into account the above results, it seems also likely that the redistribution of the injected carriers by the Coulomb repulsion of filled traps causes the dependence of the experimentally determined value
Transport Effects in Charge Trapping
179
of capture cross-section on the injected carrier density observed in the case of electron capture by neutral traps in thermal SiO2 (Sune et al., 1990; Williams, 1992). One might notice here that the spatial extent of the Coulomb repulsive potential well in SiO2 is in the range of several nanometres, while the field of a local structural strain (Williams, 1992) may be expected to be in the order of few bond lengths in an amorphous solid (the length of Si O bond in SiO2 is about 0.154 nm). Therefore, Coulomb effects may be expected to be by far more significant than the trapping-induced structural stress. Allowing for σ ∗ to be a function of the injected carrier density Ninj Nicollian replaced the multiple σ ∗ Ninj in the first-order trapping kinetics given by Eq. (7.2.6) by their integral and obtained the trapping kinetics in the following form (Williams, 1992): Ninj Nt (Ninj ) = N 1 − e− 0 σ(ξ)dξ . (8.4.6) From this equation one may derive expression allowing to determine how σ is varied with Ninj using the expression (Williams, 1992): σ(Ninj ) = −
Nt (Ninj ) d log 1 − . dNinj N
(8.4.7)
In the case of electron trapping in SiO2 it appears that the apparent cross-section decreases with increasing the injected carrier density as: b σ(Ninj ) = aNinj ,
(8.4.8)
with b ≈ −0.5 and without exhibiting any plateau regions which might be expected is traps with well defined cross-section are present in the oxide collector (cf. Fig. 4 in Williams (1992)). This functional dependence of the cross-section leads to a modified first-order kinetics which, in the case of one-trap process, can be written as: l+b Nt (Ninj ) = N 1 − e−aNinj . (8.4.9) This equation corresponds to a stretched trapping kinetics and enables much better fitting of at least some experimental datasets than the first-order model (Williams, 1992). In a similar spirit of a reduced capture probability with increasing density of the injected and trapped charges in the collector, the variation of the cross-section during carrier injection was modelled using other functional form (Sune et al., 1990): Nt , (8.4.10) σ(Ninj ) = σ0 1 − N aiming at an improved quality of the experimental data fit. This dependence of σ on Ninj results in a somewhat different functional form of the first-order kinetics which can be expressed as (Williams, 1992): Nt (Ninj ) = N 1 −
1 1 + σ0 Ninj
.
(8.4.11)
The normalized trapping kinetics for the case of Nicollian’s and Sune’s modifications of the capture cross-section formulation are compared in Fig. 8.4.1 to the first-order kinetics (solid curve). Note, in all three cases the saturation of the trapped charge is predicted to occur at the same level corresponding to the complete trap occupancy. Both the modified models predict more stretched kinetic curves than the first-order one, but Nicollian’s model also allows some accelerated initial trapping.
180
Internal Photoemission Spectroscopy: Principles and Applications First-order trapping
Trap occupancy
1.0
Nicollian 0.5
0.0
Sune
0
1
2 s*Ninj
3
Fig. 8.4.1 Schematic comparison of trapping curves predicted by Nicollian’s (normalized to match the first-order curve at σ ∗ Ninj = 1) and Sune’s models with injection-dependent values of the capture cross-section as compared to the standard first-order trapping kinetics shown by a solid curve.
Two above discussed capture cross-section models appear to be quite successful in minimizing residuals of the experimental charge trapping curve fits (Williams, 1992). Therefore, a significant retardation of the trapped charge saturation seen in Fig. 8.4.1 appears to be relevant to trap ensembles encountered in reality possibly revealing an important feature of electron transport in thin SiO2 layers. After filling a substantial portion of traps (80–90% in Fig. 8.4.1) most of the carriers appear to flow in the trap-free region which dramatically increases the time constant of filling the 10–20% of traps still remaining free. As pointed out by Williams, this is possible only if the studied traps are localized in some small collector volumes or clusters (Williams, 1992). This suggestion demonstrates, in the reassuring similarly to the case of the Coulomb trapping inhibition, that subtle details of the trap spatial distribution may have considerable influence of the shape of charge accumulation kinetic curve.
8.5 Injection Blockage and Transition to Space-Charge-Limited Current It becomes clear from the description of the Coulomb effects of filled traps on the injection and transport of charge carriers that in collector materials a high density of charge may easily be accumulated. In this case the condition of electric field compensation at the injecting interface given by Eq. (7.1.4) can be met resulting in injection blockage would the externally applied electric field remain constant. However, the picture appears to be very different if the injection current across the sample is kept constant when using the injection bias adjustment. As the strength of the electric field increases to compensate the influence of the trapped charge additional mechanisms of injection and detrapping may become important leading to significant complication of the charge accumulation kinetics. Moreover, in the measurements performed under the variable-field conditions the transport effects discussed earlier in this chapter would provide an extra variable(s) which hardly can be accounted for because of the statistical variations of the local, i.e., trap-induced, electric field strength. Taken together these effects may be expected to change the effective cross-section appearing in the experiment thus making realistic fitting of the trapping kinetics virtually impossible. For these reasons the application of the constant voltage injection mode seems to be preferred if detrapping has a minor effect on the charge accumulation in the collector. Variation of the electric field at the injecting
Transport Effects in Charge Trapping
181
interface due to charge build-up can be monitored using the injection current decay constituting a reliable criterion to be used when choosing the model of trapping process (Afanas’ev and Adamchuk, 1994). If the current decay still allows injection of carriers at a fixed field (it decays not more than by 50%) one still can use the first-order kinetics or some of its modified versions. More substantial decay of the injection rate indicates transition to some kind of transport-affected trapping kinetics. In some simple cases the trapping and transport effects still can be disentangled by analysing trapping curves obtained under different strengths of electric field in the collector. Unfortunately, this is not always the case, and the effective trapping parameters determined in some experiments might be affected by the transport and dielectric properties of the collector which makes them irrelevant to the trap characterization or classification. Detrapping effects can be identified through the injection-rate-dependent trapping parameters. This case is the most difficult one for analysis because the detrapping rate (as influenced by field, temperature, illumination spectrum, etc.) remains to be determined in a separate experiment. In combination with a high trap density and related to its transport phenomena, the extraction of trap parameters appears to be possible only when using numerical simulation of the trapping curves. As already mentioned, multi-trap models can hardly be seen as reliable sources of information in this case. Nevertheless, as the combination of high trap density with significant detrapping probability constitutes essential condition of transition to the space-charge-limited current mode, some effective parameters still can be extracted from the current–voltage curve analysis (Lampert and Mark, 1971).
CHAPTER 9
Semiconductor–Insulator Interface Barriers
With the basic principles of the internal photoemission (IPE) spectroscopy discussed, it is worth considering here application of this technique to one of the most technologically and scientifically important areas: characterization of electron states in nanometre-thin layers of insulators and their interfaces with semiconductors and metals. There are several reasons to give this subject an additional attention. First, from the point of view of demonstrating the potential of IPE in material characterization, analysis of structures with a wide bandgap insulating collector offers the best possibilities because of a large, about several electron volt, energy difference between an IPE threshold and the onset of intrinsic photo conductivity (PC) of the collector. Thus, the IPE signal can be observed in a wide photon energy range above its threshold enabling detection of additional optical or scattering-related effects. Second, a low leakage current across the insulating collector ensures the outmost sensitivity to the photoinjected currents. Third, as the trapped charge in the wide bandgap insulator is stable over an extended period of time, the photocharging or photodepopulation methods appear to be applicable in their full power. Forth, the spectrum of insulating materials and their combinations with semiconducting and conducting electrodes available for investigation became so rich in recent years (Houssa, 2004; Huff and Gilmer, 2005), that it is possible now to discuss the fundamental issues related to the mechanisms of the interface barrier formation. Finally, there is a great interest to the spectroscopic analysis of thin insulator films, which stems from their application in various microelectronic devices as gate or field insulation, tunnelling barrier, charge-storage layer, etc. The latter ensures continuation of search for new materials suitable for particular type of application and, in this way, makes the IPE spectroscopy set for further development in relationship with these new electronic materials developments. The forthcoming chapters will overview the results obtained when applying the IPE spectroscopy to the insulating films on semiconductors (this chapter) and to conductor–insulator interfaces (Chapter 10). In Chapter 11 results of charge trapping studies in SiO2 insulating layers will be discussed. In general, insulating SiO2 is seen nowadays as a model system because of vast amount of information accumulated during four decades of research regarding its injection and trapping behaviour. The understanding of the basic electronic properties of SiO2 and its interfaces have led to remarkable level of the modern semiconductor technology. Therefore, it is quite logical to transfer the material analysis approaches initially developed for SiO2 -based structures, including the IPE spectroscopy methods, to other newly developed material systems. 182
Semiconductor–Insulator Interface Barriers
183
9.1 Electron States at the Si/SiO2 Interface 9.1.1 Si/SiO2 band alignment Being under investigation since mid-1960s, the thermally oxidized silicon provides an example of IPE application to determination of the interface electron state spectrum. To keep the story, already extensively overviewed (Sze, 1981; Nicollian and Brews, 1982; Adamchuk and Afanas’ev, 1992a), short we can immediately discuss the band diagram of this interface schematically shown in Fig. 9.1.1. Barriers for electron IPE both from the silicon conduction and valence bands into the oxide conduction band can be directly determined from the IPE thresholds (cf. Figs 4.1.1 and 4.1.2) as well as the barrier for hole IPE (cf. Fig. 4.1.8). The bandgap width of SiO2 (Eg = 8.9 eV) found using the intrinsic PC measurements (see, e.g., Figs 4.4.3 and 4.4.4) appears to be in perfect agreement with the value calculated from the electron and hole IPE barrier heights using Eq. (2.2.1). The indicated band diagram parameters exhibit remarkable reproducibility between different technologies of SiO2 formation (provided no ionic species are present at the interface) making it an excellent reference for any experiment aimed at the barrier height measurement. For instance, the same interface barrier height is observed in Si crystals oxidized in pure or diluted O2 in the temperature range from 800◦ C to 1350◦ C. There is slight difference between the barrier heights at interfaces of SiO2 with Si faces of different crystallographic orientation (Adamchuk and Afanas’ev, 1992a): The conduction band offset at (111)Si/SiO2 interface is by 0.07 eV higher than at the (100)Si/SiO2 one. This was associated with an interface dipole caused by a different density of silicon surface atoms (Adamchuk and Afanas’ev, 1992a). To complete the picture, two additional defect-related components of the Si/SiO2 electron state spectrum are also indicated in Fig. 9.1.1. First, both in the hole IPE and PC measurements a ≈ 1 eV ‘tail’ of the oxide valence band is observed (Adamchuk and Afanas’ev, 1984; 1992a, b). The states responsible for this ‘tail’ are spatially located close to the interface between SiO2 and Si substrate and might be related to some intrinsic interface-specific defects. Second, the energy level of a defect state at 2.8 eV below the SiO2 conduction band edge is revealed by the photoionization (PI) and the photon-stimulated tunnelling Evac
5
EC
4 3
Energy (eV)
2
4.25 2.8 3.15 EC
1
8.9
0 1
EV 8
2 3
4.65 5.75
4 5
(100)Si
SiO2
EV
Fig. 9.1.1 Major components of electron state spectrum at the (100)Si/SiO2 interface as determined from the IPE and PC measurements. All the energies are indicated in electron volt with the origin of the energy scale placed to the top of the silicon valence band. The vacuum level Evac is shown assuming the SiO2 electron affinity of 0.8 eV.
184
Internal Photoemission Spectroscopy: Principles and Applications
measurements (cf. Figs 4.4.12 and 4.4.10, respectively). Correlation between the rate of optical transitions from these 2.8-eV deep defect levels with silicon enrichment of the oxide (Afanas’ev and Stesmans, 1997d, e) points towards some Si-rich (sub-oxide) phase in the interfacial region as their potential origin though the exact atomic configuration of these centres remains unknown. These defect-related components of the oxide electron spectrum are highly sensitive to the oxide preparation technology which makes them clearly different from the spectrum of the fundamental band states. At the same time, as these states are observed in SiO2 layers prepared by a broad variety of technological methods (thermal oxidation of Si or SiC, deposition, ion implantation, etc.), they represent intrinsic components of the electron state spectrum. 9.1.2 Si/SiO2 interface dipoles Presence of foreign atoms at the Si/SiO2 interface may affect the observed barriers. This effect is clearly observed when chlorine is added to the ambient during Si oxidation (Adamchuk and Afanas’ev, 1984; 1992a). The character of chlorine influence on the electron and hole IPE characteristics is illustrated in Fig. 9.1.2 which shows the Schottky plot of the electron IPE threshold (a) and the spectral dependences of the hole IPE yield (b) for Cl-free (oxidation of Si in pure O2 ) and Cl-containing (oxidation of Si in O2 + 1% HCl) interfaces. Electron IPE measurements indicate an upshift of the oxide conduction band edge with respect to the (111)Si emitter valence band top by ≈0.25 eV in the whole range of electric fields shown in Fig. 9.1.2a. The slope of the Schottky plot remains nearly the same as for the Cl-free Si/SiO2 interface suggesting that the observed Cl-induced barrier height variation is unlikely to be associated with buildup of a negative charge in the bulk of the oxide. Hole IPE indicates that Cl incorporation reduces the barrier height between the top of the oxide valence band and the bottom of the Si conduction band by approximately the same value as the electron barrier height increase. The bandgap width of the oxide in both types of samples remains the same, Eg = 8.9 eV, which represents a clear evidence that the oxide does not change its phase as the result of Cl incorporation. Therefore, the Cl-induced electron/hole barrier variations are the consequence of an interface dipole formation as exemplified in the insert in Fig. 9.1.2b. 4.6
IPE threshold (eV)
3
4.4 4.3
Si
2
SiO2
4.2 1
dry O2 4.1 4.0 0.0
Yield (relative units)
(111)Si/SiO2 4.5
O2 1% HCl 0.2
0.4
0.6
0.8
4.5
5.0
5.5
6.0
(Field)1/2 (MV/cm)1/2
Photon energy (eV)
(a)
(b)
0 6.5
Fig. 9.1.2 (a) Schottky plot of the spectral threshold of electron IPE from the valence band of Si(111) into the conduction band of 150-nm thick oxide thermally grown on Si at 1150◦ C in dry O2 () or in a mixture O2 + 1% HCl (). (b) Spectral curves of hole IPE from the conduction band of Si(111) into the valence band of 150-nm thick SiO2 layers grown under the above indicated conditions. The insert illustrates the mechanism of barrier variation by an interface dipole layer.
Semiconductor–Insulator Interface Barriers
185
Table 9.1.1 Band diagram parameters of Si/SiO2 interfaces prepared by oxidation of (111) or (100) Si faces in dry oxygen or in a mixture of O2 + 1% HCl. All the values are determined using electron and hole IPE measurements and are given for the final oxide thickness of 150 nm. Si face
Tox (◦ C)
Oxidant
e ±0.02 eV
h ±0.10 eV
Eg ±0.1 eV
EC ±0.02 eV
EV ±0.1 eV
(111) (111) (111) (111) (100) (100) (100) (100)
1150 1000 1150 1000 1150 1000 1150 1000
O2 + HCl O2 + HCl O2 O2 O2 + HCl O2 + HCl O2 O2
4.55 4.34 4.32 4.32 4.45 4.27 4.25 4.25
5.50 5.70 5.75 5.75 5.60 5.70 5.75 5.75
8.9 8.9 8.9 8.9 8.9 8.9 8.9 8.9
3.43 3.22 3.2 3.2 3.33 3.16 3.14 3.14
4.4 4.6 4.6 4.6 4.5 4.6 4.6 4.6
The results concerning the Si/SiO2 interface barrier heights are summarized in Table 9.1.1 for 150-nm thick oxides thermally grown on Si(100) and Si(111) surfaces, both without and with Cl present. The table also lists the value of the contact potential difference between the moderately doped n-type Si (nD = 1 × 1015 cm−3 ) substrate and the Au field electrode φms determined from the zero-IPE-current voltage, as well as the conduction and valence band offsets at the interfaces. In all cases, the bandgap of the oxide calculated using Eq. (2.2.1) remains the same, indicating the interface dipole formation as the primary mechanism of the Cl-induced barrier variations. By establishing a clear physical picture of the chlorine impact on the Si/SiO2 interface barriers it becomes possible, for the first time, to analyse the interface dipole formation not only as influenced by the silicon surface orientation but, also, by duration and the temperature of Cl incorporation during the oxide growth. Zero-field electron IPE barriers for (111) and (100) Si faces are shown in Fig. 9.1.3a as functions of the grown oxide thickness for two Si oxidation temperatures, while the barrier height dependence on the oxidation temperature is illustrated in panel (b) for the oxides of the same final thickness of 150 nm. These data indicate three essential features of the Cl-induced dipole behaviour:
• The dipole is larger at (111)Si/SiO2 interface than at (100)Si/SiO2 one which correlates with a higher density of the Si surface atoms in the former case. This behaviour would be consistent with bonding of Cl to a certain portion of the silicon surface atoms causing formation of a dipole by electron density transfer from Si atoms to Cl ones. • In the absence of Cl, the Si/SiO2 barrier height is insensitive to the oxide thickness, but it increases linearly with it when Cl is added to the ambient during Si oxidation. Therefore, incorporation of chlorine seems to be controlled by some thickness-dependent factor very different from the conventional chemosorption behaviour. • incorporation of Cl is enhanced with increasing Si oxidation temperature as the barrier variations shown in Fig. 9.1.3b indicate. This behaviour is clearly inconsistent with the surface coverage determined by adsorption–desorption equilibrium which predicts a decreasing surface coverage with adsorbate when temperature is increasing. Rather, a sort of thermally activated chemical reaction can be suspected as the rate-limiting step of Cl incorporation to the Si/SiO2 interface which is consistent with the behaviour of the Cl concentration in the Si/SiO2 interfacial region studied by the secondary ion mass-spectroscopy and the Auger profiling (Deal et al., 1978; Rouse et al., 1981; 1984; Bosenberg et al., 1984).
186
Internal Photoemission Spectroscopy: Principles and Applications 4.7
4.7
4.6
Barrier height (eV)
4.6 T 1150C
d 150 nm
4.5
4.5
4.4
4.4
4.3
4.3
4.2
0
50
100
150
200
Oxide thickness (nm) (a)
900
1000
1100
4.2 1200
Temperature (C) (b)
Fig. 9.1.3 Barrier height between the top of Si valence band and the bottom of the oxide conduction band as measured at the (111)Si/SiO2 (squares) and the (100)Si/SiO2 interfaces (circles) (a) in samples oxidized at 1150◦ C to different final thickness of the oxide or (b) in samples with approximately the same SiO2 thickness (150 nm) grown at different temperatures by scaling the time of oxidation. Open symbols correspond to oxidation in pure O2 , filled ones to the oxides grown in O2 + 1% HCl mixture. Lines guide the eye.
From these observations we may conclude that formation of the interface dipoles in the Si/SiO2 system is governed by some solid-state reaction kinetics rather than by the supply of the impurity atoms or by their adsorption–desorption equilibrium. Apparently, to create an interface dipole layer the adsorbate must be bonded to the silicon surface atoms to enable formation of a double charged layer. The latter can be described as arising from the electron density shift in Si-adsorbate bonds all occurring in the same direction. Noteworthy, the atoms with electronegativity close to that of silicon (H, N, C) cause no measurable dipoles at the Si/SiO2 interface. 9.1.3 Si/SiO2 barrier modification by trapped charges Another possibility of interface barrier modification consists in incorporation of uncompensated charges to the barrier region as was discussed theoretically in Section 2.2. Would the charge of a trapped carrier or impurity be only weakly screened by mobile carriers in the emitter electrode, the perturbation of the image-force barrier may be described as action of an isolated Coulomb potential (cf. Figs 2.2.4 and 2.2.5). Now we can demonstrate the relevance of this model to the interface barrier distortion encountered in Si/SiO2 structures after injecting holes by exposing the sample to high-energy (10-eV) photons (Adamchuk and Afanas’ev, 1988b; 1992a). A considerable portion of the injected holes is trapped in the oxide close to the Si/SiO2 interface and they appear to have substantial impact of the electron IPE spectra. The latter is illustrated in Fig. 9.1.4a which compares the electron IPE quantum yield spectral curve in the control sample () to that in the same sample after trapping 1 × 1012 holes/cm2 (). In addition to the yield values determined from the photoinjection current measurements, the spectral curve of the small-signal photocharging related to annihilation of the trapped holes by electrons photoemitted from silicon () is also shown for comparison. It is clearly seen that the positive charge of trapped holes results in an additional ‘tailing’ of electron IPE to lower photon energies as compared to the uncharged control sample suggesting a local reduction of the barrier. The origin of the observed barrier variations is clarified by the analysis of Schottky plots of different spectral thresholds shown in Fig. 9.1.4b. First, a considerable portion of the interface area remains unaffected
Semiconductor–Insulator Interface Barriers
187 4.4
(111)Si/SiO2 (150 nm) Yield (relative units)
4.2 4.1 4.0 3.9
1
3.8 3.7
IPE threshold (eV)
4.3
2
3.6 0
3.5
4.0
4.5
5.0
0.0
0.2
0.4
0.6
0.8
Photon energy (eV)
(Field)1/2 (MV/cm)1/2
(a)
(b)
3.5 1.0
Fig. 9.1.4 (a) Spectral curves of the electron IPE yield in Y 1/3 –hν co-ordinates as determined by the photocurrent measurements in the control () and charged by 1012 holes/cm2 () Si/SiO2 (150 nm)/Au samples as well as the spectral plot of the photo-annihilation () in the latter sample, all measured under +5 V bias on Au electrode. (b) The Schottky plot of electron IPE spectral thresholds in the former samples: the control (uncharged) sample (), the upper () and the lower () spectral thresholds in the sample with 1012 holes/cm2 , the lower spectral thresholds in the sample with 2 × 1012 holes/cm2 (3), and the spectral threshold of trapped holes annihilation in the sample charged by 1012 holes/cm2 (). Lines guide the eye.
by the trapped positive charge as revealed by coincidence of the upper spectral threshold observed in the charged sample () with that in the uncharged one (). Thus, the action of the trapped charge potentials is local in its nature which is consistent with the earlier discussed model of individual (discrete) charges (cf. Section 2.2.5). Next, the lowest IPE current spectral threshold is obviously associated with a locally reduced barrier regions. It appears that the doubling the density of the positive charge has only marginal effect on this threshold as suggested by the data shown by open and filled squares in Fig. 9.1.4. Therefore, the local barrier lowering can be associated with action of an individual attractive Coulomb potential. Finally, the annihilation of trapped holes is observed to occur with a significantly lower energy threshold () than the IPE of electrons into the rest of SiO2 . This lower barrier for electron trapping is consistent with the barrier shape influenced by a positive charge trapped close to the emitter surface illustrated in Fig. 2.2.4a. Annihilation of this charge by injected electrons would be governed by the lower barrier 1 , while the higher barrier 2 needs to be surmounted by an electron to be injected into the oxide bulk. Thus, the description of the image-force barrier distortion by the filed of interface charge can be done assuming a local barrier perturbation by Coulomb potential of a single-charged centre (Adamchuk and Afanas’ev, 1988b; 1992a). With this knowledge in hand, one can model the experimentally observed field dependences of the spectral thresholds shown in Fig. 9.1.4b using the potential given by Eq. (2.2.16). As it appears, both the thresholds of the IPE current and of the photocharging correspond to the barrier 1 but with different distance xc between the charged centre and the surface of emitter. The current threshold corresponds to xc = 3.5 nm while the neutralization of the trapped positive charges has spectral onset corresponding to xc = 1.5 nm. The difference between these two distances can easily be clarified if recalling that, when detecting the IPE current, one counts only the electrons travelled through the oxide layer. Therefore, the corresponding value of xc likely represents an average distance between the charged centre and the silicon surface. Indeed, this estimate appears to be in good agreement with the trapped hole in-depth
188
Internal Photoemission Spectroscopy: Principles and Applications
distributions derived from the partial neutralization experiments and shown in Fig. 6.5.4 (cf. solid curve for the dry oxide sample). On the other hand, a lower but still relatively high barrier for the trapped hole annihilation suggests existence of a charge-free layer at the interface because the barrier height is expected to decrease to zero for sufficiently small xc . Apparently then, the obtained value xc = 1.5 nm corresponds to a minimal distance between trapped hole and silicon surface. The positive charges located closer to the interface plane are likely to be neutralized by electron tunnelling from Si (Benedetto et al., 1985; Oldham et al., 1986; Schmidt and Köster, 1992). Worth of recalling here that the in-depth profiles of trapped positive charges at the Si/SiO2 interface obtained by using the tunnelling-induced neutralization indicate that most charges are located at a distance exceeding 2 nm (Schmidt and Köster, 1992). 9.1.4 Trapped ions at Si/SiO2 interface Instead of aiming at the characterization of the charge trapped near the interface one might also target the intentional barrier modification to achieve desired enhancement or blocking action on the electron injection. In this case stable charges are produced by ions which can be diffused through the SiO2 collector layer (DiStefano and Lewis, 1974) or from the silicon substrate (Afanas’ev, 1992), as well as generated at the interface by surface ionisation (Afanas’ev and Stesmans, 1999a). The mechanism of barrier perturbation can be expected to remain the same as in the case of trapped charges as long as the Coulomb potentials of the trapped ions are non-overlapping. This behaviour is most clearly exposed in the case of Li+ ions diffused through Si substrate after being deposited on its backside. The electron IPE spectral curves are shown in Fig. 9.1.5a for the control Si/SiO2 sample (), and after diffusion at 380◦ C of about 5 × 1012 ions/cm2 () or >1014 ions/cm2 () through Si. The ion-induced barrier lowering is evident. The Schottky plots shown in Fig. 9.1.5b for all three samples indicate that at low ion concentration the lowest IPE threshold exhibits an abnormally large barrier reduction, which in the framework of the classical image-force model would correspond to physically unrealistic case of εi < 1. However, when analysed in relationship with the presence of positive charges at the interface, this behaviour finds its 4.5
3 4.0 2
3.5
1
0 3.0
IPE threshold (eV)
(Yield)1/3 (relative units)
(100)Si/SiO2:Li
3.0 3.5 4.0 4.5 Photon energy (eV) (a)
0.0
0.5 1.0 (Field)1/2 (MV/cm)1/2 (b)
Fig. 9.1.5 Electron IPE spectral curves in Y 1/3 –hν co-ordinates (a) and the Schottky plots of the corresponding spectral thresholds (b) for the control Si/SiO2 sample (), and after in-diffusion of about 5 × 1012 Li+ -ions/cm2 () or >1014 Li+ -ions/cm2 () through Si substrate at 380◦ C.
Semiconductor–Insulator Interface Barriers
189
logical explanation as the local barrier reduction by a positive charge located close to the interface plane (cf. Section 2.2.5). A very similar barrier behaviour is also reported for H+ ions trapped at the Si/SiO2 interface (Afanas’ev and Stesmans, 1998b; 1999a) suggesting its universal character. With increasing the ionic charge density, the barrier dependence on the applied external field changes dramatically. It becomes nearly field-insensitive ( in Fig. 9.1.5) indicating that the strength of the external field is much lower than that of electric field induced by the trapped ions. As a result of combined action of the field and the local barrier reduction the IPE threshold appears to be almost 1 eV lower than at the uncharged interface. It seems possible to drive the barrier height even lower by increasing the density of ions trapped in the bulk of the oxide. Barriers as low as 2.5 eV were reported by DiStefano when Na+ ions were diffused from the oxide surface towards the Si substrate (DiStefano and Lewis, 1974). The limit of the interface barrier lowering is likely to be set by the thermoionic (Schottky) electron emission which might compensate a portion of the ions trapped in the oxide. 9.2 High-Permittivity Insulators and Associated Issues 9.2.1 Application of high-permittivity insulators In recent few years, the interface properties of metal oxide insulators with high dielectric constant εD (also often symbolized as κ or k) in semiconductor heterostructures attract an unprecedented attention because these materials are projected to replace soon the standard SiO2 as gate insulator in advanced silicon metal–oxide–semiconductor (MOS) devices (Wilk et al., 2001; Houssa, 2004; Huff and Gilmer, 2005). The necessity of using a high-permittivity gate insulators (often termed as high-κ materials) is dictated by continued efforts to reduce the size of the active device area, e.g., the transistor channel. The dielectric constant here is defined as εD = κ = ε/ε0 where ε and ε0 represent the permittivity of the considered material and vacuum (ε0 = 8.854187817 × 10−12 F/m), respectively. The notion ‘high’ here means large compared to the value for standard SiO2 , given as εD (SiO2 ) = κSiO2 = 3.9. In addition to downscaling issues relevant to Si integrated circuits, development of a non-native oxide insulator technology for the conventionally used semiconducting silicon makes potentially feasible the application of a similar approach to other semiconductors promising improved MOS device performance (e.g., Ge, SiC, AIII BV materials) in semiconductor heterostructures. Obviously, within the context of the current Si-based integrated circuit technology there is great technological concern as a viable consolidated and world impacting technology may be at stake. One crucial element in this envisioned redirectioning in MOS devices is that the electronic properties of high-permittivity insulators raise a number of fundamental physical questions and concerns. First, the thickness of these layers is typically in the range of few nanometres which might lead to significant deviation of the solid-state oxide properties from those of the bulk crystal or an amorphous material. Second, the oxide growth (deposition) is usually performed at relatively low temperature, in most cases below 500◦ C, to enable effective thickness control and to suppress the intermixing with the semiconductor substrate. As a result of low growth temperature the atomic network of the insulator is generally far from the thermodynamically equilibrium state and may contain significant irregularities. Related to this, depending on the deposition or growth conditions, insulating oxides may take the crystalline, polycrystalline, or amorphous nature which structures will also differ in atomic density. The effect of the growth temperature on the electronic properties of the oxide is illustrated in Fig. 9.2.1, which summarizes the literature results on the measured barrier height between the Fermi level of Al metal and the conduction band states of aluminium oxide as a function of alumina growth temperature (Brauenstein et al., 1965a, b; Shepard, 1965; Nelson and Anderson, 1966; Schuermeyer and Crawford, 1966; Ludwig
190
Internal Photoemission Spectroscopy: Principles and Applications
Φ (Al/Al2O3) (eV)
3.5
DiMaria, 1974a Szydlo & Poirier, 1971 Afanas'ev et al., 2002d
3.0
Shepard, 1965 sapphire Viswanathan & Loo, 1972a,b Maillet et al., 1983 Ludwig & Korneffel, 1967 EC Φ Goodman, 1970 EF Al AlOx
2.5
2.0
1.5
0
200
400 600 Tgrowth (˚C)
800
1000
Fig. 9.2.1 Literature results on the energy barrier height between the Fermi level of Al and the bottom of aluminium oxide conduction band (cf. insert) as a function of the oxide growth temperature. The bold dotted line marks the result for Al evaporated onto crystalline Al2 O3 (sapphire) according to (Viswanathan and Loo, 1972a, b; Maillet et al., 1983). Lines guide the eye.
and Korneffel, 1967; Goodman, 1970; Szydlo and Poirier 1971; DiMaria, 1974; Afanas’ev et al., 2002a, d). The result for the bulk Al2 O3 crystal (sapphire) (Viswanathan and Loo, 1972a, b; Maillet, et al., 1983) is indicated by the dashed line for comparison. It is clearly seen that a lower growth temperature leads to a large downshift of the alumina conduction band. It is worth of adding here is that the nanometre-thin alumina layers may yield even lower barriers (1.2 eV at Co/Al2 O3 interfaces, Rippard et al. (2002)). It has recently been hypothesized that the reduction of the Al ion co-ordination number may lead to a gap narrowing in amorphous Al2 O3 (Momida et al., 2006), but the exact reason of this behaviour is still under debate. Finally, stoichiometry of the thin oxide is not necessarily the same as the bulk crystal composition, which may also affect the electronic properties of the insulator. Moreover, experimental studies have evidenced a significant barrier asymmetry (∼0.5 eV) in Al/AlOx Al (Gundlach and Kadlec, 1975; Kadlec and Gundlach, 1975) and Al/Y2 O3 /Al (Riemann and Young, 1973) sandwiches, suggestive of in-depth non-uniformity of the thin oxide films. Taken together, the above features clearly show that the combined effect of stoichiometry, structure, and size may affect fundamental electronic properties of thin insulators substantially, which requires thorough physical analysis. In particular, the fundamental question arises about the possibility of combining a high dielectric permittivity value with sufficiently high energy barriers at the oxide interfaces. The available compilations of bulk crystal data correlate the bandgap width decrease with increasing dielectric constant (Robertson, 2000; 2004; Schlom and Haeni, 2002), and the energy barriers determining carrier transport across the insulator are expected to follow this trend. However, as the applicability of the bulk crystal description to drastically size-reduced amorphous insulators is highly questionable, the need of experimental characterization of thin insulating films becomes acute. While the determination of the εD value from the specific capacitance measurements appears to be rather straightforward, quantification of the energy band alignment is much more sophisticated both from the viewpoint of physical description and practical realisation of the experiment. Some degree of general understanding of the trends in band alignment at interfaces can be gained from theoretical calculations, which, again use bulk crystal values of the oxide
Semiconductor–Insulator Interface Barriers
191
bandgap, but the real applicability and limits in performance of technologically relevant materials remain largely unexplored. This situation urges implementation of physically reliable procedures of characterizing the electronic structure of thin insulating layers, in particular, the interface band alignment quantification. IPE spectroscopy appears to be the method of choice when considering this characterization challenge. In the remaining part of this chapter we will overview the results obtained when analysing different material systems to provide the reader with an adequate, and hopefully, reliable reference framework for analysing future data of both IPE and electrical measurements. The latter is of particular importance because in the IPE experiment the externally applied electric field prevents distortion of the electrostatic potential distribution at the interface due to the insulator charging. Otherwise, such as, e.g., in the non-gated structures used in photoelectron spectroscopy or surface potential measurements, the charges trapped in the insulator may cause significant apparent barrier variations and errors in determining band offsets unless corrected properly (Nohira et al., 2002; Toyoda et al., 2005). The charging of an insulating collector may be of crucial importance even in the case of layers of only a few nanometre thick. This is illustrated by the capacitance–voltage (CV) curves measured on Si/Al2 O3 (3 nm)/Au structures shown in Fig. 9.2.2. One may notice that photogeneration of electron–hole pairs in the oxide has caused a shift of about 0.3 V of the CV characteristics towards negative voltage suggesting positive charging of the oxide. Would the energy of electron states at the oxide surface be measured without fixing the surface potential by a metal electrode, the corresponding electrostatic shift will result in a systematic deviation of the measured value from the real one. Accordingly, and unless properly addressed, one should be aware that the predominantly positive charging observed in a number at high-κ oxides, leading to the systematic downshift of the energy levels of the insulator electron states. The latter has likely resulted in inference of apparently lower conduction band offsets by the ‘non-gated sample methods’ than those obtained using the IPE measurements in which the influence of charging is minimal. Although the use of a biased MOS structure allows one to reduce the influence of oxide charging, injection of a large carrier density into an insulator may also lead to a significant perturbation of the internal electric field distribution. As a result, the ideal image-force barrier lowering may be superposed 1.0 Control
C/Cmax
No metal
0.5
hn 10eV, 600s f 100kHz
Au, 3.5V
p-Si(100)/3nm Al2O3 0.0
0
1 Voltage (V)
2
Fig. 9.2.2 Normalized 100-kHz CV curves observed on Si/Al2 O3 (3 nm)/Au (15 nm) capacitors prior (solid line) and after irradiation by ≈5 × 1016 cm−2 of 10-eV photons (dashed lines) performed before evaporation of the metal electrode or after the metallization, with +3.5 V bias applied to the metal gate. The curves are shown for two directions of voltage sweep.
192
Internal Photoemission Spectroscopy: Principles and Applications
with charge effects leading to a non-Schottky behaviour as discussed in the first section of this chapter in relationship with IPE at Si/SiO2 interface. For this reason extrapolation of the measured IPE threshold to zero field remains necessary even if the image-force model would predict insignificant (<0.1 eV) Schottky barrier reduction for high-permittivity insulator layers. Direct measurements of trapped charge in the IPE/PC experiments (Afanas’ev and Stesmans, 2002; 2004b) indicate a non-negligible charging to occur at injection of ∼1013 carriers/cm2 . This result suggests that the total injected carrier density should preferably be kept below this limit. The silicon crystal substrate represents the obvious choice as initial platform for high-permittivity insulator studies. First, it allows a meaningful and supporting comparison of the electronic structure of the Si/high-permittivity insulator interface to the conventional Si/SiO2 system. Second, from the practical point of view, with some SiO2 interlayer (IL) inserted, the generally high electrical quality of Si/SiO2 interface is retained. This enables effective Si surface passivation in the presence of an insulator on top of it. Though the scalability of this two-layer stack is limited, it is compensated by the improved surface carrier mobility and acceptable stable threshold voltage behaviour (Houssa et al., 2006). Finally, the Si platform provides potentially the easiest way to implement the high-permittivity insulating materials into device production with minimal modifications of the mainstream fabrication process. Within the framework of these ideas most of the IPE studies of novel insulators have so far been performed using Si-based samples. In the coming sections the results will be overviewed addressing three major issues: (1) relevance of the bandgap values measured in millimetre-thin oxide layers with respect to the bulk bandgap widths; (2) influence of the interface dipoles on band alignment; (3) general trends in the band alignment at interfaces of Si with elemental and complex oxides. 9.2.2 Bandgap width in deposited oxide layers As already mentioned earlier, the atomic structure of thin deposited oxide layers is not expected to be exact replicas of the structure of the stoichiometric thermodynamically stable bulk phase, and this, of course, may affect the electronic structure of the film. To illustrate this point, one may retake the above considered case of alumina films, which exhibit a large variation in the conduction band energy with oxide growth temperature as suggested by the literature data (cf. Fig 9.2.1). In Fig. 9.2.3 are shown the IPE/PC spectra obtained from (100)Si/Al2 O3 (50 nm)/Au samples grown by atomic layer deposition on (100)Si and subsequently subjected to annealing at different temperatures in N2 + 5% O2 for 10 min (Afanas’ev et al., 2002e). The as-deposited layers exhibit a bandgap width Eg (Al2 O3 ) of only ∼6 eV, which is to be compared with the bulk crystal value for sapphire of 8.7 eV (Bortz and French, 1989; French, 1990). Annealing at temperatures higher than 800◦ C results in the gradual disappearance of the low-energy PC (cf. , , and 3 in Fig. 9.2.3) suggesting a bandgap widening due to structural transformation of the alumina. The latter is caused by crystallization of Al2 O3 into a cubic phase (Afanas’ev and Stesmans, 2002e) characterized by a bandgap width of 8.7 eV (Ealet et al., 1994). The insert in Fig. 9.2.3 shows the remaining fraction of the low-bandgap (amorphous) alumina phase as determined from the relative variation of the PC quantum efficiency in the spectral range hν > 6 eV. It indicates that crystallization has almost reached completion for annealing at T ≥ 900◦ C. Interestingly, as indicated by the low-energy (hν < 5 eV) portion of the spectra shown in Fig. 9.2.3, the energy of the alumina conduction band bottom measured relative the Fermi level of Au using the IPE of electrons from this metal is increased by ∼0.5 eV. This result is qualitatively consistent with measurements relative the Fermi level of Al (Fig. 9.2.1) and indicates that most (∼80%) of the ∼2.5 eV bandgap widening observed in alumina upon annealing
Semiconductor–Insulator Interface Barriers
105 104 103 102
1.0 Fraction
IPE/PC yield (relative units)
106
193
0.5 0.0
400 600 800 Temperature (C) (Au)
101 Eg(Al2O3)
100 101 3
4
5
6
Photon energy (eV)
Fig. 9.2.3 Logarithmic plot of the IPE/PC spectra of (100)Si/Al2 O3 (50 nm)/Au capacitors measured under −5 V bias on the Au contact for the as-deposited () Al2 O3 layers and after annealing for 10 min in N2 + 5% O2 at 800 (), 850 (), and 900 () and 950 (3)◦ C. The arrows labelled as (Au) and Eg (Al2 O3 ), indicate the spectral thresholds of electron IPE from Au into the conduction band of the oxide and of the intrinsic carrier photogeneration in Al2 O3 , respectively. Bold arrows indicate the evolution of the spectra with increasing annealing temperature. The insert shows the relative content of the low-bandgap (amorphous) alumina phase after anneal at various temperatures as determined from the relative variation of the intrinsic PC yield.
occurs due to downshift of the oxide valence band. The latter observation clearly contradicts the results of recent calculations (Momida et al., 2006) indicating a larger downshift of the alumina conduction band in energy (∼3.5 eV) when comparing crystal and amorphous Al oxide phases. Obviously, more theoretical efforts will be required to understand the trends in band structure properties of low-temperature deposited alumina films as well as other insulating materials. As compared to the bulk crystalline material, the atomically altered structure, specific for the lowtemperature deposited oxides, may cause not only narrowing of the bandgap as observed in alumina but, also, the gap widening can occur. For instance, deposited TiO2 layers exhibit a bandgap width of 4.2–4.4 eV as compared to the 3.1 eV gap of rutile (see, e.g., Persson and Ferreira da Silva, 2005). This considerable difference does definitely not concern an experimental flaw caused by the low optical absorption in thin TiO2 layers, which potentially might impair the sensitivity of PC measurements. As one can see from the PC spectra shown in Fig. 9.2.4, annealing of physically the same sample at 800◦ C leads to crystallization of the film and, attendantly, the PC threshold at ∼3.2 eV becomes clearly visible (Afanas’ev et al., 2005a). The widening of the gap in amorphous phase seems to be mostly caused by a shift in the Ti-derived energetically lowest states in the oxide conduction band. Apparently, the high symmetry of the surrounding of the Ti atoms in the dense crystalline material enables attaining the low energy of the conduction band bottom edge. The bandgap width may even be different in the as-deposited insulating layers if their atomic structure is different. For instance, when comparing PC spectra shown in Fig. 9.2.5 for amorphous Sc2 O3 films grown on (100)Si to their epitaxial counterparts with cubic bixbyite crystal structure (Klenov et al., 2005), one easily notices a higher bandgap of the epitaxial oxide which value is close to the optical gap observed in bulk crystal material (Eg = 6.0 eV, according to Tippins (1966)), while the amorphous layer exhibits gap by approximately 0.4 eV lower. In addition to a lower bandgap, the amorphous layer exhibits considerable density of ‘tail’ states probably associated with significant degree of film disorder.
194
Internal Photoemission Spectroscopy: Principles and Applications
(PC yield)1/2 (relative units)
(100)Si/TiO2 800 4.4 eV 600 400
N2 5% O2 3.2 eV 30 min 800C as-deposited
200 0
3
4
5
6
Photon energy (eV)
(PC yield)1/2 (relative units)
Fig. 9.2.4 PC spectra of TiO2 layers grown from a metallo-organic precursor in the as-deposited state () and after densification by a 30 min post-deposition annealing (PDA) at 800◦ C (). The arrows indicate the inferred PC thresholds corresponding to the oxide bandgap width.
0.004
Sc2O3
0.003
Eg(c-Sc2O3)
Amorphous Epitaxial
0.002
Eg(a-Sc2O3)
0.001 0.000
4
5 Photon energy (eV)
6
Fig. 9.2.5 PC spectra of Sc2 O3 layers grown molecular beam epitaxy on (100)Si with amorphous oxide structure () and epitaxially on (111)Si with cubic bixbyite structure (). The arrows indicate the inferred PC thresholds corresponding to the oxide bandgap width.
Some of the deposited oxide insulator films exhibit a bandgap width close to the accepted crystal values (e.g., HfO2 , ZrO2 , Ta2 O5 , …). (Afanas’ev and Stesmans, 2004a). This can be related to the significant degree of material crystallization occurring during film deposition, as clearly happens in the case of HfO2 . In the case of amorphous layers the general trend, however, is that the bandgap exceeds the crystalline value. For instance, the available PC results for rare-earth (RE) oxide layers indicate that for most of the RE2 O3 compounds the bandgaps fall within a narrow range between 5.6 and 5.9 eV, while the optical gaps derived for crystal samples (see compilation in Prokofiev et al. (1996)) in most of the cases lie systematically 0.5–1.0 eV lower. Therefore, the bulk values cannot be considered as directly applicable to thin amorphous layers. To provide the reader with pertinent reference material, the bandgap values of some deposited metal oxide films (5–40-nm thick) determined using PC measurements are summarized in Table 9.2.1, and compared to the crystal values when available (cf. Table 6 in Norton (2004)).
Semiconductor–Insulator Interface Barriers
195
Table 9.2.1 Bandgap width of some deposited metal oxide insulators determined from PC measurements in 5–40 nm thick deposited films as compared to the crystal bandgap (Norton, 2004). Oxide Al2 O3 ZrO2 HfO2 TiO2 CeO2 Ta2 O5 Nb2 O5 Sc2 O3 Ga2 O3 LaAlO3 LaScO3 LaLuO3 GdScO3 DyScO3 Lu2 O3 Gd2 O3 La2 Hf2 O7 HfAlOx ZrAlOx
Eg ± 0.1 eV
Reference
Eg (crystal)
6.2 5.5 5.6/5.9 4.4 3.3 4.4 4.0 5.6 4.0 5.7 5.7 5.6 5.6 5.7 5.8 5.4 5.8 5.6 5.9 6.0 5.5
Afanas’ev et al. (2002e) Afanas’ev and Stesmans (2004a) Afanas’ev et al. (2002b) Afanas’ev and Stesmans (2004a) Afanas’ev et al. (2006b) Afanas’ev and Stesmans (2004a) Afanas’ev and Stesmans (2004a) Afanas’ev et al. (2006a) Afanas’ev et al. (2006c) Afanas’ev et al. (2004a; 2006a) Afanas’ev et al. (2004a; 2006a) this work Afanas’ev et al. (2004a) Afanas’ev et al. (2004a) Seguini et al. (2004) this work Afanas’ev et al. (2006b) Seguini et al. (2006) Afanas’ev et al. (2006b) Afanas’ev et al. (2003a) this work
8.8 5.2 5.8 3.0/3.2 3.3 4.5 6.0 4.4/4.9 5.8
5.4 5.3
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 The analysis of the band alignment between Si and elemental oxides allows us to address the potential role of interfacial effects because the oxide composition may be well controlled. In addition, the electronic structure of elemental oxides is expected to be more simple than in complex oxides, in which contributions of different cations give rise to several electron density of state (DOS) components. This more simple DOS distribution in elemental oxides makes it easier to isolate the effects associated with ‘insertion’ of different IL at the interface. We first address the Al2 O3 and SiO2 insulators. The spectral dependences of electron IPE from the valence band of (100) Si into Al2 O3 () and SiO2 () layers are exemplified in Fig. 9.3.1 using Y 1/3 –hν co-ordinates to determine the spectral thresholds (Powell, 1970). One might notice a considerable difference in the spectral thresholds between the two insulating materials, indicative of a difference in the energy of the oxide conduction band bottom edge. The near-threshold portions of the spectra can be well approximated by the Y ∼ (hν − )3 dependence predicted by Powell’s model, albeit the range of photon energies is rather limited (<0.5 eV) because of significant changes in the optical properties of the Si crystal at hν ≈ 3.4 eV and hν ≈ 4.4 eV (DiStefano and Lewis, 1974). The latter changes are related to excitation of optical transitions in the Brillouin zone of Si and correspond to known E1 and E2 peaks in the optical spectra of Si as already discussed in Section 4.2. The energies of these transitions are indicated by the arrows in Fig. 9.3.1 for clarity. These optical features are characteristic of the semiconductor crystal
196
Internal Photoemission Spectroscopy: Principles and Applications
(IPE yield)1/3 (relative units)
d(hn) 0.02 eV e
4
E2 Si Ox Me
E1
2 e(Si/Al2O3) e(Si/SiO2) 0
3
4 Photon energy (eV)
Fig. 9.3.1 Cube root of the IPE yield from silicon as a function of photon energy for Au-metallized MOS structures with as-deposited 5-nm thick Al2 O3 (), after annealing of the alumina layer for 30 min at 650◦ C () or for 10 min at 800◦ C (), as compared to 4.1-nm thick SiO2 () thermally grown on Si. All curves are measured under an electric field of 2 MV/cm in the insulating layer, with the metal biased positively. The insert shows the scheme of electron transitions observed. The arrows E1 and E2 indicate the onsets of direct optical transitions in the Si crystal. The spectral thresholds are indicated for the different oxides studied. The energy width of the monochromator slit is indicated for reference.
and are also observed at interfaces of Si with different insulators serving in this way as fingerprints of IPE from electron states belonging to the Si crystal. The Schottky plots of IPE thresholds are shown in Fig. 9.3.2 for SiO2 layers of different thickness, Al2 O3 (), and two other high-permittivity metal oxides: ZrO2 (3) and HfO2 ( ). The image-force barrier model is seen to give a good description of the interface barrier reduction except in
IPE threshold (eV)
4.0
3.5
SiO2
Al2O3
3.0 HfO2 ZrO2 0
1
2
3
(Field)1/2 (MV/cm)1/2
Fig. 9.3.2 Schottky plot of the measured spectral thresholds for IPE from the Si valence band into the conduction band of SiO2 layers of different thickness (in nm): 55 (), 5.8 (), 4.1 (), compared to results on 5-nm thick Al2 O3 (), 7.4-nm thick ZrO2 (3), and 10-nm thick HfO2 ( ) layers. The symbol size corresponds to the error attained on the threshold determination. The lines represent linear fits according to the ideal image force model.
Semiconductor–Insulator Interface Barriers
197
the high field region for the Si/SiO2 interface. Here the high electric field may penetrate into the semiconductor causing a variation of electrostatic potential over the photoelectron escape depth length scale (cf. Fig. 2.1.3), thus leading to an additional reduction of the IPE spectral threshold energy (Adamchuk and Afanas’ev, 1992a). For the sake of comparison, also shown in Fig. 9.3.1 are the IPE spectra measured in Si/Al2 O3 samples subjected to thermal treatment in oxygen (, ) intended to grow a thin interfacial SiO2 -like barrier layer (for details see Afanas’ev et al. (2002a)). The yield of electron IPE is seen to decrease after oxidation, which is consistent with additional scattering of electrons attempting to surmount the barrier. However, no measurable shift in the electron IPE spectral threshold is noticeable after the oxidation treatment at 650◦ C (cf. symbols and in Fig. 9.3.1). For the higher oxidation temperature (800◦ C), no welldefined IPE threshold is observed anymore ( in Fig. 9.3.1) suggesting smearing out of the oxide CB edge, probably caused by formation of an aluminosilicate IL.
(IPE yield)1/3 (relative units)
Similarly to the case of Al2 O3 , the Si/SiO2 /ZrO2 and Si/AlOx /ZrO2 interfaces show no significant influence of the IL oxide composition on the barrier height at the interface, as revealed by the IPE spectra shown in Fig. 9.3.3. This observation suggests that, in the absence of a polar adsorbate, the processing-induced dipoles have a minor influence of the interface barrier height. Consistent with this observation, changing the HfO2 deposition chemistry is also found to have no measurable influence on the electron IPE threshold at Si/HfO2 interfaces, as evidenced by the IPE spectra shown in Fig. 9.3.4. Electron IPE spectra are compared as measured on three types of (100)Si/HfO2 entities with a 10-nm thick HfO2 layers deposited by three different methods, i.e., atomic layer deposition (AL), chemical vapour deposition (CVD) at 300◦ C using HfCl4 and H2 O as precursors, CVD at 485◦ C using metalloorganic precursor (tetrakis-diethylaminohafnium) and O2 , and CVD at 450◦ C using the nitrato precursor Hf(NO3 )4 (N-CVD). At the same time, the composition and the thickness of the IL do have a significant influence on the IPE yield indicating that, similarly to the case of Si/SiOx /Al2 O3 stacks, electrons experience an additional scattering in the barrier region. Thus, as an important finding, the total of these experimental observations indicate that the Si-oxide IL provides no substantial interfacial dipoles. The absence of the IL-related dipoles also appears from results of IPE experiments on Si/HfO2 structures (100)Si/AlOx/ZrO2
(100)Si/SiO2/ZrO2 4
4
Φe
E2 E1
2
Si Ox Me
Φ(ZrO2)
2 Φ(ZrO2) (a)
0 2.5
3.0
3.5
4.0
4.5
(b) 2.5
3.0
3.5
4.0
4.5
0 5.0
Photon energy (eV)
Fig. 9.3.3 Cube root of the IPE yield as a function of photon energy for MOS structures with different dielectrics: (a) 7.4 nm ZrO2 (O), stacks of 0.5 nm SiO2 /5 nm ZrO2 (), 1.3 nm SiO2 /5 nm ZrO2 (), 2.5 nm SiO2 /7.4 nm ZrO2 (), and 3.2 nm SiO2 /7.4 nm ZrO2 (3); (b) 7.4 nm ZrO2 (O), stacks of 0.5 nm Al2 O3 /5 nm ZrO2 (), 1.5 nm Al2 O3 /5 nm ZrO2 (), and the latter stack oxidized in O2 at 800◦ C for 10 min (dSiO2 = 1.2 nm, ). All curves are measured under an applied electric field of 2 MV/cm in the insulating layer with the metal biased positively. The arrows E1 and E2 indicate onsets of direct optical transitions in the Si crystal. The spectral threshold e for electron IPE from Si into ZrO2 layer is indicated. The insert illustrates the scheme of the observed electron transitions.
198
Internal Photoemission Spectroscopy: Principles and Applications 8 (IPE yield)1/3 (relative units)
(100)Si/HfO2 (10 nm) 6
E2 e 3.1eV
E1
4
MO-CVD N-CVD
2
0 2.5
AL-CVD
3.0
3.5 4.0 Photon energy (eV)
4.5
5.0
Fig. 9.3.4 Spectral dependences of electron IPE from the (100)Si valence band into 10-nm thick as-deposited HfO2 layers grown by ALD at 300◦ C (), CVD from metalloorganic precursor at 485◦ C () and CVD using a nitrato precursor Hf(NO3 )4 at 350◦ C (). The arrows mark the energies E1 and E2 of direct optical transitions in the crystalline Si substrate.
with ILs-containing nitrogen (SiON) or even the O-free Si3 N4 . As revealed by the electron and hole IPE spectra (cf. Fig. 4.1.7) (Afanas’ev et al., 2002b), the energy band diagrams for these interfaces are the same and, moreover, coincide with that of Si/SiO2 /HfO2 structures. In this respect, another pertinent and interesting piece of information comes from comparison of the IPE results of Si/LaAlO3 samples with atomically abrupt interfaces obtained by growing the LaAlO3 layer using molecular beam deposition (MBD) technology (Edge et al., 2004) and Si/SiOx /LaAlO3 structures fabricated by pulsed laser deposition (PLD) of the LaAlO3 film onto a chemical SiOx IL about 1 nm thick (Heeg et al., 2005). In both cases, the same electron IPE barrier height is found as indicated by the spectra compared in Fig. 9.3.5. All together, the above results suggest that the property of no or only a marginal influence of dipoles related to the particular IL composition or to the particular bond arrangement at the interface can be considered as a general feature of Si/metal oxide interfaces (Afanas’ev et al., 2006a). In addition, the latter result also provides more insight into the DOS energy distribution at interfaces in the IL-containing Si/insulator structures. One may also notice in the field-dependent IPE spectra that, even in the presence of a high electric field, the about 1-nm thick SiOx IL does not result in any measurable variation of the value of electrostatic potential measured at the position of potential barrier maximum, e.g., in LaAlO3 (cf. Fig. 4 in Afanas’ev et al. (2006a)). This can be explained by penetration (the quantum-mechanical ‘tailing’) of a considerable DOS of the overlaying metal oxide into the IL, so the barrier maximum will be located at the same energy position with and without the SiO2 layer present. This hypothesis also clarifies why the bandgap edges of high-permittivity oxides can still be observed in IPE experiments with a 1.5–2-nm-thick IL of a chemically different material-like SiO2 or Si3 N4 (Afanas’ev et al., 2002a, b, d). Apparently, the extended states characteristic for conduction band DOS of the metal oxide penetrate into the silicon oxide/nitride bandgap to a depth of at least a few nm as inferred empirically. 9.3.2 Interfaces of Si with complex metal oxides The interest in complex oxides as possible high-permittivity gate insulator materials is related to several factors. First, there is the hope to combine in one oxide most of the beneficial properties of each
Semiconductor–Insulator Interface Barriers 105
1MV/cm
LaAlO3
PLD
103
MBD
102
8 Y1/3 (relative units)
IPE yield (relative units)
104
199
101 100 101 2
3
e
4
0
2 4
3 hn (eV) 4 5
6
Photon energy (eV)
Fig. 9.3.5 IPE/PC yield as a function of photon energy measured in MOS capacitors with ≈20-nm-thick layers of amorphous LaAlO3 deposited by PLD on (100) Si covered with a ∼1-nm-thick chemical oxide () or by MBD directly on the atomically clean (100) Si surface (). The data are taken with positive bias on the applied Au electrode corresponding to the average electric field strength in the oxide of 1 MV/cm. The insert illustrates the determination of the spectral threshold e of electron IPE using the power plots of the quantum yield versus photon energy.
of the elemental components, such as the high dielectric permittivity (e.g., TiO2 , Ta2 O5 ) and large bandgap (e.g., Al2 O3 , ZrO2 , HfO2 ). Second, one may target improved chemical stability of the complex oxides as compared to less stable elemental components, e.g., suppress undesired properties such as the hydrophilicity of La2 O3 (Zhao et al., 2006). Finally, complex oxides often exhibit a much higher crystallization temperature than their elemental counterparts which is seen as an important benefit allowing the preservation of the gate oxide integrity during high-temperature steps necessary in device manufacturing (C. Zhao et al., 2003). From the point of view of the electron band structure, the major difference between the elemental and complex oxides consists in the co-presence of two different cation sub-networks which may give rise to different contributions to the oxide DOS (Lucovsky et al., 2004). In particular, the lowest portion of the oxide conduction band is usually associated with electron states derived from unoccupied atomic orbitals of metal cations (Lucovsky, 2002). The details of band structure in this energy range are determined by the overlap of these states. In most of the high-permittivity oxides the lowest unoccupied states are derived from atomic d-states (Lucovsky, 2002), which makes the lowest portion of the conduction band highly sensitive to the structural aspects of the complex compound (cation network dilution, phase separation, etc.). Apparently, the most simple case in terms of a possible variation of the oxide composition is provided by stoichiometric complex oxides with cations concentration ratio close to 1:1, like LaAlO3 , LaScO3 , DyScO3 , GdScO3 , La2 Hf2 O7 (Afanas’ev et al., 2004a). The electron and hole IPE spectra at interfaces of (100)Si with several amorphous RE scandate and aluminate layers are compared in Fig. 9.3.6. These data clearly indicate that barriers for electrons and holes are insensitive to the type of RE cation suggesting a close bandgap width of these materials. The latter is quite in contrast with the behaviour of crystalline RE oxides as revealed by optical measurements (Prokofiev et al., 1996). This, in turn, may suggest that dilution of the cation network and/or transition to an amorphous structure would make the electron states close to the oxide conduction band bottom insensitive to the occupancy of the 4f shell in RE ions.
200
Internal Photoemission Spectroscopy: Principles and Applications 105
Yield (relative units)
104 103 102
LaScO3
101
GdScO3 DyScO3
100
LaAlO3 1 MV/cm
101 Y 1/3 (relative units)
(Yield)1/2 (relative units)
102
(a)
1 MV/cm
300
200
100
6 4
e e* h
2
0 2.0 2.5 3.0 3.5 4.0 4.5 hn (eV) Eg* Eg (b)
0
2
3
4 5 Photon energy (eV)
6
Fig. 9.3.6 IPE/PC yield (a) and its square root (b) as a function of photon energy measured in MOS capacitors with different (≈20-nm thick) complex amorphous RE oxide insulators. The open and filled symbols correspond to an applied oxide electric field of +1 and −1 MV/cm, respectively. The insert in panel (b) illustrates determination of the IPE thresholds using the Y 1/3 –hν plot. The IPE (e , ∗e , h ) and PC (Eg , Eg∗ ) thresholds are indicated by arrows. Lines guide the eye.
Indeed, when compared to the HfO2 and La2 Hf2 O7 layers, in which Hf has the completely occupied 4f-states (4f14 electronic configuration), the results appear to be the same within the measurement error as indicated by the electron IPE data shown in Fig. 9.3.7. This conclusion is supported by results of independent IPE experiments on (100)Si/Lu2 O3 (Seguini et al., 2004), (100)Si/La2 Hf2 O7 (Seguini et al., 2006), (100)Si/Yb2 O3 (Rozhkov et al., 1998a; Rozhkov and Trusova, 1999) and (100)Si/Sm2 O3 (Rozhkov et al., 1998a, b; Rozhkov and Trusova, 1999) structures with amorphous oxide layers. All the results here indicate the barrier height for electrons in the Si VB to be close to 3.0 eV. The IPE/PC-derived barrier height, band offsets and barrier data for interfaces of Si with different amorphous insulating oxides are summarized in Table 9.3.1. The data reveal a most remarkable feature which, taking into account the substantial number of studied oxides of different composition, may come as a general finding. For the (studied) oxides with close bandgaps (Eg = 5.6–5.9 eV) the band alignment at the interface with Si appears to be insensitive to the atomic composition of the insulator, the band diagram being characterized by the conduction and valence band offsets of approximately EC = 2.0 eV and EV = 2.5 eV, respectively. Though the observation of the same energy of the upper valence band edge might come as little surprise because the corresponding electron states are derived from the same
Semiconductor–Insulator Interface Barriers
(IPE yield)1/3 (relative units)
8
201
(100)Si
6
E2 e 3.1eV HfO2(AL-CVD)
4
E1 La2Hf2O7 (MBE)
2
0 2.5
3.0
3.5
4.0
4.5
5.0
Photon energy (eV)
Fig. 9.3.7 Cube root of the electron IPE yield as a function of photon energy for MOS structures with the as-deposited 10-nm-thick amorphous La2 Hf2 O7 () and HfO2 () insulators. The curves are measured under an applied electric field of 2 MV/cm in the insulating film. The arrows E1 and E2 indicate the onsets of direct optical transitions in the Si substrate crystal.
Table 9.3.1 Electron and hole barrier heights (e and h ) and the conduction and valence band offsets (EC and EV ) (in eV, ±0.1 eV) of interfaces between (100)Si and several oxide insulators determined from IPE experiments. Oxide
Eg
e
EC
h
SiO2 Al2 O3 ZrO2 HfO2 Sc2 O3 LaAlO3 LaScO3 GdScO3 DyScO3 La2 Hf2 O7
8.9 6.2 5.5 5.6 5.6 5.7 5.7 5.6 5.7 5.6 5.9 5.8 5.4 5.5 5.8
4.25 3.25 3.1 3.1 3.1 3.1 3.1 3.1 3.1 3.2 3.15 3.2 3.1 3.1 3.2
3.15 2.1 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.1 2.0 2.1 2.0 2.0 2.1
5.8
4.7
3.6 3.6 3.7 3.7 3.6 3.6 3.6 3.5 3.7 3.7 3.3 3.4 3.7
2.5 2.5 2.6 2.6 2.5 2.5 2.5 2.4 Seguini et al. (2006) 2.6 2.6 Seguini et al. (2004) 2.2 2.3 2.6
Lu2 O3 LaLuO3 Gd2 O3
EV
2p lone-pair states of O anions (Lucovsky, 2002), the insensitivity of the metal-derived conduction band states to the kind of the originating cation cannot be explained in a straightforward way. Nevertheless, this trend is perfectly consistent with the already discussed insensitivity of the interface barriers to the details of the atomic bonding at the interface, e.g., to the presence of an IL and to its composition. Thus, it seems reasonable to infer that the bulk electron DOSs of silicon and the oxide play the key roles in determining the band alignment at the interface.
202
Internal Photoemission Spectroscopy: Principles and Applications
2 V 1000
Eg
(IPE/PC yield)1/2 (relative units)
Si 500
Ta content (%): 100 Eg(HfO2) 85 50 Me 15 0
Ox (a)
Eg(Ta2O5) 0 2
5
3
4
5
6
2 V e(Au)
4 3 2
Si
Ox Au
1 0 2.0
(b) 2.5
3.0 3.5 4.0 Photon energy (eV)
4.5
Fig. 9.3.8 Spectral curves of the square root of the PC (a) and IPE (b) yield with −2 V bias applied to the Au electrode of MOS capacitors with Ta Hf oxide insulators of different composition. The inserts show the schemes of electron transitions involved. The lines illustrate determination of the spectral thresholds from the shown Y 1/2 –hν plots. The arrows in panel (a) mark the bandgap values of HfO2 and Ta2 O5 .
To get more insight with respect to the electronic structure of interfaces of complex metal oxides with silicon, we addressed two high-permittivity amorphous insulators with more narrow bandgaps, namely, TiO2 and Ta2 O5 . It appeared, however, that MOS capacitors with these oxides exhibit too high leakage currents thus preventing reliable measurements of the IPE current. To overcome this problem, the solid amorphous solutions of these oxides in the already well characterized HfO2 matrix were investigated as functions of cation composition (Afanas’ev et al., 2004c; 2005a, b). A striking result consists in the observation of a downshift of the oxide conduction band by ∼1.4 eV with respect to the conduction band of HfO2 , as measured relative to the Fermi level of the applied reference Au electrode. This is illustrated in Fig. 9.3.8 for Hfx Ta1−x Oy oxides showing spectra of PC (a) and electron IPE from the Au electrode (b), which indicate the development of an energetically lower conduction band DOS sub-band in correlation with increasing Ta content. An important feature here consists in the gradual character of the conduction band edge shift while in Hf Ti oxide (Afanas’ev et al., 2005b) and in another studied complex system, Hfx Al1−x Oy (Afanas’ev et al., 2003a), the transition to the bandgap value characteristic of the second cation occurs abruptly, already at a mole fraction of ∼0.3. The latter is also illustrated in Fig. 9.3.9 which shows the bandgap and electron barrier height evolution as a function of the oxide composition in Hfx Al1−x Oy , Hfx Ti1−x Oy , and Hfx Ta1−x Oy layers. Understanding of the underlying principle(s) of this unveiled remarkable evolution in band diagram properties of two-cation oxides may appear very important. The gradual shift of the conduction edge in Hf Ta oxides may be suggestive of quantum intermixing of 5d*-states of these cations, while no mixing of Hf5d* states with Al3p* and Ti3d* states is observed. It suggests that the quantum mixing is possible
Semiconductor–Insulator Interface Barriers
Bandgap width (eV)
6.0
Al:Hf
5.5 5.0
Ta:Hf
4.5 Ti:Hf
4.0 3.5
(a) Au
4.0 Barrier height (eV)
203
3.5 3.0 2.5
Si (b)
2.0 0.0
0.2
0.4
0.6
0.8
1.0
[Me]/([Me]+[Hf])
Fig. 9.3.9 (a) Plot of the observed lowest metal oxide bandgap as a function of the two-cation oxide composition for ALCVD Al:Hf (), ALCVD Ta:Hf (), and Ti:Hf oxides grown by ALCVD () or by CVD from a metallo-organic precursor (). (b) Evolution of the barrier heights for electrons in the Si valence band (Si ; open symbols) and at the Fermi level of Au (Au ; filled symbols) as functions of oxide composition in ALCVD Al:Hf (circles), Ta:Hf (squares), and Ti:Hf oxides (triangles). Lines guide the eye.
only between electron states of the same symmetry and the same principal quantum number, while in other cases two only weakly interacting cation sub-networks are encountered in the oxide (Afanas’ev et al., 2005a). It is worth adding here that, even in the case of oxide networks with significantly reduced bandgap, the energy of the oxide valence band top remains insensitive (within accuracy limit ±0.1 eV) to the type of cation, i.e., the bandgap narrowing occurs almost entirely by a downshift of the cationderived conduction band states. This means that for all the studied amorphous oxides of d- and f-metals the valence band offset is approximately the same as indeed born out in Table 9.3.1.
9.3.3 Interfaces of Si with non-oxide insulators In addition to oxide dielectrics, other types of insulating materials of different chemical composition are considered as potential candidates for integration in electronic devices. In particular, nitride compounds like Si or Al nitrides are believed to offer certain advantages over oxide-based insulation in terms of preventing semiconductor oxidation, e.g. in the case of GaAs, in creating an efficient diffusion barrier at the surface of semiconductor, and, in some cases, to offer a broad spectrum of trapping sites to immobilize the injected charge carriers in active areas of non-volatile memory devices. Other materials like alkali halide crystals may be applied to grow epitaxial insulators with a variable lattice constant aiming at monolytic integration of different semiconductors, e.g., Si and GaAs or Si and halcogenide materials (Schowalter and Fathauer, 1986; Zogg et al., 1990; Masek et al., 1990). What is interesting here is the influence of the anion change from oxygen to some other atom on the interface band alignment which was already addressed by IPE spectroscopy in several works.
204
Internal Photoemission Spectroscopy: Principles and Applications
Historically, the first extensively studied non-oxide insulator was silicon nitride Si3 N4 which can easily be deposited on Si using CVD. Rather surprisingly, the results of IPE experiments using a blocking (water) field electrode (Goodman, 1968) and metal–insulator–semiconductor (MIS) structures with different metal electrodes (DiMaria and Arnett, 1975) were interpreted in a different way. In the first case all the current was believed to originate from electron and hole IPE from Si under positive and negative bias respectively which appear to exhibit nearly the same spectra thresholds (3.17 and 3.06 eV) (Goodman, 1968). When using metal electrodes, DiMaria and Arnett ascribed the photocurrents measured at the positive bias to IPE of holes from a metal based on subtle differences observed in the spectra when replacing one metal by another one with a different work function (Mg, Al, Au) and assuming the injection currents in Si3 N4 to be predominantly associated with transport of holes (DiMaria and Arnett, 1975; 1977). Under supposition that the Si3 N4 films studied by these authors have had the same spectrum of electron states, one might wonder why replacement of the field electrode material have lead to so significant differences in interpretation of the results of a physically similar experiment. A possible answer was later suggested by results of Jacobs and Dorda (1977a) who revealed that the traps in Si3 N4 can be photoionized leading to significant trap-related photocurrents. Taking into account a high trap density in Si3 N4 , in excess of 1018 cm−3 , the scheme of ‘pseudo’-IPE transitions when a charge carrier first tunnels to the trap and then optically excited to a transport band of the insulating collector layer seems to be feasible explanation of the indicated discrepancies in interpreting the IPE results. From the experimental photocurrent spectra shown in Fig. 9.3.10 for the case of a relatively thin (15 nm) Si3 N4 layer on Si and a high applied electric field one can see that neither reversal of the electric field orientation nor change of the field electrode material from Au to Al have an effect on the photocurrent spectra. In addition, there is no sign that the variation of Si optical characteristics in vicinity of E1 = 3.4 eV and E2 = 4.3 eV critical points affects any of the shown photocurrent yield spectral curves. At the same time, the influence of these transitions is clearly visible for other collector materials (cf. Figs 9.3.1, 9.3.3–9.3.7 in this chapter). Therefore, one must admit that no IPE signal can be distinguished in the shown spectra. Most of the photocurrent originates from ionisation of defect states with energy levels 102
(100)Si/Si3N4 (15nm)
Photo current yield (relative units)
101
Au gate, 5 V Au gate, 6 V Al gate, 6 V
100 101 102 103 104 105 106 107 108
2
3
4
5
Photon energy (eV)
Fig. 9.3.10 Logarithmic plot of the photocurrent yield spectral dependences in (100)Si/Si3 N4 (15 nm)/Au(Al) samples measured under different polarities of the bias voltage applied to the metal electrode. The insert indicates the scheme of trap-assisted electron transitions dominating in the observed photocurrent.
Semiconductor–Insulator Interface Barriers
205
in the Si3 N4 bandgap as illustrated in the insert for the case of the current carried by electrons (the scheme for the case of hole excitation would look symmetrically). It is still possible that the trap occupancy will be sensitive to the energy position of the Fermi level in the conduction electrodes which would explain observations of DiMaria and Arnett. However, if a voltage larger than the work function difference between different electrode materials is applied, the trap occupancy becomes marginally sensitive to the work function resulting in the electrode material-independent spectral curves shown in Fig. 9.3.10 which are, in fact, consistent with Goodman’s observations. The traps are constantly re-filled by charge carriers supplied from the electrodes resulting in a non-decaying steady-state photocurrent signal. Unfortunately, the dominance of these defect-mediated optical transitions makes reliable extraction of the interface barrier height impossible at present. The interface properties of Si/AlN structures were first reported by Morita et al. (1982) for thick (about 1 μm) layers of epitaxial nitride grown on (111)Si. Again, like in the case of Si3 N4 , the initial interpretation of the spectra was done assuming the absence of any defect-mediated photocurrent in the structure. Moreover, all the measurements in this work were done when the strength of electric field in the nitride was low, about 1 × 105 V/cm, which would lead to a weak IPE signal because of carrier scattering in the barrier region. As it appears, interpretation of the observed signals is possible only if assuming exclusively hole transport in the layer which makes it highly doubtful taking into account extremely low lifetime of the deep photo-holes in metals. In attempt to clarify the picture by reducing the rate of bulk trap PI, the IPE experiments were recently repeated using thin AlN layers grown on Si using the atomic layer deposition. The photocurrent spectra shown in Fig. 9.3.11 appear to exhibit all the spectral thresholds reported by Morita et al., but, in addition, reveal important trends allowing us to propose a more realistic interpretation. The change of the applied voltage polarity results in considerable variations on the low-photon energy portion of the spectral curves (hν < 4 eV) which would be consistent with some electrode-dependent injection process. The curve taken under the positive metal voltage () exhibits kinks at hν = 3.4 and hν = 4.4 eV corresponding to the energies of optical singularities in Si E1 and E2 , respectively. The latter allows interpretation the observed spectrum as that one of electron IPE from Si and to infer (by using Y 1/3 –hν plot shown in the upper left insert) the threshold for electron IPE from the valence band of Si into the conduction band of AlN e (Si) = 3.2 ± 0.1 eV. As the spectral curves measured under negative bias show no such features, they are unlikely to be associated with IPE (of holes) from Si. At the same time, the replacement of Au field electrode () with Al one () leads to some change in the photocurrent but to a much smaller extent than might be expected for a ≈1 eV energy difference between the Fermi levels of these metals. Actually, the same kind of photocurrent enhancement is seen when simply increasing the bias to the Al electrode ( in Fig. 9.3.11). Therefore, it is impossible to associate the photocurrents observed under negative biases neither to the IPE from Si nor to the IPE from a metal. Once again, it seems that the pseudo-IPE transitions may account for this kind of behaviour and the spectral threshold of around 2 eV which can be inferred from the spectral curves corresponds to the energy of some trap level. Remarkably, all the spectra reported by Morita et al. (1982) for a thick epitaxial AlN layer do exhibit this spectral threshold suggesting the traps to be related to some intrinsic imperfection. In the high-energy portion of the spectra shown in Fig. 9.3.11 one can observe two spectral thresholds Eg∗ and Eg as indicated in the bottom right insert in Fig. 9.3.11. As they appear independently of the electric field orientation in the AlN and of the material of the field electrode, these thresholds are likely to be associated with the intrinsic optical excitations in AlN. The threshold Eg = 5.8 eV is related to the bandgap of AlN because the optical absorption analysis performed for the same films using the spectroscopic ellipsometry revealed the same energy of the optical absorption edge. This bandgap value is somewhat lower than the values commonly reported for the epitaxial layer of AlN or its single-crystal samples (around 6.2–6.3 eV Yim et al. (1973), Perry and Rutz (1978), Strite and Morkoc (1992), Rubio et al. (1993), Li et al. (2003), Silveira et al. (2005)), which might be related to the amorphous structure of the studied thin
Internal Photoemission Spectroscopy: Principles and Applications Y1/3 (relative units)
101
Photo current yield (relative units)
102
103
0.03
e(Si)
0.02 0.01 E1 0.00 2.0 2.5 3.0 3.5 4.0 hn (eV)
Vg: Au, 1V Au, 1V Al, 2 V Al, 3 V
104 E2
Y 1/2 (relative units)
206
105 E1
106
107
0.3 Eg*
0.2 0.1 0.0
Eg 3
4
5 6 hn (eV) (100)Si/AlN(15nm)
e(Si) 2
3
4
5
6
X-axis
Fig. 9.3.11 Logarithmic plot of the photocurrent yield spectral dependences in (100)Si/AlN(15 nm)/Au(Al) samples measured under different polarities of the bias voltage applied to the metal electrode. The bottom right insert shows the (Y )1/2 –hν plot of the high-energy portion of the curves used to determine the onset of the PC. The upper left insert illustrates determination of the threshold of electron IPE from the valence band of Si into the conduction band of AlN. Arrows indicate the points of optical singularities in Si substrate crystal, and the inferred spectral thresholds of the electron IPE from the Si valence band e (Si) and the intrinsic PC of AlN, Eg∗ and Eg .
layers. The threshold Eg∗ ≈ 4 eV is likely caused by some defect photoexcitation because the photocurrents exhibit a trend to exhausting of the signal. When a high electric field is applied to assist the carrier escape one notices a reduction in the photocurrent at hν = 5.0–5.5 eV suggesting a lower density of electron states available for optical excitation (cf. Fig. 9.3.11). Interestingly, Morita et al. (1982) also inferred spectral threshold at close energy (3.6 eV) from all spectra they observed. The difference between their value and that shown in Fig. 9.3.11 might be caused by a limited spectral range (hν < 4.5 eV) used in the cited work for the IPE experiments. The origin of the electron state in the AlN bandgap remains unclear. It was suggested that oxygen impurity might give a deep state in the AlN gap (Yim et al., 1973), while other contaminants, e.g., carbon traces originating from the metalloorganic precursors, also deserve to be considered. As a sort of general trend in the studied nitride insulators it appears that the trap-assisted pseudo-IPE excitations gain more importance as compared to the insulating oxides. This observation seems to be consistent with more efficient trapping of injected charge carriers in nitrides, at least in amorphous ones, and indicates the issue of identifying the relevant electron excitation as the most important when studying these layer. As another manifestation of this problem one may indicate the work of Hirota and Mikami (1988) on IPE in InP/P3 N5 /metal structures in which the photocurrent yield spectra appear to have the same spectral thresholds independently of the applied bias polarity – the feature much more consistent with defect ionisation than with IPE from an electrode. Therefore, it seems logical to conclude that in the nitride insulator analysed so far the defect-assisted injection often prevails over the direct IPE from a contact.
Semiconductor–Insulator Interface Barriers
207
Another type of insulating materials applied to silicon are the alkali-halides, in particular fluorite (CaF2 ), which has a lattice matched interface with (111)Si at 600–620◦ C and, therefore, can be grown epitaxially providing the atomically abrupt (O-free!) interface (Yamada et al., 1988a, b; Himpsel et al., 1989). Taking into account a ≈12-eV wide bandgap of fluorite, the insulating quality of these layer is expected to be outstanding offering possibility of fabricating three-dimensional device structures as well as semiconductor surface passivation by a non-native insulator (Schowalter and Fathauer, 1986). However, experiments reveal an increased of leakage current across CaF2 insulators (Waho and Yanagawa, 1988; Paul and Bose, 1990) as compared to the conventional SiO2 . The reason for this behaviour appears to be related to the variation of the effective barrier height at the interface and was revealed by IPE (Adamchuk and Afanas’ev, 1992a). From the spectral plots of the photocurrent shown in Fig. 9.3.12 for (111)Si/CaF2 (300 nm)/Au structure one can see that the curves measured at different orientations of electric field in the fluorite have close spectral thresholds and similar photocurrent modulation pattern due to optical interference in this relatively thick film. This kind of behaviour would suggest the optical excitation of some defect states to provide the largest contribution to the measured photocurrent. Taking into account that the fluorine-derived valence states in CaF2 are so deep energetically (≈14 eV below vacuum level, Himpsel et al. (1989)) that optical transitions involving them are impossible in the photon energy range shown in Fig. 9.3.12, excitation of electrons represents the only feasible model to analyse the photocurrent spectra. Therefore, as the current observed at the positive metal bias is much higher than that under the opposite bias polarity, most of electrons must be excited in CaF2 close to the surface of silicon. This interpretation is supported by the observed exhaustion of the photocurrent observed under negative bias (filled symbols in Fig. 9.3.12) when repeating the measurements with increasing strength of electric field. Therefore, the likely scheme of photoexcitation includes electron tunnelling from (111)Si to a some trap in CaF2 and the subsequent optical ionisation of the latter (Adamchuk and Afanas’ev, 1992a), i.e., the pseudo-IPE injection process. Besides revealing a high density of electron traps in the near-interfacial CaF2 layer, the IPE analysis enabled another important observation. The threshold of electron excitation observed at around 3 eV in Fig. 9.3.12 was found to depend on the thickness of the grown epitaxial CaF2 layer with a trend to the electron barrier reduction with increasing the fluorite thickness (Afanas’ev et al., 1991). This (111)Si/CaF2 Photocurrent yield (relative units)
15
10
F (MV/cm): 0.09 0.15 0.21 0.15 0.21 0.30
5
0 3
4
5
Photon energy (eV)
Fig. 9.3.12 Photocurrent yield spectral curves in the (111)Si/CaF2 (300 nm)/Au structure observed under electric field of different strength and orientation. The spectral curves are modulated by optical interference in the studied thick CaF2 layer.
Internal Photoemission Spectroscopy: Principles and Applications
Specteal threshold (eV)
(111)Si/CaF2
3.4 3.2
3.5 3.0 2.8 3.0
2.6
Line shift (nm)
208
2.4 2.5
0
200
400
2.2 600
Fluorite thickness (nm)
Fig. 9.3.13 Barrier height for electron injection at (111)Si/CaF2 interface () and the half-width of the phononless line in the Sm2+ photoluminescence spectrum ( ) as functions of the thickness of the CaF2 layer epitaxially grown on (111)Si at 620◦ C.
•
trend is exemplified by open symbols in Fig. 9.3.13. In the same figure are shown by filled symbols the results of measurements of the width of the Sm2+ ion phononless photoluminescence line (Sokolov et al., 1990). These ions were intentionally introduced to a 2–3 nm thick CaF2 layer in the initial stages of the epitaxial growth and served as imbedded luminescent sensors of their local atomic surrounding. The results shown in Fig. 9.3.13 indicate the broadening of the Sm2+ emission line with increasing CaF2 thickness suggestive of increasing internal strain in the insulator. Correlation between the increasing strain and the observed lowering of the spectral threshold of trap ionisation suggests a strain-induced Si/CaF2 barrier lowering. Interestingly, the extrapolation of the barrier height to zero fluorite thickness gives the barrier height of 3.6 eV which appears to be in close agreement with the value derived from the external photoemission experiments conducted at the initial stages of CaF2 growth on silicon (Himpsel et al., 1989). As the possible mechanism of this barrier variation one might consider reduction of the F atoms density at the Si surface or in the near-interfacial layer of the fluorite resulting in changes of the interface dipole. This effect together with the above discussed observation of the Cl-related Si/SiO2 interface dipoles would indicate the dipoles associated with halide ions (F− , Cl− ) as potentially important contributions to the interface barrier height.
9.4 Band Alignment between Other Semiconductors and Insulating Films Recent successes in the development of non-native high-permittivity insulators for Si-based MOS devices have fuelled significant interest in the potential transfer of the corresponding technologies to other semiconductor materials promising an improved, as compared to Si, performance. These materials can be split in two groups: the high-mobility semiconductors (Ge, GaAs and other AIII BV compounds) and the wide bandgap semiconductors like SiC and GaN (see, e.g., Gila et al. (2004) for a review). The latter group of semiconductors is projected to extend applications of MOS devices to higher temperatures, voltages and power, which, at least in the case of SiC, cannot be achieved to full scale by just employing the native oxide insulator SiO2 (for a recent review see, e.g., Afanas’ev et al. (2004c)). In the case of high-mobility semiconductor materials the lack of suitable native insulator has long been recognized as most significant barrier for realization of functional MIS devices (Swanson, 1993). Though the information here regarding band alignment is still rather limited, we will, in synthesizing, attempt to follow
Semiconductor–Insulator Interface Barriers
209
the trends revealed in the case of Si/high-permittivity oxide interfaces for other semiconductor/oxide interfaces. 9.4.1 Ge/high-permittivity oxide interfaces As the native oxide on Ge is found to yield relatively low band offsets with the substrate (<2 eV, Kasumov and Kozlov (1988); Oishi and Matsuo (1996)) and, in addition, suffers from poor thermo-chemical stability, realisation of functional semiconductor–insulator interfaces on Ge requires application of an extrinsic insulating material. The first issue to be addressed in the case of Ge interfaces with metal oxides concerns the possible impact of the IL on the interface barriers. As Ge is easily oxidized and highly diffusive, the pre-deposition surface treatment can be used to create a, hopefully suitable, barrier layer at the interface. Among the possible options, surface nitridation in NH3 resulting in the formation of Ge N bonds and deposition of a thin (≈1 nm) Si overlayer followed by chemical oxidation in ozonated water are proposed as treatments to passivate (100)Ge surface. Obviously, these two types of treatments result in ILs of different composition, Ge oxynitride and Si oxide, respectively, which raises the question about the influence of these ILs on the interface band alignment. This quest has been addressed by IPE studies. The electron IPE spectra from (100) Ge into the most studied high-permittivity insulator HfO2 are compared in Fig. 9.4.1 for the GeNx Oy () and Si/SiOx () ILs with the corresponding spectra of the (100)Si/SiOx /HfO2 structure ( ). A distinct difference between the two semiconductor substrates consists in a shift of the spectral threshold of the electron IPE from the semiconductor valence band by e ∼ 0.4 eV towards a lower photon energy in Ge MOS samples (Afanas’ev and Stesmans, 2004c; 2006). This suggests that the difference in the bandgaps between Si and Ge (1.12 and 0.67 eV at 300 K) is almost entirely accounted for by a change in the valence band edge energy. At the same time, the composition of the IL at the Ge/HfO2 interface is seen to affect the quantum yield of electron IPE from Ge but not the spectral threshold. This observation is similar to the results for Si/HfO2 interfaces (data shown in Fig. 9.3.4) indicating that the IL may cause significant differences in the electron scattering probability, yet there are no dipoles associated with it.
•
IPE/PC yield (relative units)
106
HfO2 (100)Ge/Si/SiOx /HfO2
105
(100)Ge/GeNxOy /HfO2
Ge
104 103
Eg(HfO2) 5.6 eV
102 101 SiOx
100
e 0.4 eV
101 102
(100)Si/HfO2 1
2
3 4 5 Photon energy (eV)
6
7
Fig. 9.4.1 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 different IL composition (() SiOx ; () GeNx Oy ) as compared to observations on a n-Si/HfO2 (10 nm)/Au ( ) capacitor. The insert illustrates the effect of the SiOx IL on the Ge/HfO2 interface band diagram. Arrows indicate the onset of intrinsic oxide PC, Eg (HfO2 ), and the shift in threshold of the electron IPE from the semiconductor valence band between Si and Ge substrates, e .
•
210
Internal Photoemission Spectroscopy: Principles and Applications
The energies of the bottom of the conduction bands of Si and Ge measured with respect to the top of the HfO2 valence band are found to be the same as indicated by the coinciding hole IPE thresholds h = 3.7 ± 0.1 eV (cf. Fig. 2 in Afanas’ev and Stesmans (2004c)). Therefore, the conduction band offsets at Ge/HfO2 and Si/HfO2 interfaces are nearly the same (2 eV) and promise the Hf-oxide to be a satisfactory candidate from the point of view of electron tunnelling suppression.
Ge/Gd2O3/Au Ge/La2Hf2O7/Au Si/La2Hf2O7/Au
105 104
2 MV/cm
103
e
102 h
Eg(ox)
101 2 MV/cm Ge Y 1/3 (relative units)
(Yield)1/2 (relative units)
IPE/PC yield (relative units)
Next, with the results for Si as backup, one may wonder about the band alignment of Ge with highpermittivity oxides of interest other than HfO2 . Here, the IPE spectroscopy of interfaces between Ge and other metal oxides revealed that the barrier values are similar to that in Ge/HfO2 structures (Afanas’ev et al., 2006b). This is illustrated in Fig. 9.4.2 by comparison of electron (open symbols) and hole (filled symbols) IPE spectra for HfO2 , Gd2 O3 and La2 Hf2 O7 films grown using a MBD method (Dimoulas et al., 2005). In all the cases the barrier for electron IPE from the Ge valence band is found to be in the range 2.7–2.8 eV while the top of the valence band remains at the same energy of about 3.6– 3.7 eV below the semiconductor conduction band bottom, i.e., at the same energy as for Si/metal oxide interfaces. Thus, the IPE results suggest a similar band diagrams for all studied interfaces between Ge and wide-gap amorphous oxide insulators. Independent affirmation of this conclusion came recently
800 600 400
10
Ox
(a)
e
5 h 0
2
3 hn (eV)
4
Eg(ox)
200 (b) 0
2
3
4 5 Photon energy (eV)
6
Fig. 9.4.2 (a) IPE/PC quantum yield as a function of photon energy measured on (100)Ge MOS capacitors with 10-nm thick Gd2 O3 (circles), 7-nm thick La2 Hf2 O7 (squares) insulators, and a (100)Si/LaHfOx (10 nm) sample (triangles). Open and closed symbols correspond to positive and negative bias on the evaporated Au electrode, respectively, with the average strength of electric field in the oxide of 2 MV/cm. The insert shows the interface band diagram with the observed threshold energies of optical electron transitions indicated. Panel (b) and the insert illustrate the determination of the spectral thresholds from the power plots of the quantum yield versus photon energy. The arrows indicate the derived spectral threshold energies. Lines guide the eye.
Semiconductor–Insulator Interface Barriers
211
Table 9.4.1 Band diagram parameters (in eV, ±0.1 eV) of interfaces between (100)Ge and deposited metal oxides inferred from IPE experiments (Afanas’ev and Stesmans, 2004c; 2006; Afanas’ev et al., 2006b; Perego et al., 2006a, b). Oxide HfO2 (CVD) HfO2 (MBE) Gd2 O3 La2 Hf2 O7 Lu2 O3
Eg (ox)
e
EC
h
EV
5.6 5.9 5.9 5.9 5.8
2.7 2.8 2.8 2.8 2.8
2.0 2.1 2.1 2.1 2.1
3.7 3.7 3.6 3.7 3.7
3.0 3.0 2.9 3.0 3.0
from the determination of band offsets using IPE at the interface of Ge with Lu2 O3 (Perego et al., 2006a) and HfO2 layers deposited using different oxygen precursors (Perego et al., 2006b). This is also very prominent from the compilation of band diagram parameters inferred from IPE analysis of (100)Ge/metal oxide insulator structures listed in Table 9.4.1. Therefore, the trend observed previously at interfaces of Si with high-permittivity metal oxides seems to be followed by Ge/oxide interfaces as well. Though the fundamental (band-related) portion of the DOS at interfaces of Ge with high-permittivity oxides thus appears to be nearly insensitive to the oxide composition, the IPE data shown in Fig. 9.4.2 reveal significant differences in the quantum yield of the sub-threshold IPE, which can be associated with photoinjection of electrons into the CB tail states. This feature, already mentioned when discussing interfaces between (100)Si and RE oxides would point to some intrinsic irregularity in the oxide structure which results in a ∼1 eV down shift of the states near the conduction band bottom edge. Tracing the origin of this is of fundamental interest. As one of the hypothetical mechanisms, transitions of RE ions from the +3 to +4 oxidation state can be considered which, as suggested by a much more narrow bandgap (3.3 eV) of CeO2 compared to RE2 O3 oxides (5.6–5.9 eV, cf. Table 9.2.1), might result in a tail-like DOS near the conduction band edge (Afanas’ev and Stesmans, 2006; Afanas’ev et al., 2006b). Another important feature of Ge/oxide interfaces concerns the redistribution of the DOS as a result of thermal treatment. This is exposed in Fig. 9.4.3: annealing of the Ge/HfO2 interface at 650◦ C is found to lead to a red shift of the hole IPE threshold (filled symbols in Fig. 9.4.3) as indicated by the bold horizontal arrow, while the electron IPE yield (open symbols) appears only somewhat attenuated indicative of an (a weak) IL growth (Afanas’ev and Stesmans, 2004c). The charge state of the interface after the annealing is close to neutral and characterized by a fixed charge and interface trap densities not exceeding 1 × 1012 cm−2 . Thus, the perturbation of the electrostatic potential distribution at the interface by defects cannot be responsible for the lowering of the barrier for holes in Ge upon thermal treatment. Apparently, a GeOx -type IL grown at the interface effectively reduces the barrier. This hypothesis is supported by the close energy values of the electron states revealed by the IPE from Ge into HfO2 in the IPE/PC experiments on the Ge/GeO2 entities (Oishi and Matsuo, 1996). It is also possible that highly diffusive Ge penetrates into the HfO2 layer leading to formation of a sub-band split up from the oxide VB due to interaction of oxygen atoms with Ge. As the final point in discussing the properties of interfaces of Ge with metal oxides one should recall the early results on IPE of electrons from a Ge layer deposited on sapphire (Maillet et al., 1983). The barrier for electrons in Ge was found to be as high as 4 eV which is significantly larger than that found for other studies Ge/metal oxide structures (i.e., e ∼ 2.7–2.8 eV; cf. Table 9.4.1). The result, however, is consistent with the known upward shift in conduction band bottom energy in going from the deposited amorphous Al oxide to its bulk crystal phase (cf. Fig. 9.2.3 for Al2 O3 ). However, for the
212
Internal Photoemission Spectroscopy: Principles and Applications
IPE/PC yield (relative units)
106
Eg(HfO2)5.6 eV
105 104
Ge/GeNxOy /HfO2
103 102 101 100 101 102
2
3
4 5 Photon energy (eV)
6
7
Fig. 9.4.3 IPE yield as a function of photon energy measured with +1 (open symbols) and −1 V (filled symbols) bias on the metal electrode in n- and p-type Ge/HfO2 (10 nm)/Au MOS capacitors, respectively. The results are shown for the samples in the as-deposited state (circles) or additionally subjected to 10 min anneal in O2 at 650◦ C (squares). The arrows indicate direction of changes in the IPE spectra discussed in the text.
Ge substrate/deposited Al2 O3 structures this barrier height is unlikely to be in reach because of the low melting point of Ge, limiting the processing temperature range to T < 700◦ C, at which temperature the crystallization of alumina is unlikely to occur (crystallization is observed at T > 800◦ C; cf. Fig. 9.2.3).
9.4.2 GaAs/insulator interfaces A major obstacle encountered in the development of MOS devices on GaAs consists in the occurrence of a high density of interface states. These states ‘pin’ the Fermi level in the semiconductor thus preventing the transistor channel conductivity modulation (see, e.g., Swanson (1993) and references therein). Recently, several approaches to passivate the GaAs surface by non-intrinsic oxides have been discussed (Passlack et al., 2003; Droopad et al., 2005). Passivation by Ga2 O3 has led to a number of promising results, but the narrow gap of this oxide (∼4 eV according to the PC measurements) cannot provide a barrier at GaAs/Ga2 O3 interfaces sufficiently high to efficiently block injection of charge carriers. One might recall here earlier works on the anodically oxidized GaAs suggesting 3.7–3.9 eV high barrier between the valence band of GaAs and the conduction band of the native oxide (Yokoyama et al., 1981; Kashkarov et al., 1983). As it seems now, this onset of the photocurrent in GaAs-anodic oxide-metal structures is likely to be related to photoexcitation of Ga2 O3 -sub-network in the oxide film. For instance, the photocurrent spectra of pure Ga2 O3 grown on atomically clean GaAs surface using the molecular beam effusion exhibit the onset of intrinsic PC at around 4 eV as shown in Fig. 9.4.4 (Afanas’ev et al., 2006c). Obviously, an oxide layer with such narrow gap cannot provide energy barriers of sufficient height for electrons and holes in GaAs and, therefore, serve as a good gate insulator in GaAs device structures. As a possible solution aimed at a reduced carrier injection rate stacked Ga2 O3 /GaGdOx gate insulators are considered. Figure 9.4.5 shows spectra of electron IPE from the (100)GaAs substrate into such stack on top (Afanas’ev et al., 2004d). These exhibit a complicated structure characterized by two spectral thresholds, corresponding to the bottom edges of the Gd-oxide (the energetically highest threshold) and Ga-oxide (the energetically lowest threshold) related DOS in the oxide conduction band. The Schottky plot shown in Fig. 9.4.6 reveals an anomalously strong field dependence of the highest spectral threshold
Semiconductor–Insulator Interface Barriers Y 1/2 (relative units)
106
Yield (relative units)
105 104 103
213
Eg(Ga2O3)
300 200 100 0
3
4 hn (eV)
Current from Au
Current from GaAs
102 n-GaAs/Ga2O3/Au 101
2
3
4
5
Photon energy (eV)
Fig. 9.4.4 PC yield as a function of photon energy measured in n-type GaAs(100)/Ga2 O3 (16.2 nm)/Au MIS capacitors under voltages corresponding to different current flow directions. The determination of the oxide bandgap width Eg using the Y 1/2 –hν plot is illustrated by the insert.
associated with the Gd2 O3 sub-network suggestive of the presence of an internal electric field at the interface. Nevertheless, extrapolation to zero field allows determination of the real barrier height as the zero-field spectral threshold which is found to be close to 3 eV (Afanas’ev et al., 2004d). A close barrier value is also found in an independent IPE experiments for GaAs(100)/Gd2 O3 interface in which the Ga2 O3 IL influence is eliminated resulting in the expected weak dependence of the IPE threshold on the applied electric field (Afanas’ev et al., 2006c). Apparently, as a synthesis of all the experimental work performed so far, the most remarkable result of the GaAs (100)/metal oxide interface analysis using IPE consists in the finding of only a marginal sensitivity of the interface band diagram to the type of cation present in the amorphous oxide insulator. Indeed, a nearly identical barrier between the top of the GaAs valence band and the bottom of the oxide conduction band is found for the (100)GaAs/LaAlO3 interface (Afanas’ev et al., 2006c). This result is similar to that obtained for the already described cases of Si and Ge substrates and amorphous oxide insulators with similar width of the bandgap (5.6–5.9 eV). To be noted here is that the bulk DOS in these oxides is quite similar, with the valence band top edge dominated by the O2p states and the lowest conduction band determined by the d-states of the metal cations. It now appears that this bulk DOS in the insulator and its counterpart in the semiconductor substrates are determining the relative energy position of electron energy bands at the interface. It comes as a general trend. As GaAs has a wider bandgap than Si (1.42 versus 1.12 eV at 300 K), with the barrier height between the valence bands of two semiconductors with oxide insulators being very similar, the conduction band offset for the GaAs case will generally be somewhat lower. Though this ∼0.3 eV decrease in Ec may look insignificant, the potential danger arises from the previously mentioned band tails in the RE-based oxides. It takes little effort to see that a conduction band tail of ∼1 eV wide would bring the conduction band offset at the interface to the range EC < 1 eV which, very pertinently, is considered to be insufficient to provide reliable insulation of the semiconductor channel region. As a result, not only an enhanced leakage current but also the trapping-induced threshold voltage instability may hamper the GaAs MOSFET performance. As a remedy, there is a decided hope to improve the oxide conduction structure by admixing some group IV element (Hf, for instance) to the oxide insulator, or by finding
214
Internal Photoemission Spectroscopy: Principles and Applications GaAs/Ga2O3/Gd0.31Ga0.09O0.6
IPE/PC yield (relative units)
106 105 104 103
V (volt): 1.5 2 3 5 7 10
102 101 100 101 102 2
3
4
5
6
(Yield)1/2 (relative units)
2000
1500
Y1/3 (relative units)
(a)
1000
500
0 4.0
14 1 12 10 8 2 6 4 2 0 2.0 2.5 3.0 3.5 4.0 4.5 hn (eV)
5.8 eV
4.8 eV
4.5
5.0
5.5
6.0
6.5
Photon energy (eV) (b)
Fig. 9.4.5 (a) IPE/PC yield Y as a function of photon energy measured in n-type GaAs/Ga2 O3 (1 nm)/ Gd0.31 Ga0.09 O0.6 (63 nm)/Au capacitors under different positive voltages on the metal electrode. The determination of the bandgap width from the Y 1/2 –hν plot and the IPE thresholds using the Y 1/3 –hν plot are illustrated in panel (b) and included insert, respectively. The arrows indicate the resolved spectral thresholds.
another way to reduce the tails of DOS in the oxide. Alternatively, one might also hope to gain in the conduction band offset energy by choosing AIII BV semiconductor crystal with a substantially reduced bandgap width. Another possible solution of the indicated band offset problem at the interfaces of AIII BV semiconductors is to apply a non-oxide insulating layer with considerably larger bandgap than that of metal oxides. For instance, epitaxial growth of cubic Ca or Sr fluorides as well as their mixtures was shown to result in the electron IPE threshold from the GaAs valence band into the insulator approaching 4 eV (cf. Fig. 4.2.10) (Afanas’ev et al., 1991; 1992a). At the same time CV measurements indicate modulation of the GaAs band bending suggesting that the Fermi level of the semiconductor is at least partially unpinned. A remarkable feature of GaAs/fluoride interfaces consists in their sensitivity to the cation composition of the insulator, quite in contrast to the discussed earlier case of Si/oixde or Ge/oxide systems. This effect is
Semiconductor–Insulator Interface Barriers 3.0
215
(Gd2O3)2.9 / 0.1 eV EC(Gd2O3)
IPE threshold (eV)
2.8
EC(Ga2O3)
2.6
x: 0.31 0.26 0.21
2.4
EV(GaAs)
2.2 (Ga2O3) 2.2 / 0.1 eV 2.0 0.0
0.5 (Average
1.0 field)1/2
1.5
2.0
(MV/cm)1/2
Fig. 9.4.6 Schottky plot of the spectral thresholds corresponding to the IPE of electrons from the GaAs valence band into the conduction band of Ga2 O3 /Gdx Ga0.4−x O0.6 insulating stacks of different composition x: 0.31 (), 0.26 (), and 0.21 (). The insert illustrates the inferred energy band diagram at the GaAs/Ga2 O3 /Gdx Ga0.4−x O0.6 interface. The lines represent linear fit of the experimental thresholds.
clearly seen from the spectral curves of the field-dependent electron IPE from the valence band of GaAs into the conduction band of fluorides of different composition shown in Fig. 9.4.7 using the Y 1/3 –hν co-ordinates. All the fluoride layers were grown at 500–550◦ C on the atomically clean GaAs(111)B (As-terminated) surface using molecular-beam epitaxy of the fluoride sublimated from a solid source. The IPE spectra are modulated by the optical singularities of the GaAs substrate crystal indicated by arrows in the panel (a) and already discussed in Section 4.2. This observation makes identification of the dominant electron excitation, i.e., the electron IPE from GaAs into the insulator, straightforward. The field-dependent spectral thresholds obey the Schottky law as exemplified in Fig. 9.4.8a with the effective image force dielectric constant close to 2.0 which agrees well with the theoretical estimate based on the refractive index value εi ≈ n2 = 2.1 (Afanas’ev et al., 1991). This nearly ideal barrier behaviour indicates a low density of interface charges. The zero-field barrier height appears to be a non-monotone function of the Sr and Ca cation concentrations in the insulating layer. As one might notice, the barrier height for the intermediate composition of the fluoride appears to be the maximal as illustrated in Fig. 9.4.8b. Unfortunately, it is still difficult to interpret this observation because both CaF2 and SrF2 have a wide bandgap, 12.1 and 11.2 eV, respectively, which cannot be directly measured using conventional experimental facilities and requires vacuum ultraviolet instrumentation. Two scenarios can be discussed: first, the shift of the fluoride conduction band, and, second, variation of an interface dipole caused by different areal density of fluorine atoms bonded to the GaAs surface. Another important effect observed at the interfaces of GaAs with epitaxial fluoride layers consists in the possibility to modulate the barrier by selectively doping the near-interfacial layer of insulator with positive or negative ions (Afanas’ev et al., 1992a). In the case of fluorides this is achieved by introducing positive (Sm) or negative (Eu) substitutional RE impurities. The barrier modification becomes evident when analysing the electron IPE spectra of the interfaces selectively doped in this way. For instance (cf. Fig. 9.4.9), in the presence of Sm ions the spectral threshold of electron IPE is seen to be shifted towards lower photon energies as shown in panel (a). This is consistent with positive charge on these ions in the fluoride. The field-dependent IPE barrier shown in Fig. 9.4.9b can be modelled using potential given by
216
Internal Photoemission Spectroscopy: Principles and Applications 5 GaAs(111)B/SrF2
8 7 X7 X6
4 F (MV/cm): 3 2
0.07 0.11 0.28 0.40
(Yield)1/3 (relative units)
1 0 6
(a) GaAs(111)B/CaF2
5 4 3 2 1
F (MV/cm): 0.05 0.09 0.175 0.26 0.34 0.425
(b)
0 GaAs(111)B/Ca0.5Sr0.5F2
4 3
F (MV/cm): 0.03 0.20 0.28
2 1 0
(c) 3.0
3.5
4.0
4.5
5.0
5.5
Photon energy (eV)
Fig. 9.4.7 Cube root of the electron IPE yield as a function of photon energy at the interfaces of GaAs(111)B with epitaxial SrF2 (a), CaF2 (b), and Ca0.5 Sr0.5 F2 (c) insulators as measured in the capacitor structures with Au field electrodes under different strength of externally applied electric field F. Arrows in panel (a) indicate energies of optical transitions between the points of high symmetry in the GaAs Brillouin zone modulating the IPE yield spectral dependences.
Eq. (2.2.16) and yields an estimate for the average distance between a Sm ion an GaAs surface xc = 1 nm, which is in good agreement with the expected thickness of the Sm-doped layer of the insulator. The effect of negative charges introduced by Eu ions to the GaAs/SrF2 interface is exemplified by electron IPE spectra shown in Fig. 9.4.10 for the sample with the interfacial fluoride layer doped by 0.3 at.% of Eu. The doping shifts the onset of the electron IPE to higher photon energies and makes it nearly field-insensitive (Afanas’ev et al., 1992a). This effect can be pictured as a ‘pinning’ of the potential barrier top by a negatively charged plane located at a distance of few tens of a nanometre above the surface of GaAs photoemitter as illustrated in the insert. The electrostatic potential variation between the emitter and the charge plane would account for the observed barrier enhancement. At the same time the effect of the externally applied electric field will be minimized by a small distance between the interface plane and the charged plane which determines the spatial position of the barrier top.
Semiconductor–Insulator Interface Barriers
217
4.2
4.3 Ca0.5Sr0.5F2
4.2
4.0
4.1
3.9
4.0
CaF2
3.8
3.9
3.7
3.8
3.6
3.7
3.5
SrF2
3.4
Barrier height (eV)
IPE threshold (eV)
4.1
3.6
GaAs(111) B
3.3 0.0
0.2
0.4
0.6
0.8 0.0
3.5 1.0
0.5
(Field)1/2 (MV/cm)1/2
[Ca]/([Ca][Sr])
(a)
(b)
Fig. 9.4.8 (a) Schottky plots of the electron IPE spectral thresholds at the interfaces of GaAs(111)B with different epitaxially grown fluoride insulators. (b) Dependence of the zero-field barrier height between the valence band of GaAs and the conduction band of a fluoride as a function of cation composition of the insulator. 4.5
4 3 2
Control
F (MV/cm):
4.0
0.24 0.33 0.44 0.50 Sm2-doped
3.5
IPE threshold (eV)
(Yield)1/3 (relative units)
GaAs(111)B/Ca0.5Sr0.5F2:Sm2
1 0 3.0
3.0 3.5
4.0
4.5
5.0
Photon energy (eV) (a)
0.0
0.2
0.4
0.6
0.8
(Field)1/2 (MV/cm)1/2 (b)
Fig. 9.4.9 (a) Cube root of the electron IPE yield as a function of photon energy at the interface between GaAs(111)B with epitaxial Ca0.5 Sr0.5 F2 insulator with the interface layer of the fluoride doped with 0.1 at.% of Sm. (b) Schottky plot of the electron IPE spectral threshold in the control GaAs/Ca0.5 Sr0.5 F2 sample () and that with Sm doping indicated above ().
9.4.3 SiC/insulator interfaces Thanks to its wide bandgap (2.38–3.25 eV for different polytypic modifications of SiC, Choyke (1990)), high electron saturation velocity and large thermal conductivity, SiC is seen as a semiconductor material capable of extending the application area of MIS devices to larger voltages, higher frequencies, and higher temperatures. Thermally grown SiO2 on SiC provides excellent electrical insulation thanks to high interface barriers. Electron IPE measurements were already discussed in Section 4.1 and their major
218
Internal Photoemission Spectroscopy: Principles and Applications
(Yield)1/3 (relative units)
2 -
GaAs(111)B/SrF2:Eu2
1 F (MV/cm): 0.15 0.21 0.26 0.32 0 3.5
4.0
4.5
5.0
5.5
Photon energy (eV)
Fig. 9.4.10 Cube root of the electron IPE yield as a function of photon energy at the interface between GaAs(111)B with epitaxial SrF2 insulator with the interface layer of the fluoride doped with 0.3 at.% of Eu. The insert illustrates the proposed scheme of the interface barrier perturbation by negatively charged centres associated with Eu dopant.
IPE yield (relative units)
40
30
20
IPE yield (relative units)
result consists in a polytype-independent (within the measurement error of 0.1 eV) 6-eV energy barrier between the top of the SiC valence band and the bottom of the oxide conduction band (the barrier 3 in Figs 4.1.3 and 4.1.4) (Afanas’ev et al., 1996a). Later this conclusion gained an independent support based on the hole IPE threshold determination between the valence band tops of SiC and SiO2 (Afanas’ev and Stesmans, 2000b; Afanas’ev et al., 2004c). As one can see from the spectral curves shown in Fig. 9.4.11, 4H–SiC
1.0 Laser Excitation
x10 6H–SiC
0.5
0.0 2.4
2.5 2.6 hn (eV)
2.7
10
0 2.0
2.2
2.4 2.6 2.8 3.0 Photon energy (eV)
3.2
3.4
Fig. 9.4.11 Hole IPE yield as a function of photon energy for a p+ -6H SiC MOS structure (na ≈ 1018 cm−3 ) with a 100-nm thick oxide at different electric field strengths in the oxide (in MV/cm): 0.5 (), 1 (), 2 (3), 3 (), 4 (), and 5 ( ). The IPE yield for the p-4H SiC MOS structure (na = 4 × 1016 cm−3 ) with 100-nm thick oxide is shown for the oxide field of 4 MV/cm ( ). The insert shows the spectral curves measured under laser excitation with an applied oxide field of 4 MV/cm in p-6H SiC (na = 4 × 1016 cm−3 ) (), p-4H SiC (na = 4 × 1016 cm−3 ) ( ), and p+ -6H SiC (na ≈ 1018 cm−3 ) () MOS structures. The lines guide the eye.
•
•
Semiconductor–Insulator Interface Barriers
219
a 2.9-eV barrier for holes is observed which, in combination with the just mentioned 6 eV electron IPE barrier for the same initial state yields the oxide bandgap of 8.9 eV, the value well known for the thermally grown SiO2 (DiStefano and Eastman 1971b; Adamchuk and Afanas’ev 1984). In agreement with this assignment are also the ‘tails’ in the hole IPE spectra shown in the insert in Fig. 9.4.11 which are consistent with the similar features observed in the hole IPE spectra from Si into SiO2 (cf. Fig. 4.1.8). With the oxide valence band located at 2.9 eV below the valence band in all the studied SiC polytypes (Afanas’ev et al., 1996a), the energy of the semiconductor conduction band can be calculated simply by adding the SiC bandgap width leading to the SiC/SiO2 interface band diagram shown in Fig. 9.4.12 for 3C , 15R , 4H , and 3C SiC. The conduction and valence band offsets appear to be close, i.e., the bandgap of SiC is located in an optimal way to ensure the high insulation performance of SiO2 . The revealed by IPE high interface barriers are consistent with good insulation quality of the oxide thermally grown on SiC (Friedrichs et al., 1994). However, the SiC-oxide interface quality in terms of interface traps and charges appears to be significantly inferior to that of the Si/SiO2 system. High interface states density was ascribed to the presence of carbon clusters of different size and the SiO2 specific interface defects (Afanas’ev et al., 1996a; 1997a; 2004c, e). It might be noticed, for instance, that the energy level of 2.8-eV deep oxide traps lies close to the conduction band of the wide bandgap polytypes of SiC leading to a high density of acceptor traps at 4H SiC/SiO2 interfaces (Afanas’ev et al., 1997a; 2000). To avoid the oxide trap influence, one might opt for using of more narrow bandgap 3C SiC in electronic devices (Ciobanu et al., 2003) but the carbon-related states and, in particular, their donor-type DOS component in the lower part of the SiC bandgap still remain a significant problem.
7
Evac
EC
6 5
Energy (eV)
4 3
EC
2.75
2.8 6.0
4H– 6H– 15R– 3C–
2
4.5
1 0 1
8.9
3.25 8 EV 2.9
2 3 4
SiC
SiO2
EV
Fig. 9.4.12 Major components of electron state spectrum at SiC/SiO2 interface as determined from the IPE measurements on four polytype modifications of SiC (3C , 15R , 4H , and 6H ). All the energies indicated in electron volt for the case of 4H SiC/SiO2 interface with the origin of the energy scale placed to the top of the SiC valence band. The energy of the conduction band bottom for three other SiC polytypes are indicated by thin lines. The vacuum level Evac is shown assuming the SiO2 electron affinity of 0.8 eV. The energy levels of electron states in the SiO2 gap stem from the intrinsic oxide defects (2.8 eV below the conduction band of SiO2 ), the valence band ‘tails’ of SiO2 (≈8 eV), and the carbon-cluster-related state which, depending on the sp2 -bonded cluster size, may cover the entire bandgap of SiC with the highest DOS in its lower half, i.e., at 4.5 eV below the oxide conduction band bottom.
220
Internal Photoemission Spectroscopy: Principles and Applications
In addition to the intrinsic interface defects, application of high electric fields to the SiC surface drives the conventional SiO2 gate insulators to the reliability limit (Agarwal et al., 2004). Therefore, replacement of the thermal oxide by a suitable high-permittivity insulator also in the SiC case appears to be of much interest (Afanas’ev et al., 2004e). A favourable element with respect to the SiC/oxide structures consists in the fact that the requirements on the downscaling of the gate oxide thickness are still relaxed as compared to the advanced Si technology, which allows more freedom in the gate stack engineering than in the case of Si. Thus, research has been carried out on SiC substrates combined with high-permittivity oxide insulating layers. As it appears, direct deposition of high-permittivity insulators onto SiC surfaces leads to interfaces with untolerably high trap and charge densities (Afanas’ev et al., 2003b). But, as a rescue, improvement could come from another side. Indeed, over the investigations carried out, a substantial improvement of the SiC/thermal SiO2 interface quality is observed when limiting the thickness of the SiO2 layer to few nanometres (Afanas’ev et al., 2003b). The latter is likely related to a limited supply of carbon from the SiC surface layer consumed during thermal oxidation which otherwise would cluster and create additional interface states. Therefore, a stack composed of an ultra thin SiO2 layer with a high-permittivity metal oxide insulator on top appears to be a viable option for a suitable gate insulator for SiC, as demonstrated by the low trap density and low leakage current at both gate bias polarities. The electron energy band alignment at the interface of 4H SiC with a SiO2 (3.9 nm)/HfO2 gate stack appears to be the same as encountered at the Si/SiO2 (20 nm) interface. This can be seen from the IPE spectra shown in Fig. 9.4.13, in which the indicated spectral thresholds 1 , 2 and 3 correspond to the excitation of electrons from the occupied SiC conduction band states in accumulation, the SiC/SiO2 interface carbon-related defects (Afanas’ev et al., 1996a), and the valence band of SiC, respectively (see also Section 4.1 and Figs 4.1.3 and 4.1.4). The barrier 3 = 6.0 eV is not measurable in the SiO2 /HfO2 samples (, ) because of the intrinsic PC of HfO2 which has a lower threshold (5.6/5.9 eV) and a considerably higher photocurrent quantum yield. The SiC/SiO2 -like band diagram is preserved even after high-temperature (800◦ C) anneal in N2 + 5% O2 as indicated by the IPE spectrum shown in Fig. 9.4.13 () exposing the same spectral threshold values.
IPE/PC yield (relative units)
104
SiO2 Eg(HfO2) SiO2/HfO2 SiO2/HfO2/800CPDA
103 102 101
3
100 101
1 2
102 103 104
Eg(4H–SiC) 3
4H–SiC(0001)
4 5 Photon energy (eV)
6
Fig. 9.4.13 IPE spectra measured in n-type 4H SiC MOS capacitors with different insulators: 20 nm thick thermal SiO2 (), a stack of SiO2 (3.9 nm)/HfO2 (20 nm) (), and the latter stack after 10 min PDA at 800◦ C in 5% O2 + N2 (). The spectra are measured under +3 V bias on the metal (Au) electrode. The IPE yield is defined in terms of photocurrent normalized to the incident photon flux. The arrows 1 –3 correspond to the IPE thresholds as discussed in the text. The bandgaps of 4H SiC and HfO2 are also indicated.
Semiconductor–Insulator Interface Barriers
221
Table 9.4.2 Conduction and valence band offsets, EC abd EV , at the interfaces of Si and SiC with different insulators (in eV) (Afanas’ev et al., 2004c). Insulator
SiO2
Al2 O3
ZrO2
HfO2
Eg (eV)
8.9
6.2
5.5
5.6/5.9
Semiconductor
EC /Ev
EC /EV
EC /EV
EC /EV
3.1/4.7 3.6/2.9 3.0/2.9 2.95/2.9 2.7/2.9
2.1/3.0 2.6/1.2 2.0/1.2 1.95/1.2 1.7/1.2
2.0/2.5 2.5/0.5 1.9/0.5 1.85/0.5 1.6/0.5
2.0/2.5 2.5/0.7 1.9/0.7 1.85/0.7 1.6/0.7
Si 3C SiC 15R SiC 6H SiC 4H SiC
Bold numbers indicate experimental bandgap and band offset values directly measured using internal electron photoemission and PC spectroscopy (accuracy ±0.1 eV). The other values are inferred from the known conduction band offsets between SiO2 and the indicated metal oxides.
Therefore, the band offsets at interfaces of SiC with metal oxide insulators can be evaluated from the IPE results concerning the energy band diagram of SiC/SiO2 interfaces and using the value of about ≈1.15 eV for the energy difference between the CB bottom of SiO2 and of the high-permittivity oxides. The latter can be evaluated, for instance, as the difference between the thresholds of electron IPE from Si into these materials (cf. Fig. 9.3.2). As already demonstrated in the case of (100) Si substrates, a thin SiO2 IL causes no additional shift of the bandgap edges of a high-permittivity insulator with respect to the semiconductor bands. The results obtained using this model are summarized in Table 9.4.2 for Si and four different polytypic modifications of SiC (3C , 15R , 6H , and 4H ) and four different insulating oxides: thermally grown SiO2 and deposited Al2 O3 , ZrO2 , and HfO2 (Afanas’ev et al., 2004c). The important feature revealed by the inferred SiC/metal oxide band offset values is the relatively low valence band offset EV , which appear to be smaller than the required ∼1 eV limit considered to be sufficient for electrical insulation. Therefore, an additional IL is necessary to provide a barrier of sufficient height to suppress the hole injection from SiC into the oxide. In the case of SiO2 /metal oxide stacks, the SiO2 layer will suite perfectly as hole injection blocking layer because of the sufficiently high valence band offset EV = 2.9 eV of the various SiC polytypes with SiO2 (cf. Table 9.4.2). Worth adding in conclusion is that the direct deposition of nitride-based insulators on SiC is unlikely to provide a VB offset sufficient to block hole injection. The VB offset appears to be nearly absent at the 6H SiC/AlN interface (Afanas’ev et al., 2004c), while SiC/Si3 N4 contacts exhibit large leakage currents and charge instability (see, e.g., Berberich et al., 1998). Finally, we also mention that the question regarding the behaviour of interfaces of other wide-gap semiconductors (like GaN or diamond) still remains open because no reliable band diagram analysis of their interfaces is available yet (see, e.g., Gila et al., (2004) for review concerning GaN insulator structure properties). Interfaces of these materials obviously represent important objects for IPE spectroscopy application in the near future.
9.5 Contributions to the Semiconductor–Insulator Interface Barriers The overviewed results clearly demonstrate the suitability of the IPE technique for quantification of the interface barriers of various insulators. Though the list of the studied MOS material systems, without doubt, will further be extended in the near future, several important conclusions going beyond the simple barrier quantification can already be established.
222
Internal Photoemission Spectroscopy: Principles and Applications
First, as it appears to occur at the interfaces of high-permittivity insulators with Si, Ge and GaAs, the atomic (cation) composition of the oxide and IL have a negligible effect on the band alignment if the oxide bandgap have close widths (5.6–5.9 eV for typically used oxides). As these interfaces contain only a low density of charged defects (<1013 cm−2 ≈ 10−2 ML effective surface coverage) it is likely that the revealed trend here corresponds to the intrinsic (i.e., not affected by Coulomb and/or dipole contributions) band alignment at the semiconductor/oxide interface, and, therefore, is expected to be a reproducible, independently of the processing technology applied, characteristic of the interface. In this context it is not amiss reiterating here the argument (Tung, 2001) that the low density of electron states available in the semiconductor gap would preclude the ‘tailing’ of any measurable DOSs into the insulator gap in the vicinity of the Fermi level. Therefore, the application of ‘the metal-induced gap state’ approach imported from the Schottky barrier theory (Tersoff, 1984a, b) to describe the devicerelevant semiconductor–insulator interfaces would be unsubstantiated. Rather, the picture in which the distribution of the charge at the interface is seen to be the same as in the bulk of the solids in contact (Tung, 2001; Harrison, 1977; 1981; Kraut, 1984) seems to be more relevant. As the mutual penetration of the unoccupied band states of the semiconductor and the insulator at the interface does not lead to any charge transfer, it is unlikely to affect the band alignment directly. One suggestion is that the ‘dipole’ contribution may potentially arise in this case from the ‘tailing’ of occupied (bonding) states from each of the two solids into one another, which will give rise to two compensating dipoles as schematically illustrated in Fig. 9.5.1. From the oxide side of the interface, the dominant contribution to the dipole will likely be provided by oxygen 2p lone-pair states near the top of the valence band (Lucovsky, 2002). Thus, one may expect the interface dipole component stemming from oxide states to be approximately the same in the studied oxides with exception, perhaps, of dense-packed ones (e.g., SiO2 , high-temperature phases of Al2 O3 ). From the semiconductor side of the interface, the ‘tailing’ of valence states into the oxide gap is unlikely to produce significant charge transfer because of the high interface barrier (EV ≈ 2.5 eV). Probably then, the states of the oxide valence band will provide the dominant contribution, depending on their density and type of the wavefunction. In the case of Si substrate, the edge of the oxide valence states is found at 2.4–2.6 eV below the semiconductor valence band top. This also appears to be true for oxides with a more narrow gap like TiO2 and Ta2 O5 (Afanas’ev et al., 2005a). Moreover, the band offsets at the interfaces of SiTiO3 and BaTiO3 with Si(100) were also found to fall in the same energy range (Amy et al., 2004). In the last case the effect of irradiation-induced oxide charging is likely to be insignificant because of the negative conduction band offset at these interfaces. For the oxides with wider gaps the XPS/UPS band offset data cannot be used
EC Semiconductor Insulator EC EV
EV
Fig. 9.5.1 Schematic energy band diagram of the semiconductor–oxide interface with arrows indicating electron density transfer between the occupied states of the two solids in contact, which process is suggested as determining the band alignment at the interface.
Semiconductor–Insulator Interface Barriers
223
for this analysis unless corrected for the oxide charging effects (Nohira et al., 2002). On the basis of available data, the electron density ‘tailing’ from Si into the oxide might be expected to be very similar for different oxide materials. As a result, the valence band offsets of insulators with close dielectric constants (κ ≈ 15–20) will generally be insensitive to the type of oxide cation(s) if one semiconductor material is considered. Next, the influence of the IL on the semiconductor–oxide band alignment appears to be insignificant, at least in the case of low interface trap/charge densities. One may consider this as a partial case of the semiconductor band offset ‘transitivity’ rule (cf. Eq. (3.1.4) in Tung (2001)). In other words, the dipole barrier components related to the electron density ‘tailing’ from the IL into the semiconductor and into the oxide exactly (within the ±0.1 eV experimental accuracy limit) compensate each other. More interesting, perhaps, is to address possible reasons for the negligible influence of the IL on the field-dependent barrier height. Here, we may start from remarkable notion that a number of simulations (Casperson et al., 2002; Cimpoiasu et al., 2004) are essentially based on assuming an influence of the IL on the barrier height in an attempt to modify the transparency of tunnelling barriers. But, as it comes out now, the effect appears to be unobservable. Apparently, the total DOS at the interface is only marginally sensing the states arising from a 1–2 nm thick IL because the number of the contributing atoms in the IL is much less than that in the rest of the oxide insulator. As a result, the states belonging to the oxide conduction band extend to the interface region and determine the ultimate barrier characteristics. Actually, it was suggested long ago that the electronic structure of barriers of few atomic layers in thickness cannot be described by the bulk band scheme so the electrons excited in an emitter do not see the corresponding barrier (Card and Rhoderick 1971; Arora et al., 1982). This photoemission picture essentially employs the band character of states at the interface, which is dominated by the bulk contributions of the semiconductor and oxide. Would the carrier injection be controlled by some trap-mediated process rather than by the band-to-band tunnelling transitions, the effect of the IL might then be considerable because of the localized character of the involved electron states (defects, impurities, dopants) (Afanas’ev et al., 2002a). The variable components of semiconductor–insulator barriers are found to be associated either with dipoles induced by highly electronegative atoms (F, Cl) or, else, with uncompensated charges of electronic or ionic origin. In the first case the formation of dipole seems to follow the conventional scheme of double electrical layer caused by charge transfer in the ordered array of polar bonds between surface atoms of a substrate and the first layer of adsorbate or the collector material. What appears to be new when discussing the interfaces is that the density of atoms contributing to the dipole is controlled by a number of additional factors like kinetics of chlorine incorporation to the Si/SiO2 interface or the strain-induced loss of interfacial fluorine in Si/CaF2 structures. Simple description of interfacial dipoles based on the adsorption-desorption balance appears to be inadequate. The action of uncompensated charges on the interface barrier is unique for interfaces of dielectrics because this configuration cannot be kept stable at a clean surface of a metal or semiconductor. As nearly all the available bonds of substrate surface atoms are saturated at the interface by atoms of the second phase, the charged centres cause not a dipole formation but create a long-range Coulomb potential. As a result, even a marginal, in terms of surface atom density coverage of the interface by charged traps or ions (<1013 cm−2 , i.e., <1% of a monolayer), may lead to significant variation of the interface barrier height.
CHAPTER 10
Electron Energy Barriers between Conducting and Insulating Materials
At first sight the energy barrier between a metal and an insulator looks very similar to that at the metal surface except of a different (typically lower) energy an electron needs to enter the conduction band of the insulator than that necessary for emission into vacuum. Therefore, one might expect the barrier height for electrons at the metal–insulator interface to be smaller than the metal work function by the value of electron affinity of the insulating collector material (Mott and Gurney, 1946). For barriers of sufficient height, emission of holes from a metal seems to have a low probability because of high density of occupied electron states above the energy corresponding to the top edge of the insulator valence band. This is expected to result in a low lifetime of holes and, accordingly, lead to a low quantum yield of the hole internal photoemission (IPE) (Powell, 1969). Indeed, there are no experimental indications of hole IPE from a metal into another solid over a barrier with height exceeding 2 eV. The simple vacuum-like scenario, however, is rarely followed by real interfaces. Even in the case of the thermally grown oxide on silicon routinely considered to be the most close approach to an ideal insulator, substantial deviations of the metal/insulator barrier behaviour from that predicted by the image-force model were observed leading to a hypothesis regarding formation of a polarization layer (Wang and DiStefano, 1975). Several components of the polarization layer were revealed experimentally at metal– SiO2 interface including adsorption-induced dipoles (Lundstrom and DiStefano, 1976a, b), interface charges (Wang and DiStefano, 1975), and formation of an interlayer (Solomon and DiMaria, 1981). It appears that even subtle details of the interface fabrication, in particular thermal treatments, have considerable impact on the barrier height which is tentatively attributed to the influence of uncontrolled charges and impurities. The issues concerning band alignment become even more important at the interfaces between the highpermittivity insulators and the conducting gate electrode materials in electronic devices. The barrier height for electrons at the gate/insulator interface is significant not only from the point of view of the injection suppression but, also, it is needed to control the transistor threshold voltage. The work function of the metal electrode directly affects the electric field at the surface of the semiconductor and influences the charge carrier density in the transistor channel. It needs to be also mentioned that the interface barrier formation at the conductor/insulator interface is unlikely to be similar to the previously 224
Electron Energy Barriers between Conducting and Insulating Materials
225
discussed semiconductor/oxide interfaces because the high electron density close to the Fermi level may lead to an enhanced polarization layer contribution to the barrier. The near-interfacial charges may potentially contain contributions of different origin, ranging from the ‘intrinsic’ metal-induced gap states (Tersoff, 1984a, b) to the impurity-related charges and dipoles. The role of each of the interface charge components remains largely unknown raising questions about the relative importance of the intrinsic and the extrinsic contributions to the barrier height. The results that will be reviewed below suggest that, unlike semiconductor/high-permittivity oxide interfaces, the gate-oxide chemical reactions and foreign atoms may add a considerable (about 1 eV) contribution to the observed barrier height. 10.1 Interface Barriers between Elemental Metals and Oxide Insulators 10.1.1 Metal–SiO2 interfaces In general, sufficiently abrupt interfaces between SiO2 and elemental metals follow the expected trend of barrier height increase with increasing metal work function. This is seen from the data compiled in Fig. 10.1.1 using IPE barrier height data available in the literature (Deal et al., 1966; Powell and Beairsto, 1973; Lundstrom, 1976a, b; Afanas’ev et al., 2002a; Afanas’ev and Stesmans, 2004a) and the values of the metal work function from Table 2.1 in Rhoderick (1978). At the same time it is observed that the spread in the barrier height between the metals with close work function may exceed 0.5 eV which is huge effect when considering application of a metal as gate electrode material in electron devices. These variations suggest that the barrier is not uniquely defined by the electronic structure of the contacting materials but, also, contains additional contributions which are routinely ascribed to the already mentioned polarization layer at the interface. One of the important factors responsible for the interface barrier variation is associated with chemical interaction between metal and oxide which may lead to incorporation of charges and processing sensitive interface dipoles. The first direct evidence of such effect was provided by Solomon and DiMaria (1981) who reported a 0.25 eV increase of the Al/SiO2 barrier height upon annealing in forming gas (N2 + 10% H2 ) at 400◦ C. In fact, the influence of the thermally induced metal oxide reaction may be even larger as the data presented in Fig. 10.1.2 for the Mo/SiO2 interface suggest. The figure shows the Schottky plot of the electron IPE spectral thresholds measured in samples subjected to a rapid (30 s) Ag
IPE barrier (eV)
4 Mo 3
Pd
Pt
Cu
Au
W
Ni
Al Mg SiO2
2
3
4
5
Work function (eV)
Fig. 10.1.1 Barrier height between the Fermi level of different metals and the conduction band of thin SiO2 layer as a function of the vacuum work function of the metal. Line shows the ideal case = WF − χ where the electron affinity χ of the oxide is assumed to be equal to 0.8 eV (WF: work function).
226
Internal Photoemission Spectroscopy: Principles and Applications 4.5
IPE threshold (eV)
Mo/SiO2
4.0 1050C 3.5
700C As-deposited 0
1 (Field)1/2
400C 2
3
(MV/cm)1/2
Fig. 10.1.2 Schottky plot of electron IPE spectral threshold from a sputtered Mo into a 10-nm thick SiO2 layer on Si(100) as measured after 30 s annealing at different temperatures. Lines guide the eye by indicating behaviour of the barrier in differently processed samples.
annealing in dry nitrogen at increasing temperatures. Despite refractory nature of the molybdenum, a progressive increase of the barrier height is clearly seen which exceeds 0.5 eV at 1050◦ C. Even more complex barrier behaviour is encountered in the case of chemically active metals which may lead to the formation of additional chemically induced dipoles at the interface. For instance, metals of platinum group are known to create positive dipoles in the presence of hydrogen (Lundstrom and DiStefano, 1976a, b; 1996). When such a material is applied as photoemitter to an insulating collector, reversible barrier behaviour is expected to occur with respect to introduction and removal of H-containing gases. However, in some cases chemical reactions may hamper reversibility leading to rather complicated picture. The latter is exemplified in Fig. 10.1.3 which shows the Schottky plot for Ru electrodes deposited on SiO2 and subjected to 20 min annealing in the forming gas (N2 + 10% H2 ) at 400◦ C ()
Ru/SiO2
4.6 IPE threshold (eV)
O2 4.4 O2/N2 H2 4.2 4.0
N2 H2
3.8 0
1
2
3
(Field)1/2 (MV/cm)1/2
Fig. 10.1.3 Schottky plot of electron IPE spectral threshold from a 10-nm thick layer of deposited Ru into a 10-nm thick SiO2 layer on Si(100) as measured after 20 min annealing at 400◦ C in the forming gas (N2 + 10% H2 ) at 400◦ C () or 1 min treatment in O2 at 520◦ C (), or the sequence of the oxidizing and reducing thermal treatments. Lines guide the eye by indicating behaviour of the barrier in samples processed using different annealing schemes.
Electron Energy Barriers between Conducting and Insulating Materials
227
or 1 min treatment in O2 at 520◦ C () (Pantisano et al., 2006a). A strong effect of the annealing ambient composition which consists in variation of interface barrier height by almost 0.5 eV is clearly seen from these data. Moreover, when the forming gas annealing is applied after the oxidizing treatment () the barrier is still higher than in the ‘no-O2 ’ case () indicating a kind of irreversible chemical modification of the Ru/SiO2 interface. The problem in analysis of the barrier data shown in Fig. 10.1.3 consists in deviation of its field dependence from the classical image-force picture which cannot be interpreted straightforwardly. First, there is an option that oxidation of Ru will lead to the formation of a new phase at the interface as indicated by the compositional analysis of the Ru/oxide interface (Li et al., 2007). Second, taking into account microcrystalline structure of a thin (10 nm) metal layer, the chemical reactions may occur in a laterally non-uniform manner leading to a ‘spotty’ interface with local variation of the barrier height. Finally, in the framework of laterally uniform barrier picture, the transition of the Schottky plot in Fig. 10.1.3 from one linear portion to another may be interpreted as formation of an interlayer with the energy of the conduction band bottom edge different than that one in the rest of SiO2 collector (DiStefano, 1976). To distinguish between these mechanisms additional physical information regarding interface barrier structure is necessary. Worth of mentioning, that similar effects may be expected to occur at the interfaces of the chemically active metals with other insulators. For instance, dipoles recently reported at Re/HfO2 interface (Liang et al., 2006) follow the pattern of behaviour of the above described hydrogen-induced ones. The sensitivity of the barriers at the interfaces between metals and SiO2 to fabrication conditions not only explains the considerable spread of experimental points in the barrier height–work function diagram shown in Fig. 10.1.1 but, at the same time, indicates the fundamental difference between interfaces of insulators with conductors and semiconductors. In the latter case the barriers appear to be remarkably stable against variations caused by changes of interlayer composition (cf. Figs 9.3.4, 9.3.7 and 9.4.1). By contrast, the metal–insulator contacts exhibit great sensitivity to even minor changes in the interface structure or composition, metal deposition technique, and the sample processing. If one neglects chemical conversion of the metal surface layer into another chemical compound, the major effect seems to be associated with incorporation of charges to the insulating collector material because all the charges on the opposite site of the interface will be screened by free electrons of the metal. Therefore, it is logical now to address interfaces of elemental metals with insulators of other than SiO2 chemical composition. 10.1.2 Interfaces of elemental metals with high-permittivity oxides Comparison of the energy barriers encountered at interfaces between different metals and highpermittivity insulating oxides to those occurring at metal/SiO2 interfaces indicates several significant differences between the two types of insulators (Afanas’ev et al., 2002a, d; Afanas’ev and Stesmans, 2004a). At first one might suppose that the lower conduction offset at the Si/insulator interface with respect to the Si/SiO2 case will lead to an equal lowering of the metal/insulator barrier as compared to the interface of the same metal with SiO2 . However, in reality the difference between the barriers encountered at the interfaces of different metals with Si and high-permittivity oxides appears to be much smaller than expected. The latter is exemplified by the electron IPE spectral curves shown in Fig. 10.1.4 as the Fowler plot (Y 1/2 –hν) for several metals thermally evaporated onto ZrO2 (Afanas’ev et al., 2002a). The barrier lowering with respect to the interfaces of the same metals deposited onto SiO2 appears to be approximately ∼0.5 eV. It can also be noticed that the spectral threshold difference between the highest (Au) and lowest (Mg) work function metals is only ∼1 eV in the case of ZrO2 , while it amounts to nearly 2 eV for SiO2 (Deal et al., 1966). This result indicates that the interface barrier in the case of ZrO2 is not uniquely determined by the work function of the metal but contains some other significant contribution(s). An important observation in revealing the origin of additional barrier contributions at the interfaces between metals and high-permittivity oxides consists in a limited sensitivity of the barrier height to the
228
Internal Photoemission Spectroscopy: Principles and Applications
(IPE yield)1/2 (relative units)
Mg
Al
Ni
4 3 Cu Au
Si Ox Me 2
1 ZrO2 0 2.0
2.5
3.0
3.5
4.0
Photon energy (eV)
Fig. 10.1.4 Square root of the IPE yield from the gate metal as a function of photon energy (the Fowler plot) for MOS structures with different metals deposited on a 5-nm thick as-deposited ZrO2 layer. The scheme of electron IPE transitions is shown in the insert. The strength of electric field in the oxide is 2 MV/cm, with the metal biased negatively. The lines illustrate the determination of the IPE spectral thresholds.
energy of the oxide conduction band. One may notice that, when measured with respect to the silicon valence band top, the bottom of conduction band in Al2 O3 is lying energetically by 0.15 eV higher than that in ZrO2 or HfO2 (cf. Fig. 9.3.2 for the case of electron IPE from Si into these insulators). However, the spectral threshold of electron IPE from the Fermi level of Au into the oxide conduction band is approximately 0.5 eV higher in Al2 O3 than in ZrO2 as the spectral curves shown in Fig. 10.1.5 indicate. It is likely that some additional contribution to the barrier is more sensitive to the chemical composition of the oxide than to its electronic structure.
(IPE yield)1/2 (relative units)
Al 4
Au dhn 0.02 eV
3 Si Ox Me 2
1 Al2O3 0 2.0
2.5
3.0
3.5
4.0
4.5
Photon energy (eV)
Fig. 10.1.5 Square root of the IPE yield from the metal as a function of photon energy for MOS structures with Al and Au electrodes deposited on a 5-nm thick as-deposited (open symbols) and oxidized at 800◦ C for 10 min (filled symbols) Al2 O3 insulator. The strength of the electric field in the oxide is (in MV/cm) as follows. Al on as-deposited oxide: 0.2 (), 0.5 (), 1.0 (), 1.5 (), 3.0 (3); Al on oxidized Al2 O3 : 0.5 ( ), 1.0 (), 2.0 (), 4.0 (); Au on as-deposited oxide: 0.5 (), 1.0 (), 2.0 (), 3.0 (), 4.0 (3), metal bias is negative.
•
IPE spectral threshold (eV)
Electron Energy Barriers between Conducting and Insulating Materials
4.0
229
Au ZrO2
Al2O3 Au
3.5 (100)Si
(100)Si 3.0 Al
Al
2.5 0
1
2 0 (Field)1/2
(a)
1
2
(MV/cm)1/2 (b)
Fig. 10.1.6 Schottky plot of the spectral thresholds for IPE into the conduction band of Al2 O3 (a) and ZrO2 (b) layers from the Si valence band states (, ), and from the states near the Fermi level of Al (, ) and Au (, ). Open and filled symbols correspond to the as-deposited (unannealed) state and after treatment in O2 for 10 min at 800◦ C, respectively. The lines show linear fits to the threshold data.
•
Next, a deviation of the IPE spectra from the Fowler law in the near-threshold region is seen in Figs 10.1.4 and 10.1.5 suggests a lateral non-uniformity of the interfacial barrier. Two more features are revealed by these data. First, the pre-metallization treatment in O2 at a temperature as high as 800◦ C does not change the metal/insulator barrier significantly as compared to the as-deposited state (cf. data for Al in Fig. 10.1.5). Second, the electric field has only a weak effect on the spectral thresholds (within the indicated accuracy limit of 0.1 eV) suggesting a weak (if measurable) image-force interaction at all the high-permittivity oxide/metal interfaces. As can be seen from the Schottky plots shown in Fig. 10.1.6 for Al2 O3 (a) and ZrO2 (b), the field-induced barrier lowering is much weakened at the interfaces of Au and Al with the insulator as compared to the interfaces of Si with the same oxide, both in the as-deposited state (open symbols) and after 800◦ C pre-metallization anneal (filled symbols) (Afanas’ev and Stesmans, 2004a). This can be explained by ‘pinning’ of the barrier top by a plane of negative charges located close to the metal surface, which would dramatically reduce the influence of the electric field on the barrier height. A similar ‘disappearance’ of the image-force effect was already discussed in the previous chapter to explain IPE results in GaAs(111)B/SrF2 structures after doping of the near-interfacial insulator layer with Eu (cf. Fig. 9.4.10). It is likely then that the observed barrier increase at the metal/oxide interfaces as compared to the value expected from the metal work function value is caused by a negative charge near the interface associated with interaction of some chemical species with the oxide. At the same time, as the high-temperature oxidizing treatment has no measurable influence on the barrier height, oxygen deficiency of the oxides is unlikely to be among the most important factors affecting the barrier. Barrier heights between the Fermi level of a metal and the oxide conduction band are listed in Table 10.1.1 for several studied insulator/metal pairs together with the barrier height for electrons in the Si valence band V . Now one can analyse the barrier heights at different metal/oxide interfaces as a functions of the polycrystalline metal work function. The case of Al2 O3 closely resembles the ‘classical’ SiO2 behaviour as exemplified by the barrier height–work function plot shown in Fig. 10.1.7. The data for high-temperature () (DiMaria, 1974; Ludeke et al., 2000a, b) and low-temperature () (Afanas’ev and Stesmans, 2004a) amorphous deposited layers of alumina are close to the results obtained from IPE of electrons into crystalline Al2 O3 (sapphire) () (Viswanathan and Loo, 1972a, b) indicating that the sensitivity of the barrier height to atomic structure of the alumina is limited. This conclusion
230
Internal Photoemission Spectroscopy: Principles and Applications
Table 10.1.1 Interface barrier heights between the valence band of (100)Si or the Fermi level of several metals and the conduction bands of SiO2 , Al2 O3 , ZrO2 , and HfO2 insulators. Emitter Insulator SiO2 (±0.05 eV) Al2 O3 (±0.1 eV) ZrO2 (±0.1 eV) HfO2 (±0.1 eV)
(100)Si
Mg
Al
Ni
Cu
Au
4.25 3.25 3.1 3.1
2.50 2.6 2.6 2.5
3.15 2.9 2.7 2.5
3.70 3.5 3.2 3.4
3.85 3.6 3.25 3.3
4.10 4.1 3.5 3.7
W
IPE barrier (eV)
4
Au Ag Al
Cu
Ni
3 Mg Al2O3 3
4
5
Work function (eV)
Fig. 10.1.7 Barrier height between the Fermi level of different metals and the conduction band of Al2 O3 as a function of the vacuum work function of the metal. The results are shown for high-temperature treated layers of alumina on Si () (DiMaria, 1974; Ludeke et al., 2000a, b), grown on Si at 300◦ C by atomic layer deposition () (Afanas’ev and Stesmans, 2004a), and for the polished single-crystal sapphire surfaces () (Viswanathan and Loo, 1972a, b). Line guides the eye.
might look surprising in view of the results indicating an increase of the Au/Al2 O3 by nearly 0.5 eV after high-temperature crystallization of the film shown in Fig. 9.2.3 (Afanas’ev et al., 2002e). It seems, however, that this apparent discrepancy might indicate an important role of the pre-metallization impurity adsorption, e.g., moisture (Zhao et al., 2006), onto the oxide surface which was carefully avoided when studying impact of alumina crystallization (Afanas’ev et al., 2002e) but likely allowed to happen in the earlier studies. For instance, the results for sapphire were obtained on the samples with polished surfaces (Viswanathan and Loo, 1972a, b). By contrast to SiO2 and Al2 O3 , a change of the metal work function at interfaces with ZrO2 or HfO2 insulators provides only a limited variation in the barrier height as indicated by the IPE barrier values shown in Fig. 10.1.8. This clearly ‘non-ideal’ behaviour is often described using the Metal-Induced GapState (MIGS) model (Tersoff, 1984a, b) and the empirically derived charge neutrality levels (CNL) of the contacting materials (Robertson and Chen, 1999; Yeo et al., 2002; Gu et al., 2006) which essentially reflect the bulk properties of the materials. As it appears now, the interface-related extrinsic contributions to the barrier are of much importance for the metal–insulator barriers. The already mentioned adsorption of water molecules at the oxide surface and their in-diffusion into the sub-surface layer may lead to an additional dipole at the interface. This brings up an important question regarding the role of the chemical
IPE barrier (eV)
Electron Energy Barriers between Conducting and Insulating Materials
4
HfO2
ZrO2
Ni
Ni Cu
Cu 3
Au
Au
Mg
231
Mg
Al Al 2 3.5
4.0
4.5
5.0
3.5
4.0
4.5
5.0
Metal work function (eV) (a)
(b)
Fig. 10.1.8 Barrier height between the Fermi level of different metals and the conduction band of ZrO2 (a) and HfO2 (b) as a function of the vacuum work function of the metal. The results are shown for as-grown at 300◦ C by atomic deposition layers on Si () and those annealed for 30 min in O2 at 650◦ C prior to metal deposition by thermoresistive evaporation () (Afanas’ev and Stesmans, 2004a). Lines guide the eye.
composition of the near-interfacial insulator layer on the distribution of the electrostatic potential across the interface and the possible ways of its control and stabilization. In addition to the observed higher barrier and a weakened sensitivity to the externally applied electric field, the presence of negative charges in Si-based MOS structures with Al2 O3 and HfO2 insulators is further evidenced by the comparison of the flatband voltage (VFB ) values determined from capacitance–voltage (CV) characteristics of MOS capacitors to the ‘ideal’ values calculated as the metal–semiconductor work function difference (ms ) using the barrier heights measured by IPE. These VFB values are plotted in Fig. 10.1.9 as functions of the Pauling electronegativity of different metal atoms on three insulating stacks (Afanas’ev et al., 2002a). For the sake of comparison the dotted lines indicate ms changes in n-Si/SiO2 /metal structures. Three major features are revealed by comparing the VFB and ms values: (1) For the same metal, ms values in MOS capacitors with high-κ oxides are substantially higher than in the case of SiO2 (cf. n-type substrate data). (2) There is a systematic trend in structures with as-deposited Zr oxides that VFB > ms , indicating a considerable density of negative charge in oxide. The density of this charge can be substantially reduced by a high-temperature anneal. (3) In the Al-metallized samples a systematic shift of VFB towards a value lower than ms is observed suggesting an additional (positive) charge contribution which might be related to the formation of protonic species. These features again bear out a significant sensitivity of the metal/high-permittivity oxide barrier to the chemistry of the oxide surface, which is in a sharp contrast with the behaviour of the semiconductor/oxide interface discussed in the preceding sections. It concerns a very pertinent finding, the microscopic origin of which non-ideal behaviour is still under investigation. 10.2 Polycrystalline Si/Oxide Interfaces In attempt to get insight into (the) reason(s) for the different barrier behaviour at semiconductor/insulator and conductor/insulator interfaces, the band alignment between highly conductive doped polycrystalline silicon (poly-Si) layers and insulating SiO2 , SiO2 /HfO2 or HfO2 layers might be addressed because, from the chemical point of view, these interfaces are very similar to the interfaces of crystalline Si with the
232
Internal Photoemission Spectroscopy: Principles and Applications 2
ms(n-type)
Ni
ms(p-type)
1 Mg
Au
Al Cu
0 Al2O3
1
(a)
(b)
Flatband voltage V FB (V)
ms(n-type) 1
ms(p-type)
0 Al2O3/ZrO2
1
ms(n-type) 1
ms(p-type)
0
(c)
ZrO2
1 1.0
1.5
2.0
2.5
Pauling electronegativity
Fig. 10.1.9 Flatband voltages of n- (filled symbols) and p-type (open symbols) MOS capacitors with 5-nm thick Al2 O3 (a), stacked 1.5 nm Al2 O3 /5 nm ZrO2 (b), and 5-nm thick ZrO2 (c) insulators on (100)Si as a function of gate metal electronegativity. Circles correspond to as-deposited oxide samples, and squares and triangles correspond to those oxidized at 650◦ C for 30 min and at 800◦ C for 10 min, respectively. Solid and dashed lines show correspondingly the ‘ideal’ behaviour of the metal–semiconductor work function difference φms for n- and p-type Si as calculated from the barrier heights determined by IPE; dotted lines indicate φms for an n-type MOS structure with a thermal SiO2 insulator.
same oxides. At the same time, the Fermi energy in the poly-Si can be shifted across its entire bandgap by introducing the appropriate doping impurity during deposition and subsequent high-temperature activating anneal. It was demonstrated that, similarly to the above discussed case of elemental metal electrodes, the VFB values in the poly-Si gated MOS capacitors are different if SiO2 is replaced by another oxide insulator (HfO2 , Al2 O3 ) (Hobbs et al., 2004a, b). As the trends observed in n+ - and p+ -doped poly-Si electrodes indicate the opposite directions of the VFB shift, one assumed, quite conceivably, different signs of the net interface charge in these two cases. This would be easy to analyse when applying the IPE barrier measurements and comparing the results to the case of crystalline-Si/insulator interfaces at which no doping-correlated charging is observed. The IPE spectra of polycrystalline layers of Si deposited on SiO2 are quite similar to those observed for the crystalline Si/SiO2 interfaces as one can see from the spectral plots shown in Fig. 10.2.1a for
Electron Energy Barriers between Conducting and Insulating Materials
IPE yield (relative units)
105
233
p-poly-Si(15 nm)/SiO2(10 nm)/p-Si(100) V (Volt): 1000C spike anneal poly
104 103 102
1 2 3 4 5
Vpoly (Volt): 0.5 0.3 0.1 0.1
101 100 101 102 2.5
3.0
(a)
3.5
4.0
4.5
5.0
5.5
Photon energy (eV)
(Yield)1/3 (relative units)
14 12 10 8 6 4 2 0 2.5 (b)
3.0
3.5 4.0 Photon energy (eV)
4.5
5.0
Fig. 10.2.1 (a) IPE yield from the polycrystalline Si electrode as a function of photon energy in the poly-Si/SiO2 /Si(100) structure as measured under different voltages applied to the poly-Si emitter. Panel (b) illustrates determination of the spectral threshold of electron IPE from the valence band of poly-Si into the conduction band of SiO2 using Y 1/3 –hν plots. Lines guide the eye.
p+ -poly-Si/SiO2 /Si samples with boron dopant activated by 1000◦ C spike anneal. In addition to the IPE of electrons from the valence band of poly-Si into the oxide conduction band, the spectra also show a low-energy photocurrent originating from ionization of the already discussed 2.8-eV deep electron states in the near-interfacial SiO2 . There is, however, a difference in articulation of the E2 singularity at hν = 4.3 eV which appears to be much less pronounced than in the case of IPE at (100)Si/SiO2 interface (cf. Fig. 4.2.6). This difference can logically be expected based on the polycrystalline structure of Si emitter in the present case. The spectral thresholds of electron IPE can be determined using Y 1/3 –hν plots shown in Fig. 10.2.1b and agree well with the results obtained for the crystalline (100)Si emitter as will be discussed later. Deposition of the polycrystalline Si onto HfO2 leads to the shift of the IPE threshold by approximately 1 eV towards lower photon energies as indicated by the spectral curves shown in Fig. 10.2.2 for the as-deposited (550◦ C) and annealed at 1000◦ C poly-Si electrodes. To avoid contribution of hole IPE from Si substrate to the measured photocurrent, a blocking SiO2 under-layer was fabricated on the substrate prior to HfO2 deposition. The downshift in energy of the electron IPE threshold is in general
Internal Photoemission Spectroscopy: Principles and Applications 107 IPE yield (relative units)
106
p-Si(100)/SiO2(1.5 nm)/HfO2(10 nm)/poly-Si(20 nm) V1 Volt
105 Annealed1000C
104
30
103
Y 1/3
234
102
e
E2
E1
20 10
101
As-deposited
0
3
100 3
4 5 Photon energy (eV)
4
hn (eV)
5
6
Fig. 10.2.2 IPE yield from the polycrystalline Si electrode as a function of photon energy in the poly-Si/HfO2 /SiO2 / Si(100) structures as measured −1 V bias applied to the poly-Si emitter in the samples with poly-Si layer deposited at 550◦ C or additionally subjected to 1000◦ C anneal to activate boron dopant. Insert illustrates the determination of the spectral thresholds of electron IPE from the valence band of poly-Si into the conduction band of HfO2 using Y 1/3 –hν plots. Lines guide the eye. Arrows indicate the energies of the electron IPE spectral threshold e as well as of the optical transitions between the points of high symmetry in the Brillouine zone of silicon crystal (E1 and E2 ).
consistent with the corresponding shift of the conduction band bottom between SiO2 and HfO2 . Electron IPE thresholds determined using the Y 1/3 –hν plots and exemplified in the insert indicate that both the as-deposited, predominantly amorphous, silicon layer and that annealed at high temperature have the same barrier height e at the interface with HfO2 . Upon annealing, the poly-Si layer exhibits well pronounced optical features E1 and E2 as indicated by arrows in the insert indicating partial crystallization of the material. Also, an additional spectra threshold at around hν = 3.7 eV becomes noticeable after annealing indicating growth of some SiO2 -like interlayer (Afanas’ev et al., 2001b). The latter is suggestive of oxidation of poly-Si by the oxygen supplied from HfO2 . Investigation of the interface barrier variations caused by the poly-Si doping was performed by observing electron IPE from the p+ -doped (B-doped), n+ -doped (P- or As-doped), or undoped poly-Si electrodes into SiO2 thermally grown on (100)Si, SiO2 with some traces of HfO2 on top introduced by several atomic layer deposition cycles of HfCl4 and H2 O (8 cycles correspond to approximately 1 monolayer (ML) HfO2 coverage of SiO2 ), and HfO2 with or without SiNx diffusion barrier on top (Afanas’ev et al., 2005c). The observed IPE spectra from the valence states of poly-Si and those of (100)-oriented Si crystal into SiO2 are similar to each other and show only a marginal sensitivity to the type of poly-Si doping as indicated by the Y 1/3 –hν plots shown in Fig. 10.2.3. This result is consistent with the data obtained using CV measurements indicating ∼1 V difference in the flatband voltages between n+ - and p+ -poly-Si gated MOS capacitors (curves not shown). The latter would suggest that no barrier variation occurs because the flatband voltage variation appears to be equal to the shift of the Fermi level in the poly-Si gate electrode. However, incorporation of a metal impurity (Hf ) to the interface by exposing the oxide surface to several cycles of HfCl4 and H2 O (as used in the atomic layer deposition technology (Ritala, 2004)) leads to splitting of the IPE threshold. In the p+ -poly-Si case the IPE onset is seen to occur at a lower photon energy in the Hf-contaminated samples than in the Hf-free ones. In order to clarify the mechanism of the barrier variation, the field dependence of the spectral thresholds was analysed (Afanas’ev et al., 2005c). The corresponding Schottky plots are shown in Fig. 10.2.4 for
Electron Energy Barriers between Conducting and Insulating Materials
235
(IPE yield)1/3 (relative units)
Poly-Si/HfO2/10 nm SiO2/(100)Si 15 HfO2: 0 cy 1 cy 5 cy 10 cy
10
IPE
(100)Si/SiO2 5
p-poly-Si n-poly-Si
0 2.5
3.0
3.5
4.0
4.5
5.0
Photon energy (eV)
Fig. 10.2.3 The cube root of the IPE yield as a function of photon energy at the interfaces of the n+ - (filled symbols) and p+ -doped (open symbols) poly-Si with 10-nm SiO2 covered with different amounts of HfO2 (1 cy ≈ 0.1 ML). The result for the low-doped p-type (100)Si/SiO2 interface is shown for comparison (3). The average strength of electric field in the oxide is 1 MV/cm. The bold line illustrates the determination of the IPE spectral threshold .
IPE spectral threshold (eV)
4.50
HfO2 cycles: 10
4.25 4.00
Poly-Si/HfO2/SiO2/(100)Si n-poly-Si
0 SiO2(εi 2.1)
1 5
3.75 10 3.50 3.25 3.00 0.0
p-poly-Si 0.5
1.0
1.5
2.0
2.5
(Electric field)1/2 (MV/cm)1/2
Fig. 10.2.4 Schottky plot of the spectral threshold of electron IPE at poly-Si/HfO2 /SiO2 interfaces from the valence band of poly-Si electrodes into the conduction band of 10-nm thick thermal SiO2 for nominally undoped, p+ -, and n+ -doped poly-Si electrodes (grey, open, and filled symbols, respectively). The numbers indicate the number of the atomic-layer HfO2 deposition cycles on SiO2 prior to the poly-Si growth. Lines guide the eye.
poly-Si/SiO2 and poly-Si/HfO2 /SiO2 interfaces. In the case of the Hf-free interface, the electron IPE threshold obeys the Schottky law with an effective dielectric constant of the oxide of εi = 2.1 ≈ n2 , where n is the refractive index of the insulator. This behaviour is expected for the ideal case of image-force potential barrier (Williams, 1970). In the high field region (F > 1.5 MV/cm), as compared to the n− poly-Si/SiO2 case, the p+ -poly-Si/SiO2 samples exhibit an additional IPE threshold lowering which can be explained by a potential drop in the surface Si layer which was discussed earlier in Chapter 2 (cf. Fig. 2.1.3).
236
Internal Photoemission Spectroscopy: Principles and Applications
Incorporation of Hf at the n+ -poly Si/SiO2 interface results in a barrier height gradually increasing with increasing number of Hf deposition cycles suggesting the formation of a negative dipole at the interface. In the case of the p+ -poly-Si electrode, the presence of Hf leads to a lower barrier while, attendantly, the slope of the Schottky plot is seen to become larger which would be consistent with a local lowering of the potential barrier by a Coulomb attractive (i.e., positively charged) centre located at the interface plane (Adamchuk and Afanas’ev, 1992a). With increasing amount of Hf at the interface, the IPE threshold is lowered further. At the same time the data also reveal a decrease of the zero-field barrier height suggesting an overlap in interaction of these attractive Coulomb potentials. Though details of the interface barrier perturbation will not be discussed any further here, the results directly indicate that charges of opposite sign are introduced near the interface in the presence of Hf leading to a higher barrier at n+ -poly-Si/SiO2 and to a lower barrier at p+ -poly-Si/SiO2 interfaces. A very similar trend in charging as revealed in the Hf-containing poly-Si/SiO2 structures is also observed at interfaces of poly-Si with a 10-nm thick HfO2 layer as can be seen from the VB IPE spectra shown in Fig. 10.2.5 for both poly-Si/HfO2 (a) and poly-Si/SiNx /HfO2 (b) interfaces. The IPE threshold for p+ -poly-Si/SiO2 is seen to be lower by ∼0.25 eV than that of n+ -poly-Si. It is also noteworthy that the sub-threshold ‘tail’ of the IPE from poly-Si electrodes is considerably enhanced in the p+ -poly-Si-case. IPE(c-Si)
E1
E2
IPE(n) 10
IPE(undoped)
(IPE yield)1/3 (relative units)
IPE(p)
c-Si/HfO2 poly-Si/HfO2 Undoped p-doped n-doped (a)
5
0 IPE(c-Si) IPE(n) 10 IPE(undoped) IPE(p) c-Si/HfO2 Poly-Si/SiNx /HfO2 Undoped p-doped n-doped (b)
5
0 2.0
2.5
3.0 3.5 4.0 Photon energy (eV)
4.5
5.0
Fig. 10.2.5 The cube root of the IPE yield as a function of photon energy at the interfaces of nominally undoped, p+ -, and n+ -doped poly-Si electrodes (shown by grey, open, and filled symbols, respectively) with 10-nm HfO2 without (a) and with a 0.5-nm thick SiNx capping layer (b). The result for a low-doped p-type Si(100)/HfO2 interface is shown for comparison (). The average strength of electric field in the oxide is 1 MV/cm. The lines illustrate the determination of the IPE spectral threshold IPE for different electrodes. The arrows E1 and E2 indicate singularities in the optical characteristics of silicon.
Electron Energy Barriers between Conducting and Insulating Materials
237
EC EC
Positive charge
EV p-poly-Si
HfO2 EV
Fig. 10.2.6 Schematic energy band diagram of the polycrystalline Si/HfO2 interface illustrating the influence of a near-interfacial positively charged layer on the barrier shape and the p+ -poly-Si surface depletion.
This ‘tail’ in the spectral plots is mostly caused by electron IPE from the high density of gap states in the poly-Si electrode. A similar tail states were reported earlier at the interface of amorphous silicon with SiO2 (Tomio et al., 1981). The electron occupancy of these states apparently increases upon activation of the p+ -dopant (boron) by a high-temperature (1000◦ C) anneal. This effect suggests an increasing downward band bending in the poly-Si electrode consistent with the observation of poly-Si depletion in other electrical measurements (Afanas’ev et al., 2005c). These observations indicate formation of a positively charged layer at the surface of the polycrystalline Si or above it as schematically illustrated in Fig. 10.2.6. Generation of this positive charge is seen occur on HfO2 and HfO2 /Si insulators, i.e., it is correlated with the presence of Hf at the poly-Si/oxide interface. Another interesting aspect concerns a slight but still measurable difference (∼0.15 eV) between the IPE threshold for the valence band emission from the poly-Si and the (100)Si crystal (cf. and in Fig. 10.2.5). Taking into account that the corresponding thresholds at interfaces with SiO2 coincide, as shown in Fig. 10.2.3, it is likely that deposition of poly-Si onto HfO2 and the subsequent activation annealing result in significant chemical changes of the interface. This feature is, again, in sharp contrast with Si crystal/HfO2 interfaces, which were found to be virtually insensitive to the method of HfO2 growth and subsequent treatments. As one possible explanation of the difference in behaviour of poly-Si/SiO2 and poly-Si/HfO2 contacts one might consider partial reduction of the Hf oxide in the hydrogen-containing ambient present during poly-Si deposition. The latter potentially leads to the formation of electrically active Si–Hf bonds as suggested by Hobbs et al. (2004a, b). Noteworthy here is that this effect is already observed at a submonolayer coverage of SiO2 by HfO2 (Afanas’ev et al., 2005c), indicating that the widely used models invoking formation of oxygen vacancies in HfO2 (see, e.g., (Shirashi et al., 2004; Takahashi et al., 2006)) would be unrealistic. Also, one could imagine a kind of chemical interaction in which the metal oxide is partially reduced by silicon leading to formation of metal-containing charged centres at the surface of poly-Si electrode. 10.3 Complex Metal Electrodes on Insulators Though the poly-Si electrodes offer thermal stability sufficient to sustain necessary source/drain activation annealing, they suffer, as well known, from the silicon surface depletion, which hampers downscaling of the poly-Si-based gate stacks. Together with the above discussed doping-dependent charging of polySi/high-permittivity oxide interfaces, this factor makes the consideration for transition to metal gates with different work function values very attractive, if not compulsory. So stepping to suitable elemental metals
238
Internal Photoemission Spectroscopy: Principles and Applications
would appear a first obvious choice. However, the elemental metals, particularly those with low work function, lack stability in contact with metal oxides (see, e.g., Chen et al., 2005), so considerable interest is attracted nowadays to the development of thermally stable complex metal electrodes based on nitrides, carbides, and silicides of transition and refractory metals (Ti, Ta, W, Hf,. . .). With respect to these compounds several important questions arise, including chemical composition and phase control, structural and chemical thermal stability and the required possibility for work function tuning aimed at ∼1 eV difference for gates applied to n- and p-channel MOS transistors (Pourtois et al., 2005). Taking into account the increasing complexity of the interface, the most direct barrier characterization technique – IPE – would also appear of much value here. Some work has already been performed aiming at understanding of basic features of the barrier dependence on the conductor composition and processing. The very first issue concerns the possibility to vary the barrier height technologically by changing composition of the complex metal material. This seems to be in reach when analysing the electron IPE spectra from as-deposited metal-rich TiNx and TaNx (x ≈ 0.5) layers into two different insulators (SiO2 and HfO2 ) shown in Fig. 10.3.1a and b, respectively (Afanas’ev et al., 2005d). The spectra of TiNx on each of these oxides are shifted towards higher photon energy as compared to TaNx , indicating a higher energy barrier between the metal Fermi level EF and the bottom of the oxide conduction band (cf. the insert in Fig. 10.3.1a). In turn, the ∼1 eV shift to lower photon energy of the spectra measured for the
103 102
EF
EC
101 Me Ox
TiNx /SiO2 Vg 1 V 2 V 3 V
IPE yield (relative units)
100 101
TiNx /HfO2
(a) 103
TaNx /HfO2
102 101 TaNx /SiO2 Vg 1 V 2 V 3 V
100 101
(b) 102
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Photon energy (eV)
Fig. 10.3.1 Spectra of electron IPE from 10-nm thick layers of metallic TiNx (a) and TaNx (b) into 10-nm thick SiO2 or HfO2 insulators measured at different negative biases (Vg ) applied to the conducting nitride gate electrodes. The insert to panel (a) shows the scheme of the observed electron transitions.
Electron Energy Barriers between Conducting and Insulating Materials
239
(Yield)1/2 (relative units)
NiSi/SiO2(7.5 nm)/(100)Si 15
10
5
0 3.0
Vg ( Volt): 0.25 0.5 1 1.5 2 2.5 3 3.5
3.5
4.0
4.5
5.0
Photon energy (eV)
Fig. 10.3.2 Fowler plots of the quantum yield of electron IPE from NiSi layer grown using full silicidation technology onto 7.5-nm thick SiO2 measured under different values of a negative bias (Vg ) applied to the photoemitting silicide electrode.
same gate materials on HfO2 as compared to SiO2 reveals a substantial difference in the conduction band energy between these oxides (∼1.15 eV). Thus, one may conclude that for the as-deposited metal layers, TaNx and TiNx do provide the desirable barrier height difference both on SiO2 and HfO2 insulators. In general, the spectral curves of electron IPE from the studied complex conductors exhibit behaviour similar to that of conventional elemental metals. This is exemplified in Fig. 10.3.2 by the Fowler plot of IPE spectra measured under different voltages applied to 20-nm thick NiSi electrode fabricated onto 7.5-nm thick SiO2 using the full silicidation technology. The spectra are seen to obey the Fowler law over 1-eV photon energy range above the threshold making possible reliable extraction of the relevant spectral thresholds. In fact this result comes as a surprise because several phases of nickel silicide are expected to be stable and to provide areas with significantly different work function at the interface (see, e.g., Kittl et al., 2006a, b). Obviously, this issue is to be investigated further. The results obtained for several complex conducting materials deposited onto SiO2 are compiled in the Schottky plot as shown in Fig. 10.3.3. For the sake of comparison are also shown the data for Al/SiO2 and Au/SiO2 interfaces which represent the ‘classical’ cases of interfaces between the oxide and a metal with low and high work function, respectively. It is seen that the conductors of complex composition cover practically the whole barrier height range typical of the elemental metals. Moreover, when comparing the results shown in Fig. 10.3.3 to the work function of p+ - and n+ -doped poly-Si, the analysed conductors demonstrate the ability to provide the same range of work function control therefore, have a potential of replacing the poly-Si electrodes in the gate stacks of electron devices. The slope of the Schottky plots for all the materials deposited onto SiO2 appear to be close, but reveal a slightly higher effective image-force dielectric constant than that expected for the ideal metal/SiO2 interface (εi = n2 = 2.1). This deviation might indicate the presence of a transition, metal-doped oxide layer at the interface with somewhat larger polarizability than that of pure silicon dioxide. What appears to be the crucial issue when applying complex conductors to high-permittivity insulating layers is thermal stability of the interface barrier. This problem is exemplified by the IPE results on the annealing-induced barrier variations of TaNx and TiNx (x = 0.5) electrodes on HfO2 (Afanas’ev et al., 2005d). After high-temperature post-deposition anneal (PDA, 10 s in N2 at the indicated temperature in Fig. 10.3.4) the properties of the two studied conductive nitrides exhibit different trends as evidenced
240
Internal Photoemission Spectroscopy: Principles and Applications 4.4
TiN/SiO2 HfN/SiO2
4.2
SiO2
IPE threshold (eV)
4.0 Au/SiO2
3.8 3.6 3.4 3.2 3.0
NiSi/SiO2 TaN/SiO2 Ta2C/SiO2
2.8 2.6
0
Al/SiO2
1
2
(Field)1/2 (MV/cm)1/2
Fig. 10.3.3 Schottky plots of the electron IPE spectral thresholds for different complex conductors deposited onto SiO2 as compared to the elemental metal electrodes (Al and Au). Lines guide the eye.
by the IPE Fowler plots shown in Fig. 10.3.4. The TiNx electrodes (filled symbols) exhibit stable characteristics with the only influence of the annealing seen as some reduction in IPE yield. The latter might be related to additional scattering of electrons at the TiNx /HfO2 interface. By contrast, annealing of TaNx (open symbols in Fig. 10.3.4) results in a considerable (∼1 eV) increase of the barrier height and is accompanied by a significant reduction of the IPE quantum yield suggesting a chemical reaction to occur at the interface. The IPE thresholds found from the shown Fowler plots are plotted as functions of the square root of the electric field (Schottky plot) in Fig. 10.3.5 for TiNx (a) and TaNx (b) deposited directly on SiO2 As-deposited 600C 700C 900C 1000C
(IPE yield)1/2 (relative units)
20
15
TaNx /HfO2 10 TiNx /HfO2
5
Vg2 V 0
2.0
2.5
3.0
3.5
4.0
4.5
Photon energy (eV)
Fig. 10.3.4 Fowler plots of the quantum yield of electron IPE from TaNx (open symbols) and TiNx (filled symbols) into 10-nm thick HfO2 measured under a negative bias (Vg ) of −2 V on the as-deposited samples (, ) or samples subjected to 10-s annealing in N2 at the indicated temperature.
•
Electron Energy Barriers between Conducting and Insulating Materials
241
TiNx /Ox 4.0 SiO2
3.5
(a)
IPE threshold energy (eV)
3.0 2.5
HfO2
2.0 TaNx /Ox SiO2
4.0 3.5 HfO2
3.0 2.5
High Low
2.0 (b)
0
1 (Field)1/2
2 (MV/cm)1/2
Fig. 10.3.5 Schottky plots of inferred spectral thresholds of electron IPE from TiNx (a) and TaNx (b) into different insulators: 10 nm SiO2 (, ), 10 nm SiO2 /1 ML HfO2 (, ), and 10 nm HfO2 (, , ). The open and filled symbols correspond to the as-deposited samples and the samples after 1000◦ C PDA, respectively. For the TaNx /HfO2 interface, the behaviour of both spectral thresholds (, ) appearing after annealing (cf. Fig. 10.3.4) is shown. Lines illustrate the determination of the barrier height by extrapolation of the spectral threshold to zero field.
•
(circles), SiO2 /HfO2 (1 ML) stack (squares), and HfO2 (upright triangles). The open and filled symbols correspond to the as-deposited and annealed at 1000◦ C samples, respectively. The energy barrier height for electrons is obtained by linear extrapolation of the Schottky plot to zero field to account for the influence of the field-induced reduction of the image-force potential barrier. For TiNx /SiO2 one obtains = 4.15 ± 0.05 eV which, accepting an electron affinity for SiO2 of 0.8 eV, gives a work function of 4.95 eV both in the as-deposited and annealed samples. For both as-deposited and annealed TiNx /HfO2 samples we found = 3.0 ± 0.05 eV which, taking into account the earlier indicated conduction band offset of 1.15 eV between HfO2 and SiO2 , yields the same work function of 4.95 eV. This value is close to the work function of pure Au of about 5 eV (determined from = 4.10 ± 0.05 eV in Au/SiO2 , cf. Fig. 10.3.3). As evident from Fig. 10.3.5a (squares), a remarkable feature of the TiNx /HfO2 (1 ML)/SiO2 samples consists in a ≈0.2 eV upward shift of after 1000◦ C anneal despite the fact that, in the as-deposited state, Hf has no measurable effect on the barrier. An even larger barrier increase (∼0.3 eV) caused by the HfO2 ML is observed for the TaNx /HfO2 /SiO2 interface, as indicated by the data shown by squares in Fig. 10.3.5b. As no such effect is found for TiNx /SiO2 , TiNx /HfO2 , and TaNx /SiO2 interfaces upon PDA, we conclude that the co-presence of Si and Hf atoms gives rise to a negative dipole layer. This
242
Internal Photoemission Spectroscopy: Principles and Applications
conclusion agrees with the suggestion of Hobbs et al. regarding the involvement of Si Hf or Si O Hf bonds in Fermi level pinning at the interfaces of Hf with polycrystalline Si (Hobbs et al., 2004a, b). A more complex behaviour is observed for the TaNx interfaces (Fig. 10.3.5b). While in TaNx /SiO2 the 1000◦ C PDA has a marginal impact on (within ∼0.1 eV), the work function value of 4.35 eV obtained from = 3.55 ± 0.05 eV is in this case considerably higher than that (4.05 eV) calculated for TaNx /HfO2 interface using = 2.1 ± 0.05 eV derived in the as-grown state from Fig. 10.3.5b. This suggests a difference in the polarization layers at two interfaces. As mentioned earlier, annealing of the TaNx /HfO2 entities splits the IPE threshold into two (cf. Fig. 10.3.4), yielding two Schottky plots in Fig. 10.3.5b corresponding to the high () and low () IPE thresholds. As compared to the case of as-deposited TaNx on HfO2 (), PDA increases the lowest by 0.3 eV, while the highest one reaches 3.0 eV (cf. Fig. 10.3.5b) yielding the work function of 4.95 eV. The latter is by 0.5 eV above that of TaNx in contact with SiO2 , but close to the value for TiNx on HfO2 . As no such effect is observed for the TaNx /SiO2 system, the annealing-induced phase transition in the Ta nitride cannot account for such dramatic work function changes. On the other hand, HfO2 preserves its conduction band edge energy after annealing as indicated by stability of the barrier at the TiNx /HfO2 interface. Then, the strong impact of PDA on the work function of TaNx in contact with HfO2 should be due to a chemical reaction between these two materials. Interestingly, the barrier instability effect is not observed at the interface between pure TaNx and SiO2 , but becomes noticeable if only a trace of Hf equivalent to 1 ML of HfO2 is introduced at the interface (Afanas’ev et al., 2005d). Apparently, subtle details in the chemical bonding at the interface may effectuate a considerable impact on the TaN conductor/oxide oxide barrier height. It is worth adding here that a similar barrier increase is observed if the N concentration in TaNx is increased by using different deposition processes or, else, if water is allowed to adsorb onto the HfO2 surface prior to TaNx deposition. A similar trend of increasing the barrier between the metal Fermi level and the oxide conduction band is also observed for TaCx electrodes on HfO2 after applying a high-temperature anneal (not shown). Taken together, these observations suggest that the oxidation of Ta at the interface may be the possible reason for the thermal instability of the TaNx /HfO2 barrier. This type of behaviour is, again, in sharp contrast with that of semiconductor/high-permittivity oxide interfaces. The latter exhibit barriers of height only marginally sensitive to the presence or absence on an interlayer, its composition, and even to the composition of the high-permittivity oxide, provided that the bandgap width is not affected strongly. This does not exclude, however, significant influence of interlayer on the interface traps and charges associated with defects. 10.4 Modification of the Conductor/Insulator Barriers The observed sensitivity of the conductor/high-permittivity oxide barrier to the details of atomic bonding at the interface would, very interestingly, signal the possibility of barrier control by using an interlayer introduced at the interface prior to metal deposition (Pantisano et al., 2006b). This effect is clearly seen, for instance, at the interfaces of TiNx and TaNx with SiO2 in which the deposition of ∼1 ML of HfO2 results (after annealing) in a 0.1–0.15 eV increase in barrier height (cf. the Schottky plots shown in Fig. 10.3.5). It appears also possible to reduce the TaNx /HfO2 barrier by ∼0.2 eV by introducing a thin (1 or 2 ML) La2 Hf2 O7 interlayer (Pantisano et al., 2006b). This effect is revealed by the electron Fowler plot of IPE spectra shown in Fig. 10.4.1 for TaNx layers in situ deposited onto HfO2 or HfO2 /La2 Hf2 O7 insulators and independently affirmed by the corresponding shift of CV curves. The observed shift of the IPE barrier corresponds to the lowering of the effective work function of the TaNx emitter in the presence of La2 Hf2 O7 . The latter conclusion is based on the same energy of the conduction band edge in HfO2 and La2 Hf2 O7 layers measured with respect to the top of silicon valence band as indicated by nearly coinciding IPE spectra exemplified in Fig. 10.4.2. Therefore, as the most
Electron Energy Barriers between Conducting and Insulating Materials
243
Yield1/2 (arbitrary units)
2 SiO2/ALD HfO2/2ML LHO In-situ TaN deposition 950C hn VG5 V
1
EC EV HfO2
FGA
4 MG
LHO WF~200mV
0 2.0
2.5
3.0
3.5
4.0
Photon energy (eV)
Fig. 10.4.1 The Fowler plot of IPE yield for the TaNx /HfO2 samples with 2-MLs thick La2 Hf2 O7 (LHO) prior () and after activation () by 10-s annealing in N2 at 950◦ C. In the insert the interface band diagram and the electron transition during the IPE experiment are schematically shown.
probable mechanism of barrier modification, formation of a near-interface charged layer is suggested. This suggestion is supported not only by the decrease of barrier height but, also, by significant reduction of the IPE quantum yield in the La2 Hf2 O7 -containing sample. The latter would indicate an enhanced scattering of electrons entering the oxide from TaNx by the weakly screened (La-induced?) charges. The briefly discussed approach to interface barrier engineering is by far not the only one possible. Suggestions of using multi-layered conducting electrodes, interface selective doping, and other technological approaches are often made. Surely, this area is set for further development in the near future and the IPE appears to be the most relevant experimental method to analyse the barrier variations. What is worth of adding here is that IPE has demonstrated a unique potential of analysing laterally non-uniform barriers
IPE yield (arbitrary units)
104 F 1MV/cm 103
(100)Si/HfO2
e(Si) (100)Si/La2Hf2O7
102
101
100
2
3
4
5
Photon energy (eV)
Fig. 10.4.2 Quantum yield of electron IPE from the valence band of (100)Si into the conduction band of HfO2 () and La2 Hf2 O7 ( ) insulators as a function of photon energy. The spectra are taken at the same strength of electric field in the insulator of 1 MV/cm with the gate electrode biased positively. The arrow indicates the spectral threshold of IPE inferred for both insulating materials from the Y 1/3 –hν plots (not shown).
•
244
Internal Photoemission Spectroscopy: Principles and Applications
both in the differential spectroscopy mode (Okumura, 1982) and using the scanning light spot microscopy (DiStefano, 1971; Williams and Woods, 1972; Okumura and Shiojima, 1989). Despite the fact that in the latter case the lateral resolution of IPE is considerably lower than that of ballistic electron emission microscopy (BEEM), IPE has advantage of working with relatively thick conducting electrodes (>10 nm) which makes it suitable for analysis of materials and structures fabricated in an industrial environment. Without doubt, this feature can be of much benefit for both fundamental barrier analysis and the material technology optimization.
CHAPTER 11
Spectroscopy of Charge Traps in Thin Insulating SiO2 Layers
Charge trapping in insulating materials expresses a natural property associated with presence of intrinsic defects or impurities with energy levels energetically located deep in the insulator bandgap. Particular interest in this issue originates from widespread applications of these materials in various electronic devices. Here, trapped charge directly contributes to the strength of the electric field at the surface of the applied electrodes including active regions, e.g., the channel of a transistor. This additional field may affect the device operation causing undesirable variation of its parameters, e.g., the shift of the threshold voltage in the metal–oxide–semiconductor (MOS) transistor, reduction of carrier mobility by scattering, or increase of leakage current across the a surface p–n junction region. On the other hand, charge trapping can also be turned to the benefit, namely, as a physical method for information recording and, in this way, can be used in non-volatile memory devices. In both cases, be it to minimize influence of the traps or to ensure effective charge trapping and storage, the nature and the properties of the corresponding defects need to be evaluated. For nearly four decades most of the attention to trap spectroscopy was concentrated on imperfections in thin SiO2 layers on semiconductor surfaces, mostly on crystalline silicon. The oxidized silicon was and still remains at the core of the modern integrated circuit technology in which SiO2 is used as the gate, field, or inter-level insulator. For this reason, most of the results discussed in this chapter will concern this material system. Until recently, technology of other dielectric materials was not mature enough to provide layers of sufficient quality and acceptably low trap density. For instance, despite being used for several decades, silicon nitride (Si3 N4 ) still contains such a large concentration of traps that applying capture cross-section spectroscopy to these remains hardly possible. Other insulating materials, mostly the high-permittivity insulators for gate stacks and capacitors as well as the low-permittivity insulators projected to replace SiO2 in the inter-level insulation, are just entering the research field. So far, only a few experimental works reaching the spectroscopy level have been performed on these yet. In the absence of experimental observations of more general character, the analysis of traps in SiO2 would provide an interested reader with well-proven methodological framework of experimental research in which this insulator serves as the prototype trap-hosting material. 245
246
Internal Photoemission Spectroscopy: Principles and Applications
11.1 Trap Classification through Capture Cross-Section The main goal of trap spectroscopy may be formulated as the determination of the contribution of different centres to the charge trapping and quantification of this trapping in terms of trap charge and density per unit area, as well as the distribution profile as a function of depth. This goal ultimately aims at the atomic identification of the trap, i.e., at association of the particular trap with some atomically (defect) or chemically (impurity) identified site in the crystalline lattice or amorphous network of an insulator. As the basis for this characterization is provided by the measurements of the trapped charge sign and density, only the net total charge is observed. Further analysis is intended to separate charges stemming from different kinds of traps. One might consider to analyse the traps by using different physical properties of the captured charge carriers, like optical (Bourcerie et al., 1989; Vuillaume and Bravaix, 1993), thermal trap ionization (Li and Sahr, 1995; Fujieda, 2001), radiative optical transitions, optical absorption, electron spin resonance (ESR), positron annihilation spectroscopy, etc. However, these effects do not necessarily occur with the same probability for all the traps detected through their charge because of existence of different electronic configurations of captured carriers. What emerges as the only universally applicable parameter of all the trapping centres is the capture cross-section which characterizes the carrier trapping per se. Would a certain capture cross-section window be absent in an experimentally observed set of σ values, centres with such cross-section can be considered as irrelevant to the charge trapping. Different relevant contributions to the charge trapping can be separated on the basis of their specific cross-sections and then, would some of the trap spectrum components exhibit additional optical or magnetic activity, be correlated with particular defect or impurity sites. Therefore, the capture cross-section determination represents the base for further trap spectroscopy, at least if attempting to understand the electrical behaviour of a particular insulating material. In the framework of these ideas, a scheme of charge trap characterization can be proposed as follows. First, on the basis of the trapped charge sign, one can identify the type of the trapped charge carriers. Though this step might look trivial at first sight, it is absolutely necessary if recalling that not only electronic but also ionic charges may be generated in the course of charge injection. A good example here is provided by thin layers of thermally grown SiO2 on Si in which the avalanche injection of electrons from silicon was found to lead, quite counter to expectations, to positive charging of the Si/SiO2 interface (Gdula, 1976; Feigl et al., 1981; Trombetta et al., 1988) – the charge later appeared to be of non-electronic origin and associated with protonic species trapped in the oxide near its interface with silicon (de Nijs et al., 1994). Second, the capture cross determination can be addressed provided that the conditions of the first-order trapping model or its modifications, as discussed in Chapters 7 and 8 are met. The cross-section of a trap reflects the probability of a charge carrier to be transferred from a band state of the insulating material to a localized state corresponding to a defect level and, in this way, indirectly senses the spatial extent of the carrier-trap interaction. This idea was put as the cornerstone of a trap classification scheme which relates the cross-section to the spatial span of the trap electrostatic potential (for reviews see, e.g., Rose, 1963; DiMaria, 1978; Young, 1980; Aitken, 1980). In a nutshell, traps with different types of electrostatic potential would result in different cross-section values as illustrated in Fig. 11.1.1. The attractive Coulomb potential of a charged site (a) would lead to the largest σ (as long as an imperfection with a size comparable to the inter-atomic distances are considered) because of the long-range nature of this potential. In SiO2 , cross-sections of about 10−12 cm2 were reported at room temperature and low field (≈0.1 MV/cm), which decreases to the range of 10−15 cm2 if a high electric field (>5 MV/cm) is applied to the oxide (Ning, 1976a; DiMaria, 1978). A neutral centre (b) is expected to give a trap with cross section of the order of the square of the interatomic distance (0.154 nm Si O bond length in SiO2 ). A somewhat larger section can be expected for
247
Energy
Spectroscopy of Charge Traps in Thin Insulating SiO2 Layers
(b)
(a)
(c)
Distance
Fig. 11.1.1 Schematic representation of the electrostatic centre potential for the case of a Coulomb attractive trap (a), a neutral trap (b), and a repulsive trap (c).
a dipole trap, which remains electrically neutral but would have a larger effective carrier capture radius (Aitken et al., 1978). A rough estimate of the cross-section for the dipole trap can be obtained using the expression (Belmont, 1975): σ≈
q2 δ , 32kT εD
(11.1.1)
where q is the elementary charge, δ is the spatial separation between the trap poles, k is the Boltzmann constant, and T is the sample temperature. In a more elaborate treatment one considers the dipole induced by the approaching charge carrier which results in cross-section values up to the 10−14 cm2 range (Boesh et al., 1986; Krantz et al., 1987). The lower border of the neutral trapping is conventionally set at around 10−17 cm2 , assumedly to account for electron trapping by SiOH groups in SiO2 (DiMaria, 1978). The latter case, however, does not represent a purely electronic process because an attendant liberation of hydrogen from the hydroxile group is observed upon trapping of an electron (Nicollian et al., 1971; Nicollian and Brews, 1982; Gale et al., 1988). This ‘rearrangement’ of the trap atomic configuration would require the involvement of some vibronic excitation with energy sufficient to dissociate hydrogen from oxygen. The necessity of such excitation reduces the trapping probability (and the corresponding cross-section value). In fact, replacement of hydrogen with deuterium in the hydroxile group leads to even smaller electron capture cross-section, in the range of 10−18 cm2 , exposing reduction of the trapping probability because of the lower energy of the vibronic modes specific to the O D bond (Gale et al., 1988). It may appear evident from the above discussion on the cross-section of neutral traps that additional processes of the defect rearrangement might also lower the cross-section value. Therefore, the case of ‘repulsive’ trapping shown in Fig. 11.1.1c (DiMaria, 1978) may not necessarily only be associated with a repulsive potential in the vicinity of the trap but, also, with the need for some extra energy to enable the trapping. For this reason, such trapping processes accompanied by significant atomic rearrangement may also have a low cross-section. In SiO2 this kind of ‘repulsive’ or, perhaps better termed as ‘hindered’ trapping refers to the cross-sections below 10−18 cm2 , and values as low as in the 10−20 cm2 range can be found in the literature (see, e.g., DiMaria et al., 1976). It must be reminded, once again, that these extremely small cross-sections for trapping are unlikely to just reflect the bare electrostatic potential of a trap, but might be affected by some other processes which normally should
248
Internal Photoemission Spectroscopy: Principles and Applications
not be described using the classical picture of carrier trapping in a solid. In some cases these may concern carrier transport peculiarities, like it happens if considering charge trapping in collectors with thicknesses comparable to the carrier tunnelling length (Afanas’ev and Stesmans, 2002; Afanas’ev et al., 2004b). In other experiments interaction of injected carriers with electrodes of a collector may be important if, e.g., leading to secondary effects like liberation of hydrogenic species. The latter effect is suggested, for instance, in the case of the injection-induced trap generation in SiO2 on the bases of strong temperature dependence of the trap generation rate, indicative of a diffusion-limited process (DiMaria, 1990). In any event, irrespective of the extent to which the secondary effects are involved or not, the measured value of the apparent cross-section can still be used to characterize the charging process as a whole. Finally, the spatial distribution of traps can be assessed through the analysis of trapping in the samples with variable collector thickness (Walters and Reisman, 1990), centroid measurements using internal photoemission (IPE) (DiMaria, 1976), etch-back profiles, or other approaches discussed in Chapter 6. Being performed after filling the traps with a particular cross-section, this analysis allows one to separate the near-interface traps from those distributed in the bulk of the insulator. In the case of traps introduced into the collector by ion implantation one may even correlate the centroid of the trapped charge distribution to that of the implanted species (DeKeersmaecker and DiMaria, 1980).
11.2 Electron Traps in SiO2 11.2.1 Attractive Coulomb traps Attractive Coulomb traps represent the best studied trapping centres because they can be produced in large amounts by simple exposure of SiO2 films to ionizing radiation or to injection of holes. The most important features of these traps are a large value of the low-field capture cross-section and its strong dependence on the strength of the applied electric field. The latter is exemplified in Fig. 11.2.1, which compiles the results of several experimental studies of annihilation of positive charge in SiO2 by electrons injected by IPE (Buchanan et al., 1991; Adamchuk and Afanas’ev, 1992a) or optically stimulated non-avalanche carrier injection from silicon (Ning et al., 1975; Ning, 1976a). The low-field (<1 MV/cm)
Cross-section (cm2)
1012 s~F 3/2
300 K Buchanan 300 K Adamchuk 300 K Ning 77 K Ning
1013
1014 SiO2 1015 5 10
s~F 3
106 Electric field (V/cm)
107
Fig. 11.2.1 Capture cross-section of electrons at positive charges induced by hole injection into SiO2 at room temperature (Buchanan, 1991; Adamchuk and Afanas’ev, 1992a; Ning, 1976a) and at 77 K (Ning, 1976a). The lines illustrate two regions of the field dependence (Ning, 1976a; Buchanan, 1991).
Spectroscopy of Charge Traps in Thin Insulating SiO2 Layers
249
range of the capture cross-section field dependence closely follows the theoretically predicted law σ ∝ F −3/2 (Dussel and Bube, 1966; Dussel and Böer, 1970), while at a higher field the cross-section decreases with increasing field as σ ∝ F −3 . This enhancement of the field dependence is explained by additional electron heating in SiO2 and field-stimulated electron escape from the positive charge potential well (Buchanan et al., 1991). However, the theoretically predicted temperature dependence of the Coulomb attractive centre (Dussel and Bube, 1966) is not observed, at least not in the range of high electric fields, which is attributed to saturation of the electron velocity in SiO2 (Ning, 1976a). The origin of the Coulomb attractive centres for electrons in SiO2 can be traced back to any kind of positive charge centre with an energy level of the bonded electron state located sufficiently deep in the oxide bandgap to keep the captured carriers trapped. In addition to the mentioned positive charges induced by hole trapping, Na+ ions result in impurity centres with similar trapping properties (DiMaria et al., 1975; DiMaria, 1981). In fact, positive charges often referred to as ‘trapped holes’ also appear to be of ionic origin, namely protons. The latter are generated either by trapping a hole on a Si H bond in SiO2 (Afanas’ev and Stesmans, 2000a; 2001a) or by hole capture on hydrogen atoms liberated at the gate electrode/oxide interface (Afanas’ev et al., 1995b). It then seems logical that the cross-section (corresponding to a spatial span of the Coulomb potential of several nanometres) shows little sensitivity to the atomic composition and configuration of the defect itself. However, the centres behave very differently upon trapping a neutralizing electron: protons are mostly converted to a highly mobile atomic hydrogen which either escapes from the SiO2 or undergoes dimerization (Afanas’ev and Stesmans, 2001a), while neutralization of Na+ ions results in an optically active centre with energy depth of approximately 2.4 eV below the oxide CB (DiMaria et al., 1975; Kapoor et al., 1977a). As a final point, worth of adding here is that in stacks of high-permittivity oxides on silicon, the dominant positive charging process is also associated with a thin interfacial SiO2 -like layer, low dielectric constant of which accounts for the observed relatively large annihilation cross-section (Afanas’ev and Stesmans, 2004b). In this case liberation of atomic hydrogen upon annihilation of the ‘trapped holes’ is again observed. The latter suggests the immobilized protons as the dominant source of the stably trapped positive charge in ultrathin insulating films.
11.2.2 Neutral electron traps in SiO2 Neutral traps represent the most numerous family of electrically active defects in silicon dioxide, for which one may encounter in the literature practically every value of cross-section in the range from 10−14 to 10−18 cm2 . Here, we will discuss only the traps which are not only reproducibly reported by several authors but, at the same time, are identified by complementary analytical methods and related to a specific defect in the oxide. The water-related traps are definitely the most intensively studied ones. These are characterized by an electron capture cross-section of (1–2) × 10−17 cm2 (see, e.g., Young, 1981) and their contribution to trapping is particularly prominent in oxides grown in the presence of water (Nicollian et al., 1971) or exposed to it afterwards (Feigl et al., 1981). The capture cross exhibits no measurable field dependence but decreases to (2–4) × 10−18 cm2 when hydrogen is exchanged for deuterium by using a high-temperature treatment in D2 O (Gale et al., 1988). Electron trapping is seen to be associated with the liberation of hydrogen as indicated by tritium radioactive marker experiments (Nicollian et al., 1971). This correlation between electron trapping and liberation of atomic hydrogen also was independently inferred from boron acceptor deactivation measurements (Sah et al., 1983c). Finally, the correlation of the density of the indicated traps with the intensity of the IR optical absorption in the 3640 cm−1 band corresponding to hydroxile groups in SiO2 , pointing at the SiOH fragment in the oxide network as the most probable origin of the trapping site (Hartstein and Young, 1981).
250
Internal Photoemission Spectroscopy: Principles and Applications
The SiOH traps also exhibit remarkable thermo-chemical behaviour, which basically consists in the elimination in the occurring atomic hydrogen. Upon annealing in forming gas (90% N2 + 10% H2 ) with a metal electrode on top of the oxide, these traps disappear almost entirely. Instead, traps with crosssection of 2 × 10−18 cm2 appear, which were tentatively associated with H2 O molecules in the SiO2 on the basis of IR absorption measurements (Hartstein and Young, 1981). The suggested chemical reaction predicts breaking of Si O bond according to: Si O H + 2H → Si H + H O H,
(11.2.1)
which would lead to Si H bond formation in the oxide on one-to-one correlation with the removal of SiOH traps (Young, 1981). Unfortunately, the investigated correspondence of the thermal process with the Si H IR optical absorption band exhibits no behaviour consistent with the sample processing (Hartstein and Young, 1981) which leaves the feasibility of this description still an open question. A very similar reaction pointing to the elimination of SiOH groups is also suggested to occur under extended exposure of SiO2 to radiolytic atomic hydrogen or an electron–hole plasma optically excited in the oxide (Afanas’ev et al., 1995a). Again, the decrease in the SiOH trap density appears to be ‘compensated’ by an increase in the density of traps with 2 × 10−18 cm2 cross-section. Moreover, the application of ESR spectroscopy reveals the formation of a corresponding number of silicon dangling bonds. The latter is seen as the consequence of H liberation from the SiH bonds in SiO2 by hole trapping which will be discussed in more detail in the next section. It is likely then that reaction (11.2.1) may result in the generation of unpassivated, ESR-active silicon dangling bonds if the supply of atomic H is limited. There seems to be another sort of SiOH-related neutral electron trap in SiO2 originating from radiation damage or hole injection into the oxide. It has a larger cross-section with typical low-field value of (2–4) × 10−15 cm2 (Alexandrova and Young, 1983; Walters and Reisman, 1990; Adamchuk et al., 1990; Buchanan et al., 1991; Kimura and Ohmi, 1996) and a high-field value of about 1 × 10−15 cm2 (Aitken et al., 1978a, b). The thermo-chemical behaviour of these traps, i.e., their disappearance upon annealing in forming gas or after extended (in time) electron–hole pair generation in the oxide (Afanas’ev et al., 1995a) suggests the SiOH fragment to be also involved in the trap structure. It is likely that these traps are formed as a result of a (strained) Si O Si bridge rupture assisted by a hydrogen atom or proton leading to SiOH HSi or SiOH HOSi centres in SiO2 . Among other electron traps with tentatively assigned atomic structure one should mention the hydrogen terminated oxygen vacancy centre (O3 ≡Si H H Si≡O3 ) which gives rise to an acceptor state with electron energy level at 3.1 eV below the SiO2 conduction band edge (Afanas’ev and Stesmans, 1997c). This generation is ascribed to hydrogen (proton)-assisted breaking of a Si O Si bridge followed by removal of the H-decorated oxygen to a nearby interstice position in the form of H2 O (Afanas’ev et al., 1995a). These defects exhibit the capture cross-section of about 10−18 cm2 , i.e., close to that of the H2 O molecule in SiO2 (Hartstein and Young, 1981). However, in contrast to the H2 O traps in as-grown SiO2 , the trapped electrons can be optically excited, i.e., PI is observed. Additionally, the PI cross-section is seen to be sensitive to hydrogen passivation of the unsaturated bonds on the involved silicon atoms remaining after oxygen removal. The latter clearly indicates the trapped site to be located on the oxygen vacancy centre. A likely scenario then may be that an electron initially trapped by H2 O is transferred by tunnelling to an energetically more favourable state offered by the nearby vacancy (Afanas’ev and Stesmans, 1997c). The importance of the close spatial localization of the generic H2 O and the O3 ≡Si H H Si≡O3 centre left behind is also suggested by the disappearance of the PI effect after high-temperature annealing which allows H2 O to diffuse away from the network site at which it was created. At the same time it seems that neither the oxygen vacancy nor SiH bond in SiO2 represent efficient electron traps themselves.
Spectroscopy of Charge Traps in Thin Insulating SiO2 Layers
251
Finally, it needs to be mentioned that large number of impurities implanted as ions into SiO2 were found to generate neutral electron traps. Both P and As implants lead to formation of optically active neutral traps with cross-section in the range of 10−15 –10−16 cm2 (DiMaria et al., 1978a; DeKeersmaecker and DiMaria, 1980). Some of these centres are believed to result from silicon substitution by these group V elements in the oxide network (Alexandrova and Young, 1983). Ion implantation of germanium is also found to result in electron traps with cross-section 1.5 × 10−15 and 2 × 10−16 cm2 when implanted into SiO2 (de Nijs and Balk, 1993). Similarly, implantation of Al ions is reported to lead to electron trap formation (DiMaria et al., 1978b; Young et al., 1978). In some cases implantation of an impurity may even reduce the trapping instability of the oxide as it happens in the case of fluorine implantation (Afanas’ev et al., 1993; 1994a). Interestingly, in the latter case the trap density reduction is observed after implanting extremely low doses of the impurity (1010 cm−2 ). As the number of the ‘passivated’ traps appears to be a multiple of the implanted fluorine ion dose, it was suggested that fluorine acts as a catalyst in some chemical, possibly hydrogen-related process.
11.2.3 Repulsive electron traps in SiO2 As the origin of repulsive trapping, DiMaria initially suggested this to result from a polarized layer of the dielectric surrounding the traps which creates a potential barrier a carrier would need to surmount to be trapped (DiMaria et al., 1976; DiMaria, 1978). Alternatively, one might consider trapping of several carriers of the same charge sign by the same defect (multiple acceptor in the case of electrons) (Rose, 1963). Another, already mentioned mechanism consists in a dissociative trapping mechanism that requires some vibronic assistance. In any case, observation of repulsive electron traps in SiO2 refers to the injection experiments in which the injected charge density approaches or even exceeds 1 C/cm2 . In principle, from each such experiment involving high-injected charge density range the corresponding value of capture cross-section may be extracted. However, despite numerous speculations, the microscopic origin of these traps with σ < 10−18 cm2 remains unknown because no systematic variation of the particular trap density as a function of sample processing can be traced. The latter is largely due to the poor reproducibility of the experimental cross-section values reported by different authors (Feigl et al., 1981; Aslam, 1987). In fact, a large scatter in the inferred electron capture cross-section values is already seen for the traps with σ in the range of 10−18 cm2 as indicated by the data compiled in the Table II in the work of Wolters and van der Schoot (1985). One probable explanation of the fluctuation in the trapping data might be related to the fact that the traps with small cross-section get sequentially occupied after filling all the traps with larger sections. Then, as it was discussed in Chapter 8, the presence of negatively charged (i.e., repulsive) centres in the dielectric would redistribute the subsequently injected carriers such as to make their flow spatially non-uniform. The latter, in turn, will lead to spatial variations of the trap filling probability resulting in smearing out the extracted cross-section values and, at the same time, making them field dependent (Wolters and van der Schoot, 1985) or injected charge density dependent (Sune et al., 1990; Williams, 1992). Therefore, different concentrations of traps with large cross-section in a sample would ensue a different influence on the parameters of traps with small cross-section. Apparently, there is still no way to obtain more reliable repulsive trap parameters. It seems that more success must await the fabrication of layers with negligibly low density of large cross-section traps, which would enable a substantiated discussion regarding their behaviour in the future.
11.3 Hole Traps in SiO2 Investigation of hole trapping in SiO2 faces significant difficulties because of the approximately 1.5 eV higher barrier for the hole injection than that for the electron injection (cf. Table 9.1.1 for dry oxides
252
Internal Photoemission Spectroscopy: Principles and Applications
on Si). In the case of high-field injection or optically excited IPE, this barrier asymmetry would always lead to a higher electron injection current from the opposite electrode than that of the desirable hole current. Therefore, successful analysis of hole trapping properties of SiO2 was delayed until avalanche hole injection (Aitken and Young, 1977) and a quasi-monopolar photoconductive (PC) injection (Stivers and Sah, 1980) (already discussed in Section 5.5) were experimentally realized. At the same time, an observation of much practical interest is that hole trapping in SiO2 appears to be much more efficient than the trapping of electrons leading to predominantly positive charging of this insulator in a radiation environment (Powell and Derbenwick, 1971). For the last reason the hole traps received much attention and considerable experimental detail has become available over the years.
11.3.1 Attractive Coulomb hole traps Just from the electrostatic potential considerations, it would be logic to expect that a negatively charged centre will exhibit similarly large cross-section of hole capture as the Coulomb attractive cross-section for electrons. The experimental verification of this supposition, however, appears to be greatly complicated by the presence of high concentrations of background neutral hole traps as compared to the density of usually occurring negatively charged centres which may potentially serve as attractive Coulomb potentials for holes injected into SiO2 . The only result so far known in this field is presented in Fig. 7.3.2 showing the difference in trapping kinetics between a Si/SiO2 /Au sample pre-injected with electrons to create negative charges in the oxide (mostly electrons trapped by SiOH-related traps discussed in Section 11.2.2) and that in the pristine control sample (Afanas’ev and Adamchuk, 1994). Indeed, as expected, the Coulomb attractive cross-section for holes appears to be close to 1 × 10−13 cm2 at electric field strength in the oxide of approximately 1 MV/cm. This result is in good agreement with the electron trapping data shown in Fig. 11.2.1, suggesting that the same field-dependent cross-section may be used to describe the capture of electrons and holes by the attractive traps.
11.3.2 Neutral hole traps in SiO2 Most of the hole traps in SiO2 layers thermally grown on Si are initially neutral and give rise to a positive charge when trapping a hole (Powell and Derbenwick, 1971; Woods and Williams, 1976). Though this process looks like a simple trapping, its description is significantly complicated by the generally high density of hole traps encountered in SiO2 per unit area, often exceeding 1 × 1013 cm−2 in a 100-nm thick film. This leads to the strong trapping regime, resulting in the Coulomb interaction effects between trapped and drifting carriers as discussed in Chapter 8. When neglected, these effects led to the paradoxical conclusion that both the cross-section of hole capture by a trap and the cross-section of its annihilation by subsequently injected electrons are about 10−13 cm2 at 1 MV/cm. The explanation of this result would require to invoke the physically unrealistic picture of the co-presence of positive and negative centres in numbers exactly compensating each other. Clarification of this paradox can be found in Fig. 8.3.4 indicating that, in the strong trapping limit, the apparent cross-section corresponds to the area screened by the Coulomb potential of the filled trap. This area has a value close to the capture cross-section of the attractive Coulomb traps as can be noticed when comparing Figs 8.3.4 and 11.2.1. The microscopic cross-section of the dominant hole traps in SiO2 appears to be much smaller, about 3 × 10−14 cm2 . The latter was measured in Si/SiO2 samples with low trap density (<1012 cm−2 ) fabricated by cooling the oxidized Si wafers in oxygen ambient (Afanas’ev and Stesmans, 2001b). The same value can also be extracted from the experimentally measured field-dependent apparent cross-section by extrapolating the Coulomb screened area to zero (cf. Eq. (8.3.6)). Hole traps with close cross-section were also found in the SiO2 layers grown by thermal oxidation of SiC (Afanas’ev and Stesmans, 1996), suggesting these to be sort of an intrinsic oxide defect.
Spectroscopy of Charge Traps in Thin Insulating SiO2 Layers
253
The atomic nature of defects responsible for hole trapping in SiO2 also was a subject of confusion for a long time. Quite some time ago, it was discovered that accumulation of the radiation-induced positive charge due to trapped holes correlates with the appearance of ESR-active E centres in the SiO2 (O3 ≡Si• defect where the dot symbolizes an unpaired electron) (Witham and Lenahan, 1987a, b; Kim and Lenahan, 1988). Subsequent prolonged post-irradiation electron injection using IPE was observed to annihilate the positive charge and, at the same time, leads to decrease of the E signal interpreted in favour of the model ascribing hole trapping to the oxygen vacancy centres in SiO2 as: O3 ≡Si Si≡O3 + h+ → O3 ≡Si• + Si+ ≡O3 .
(11.3.1)
Thus, this positive centre would recover its original neutral diamagnetic configuration upon re-trapping an electron. Universality of this description was countered by the report on the observation of an entirely diamagnetic (ESR-inactive) injection-induced positive charge in SiO2 , which cannot be explained by the oxygen vacancy trapping model (Trombetta et al., 1988). Moreover, it appeared later that the rate of positive charge annihilation is much higher than the rate of E -centre deactivation, where a large portion of these defects remains in the paramagnetic state after all the positive charge is removed (Conley et al., 1994). This led to the supposition that several types of E -centre precursors are co-present in SiO2 , leading to an uncorrelated behaviour of their density with the hole-induced positive charge. The above suggestion would indicate the presence of several types of hole traps in SiO2 which, however, looks to be unrealistic because one cross-section value of (3–4) × 10−14 cm2 is generally found in the SiO2 layers fabricated on different substrates using various technologies of thermal oxidation (see, e.g., (Krantz et al., 1987; Adamchuk et al., 1990; Afanas’ev et al., 1995b; Afanas’ev and Stesmans, 1996; 2000a; 2001b). Therefore, to resolve this issue regarding the discrepancy between the annihilation crosssection of the positive charge created by hole trapping and the deactivation of E -centres, a correlative analysis of the field dependence of positive charge and the E centre density was performed (Afanas’ev and Stesmans, 2000a). The stimulus for this experiment was the previous observation of the strong field dependence of the trapped hole annihilation cross-section shown in Fig. 11.2.1. The latter would lead to the corresponding field-dependent balance between hole trapping and annihilation when electron–hole pairs are generated in the oxide by photons with hν > Eg (SiO2 ) = 8.9 eV. If both the positive charge and the paramagnetic E centre located at the same network site as Eq. (11.3.1) would predict the field-dependent densities of these centres would match quantitatively. The results of the comparison between the saturation density of trapped positive charge as determined from the capacitance–voltage (CV) curve shift and that of ESR-active centres measured in physically the same samples of oxidized silicon are shown in Fig. 11.3.1. The charge density (filled symbols) resulting from the electron–hole generation by 10 eV photons is seen to be maximal when a positive bias is applied to the semitransparent metal electrode which corresponds predominantly to hole transport through the oxide while most of the electrons are extracted to the metal, as already discussed in Section 5.5. When the oxide field becomes low, the trapped charge can be efficiently neutralized (annihilated) by electrons. The latter occurs because the capture cross-section of a hole trap (3 × 10−14 cm2 ) is much smaller that the cross-section of the trapped hole neutralization by an electron which approaches 10−12 cm2 in low fields as can be seen from the data shown in Fig. 11.2.1. When the field orientation is reversed, electrons are predominantly transported across the oxide (cf. Fig. 5.5.2) and the density of trapped holes appears to be low as expected. Only at the highest applied field of −3 MV/cm, when the neutralization cross-section falls to the 10−15 cm2 range (cf. Fig. 11.2.1), the trapped hole density starts to increase. By contrast, in two samples with significantly different SiO2 growth conditions including one with a very low hole trap density (sample A in Fig. 11.3.1), no correlated to the charge field-dependent E centre density is observed (open symbols in Fig. 11.3.1). At the same time, the density of the ESR-active defects is seen to be comparable to the trapped charge density under the positive bias which is consistent with
254
Internal Photoemission Spectroscopy: Principles and Applications
[E], VFBCOX/e (1012 cm2)
8
Si/SiO2/Au
hn 10 eV
6
4
B
2 A 0 3
2
1 0 1 Electric field (MV/cm)
2
3
•
Fig. 11.3.1 Densities of E centres (, ) and the positive charge ( , ) observed after injection of 1015 electron/ hole pairs cm−2 as a function of the strength of the electric field for MOS structures with oxide in the as-grown state (A: , ) and after degradation by a high-temperature annealing (B: , ). Lines are guides to the eye.
•
previous experimental reports. The absence of any correlation between E centres and the annihilationcontrolled trapped positive charge density indicates that most of the observed E centres are related to electrically neutral fragments of the SiO2 network. This conclusion excludes the trapping scheme given by Eq. (11.3.1) as the dominant mechanism of hole capture in the thermally grown oxides on Si or SiC (Afanas’ev and Stesmans, 2000a). One now might address the scheme of hole trapping that would result in the formation of an electrically neutral O3 ≡Si• entity and a positive charge at a different location. The latter would require some mobility of the charged entity logically leading to the proton hypothesis suggested by Revesz to describe radiation response of SiO2 insulating films (Revesz, 1977) (see also McLean, 1980; Saks and Rendell, 1992; Rivera et al., 2002). Assuming the positively charged proton and the neutral E centre to be created in a single hole capture event the following scheme of trapping was advanced (Afanas’ev and Stesmans, 2000a; 2001a, b): O3 ≡Si H + h+ → O3 ≡Si• + H+ ,
(11.3.2)
in which the proton is supposed to drift a certain distance before being trapped by some network site in SiO2 . Upon annihilation, the proton becomes mobile in the form of neutral atomic hydrogen which can partially passivate E centres prone to hydrogen bonding (see, e.g., Stahlbush et al., 1993), dimerize with another hydrogen atom, or, else, enter one of the electrodes applied to the SiO2 layer. By using the a boron doped p-type silicon electrode as detector of atomic hydrogen discussed in Section 6.6, hydrogen liberation was directly observed, by the process of B-acceptor inactivation, both during the hole trapping and subsequent annihilation of the trapped charge by injected electrons (Afanas’ev and Stesmans, 2001a, b). These observations point to the process given by Eq. (11.3.2) as the major contribution to hole trapping in thermally grown SiO2 on Si. A second paramount argument supporting the proton nature of the trapped charge was given by the hydrogen isotope mass effect observed in the post-injection relaxation of the hole-trapping-induced charge (Afanas’ev and Stesmans, 2001a) which suggests, indeed, the motion of the radiolytic protons in SiO2 to have an influence on the trapped charge density. The latter conclusion
Spectroscopy of Charge Traps in Thin Insulating SiO2 Layers
255
is also consistent with the hydrogen isotope effect exposed in the post-irradiation Si/SiO2 interface trap generation reported by Stahlbush et al. (1993) and with the results of mass-spectrometry experiments in the deuterated SiO2 samples (Rivera et al., 2002). Though the O3 ≡Si H network fragments appear to be the major source of hole traps in thin layers of SiO2 on Si (σ = 3 × 10−14 cm2 ), there were also observed traps with a smaller cross-section (σ < 10−15 cm2 ) that seems to be related to the presence of radiolytic atomic hydrogen in SiO2 (Afanas’ev et al., 1995a, b). The density of these traps is determined by the carrier injection rate leading to a current-dependent saturation charge density. These traps are thought to be associated not with any particular defect site in SiO2 but rather with atomic H liberated from Si H groups in the SiO2 matrix or from an external source like a metal electrode. Being trapped in SiO2 , the charge of the protons slowly decays with time exhibiting, again, a sensitivity of the charge relaxation rate to the type of hydrogen isotope (hydrogen or deuterium) involved (Afanas’ev et al., 1995b). Despite, as compared to the O3 ≡Si H group, the small capture cross-section of the H-related hole traps, the latter appear to play a decisive role in that the created protons seem to be involved in the initiation of the bond breaking in SiO2 – a crucial degradation process. Thus, formation of protons through a hole capture appears to lead to proton interaction with Si O bonds in the oxide matrix. As the first result pointing in this direction, annihilation of the proton is hinted to lead to the formation of the O3 ≡ Si OHrelated electron traps (σ = 10−17 cm2 ) suggesting the Si O bond rupture to occur as expressed in Eq. (11.3.3a). Next, the second Si O bond is ruptured in a similar way resulting in the generation of an interstitial H2 O molecule and leaving an oxygen vacancy (Eq. (11.3.3b)) (Afanas’ev et al., 1995a): O3 ≡Si O Si≡O3 + H+ + e → O3 ≡Si OH O3 ≡Si OH Si≡O3 + H+ + e → O3 ≡Si•
H2 O
•Si≡O3 , •Si≡O3 .
(11.3.3a) (11.3.3b)
As to the latter atomic configuration, upon H2 O removal from the position between two silicon atoms, two hydrogen atoms can now be added to terminate the dangling bonds of silicon atoms. Schematic given by Eqs (11.3.3a and 11.3.3b) actually represents an electrochemical reduction of silicon dioxide by hydrogen stimulated by electron and hole injection. Its most attractive feature consists in the fact that nearly all products of the reactions would be observable as traps in SiO2 . These were assigned on the basis of their capture cross-section of electrons (SiOH and H2 O traps) or holes (O3 ≡Si H traps). As an independent affirmation, ESR analysis of the samples reveals generation of a high density of additional E centres after ‘degrading’ the oxide by combining electron, hole, and atomic hydrogen injection in the process of exposing Si/SiO2 /metal samples to 10-eV photons (Afanas’ev et al., 1995a). As appeared later, this type of defect generation ultimately leads to the development of electrical conduction causing leakage currents across initially highly insulating SiO2 layers, an effect similar to the stress-induced leakage currents in silicon MOS devices (Afanas’ev and Stesmans, 1997c; 1999c; 2000c, d). It is also well possible that the bond rupture (defect generation) tends to cluster, as ESR results may suggest (Afanas’ev et al., 1995a), leading to the formation of defective regions in SiO2 which are routinely seen as precursors of the oxide dielectric breakdown. At the current high – quality level of SiO2 fabrication technology, the hole trapping by neutral centres, putatively – as interpreted, mostly by O3 ≡Si H traps – is still by far more efficient than would be the trapping by any repulsive centre (σ < 10−18 cm2 ) at any realistic defect density. Taking into account the possibility of concomitant electron injection which would lead to partial annihilation of the trapped charge, particularly in vicinity of the interfaces, the Coulomb screening of traps, and the current redistribution effects described in Chapter 8, analysis of the trapping kinetics at large injected hole fluxes
256
Internal Photoemission Spectroscopy: Principles and Applications
cannot be considered as reliable. The latter effectively excludes identification of repulsive hole traps in SiO2 , thus limiting the present discussion to the cases of only attractive and neutral centres.
11.4 Proton Trapping in SiO2 As might have become clear from the description of positive charging of SiO2 caused by hole trapping, a third type of charge carriers, i.e., protons, is needed to describe the effects of injection-induced charge adequately. One may notice, for instance, that when considering the process described by Eq. (11.3.2), the rate of positive charging during hole injection will be determined not only by the hole trapping rate but, also, by the probability of the subsequent proton trapping. However, very little is known regarding the latter process because quantification of the proton density or concentration in SiO2 during carrier injection is still not in reach. In one approach, to shed some light on the proton trapping problem, it was attempted to quantify the flux of injected (implanted) protons from an external ion source into SiO2 by using the external current density (Afanas’ev et al., 2001a; 2002c). A basic precaution in this experiment was to reduce the secondary ion–electron emission current to a negligible level through limiting the energy of protons (Ep ) directed to the Si/SiO2 target to such low levels that excitation of core levels of O (1s level with binding energy of about 530 eV) and Si (2p level with binding energy of 104 eV) atoms in SiO2 matrix becomes impossible. Thus, by using protons with kinetic energy less than 100 eV one can then directly associate the target current with the current of injected protons (Afanas’ev et al., 2002c). Under influence of an applied electric field, the protons, implanted into SiO2 to a depth of a few nanometres, will be pushed through the oxide layer in the similar way as photoinjected charge carriers and will interact with the oxide on their way to the silicon substrate serving as the cathode electrode. After exposure to a certain dose of protons, MOS capacitors were formed through thermo-resistive evaporation of gold electrodes on the samples kept at room temperature to prevent annealing of the trapped charge. Then the charge density was evaluated using CV measurements. Results of these experiments are exemplified in Fig. 11.4.1 showing the detected oxide charge (the effective charge density is calculated from the CV curve shift, cf. Eq. (6.2.1)) as a function of the proton density implanted into the oxide of three differently oxidized silicon samples (A–C). These samples exhibit strongly differing densities of E centres as revealed by the ESR measurements in the control, not exposed to protons, samples (in 1012 cm−2 , measured after optical injection of 1015 holes/cm2 ): 0.4 (A), 2.5 (B), and 1.9 (C) (Afanas’ev et al., 2002c). For the sake of comparison, the charging kinetics are also shown for Ar+ ion implantation as well as for low-field hole injection using PC excited by 10-eV photons in the same samples. A remarkable feature of the proton-induced charge consists in the 100% initial trapping probability in all the samples, irrespective of the E centres density initially present in the as-fabricated films. By contrast, the charging kinetics in the case of Ar+ implantation and hole photogeneration are correlated with the density of E centers available in the as-grown oxide. The latter suggests the charging to occur following the scheme described by Eq. (11.3.2). At the same time, neutralization of the trapped positive charge by photoinjection of electrons in all cases occurs with the same kinetics indicating that no differences between positive centres can be traced and, therefore, these states are apparently to be of the same type (cf. Fig. 2 in Afanas’ev et al. (2002c)). The universally observed 100 % efficiency of this proton trapping in SiO2 would logically explain why not this process itself, but the initial hole interaction with occurring O3 ≡Si H defects represents the rate-limiting step of the positive charging. This, importantly, raises the question as to the nature of the proton traps in SiO2 . Obviously, these must be so abundant to result in a total trapping, that high, that no naturally occurring point defect, let alone any impurity, in the oxide would be able to account for that density. So, it would indicate the proton to react with the SiO2 network (bonds) directly. Among
Spectroscopy of Charge Traps in Thin Insulating SiO2 Layers
257
3 H implantation 2
Trapped charge centres (1012 cm2)
1 (a) 0 Ar implantation 2
1 (b) 0 Hole injection F 0.1 MV/cm
2
1 (c) 0 0
50 Injected ion/hole dose
100 (1012 cm2)
Fig. 11.4.1 Effective positive charge density observed in samples A(), B(), and C() after implantation of H+ (a) and Ar+ (b) ions or hole photoinjection (c). For the ion-implanted samples, each point corresponds to a separately implanted specimen. The hole trapping data are obtained through sequential hole injection at an oxide field of F = 0.1 MV/cm, interrupted by CV curve recording.
the experiments suggesting interaction of protons with regular (or slightly strained) bonds of the SiO2 network one may envision the etch-back profiles of the trapped charge shown in Fig. 11.4.2. First, the results bear out the presence of a significant Si/SiO2 interface-related component of the charge. At the same time, the deviation of the observed dependences from the straight line suggests that there is also a significant portion of protons trapped in the bulk of the amorphous oxide (cf. Section 6.2). Note that in the shown case of thick oxides, the influence of ion implantation damage (knock-off effect) is excluded because most of the probed SiO2 volume lies outside of the narrow near-surface layer (<20 nm) in which the low-energy protons can penetrate ballistically. Second, the proton implantation appears to generate E centres to a density almost two orders of magnitude larger than that observed in the as-oxidized silicon samples (see Fig. 5 in Afanas’ev et al. (2002c)). This result provides evidence for the Si O bond breaking process, probably according to the scheme given by Eq. (11.3.3), which would mean that the proton is likely to be attached to the oxygen atom in a Si O Si bridge, causing its subsequent rupture. Finally, once stable positive charge is generated in the oxide by proton trapping, the sample can be subjected to thermal annealing with the view to determine binding energies of the protons. The inverse time
258
Internal Photoemission Spectroscopy: Principles and Applications 1.0
VFB(x)/VFB(dOX)
0.8 0.6 0.4 0.2 0.0
dOX1 0
dOX2
50 100 150 200 Remaining oxide thickness (nm)
250
Fig. 11.4.2 Variation of flatband voltage (VFB ) shift normalized to that observed on the un-etched sample as a function of the remaining oxide thickness x for the samples implanted with H+ with energy Ep ≤ 100 eV and dose ≈ 1 × 1014 cm−2 (), and with Ep ≤ 300 eV and dose ≈1018 cm−2 (). The solid line shows the flatband voltage variation expected if the charge would be located at the Si/SiO2 interface. The solid line indicates the VFB behaviour expected for the charge located in the geometrical plane of Si/SiO2 interface. The dashed lines indicate the oxide thickness dox prior to the etching.
ln (1/t)
4 5
SiO2 : H
6
(100)Si
(0001)4H-SiC (0001)6H-SiC
7 (111)Si 8 9 10 11 2.1
Ea 1.7 eV 2.2
2.3 2.4 1000/T (K1)
2.5
Fig. 11.4.3 Arrhenius plot of the inverse annealing time constant of positive charges produced by proton implantation in the oxides thermally grown on (111) () and (100)Si (), and on (0001) faces of 4H SiC () and 6H SiC().
constant of charge detrapping can be considered to be equal to the proton liberation rate and, being plotted as a function of inverse temperature, would then allow determination of the corresponding activation energy. The results of such experiments are depicted by the Arrhenius plot shown in Fig. 11.4.3 for the proton-implanted SiO2 layers obtained by thermal oxidation of Si or SiC (Afanas’ev et al., 2002c). In the Si/SiO2 structures, the inferred activation energy for proton liberation can be estimated as 1.7 eV, while slightly lower values are found for the oxidized SiC. This energy can be compared to the activation energy of ‘trapped holes’ removal in Si/SiO2 entities found to be close to 1.4 eV (Li and Sah, 1995). This finding, i.e., nearly the same annealing activation energies for proton and hole detrapping, provides an additional support to the hypothesis regarding the proton origin of the hole-trapping-induced positive charge in SiO2 .
Spectroscopy of Charge Traps in Thin Insulating SiO2 Layers
259
The current overview of the ‘initial’ results on proton trapping in SiO2 indicates these ions to be sufficiently mobile to drift across SiO2 layers of hundreds of nanometres in thickness, and to undergo trapping and detrapping processes, in other words, to behave like charge carriers of electronic origin (electrons and holes). This conclusion potentially allows one to describe proton trapping kinetics using the same approach as discussed in Chapters 7 and 8 for the case of electronic charges. Though the proton trapping regime encountered in SiO2 is such strong that extraction of the meaningful capture cross-section value is precluded, this possibility remains to be explored in insulators of a different composition. Concluding this chapter, one can formulate two major outcomes of the trapping studies in SiO2 layers. First, the injection spectroscopy of charge traps based on measuring capture cross-sections value offers a tool of unprecedented sensitivity to study the generation and behaviour of defects in thin layers of insulating solids. For instance, with the measurement sensitivity to electron trap density of 1011 cm−2 , hardly any other experimental technique can compete with injection spectroscopy. An important feature here consists in the highly valuable observations of the field-dependent trapping phenomena which makes the application of IPE and PC-based charge injection techniques highly attractive. Second, as it also emerges in the case of SiO2 layers, the description of charge accumulation phenomena based on electron and hole trapping is significantly incomplete. Ionic charges, e.g., proton species, appear to play a dominant role under certain injection conditions. Further, it might be expected that, as the thickness of the collector material decreases to the range of a few nanometres, the role of ionic charges will become larger and other species with lower diffusivity or mobility will gain an importance. Therefore, one may expect significant development in the ion-transport studies in the nanometre-sized structures in the very near future.
CHAPTER 12
Conclusions
With the basic principles of internal photoemission (IPE) spectroscopy techniques outlined and discussed, and several examples of studies presented, one might consider the perspectives of its application for material analysis in the near future. In looking for potential fields of new research, we may envision two large groups. First, the IPE spectroscopy will definitely be applied as a well-established technique of electron state characterization to new material systems, particularly in the areas of semiconductor electronics, nanotechnology and molecular functional materials. The experimental instruments for this research are already available, as outlined earlier in this book. Second, the continuing progress in experimental physics and solid-state technology offers new methodological possibilities to realize IPE experiments aiming at the determination of new physical properties of the analysed materials, like electron and ion transport parameters or the lateral distribution of electron states over the sample area. The latter would imply that development of novel spectroscopy or microscopy tools enabling IPE methods to enter new research areas. In an exploring attitude, we may address some specific items below. One of the most important fields of application of the IPE technique in the coming years will likely be associated with the introduction of new material systems to the technology of integrated semiconductor devices for electronic and opto-electronic applications. The trend of continuing downscaling of the semiconductor devices urges departure from the classical silicon/silicon dioxide/polycrystalline silicon structure towards heterostructures involving insulating materials of high dielectric constant (Wilk et al., 2001; Houssa, 2004; Huff and Gilmer, 2005; Houssa et al., 2006), semiconductors with enhanced carrier mobility, and highly conductive composite gate electrode materials. In addition, wide bandgap semiconductors become more and more actively used in heterojunction devices, which necessitates spectroscopic characterization of newly formed interfaces (Gila et al., 2004; Afanas’ev et al., 2004e). Finally, the low-permittivity insulators of different composition intended for application in high-density interconnection architecture are approaching the point of entering real technology (Maex et al., 2003). Obviously, in all these cases, the electronic properties of the various interfaces between these materials are determined by the spectrum of the corresponding electron states, which awaits spectroscopic characterization. Taking into account that nearly half of the elements of the periodic table are currently considered as potential component of one or the other material system, the experimental research faced in this area looks formidable. Nevertheless, as hopefully demonstrated in this book, IPE assembles a highly reliable and accurate group of methods well suited to fulfil this task. 260
Conclusions
261
As to the analysis of the nanostructured materials, the application of IPE offers two major advantages over the conventional electron spectroscopy tools. First, the sensitivity of the IPE quantum yield spectroscopy becomes sufficient to characterize both the fundamental and the imperfection-related parts of the density of electron states. Second, in the case of electrically isolated nanostructures the exhaustive optical depopulation method offers the unique possibility of absolute density of states (DOS) energy distribution measurements that cannot be achieved by other means. Moreover, the electron states of the insulating matrix surrounding the nanoparticle or nanostructure also becomes within reach for characterization when using this technique. The latter feature brings the studied material systems closer to those which may be used in practical devices. Finally, the IPE spectroscopy can be applied to technologically very flexible material systems like collectors deposited on top of a nanostructure, e.g., an electrolytic contacts, which greatly widens the list of materials that may potentially be investigated. Finally, one may also point to molecular and organic materials as at the basis of another, relatively new area of high research activity. It is worth of reminding here that the electron states in these materials still retain mostly a molecular character and it remains unclear to what extent this would have an effect on electron injection out of a conventional conductor or semiconductor into these phases. In addition to this, the influence of molecular polarization might also become important as the injected carrier will be transported slowly because of molecular nature of the lowest occupied molecular orbital (LUMO) and highest occupied modular orbital (HOMO) states. Additional contributions to the interface barrier cannot be excluded as the materials under discussion are highly permeable to ions and the issue of proton charges, discussed above for the case of the inorganic SiO2 insulator, might become even more important. At the same time, the barrier sensitivity to foreign species can be used to develop ion-sensing detector devices as it is done in the Pt(Pd)/SiO2 -based structures (Lundstrom, 1996; Ekedahl et al., 1998). The sensitivity of IPE to the charges in the interface barrier region would promote it as the tool of choice in analysing the adsorbate-induced charging phenomena. In all the applications outlined above as well as in the other possible ones, IPE offers significant advantages over the photoelectron or secondary electron spectroscopy by reducing the influence of artefacts associated with sample irradiation. First, by making use of a conducting field electrode the charging effects in insulating collectors can be minimized and, also, quantified thus providing additional physical information. Second, by using photons of lower energy than invoked in photoelectron spectroscopy, possible damage of the material is avoided, which is of particular importance for organic and molecular substances. Finally, in many cases IPE measurements can be performed in device-like structures thanks to the availability of high-brightness light sources and focussing systems. These also enable the analysis of small-area samples, which might allow reduction of detrimental leakage current, thus coming to the rescue in detecting the IPE electron transitions. Envisioning basic extensions of the methodology, introduction of additional parameters into the IPE experiments scheme can be considered. Though this will unavoidably complicate the measurements technically, new physical information will become available as the benefit. For instance, by combining IPE measurements with scanning excitation (spot or probe), the lateral distribution of the photoinjected current can be recorded (DiStefano, 1971, DiStefano and Viggiano, 1974; Williams and Woods, 1972; Margaritondo, 1997) enabling imaging of inhomogeneous interface barriers. Application of this method allows one to correlate structural features of the studied materials, e.g., the grain boundaries, with particular components of the electron DOS. What remains to be evaluated is the potential spatial resolution of this IPE microscopy because, as indicated by the ballistic electron emission microscopy (BEEM) results, scattering of the injected carriers may significantly broaden their angular distribution. Next, by using IPE in the time-resolved mode the dynamics of charge carriers (time-of-flight type experiments) can also be analysed. IPE has the obvious advantage of delivering all the excited charge
262
Internal Photoemission Spectroscopy: Principles and Applications
carriers from the same geometrical plane of the emitter–collector interface. Thus, the ultimate time resolution will be primarily determined by the duration of the exciting light pulse. However, a potential problem when using ultra-short exciting pulses consists in the high power, which may lead to enhanced light absorption in the applied metal electrodes due to the free-electron excitation. Potentially this problem can be resolved by applying electrolyte or semiconductor electrodes. Furthermore, the time-resolved measurements may also enable two-photon excitation schemes to probe the DOS of unoccupied electron states – the possibility remaining yet unexplored in the IPE experiments. The latter option may also appear to be of large interest when studying nanostructures imbedded in an insulating matrix as it might reveal the principle carrier de-excitation mechanisms. Another approach for investigation of the carrier transport parameters consists in the observation of the Hall effect for the photoinjected charge carriers (Goodman, 1967). This method seems to be the only tool able to determine the carrier mobility in wide bandgap insulating collectors, given the low intrinsic carrier concentration at room temperature. With the dramatically increasing variety of insulating materials entering the electron device technology nowadays, these measurements might become the cornerstone of carrier transport analysis as it happened with the cited work of Goodman on thermally grown silicon dioxide. Worth of mentioning here is that the modern gate patterning technologies and the light focussing instrumentation may potentially enable Hall-type measurements in relatively thin layers of the insulating collector materials. One more area of possible development of novel IPE-based experimental tools concerns the electrodeless systems in which the surface of the collector is biased not by a voltage applied to the conducting field electrode, but by a layer of ions deposited on it from a liquid (electrolyte) or gas (e.g., from a discharge) phase. In this case the detection of IPE can be performed by using surface potential measurements or some field-sensitive optical effect (second harmonic generation (Wang et al., 1998), electroabsorption spectroscopy (Campbell et al., 1996b, etc.)). Among other important phenomena, the adsorbate-induced states become within reach for analysis in such experimental arrangement. Without doubts, the list of potentially new approaches to IPE experiments can be continued. In overviewing the field, it has become clear that the need for the characterization of new materials and their interfaces in heterostructures is still increasing, calling for even more novel characterization tools. These two factors make the IPE spectroscopy set for further wide development in the years to come. Therefore, it is my wish that this book may be able to serve other researches as a guide on the fundaments of the IPE spectroscopy on their road of exploration of electronic states in heterosystems of materials
References
Abstreiter, G., Prechtel, U., Weimann, G., and Schlapp, W. (1985) Internal photoemission in GaAs/(Alx Ga1−x ) As heterostructures. Physica B & C, 143B+C, 433–438. Abstreiter, G., Prechtel, U., Weimann, G., and Schlapp, W. (1986) Internal photoemission – A suitable method for determining band offsets in semiconductor heterostructures. Surface Science, 174, 312–317. Adamchuk, V. K. and Afanas’ev, V. V. (1984) Determination of the band gap of a thermal oxide on silicon. Soviet Physics-Solid State, 26, 1519–1520. Adamchuk, V. K. and Afanas’ev, V. V. (1985) Barrier energy determination at the semiconductor-insulator interface. Soviet Journal of Physics, Chemistry, and Mechanics of Surfaces, 4(10), 42–47. (in Russian). Adamchuk, V. K. and Afanas’ev, V. V. (1988a) Effect of hole scattering on their capture by the traps near Si SiO2 interface. Soviet Journal of Physics, Chemistry, and Mechanics of Surfaces, 7(9), 147–150. (in Russian). Adamchuk, V. K. and Afanas’ev, V. V. (1988b) Effect of charged centers on semiconductor-insulator potential barrier shape. Soviet Journal of Physics, Chemistry, and Mechanics of Surfaces, 7(10), 106–111. (in Russian). Adamchuk, V. K. and Afanas’ev, V. V. (1992a) Internal photoemission spectroscopy of semiconductor– insulator interfaces. Progress in Surface Science, 41, 111–211. Adamchuk, V. K. and Afanas’ev, V. V. (1992b) Photocharging technique for barrier determination on semiconductor–insulator interface. Physica Status Solidi (a), 132, 371–379. Adamchuk, V. K., Afanas’ev, V. V. and Akulov, A. Ph. (1988) Disordering of silicon surface during thermal oxidation. Soviet Journal of Physics, Chemistry, and Mechanics of Surfaces, 7(12), 106–111. (in Russian). Adamchuk, V. K., Afanas’ev, V. V., and Akulov, A. Ph. (1990) Electron trap activation in thermal SiO2 . Physica Status Solidi (a), 122, 347–354. Afanas’ev, V. V. (1991) Electron scattering in the image-force potential well during photoemission into insulator. Soviet Journal of Physics, Chemistry, and Mechanics of Surfaces, 10(7), 75–81. (in Russian). Afanas’ev, V. V. (1992) Modification of Si SiO2 interfacial barrier by lithium ions. Soviet Journal of Physics, Chemistry, and Mechanics of Surfaces, 11(5), 63–68. (in Russian). Afanas’ev, V. V. and Adamchuk, V. K. (1994) Injection spectroscopy of localized states in thin insulating layers on semiconductor surfaces. Progress in Surface Science, 47, 301–394. Afanas’ev, V. V. and Stesmans, A. (1996) Hole traps in oxide layers thermally grown on SiC. Applied Physics Letters, 69, 2252–2254. Afanas’ev, V. V. and Stesmans, A. (1997a) Photon stimulated tunnelling of electrons in SiO2 : Evidence for a defect assisted process. Journal of Physics: Condensed Matter, 9, L55–L60. Afanas’ev, V. V. and Stesmans, A. (1997b) Interfacial defects in SiO2 revealed by photon stimulated tunnelling of electrons. Physical Review Letters, 78, 2437–2440. 263
264
References
Afanas’ev, V. V. and Stesmans, A. (1997c) H-complexed oxygen vacancy in SiO2 : Energy level of a negatively charged state. Applied Physics Letters, 71, 3844–3846. Afanas’ev, V. V. and Stesmans, A. (1997d) Electrical conduction of buried SiO2 layers analyzed by photon stimulated electron tunnelling. Applied Physics Letters, 70, 1260–1262. Afanas’ev, V. V. and Stesmans, A. (1997e) Analysis of near-interfacial SiO2 traps using photon stimulated electron tunnelling. Microelectronic Engineering, 36, 149–152. Afanas’ev, V. V. and Stesmans, A. (1998a) Positive charging of thermal SiO2 /Si(100) interface by hydrogen annealing. Applied Physics Letters, 72, 79–81. Afanas’ev, V. V. and Stesmans, A. (1998b) Hydrogen-induced valence alternation state at SiO2 interfaces. Physical Review Letters, 80, 5176–5179. Afanas’ev, V. V. and Stesmans, A. (1999a) Trapping of H+ and Li+ ions at the Si/SiO2 interface. Physical Review B, 60, 5506–5512. Afanas’ev, V. V. and Stesmans, A. (1999b) Photoionization of silicon particles in SiO2 . Physical Review B, 59, 2025–2034. Afanas’ev, V. V. and Stesmans, A. (1999c) Hydrogen-related leakage currents induced in ultrathin SiO2 /Si structures by vacuum ultraviolet radiation. Journal of the Electrochemical Society, 146, 4309–4314. Afanas’ev, V. V. and Stesmans, A. (2000a) Charge state of paramagnetic E’ centre in thermal SiO2 layers on silicon. Journal of Physics: Condensed Matter, 12, 2285–2290. Afanas’ev, V. V. and Stesmans, A. (2000b) Valence band offset and hole injection at the 4H , 6H SiC/SiO2 interfaces. Applied Physics Letters, 77, 2024–2026. Afanas’ev, V. V. and Stesmans, A. (2000c) Leakage currents induced in ultrathin oxides on (100)Si by deep-UV photons. Materials Science and Engineering B, 71, 54–59. Afanas’ev, V. V. and Stesmans, A. (2000d) Correlation between development of leakage current and hydrogen ionization in ultrathin silicon dioxide layers. MRS Symposium Proceedings, 592, 192–200. Afanas’ev, V. V. and Stesmans, A. (2001a) Proton nature of radiation-induced positive charge in SiO2 . Europhysics Letters, 53, 233–239. Afanas’ev, V. V. and Stesmans, A. (2001b) Hydrogen release related to hole injection into SiO2 layers on Si. Materials Science in Semiconductor Processing, 4, 149–151. Afanas’ev, V. V. and Stesmans, A. (2002) Hole trapping in ultrathin Al2 O3 and ZrO2 insulators on silicon. Applied Physics Letters, 80, 1261–1263. Afanas’ev, V. V. and Stesmans, A. (2003) Polytype determination at the SiC–SiO2 interface by internal electron photoemission scattering spectroscopy. Materials Science and Engineering B, 102, 308–312. Afanas’ev, V. V. and Stesmans, A. (2004a) Band alignment at the interfaces of Si and metals with high-permittivity insulating oxides. In High-κ Gate Dielectrics, Houssa, M. (ed.). Institute of Physics Publishing, Bristol. 217–250 ISBN 0 7503 0906 7. Afanas’ev, V. V. and Stesmans, A. (2004b) Stable trapping of electrons and holes in deposited insulating oxides: Al2 O3 , ZrO2 , and HfO2 . Journal of Applied Physics, 95, 2518–2526. Afanas’ev, V. V. and Stesmans, A. (2004c) Energy band alignment at the (100)Ge/HfO2 interface. Applied Physics Letters, 84, 2319–2321. Afanas’ev, V. V. and Stesmans, A. (2006) Spectroscopy of electron states at interfaces of (100)Ge with high-κ insulators. Materials Science in Semiconductor Processing, 9, 764–771. Afanas’ev, V. V., Novikov, S. V., Sokolov, N. S., and Yakovlev, N. L. (1991) MBE-grown (Ca,Sr)F2 layers on Si(111) and GaAs(111): Electronic structure of interfaces. Microelectronic Engineering, 15, 139–142. Afanas’ev, V. V., Mizerov, M. N., Novikov, S. V., and Sokolov, N. S. (1992a) MBE-grown heterostructures fluoride/GaAs(111)B: Control of interfacial barrier by Eu and Sm insulator doping. Applied Surface Science, 60/61, 637–642. Afanas’ev, V. V., Akulov, A. Ph., Gorid, E. M., Petrov, V. V., and Prosolovich, V. S. (1992b) Dumping of electron heating effects in thermal oxides on Ge-doped silicon. Microelectronic Engineering, 19, 481–484.
References
265
Afanas’ev, V. V., Depas, M., de Nijs, J. M. M., and Balk, P. (1993) Simultaneous elimination of electrically active defects in Si/SiO2 structures by implanted fluorine. Microelectronic Engineering, 22, 93–96. Afanas’ev, V. V., de Nijs, J. M. M., and Balk, P. (1994a) Elimination of hydrogen-related instabilities in Si/SiO2 structures by implanted fluorine. Journal of Applied Physics, 76, 7990–7997. Afanas’ev, V. V., Revesz, A. G., Brown, G. A., and Hughes, H. L. (1994b) Deep and shallow electron trapping in the buried oxide layer of SIMOX structures. Journal of the Electrochemical Society, 141, 2801–2804. Afanas’ev, V. V., de Nijs, J. M. M., Balk, P., and Stesmans, A. (1995a) Degradation of the thermal oxide of the Si/SiO2 /Al system due to vacuum ultraviolet irradiation. Journal of Applied Physics, 78, 6481–6490. Afanas’ev, V. V., de Nijs, J. M. M., and Balk, P. (1995b) SiO2 hole traps with small cross section. Applied Physics Letters, 66, 1738–1740. Afanas’ev, V. V., Bassler, M., Pensl, G., Schulz, M., and Stein von Kamienski, E. (1996a) Band offsets and electronic structure of SiC/SiO2 interfaces. Journal of Applied Physics, 79, 3108–3114. Afanas’ev, V. V., Stesmans, A., and Andersson, M. O. (1996b) Electron states and microstructure of thin a-C:H layers. Physical Review B, 54, 10820–10826. Afanas’ev, V. V., Bassler, M., Pensl, G., and Schulz, M. (1997a) Intrinsic SiC/SiO2 interface states. Physica Status Solidi (a), 162, 321–337. Afanas’ev, V. V., Stesmans, A., Revesz, A. G., and Hughes, H. L. (1997b) Trap generation in buried oxides of silicon-on-insulator structures by vacuum ultraviolet radiation, Journal of the Electrochemical Society, 144, 749–753. Afanas’ev, V. V., Stesmans, A., Bassler, M., Pensl, G., Schulz, M., and Harris, C. I. (1999) SiC/SiO2 interface state generation by electron injection. Journal of Applied Physics, 85, 8292–8298. Afanas’ev, V. V., Stesmans, A., Bassler, M., Pensl, G., and Schulz, M. J. (2000) Shallow electron traps at the 4H-SiC/SiO2 interface. Applied Physics Letters, 76, 336–338. Afanas’ev, V. V., Adriaenssens, G. J., and Stesmans, A. (2001a) Positive charging of thermal SiO2 layers: Hole trapping versus proton trapping. Microelectronic Engineering, 59, 85–88. Afanas’ev, V. V., Houssa, M., Stesmans, A., and Heyns, M. M. (2001b) Electron energy barriers between (100)Si and ultrathin stacks of SiO2 , Al2 O3 , and ZrO2 insulators. Applied Physics Letters, 78, 3073–3075. Afanas’ev, V. V., Houssa, M., Stesmans, A., Adriaenssens, G. J., and Heyns, M. M. (2002a) Band alignment at the interfaces of Al2 O3 and ZrO2 -based insulators with metals and Si. Journal of Non-Crystalline Solids, 303, 69–77. Afanas’ev, V. V., Stesmans, A., Chen, F., Shi, X., and Campbell, S. A. (2002b) Internal photoemission of electrons and holes from (100)Si into HfO2 . Applied Physics Letters, 81, 1053–55. Afanas’ev, V. V., Ciobanu, F., Pensl, F., and Stesmans, A. (2002c) Proton trapping in SiO2 layers thermally grown on Si and SiC. Solid State Electronics, 46, 1815–1823. Afanas’ev, V. V., Houssa, M., Stesmans, A., and Heyns, M. M. (2002d) Band alignments in metaloxide-silicon structures with atomic-layer deposited Al2 O3 and ZrO2 . Journal of Applied Physics, 91, 3079–3085. Afanas’ev, V. V., Stesmans, A., Mrstik, B. J., and Zhao, C. (2002e) Impact of annealing-induced densification on electronic properties of atomic-layer-deposited Al2 O3 . Applied Physics Letters, 81, 1678–1680. Afanas’ev, V. V., Stesmans, A., and Tsai, W. (2003a) Determination of interface energy band diagram between (100)Si and mixed Al-Hf oxides using internal electron photoemission. Applied Physics Letters, 82, 245–247. Afanas’ev, V. V., Stesmans, A., Chen, F., Campbell, S. A., and Smith, R., (2003b) HfO2 -based insulating stacks on 4H-SiC(0001). Applied Physics Letters, 82, 922–924.
266
References
Afanas’ev, V. V., Stesmans, A., Zhao, C., Caymax, M., Heeg, T., Schubert, J., Jia, Y., Schlom, D. G., and Lucovsky, G. (2004a) Band alignment between (100)Si and complex rare earth/transition metal oxides. Applied Physics Letters, 85, 5917–5919. Afanas’ev, V. V., Stesmans, A., Chen, F., Li, M., and Campbell, S. A. (2004b) Electrical conduction and band offsets in Si/Hfx Ti1−x O2 /metal structures. Journal of Applied Physics, 95, 7936–7939. Afanas’ev, V. V., Ciobanu, F., Dimitrijev, S., Pensl, G., and Stesmans, A. (2004c) Band alignment and defect states at SiC/oxide interfaces. Journal of Physics: Condensed Matter, 16, S1839–S1856. Afanas’ev, V. V., Stesmans, A., Passlack, M., and Medendorp, N. (2004d) Band offsets at the interfaces of GaAs with Gdx Ga0.4−x O0.6 insulators. Applied Physics Letters, 85, 597–599. Afanas’ev, V. V., Ciobanu, F., Pensl, G., and Stesmans, A. (2004e) Contributions to the density of interface states in SiC MOS structures. In Silicon Carbide: Recent Major Advances, Choyke, W. J., Matsunami, H., Pensl, G. (eds). Springer Verlag, Berlin. 343–371. ISBN 3-540-40458-9. Afanas’ev, V. V., Stesmans, A., Zhao, C., Caymax, M., Rittersma, Z. M., and Maes, J. W. (2005a) Band alignment between (100)Si and Hf-based complex metal oxides. Microelectronic Engineering, 80, 102–105. Afanas’ev, V. V., Stesmans, A., Zhao, C., Caymax, M., Rittersma, Z. M., and Maes, J. W. (2005b) Band alignment at the interface of (100)Si with Hfx Ta1−x Oy high-κ dielectric layers. Applied Physics Letters, 86, 072108. Afanas’ev, V. V., Stesmans, A., Pantisano, L., and Chen, P. J. (2005c) Electrostatic potential perturbation at the polycrystalline Si/HfO2 interface. Applied Physics Letters, 86, 072107. Afanas’ev, V. V., Stesmans, A., Pantisano, L., and Schram, T. (2005d) Electron photoemission from conducting nitrides (TiNx , TaNx ) into SiO2 and HfO2 . Applied Physics Letters, 86, 232902. Afanas’ev, V. V., Stesmans, A., Edge, L. F., Schlom, D. G., Heeg, T., and Schubert, J. (2006a) Band alignment between (100) Si and amorphous LaAlO3 , LaScO3 , and Sc2 O3 : Atomically abrupt versus interlayer-containing interfaces. Applied Physics Letters, 88, 032104. Afanas’ev, V. V., Shamuilia, S., Stesmans, A., Dimoulas, A., Panayiotatos, Y., Sotiropoulos, A., Houssa, M., and Brunco, D. P. (2006b) Electron energy band alignment at interfaces of (100)Ge with rare-earth oxide insulators. Applied Physics Letters, 88, 132111. Afanas’ev, V. V., Stesmans, A., Droopad, R., Passlack, M., Edge, L. F., and Schlom, D. G. (2006c) Electron energy barriers at interfaces of GaAs(100) with LaAlO3 and Gd2 O3 . Applied Physics Letters, 89, 092103. Agarwal, A., Ryu, S. H., and Palmour, J. (2004) Power MOSFETs in 4H SiC: Device design and technology. In Silicon Carbide: Recent Major Advances, Choyke, W. J., Matsunami, H., Pensl, G. (eds). Springer Verlag, Berlin. 785–811. ISBN 3-540-40458-9. Aitken, J. M. (1980) Radiation-induced trapping centers in thin SiO2 films. Journal of Non-Crystalline Solids. 40, 31–47. Aitken. J. M. and Young, D. R. (1976) Electron trapping by radiation-induced charge in MOS devices. Journal of Applied Physics, 47, 1196–1198. Aitken, J. M. and Young, D. R. (1977) Avalanche injection of holes into SiO2 . IEEE Transactions on Nuclear Science, NS-24, 2128–2134. Aitken, J. M., Serrano, C. M., and VanVechten, J. A. (1978a) Temperature and intensity dependence of rate of introduction of neutral traps in SiO2 by e-beam irradiation. Journal of the Electrochemical Society, 125, C127. Aitken, J. M., Young, D. R., and Pan, K. (1978b) Electron trapping in electron-beam irradiatted SiO2 . Journal of Applied Physics, 49, 3386–3391. Alexandrova, S. and Young, D. R. (1983) Microscopic location of electron traps induced by arsenic implantation in silicon dioxide. Journal of Applied Physics, 54, 174–178. Allen, F. G. and Gobeli, C. W. (1966) Energy structure in photoelectric emission from Cs-covered silicon and germanium. Physical Review, 144, 558–568.
References
267
Almeida, J., dell’Orto, T., Coluzza, C., Fasso, A., Baldereschi, A., Margaritondo, G., Rudra, A., Buhlamnn, H. J., and Ilegems, M. (1995) Inhomogeneous and temperature-dependent p-InGaAs/nInP band offset modification by silicon δ doping: An internal photoemission study. Journal of Applied Physics, 78, 3258–3261. Almeida, J., Margaritondo, G., Coluzza, C., Davy, S., Spajer, M., and Courjon, D. (1998) Laterally-resolved study of Au/SiNx /GaAs(100) interface. Applied Surface Science, 125, 6–10. Amy, F., Wan, A. S., Kahn, A., Walker, F. J., and McKee, R. A. (2004) Band offsets at heterojunctions between SrTiO3 and BaTiO3 and Si(100). Journal of Applied Physics, 96, 1635–1639. Anderson, C. L., Crowell, C. R., and Kao, T. W. (1975) Effects of thermal excitation and quantummechanical transmission on photothreshold determination of Schottky barrier height. Solid State Electronics, 18, 705–713. Ang, S. S., Shi, Y. J., and Brown, W. D. (1994) Comparison of square, triangular, and sinusoidal waveforms used for avalanche electron injection on MOS structures. Solid State Electronics, 37, 415–419. Arnett, P. C. and Klein, N. (1975) Poole-Frenkel conduction and neutral trap. Journal of Applied Physics, 46, 1399–1400. Arnett, P. C. and Yun, B. H. (1975) Silicon nitride trap properties as revealed by charge-centroid measurements in MNOS devices. Applied Physics Letters, 26, 94–96. Arora, B. M., Srivastava, A. K., and Guha, S. (1982) On the measurement of barrier height in metalinsulator-semiconductor (GaAs) structures by internal photoemission technique. Journal of Applied Physics, 53, 1820–1822. Aslam, M. (1987) Electron self-trapping in SiO2 . Journal of Applied Physics, 62, 159–162. Aslan, B., Turan, R., and Liu, H. C. (2005) Study of the long wavelength SiGe/Si heterojunction internal photoemission infrared photodetectors. Infrared Physics and Technology, 47, 195–205. Badihi, A., Eitan, B., Cohen, I., and Shappir, J. (1982) Current induced trap generation in SiO2 . Applied Physics Letters, 40, 396–398. Balk, P. (ed.) (1988) The Si–SiO2 System. Elsevier, Amsterdam. ISBN 0-444-42603-5. Ballantyne, J. M. (1972) Effect of phonon energy loss on photoemissive yield near threshold. Physical Review B, 6, 1436–1455. Barbottin, G. and Vapaille, A. (eds) (1989) Instabilities in Silicon Devices: Silicon Passivation and Related Instabilities, North-Holland, Amsterdam. ISBN 0-444-70016-1. Bard, A. J., Utaya, K., Malpas, R. E., and Teherani, T. (1980) Electrochemical and photoelectrochemical studies of excess electrons in liquid ammonia. Journal of Physical Chemistry, 84, 1262–1266. Barker, G. C. (1971) Electrochemical effects produced by light-induced electron emission. Berichte des Bunsengesellschaft Physical Chemistry, 75, 728–739. Barker, G. C., McKeown, D., Williams, M. J., Bottura, G., and Conciali, V. (1973) Charge transfer reactions involving intermediates formed by homogeneous capture of laser-produced photoelectrons. Faraday Discussions, 56, 41–51. Bässler, H. and Vaubel, G. (1968) Photoemission of electrons from alkali metals. Solid State Communications, 6, 97–99. Bassler, M., Afanas’ev, V. V., Pensl, G., and Schulz, M. (1999) Degradation of 6H–SiC MOS capacitors operated at high temperature. Microelectronic Engineering, 48, 257–260. Belmont, M. R. (1975) The capture cross-section of a dipole trap. Thin Solid Films, 28, 149–156. Benderskii, V. A. and Benderskii, A. V. (1995) Laser Electrochemistry of Intermediates. CRC-Taylor & Francis, New York. Benderskii, V. A. and Brodsky, A. M. (1977) Photoemission from Metals into Electrolyte Solutions, Nauka, Moscow (in Russian). Benderskii, V. A. and Grebenshchikov, S. Yu. (1993) Photoemission from metals and the slowing of low energy electrons in water. Journal of Electroanalytical Chemistry, 358, 111–125.
268
References
Benderskii, V. A., Babenko, S. D., Zolotovitskii, Ya. M., Krivenko, A. G., and Rudenko, T. S. (1974) Physical aspects of one- and two-photon photoemission from metals into electrolyte solutions. Journal of Electroanalytical Chemistry, 56, 325–344. Benedetto, J. M., Boesh, H. E., McLean, F. B., and Mize, J. P. (1985) Hole removal in thin-gate MOSFETs by tunnelling. IEEE Transactions on Nuclear Science, NS-32, 3916–3920. Bennett, G. T. and Thompson, J. C. (1986) A model for photoinjection into polar fluids. Journal of Chemical Physics, 84, 1901–1904. Bennett, G. T., Coffmann, R. B., and Thompson, J. C. (1987) Photoemission from silver into liquid ammonia. Journal of Chemical Physics, 87, 7242–7247. Berberich, S., Godignon, P., Millan, J., Planson, D., Hartangel, H. L., and Sanes, A. (1998) Metal-nitride-semiconductor capacitors on 6H–SiC. Materials Science Forum, 264–268, 881–884. Berglund, C. N. and Powell, R. J. (1971) Photoinjection into SiO2 : Electron scattering in the image-force potential well. Journal of Applied Physics, 42, 573–579. Berglund, C. N. and Spicer, W. E. (1964a) Photoemission studies of copper + silver: Theory. Physical Review, 136, A1030–A1043. Berglund, C. N. and Spicer, W. E. (1964b) Photoemission studies of copper + silver: Experiment. Physical Review, 136, A1044–A1056. Bernas, A., Ferradini, C., and Jay-Gerin, J.-P. (1997) On the electronic structure of liquid water: Facts and reflections. Chemical Physics, 222, 151–160. Bibyk, S. B. and Kapoor, V. J. (1984) Trapping kinetics in high trap density silicon nitride insulators. Journal of Applied Physics, 56, 1070–1079. Binks, A. E., Campbell, A. G., and Sharples, A. (1970) Photocurrents in simple polymer systems. Journal of Polymer Science, Part A-2, 8, 529–535. Blat, C. E., Nicollian, E. H., and Poindexter, E. H. (1991) Mechanism of negative-bias-temperature instability. Journal of Applied Physics, 69, 1712–1720. Blauärmel, A., Brauer, M., Hoffmann, V., and Schmidt, M. (2000) Ballistic electron emission microscopy and internal photoemission in Au/Si-structures – a comparison. Applied Surface Science, 166, 108–112. Blyth, R. I. R., Sardar, S. A., Netzer, F. P., and Ramsey, M. G. (2000) Influence of oxygen on band alignment at the organic/aluminium interface. Applied Physics Letters, 77, 1212–1214. Boesh, H. E., McLean, F. B., Benedetto, J. M., McGarrity, J. M., and Bailey, W. E. (1986) Saturation of threshold voltage shift in MOSFETs at huge total dose. IEEE Transactions on Nuclear Science, NS-33, 1191–1197. Bortz, M. L. and French, R. H. (1989) Optical reflectivity measurements using a laser plasma light source. Applied Physics Letters, 55, 1955–1957. Bosenberg, W. A., Magee, C. W., and Botnick, E. M. (1984) Chlorine content in dry and wet MOS gate oxides. Journal of the Electrochemical Society, 131, 2397–2402. Bourcerie, M., Marchetaux, J. C., Boudou, A., and Vuillaume, D. (1989) Optical spectroscopy and fieldenhanced emission of an oxide trap induced by hot hole injection in silicon metal-oxide-semiconductor field-effect transistor. Applied Physics Letters, 55, 2193–2195. Bouthillier, T. M., Young, L., and Tsoi, H. Y. (1983) Scanning internal photoemission studies of sodiumcontaminated metal-oxide-semiconductor capacitors. Journal of Applied Physics, 54, 957–962. Bradley, D. (1996) Electroluminescent polymers: Materials, physics and device engineering. Current Opinion in Solid State and Materials Science, 1, 789–797. Bradley, S. T., Goss, S. H., Hwang, J., Schaff, W. J., and Brillson, L. (2004) Surface cleaning and annealing effects on Ni/AlGaN interface atomic composition and Schottky barrier height. Applied Physics Letters, 85, 1368–1370. Braunstein, A. I., Braunstein, M., Picus, G. S., and Mead C, A. (1965a) Photoemissive determination of barrier shape in tunnel junctions. Physical Review Letters, 14, 219–221.
References
269
Braunstein, A. I., Braunstein, M., and Picus, G. S. (1965b) Hot-electron attenuation in thin Al2 O3 films. Physical Review Letters, 15, 956–959. Brews, J. R. (1973a) Limitations upon photoinjection studies of charge distributions close to interfaces in MOS capacitors. Journal of Applied Physics, 44, 379–384. Brews, J. R. (1973b) Correcting interface-state errors in MOS doping profile determinations. Journal of Applied Physics, 44, 3228–3231. Briggs, D. and Seah, M. P. (eds) Practical Surface Analysis by Auger and X-ray Photoelectron Spectroscopy, Wiley, Chichester. ISBN 0-471-26279-X. Bright, R. and Reisman, A. (1993) Intrinsic threshold voltage shift dependence on the oxide field induced during optically assisted electron injection. Journal of the Electrochemical Society, 140, 2065–2070. Brodsky, A. M. and Pleskov, Y. V. (1972) Electron photoemission at a metal-electrolyte solution interface. Progress Surface Science, 2, 1–73. Brodskii, A. M., Gurevich Yu. Ya., and Levich, V. G. (1970) General theory of electronic emission from the surface of a metal. Physica Status Solidi, 40, 139–151. Buchanan, D. A., Fischetti, M. V., and DiMaria, D. J. (1991) Coulomb and neutral trapping centers in silicon dioxide. Physical Review B, 43, 1471–1486. Cahen, D., Kahn, A., and Umbach, E. (2005) Energetics of molecular interfaces. Materials Today, 8, 32–41. Campbell, I. H., and Smith, D. L. (1999) Schottky energy barriers and charge injection in metal/Alq/metal structures. Applied Physics Letters, 74, 561–563. Campbell, I. H., Hagler, T. W., Smith, D. L., and Ferraris, J. P. (1996a) Direct measurement of conjugated polymer electronic excitation energies using metal/polymer/metal structures. Physical Review Letters, 76, 1900–1903. Campbell, I. H., Davids, P. S., Ferraris, J. P., Hagler, T. W., Heller, C. M., Saxena, A., and Smith, D. L. (1996b) Probing electronic state charging in organic electronic devices using electroabsorption spectroscopy. Synthetic Metals, 80, 105–110. Campbell, S. A. and Smith, R. C. (2004) Chemical vapour deposition. In High-κ Gate Dielectrics, Houssa, M. (ed.). Institute of Physics Publishing, Bristol. 65–88. ISBN 0 7503 0906 7. Card, H. C. and Rhoderick, E. H. (1971) Studies of tunnel MOS diode. 1. Interface effects in silicon Schottky diodes. Journal of Physics D, 4, 1589–1596. Cardona, M. and Pollak, F. H. (1966) Energy band structure of germanium and silicon – k-p method. Physics Review, 142, 530–541. Cartier, E. and Stathis, J. H. (1995) Atomic hydrogen-related degradation of Si/SiO2 structure. Microelectronic Engineering, 28, 3–10. Casperson, J. D., Bell, L. D., and Atwater, H. A. (2002) Materials issues for layered tunnel barrier structures. Journal of Applied Physics, 92, 261–267. Chanana, R. K., McDonald, K., DiVentra, M., Pantelides, S. T., Feldman, L. C., Chung, G. Y., Tin, C. C., Williams, J. R., and Weller, R. A. (2000) Fowler–Nordheim hole tunnelling in p-SiC/SiO2 structures. Applied Physics Letters, 77, 2560–2562. Chang, C. L., Rokhinson, L. P., and Strum, J. C. (1998) Direct optical measurement of the valence band offset of p+ Si1−x−y Gex Cy /p− Si(100) by heterojunction internal photoemission. Applied Physics Letters, 73, 3568–3570. Chang, S., Raisanen, A., Brillson, L. J., Shaw, J. L., Kirchner, P. D., Pettit, G. D., and Woodall, J. M. (1992) Homogeneous and wide range of barrier heights at metal/molecular-beam epitaxy GaAs(100) interfaces observed with electrical measurements. Journal of Vacuum Science and Technology B, 10, 1932–1939. Chang, S. T. and Lyon, S. A. (1986) Location of positive charge trapped at Si–SiO2 interface at low temperature. Applied Physics Letters, 48, 136–138. Chen, B., Suh, Y., Lee, J., Gurganus, J., Misra, V., and Cabral, C. (2005) Physical and electrical analysis of Rux Yy alloys for gate electrode applications. Applied Physics Letters, 86, 053502.
270
References
Chen, I.-S. and Wronski, C. R. (1995) Internal photoemission on a-Si:H Schottky barrier structures revisited. Journal of Non-Crystalline Solids, 190, 58–66. Chen, I.-S., Jackson, T. N., and Wronski, C. R. (1996) Characterization of semiconductor heterojunctions using internal photoemission. Journal of Applied Physics, 79, 8470–8474. Choyke, W. J. (1990) Optical and electronic properties of SiC. In The Physics and Chemistry of Carbides, Nitrides, and Borides, Freer, R. (ed.), NATO ASI Series, Vol. 185, Kluwer, Dordrecht, 563–588. Cimpoiasu, E., Tolpygo, S. K., Liu, X., Simonian, N., Lukens, J. K., Likharev, K. K., Klie, R. F. and Zhu, Y. (2004) Aluminum oxide layers as possible components for layered tunnel barriers. Journal of Applied Physics, 96, 1088–1093. Ciobanu, F., Pensl, G., Nagasawa, H., Schoner, A., Dimitrijev, S., Cheong, K.-Y., Afanas’ev, V. V., and Wagner, G. (2003) Traps at the interface of 3C–SiC/SiO2 MOS structures. Materials Science Forum, 433–434, 551–554. Coluzza, C., Lama, F., Frova, A., Perfetti, P., Quaresima, C., and Capozi, M. (1988) Band offsets in GaAs/amorphous Ge and GaP/amorphous Ge heterojunctions measured by internal photoemission. Journal of Applied Physics, 64, 3304–3306. Coluzza, C., Tuncel, E., Staehli, J.-L., Baudat, P. A., Margaritondo, G., McKinley, J. T., Ueda, A., Barnes, A. V., Albridge, R. G., Tolk, N. H., Martin, D., Morier-Genoud, F., Dupuy, C., Rudra, A., and Ilegems, M. (1992) Interface measurements of heterojunctions band lineups with the Vanderbilt free-electron laser. Physical Review B, 46, 12834–12836. Coluzza, C., Almeida, J., dell’Orto, T., Barbo, F., Bertolo, M., Bianco, A., Cerasari, S., Fontana, S., Bergossi, O., Spajer, M., and Courjon, D. (1996) Spatially resolved internal and external photoemission of Pt/n-GaP Schottky barrier. Applied Surface Science, 104/105, 196–203. Conley, J. F., Lenahan, P. M., Evans, H. L., Lowry, R. K., and Morthorst, T. J. (1994) Observation end electronic characterization of new E center defects in technologically relevant thermal SiO2 on Si: An additional complexity in the oxide charge trapping. Journal of Applied Physics, 76, 2872–2880. Conwell, E. M. (1996) Definition of exciton binding energy for conducting polymers. Synthetic Metals, 83, 101–102. Cristoloveanu, S. and Williams, S. (1992) Point-contact pseudo-MOSFET for in situ characterization of as-grown silicon-on-insulator wafers. IEEE Electron Device Letters, 13, 102–104. Cuberes, M. T., Bauer, A., Wen, H. J., Vandre, D., Prietsch, M., and Kaindl, G. (1994) Ballistic-electronemission microscopy of the Au/n-Si(111) 7 × 7 interface. Journal of Vacuum Science Technology B, 12, 2422–2428. Cuniot, M. and Marfaing, Y. (1985) Study of the band discontinuities at the a-SiH/c-Si interface by internal photoemission. Journal of Non-Crystalline Solids, 77/78, 987–990. Dalal, V. L. (1971) Simple model for internal photoemission. Journal of Applied Physics, 42, 2274–2279. Dähne-Prietsch, M. and Kalka, T. (2000) Hot-electron transport processes in ballistic-electron emission microscopy at Au-Si interfaces. Journal of Electron Spectroscopy and Related Phenomena, 109, 211–222. Deal, B. E., Snow, E. H., and Mead, C. A. (1966) Barrier energies in metal-silicon dioxide-silicon structures. Journal of Physics and Chemistry of Solids, 27, 1873–1879. Deal, B. E., Hurrle, A., and Schulz, M. J. (1978) Chlorine concentration profiles in O2 –HCl and H2 O– HCl thermal silicon oxides using SIMS measurements. Journal of the Electrochemical Society, 125, 2024–2027. De Andres, P. L., Garcia-Vidal, F. J., Reuter, K., and Flores, F. (2001) Theory of ballistic electron emission microscopy. Progress in Surface Science, 66, 3–51. DeKeersmaecker, R. F. and DiMaria, D. J. (1980) Electron trapping and detrapping characteristics of arsenic-implanted SiO2 layers. Journal of Applied Physics, 51, 1085–1101. DeLeo, G. G. and Fowler, W. B. (1985) Hydrogen-acceptor pairs in silicon: Pairing effect on the hydrogen vibrational frequency. Physical Review B, 31, 6861–6864.
References
271
de Nijs, J. M. M. and Balk, P. (1993) Electron trapping properties of Ge-implanted SiO2 . Microelectronic Engineering, 22, 123–126. de Nijs, J. M. M., Druijf, K. G., Afanas’ev, V. V., van der Drift, E., and Balk, P. (1994) Hydrogen induced donor-type Si/SiO2 interface states. Applied Physics Letters, 65, 2428–2430. Derry, G. N. (1986) Validity of the work function results from photoemission techniques. Journal of Physics and Chemistry of Solids, 47, 237–238. de Sousa Pires, J., Tove, P. A., and Donoval, D. (1984) A self-consistent approach to Fowler plots. Solid State Electronics, 27, 1029–1032. DeVisschere, P. (1990) The validity of Ramo’s theorem. Solid State Electronics, 33, 455–459. Diesing, D., Kritzler, G., Stermann, M., Nolting, D., and Otto, A. (2003) Metal/insulator/metal junctions for electrochemical surface science. Journal of Solid State Electrochemistry, 7, 389–415. DiMaria, D. J. (1974) Effects on interface barrier energies of metal-aluminum oxide-semiconductor (MAS) structures as a function of metal electrode material, charge trapping, and annealing. Journal of Applied Physics, 45, 5454–5456. DiMaria, D. J. (1976) Determination of insulator bulk trapped charge densities and centroids from photocurrent-voltage characteristics of MOS structures. Journal of Applied Physics, 47, 4073–4077. DiMaria, D. J. (1978) The properties of electron and hole traps in thermal silicon dioxide layers grown on silicon. In The Physics of SiO2 and its Interfaces, Pantelides, S. T. (ed.). Pergamon Press, New York, 160–178. DiMaria, D. J. (1981) Capture and release of electrons on Na+ -related trapping sites in the SiO2 layers of metal-oxide-semiconductor structures at temperatures 77 K and 293 K. Journal of Applied Physics, 52, 7251–7260. DiMaria, D. J. (1990) Temperature dependence of trap creation in silicon dioxide. Journal of Applied Physics, 68, 5234–5246. DiMaria, D. J. (1999) Electron energy dependence of metal-oxide-semiconductor degradation. Applied Physics Letters, 75, 2427–2428. DiMaria, D. J. (2000) Defect generation in field-effect transistors under channel-hot-electron stress. Journal of Applied Physics, 87, 8707–8715. DiMaria, D. J. and Arnett, P. C. (1975) Hole injection into silicon nitride: Interface barrier energies by internal photoemission. Applied Physics Letters, 26, 711–713. DiMaria, D. J. and Arnett, P. C. (1977) Conduction studies in silicon nitride: Dark currents and photocurrents. IBM Journal of Research Development, 21, 227–244. DiMaria, D. J. and Dong, D. W. (1980) High current injection into SiO2 from Si-rich SiO2 films and experimental applications. Journal of Applied Physics, 51, 2722–2735. DiMaria, D. J. and Stasiak, J. W. (1989) Trap creation in silicon dioxide produced by hot electrons. Journal of Applied Physics, 65, 2342–2356. DiMaria, D. J., Feigl, F. J., and Butler, S. R. (1974) Trap ionisation by electron impact in amorphous SiO2 films. Applied Physics Letters, 24, 459–461. DiMaria, D. J., Feigl, F. J., and Butler, S. R. (1975) Capture and emission of electrons at 2.4-eV deep trap level in SiO2 -films. Physical Review B, 11, 5023–5030. DiMaria, D. J., Aitken, J. M., and Young, D. R. (1976) Capture of electrons into Na+ -related trapping sites in the SiO2 layer of MOS structures at 77 K. Journal of Applied Physics, 47, 2740–2743. DiMaria, D. J., Weinberg, Z. A., Aitken, J. M., and Young, D. R. (1977a) Use of photocurrent-voltage characteristics of MOS structures to determine insulator bulk trapped charge densities and centroids. Journal of Electronic Materials, 6, 207–219. DiMaria, D. J., Weinberg, Z. A., and Aitken, J. M. (1977b) Location of positive charges in SiO2 on Si generated by VUV photons, X rays, and high-field stressing, Journal of Applied Physics, 48, 898–906. DiMaria, D. J., DeKeersmaecker, R. F., and Young, D. R. (1978a) Light-activated storage device (LASD), Journal of Applied Physics, 49, 4655–4659.
272
References
DiMaria, D. J., Young, D. R., Hanter, W. R., and Serrano, C. M. (1978b) Location of trapped charge in aluminium-implanted SiO2 . IBM Journal of Research and Development, 22, 289–294. DiMaria, D. J., Ghez, R., and Dong, D. W. (1980) Charge trapping studies in SiO2 using high-current injection from Si-rich SiO2 films. Journal of Applied Physics, 51, 4830–4841. DiMaria, D. J., Demeyer, K. M., Serrano, C. M., and Dong, D. W. (1981) Electrically alterable readonly-memory using Si-rich SiO2 injectors and a floating polycrystalline Si storage layer. Journal of Applied Physics, 52, 4825–4842. Dimoulas, A., Mavrou, G., Vellianitis, G., Evangelou, E., Boukos, N., Houssa, M., and Caymax, M. (2005) HfO2 high-κ gate dielectrics on Ge(100) by atomic oxygen beam deposition. Applied Physics Letters, 86, 032908. DiStefano, T. H. (1971) Barrier inhomogeneities on a Si–SiO2 interface by scanning internal photoemission. Applied Physics Letters, 19, 280–282. DiStefano, T. H. (1976) Field-dependent internal photoemission probe of electronic structure of Si–SiO2 interface. Journal of Vacuum Science and Technology, 13, 856–859. DiStefano, T. H. and Eastman, D. E. (1971) The band edge of amorphous SiO2 by photoinjection and photoconductivity measurements. Solid State Communications, 9, 2259–2261. DiStefano, T. H. and Lewis, J. E. (1974) Influence of sodium on Si–SiO2 interface. Journal of Vacuum Science and Technology, 11, 1020–1024. DiStefano, T. H. and Viggiano, J. M. (1974) Interface imaging by scanning internal photoemission. IBM Journal of Research and Development, 18, 94–99. Dose, V. (1983) Ultraviolet Bremsstrahlung spectroscopy. Progress in Surface Science, 13, 225–284. Dressendorfer, P. V. and Barker, R. C. (1980) Photoemission measurements of interface barriers energies for tunnel oxides on silicon. Applied Physics Letters, 36, 933–935. Droopad, R., Passlack, M., England, N., Rajagopalan, K., Abrokwah, J., and Kummel, A. (2005) Gate dielectrics on compound semiconductors. Microelectronic Engineering, 80, 138–145. Druijf, K. G., de Nijs, J. M. M., van der Drift, E., Granneman, E. H. A., and Balk, P. (1993) Charge exchange mechanisms of slow states in Si/SiO2 . Microelectronic Engineering, 22, 231–234. Druijf, K. G., de Nijs, J. M. M., van der Drift, E., Afanas’ev, V. V., Granneman, E. H. A., and Balk, P. (1995) The microscopic nature of donor-type Si–SiO2 interface states. Journal of Non-Crystalline Solids, 187, 206–210. Dubridge, L. A. (1935) New Theories of Photoelectric Effect. Hermann, Paris. Dussel, G. A. and Böer, K. W. (1970) Field-enhanced ionization. Physica Status Solidi, 39, 375–389. Dussel, G. A. and Bube, R. (1966) Electric field effects in trapping processes. Journal of Applied Physics, 32, 2797–2804. Ealet, B., Elyukhloufi, M. H., Gillet, E., and Ricci, M. (1994) Electronic and crystallographic structure of γ-alumina thin films. Thin Solid Films, 250, 92–100. Edge, L. F., Schlom, D. G., Williams, J. R., Chambers, S. A., Hinkle, C., Lucovsky, G., Yang, Y., Stemmer, S., Copel, M., Höllander, B., and Schubert, J. (2004) Suppression of subcutaneous oxidation during the deposition of amorphous lanthanum aluminate on silicon. Applied Physics Letters, 84, 4629–4631. Eitan, B., Frohman-Bentchkowsky, D., Shappir, J., and Balog, M. (1982) Electron trapping in SiO2 – An injection mode dependent phenomenon. Applied Physics Letters, 40, 523–525. Ekedahl, L. G., Eriksson, M., and Lundstrom, I. (1998) Hydrogen sensing mechanisms of metal-insulator interfaces. Accounts of Chemical Research, 31, 249–256. Elabd, H. and Kosonocky, W. F. (1982) The photoresponce of thin film PtSi Schottky barrier detector with optical cavity. RCA Review, 43, 542–547. Engelbrecht, F. and Helbig, R. (1993) Effect of crystal anisotropy on infrared reflectivity of 6H–SiC. Physical Review B, 48, 15698–15707. Engstrom, O., Pettersson, H., and Sernelius, B. (1986) Photoelectric yield spectra of metal-semiconductor structures. Physica Status Solidi (a), 95, 691–701.
References
273
Falcony, C., DiMaria, D. J., and Guarnieri, C. R. (1982) Enhanced electron injection into SiO2 layers using granular metal films. Journal of Applied Physics, 53, 5347–5349. Fedurco, M. and Augustynski, J. (1998) Interaction of pyridine with photoelectrons emitted at the silver/aqueous solution interface. Colloids and Surfaces A, 134, 95–102. Fedurco, M., Shklover, V., and Augustynski, J. (1997) Effect of halide ion adsorption upon plasmonmediated photoelectron emission at the silver/solution interface. Journal of Physical Chemistry B, 101, 5158–5165. Feigl, F. J., Young, D. R., DiMaria, D. J., Lai, S., and Calise, J. (1981) The effects of water on oxide and interface trapped charge generation in thermal SiO2 films. Journal of Applied Physics, 52, 5665–5682. Feuerbacher, B., Fitton, B., and Willis, R. F. (1978) Photoemission and the Electronic Properties of Surfaces, Wiley-Interscience, London. ISBN 0-471-99555X. Fitting, H. J. and Boyde, J. (1983) Monte–Carlo calculation of electron attenuation in SiO2 . Physica Status Solidi (a), 75, 137–142. Fitting, H. J. and Friemann, J. U. (1982) Monte–Carlo studies of the electron mobility in SiO2 . Physica Status Solidi (a), 69, 349–358. Fowler, R. H. (1931) The analysis of photoelectric sensitivity curves for clean metals at various temperatures. Physical Review, 38, 45–56. Fowler, R. H. and Nordheim, L. (1928) Electron emission in intense electric fields. Proceedings of Royal Society A: Mathematical and Physical Science, 119, 173–181. French, R. H. (1990) Electronic band structure of Al2 O3 , with comparison to AlON and AlN. Journal of American Chemical Society, 73, 477–489. Friedrichs, P., Burte, E. P., and Schorner, R. (1994) Dielectric strength of thermal oxides on 6H–SiC and 4H–SiC. Applied Physics Letters, 65, 1665–1667. Fujieda, S. (2001) Charge centers induced in thermal SiO2 by high electric field stress at 80 K. Journal of Applied Physics, 89, 3337–3342. Gale, R., Feigl, F. J., Magee, C. W., and Young, D. R. (1983) Hydrogen migration under avalanche injection of electrons in Si metal-oxide-semiconductor capacitors. Journal of Applied Physics, 54, 5938–5942. Gale, R., Chew, H., Feigl, F. J., and Magee, C. W. (1988) Current-induced charges and hydrogen species distributions in MOS silicon dioxide films. In The Physics and Chemistry of SiO2 and the Si–SiO2 Interface, Helms, C. R., and Deal, B. E. (ed.). Plenum Press, New York, 177–186. ISBN 0-306-43032-0. Gdula, R. A. (1976) Effects of processing on hot-electron trapping in SiO2 . Journal of the Electrochemical Society, 123, 42–47. Gerardi, G. J., Poindexter, E. H., Harmatz, M., Warren, W. L., Nicollian, E. H., and Edwards, A. H. (1991) Depassivation of damp oxide Pb centers by thermal and electric-field stress. Journal of the Electrochemical Society, 138, 3765–3770. Gila, B. P., Ren, F., and Abernathy, C. R. (2004) Novel insulators for gate dielectrics and surface passivation of GaN-based electronic devices. Materials Science and Engineering R, 44, 151–184. Giro, G. and Marco, P. (1979) Photoemission of electrons from metal electrodes into poly-Nvinilcarbazole. Thin Solid Films, 59, 91–97. Goetzberger, A. and Nicollian, E. H. (1967) MOS avalanche and tunnelling effects in silicon surfaces. Journal of Applied Physics, 38, 4582–4591. Goodman, A. M. (1966a) Photoemission of electrons from silicon and gold into silicon dioxide. Physical Review, 144, 588–593. Goodman, A. M. (1966b) Photoemission of holes from silicon into silicon dioxide. Physical Review, 152, 780–784. Goodman, A. M. (1966c) Photoemission of electrons from n-type degenerate silicon into silicon dioxide. Physical Review, 152, 785–787. Goodman, A. M. (1967) Electron Hall effect in silicon dioxide. Physical Review, 164, 1145–1151.
274
References
Goodman, A. M. (1968) Photoemission of electrons and holes into silicon nitride. Applied Physics Letters, 13, 275–277. Goodman, A. M. (1970) Photoemission of holes and electrons from aluminium into aluminium oxide. Journal of Applied Physics, 41, 2176–2179. Goulet, T., Bernas, A., Ferradini, C., and Jay-Gerin, J.-P. (1990) On the electronic structure of liquid water: Conduction band tail revealed by photoionization data. Chemical Physics Letters, 170, 492–496. Greeuw, G. and Verwey, J. F. (1984) Mobility of Na+ , Li+ , and K+ ions in thermally grown SiO2 films. Journal of Applied Physics, 56, 2218–2224. Griscom, D. L. (1990) Electron spin resonance. In Glass: Science and Technology, Uhlmann, D. R., and Kreidl, N. J. (ed.), Vol. 4B. Academic Press, New York, 151–247. ISBN 0-12-706707-8. Gu, D., Dey, S. K., and Mahji, P. (2006) Effective work function of Pt, Pd, and Re on atomic layer deposited HfO2 . Applied Physics Letters, 89, 082907. Gundlach, K. H. and Kadlec, J. (1972) Space–charge dependence of the barrier height on insulator thickness in Al-(Al-oxide)-Al sandwiches. Applied Physics Letters, 20, 445–446. Gundlach, K. H. and Kadlec, J. (1975) Spectral dependence of photoresponce in MIM structures – Influence of electrode thickness. Thin Solid Films, 28, 107–117. Gupta, H. M. and VanOverstraeten, R. J. (1976) Theory of isothermal dielectric relaxation and direct determination of trap parameters. Journal of Applied Physics, 47, 1003–1009. Haase, M. A., Emmanuel, M. A., Smith, S. C., Coleman, J. J., and Stillman, G. E. (1987) Band discontinuities in GaAs/Alx Ga1−x As heterojunction photodiodes. Applied Physics Letters, 50, 404–406. Haase, M. A., Hafich, M. J., and Robinson, G. Y. (1991) Internal photoemission and energy band offsets in GaP-GaInP p-I-N heterojunction diodes. Applied Physics Letters, 58, 616–618. Haick, H., Ambrico, M., Lignozo, T., and Cahen, D. (2004) Discontinuous molecular films can control metal/semiconductor junctions. Advanced Materials, 16, 2145–2151. Haick, H., Ambrico, M., Lignozo, T., Tuing, R. T., and Cahen, D. (2006) Controlling semiconductor/metal junction barriers by incomplete, nonideal molecular monolayers. Journal of American Chemical Society, 128, 6854–6869. Halbritter, J. (1999) Charge transfer via interfaces, especially of nanoscale materials. Applied Physics A, 68, 153–162. Harrison, W. A. (1977) Elemental theory of heterojunctions. Journal of Vacuum Science and Technology, 14, 1016–1021. Harrison, W. A. (1981) New tight-binding parameters for covalent solids obtained using Louie peripheral states. Physical Review B, 24, 5835–5843. Hartstein, A. and Weinberg, Z. A. (1978) Nature of image-force in quantum-mechanics with application to photon-assisted tunnelling and internal photoemission. Journal of Physics C, 11, L469–L473. Hartstein, A. and Weinberg, Z. A. (1979) Unified theory of internal photoemission and photon-assisted tunnelling. Physical Review B, 20, 1335–1338. Hartstein, A. and Young, D. R. (1981) Identification of electron traps in silicon dioxide. Applied Physics Letters, 38, 631–633. Hartstein, A., Weinberg, Z. A., and DiMaria, D. J. (1982) Experimental test of the quantum-mechanical image-force theory. Physical Review B, 25, 7174–7182. Heeg, T., Wagner, M., Schubert, J., Buchal Ch., Boese, M., Luysberg, M., Cicerrella, E., and Freeouf, J. L. (2005) Rare-earth scandate single- and multi-layer thin films as alternative gate oxides for microelectronic applications. Microelectronic Engineering, 80, 150–153. Heiblum, M., Nathan, M. I., and Eizenberg, M. (1985) Energy band discontinuities in heterojunctions measured by internal photoemission. Applied Physics Letters, 47, 503–505. Helman, J. S. and Sanchez-Sinencio, F. (1973) Theory of internal photoemission. Physical Review B, 7, 3702–3706. Hess, K., Kizilyalli, I. C., and Lyding, J. W. (1998) Giant isotope effect in hot electron degradation of metal oxide silicon devices. IEEE Transactions on Electron Devices, ED-45, 406–416.
References
275
Hess, K., Register, L. F., McMahon, W., Tuttle, B., Aktas, O., Ravaiol, U., Lyding, J. W., and Kizilyalli, I. C. (1999) Theory of channel hot-carrier degradation in MOSFETs. Physica B, 272, 527–531. Heyns, M. M., Rao, D. K., and DeKeersmaecker, R. F. (1989) Oxide field dependence of Si–SiO2 interface state generation and charge trapping during electron injection. Applied Surface Science, 39, 327–338. Hickmott, T. W. (1980) Dipole layers at metal-SiO2 interface. Journal of Applied Physics, 51, 4269–4281. Himpsel, F. J., Heinz, T. F., McLean, A. B., and Palange, E. (1989) Bonding at silicon-insulator interfaces. Applied Surface Science, 41/42, 346–351. Hirota, Y. and Mikami, O. (1988) Energy barrier height measurements of chemically vapor-deposited P3 N5 films by internal photoinjection. Thin Solid Films, 162, 41–47. Hobbs, C. C., Fonseca, L. R. C., Knizhnik, A., Dhandapani, V., Samavedam, S. B., Taylor, W. J., Grant, J. M., Dip, L. G., Tiyoso, D. H., Hedge, R. I., Gilmer, D. C., Garcia, R., Roan, D., Lovejoy, M. L., Rai, R. S., Hebert, E. A., Tseng, H. H., Anderson, S. G. H., White, B. E., and Tobin, P. J. (2004a) Fermi-level pinning at the polysilicon/metal oxide interface, Part I. IEEE Transactions on Electron Devices, 51, 971–977. Hobbs, C. C., Fonseca, L. R. C., Knizhnik, A., Dhandapani, V., Samavedam, S. B., Taylor, W. J., Grant, J. M., Dip, L. G., Tiyoso, D. H., Hedge, R. I., Gilmer, D. C., Garcia, R., Roan, D., Lovejoy, M. L., Rai, R. S., Hebert, E. A., Tseng, H. H., Anderson, S. G. H., White, B. E., and Tobin, P. J. (2004b) Fermi-level pinning at the polysilicon/metal oxide interface, Part, II. IEEE Transactions on Electron Devices, 51, 978–984. Honda, K. (2004) Dawn of the evolution of photoelectrochemistry. Journal of Photochemistry and Photobiology A, 166, 63–68. Houssa, M. (ed.) (2004) High-κ Gate Dielectrics. Institute of Physics Publishing, Bristol. ISBN 0 7503 0906 7. Houssa, M., Naili, M., Zhao, C., Bender, H., Heyns, M. M., and Stesmans, A. (2001) Effect of O2 postdeposition anneals on the properties of ultra-thin SiOx /ZrO2 gate dielectric stacks. Semiconductor Science and Technology, 16, 31–38. Houssa, M., Pantisano, L., Ragnarsson, L. A., Degraeve, R., Schram, T., Pourtois, G., De Gendt, S., Groeseneken, G., and Heyns, M. M. (2006) Electrical properties of high-κ gate dielectrics: Challenges, current issues, and possible solutions. Materials Science and Engineering R, 51, 37–85. Hsu, J. W. P., Loo, Y. L., Lang, D. V., and Rogers, J. A. (2003) Nature of electrical contacts in a metal-molecule-semiconductor system. Journal of Vacuum Science and Technology B, 21, 1928–1935. Hsu, J. W. P., Lang, D. V., West, K. W., Loo, Y. L., Halls, M. D., and Raghavachari, K. (2005) Probing occupied states of the molecular layer in Au-alkanedithiol-GaAs diodes. Journal of Physical Chemistry B, 109, 5719–5723. Huang, H. G., Zheng, Z. X., Luo, J., Zhang, H. P., Wu, L. L., and Lin, Z. H. (2001) Internal photoemission in polyaniline revealed by photoelectrochemistry. Synthetic Metals, 123, 321–325. Huff, H. R. and Gilmer, D. C. (eds) (2005) High Dielectric Constant Materials. Springer-Verlag, Berlin. ISBN 3540210814. Hughes, R. C. (1973) Charge-carrier transport phenomena in amorphous SiO2 – direct measurement of drift mobility and lifetime. Physical Review Letters, 30, 1333–1336. Hughes, R. C. (1975a) Hot electrons in SiO2 . Physical Review Letters, 35, 449–452. Hughes, R. C. (1975b) Hole mobility and transport in thin SiO2 films. Applied Physics Letters, 26, 436–438. Hughes, R. C. (1977) Time-resolved hole transport in α-SiO2 . Physical Review B, 15, 2012–2020. Hughes, R. C. (1978) High-field electronic properties of SiO2 . Solid State Electronics, 21, 251–258. Hughes, A. L. and Dubridge, L. A. (1932) Photoelectric Phenomena, Mac-Graw-Hill, New York. Im, C., Engenhardt, K. M., and Gregory, S. (1999) Light-induced transient currents from molecular films in a tunnelling microscope junction. Physical Review B, 59, 3153–3159.
276
References
Ishida, T. and Ikoma, H. (1993) Bias dependence of Schottky barrier height in GaAs from internal photoemission and current-voltage characteristics. Journal of Applied Physics, 74, 3977–3982. Jacobs, E. P. and Dorda, G. (1977a) Charge storage by irradiation with UV light of non-biased MNOS structures. Solid State Electronics, 20, 361–665. Jacobs, E. P. and Dorda, G. (1977b) Optically induced charge storage in ion-implanted SiO2 . Solid State Electronics, 20, 367–672. Jan, G. J., Pollak, F. H., and Tsu, R. (1982) Optical properties of disordered silicon in the range 1–10 eV. Solar Energy Materials, 8, 241–248. Johnson, M. (1980) The dynamic image potential for tunnelling electrons. Solid State Communications, 33, 743–746. Johnson, N. M. (1985) Mechanism for hydrogen compensation of shallow-acceptor impurities in single-crystal silicon. Physical Review B, 31, 5525–5528. Jonda Ch., Mayer, A. B. R., and Grothe, W. (1999) Determination of barrier heights for electron injection in organic light emitting devices. Journal of Applied Physics, 85, 6884–6888. Kadlec, J. (1976) Theory of internal photoemission in sandwich structures. Physics Reports, 26, 69–98. Kadlec, J. and Gundlach, K. H.(1975) Dependence of barrier height on insulator thickness in Al-(Al oxide)-Al sandwiches. Solid State Communications, 16, 621–623. Kadlec, J. and Gundlach, K. H. (1976) Internal Photoemission and Quantum-Mechanical Transmission Coefficient. Physica Status Solidi (a), 37, 385–398. Kaiser, W. J. and Bell, L. D. (1988a) Direct investigation of subsurface interface electronic structure by ballistic electron emission microscopy. Physical Review Letters, 60, 1406–1409. Kaiser, W. J. and Bell, L. D. (1988b) Observation of interface band-structure by ballistic electron emission microscopy. Physical Review Letters, 61, 2368–2371. Kalugin, A. I., Konovalov, V. V., Shokhirev, N. V., and Raitsimiring, A. M. (1993) Photoelectron injection into dilute electrolyte solutions. 1. Methodology. Journal of Electroanalytical Chemistry, 359, 63–80. Kampen, T., Bekkali, A., Thurzo, U., Zahn, D. R. T., Bolognesi, A., Ziller, T., Di Carlo, A., and Lugli, P. (2004) Barrier heights of organic modified Schottky contacts: Theory and experiment. Applied Surface Science, 234, 313–320. Kane, E. O. (1962) Theory of photoelectric emission from semiconductors. Physical Review, 127, 131–141. Kane, E. O. (1966) Simple model for collision effects in photoemission. Physical Review, 147, 335–339. Kao, C. W., Anderson, C. L., and Crowell, C. R. (1980) Photoelectron injection at metal-semiconductor interfaces. Surface Science, 95, 321–339. Kapoor, V. J., Feigl, F. J., and Butler, S. R. (1977a) Energy and spatial distribution of an electron trapping center in the MOS insulator. Journal of Applied Physics, 48, 739–749. Kapoor, V. J., Feigl, F. J., and Butler, S. R. (1977b) Low-temperature photocurrent spectroscopy of localized states in SiO2 films. Physical Review Letters, 39, 1219–1222. Kashkarov, P. K., Kazior, T., Lagowski, J., and Gatos, H. C. (1983) Interface states and internal photoemission in p-type GaAs metal-oxide-semiconductor surfaces. Journal of Applied Physics, 54, 963–970. Kasumov, Yu. N. and Kozlov, S. N. (1988) On energy diagram of Ge–GeO2 system. Soviet Journal of Physics, Chemistry, and Mechanics of Surfaces, 7(3), 78–81. (in Russian). Kim, Y. Y. and Lenahan, P. M. (1988) Electron-spin-resonance study of radiation-induced paramagnetic defects in oxides grown on (100) silicon substrates. Journal of Applied Physics, 64, 3551–3557. Kimura, M. and Ohmi, T. (1996) Conduction mechanism and origin of stress-induced leakage current in thin silicon dioxide films. Journal of Applied Physics, 80, 6360–6369. Kiselev, V. F., Kozlov, S. N., and Levshin, N. L. (1981) On the mechanism of dissipation of energy released in the capture of charge carriers to adsorptive slow states of a semiconductor. Physica Status Solidi (a), 66, 93–101. Kittl, J. A., Pawlak, M. A., Lauwers, A., Demeurisse, C., Opsomer, K., Anil, K. G., Vranken, C., van Dal, M. J. H., Veloso, A., Kubicek, S., Absil, P., Maex, K., and Biesemans, S. (2006a) Work
References
277
function of Ni silicide phases on HfSiON and SiO2 : NiSi, Ni2 Si, Ni31 Si12 , and Ni3 Si fully silicided gates. IEEE Electron Device Letters, 27, 34–36. Kittl, J. A., Lauwers, A., Veloso, A., Hoffmann, T., Kubicek, S., Niwa, M., van Dal, M. J. H., Pawlak, M. A., Brus, S., Demeurisse, C., Vranken, C., Absil, P., and Biesemans, S. (2006b) CMOS integration of dual work function phase-controlled Ni fully silicided gates (NMOS : NiSi, PMOS : Ni2 Si, and Ni31 Si12 ) on HfSiON. IEEE Electron Device Letters, 27, 966–968. Klenov, D. O., Edge, L. F., Schlom, D. G., and Stemmer, S. (2005) Extended defects in epitaxial Sc2 O3 films grown on (111)Si. Applied Physics Letters, 86, 051901. Knights, J. C. and Davis, E. A. (1974) Photogeneration of charge carriers in amorphous selenium. Journal of Physics and Chemistry of Solids, 35, 543–554. Knoll, M., Braunig, D., and Fahrner, W. R. (1982) Comparative studies of tunnel injection and irradiation on metal-oxide-semiconductor structures. Journal of Applied Physics, 53, 6946–6952. Koch, N., Pop, D., Weber, R. L., Bowering, N., Winter, B., Wick, M., Leising, G., Hertel, I. V., and Braun, W. (2001) Radiation induced degradation and surface charging of organic thin films in ultraviolet photoemission spectroscopy. Thin Solid Films, 391, 81–87. Konovalov, V. V., Raitsimring, A. M., and Tsvetkov, I. D. (1988) Quantum yields of the photoinjection of electron from mercury into aqueous-electrolyte solutions. Doklady Akademii Nauk SSSR, 299, 1166–1170. Konovalov, V. V., Raitsimring, A. M., and Tsvetkov, I. D. (1990) Photoelectron injection from mercury into aqueous electrolyte solutions in the range 427–193 nm. Journal of Electroanalytical Chemistry, 292, 33–52. Korzo, V. F., Kireev, P. S., and Lyaschenko, G. A. (1968) On band structure of Si–SiO2 . Soviet Physics Semiconductors – USSR, 2, 1852–1854. Kostecki, R., and Augustynski, J. (1995) Effect of surface roughness on the spectral distribution of photoemission current at the silver/solvent contact. Journal of Applied Physics, 77, 4701–4705. Krantz, R. J., Aukerman, L. W., and Zietlow, T. C. (1987) Applied field and total dose dependence of trapped charge buildup in MOS devices. IEEE Transactions on Nuclear Science, NS-34, 1196–1201. Kraut, E. A. (1984) Heterojunction band offsets variations with ionisation potential compared to experiment. Journal of Vacuum Science and Technology B, 2, 486–490. Krebs, P. (1984) Localization of excess electrons in dense polar vapors. Journal of Physical Chemistry, 88, 3702–3709. Krohn, C. E., Antoniewicz, P. R., and Thompson, J. C. (1980) Energetics for photoemission of electrons into NH3 and H2 O. Surface Science, 101, 241–250. Lagowski, J. and Edelman, P. (1998) Contact potential difference methods for full wafer characterization of oxidized silicon. Institute of Physics Conference Series, 160, 133–140. Lakatos, A. I. and Mort, J. (1968) Photoemission of holes from metals into organic polymer poly-N-vinil-carbazole. Physical Review Letters, 21, 1444–1447. Lam, Y. W. (1970) Interface studies of MIS structure by surface photovoltage measurements. Electronic Letters, 6, 153–155. Lam, Y. W. (1971) Surface-state density and surface potential in MIS-capacitors by surface photovoltage measurements. 1,2. Journal of Physics D: Applied Physics, 4, 1370–1381. Lampert, M. A. and Mark, P. (1970) Current Injection in Solids. Academic Press, New York. Landsberg, P. T. (1991) Recombination in Semiconductors. Cambridge University Press, Cambridge, ISBN 0 521 36122 2. Lange, P., Sass, J. K., R. Unwin, and Tench, D. M. (1981) Improved analysis of the power law in photoemission yield spectroscopy. Journal of Electroanalytical Chemistry, 122, 387–391. Lange, P., Grider, D., Neff, H., Sass, J. K., and Unwin, R. (1982) Limitations of the Fowler method in photoelectric work function determination: Oxygen on magnesium single crystal surfaces. Surface Science, 118, L257–L262.
278
References
Lax, M. (1960) Cascade capture of electrons in solids. Physical Review, 119, 1502–1511. Lee, C. H., Lambrecht, W. R. L., Segall, B., Kelires, P. C., Frauenheim Th., and Stephan, U. (1994) Electronic structure of dense amorphous carbon. Physical Review B, 49, 11448–11451. Lehovec, K., Chen, C. H., and Fedotovsky, A. (1978) MNOS charge versus centroid determination using staircase charging. IEEE Transactions on Electron Devices, ED-25, 1030–1036. Lenzlinger, M. and Snow, E. H. (1969) Fowler–Nordheim tunneling into Thermally Grown SiO2 . Journal of Applied Physics, 40, 278–283. Lewicki, G. and Maserjian, J. (1975) Oscillations in MOS tunnelling. Journal of Applied Physics, 46, 3032–3039. Li, Y. and Sah, C. T. (1995) Thermal emission of trapped holes in thin SiO2 films. Journal of Applied Physics, 78, 3156–3159. Li, J., Nam, K. B., Nakarmi, M. L., Lin, J. Y., Jiang, H. X., Carrier, P., and Wei, S. H. (2003) Band structure and fundamental optical transitions in wurtzite AlN. Applied Physics Letters, 83, 5163–5165. Li, Z., Schram, T., Pantisano, L., Conard, T., Van Elschot, S., Deweerd, W., De Gendt, S., De Meyer, K., Stesmans, A., Shamuilia, S., Afanas’ev, V. V., Akheyar, A., Brunco, D. P., Yamada, N., and Lehnen, P. (2007) Flatband voltage shift of the ruthenium gates stacks and its link with the formation of a thin ruthenium oxide layer at the ruthenium/dielectric interface. Journal of Applied Physics, 101, 034503. Liang, Y., Curless, J., Tracy, C. J., Gilmer, D. C., Schaeffer, J. K., Tiyoso, D. H., and Tobin, P. J. (2006) Interface dipole and effective work function of Re in Re/HfO2 /SiOx /n-Si gate stack. Applied Physics Letters, 88, 072907. Lonergan, M. C. and Jones, F. E. (2001) Calculation of transmission coefficients at nonideal semiconductor interfaces characterized by a spatial distribution of barrier heights. Journal of Chemical Physics, 115, 433–445. Lucovsky, G. (1965) On the photoionization of deep impurity centers in semiconductors. Solid State Communications, 3, 299–302. Lucovsky, G. (2002) Correlations between electronic structure of transition metal atoms and performance of high-κ gate dielectrics in advanced Si devices. Journal Non-Crystalline Solids, 303, 40–49. Lucovsky, G., Zhang, Y., Whitten, J. L., Schlom, D. G., and Freeouf, J. L. (2004) Separate and independent control of interfacial band alignments and dielectric constants in transition metal rare earth complex oxides. Microelectronic Engineering, 72, 288–293. Ludeke, R. (1986) The effects of microstructure on interface characterization. Surface Science, 168, 290–300. Ludeke, R., Cuberes, M. T., and Cartier, E. (2000a) Local transport and trapping issues in Al2 O3 gate oxide structures. Applied Physics Letters, 76, 2886–2888. Ludeke, R., Cuberes, M. T., and Cartier, E. (2000b) Hot carrier transport effects in Al2 O3 -based metal-oxide-semiconductor structures. Journal of Vacuum Science and Technology B, 18, 2153–2159. Ludwig, W., and Korneffel, B. (1967) Photoemission studies of thin metal-insulator-metal sandwiches. Physica Status Solidi, 24, K137–138. Lundstrom, I. (1996) Chemical sensors with cathalytic metal gates. Journal of Vacuum Science and Technology A, 14, 1539–1545. Lundstrom, I. and DiStefano, T. (1976a) Hydrogen-induced interfacial polarization at Pd-SiO2 interfaces. Surface Science, 59, 23–32. Lundstrom, I. and DiStefano, T. (1976b) Influence of hydrogen on Pt-SiO2 -Si structures. Solid State Communications, 19, 871–875. Lundstrom, I. and Svensson, C. (1972) Tunnelling to traps in insulators. Journal of Applied Physics, 43, 5045–5047. Lynch, W. T. (1972) Predicted effect of exponential charging profiles on photoinjected current in silicon dioxide. Journal of Applied Physics, 43, 3023–3025.
References
279
Maex, K., Baklanov, M. R., Shamiryan, D., Iacopi, F., Brongersma, S. H., and Yanovitskaya, Z. S. (2003) Low dielectric constant materials for microelectronics. Journal of Applied Physics, 93, 8793–8841. Maillet, A., Balland, B., and Peisner, B. (1983) Photo-injection of electrons from metal films into single-crystal Al2 O3 layers. Thin Solid Films, 109, 225–236. Margaritondo, G. (1997) Spectromicroscopy and internal photoemission spectroscopy of semiconductor interfaces. Progress in Surface Science, 56, 311–346. Margaritondo, G. (1999) Interface states at semiconductor junctions. Reports on Progress in Physics, 62, 765–808. Masek, J., Maissen, S., Zogg, H., Platz, W., Riedel, H., Koniger, M., Lambrecht, A. L., and Take, M. (1990) Photovoltaic lead-chalcogenide IR-sensor arrays on Si for thermal imaging applications. Nuclear Instruments and Methods A, 288, 104–109. Maserjian, J. and Zamani, N. (1982) Observation of positively charged state generation near the Si– SiO2 interface during Fowler–Nordheim tunnelling. Journal of Vacuum Science and Technology, 20, 743–746. Mazara, W. P. (1993) Wafer bonding: SOI, generalized bonding, and new structures. Microelectronic Engineering, 22, 299–306. McIntyre, R. and Sass, J. K. (1986) Inverse-photoemission spectroscopy at the metal-electrolyte interface. Physical Review Letters, 56, 651–654. McKinley, J. T., Albridge, R. G., Barnes, A. V., Ueda, A., Tolk, N. H., Coluzza, C., Gozzo, F., Margaritondo, G., Martin, D., Moriergenoud, F., Dupuy, C., Rudra, A., and Ilegems, M. (1993) Freeelectron laser internal photoemission measurements of heterojunction band discontinuities. Journal of Vacuum Science and Technology B, 11, 1614–1616. McLean, F. B. (1980) A framework for understanding radiation-induced interface states in SiO2 MOS structures. IEEE Transactions on Nuclear Science, NS-27, 1651–1657. McWhorter, P. J. and Winokur, P. S. (1986) Simple technique for separating the effects of interface traps and trapped-oxide charge in metal-oxide-semiconductor transistors. Applied Physics Letters, 48, 133–135. Mead, C. A. (1966) Metal-semiconductor surface barriers. Solid State Electronics. 9, 1023–1033. Mehta, D. A., Butler, S. R., and Feigl, F. J. (1972) Electronic charge trapping in chemical vapour-deposited thin films of Al2 O3 on silicon. Journal of Applied Physics, 43, 4631–4638. Mimura, H. and Hatanaka, Y. (1987) Energy band discontinuities in a heterojunction of amorphous hydrogenated Si and crystalline Si measured by internal photoemission. Applied Physics Letters, 50, 326–328. Miyazaki, S., Okumura, T., Miura, Y., Aizawa, K., and Hirose, K. (1994) Imaging of Schottky-barrier inhomogeneity at epi-Al/(111)Si interface introduced by annealing. Institute of Physics Conference Series, 135, 361–364. Momida, H., Hamada, T., Takagi, Y., Yamamoto, T., Uda, T., and Ohno, T. (2006) Theoretical study on dielectric response of amorphous alumina. Physical Review B, 73, 054108. Mönch, W. (2004) Electronic Properties of Semiconductor Interfaces. Springer Verlag, Berlin. ISBN 3-540-20215-3. Morita, M., Tsubouchi, K., Mikoshiba, N., and Yokoyama, S. (1982) Interface barrier heights in metal-aluminum nitride-silicon structure by internal photoemission. Journal of Applied Physics, 53, 3694–3697. Mott, N. F. and Davis, G. A. (1979) Electronic Properties of Non-Crystalline Materials, 2nd edition. Clarendon Press, Oxford. ISBN 0-19-851288-0. Mott, N. F. and Gurney, R. W. (1946) Electronic Processes in Ionic Crystals. Clarendon Press, Oxford, 73. Myrtveit, T. (1993) Modelling of photoresponce in metal-semiconductor junctions. Applied Surface Science, 73, 225–231. Nabok, A. V., Nesterenko, B. A., Shirshov, Y. M., Goltvianskii, Y. V., and Dubchak, A. P. (1984) Profile of trapped charge in silicon nitride films in MNOS structures. Physica Status Solidi (a), 82, 221–227.
280
References
Nagai, K., Sekigawa, T., and Hayashi, Y. (1985) Capacitance-voltage characteristics of semiconductorinsulator-semiconductor (SIS) structure. Solid State Electronics, 28, 789–798. Neff, H., Sass, J. K., Lewerenz, H. J., and Ibach, H. (1980) Photoemission studies of electron localization at very low excess energies. Journal of Physical Chemistry, 84, 1135–1139. Neff, H., Sass, J. K., and Lewerenz, H. J. (1984) A photoemission-into-electrolyte study of surface plasmon excitation on high index faces of silver. Applied Surface Science, 143, L356–L362. Neff, H., Lange, P., Duwe, H., and Sass, J. K. (1985) In-situ photoemission from copper high index faces near threshold. Journal of Electroanalytical Chemistry, 194, 149–154. Nelson, O. L. and Anderson, D. E. (1966) Potential barrier parameters in thin film Al-Al2 O3 -metal diodes. Journal of Applied Physics, 37, 77–81. Nicollian, E. H. and Berglund, C. N. (1971) Avalanche injection of electrons into insulating SiO2 using MOS structures. Journal of Applied Physics, 41, 3052–3060. Nicollian, E. H. and Brews, J. R. (1982) MOS (Metal Oxide Semiconductor) Physics and Technology. Wiley, New York, ISBN 0-471-08500-6. Nicollian, E. H., Goetzberger, A., and Berglund, C. N. (1969) Avalanche injection currents and charging phenomena in thermal SiO2 . Applied Physics Letters, 15, 174–176. Nicollian, E. H., Berglund, C. N., Schmidt, P. F., and Andrews, P. F. (1971) Electrochemical charging of thermal SiO2 films by injected electron currents. Journal of Applied Physics, 42, 5654–5666. Nicollian, E. H., Hanes, M. H., and Brews, J. R. (1973) Using MIS capacitor for doping profile measurements with minimal interface state error. IEEE Transactions on Electron Devices, ED-20, 380–389. Ning, T. H. (1976a) High-field capture of electrons by Coulomb attractive centers in silicon dioxide. Journal of Applied Physics, 47, 3203–3208. Ning, T. H. (1976b) Capture cross-section and trap concentration of holes in silicon dioxide. Journal of Applied Physics, 47, 1079–1081. Ning, T. H. (1978) Electron trapping in SiO2 due to electron-beam deposition of aluminium. Journal of Applied Physics, 49, 4077–4082. Ning, T. H. and Yu, H. N. (1974) Optically-induced injection of hot electrons into SiO2 . Journal of Applied Physics, 45, 5373–5379. Ning, T. H., Osburn, C. M., and Yu, H. N. (1975) Electron trapping at positively charged centres in SiO2 . Applied Physics Letters, 26, 248–250. Nishi, K., Morota, N., Murase, Y., and Nakashima, H. (1998) Interfaces of semiconductor heterojunctions studied using a FEL. Nuclear Instruments and Methods B, 144, 107–114. Nissan-Cohen, Y., Shappir, J., and Frohman-Betchkowsky, D. (1986) Trap generation and occupation dynamics in SiO2 under charge injection stress. Journal of Applied Physics, 60, 2024–2035. Nohira, H., Tsai, W., Besling, W., Young, E., Petry, J., Conard, T., Vandervorst, W., De Gendt, S., Heyns, M., Maes, J., and Tuominen, M. (2002) Characterization of ALCVD Al2 O3 and ZrO2 layer using X-ray photoelectron spectroscopy. Journal of Non-Crystalline Solids, 303, 83–87. Norton, D. P. (2004) Synthesis and properties of epitaxial electronic oxide thin-film materials. Materials Science and Engineering R, 43, 139–247. Oishi, K. and Matsuo, Y. (1996) Internal photoemission and photoconduction of GeO2 /Ge films. Thin Solid Films, 274, 133–137. Okumura, T. and Shiojima, K. (1989) Scanning internal-photoemission microscopy – New mapping technique to characterize electrical inhomogeneity of metal-semiconductor interface. Japanese Journal of Applied Physics Part 2, 28, L1108–L1111. Okumura, T. and Tu, K. N. (1983) Analysis of parallel Schottky contacts by differential internal photoemission spectroscopy. Journal of Applied Physics, 54, 922–927. Oldham, T. R., Lelis, A. J., and McLean, F. B. (1986) Spatial dependence of trapped holes determined from tunnelling analysis and measured annealing. IEEE Transactions on Nuclear Science, NS-33, 1203–1209.
References
281
Onn, D. G. and, M. Silver (1969) Attenuation and lifetime of hot electrons injected into liquid helium. Physical Review, 183, 295–302. Onn, D. G. and Silver, M. (1971) Injection and thermalization of hot electrons in solid, liquid, and gaseous helium at low temperatures. Physical Review A, 3, 1773–1781. Pan, C. A. and Ma, T. P. (1980a) High-quality transparent conductive indium oxide-films prepared by thermal evaporation. Applied Physics Letters, 37, 163–165. Pan, C. A. and Ma, T. P. (1980b) Work function of In2 O3 film as determined from internal photoemission. Applied Physics Letters, 37, 714–716. Pankove, J. I. (1975) Optical Processes in Semiconductors. Dover, New York. ISBN 0-486-60275-3. Pankove, J. I., Carlson, D. E., Berkeyheiser, J. E., and Wance, R. O. (1983) Neutralization of shallow acceptor levels in silicon by atomic hydrogen. Physical Review Letters, 51, 2224–2225. Pantisano, L., Schram, T., Li, Z., Lisoni, J. G., Pourtois, G., De Gendt, S., Akheyar, A., Afanas’ev, V. V., Shamuilia, S., and Stesmans, A. (2006a) Ruthenium gate electrodes on SiO2 and HfO2 : Sensitivity to hydrogen and oxygen ambients. Applied Physics Letters, 88, 243514. Pantisano, L., Schram, T., O’Sullivan, B., Conard, T., De Gendt, S., Groeseneken, G., Zimmerman, P., Akheyar, A., Heyns, M. M., Shamuilia, S., Afanas’ev, V. V., and Stesmans, A. (2006b) Effective work function modulation by controlled dielectric monolayer deposition. Applied Physics Letters, 89, 113505. Passlack, M., Yu, Z., Droopad, R., Abrokwah, J. K., Braddock, D., Yi, S.-I., Hale, M., Sexton, J., and Kummel, A. C. (2003) Gallium oxide on gallium arsenide: Atomic structure, materials, and devices. In III–V Semiconductor Heterostructures: Physics and Devices, Cai, W. C. (ed.). Research Signpost, Kerala, India, 327–355. ISBN 81-7736-170-8. Paul, T. K. and Bose, N. (1990) Fluoride dielectric films on InP for metal-insulator-semiconductor applications. Journal of Applied Physics, 67, 3744–3749. Perego, M., Seguini, G., Scarel, G., and Fanciulli, M. (2006a) X-ray photoelectron spectroscopy study of energy band alignments of Lu2 O3 on Ge. Surface and Interface Analysis, 38, 494–497. Perego, M., Seguini, G., and Fanciulli, M. (2006b) Energy band alignment of HfO2 on Ge. Journal of Applied Physics, 100, 093718. Perry, P. B. and Rutz, R. F. (1978) The optical absorption edge of single crystal AlN prepared by a close-spaced vapor process. Applied Physics Letters, 33, 319–321. Persson, C. and Ferreira da Silva, A. (2005) Strong polaronic effects on rutile TiO2 electronic band edges. Applied Physics Letters, 86, 231912. Philipp, H. R. (1971) Optical properties of non-crystalline Si, SiO, SiOx , and SiO2 . Journal of Physics and Chemistry of Solids, 32, 1935–1943. Pleskov, Yu. V. and Rotenberg, Z. A. (1972) Photoemission of electrons from metals into electrolyte solutions. Russian Chemical Review, 41, 21–35. Pohlack, H. (1986) Optically enhanced Schottky barrier photodetectors for IR image sensor application. Physica Status Solidi (a), 97, K211–K214. Pollak, F. H. and Rubloff, G. W. (1972) Piezo-optical evidence for lambda optical transitions at 3.4-eV optical structure of silicon. Physical Review Letters, 29, 789–792. Porod, W. and Kamocsai, R. L. (1990) Microscopic model for hot-electron trapping and detrapping in silicon dioxide. Applied Physics Letters, 57, 2318–2320. Pourtois, G., Lauwers, A., Kittl, J., Pantisano, L., Soree, B., DeGendt, S., Magnus, W., Heyns, M., and Maex, K. (2005) First-principle calculations on gate/dielectric interfaces: On the origin of work function shifts. Microelectronic Engineering, 80, 272–279. Powell, R. J. (1969) Photoinjection into SiO2 : Use of optical interference to determine electron and hole contributions. Journal of Applied Physics, 40, 5093–5101. Powell, R. J. (1970) Interface barrier energy determination from voltage dependence of photoinjected currents. Journal of Applied Physics, 41, 2424–2432.
282
References
Powell, R. J. (1976) Photoconductive processes in Al2 O3 films. Journal of Applied Physics, 47, 4598–4604. Powell, R. J. (1977) Determination of charge centroids in insulators by photoinjection or photodepopulation. Applied Physics Letters, 31, 290–291. Powell, R. J. and Beairsto, R. C. (1973) Properties of the tungsten-silicon dioxide interface. Solid State Electronics, 16, 265–267. Powell, R. J. and Berglund, C. N. (1971) Photoinjection studies of charge distributions in oxides of MOS structures. Journal of Applied Physics, 42, 4390–4398. Powell, R. J. and Derbenwick, G. F. (1971) Vacuum ultraviolet radiation effects in SiO2 . IEEE Transactions on Nuclear Science, NS-18, 99–112. Powell, R. J. and Morad, M. (1978) Optical absorption and photoconductivity in thermally-grown SiO2 films. Journal of Applied Physics, 49, 2499–2502. Prietsch, M. (1995) Ballistic-electron-emission microscopy (BEEM) – studies of metal–semiconductor interfaces with nanometer resolution. Physics Reports, 253, 164–233. Prietsch, M. and Ludeke, R. (1991) Ballistic-electron-emission microscopy and spectroscopy of GaP(110)-metal interfaces. Physical Review Letters, 66, 2511–2514. Prokofiev, A. V., Shelykh, A. I., and Melekh, B. T. (1996) Periodicity in the band gap variation of Ln2 X3 (X = O, S, Se) in the lanthanide series. Journal of Alloys and Compounds, 242, 41–44. Przewlocki, H. M. (1985) Determination of trapped charge distributions in the dielectric of a metal-oxide-semiconductor structure. Journal of Applied Physics, 57, 5359–5366. Puri, A. and Schaich, W. L. (1983) Comparison of image-potential theories. Physical Review B, 28, 1781–1784. Quinn, J. J. (1962) Range of excited electrons in metals. Physical Review, 126, 1453–1457. Raitsimring, A. (1993) Comment on: Photoinjection into electrolyte solutions. The role of thermalization. Journal of Chemical Physics, 98, 4311. Renard, C., Bodnar, S., Badoz, P. A., and Sagnes, I. (1995) Tunable infrared photoemission sensor on silicon using SiGe/Si epitaxial heterostructures. Journal of Crystal Growth, 157, 195–200. Revesz, A. G. (1977) Chemical and structural aspects of irradiation behavior of SiO2 films on silicon. IEEE Transactions on Nuclear Science, NS-24, 2102–2107. Revesz, A. G. and Hughes, H. L. (1997) Properties of the buried oxide layer in SIMOX structures. Microelectronic Engineering, 36, 343–350. Rhoderick, E. H. (1978) Metal-Semiconductor Contact. Clarendon, Oxford. ISBN 0-19-859323-6. Rhoderick, E. H. and Williams, R. H. (1988) Metal-Semiconductor Contacts. Clarendon, Oxford. ISBN 0-19-859336-8. Riemann, E. and Young, L. (1973) Conduction, permittivity, internal photoemission, and structure of electron-beam-evaporated yttrium oxide films. Journal of Applied Physics, 44, 1044–1049. Rikken, G. L. J. A., Kessener, Y. A. R. R., Braun, D., Starling, E. G. J., and Demandt, R. (1994a) Internal photoemission studies of metal/polymer interfaces. Synthetic Metals, 67, 115–119. Rikken, G. L. J. A., Braun, D., Starling, E. G. J., and Demandt, R. (1994b) Schottky effect at metal-polymer interface. Applied Physics Letters, 65, 219–221. Rippard, W. H., Perrella, A. C., Albert, F. J., and Buhrman, R. A. (2002) Ultrathin aluminum oxide tunnel barriers. Physical Review Letters, 88, 046805. Rips, I. and Urbakh, M. I. (1991) Photoinjection into electrolyte solutions. The role of thermalization. Journal of Chemical Physics, 95, 2975–2979. Ristein, J., Schäfer, J., and Ley, L. (1995) Effective correlation energies for defects in a-C:H from a comparison of photoelectron yield and electron spin resonance experiments. Diamond and Related Materials, 4, 508–516.
References
283
Ritala, M. (2004) Atomic layer deposition. In High-κ Gate Dielectrics, Houssa, M. (ed.). Institute of Physics Publishing, Bristol, 17–64. ISBN 0 7503 0906 7. Rivera, A., Van Veen, A., Schut, H., de Nijs, J. M. M., and Balk, P. (2002) Hydrogen-related hole capture and positive charge build up in buried oxides. Solid State Electronics, 46, 1775–1785. Robertson, J. (2000) Band offsets of wide bandgap oxides and implications for future electronic devices. Journal of Vacuum Science and Technology B, 18, 1785–1791. Robertson, J. (2004) High dielectric constant oxides. European Physical Journal: Applied Physics, 28, 265–291. Robertson, J. and Chen, C. W. (1999) Schottky barrier heights of tantalum oxide, barium strontium titanate, lead titanate, and strontium bismuth tantalate. Applied Physics Letters, 74, 1168–1170. Ron, A. and DiMaria, D. J. (1984) Theory of the current-field relation in silicon-rich silicon dioxide. Physical Review B, 30, 807–812. Rose, A. (1963) Concepts in Photoconductivity and Allied Problems. Interscience Publishing, New York, London, LCCCN 63-19666. Rotenberg, Z. A. and Gromova, N. V. (1986) Electron work function of metals in solutions, and the photoemission law. Soviet Electrochemistry, 22, 132–137. Rotenberg, Z. A., Gromova, N. V., and Kazarinov, V. E. (1986) Photoemission approach to the investigation of the electric double layer. Journal of Electroanalytical Chemistry, 204, 281–290. Rouse, J. W., Helms, C. R., Deal, B. E., and Razouk, R. R. (1981) Auger sputter profiling studies of SiO2 grown in O2 /HCl mixtures. Journal of Vacuum Science and Technology, 18, 971–972. Rouse, J. W., Helms, C. R., Deal, B. E., and Razouk, R. R. (1984) Auger sputter profiling and secondary ion mass spectroscopy studies of SiO2 grown in O2 /HCl mixtures. Journal of the Electrochemical Society, 131, 887–894. Rowe, J. E. and Ibach, H. (1974) Surface and bulk contributions to ultraviolet photoemission spectra of silicon. Physical Review Letters, 32, 421–424. Rozhkov, V. A. and Trusova, A. Yu. (1999) Energy barriers at the interfaces in the MIS system Me-Yb2 O3 -Si. Technical Physics, 44, 404–408. Rozhkov, V. A., Trusova, A. Yu., and Berezhnoi, I. G. (1998a) Energy barriers and trapping centers in silicon metal-insulator-semiconductor structures with samarium and ytterbium oxide insulators. Technical Physics Letters, 24, 217–219. Rozhkov, V. A., Trusova, A. Yu., and Berezhnoi, I. G. (1998b) Silicon MIS structures using samarium oxide films. Thin Solid Films, 325, 151–155. Rubio, A., Corkill, J. R., Cohen, M. L., Shirley, E. L., and Louie, S. G. (1993) Quasiparticle band structure of AlN and GaN. Physical Review B, 48, 11810–11816. Sah, C. T. (1990) Models and experiments on degradation of oxidized silicon. Solid State Electronics, 33, 147–167. Sah, C. T., Sun, J. Y. C., and Tzou, J. J. T. (1983a) Deactivation of the boron acceptor in silicon by hydrogen. Applied Physics Letters, 43, 204–206. Sah, C. T., Sun, J. Y. C., Tzou, J. J. T., and Pan, S. C. S. (1983b) Deactivation of group-III acceptors in silicon during keV electron irradiation. Applied Physics Letters, 43, 962–964. Sah, C. T., Sun, J. Y. C., and Tzou, J. J. T. (1983c) Study of the atomic models of 3 donor-like traps on oxidized silicon with aluminium gate from their processing dependences. Journal of Applied Physics, 54, 5864–5879. Saks, N. S. and Rendell, R. W. (1992) The time dependence of post-irradiation interface trap buildup in deuterium annealed oxides. IEEE Transactions on Nuclear Science, NS-39, 2220–2229. Sass, J. K. (1975) Evidence for an anisotropic volume photoelectric effect in polycrystalline nearly free electron metals. Surface Science, 51, 199–212. Sass, J. K. (1980) In situ photoemission. Surface Science, 101, 507–517.
284
References
Sass, J. K., Laucht, H., and Kliewer, K. L. (1975) Photoemission studies of silver with low-energy (3 to 5 eV), obliquely incident light. Physical Review Letters, 35, 1461–1464. Scharf, S., Schmidt, M., and Braunig, D. (1996) Trapping kinetics of thin layers influenced by tunnelling. Materials Chemistry and Physics, 43, 187–190. Schlom, D. G. and Haeni, J. H. (2002) Thermodynamic approach to selecting alternative gate dielectrics. MRS Bulletin, 27, 198–204. Schmidt, M. and Köster, H. (1992) Hole trap analysis in Si/SiO2 structures by electron tunnelling. Physica. Status Solidi (b), 174, 53–66. Schmidt, M., Brauer, M., and Hoffmann, V. (1996) Influence of scattering on internal photoemission in heterostructures. Applied Surface Science, 102, 303–307. Schmidt, M., Brauer, M., and Hoffmann, V. (1977) Internal photoemission in heterostructures affected by scattering processes. Journal of Physics D. Applied Physics, 30, 1442–1445. Schmitz, W. and Young, D. R. (1983) Radiation-induced electron traps in silicon dioxide. Journal of Applied Physics, 54, 5443–5447. Schowalter, L. J. and Fathauer, R. (1986) Molecular-beam epitaxy growth and applications of epitaxial fluoride films. Journal of Vacuum Science and Technology A, 4, 1026–1032. Schroder, D. K. (2001) Surface voltage and surface photovoltage: History, theory, and applications. Measurements Science and Technology, 12, R16–R31. Schuermeyer, F. L. and Crawford, J. A. (1966) Photovoltage measurements on an Al-Al2 O3 -Al thin film sandwiches. Journal of Applied Physics, 37, 1998–2004. von Schwerin, A., Hyens, M. M., and Weber, W. (1990) Investigation of the oxide field dependence of hole trapping and interface state generation in SiO2 layers using homogeneous non-avalanche injection of holes. Journal of Applied Physics, 67, 7595–7601. Scoggan, G. A. and Ma, T. P. (1977) Effects of electron-beam radiation on MOS structures as influenced by silicon dopant. Journal of Applied Physics, 48, 294–300. Sebenne, C., Bolmont, D., Guichar, G., and Balkanski, M. (1975) Surface states from photoemission threshold measurements on a clean, cleaved, Si(111) surface. Physical Review B, 12, 3280–3285. Seguini, G., Bonera, E., Spiga, S., Scarel, G., and Fanciulli, M. (2004) Energy-band diagram of metal/Lu2 O3 /silicon structures. Applied Physics Letters, 85, 5316–5318. Seguini, G., Spiga, S., Bonera, E., Fanciulli, M., Reyes Huamantinco, A., Forst, C. J., Ashman, C. R., Blochl, P. E., Dimoulas, A., and Mavrou, G. (2006) Band alignment at the La2 Hf2 O7 /(001)Si interface. Applied Physics Letters, 88, 202903. Seidel, W., Krebs, O., Voisin, P., Harmand, J. C., Aristone, F., and Palmier, J. F. (1997) Band discontinuities in Inx GaAs1−x As-InP and InP-Aly In1−y As heterostructures: Evidence of noncommutativity. Physical Review B, 55, 2274–2279. Shalish, I., Kronik, L., Segal, G., Shapira, Y., Eizenberg, M., and Salzman, J. (2000) Yellow luminescence and Fermi level pinning in GaN layers. Applied Physics Letters, 77, 987–989. Shamuilia, S., Afanas’ev, V. V., Somers, P., Stesmans, A., Li, Y.-L., Tökei, Zs., Groeseneken, G., and Maex, K. (2006) Internal photoemission of electrons at interfaces of metals with low-κ insulators. Applied Physics Letters, 89, 202909. Shanfield Z., and Morivaki, M. M. (1987) Critical evaluation of the midgap voltage shift method for determining oxide trapped charge in irradiated MOS devices. IEEE Transactions on Nuclear Science, NS-34, 1159–1165. Shepard, K. W. (1965) Photocurrents through thin films of Al2 O3 . Journal of Applied Physics, 36, 796–799. Shigiltchoff, O., Bai, S. Devaty, R. P., Choyke, W. J., Kimoto, T., Hobgood, D., Neudeck, P. G., and Porter, L. M. (2002) Schottky barriers for Pt, Mo and Ti and 4H–SiC faces measured by I-V, C-V, and internal photoemission. Materials Science Forum, 433–434, 705–708.
References
285
Shirashi, K., Yamada, K., Torii, K., Akasaka, Y., Nakajima, K., Konno, M., Chikyow, T., Kitajima, H., and Arikado, T. (2004) Oxygen vacancy induced substantial threshold voltage shifts in the Hf-based high-κ MISFET with p+ -poly-Si gates – a theoretical approach. Japanese Journal of Applied Physics Part 2, 43, L1412–1415. Shousha, A. H. M. (1980) On the charge profiles in thin dielectric films. Physics Letters A, 80, 305–308. Siegrist, K., Ballarotto, V. W., Breban, M. Yongsunthon, R. and Williams, E. D. (2004) Imaging buried structures with photoelectron emission microscopy. Applied Physics Letters, 84, 1419–1421. Sigaud, Ph., Chazalviel, J. N., Ozanam, F., and Stephan, O. (2001) Determination of energy barriers in organic light-emitting diodes by internal photoemission. Journal of Applied Physics, 89, 466–470. Sigaud, Ph., Chazalviel, J. N., and Ozanam, F. (2002) Barrier lowering and reorientation of dipoles grafted at indium-tin-oxide/polymer interfaces. Journal of Applied Physics, 92, 992–996. Silveira, E., Freitas, J. A., Glembocki, O. J., Slack, G. A., and Schowalter, L. J., (2005) Excitonic structure of bulk AlN from optical reflectivity and cathodoluminescence measurements. Physical Review B, 71, 041201(R). Silver, M. and Smejtek, P. (1973) Comment on electron scattering in the image-force potential well. Journal of Applied Physics, 43, 2451–2453. Silver, M., Onn, D. G., Smejtek, P., and Masuda, K. (1967) Hot electron injection into helium and other insulating liquids from a tunnel junction. Physical Review Letters, 19, 626–628. Simmons, J. G. and Tam, M. C. (1973) Theory of isothermal currents and direct determination of trap parameters in semiconductors and insulators containing arbitrary trap distributions. Physical Review B, 7, 3706–3713. Smith, R. (1959) Semiconductors. (1959) Cambridge University Press, Cambridge. Sokolov, N. S., Yakovlev, N. L., and Almeida, J. (1990) Photoluminsecence of Eu2+ and Sm2+ ions in CaF2 pseudomorphic layers grown by MBE on Si(111). Solid State Communications, 76, 883–885. Solomon, P. M. and DiMaria, D. J. (1981) Effect of forming gas anneal on Al-SiO2 internal photoemission characteristics. Applied Physics Letters, 52, 5867–5869. Snow E. H. (1967) Fowler–Nordheim tunnelling in SiO2 films. Solid State Communications, 5, 813–815. Spitzer, W. G., Crowell, C. R., and Atalla, M. M. (1962) Mean free path of photoexcited electrons in Au. Physical Review Letters, 8, 57–58. Stahlbush, R. E., Edwards, A. H., Griscom, D. L., and Mrstik, B. J. (1993) Post-irradiation crackling of H2 and formation of interface states in irradiated metal-oxide-semiconductor field-effect transistors. Journal of Applied Physics, 73, 658–667. Stesmans, A. (1996) Revision of H2 passivation of Pb interface defects in standard (111)Si/SiO2 . Applied Physics Letters, 68,2723–2725. Stesmans, A. (2002) Influence of interface relaxation on passivation kinetics in H2 of coordination Pb defects at the (111)Si/SiO2 interface revealed by electron spin resonance. Journal of Applied Physics, 92, 1317–1328. Stesmans, A. and Afanas’ev, V. V. (1998) Electrical activity of interfacial paramagnetic defects in thermal (100)Si/SiO2 . Physical Review B, 57, 10030–10034. Stesmans, A. and Afanas’ev, V. V. (2004) Defects in stacks of Si with nanometre thick high-κ dielectric layers: Characterization and identification by electron spin resonance. In High-κ Gate Dielectrics, Houssa, M. (ed.). Institute of Physics Publishing, Bristol. 190–216. ISBN 0 7503 0906 7. Stivers, A. R. and Sah, C. T. (1980) A study of oxide traps and interface states of the silicon–silicon dioxide interface. Journal of Applied Physics, 51, 6292–6304. Strite, S. and Morkoc, H. (1992) GaN, AlN, and InN: A review. Journal of Vacuum Science and Technology B, 10, 1237–1252. Stuart, R., Wooten, F., and Spicer, W. E. (1964) Monte–Carlo calculations pertaining to transport of hoe electrons in metals. Physical Review, 135, A495–A506.
286
References
Sune, C. T., Reisman, A., and Williams, C. K. (1990) A new electron-trapping model for the gate insulator of insulated gate field-effect transistors. Journal of Electronic Materials, 19, 651–655. Swanson, J. G. (1993) Compound semiconductor/insulator device interfaces – present status and requirements. Microelectronic Engineering, 22, 111–118. Sze, S. M. (1981) Physics of Semiconductor Devices, 2nd edition. Wiley, New York, ISBN 0-471-05661-8. Szydlo, N. and Poirier, R. (1971) Internal photoemission measurements in a metal-Al2 O3 -system. Journal of Applied Physics, 42, 4880–4882. Takahashi, H., Okabayashi, J., Toyoda, S., Kumigashira, H., Oshima, M., Ikeda, K., Liu, G. L., Liu, Z. and Usuda, K. (2006) Annealing-time dependence in interfacial reaction between poly-Si electrode and HfO2 /Si gate stack studied by synchrotron radiation photoemission and x-ray absorption spectroscopy. Applied Physics Letters, 89, 012102. Tanabe, A., Konuma, K., Teranishi, N., Tohyama, S., and Masubuchi, K. (1991) Influence of Fermi-level pinning on barrier height inhomogeniety in PtSi/p-Si Schottky contacts. Journal of Applied Physics, 69, 850–853. Tersoff, J. (1984a) Schottky barrier heights and the continuum of gap states. Physical Review Letters, 52, 465–468. Tersoff, J. (1984b) Theory of semiconductor heterojunctions. – The role of quantum dipoles. Physical Review B, 30, 48744877. Thomas, III, J. H. and Feigl, F. J. (1970) Spectrally resolved photodepopulation of electron trapping defects in amorphous silica films. Solid State Communications, 8, 1669–1672. Tippins, H. H. (1966) Absorption edge spectrum of scandium oxide. Journal of Physics and Chemistry of Solids, 27, 1069–1074. Tomio, Y., Yasuoshi, M., Matsataka, H., and Yukio, O. (1981) Internal photoemission in a-Si:H Schottky barrier and MOS structures. Japanese Journal of Applied Physics Supplement 2, 20, 185–198. Toyoda, S., Okabayashi, J., Kumigashira, H., Oshima, M., Liu, G. L., Liu, Z., Ikeda, K., and Usuda, K. (2005) Precise determination of band offsets and chemical states in SiN/Si studied by photoemission spectroscopy and X-ray absorption spectroscopy. Applied Physics Letters, 87, 102901. Travkov, I. V., Gadijak, G. V., and Sinitsa, S. P. (1987) Monte–Carlo modeling of current transport in silicon nitride. In Preprint N7-87 of the Institute of Theoretical and Applied Mechanics, Siberian Branch of the Academy of Sciences of USSR, Novosibirsk, USSR, (in Russian). Trombetta, L. P., Gerardi, G. J., DiMaria, D. J., and Tierney, E. (1988) An electron paramegnetic resonance study of electron injected oxides in metal-oxide-semiconductor capacitors. Journal of Applied Physics, 64, 2434–2438. Tung, R. T. (2001) Recent advances in Schottky barrier concepts. Materials Science and Engineering R, 35, 1–138. Tutis, E., Bussac, M. N., and Zippiroli, L. (1999) Image-force effects at contacts in organic light-emitting diodes. Applied Physics Letters, 75, 3880–3882. Vanheusden, K., Stesmans, A., and Afanas’ev, V. V. (1995) Hydrogen-annealing induced positive charge in buried oxides: Correspondence between ESR and C-V results. Journal of Non-Crystalline Solids, 187, 253–256. Vanheusden, K., Warren, W. L., Devine, R. A. B., Fleetwood, D. M., Schwank, J. R., Shaneyfelt, M. R., Winokur, P. S., and Leminos, Z. J. (1997) Non volatile memory device based on mobile protons in SiO2 thin films. Nature, 386, 587–589. van Otterloo, J. D. and Gerritsen, L. J. (1978) The accuracy of Schottky barrier-height measurements on clean-cleaved silicon. Journal of Applied Physics, 49, 723–729. Vargheze, D., Mahapatra, S., and Alam, M. A. (2003) Hole energy dependent interface trap generation in MOSFET Si/SiO2 interface. IEEE Electron Device Letters, 26, 572–574.
References
287
de Vasconcelos, E. A. and da Silva Jr, E. F. (1997) Correlation between dopant reduction and interfacial defects in low-energy X-ray-irradiated MOS capacitors. Semiconductor Science and Technology, 12, 1032–1037. de Vasconcelos, E. A. and da Silva Jr, E. F. (1998) Post-irradiation dopant passivation in MOS capacitors exposed to high doses of X-rays. Semiconductor Science and Technology, 13, 1313–1316. de Vasconcelos, E. A., da Silva Jr, E. F., Khoury, H. J., and Freire, V. N. (2000) Effect of ageing on X-ray induced dopant passivation in MOS capacitors. Semiconductor Science and Technology, 15, 794–798. Verwey, J. F. (1973) Non-avalanche injection of hot carriers into SiO2 . Journal of Applied Physics, 44, 2681–2687. Viswanathan, C. R. and Loo, R. Y. (1972a) Photo-injection of electrons from metal films into single-crystal Al2 O3 layers. Thin Solid Films, 13, 87–92. Viswanathan, C. R. and Loo, R. Y. (1972b) Internal photoemission in sapphire substrates. Applied Physics Letters, 21, 370–372. Vogel, E. M., Edelstein, M. D., and Suehle, J. S. (2001) Defect generation and breakdown of silicon dioxide induced by substrate hot-hole injection. Journal of Applied Physics, 90, 2338–2346. Vouagner, D., Beleznai, Cs., and Girardeau-Montaut, J. P. (2001) “Characterization of surface processes on metals under pulsed picosecond laser irradiation by photoelectric work function measurements. Applied Surface Science, 171, 288–305. Vuillaume, D. and Bravaix, A. (1993) Charging and discharging properties of electron traps created by hot-carrier injections in gate oxide of n-channel metal oxide semiconductor field effect transistor. Journal of Applied Physics, 73, 2559–2563. Vuillaume, D., Boulas, C., Collet, J., Allan, G., and Delerue, C. (1998) Electronic structure of a heterostructure of an alkylsiloxane self-assembled monolayer on silicon. Physical Review B, 58, 16491–16498. Waho, T. and Yanagawa, F. (1988) A GaAs MISFET using an MBE-grown CaF2 gate insulator layer. IEEE Electron Device Letters, 9, 548–549. Walters, M. and Reisman, A. (1990) The distribution of radiation-induced charged defects and neutral electron traps in SiO2 , and the threshold voltage shift dependence on the oxide thickness. Journal of Applied Physics, 67, 2992–3002. Wang, C. G. and DiStefano, T. H. (1975) Polarization layer at metal-insulator interfaces. CRC Critical Reviews in Solid State Science, 5, 327–335. Wang, W., Lupke, G., DiVentra, M., Pantelides, S. T., Gilligan, J. M., Tolk, N. H., Kizilyalii, I. C., Roy, P. K., Margaritondo, G., and Lucovsky, G. (1998) Coupled electron-hole dynamics at the Si/SiO2 interface. Physical Review Letters, 81, 4224–4227. Waters, R. and Van Zeghbroeck, B. (1998) Fowler–Nordheim tunnelling of holes through thermally grown SiO2 on p+ -6H–SiC. Applied Physics Letters, 73, 3692–3694. Waters, R. and Van Zeghbroeck, B. (1999) On field emission from a semiconducting substrate. Applied Physics Letters, 75, 2410–2412. Watkins, G. D., Fowler, W. B., Stavola, M., DeLeo, G. G., Kozuch, D. M., Pearton, S. J., and Lopata, J. (1990) Identification of a Fermi resonance for a defect in silicon: Deuterium-Boron pair. Physical Review Letters, 64, 467–470. Weinberg, Z. A. (1977) Tunnelling of electrons from Si into thermally grown SiO2 . Solid State Electronics, 20, 11–18. Weinberg, Z. A. (1982) On tunnelling in metal-oxide-silicon structures. Journal of Applied Physics, 53, 5052–5056. Weinberg, Z. A., Rubloff, G. W., and Bassous, E. (1979) Transmission, photoconductivity, and the experimental bandgap of thermally grown SiO2 films. Physical Review B, 19, 3107–3117.
288
References
Weinberg, Z. A., Fischetti, M. V., and Nissan-Cohen, Y. (1986) SiO2 -induced substrate current and its relation to positive charge in field-effect transistors. Journal of Applied Physics, 59, 824–832. Wilk, G. D., Wallace, R. M., and Anthony, J. M. (2001) High-κ gate dielectrics: Current status and material considerations. Journal of Applied Physics, 89, 5243–5275. Williams, R. (1962) Photoemission of holes from tin into gallium arsenide, Physical Review Letters, 8, 402–404. Williams, R. (1965) Photoemission of electrons from silicon into silicon dioxide. Physical Review, 140, A569–A575. Williams, R. (1970) Injection by internal photoemission. In Semiconductors and Semimetals. Injection Phenomena, Chapter 2, Willardson, R. K. and Beer, A. C. (eds). Academic Press, New York. ISSN 0080-8784. Williams, R. (1974) Behaviour of ions in SiO2 . Journal of Vacuum Science and Technology, 11, 1025–1027. Williams, C. K. (1992) Kinetics of trapping, detrapping and trap generation. Journal of Electronic Materials, 21, 711–720. Williams, R. and Dresner, J. (1967) Photoemission of holes from metals into anthracene. Journal of Chemical Physics, 46, 2133–2135. Williams, R. and Woods, M. H. (1972) Laser-scanning photoemission measurements of the silicon-silicon dioxide interface. Journal of Applied Physics, 43, 4142–4147. Williams, F., Varma, S. P., and Hillenius, S. (1976) Liquid water as a lone-pair amorphous semiconductor. Journal of Chemical Physics, 64, 1549–1554. Winer, K. and Ley, L. (1987) Surface states and the exponential valence-band tail in a-Si:H. Physical Review B, 36, 6072–6078. Witham, H. S. and Lenahan, P. M. (1987a) Nature of the E deep hole trap in metal-oxide-semiconductor oxide. Applied Physics Letters, 51, 1007–1009. Witham, H. S. and Lenahan, P. M. (1987b) The nature of deep hole trap in MOS oxides. IEEE Transactions on Nuclear Science, NS-34, 1147–1151. Witte, G., Lucas, S., Bagus, P. S., and Wöll, C. (2005) Vacuum level alignment at organic/metal junctions: ‘Cushion’ effect and the interface dipole. Applied Physics Letters, 87, 263502. Wolters, D. R. and van der Schoot, J. J. (1985) Kinetics of charge trapping in dielectrics. Journal of Applied Physics, 58, 831–837. Wolters, D. R. and Zegers van Duinhoven, A. T. A. (1989) Trapping of hot electrons. Applied Surface Science, 39, 565–577. Woods, M. H. and Williams, R. (1973) Injection and removal of ionic charge at room temperature through interface of air with SiO2 . Journal of Applied Physics, 44, 5506–5510. Woods, M. H. and Williams, R. (1976) Hole traps in silicon dioxide. Journal of Applied Physics, 47, 1082–1089. Wrana, M., Schmidt, M., and Bräunig, D. (1977) Thermal and optical stability of injected charge in stacked dielectric layers. Semiconductor Science and Technology, 12, 369–374. Wronski, C. R. (1992) Review of direct measurements of mobility gaps in a-Si:H using internal photoemission. Journal of Non-Crystalline Solids, 141, 16–23. Wronski, C. R., Lee, S., Hicks, M. and Kumar, S. (1989) Internal photoemission of holes and the mobility gap of hydrogenated amorphous silicon. Physical Review Letters, 63, 1420–1423. Wu, H. H., Chang, R. S., and Horn, G. H. (2004) Microstructure, electrical and optical properties of evaporated PtSi/p-Si(100) Schottky barriers as high quantum efficient infrared detectors. Thin Solid Films, 466, 314–319. Yamabe, K. and Miura, Y. (1980) Discharge of trapped electrons from MOS structures. Journal of Applied Physics, 51, 6258–6264.
References
289
Yamada, Y., Oshima, M., Waho, T., Kawamura, T., Maeyama, S., and Miyahara, T. (1988a) Structure and bonding at the CaF2 /GaAs(111) interface. Japanese Journal of Applied Physics, 27, L1196–L1198. Yamada, Y., Oshima, M., Maeyama, S., Kawamura, T., and Miyahara, T. (1988b) Determination of Ca-As bonding at the CaF2 /GaAs(111) interface. Applied Surface Science, 33/34, 1073–1080. Yeo, Y. C., King, T. J. and Hu, C. M. (2002) Metal-dielectric band alignment and its implications for metal gate complementary metal-oxide-semiconductor technology. Journal of Applied Physics, 92, 7266–7271. Yim, W. M., Stofko, E. J., Zanzucchi, P. J., Pankove, J. I., Ettenberg, M., and Gilbert, S. L. (1973) Epitaxially grown AlN and its optical bandgap. Journal of Applied Physics, 44, 292–296. Yokoyama, S., Hirose, M., Osaka, Y., Sawada, T., and Hasegawa, H. (1981) Internal photoemission in the anodic oxide-GaAs interface. Applied Physics Letters, 38, 97–99. Young, D. R. (1980) Electron trapping in SiO2 . In Insulating Films on Semiconductors – 1979, Roberts, G. G. and Morant, M. J. (eds). The Institute of Physics, London, 28–39. Young, D. R. (1981) Characterization of electron traps in SiO2 as influenced by processing parameters. Journal of Applied Physics, 52, 4090–4094. Young, L. A. and Bradbury, N. E. (1933) Photoelectric currents in gases between parallel plate electrodes. Physical Review, 43, 34–41. Young, D. R., DiMaria, D. J., Hunter, W. R., and Serrano, C. M. (1978) Characterization of electron traps in aluminum-implanted SiO2 . IBM Journal of Research and Development, 22, 285–288. Young, D. R., Irene, E. A., DiMaria, D. J., DeKeersmaecker, R. F., and Massoud, H. (1979) Electron trapping in SiO2 at 295 and 77 K. Journal of Applied Physics, 50, 6366–6372. Yun, B. H. (1973) Direct display of electron back tunnelling in MNOS memory capacitors. Applied Physics Letters, 24, 152–153. Yun, B. H. (1974) Measurements of charge propagation in Si3 N4 films. Applied Physics Letters, 25, 340–342. Yun, B. H. (1975) Silicon nitride trap properties as revealed by charge-centroid measurements on MNOS devices. Applied Physics Letters, 26, 94–96. Zavracki, P. M., Vu, D. P., and Batty, M. (1991) Silicon-on-insulator wafers by zone-melting recrystallization. Solid State Technology, 34, 55–57. Zhao, H. B., Ren, Y. H., Sun, B., Lupke, G., Hanbicki, A. T., and Jonker, B. T. (2003a) Band offsets at CdCr2 Se4 -(AlGa)As and CdCr2 Se4 -ZnSe interfaces. Applied Physics Letters, 82, 1422–1424. Zhao, C., Cosnier, V., Chen, P. J., Richard, O., Roebben, G., Maes, J., Van Elshocht, S., Bender, H., Young, R., Van Der Biest, O., Caymax, M., Vandervorst, W., DeGendt, S., and Heyns, M. (2003b) Thermal stability of high-κ layers. Materials Research Society Symposium Proceedings, 745, 9–14. Zhao, Y., Toyama, M., Kita, K., Kyuno, K., and Toriumi, A. (2006) Moisture-absorption-induced permittivity deterioration and surface roughness enhancement of lanthanum oxide films on silicon. Applied Physics Letters, 88, 072904. Zogg, H., Masek, J., Maissen, C., Blunier, S., and Weibel, H. (1990) IV–VI compounds on fluoride-silicon heterostructures and IR devices. Thin Solid Films, 184, 247–252.
This page intentionally left blank
Index
Note: Page numbers in italics refer to illustrations. Adsorption: desorption equilibrium, 185, 186, 223 induced charging phenomenon, 261 induced dipoles, 224 Annealing, 225 high-temperature, 3 Arrhenius plot, 258 Avalanche carrier injection (ACI), 114–16 Ballistic electron emission microscopy (BEEM), 244, 261 as injection technique, 11 Band alignment: at interfaces of silicon with high-permittivity insulators: Si with complex metal oxides, 198–203 Si with elemental metal oxides, 195–8 Si with non-oxide insulators, 203–8 between other semiconductors and insulating films, 208 GaAs/insulator interfaces, 212–17 Ge/high-permittivity oxide interfaces, 209–12 SiC/insulator interfaces, 217–21 Band bending, in semiconductor under illumination, 60, 61, 62 Bandgap width, of collector, 35 Brillouine zone, 234 Brodsky-Gurevich law, 21 Buger’s law, 26 Capacitance voltage (CV), 191 Capture cross-section, 246–248, 248, 259 Carrier trapping regime, strong, 164–9 Charge, as intrinsic defect, 245 discrete, 43–5 ionic, 72, 188 Charge-annihilation profiling method, 141–5 Charge carrier injection: basic approaches, 108–9
carriers excitation in emitter using electric field, 114–17 charge injection by tunnelling, 112–14 charge injection using IPE, 109–11 disadvantages of PC spectroscopy for, 118 electron-hole plasma generation in collector, 117–21 radiation method of, 118 selection of charge injection technique, 121–3 trap generation during, 160–1 Charge carrier scattering spectroscopy: in collector, 88–92 in emitter, 85–8 Charge carrier traps, 107–8 charge injection techniques for see under Charge carrier injection injected carriers interaction with see under Charge trapping kinetics monitoring and characterization, 124–47 charge probing by electron IPE, 133–7 charge probing by trap depopulation, 137–41 charge probing using neutralization (annihilation), 141–5 injection current monitoring, 124–7 injection-induced liberation of hydrogen, monitoring of, 145–7 semiconductor field-effect techniques, 127–33 trapping equation, 174 Charge neutrality level (CNL), 230 Charge probing techniques: by electron IPE, 133–7 by trap depopulation, 137–41 using neutralization (annihilation), 141–5 Charge trap characterization, 108–9, 246–8 Charge trapping kinetics: carrier transport effects on, 164–81 carrier redistribution by Coulomb repulsion, 177–80 carrier trapping near injecting interface, 169–72 space-charge-limited current, injection blockage and transition to, 180–1
291
292 Charge trapping kinetics (Contd.) strong carrier trapping regime, 164–9 trapping inhibition by Coulomb repulsion, 172–7 effect of local blockage of injection on shape of, 170 in injection-limited current regime, 148–63 application of, 161–3 carrier recombination effects, 158–9 detrapping effects, 154–8 multiple trap model for, 152–4 single trap model for, 150–2 trap generation during injection, 160–1 Collectors: charge carrier scattering in, 88–92 collector bandgap width, 35 configuration of IPE experiments, 62–4 electrolyte collector configuration, 64 thick-collector configuration, 63–4 thin-collector configuration, 62–3 DOS, effect on IPE, 32–4 effects associated with occupied electron states in, 34–5 effects of fixed charge in, 42–5 electron-hole plasma generation in, 117–21 electron scattering in, 39–41 intrinsic photoconduction (PC) of, 92–7 PI spectroscopy of near-interface states in, 101–6 recombination of trapped carriers, 158 suitable for IPE current detection, 59 Complex metal electrodes on insulators, 237–42 Complex metal oxides, 198–203 Conducting and insulating materials, 224–49 Conductor/insulator barriers, modification of, 242–4 Coulomb hole traps, 252 Coulomb-limited trap density, 175 Coulomb potential, 36–7 and carrier trapping, 162 scattering, 41 Coulomb repulsion: carrier redistribution by, 177–80 charge trapping inhibition by, 172–7 Coulomb traps, 248–9 Cross-over voltage, 137 Debye length, 28, 43 Defect(s): assisted injection, 206 charge as intrinsic, 245 density of charged, 222 mediated optical transition, 205 monitoring methods, 109 see also under Charge carrier injection Density of charged defects, 222 Density of states (DOS), 195, 214, 261 see also under Electron density of states Detrapping, charge, 138–41, 181 effects of, 154–8
Index optical radiation and, 156 via electron tunnelling, 157–8 Detrapping process, 259 Electric fields: carriers excitation in emitters using, 114–17 IPE quantum yield sensitive to, factors making, 53–7 electron–phonon scattering effect, 54–6 field-dependent transport of charge carriers, 57 field-induced barrier lowering, 53–4 Electron density of states (electron DOS), 3 characterization by electron spectroscopy, 3 collector, impact on IPE, 32–4 of polar liquid, 19 Electron energy barriers: complex metal electrodes on insulators, 237–42 conductor/Insulator barriers see under Conductor/insulator barriers, modification of interface barriers see under Interface barriers between elemental metals and oxide insulators polycrystalline Si/oxide interfaces, 231–7 Electron escape condition, by Fowler model, 6–7, 9, 29–32 Electron-hole plasma generation, in collector, 117–21 Electron IPE spectra, 15, 71, 86, 106, 188, 197, 209, 215, 217, 226, 238, 240 Electron-phonon scattering, 26, 40 impact on quantum yield, 54–6 quasi-elastic, 10 Electron scattering in collector, effects on IPE, 39–41 Electron spectroscopy, 3 Electron states at Si/SiO2 interface: Si/SiO2 band alignment, 183–4 Si/SiO2 barrier modification by trapped charges, 186–8 Si/SiO2 interface dipoles, 184–6 trapped ions at Si/SiO2 interface, 188–9 Electron state spectrum, 183, 219 Electron transport: in device structures, 2, 3–4 model, 4 Electron traps in SiO2 : attractive Coulomb traps, 248–9 neutral electron traps in SiO2 , 249–51 repulsive electron traps in SiO2 , 251 Elemental metal oxides, 195–8 Emitters: carriers excitation in, using electric field: avalanche carrier injection (ACI), 114–16 non-avalanche injection method, 114, 116–17 charge carrier scattering in, 85–8 charge injection rate increase in, 110 electric field penetration effect into, 13 excited electron transport to, 25–9 Fowler model for electron escape from, 29–32 optical excitation in, 24–5
Index Energy band diagram: emitter–collector–metal structure, 43 between metal and molecular material, 16 metal–electrolyte solution contact, 19 semiconductor–insulator–conductor structure, 60, 61 semiconductor–insulator–metal structure, 127 showing IPE of electrons, 49 of two-layer polymer device, 14, 15 Energy barriers: at interfaces of organic solids and molecular layers, 14–18 at interfaces of solids with electrolytes, 18–22 at semiconductor heterojunctions, 12–14 Experimental observation of IPE see IPE experiments External photoemission, 1 common steps in internal and, 23–32 differences in internal and, 32–47 see also under IPE, and external photoemission External quantum efficiency see External quantum yield External quantum yield, 49, 50 Fermi level, 205, 212, 214, 222, 224–5, 230, 231, 234 Field sensitive optical effect, 262 First-order trapping kinetics see Charge trapping kinetics Flatband voltage, 231, 232, 234, 258 Forming gas annealing, 227, 250 Fowler law, 31, 229, 239 Fowler model, for electron escape, 9, 29–32, 51 Fowler plots, 5, 239, 240, 243 GaAs/fluoride, 214 GaAs/insulator, 212–17 GaAs/insulator interfaces, 212–17 GaAs MOSFET, 213 Ge/high-permittivity oxide interfaces, 209–12 Giant potential well, 135, 141 Hall effect, 262 Helmholtz layer, 19 Highest occupied molecular orbital (HOMO), 261 High-permittivity insulators, 195–204 see also under Band alignment at interfaces of silicon with high-permittivity insulators application of, 189–92 bandgap width in deposited oxide layers, 192–5 Hole traps: neutral, 252–6 in SiO2 , 251 attractive Coulomb hole traps, 252 neutral hole traps in SiO2 , 252–6 ‘Hot’ carriers, 112–13 Hydrogen: isotope effect, 255 in situ detection of atomic, 146
293 Image force model, 192, 196, 224, 229, 235 for metal-vacuum barriers, 36 Injection current monitoring, for trapped charges, 124–7 Injection-induced trap, 160 generation in SiO2 , 248 Injection-limited current regime, charge trapping kinetics in see Charge trapping kinetics, in injection-limited current regime Injection spectroscopy see Charge carrier injection Interface barriers: characterization, 4 effects of condensed phase collector on shape of, 35–9 image-force model and, 36 of organic solids and molecular layers, 14–18 at solids with electrolytes, 18–22 Interface barriers between elemental metals and oxide insulators: interfaces of elemental metals with high-permittivity oxides, 227–31 metal–SiO2 interfaces, 225–7 Interface selective doping, 243 Internal photoeffect see Photoconduction Internal photoemission (IPE), see also separate entry concept of, 1–2 definition, 1 external photoemission and, 1 see also under IPE, and external photoemission partial neutralization method, 144 transitions in semiconductor heterojunction, 12 Internal quantum efficiency see Internal quantum yield Internal quantum yield, 48–9 IPE, and external photoemission: common features: escape of electron from emitter into another phase, 29–32 excited electron transport to emitter surface, 25–9 optical excitation, 24–5 dissimilar features, 32–47 collector transport effects, 45–7 effects associated with occupied electron states in collector, 34–5 effects of collector DOS, 32–4 effects of fixed charge in collector, 42–5 electron scattering in image-force potential well, 39–41 interface barrier shape, 35–9 IPE experiments: approaches to, 62–6 IPE configuration, 62–4 IPE signal detection, 65–6 optical input designs, 64–5
294 IPE experiments (Contd.) observation, conditions for, 57–62 injection-limited versus transport-limited current, 57–9 photocurrents related to light-induced redistribution of electric field, 60–2 thermoionic emission versus photoemission, 59–60 IPE experiments configuration: electrolyte collector configuration, 64 thick-collector configuration, 63–4 thin-collector configuration, 62–3 IPE spectroscopy, 1, 182, 215, 220, 226 applications see under IPE spectroscopy applications as charge carrier injection method, 109–11 effects of condensed phase collector, 32–47 experimental realization see under IPE experiments external quantum yield and, 50 as injection techniques, 11 see also under Charge carrier injection and materials analysis issues, 2–5 for metal-semiconductor interface barrier structures, 8–11 model for see under Quantum yield, of photoemission multi-step model of, 7–8 organic solids and molecular layers, 14–18 photocharging detection of, 65–6 quantum yield of, 7, 10, 67 see also under Quantum yield, of photoemission at semiconductor heterojunctions, 12–14 at solids with electrolytes, 18–22 for wide bandgap insulators, 5–8 IPE spectroscopy applications, 67–106 charge carrier scattering spectroscopy, 85–92 in collector, 88–92 in emitter, 85–8 photoconductivity (PC) and photoionization (PI) spectroscopy, 92–106 spectral threshold determination, 68–75 see also under IPE threshold spectroscopy total yield spectroscopy, 75–85 see also under IPE yield spectroscopy IPE threshold spectroscopy, 68–75 energy band offset to IPE, contributions of different, 68–71 Schottky plot analysis, 72–3 separation of processes contributing to photocurrent, 73–5 IPE yield, 196, 197, 199, 200, 201, 202, 209, 228, 233, 234, 235, 243 IPE yield spectroscopy, 75–85 see also under Quantum yield, of photoemission IPE yield modulation, 75–8 aplication to Si surface monitoring, 78–82 optically induced yield modulation, 82–5
Index Lowest occupied molecular orbital (LUMO), 261 Metal induced gap state, 222, 225, 230 Metal insulator semiconductor (MIS), 204, 208, 217 Metal oxide semiconductor (MOS), 189, 191 Metal-semiconductor interface barrier structures, 8–11 Molecular beam deposition (MBD), 198 Monopolar injection current, 126, 148 Multiple trap model, for first-order trapping, 152–4 Multi-step photoemission model, 23–4 of electron IPE at metal electrolyte interface, 20 IPE process, 7–8 Neutralization (annihilation), for carrier trapping monitoring see Charge-annihilation profiling method Non-native insulator technology, 189 Non-volatile memory devices, 203, 245 Optical excitation, in emitter, 24–5 see also under Photoconduction and carrier injection, 122 stages of, 7, 20 Optically stimulated non-avalanche carrier injection, 248 Optical radiation and detrapping, 156 Optical spectroscopy, 108 Optical transparency, 64–5 Organic solids and molecular layers, energy barriers at interfaces, 14–18 Oxide trap influence, 219 Pauling electronegativity, 231, 232 Phononless photoluminescence, 208 Photocharging detection, of IPE, 46, 65–6 hole IPE spectra using, 75 Photoconduction (PC), 35 of collector, 92–7 disadvantages for carrier traps characterization, 118 Photoconductivity see Photoconduction Photoconductivity spectroscopy see Photoconduction Photocurrent (PC): generation from electron photoemission, 20 measurement for IPE signal detection, 65–6 related to light-induced redistribution of electric field and IPE experiments, 60–2 yield, 206, 213 Photodepopulation effects, in IPE injection, 111 Photoemission: quantum yield technique, 4–5 see also under Quantum yield, of photoemission thermoionic emission versus, 59–60 into vacuum, 1, 2 see also under External photoemission see also Internal photoemission
Index Photoionization (PI), 183 Photoionization (PI) spectroscopy, 97–101 of near-interface states in collector, 101–6 Photon energy, 1, 4, 21 and IPE quantum yield, 50–3, 76–8, 85 photocharging/photocurrent ratio at, 94 region, 119 Photon stimulated tunnelling, 183 Pinning of the Fermi level, 212, 216, 229, 242 Polarization layer, 224–5, 242 Polycrystalline Si/Oxide interfaces, 231–7 Powell’s model, 195 Proton trapping in SiO2 , 256–9 Pseudo-IPE transitions, 204, 205 quantum yield of, 17, 100–6 Quantum mixing, 202–3 Quantum yield, of photoemission, 7, 10, 48–50 see also under IPE yield spectroscopy definition, 48 electron-phonon scattering impact, 54–6 expression as function of electric fields, 53–7 expression as function of photon energy and interface barrier height, 50–3 external quantum yield, 49, 50 internal quantum yield, 48–9 of pseudo-IPE transitions, 17, 100–6 spectral dependences, 16, 17, 29, 33 functional form, at emitter surface, 52 Quasi monopolar photoconductive injection, 252 Quasi-stationary current, 166 Radiative optical transition, 246 Random walk model, 26 Recombination of trapped carriers, 158–9 Reversible barrier behaviour, 226 Scanning IPE microscopy, 11, 261 Schottky barrier theory, 222 Schottky plot, 184, 196, 212, 215, 217, 225, 226, 227, 229, 235, 236, 239, 240, 241 analysis, for IPE, 72–3 Secondary electron spectroscopy, 261 Semiconductor field-effect techniques, for carrier trapping, 127–33 capacitance-voltage (CV) measurements, 127–130, 132 charge centroid approach, 132–3 etch-back technique, 131–2 photovoltage dependence, 129 Semiconductor–insulator interface barriers, 221–3 Semiconductor(s): energy band diagram of, 49 heterojunctions, energy barriers at, 12–14 IPE experiments and optical transparency of, 64–5 IPE yield modulation for crystalline quality evaluation, 78–82
295 Semiconductors and insulating films, band alignment between other, 208 GaAs/insulator interfaces, 212–17 Ge/high-permittivity oxide interfaces, 209–12 SiC/insulator interfaces, 217–21 Si (Silicon): with complex metal oxides, 198–203 with elemental metal oxides, 195–8 with non-oxide insulators, 203–8 SiC/insulator, 217–21 Single trap model, for first-order trapping, 150–2 SiO2 : electron traps in: attractive Coulomb traps, 248–9 neutral electron traps in SiO2 , 249–51 repulsive electron traps in SiO2 , 251 hole traps in, 251 attractive Coulomb hole traps, 252 neutral hole traps in SiO2 , 252–6 injection-induced trap generation in, 248 proton trapping in, 256–9 Si/SiO2 : band alignment, 183–4 barrier modification by trapped charges, 186–8 interface, trapped ions at, 188–9 interface dipoles, 184–6 Space-charge-limited current, transition from injection-limited, 149, 180–1 Spatial distribution of traps, 130–1, 142–5, 248 Spectral threshold determination, by IPE spectroscopy see IPE threshold spectroscopy Surface-sensitive analysis, of electron states, 3 Swensson-Becquerel effect, 18 Tailing (or Tail) of band states, 219, 222, 223, 236, 237 Thermalization law, exponential, 171–2 Thermalized charge carriers transport, limitations in, 4 Thermoionic emission, 121 versus photoemission, 59–60 Traps: classification through cross-section, 246–8 spatial distribution of, 142–5, 248 Trap-assisted pseudo IPE excitation, 206 Trap-assisted tunnelling, 113–14 Trap depopulation: approaches to, 138 charge probing by, 137–41 during IPE injection, 111 Trapped charges see Charge carrier traps Trapping, charge carrier see Charge trapping kinetics Tunnel carrier injection, 112–14 Two photon excitation scheme, 262 Wide-gap insulators: interfaces of, 5–8 tunnelling current–voltage characteristics in, 4 Yun’s trap profiling method, 168
