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Anisotype heterojunctions involving wide band gap II-VI semiconductors Taneja, Narayan Dass 1971

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ANISOTYPE HETEROJUNCTIONS INVOLVING WIDE BAND GAP I I - V I SEMICONDUCTORS by NARAYAN DASS TANEJA B . S c , Agra U n i v e r s i t y , I n d i a , 1961 M.Sc, Agra U n i v e r s i t y , I n d i a , 1963 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of E l e c t r i c a l Engineering We accept t h i s t h e s i s as conforming to the r e q u i r e d standard Research Supervisor. Members of the Committee Head of the Department Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA January, 1971 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of P Lktf.l Q.\C(3-L EMCrCr-The University of British Columbia Vancouver 8, Canada Date Na^K M , mi ABSTRACT This t h e s i s i s concerned w i t h ( i ) the theory of anisotype hetero-j u n c t i o n s and ( i i ) the f a b r i c a t i o n and study of h e t e r o j u n c t i o n s of wide band, gap II-VI compounds"with other semiconductors. The theory of anisotype h e t e r o j u n c t i o n s without i n t e r f a c e s t a t e s i s d i s c u ssed on the b a s i s of m i n o r i t y c a r r i e r i n j e c t i o n . Expressions f o r the b u i l t - i n v o l t a g e and c u r r e n t v o l t a g e r e l a t i o n s are d e r i v e d . The recom-b i n a t i o n - g e n e r a t i o n of the c a r r i e r s i n h e t e r o j u n c t i o n s w i t h i n t e r f a c e s t a t e s i s considered, using Sah-Shockley-Noyce. theory. The expressions f o r the recombination-generation r a t e of the c a r r i e r s f o r nine d i f f e r e n t cases are d e r i v e d c o n s i d e r i n g three c a r r i e r t r a n s p o r t mechanisms. ZnSe f i l m s were deposited on Ge, GaAs and mica by s u b l i m a t i o n under n e a r - e q u i l i b r i u m c o n d i t i o n s i n an u l t r a h i g h vacuum. The c r y s t a l l i t e s i z e i n the f i l m s deposited on mica at 500°c was about 15u. E p i t a x y of ZnSe on GaAs was observed around 380°C. The c o n d u c t i v i t y and H a l l m o b i l i t y of the f i l m s on mica were measured under i l l u m i n a t i o n and the r e s u l t s are explained on the b a s i s of a mosaic f i l m model. The p h o t o c o n d u c t i v i t y of the f i l m s was b a r r i e r l i m i t e d at low i n t e n s i t i e s but c a r r i e r l i m i t e d at high i n t e n s i t i e s . The nlnAs-pZnTe h e t e r o j u n c t i o n s were f a b r i c a t e d by the i n t e r f a c e a l l o y i n g technique. The c u r r e n t v o l t a g e and capacitance-voltage c h a r a c t e r i s t i c s of the devices were s t u d i e d , and t h e i r t h e o r e t i c a l r e l a t i o n s are d e r i v e d . L i g h t emission was observed i n these h e t e r o j u n c t i o n s under reverse b i a s c o n d i t i o n s . The spectrum of the emitted l i g h t was i n the energy range of 1.69 eV to 3.5' eV. A number, of peaks were observed i n the spectrum at low currents w h i l e at high currents only one peak at 2.04 eV was observed. An energy band diagram of ZnTe w i t h d i f f e r e n t i m p u r i t y centers i s developed to e x p l a i n the electroluminescence c h a r a c t e r i s t i c s . The pGe-CdS '(photosensitive) heterojunctions were made by a simple a l l o y i n g technique. The current-voltage and capacitance-voltage c h a r a c t e r i s t i c s of the heterojunctions were studied under d i f f e r e n t i l l u m i n a -t i o n i n t e n s i t i e s . The I-V c h a r a c t e r i s t i c s were n o n - r e c t i f y i n g at low i n t e n s i t i e s but r e c t i f y i n g at high i n t e n s i t i e s . Energy band diagrams, equivalent c i r c u i t s and the theory of the prepared devices are discussed. LIST OF TABLES TABLE OF CONTENTS Page v i i LIST OF ILLUSTRATIONS v i x i ACKNOWLEDGEMENT x i i I. INTRODUCTION • • • • • 1 II. THEORY OF ANISOTYPE HETEROJUNCTIONS 1. Introduction 4. Total current 5. Summary and conclusion I l l ZnSe FILMS DEPOSITED UNDER NEAR-EQUILIBRIUM CONDITIONS 1. Introduction .3 2. Heterojunctions without interface states • 4 2.1 nSCl-pSC2 heterojunction 2.2 pSCl-nSC2 heterojunction 2.3 Isotype heterojunctions 17 18 3. Recombination-generation currents in anisotype heterojunctions 19 3.1 Mechanisms and models proposed for recombination-generation currents in heterojunctions -^q 3.2 Recombination-generation rates of the carriers on the basis of Sah-Shockley-Noyce Theory 2.2 3.3 Recombination-generation current 37 39 39 41 2.'. Survey of literature, of ZnSe..'films on ordered substrates.. 43 3. Principle of near-equilibrium conditions sublimation and i t s application to the sublimation of ZnSe on Ge GaAs . and mica . . 44 4. Design and fabrication of the apparatus for near e q u i l i -brium conditions sublimation 46 4.1 Ultra high vacuum (U.H.V) system . . 47 4.2 Sublimation assembly 50 4.3 Performance of U.H.V. system 50 5. Experimental procedures 52 5.1 Source preparation 52 5.2 Substrate preparation 52 5.3 Sublimation procedure 53 5.4 Residual gas analysis 55 6. Structural properties of ZnSe films . 55 6.1 ZnSe films on. mica . 55 6.2 ZnSe films on GaAs - # 5 g '6.3 ZnSe films on Ge - fi0 6.4 F i l m t h i c k n e s s measurement 62 7. E l e c t r i c a l p r o p e r t i e s •,. 54 7.1 Ohmic contacts and specimen holder 64 7.2 Pho t o - H a l l measuring apparatus 65 7.3 Accuracy of measurements 68 7.4 E l e c t r i c a l p r o p e r t i e s of ZnSe f i l m s on mica 59 7.5 ZnSe f i l m s deposited on p type Ge and GaAs 74 8. D i s c u s s i o n 77 9. Summary and c o n c l u s i o n 83 IV nlnAs-pZnTe HETEROJUNCTIONS 1. I n t r o d u c t i o n 85 2. F a b r i c a t i o n and contacts 86 2.1 F a b r i c a t i o n of devices 86 2.2 Contacts 90 3. Experimental procedures 91 3.1 Cur r e n t - v o l t a g e c h a r a c t e r i s t i c s 91 3.2 Reverse b i a s capacitance 91 3.3 Electroluminescence 92 3.3.1 I n t e n s i t y 92 3.3.2 R i s e and f a l l times 94 3.3.3 Spectrum of the emitted l i g h t 94 3.3.4 C a l i b r a t i o n of the monochromator 96 3.3.5 S p e c t r a l width ( h a l f band width) 96 4. R e s u l t s 97 4.1 Current-voltage c h a r a c t e r i s t i c s 97 4.1.1 Forward b i a s ' 97 4.1.2 Reverse b i a s 99 4.2 Reverse b i a s capacitance-voltage c h a r a c t e r i s t i c s ... 101 4.3 Reverse b i a s electroluminescence 101 4.3.1 I n t e n s i t y 106 4.3.2 R i s e and f a l l times 106 4.3.3 Electroluminescence 5. D i s c u s s i o n 110 5.1 Current-voltage c h a r a c t e r i s t i c s 110 5.1.1 Forward b i a s 110 5.1.2 Reverse b i a s 117 5.2 Reverse b i a s capacitance 125 5.3 Reverse b i a s electroluminescence 127 5.3.1 I n t e n s i t y 132 5.3.2 Rise and f a l l times 132 5.3.3 Spectrum of the emitted l i g h t 133 6. Summary and c o n c l u s i o n 137 Page V pGe-CdS ( PHOTOSENSITIVE) HETEROJUNCTIONS 1. Introduction 140 2. Sample preparation and contacts 141 3. Experimental procedures 142 3.1 Current-voltage characteristics 142 3.2 Capacitance 143 3.3 Relative illumination intensity 143 4. Results 143 4.1 Current-voltage characteristics 143 4.2 Capacitance and a.c. conductance - 153 5. Discussion 155 5.1 Current-voltage characteristics 155 5.2 Equivalent c i r c u i t 162 5.3 Capacitance 164 6. Summary and conclusion "168 VI CONCLUSION 170 Appendix 1 173 Appendix 2 180 BIBLIOGRAPHY 186 LIST OF TABLES 2.1 Recombination-generation processes i n pSCl-nSC2 heterojunctions.,. 23 2.2 Expressions of net recombination r a t e of the c a r r i e r s i n pSCl-nSC2 h e t e r o j u n c t i o n s 34, 35 3. 1 V a r i a t i o n s of c r y s t a l l i t e s i z e w i t h s u b s t r a t e temperature .... 55 4.1 P r o p e r t i e s of InAs and ZnTe -. 87 2 4.2 The values of N „ obtained from the 1/C versus V . c h a r a c t e r i s t i c s at d i f f e r e n t frequencies 126 5.1 B u i l t - i n v o l t a g e i n the pGe-nCdS h e t e r o j u n c t i o n and steady s t a t e e l e c t r o n d e n s i t y i n the CdS f o r v a r i o u s i n t e n s i t i e s obtained from F i g . 5.8 167 A l . l C l a s s i f i c a t i o n of semiconductors f o r making h e t e r o j u n c t i o n s .. 174 A1.2 Some p r o p e r t i e s of Ge, GaAs and ZnSe 175 Al.3 Some p r o p e r t i e s of InSb and CdTe 176 A1.4 Some p r o p e r t i e s of InAs, GaSb, CdSe and ZnTe 177 A1.5 Some p r o p e r t i e s of S i , GaP and ZnS 178 A1.6 Some p r o p e r t i e s of InP and CdS . 179 Figure 2.1 Energy band diagrams of heterojunctions at equilibrium 5 2.2 Different models for nSCl-pSC2 heterojunctions under forward bias conditons 20 2.3 Energy band diagrams of pSCl--nSC2 heterojunctions 24 2.4 Different recombination-generation processes in pSCl-nSC2 heterojunctions 33 3.1 Schematic diagram of the ultra high vacuum system 48 3.2 Schematic diagram of the sublimation assembly 49 3.3 A sketch of the quartz mask and shutter 49 3.4 A typical pressure versus time characteristic of the U.H..V. system 51 3.5 A typical variation of source temperature, substrate temperature and pressure with time during sublimation 55 3.6 R.G.A. spectrum at different stages of sublimation 56 3.7 Electron microprobe topographs of the ZnSe films deposited at different substrate temperatures 57 3.8 Laue X-ray back-reflection pattern of ZnSe film (about 7ythick) on GaAs (111) , the spots marked with arrow are due to ZnSe layer • 60 3.9 Electron microprobe scanning results of ZnSe film deposited on GaAs substrate 61 3.10 Laue X-ray back-reflection pattern of ZnSe film deposited on Ge at 300°C 63 3.11 Specimen holder for Hall effect measurements 65 3.12 Setup for measuring photo Hall effect of ZnSe films 66 3.13 Block diagram of Hall voltage measuring c i r c u i t 66 3.14 Photo Hall voltage versus photo current ^ (a) at magnetic f i e l d of value 0.32 Weber/n^ • 70 (b) at magnetic f i e l d of value 0:44 Weber/m ' • • . 71 3.15 Variation of photoconductivity, photo Hall mobility and photo electron density with relative photo intensity 72 3.16 Variation of photo Hall mobility with photo electron density .. 73 2 3.17 Forward current versus (voltage) characteristics of pGe-nZnSe heterojunction at several temperatures 75 3.18 Forward current versus voltage characteristic of pGe-nZnSe at room temperature 76 3.19 (a) Mosaic model for polycrystalline film 79 (b) Equilibrium energy band diagram of c r y s t a l l i t e -intercrystalline r e g i o n — c r y s t a l l i t e , structure 79 4.1 (a) Schematic diagram of the system used for making nlnAs-pZnTe heterojunctions 89 (b) Sketch of the graphiteboat with InAs and ZnTe 89 4.2 (a) Schematic diagram for measuring intensity versus diode current characteristic ... 93 (b) Sketch of the teflon holderwith device 93' 4.3 Block diagram of the setup used for measuring electro-luminescence spectrum 95 4.4 Current-voltage characteristic of nlnAs-pZnTe heterojunction .. 97 4.5 Forward bias current-voltage characteristics of nlnAs-pZnTe heterojunction at various temperatures 98 4.6 Reverse bias current-voltage characteristics of.nlnAs-pZnTe heterojunction at various temperatures . . . 100 4.7 . Reverse bias capacitance versus voltage characteristics of nlnAs-pZnTe heterojunction at various frequencies 102 4.8 Reverse bias capacitance as a function of frequency at different reverse bias voltages. 103 2 4.9 1/C versus reverse bias voltage characteristics at various frequencies • 104 4.10 Variation of a.c. resistance versus reverse bias voltage at various frequencies . . . 105 4.11 Light intensity versus reverse bias current characteristic at room temperature ...107 4.12 Simultaneous light (upper trace) and current (lower trace) pulses for reverse bias nlnAs-pZnTe heterojunction 108 4.13 Electroluminescence spectra of the light emitted from a reverse bias nlnAs-pZnTe heterojunction at various currents at room temperature 109 4.14 Energy band diagrams of nlnAs-pZnTe h e t e r o j u n c t i o n at d i f f e r e n t c o n d i t i o n s i i i 4.15 (a) The d i f f e r e n t processes by which c a r r i e r s are created i n the d e p l e t i o n regions of the two semiconductors of a revers e b i a s e d nlnAs-pZnTe h e t e r o j u n c t i o n 130 (b) The d i f f e r e n t processes by which c a r r i e r s can recombine r a d i a t i v e l y i n nlnAs-pZnTe h e t e r o j u n c t i o n 131 4.16 Energy band diagram of ZnTe w i t h d i f f e r e n t acceptor and donor centers 134 5.1 A sketch of the g r a p h i t e boat w i t h Ge and CdS 141 5.2 Current-voltage c h a r a c t e r i s t i c s of a pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n at v a r i o u s r e l a t i v e i l l u m i n a t i o n i n t e n s i t i e s (source v o l t a g e 90 v o l t s ) 144 5.3 Current-voltage c h a r a c t e r i s t i c s of a pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n at v a r i o u s r e l a t i v e i l l u m i n a t i o n i n t e n s i t i e s (source v o l t a g e 35 v o l t s ) 145 5.4 Current-voltage c h a r a c t e r i s t i c s of a pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n at v a r i o u s i l l u m i n a t i o n i n t e n s i t i e s (source v o l t a g e 90 v o l t s ) 146 5.5 (a) Capacitance versus r e l a t i v e i n t e n s i t y of a pGe-CdS (photo-s e n s i t i v e ) h e t e r o j u n c t i o n measured at lOOKHz 147. (b) Capacitance versus r e l a t i v e i n t e n s i t y of a pGe-CdS (photo-s e n s i t i v e ) h e t e r o j u n c t i o n measured at lOOKHz 148 5.6 (a) A.c. conductance (lOOKHz) and r e c t i f i c a t i o n r a t i o (D.C.) versus r e l a t i v e i n t e n s i t y of a pGe-CdS ()photosensitive) h e t e r o j u n c t i o n -149 (b) A.c. conductance (lOOKHz) versus r e l a t i v e i n t e n s i t y of a pGe-CdS (p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n 150 5.7 Reverse b i a s capacitance versus v o l t a g e c h a r a c t e r i s t i c s of pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n at v a r i o u s r e l a t i v e i n t e n s i t i e s 151 2 5.8 1/C versus V c h a r a c t e r i s t i c s of a pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n at v a r i o u s r e l a t i v e i n t e n s i t i e s i52 5.9 Energy band diagram of pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n 153 5.10 Energy band diagram of pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n at low, medium and high i n t e n s i t i e s 159 5.11 Equivalent c i r c u i t of pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n at low, medium and high i n t e n s i t i e s 163 A.2.1 Current-voltage characteristic of In-pZnTe diode 180 A.2.2 Current-voltage characteristic of In-pZnTe diode 181 2 A.2.3 1/C versus reverse bias voltage characteristics of In-ZnTe diode at various frequencies 182 A.2.4 Electroluminescence spectra of the light emitted from a reverse bias In-ZnTe diode at various currents at room temperature 183 A. 2.5 (a) Energy band diagram of In and pZnTe (isolated) 185 (b) Energy band diagram of In-pZnTe diode 185 ACKNOWLEDGEMENT I am greatly indebted to my supervisor Dr. L. Young for his invaluable guidance and personal encouragement throughout the course of this study. Many helfpul discussions with Dr. J. W. Bichard and Dr. D. L. Pulfrey are acknowledged with gratitude. I wish to thank the National Research Council for financial support under grant number A 3392. Thanks are due to Messers. H. Black, V. Loney, A. Mackenzie, J. Stuber and B. Wong for their technical assistance and to Misses Veronica Komezynski and Linda Morris for typing this thesis. Finally, 1 thank my colleagues for proof-reading the manuscript of the thesis. I . INTRODUCTION A h e t e r o j u n c t i o n i s a j u n c t i o n between two d i s s i m i l a r semiconductors. The h e t e r o j u n c t i o n i s i s o t y p e i f m a j o r i t y c a r r i e r s i n the two semiconductors are e i t h e r e l e c t r o n s or holes and anisotype i f m a j o r i t y c a r r i e r s i n one semi-conductor are e l e c t r o n s and i n the other are holes. Though Shockley (1951) proposed a device i n c o r p o r a t i n g a change i n the forbidden gap i n the t r a n s i t i o n r e g i o n of a p-n j u n c t i o n , i t was Kroemer (1957) who proposed the use of the h e t e r o j u n c t i o n as a wide band gap e m i t t e r to i n c r e a s e the i n j e c t i o n e f f i c i e n c y of t r a n s i s t o r s . Anderson (1960, 1962) proposed an energy band diagram model f o r Ge-GaAs h e t e r o j u n c t i o n . Since then, a great d e a l of t h e o r e t i c a l and experimental i n v e s t i g a t i o n s of d i f f e r e n t h e t e r o j u n c t i o n s have been made by s e v e r a l authors ( e s p e c i a l l y R. L. Anderson et a l . at Syracuse U n i v e r s i t y , A. G. Mil'nes and D. L. Feucht et a l . at Carnegie-Mellon U n i v e r s i t y , Rediker et a l . at M.I.T.).• The i n i t i a l i n t e r e s t i n h e t e r o j u n c t i o n s s t a r t e d w i t h wide band gap e m i t t e r s but most of the i n v e s t i g a t i o n s have been made w i t h h e t e r o j u n c t i o n s f a b r i c a t e d w i t h semiconductors s e l e c t e d from group IV and I I I - V compounds ( Calow et a l . 1968). The wide band gap semiconductors e s p e c i a l l y I I - V I compounds (ZnTe, ZnSe, CdS etc.) have not been used to such an extent i n the i n v e s t i g a t i o n s of semiconductor h e t e r o j u n c t i o n s . In t h i s t h e s i s , h e t e r o j u n c t i o n s of wide band gap I I - V I compounds (ZnSe, ZnTe and CdS) w i t h other semiconductors from group IV and I I I - V com-pounds are d e s c r i b e d . Since most of the I I - V I wide band gap semiconductors are non-amphoteric, the homojunctions are impossible to make and t h e i r j u n c t i o n devices can only be s t u d i e d by making h e t e r o j u n c t i o n s w i t h other semiconductors. The h e t e r o j u n c t i o n s w i t h wide band gap I I - V I compounds can be used as l i g h t e m i t t i n g (Aven, 1967; F i s c h e r , 1966) and p h o t o s e n s i t i v e devices. The general theory of the anisotype heterojunction i s discussed i n Chapter 2. The expressions for ; the current-voltage r e l a t i o n s h i p for anisotype heterojunctions are derived. Due to i n t e r f a c e states present i n heterojunctions, the recombination-generation current at i n t e r f a c e states plays an important r o l e . The d i f f e r e n t possible mechanisms by which the c a r r i e r s recombine at the i n t e r f a c e states are considered and expressions for recombination-generation rates for nine possible cases are derived. Chapter 3 deals with the deposition and study of ZnSe f i l m s . The ZnSe fi l m s were deposited on Ge, GaAs and mica by sublimation under near-equilibrium conditions i n an u l t r a high vacuum system with the f a c i l i t y of r e s i d u a l gas a n a l y s i s . The s t r u c t u r a l and p h o t o e l e c t r i c a l properties of these f i l m s were studied. The increase i n conductivity and H a l l m o b i l i t y with i l l u m i n a t i o n are explained by using a mosaic model of p o l y c r y s t a l l i n e f i l m s . In Chapter 4, nlnAs-pZnTe heterojunctions are described. These heterojunctions were made by the i n t e r f a c e a l l o y i n g technique. The e l e c t r i c a l (current-voltage and capacitance-voltage) c h a r a c t e r i s t i c s of the junctions and s p e c t r a l properties of emitted l i g h t were measured. A n upper l i m i t on the r i s e and f a l l times of the l i g h t pulse was also measured. The energy band diagrams of ZnTe with d i f f e r e n t impurity l e v e l s and of nlnAs-pZnTe are developed. Chapter 5 discusses pGe-CdS (photosensitive) heterojunctions. The current-voltage c h a r a c t e r i s t i c s of these devices were n o n - r e c t i f y i n g i n the-dark but r e c t i f y i n g under i l l u m i n a t i o n . The current-voltage and capacitance-voltage c h a r a c t e r i s t i c s were measured at d i f f e r e n t i n t e n s i t i e s of i l l u m i n a t i o n . The energy band model, theory and equivalent c i r c u i t s of these devices are discussed. In Chapter 6, the r e s u l t s of t h i s t hesis are summarized and a few areas f o r future research are suggested. II. THEORY OF ANISOTYPE HETEROJUNCTIONS The energy band models of heterojunctions can be classified into two groups: (i) Graded band gap ( i i ) Abrupt band gap In the graded band gap model, the conduction and valence band edges vary continuously as the transition from narrow band gap semiconductor to wide band gap semiconductor takes place. Kroemer (1957) presented a theory for graded band gap heterojunctions. Hinkley et a l . (1967) explained some results of InSb-GaAs heterojunctions using the graded band gap model. In' the abrupt band gap model (Anderson 1962, 1963), there i s a discontinuity in the conduction and valence band edges at the interface of the two semiconductors. The discontinuity in conduction and valence band edges depends on the electron a f f i n i t i e s and energy band gaps of the two semiconductors. Most heterojunction . energy band models are based on the abrupt band gap model. Since heterojunctions are made of two different semiconductors, there i s an interface between the two semiconductors at which transition from one semiconductor to other semiconductor takes place. If la t t i c e con-stants, orientations, and typesof bonds of the two semiconductors are not exactly the same, there i s a possi b i l i t y that some of the bonds at the interface are not satisfied. The unsatisfied bonds are expected to produce interface states in the forbidden gap of the two semiconductors (Oldham et a l . 1964). The theoretical investigations of heterojunctions can be divided into two types. (I) Heterojunctions in which the density of interface states i s very small and their effects can be ignored. ( i i ) Heterojunctions with high density of interface states producing important changes i n behaviour. Oldham et a l . (1963) estimated the d e n s i t y of i n t e r f a c e s t a t e s i n Ge-Si h e t e r o j u n c t i o n s using data on l a t t i c e mismatch and Holt (1966) estimated the d e n s i t y of i n t e r f a c e s t a t e s i n Ge-GaAs, Ge-GaP, ZnS-Si and ZnSe-GaAs h e t e r o j u n c t i o n s . This chapter deals w i t h the theory of anisotype hetero-j u n c t i o n s of both types. 2. H e t e r o j u n c t i o n s without i n t e r f a c e s t a t e s There are not very many h e t e r o j u n c t i o n s i n which the i n t e r f a c e s t a t e d e n s i t y i s expected to be so sm a l l that i t s e f f e c t s can be ignored. Appendix 1 deals w i t h the s e l e c t i o n of semiconductors f o r making h e t e r o j u n c t i o n s The Ge-GaAs h e t e r o j u n c t i o n has a l a t t i c e mismatch of 0.07% and the expected d e n s i t y of i n t e r f a c e s t a t e s i s low. E s a k i et a l . (1964) s t u d i e d Ge-GaAs h e t e r o j u n c t i o n s and could not observe d e t e c t a b l e i n t e r f a c e s t a t e s ( i . e . 5 x 10 2 10 /cm ). The Ge-GaAs h e t e r o j u n c t i o n made under proper c o n d i t i o n s can be considered as an example of a h e t e r o j u n c t i o n without i n t e r f a c e s t a t e s . F i g . 2.1(a) shows an energy band diagram of two i s o l a t e d semi-conductors. Space charge n e u t r a l i t y i s assumed to e x i s t i n both the semi-conductors. The s u b s c r i p t s l a n d 2 stand f o r semiconductors 1 and 2 r e s p e c t i v e l y The two semiconductors have band gap energies E ^ and E ^ , and e l e c t r o n a f f i n i t e s x± a n d T h e d i s c o n t i n u i t i e s i n the conduction and valence band edges (E and E^) are represented by AE^ and i\E^. The d i f f e r e n t p o s s i b l e cases of h e t e r o j u n c t i o n s at e q u i l i b r i u m are shown i n f i g . 2.1(b) to 2.1(e) corresponding to nSCl-pSC2, nSCl-nSC2 VACUUM LEVEL :c1. v! •c2 92 sci sc2 fa) ISOLATED v2 VACUUM LEVEL VACUUM LEVEL X •c1-_ vT 2 gi EC2 :92 _ L _ E, v2 nSCf-nSC2 (c) VACUUM LEVEL X. VACUUM LEVEL 2 X  1  7 X2 x< vl -Ec2 '•91 ••g2 v2 :pSCi-nSC2 (d) -91 pSC1- pSC2 c2 z92 F i g . 2.1 Energy band diagrams of h e t e r o j u n c t i o n s at e q u i l i b r i u m pSCl-nSC2 and pSCl-pSC2, r e s p e c t i v e l y . In t h i s nomenclature, SCI and SC2 stand f o r semiconductors! and 2 and the l e t t e r n or p p r e f i x to SCI or SC2 shows the type of m a j o r i t y c a r r i e r of that semiconductor. For example, nSCl-pSC2 stands f o r a h e t e r o j u n c t i o n i n which semiconductor 1 i s n-type and semi-conductor 2 i s p-type. In making these h e t e r o j u n c t i o n energy band diagrams at e q u i l i b r i u m , the f o l l o w i n g p o i n t s are considered. 1) The Fermi l e v e l s must c o i n c i d e i n SCI and SC2. 2) The vacuum l e v e l i s continuous through the t r a n s i t i o n r e g i o n and the conduction and valence band edges are p a r a l l e l to t h e i r r e s p e c t i v e vacuum l e v e l s . 3) The d i s c o n t i n u i t y i n the conduction band edges i s equal to the d i f f e r e n c e i n the e l e c t r o n a f f i n i t i e s of the two semiconductors. The d i s c o n t i n u i t y i n conduction band edges and valence band edges i s assumed i n v a r i a n t w i t h doping f o r non-degenerate semiconductors. The b u i l t - i n v o l t a g e i n SCI and SC2 are IJJ and a n ^ t n e t o t a l b u i l t - i n v o l t a g e ip i s the sum of the b u i l t - i n voltages i n SCI and SC2 % = * M - % 2 ) • - ' ' 2.1 nSCl-pSC2 H e t e r o j u n c t i o n For a n a l y s i n g anisotype h e t e r o j u n c t i o n s , nSCl-pSC2 ( F i g . 2.1(b)) i s considered. Poisson's equations f o r e i t h e r s i d e of the i n t e r f a c e are given by d \ _ _ P 1 ( X ) (2.1) f o r SCI d x 2 " £ 1 d \ . = _ (2.2) f o r SC2 d x 2 E2 where,, and £ are the p e r m i t t i v i t i e s of SCI and SC2 and, ^(x) and p(x) are the e l e c t r o s t a t i c p o t e n t i a l and net uncompensated charge d e n s i t y at p o s i t i o n x. These charge d e n s i t i e s are given by p±U) = e { N D 1 ( x ) - N M ( x ) + P l ( x ) - n ^ x ) } (2.3) P 2 ( x ) = e{K D 2(x) - N A 2 ( x ) -I- p 2 ( x ) - n 2 ( x ) } (2.4) where N and N are the uncompensated acceptor and donor charge d e n s i t i e s and, n and p are the e l e c t r o n and hole d e n s i t i e s . Assuming that the mobile charges ( e l e c t r o n s and holes) are n e g l i g i b l e i n comparison to the uncompensated charges i n the v i c i n i t y of the j u n c t i o n (Warner et a l . 1963) then eqn. (2.3) and (2.4) are P 1 a e N D 1 . • (2.3A) P 2 = - e N A 2 (2.4A) and equations (2.1) and (2.2) are r e w r i t t e n as d2^ -eN k = — — (2.5) dx^ E l ^ 2 _ ^ f A 2 (2.6) d x 2 £ 2 Assuming that the a p p l i e d e l e c t r i c f i e l d i s s m a l l enough so that i t does not a p p r e c i a b l y d i s t u r b the e q u i l i b r i u m d i s t r i b u t i o n of v e l o c i t i e s of the c a r r i e r s , the hole and e l e c t r o n c u r r e n t s i n semiconductor 1 are d n , J = -eu n 111 + eD (2.7) n l n l . 1 . , n l , dx dx d * l d P , J = -ey p - eD — (2.8) P i P l F l dx . P i d x J „ = o N 9 ~T~ + eD „ —-— (2.9) n2 nz 2 dx n/ dx JP 2 = - % 2 P 2 — -eV"dT d*2 „ d p 2 (2.10) dx The c o n t i n u i t y equations i n SCI are ^ 1 = ( g _ r ) + l ^ n l (2.11) dt 1 e dx " <«->! " I ( 2 - 1 2 ) and i n SC2 dt 1 e dx dn dJ ^ = (g-D 2 + I - ^ f (2-13) d p 2 . , 1 ^p_2 (2.14) = (g-r) — dt 2 e dx where u and u are the m o b i l i t i e s of e l e c t r o n s and h o l e s , n p ' D and D are the d i f f u s i o n c o e f f i c i e n t s of e l e c t r o n s and h o l e s , n p J and J are the e l e c t r o n and hole current d e n s i t i e s , n p ' g i s the r a t e of generation of e l e c t r o n s or holes r i s the r a t e of recombination of e l e c t r o n s or h o l e s , and s u f f i x e s l a n d 2 f o r the above symbols are f o r semiconductors 1 and 2, At e q u i l i b r i u m : At e q u i l i b r i u m J .. , J , J and J „ are a l l zero, n l p i n2 p2 From equation (2.7) d dn^ J = 0 = -e,j n + eD n l 1 n l 1 J V n l , Q X dx and the b u i l t - i n v o l t a g e i n SCI i s given by * = H A x = - L . ) ->h (x=0) } = — ^ n - ^ ±-U 1 1 e n (x=0) % 1 or n (x=-L ) = n (x=0) exp (2.15) kT where x=0 i s the boundary of the two semiconductors and x=-L^ i s the length of depletion region i n SCI x=L 2 i s the length of depletion region i n SC2. On equating J =0 i n equation (2.10) the b u i l t - i n voltage i n SC2 i s given by P ^  = {K(x=L 0) - ^(x=0)} = ~ £ n l K D 2 L T 2 v - r 2 v - " / J e p 2( X=0) • Y \ / m f^D2 (2.16) or p (x=L ) = p (x=0) exp kT From F i g . 2.1(b), the el e c t r o n concentration at x=-L^,x=0 i n SCI and hole concentration at x=L 2 > x=0 i n SC2 are given by ( m N E c i ( x = 0 ) -Ef (2.17) n, (x=0) = N . exp - x ' 1 . C l kT i m M E c 2(x=0) -E n (x=0) = N exp -° kT E - E ( x = 0 ) P l(x=0) = N exp - — — (2.19) V kT E - E ( x = 0 ) p 2(x=0) = N v 2 exp — (2.20) kT where N N „ are the d e n s i t i e s of states i n the conduction bands of SCI c l c2 and SC2 N , N are the d e n s i t i e s of states i n the valence bands of SCI and SC2 v l v2 E^ i s the Fermi l e v e l at equilibrium At e q u i l i b r i u m the r e l a t i o n s . n ^ - I ^ ) P ] ( x = - L 1 ) = n 1(x=0) p±U=0) = n ^ (2.21) n 2(x= L 2 ) P 2(*=L 2) = n 2(x=0) p 2(x=0) = n j 2 (2.22) ho l d where n., and n.„ are the i n t r i n s i c c a r r i e r c oncentrations i n SCI i i i 2 and SC2. From equation (2.15) to (2.22), the c a r r i e r c o n c e n t r a t i o n s i n the two semiconductors are r e l a t e d by N AE + ei|; n (x=-L ) = n (x=L ) — exp — (2.23) N „ kT c2 N v l ' A E v ~ 6 ^ D and p 1(x=-L 1) = p_(x=L~) exp (2.24) N ' kT v2 From (2.23) and (2.24) can be evaluated , n (x=-L ) p (x=L ) AE -AE N N , _ . ^ _ kT r _1 1 2 2_ - c v j. + kT Jin c2 v l (2.25) D 2e , _ . , _ . . _ 2e N J , P 1(x=-L 1) n 2(x=L 2) kT c l v2 Expression (2.25) give s the b u i l t - i n v o l t a g e i n a n-p h e t e r o j u n c t i o n The can be determined i f the c a r r i e r c o n c e n t r a t i o n s i n the two semi-conductors, AE , AE and d e n s i t y of s t a t e s i n conduction and valence bands c v are known. The l a s t term i s due to d i f f e r e n t e f f e c t i v e masses of e l e c t r o n s and holes i n the two semiconductors. I f e f f e c t i v e masses of e l e c t r o n s and holes are the same i n SCI and SC2 then t h i s term reduces to zero. The term (AE -AE ) i s due to the band d i s c o n t i n u i t y i n h e t e r o i u n c t i o n s . For a homo-c v j u n c t i o n , AE and AE are zero and the t h i r d term i s a l s o zero and IJJ i s given c v R D by the f i r s t term o n l y . Chang (1966) derived a s i m i l a r expression f o r the b u i l t - i n v o l t a g e i n h e t e r o j u n c t i o n s but d i d not consider the e f f e c t of d i f f e r e n t e f f e c t i v e masses of c a r r i e r s i n the two semiconductors. I f E, and E_ are the e l e c t r i c f i e l d s i n the d e p l e t i o n r e g i o n of 1 2 SCI and SC2, then, s i n c e the e l e c t r i c displacement must be continuous through the i n t e r f a c e (no i n t e r f a c e s t a t e s ) , . . = e 2 E 2 at the i n t e r f a c e (x=0) (2.26) Poisson's equations (2.5) and 2.6) are r e w r i t t e n dE +eN 1 „ DI (2.5A) -L < x < 0 i n SCI dx d E 2 _ e N A 2 (2.6A) 0 < x < L 2 i n SC2 dx £2 I n t e g r a t i n g (2.5A), (2.6A) and using ' the boundary c o n d i t i o n s x =-L1» E = 0 f o r SCI x = L 2 , E 2 = 0 f o r SC2 eN DI E 1(x) = — (x + L ± ) - L 1 < x < 0 (2.27) • e N A 2 E„(x) = (L„ - x) 0 < x < L 0 (2.28) I e 2 2 2 So l v i n g (2.26) to (2.28) at x=0, the f o l l o w i n g r e l a t i o n i s obtained £ N D 1 L 1 " e N A 2 L 2 = Q ( 2 - 2 9 ) The net uncompensated charges on e i t h e r s i d e of the h e t e r o j u n c t i o n are of course equal and opposite (the uncompensated charge due to.N i s p o s i t i v e and N _ i s n e g a t i v e ) . The r a t i o of the d e p l e t i o n r e g i o n lengths L and L i s given by equation (2.29) h. = ^ 2 (2.30) L 2 " N D 1 The reverse b i a s capacitance can be derived from equation (2.27) and (2.28) w i t h the boundary c o n d i t i o n s dij, eN E = = (x+L.) -L, < x < 0 (2.27) 1 dx E l 1 1 d^ eN E 0 = — = — — (L -x) 0 < x < L • (2.28) 1 dx E2 1 . 1 I n t e g r a t i n g (2.27).from x = -L to x=0 and t a k i n g ^ ( " L ^ ) = 0 -eN ^ ( x ) = ^  ( X + V 2 eN 2 ^ D 1 - V 1 = ^ 1(x=0) - ^ 1 ( x = - L 1 ) = — 2 ± L l ( 2- 3 1> 2 £ 1 S i m i l a r l y i n t e g r a t i n g (2.28) between x=0 to x=L 2 eN L 2 eN L 2 * N 9 - V 9 = * . ( L . ) - K ( 0 ) = — ( L L _2 } = _ A 2 (2.32) D2 Z Z I Z e2 Z Z 2 £2 2 where and are the p o r t i o n s of the a p p l i e d v o l t a g e across the d e p l e t i o n regions i n SCI and SC2. Here V i s the a p p l i e d v o l t a g e • V = V + V 2 (2.33) From equations(2.29) to (2.33) eN n l L 2 eN „ _ „, - V = __D1 _1 + _ A 2 L 2 2 £ 1 2 s 2 2 2 $ v = ^- ( ~ — + ~ — ) (2.34) 2e N D l E l A2 £ 2 The t r a n s i t i o n capacitance C i s obtained from equation (2.34) c . g . ( " A i " A i V i 1 / 2 ( 2 . 3 5 ) d v 2 < ^ v - 2 v *"-v) I? e^  = E2 t ' 1 1 5 expression reduces to the t r a n s i t i o n capacitance of a homojunction. The nSCl-pSC2 h e t e r o j u n c t i o n i s considered to be forward b i a s e d when the a p p l i e d v o l t a g e i s such that the nSCl i s at negative p o t e n t i a l w i t h respect to pSC2. For the p a r t i c u l a r case shown i n f i g . 2.1(b), the b a r r i e r f o r the e l e c t r o n s from n-type SCI going to p-type SC2 i s c o n s i d e r a b l y higher than the holes going from p-type SC2 to n-type SCI and so i n j e c t i o n of holes w i l l dominate. The c u r r e n t flow at steady s t a t e c o n d i t i o n s i s due to i n j e c t i o n of holes from SC2 to SCI. Let V , be the a p p l i e d forward b i a s such t h a t the drop of v o l t a g e across SCI i s -V^  and across SC2 i s V"2 and V = + is s a t i s f i e d . The v o l t a g e drop takes place only i n ,the d e p l e t i o n regions of the two semi-conductors. The i n j e c t e d m i n o r i t y c a r r i e r c o n c e n t r a t i o n s ( i . e . hole c o n c e n t r a t i o n at x=-L^ i n SCI and e l e c t r o n c o n c e n t r a t i o n i n SC2 at ^ L ^ ) are found from equation (2.23) and (2.24). From•equation (2.24), the h o l e c o n c e n t r a t i o n at x=-L^ due to the r e d u c t i o n of ^ by V i s given by ^ A E - ( ^ - V ) e v2 ° r " eV P 1(x=-L 1) = p 1 ( x = - L 1 ) e x P — (2.36) where p!^(x=-L^) i s the h o l e c o n c e n t r a t i o n at x=-L^ i n SCI i n the. steady s t a t e . Simi l a r l y the e l e c t r o n c o n c e n t r a t i o n n'2(x= L 2 ) i n SC2 i s given by eV n' 2(x=L 2) = n 2(x=L 2) exp — (2.37) The excess m i n o r i t y c a r r i e r s move away from the space charge r e g i o n by d i f f u s i o n and recombine w i t h the m a j o r i t y c a r r i e r s . The d i s t r i b u t i o n i n the steady s t a t e c o n d i t i o n s i s obtained by s o l v i n g the c o n t i n u i t y equations. Let the l i f e time of holes i n n-type SCI be T and of e l e c t r o n s P i n p-type SC2 be T . Then from equations(2.12) and (2.13). dp (x) p f o - - L 1 ) - p 1 ( x - - L 1 ) , , _ _ _ J p l ( x ) . o ; - <x < - L l (2.38) dn (x ) n"(x=L )-n (x=L ) , N , ~ , a n d 4 - 1 = _ ^ ? 2 2__ + _1 i _ J n 2 ( x . = 0;'L 2<x< M ' <2- 3 9> dt x e dx • z n2 Since the current i s ..due to d i f f u s i o n o n l y , then equations (2.8) and (2.9) give dp"(x) dn'(x) J , (x) = -eD • — ^ — and J = eD 0 — (2.40) p i p i dx • "2 n2 d x and s u b s t i t u t i n g i n (2.38) and (2.39) gives d 2 P ^ ( x ) P] ,(*-V - P j . C x - L ^ = o > < x < ._L ( 2 . 4 1 ) D , 0 — —" 5 1 P l d x 2 T p l d 2n"(x) n"(x=L ) - n (x=L )' D' ~ — - — — = 0; L. < x < » (2.42) n2 I x 0 2 dx n2 The s o l u t i o n s of equations(2.4i) and (2.42) w i t h boundary c o n d i t i o n s P j ( x — ) = p ^ x - - ^ ) f o r SCI ( 2 > 4 3 ) n 2'(x=oo) = n (x=L 2) f o r SC2 and d p l (x= - c o ) = 0 d x (2.44) ^ 2 (x=») = 0 dx ' and x=-°° f o r SCI i m p l i e s that -x<<-L n (the d i f f u s i o n l e n g t h of holes i n SCI) p i are obtained as (x+L ) •{pJ(x)-p 1(-L 1)} = { p J ( - L 1 ) - p 1 ( - L 1 ) } exp L where - c o < x < -1^ (2.45) P i (-x+L ) {n*^(x)-n 2(L 2) } = { n 2 ' ( L 2 ) - n 2 ( L 2 ) } exp — where L 2< x < „ " ( 2 . 4 6 ) Ln2 and the d e p l e t i o n l a y e r lengths L^, L 2 are very s m a l l as compared to t h e i r d i f f u s i o n lengths S u b s t i t u t i n g (2.45) and (2.46) and e v a l u a t i n g c u r r e n t s J ^ at x=-L^ and J „ at x=L' n2 2 eD • eD J p l ( - V = { P ^ - V - p ^ ) } = P l ( - L l ) (exp § -1} p i p i T - M > - . N A 9 J i exp ( A V e^D ) {exp eV y (2.47) p i V ~ N . kT kT p i and eD eD J n 2 < + L 2 > = " L — <n2< V V ^ ^ ' L ~ W ^ kf n2 n2 e D n 2 N H c 2 A E c + "V eV n2 c l The t o t a l c urrent d e n s i t y through the j u n c t i o n i s given by the sum of (2.47) and (2.48) J = J p l ( - L l ) + J n 2 ( + L 2 ) • . eD ' N A E eD _ N -A E -eiju „ j = ( _ E i N A 2 J l exp __v + __n2 N _c2 c. , vD eV _ J L N 0 kT L „ N , kT 6 X P kT 1 6 X P kT 1 } p i v2 n2 c l (2.49) This i s the same expression derived, by Kumar (1969) by a s l i g h t l y d i f f e r e n t way. I f ' N 1 = N _ , N 1 = N _ and AE = AE = 0 expression (2.49) reduces v l v2 c l c2 c v. to eD „ eD „ —eiif„ z p N n N v rD r eV , / 0 A. J = ( A + — D ) exp - — - [exp — -1] (2.50) p n which i s Shockley's o r i g i n a l equation f o r a homojunction. I t can be seen that the current i n a h e t e r o j u n c t i o n i s dominated e i t h e r by holes or by e l e c t r o n s . Taking the r a t i o ( - L ^ ) / J n ( L 2 ^ f r o m equations(2.47) and (2.48) V NA2 N i v l N v2 AE +AE exp c v (2.51) Jn2(L2) °n2 L 9 n2 ND1 N 0 c2 N i c l kT D 1 N.„ N and - r ^ — A2 D l L ., P i -N v l . N v 2 - Dn2 Ln2 N c2 N i c l J p l ( - L l } - A E c + A E v (2.52) J 9 ( L J 6 X p — k T " n2 2 For a h e t e r o j u n c t i o n i n which el e c t r o n , a f f i n i t y (x) of narrow band gap semiconductor (n type) i s gr e a t e r than y. of the'wide band, gap semiconductor (p t y p e ) , equation 2.52 reduces to J p l ( " L l } = exp ( E g 2 E g l ) (2.53) J 9 ( L . ) k T n2 2 where E 2 i s the energy band gap of the wide band gap semiconductor and Eg-^ i s the energy band gap of the narrow band gap semiconductor. If (E -E ) is of the order 0.7 eV (for example in the nGe-%z gi pGaAs heterojunction), the ratio J ..(-IO/J „(L„) at room temperature is pi 1 nl 2 12 of the order exp 27-10 , which shows that the current is dominated by the. injection of holes from SC2 to SCl. 2.2 pSCl-nSC2 heterojunction For a particular pSCl-nSC2 heterojunction shown in f i g . 2.1(d), the barrier for the holes going from pSCl to nSC2 is much larger than the barrier for electrons going from nSC2 to pSCl and hence the current w i l l be dominated by electrons. Following the treatment of the previous section, the expression for the b u i l t - i n voltage is n 9(L ) P i ( " L i ) 4. AE -AE N N w. = M- f , n 2 2 1 1 + c vi + KT £n _£l J 2 (2.54) VD 2e 1 J t p ( L J n.(-L.) kT ' 2e N 0 N . 2 2 1 1 c2 v l and the junction current density is given by j = J n l ( - L x ) + j p 2 a 2 ) eD 1 N AE eD . N - A E eipnT eV _ , T _ , nl N c l exp c + p2 N v2 exp " v sexp - rD{exp— - 1} T N kT L „ N . kT y kT ' k i L . c2 p2 v l nl r (2.55) The ratio D n l ND2 N i c l J n l ( - L l > L n l N 9 c2 exp Jp2(L2> V LP2 NA2 N 9 v2 N v l AE +AE . c v kT D . N D N and i f — ^ N - -P-2- N A 2 J 2 L 1 D2 N L- N nl c2 p2 v l i t becomes J ! (-LJ ,AE + AE ) nl I - exp ( c yj (2.56) JP2 ( L2> kT showing that the current i s dominated by the i n j e c t i o n of e l e c t r o n s from SC 2 to SCI. 2.3 Isotype h e t e r o j u n c t i o n s Anderson (I960, 1962) de r i v e d expressions f o r c u r r e n t d e n s i t y i n i s o t y p e h e t e r o j u n c t i o n s by f i n d i n g the number of c a r r i e r s going from one semiconductor to the other by overcoming the b a r r i e r at the i n t e r f a c e (Bethe's diode t h e o r y ) . I t was assumed that the b a r r i e r t h i c k n e s s was of the order of the mean f r e e path of the c a r r i e r s so that the c o l l i s i o n s of the c a r r i e r s w i t h i m p u r i t i e s w i t h i n the b a r r i e r t h i c k n e s s could be ignored. F i g . 2.1(c) and 2.1(e) show nSCl-nSC2 and pSCl-pSC2 h e t e r o j u n c t i o n s . Chang (1965) t r i e d to s o l v e i t more p r e c i s e l y and considered the e f f e c t of t u n n e l i n g of c a r r i e r s through the b a r r i e r . Kumar (1968) d e r i v e d e x p r e s s i o n f o r is o t y p e h e t e r o j u n c t i o n s using d i f f u s i o n theory and i n the s p e c i a l cases, the e x p r e s s i o n reduced to the u s u a l e x p r e s s i o n f o r metal-semiconductor con-t a c t s . Oldham (1963) and Van Opdorp (1967) proposed the model of two Schottky diodes connected back to.back for i s o t y p e h e t e r o j u n c t i o n s i n which the d e n s i t y of the i n t e r f a c e i s very high (such as nGe-nSi h e t e r o j u n c t i o n s ) . 3. Recombination-generation c u r r e n t s i n anisotype h e t e r o j u n c t i o n s Homojunctions are mostly made by d i f f u s i o n of a dopant i n t o a su b s t r a t e . During the process of d i f f u s i o n , the b u l k p r o p e r t i e s of the su b s t r a t e do not change. U n f o r t u n a t e l y h e t e r o j u n c t i o n s cannot be made by the d i f f u s i o n of a dopant i n t o a semiconductor. The commonly used methods f o r making h e t e r o j u n c t i o n s ( Calow et a l . 1967) are (1) i n t e r f a c e a l l o y i n g , (2) e p i t a x i a l vapour growth, and (3) vacuum d e p o s i t i o n of one semiconductor on the other. Since i n a l l three methods, one semiconductor i s put on (deposited) e x t e r n a l l y , there i s more p o s s i b i l i t y of having d e f e c t s , unwanted i m p u r i t i e s a n d d e v i a t i o n from s t o i c h i o m e t r y i n semiconductors of a h e t e r o j u n c t i o n as compared to homojunctions (Mroczkowski et a l . 1965, Rediker et a l . 1964). In short the abrupt t r a n s i t i o n from one semiconductor to another semiconductor i n h e t e r o j u n c t i o n s i s not p o s s i b l e without haying' i m p u r i t y or defect centers i n the d e p l e t i o n regions of the semiconductors. These i m p u r i t i e s and defect centers may act as traps or recombination-generation centers f o r the c a r r i e r s depending on t h e i r nature and the bulk m a t e r i a l s . The recombination-generation current due to l o c a l i z e d s t a t e s i n the d e p l e t i o n regions of a h e t e r o j u n c t i o n i s much more important than i n a homojunction. The recomb-i n a t i o n - g e n e r a t i o n current i n h e t e r o j u n c t i o n s has to be considered i n d e t a i l . I n t e r f a c e s t a t e s i n h e t e r o j u n c t i o n s may act as traps or recombination-generation centers. The behaviour of recombination-generation current at i n t e r f a c e s t a t e s i s expected to be s i m i l a r to recombination-generation currents due to i m p u r i t y centers i n the d e p l e t i o n regions of homojunctions. The formation of d i f f e r e n t kinds of b a r r i e r s due to conduction and valence band d i s c o n t i n u i t i e s i n h e t e r o j u n c t i o n s , the c a r r i e r t r a n s p o r t mechanism across the j u n c t i o n might be d i f f e r e n t f o r e l e c t r o n s and holes un-l i k e homojunctions i n which the b a r r i e r f o r e l e c t r o n and holes are almost the same. 3.1 Mechanism and models proposed f o r recombination-generation current i n h e t e r o j u n c t i o n s S e v e r a l models have been proposed to e x p l a i n current t r a n s p o r t mechanism i n h e t e r o j u n c t i o n s . These models can be d i v i d e d i n t o three important c a t e g o r i e s according to the dominant current t r a n s p o r t mechanism." (1) Capture-Capture recombination at the i n t e r f a c e s t a t e s (2) Tunneling-Tunneling recombination at the i n t e r f a c e s t a t e s (3) Tunneling-Capture recombination at the i n t e r f a c e s t a t e s -(a) CAPTURE- CAPTURE RECOMBINATION (b) TUNNELING-TUNNELING (c) TUNNELING - CAPTURE RECOMBINATION RECOMBINATION F i g . 2.2 D i f f e r e n t models f o r nSCl-pSC2 h e t e r o j u n c t i o n s under forward b i a s c o n d i t i o n s F i g . 2.2 shows these d i f f e r e n t models proposed f o r nSCl-pSC2 h e t e r o j u n c t i o n under forward b i a s c o n d i t i o n s . 1. Capture-Capture recombination at i n t e r f a c e s t a t e s This model i s shown i n F i g . 2.2(a) and was proposed by Dolega (1963). He assumed that the l i f e t i m e of the c a r r i e r s approaches zero at the i n t e r -face s t a t e s . The e l e c t r o n s and holes i n j e c t e d over t h e i r r e s p e c t i v e b a r r i e r s are captured by i n t e r f a c e s t a t e s . The h e t e r o j u n c t i o n corresponds to two metal-semiconductor contacts i n s e r i e s . 2. Tunneling-Tunneling recombination This model i s shown i n F i g . 2.2(b). The e l e c t r o n s from the con-d u c t i o n band of n-type SCI and holes from the valence band of p-type SC2 tunnel through t h e i r r e s p e c t i v e b a r r i e r s i n t o the i n t e r f a c e s t a t e s where they recombine. Riben (1966) proposed a s i m i l a r model i n which he considered a m u l t i - s t e p recombination t u n n e l i n g mechanism, i .e. a s t a i r c a s e path. E l e c t r o n s i n a f i r s t energy l e v e l tunnel to a new p o s i t i o n at the same energy and are then captured by a second l e v e l of lower energy. A f t e r t u n n e l i n g to a new p o s i t i o n i n the second l e v e l , they are captured, bya t h i r d l e v e l of lower energy. The process continues u n t i l the e l e c t r o n s are t r a n s p o r t e d from the C.B. of SCI to the V.B. of SC2. The number of steps r e q u i r e d w i l l depend .on the t o t a l width of the j u n c t i o n , d e n s i t y and d i s t r i b u t i o n of energy l e v e l s i n the f o r b i d d e n energy gaps of the two semiconductors. This process seems to be p o s s i b l e i n the h e t e r o j u n c t i o n s i n which e i t h e r defect centers of v a r i o u s energies are present i n both the semiconductors or the i n t e r f a c e s t a t e s are not l o c a l i z e d at the i n t e r f a c e but extend q u i t e deep i n t o the d e p l e t i o n regions of the two semiconductors. The spreading of i n t e r f a c e s t a t e s i n the d e p l e t i o n r e g i o n of h e t e r o j u n c t i o n s i s p o s s i b l e i f the h e t e r o j u n c t i o n s are made from semiconductors w i t h high l a t t i c e mismatches (Oldham et a l . 1964). -3. Tunneling-Capture recombination • In this case electrons tunnel from the C.B. of SCI through the b a r r i e r into interface states and holes from the V.B. of SC2 are captured at the interface. The other process of similar nature is Capture-Tunneling i n which electrons from the C.B. of SCI are captured at interface states and holes tunnel from the V.B. of SC2.through the barrier into interface s t a t e s . Donnelly et a l . (1966) proposed this kind of model, shown in Fig. 2.2(c) and derived expressions for tunneling-capture recombination current density. Durupt et a l . (1969) also proposed a tunneling-capture recombin-ation mechanism for pGe-nSi heterojunctions. 3.2 Recombination-generation rate of the carriers on the basis of Sah- Shockley-Noyce Theory The models for recombination-generation current discussed in the previous section were different from the basic model of recombination-generation of carriers in homojunctions proposed by Sah et a l . (1957). In most of the models proposed for recombination-generation currents in hetero-junctions, the recombination-generation of electrons from nSCl and holes from pSC2 were considered separately. Perhaps the holes and electrons were captured by the interface states of different energies unlike homojunctions in which both electrons and holes were captured by the same energy levels. Hovel (1968) derived expressions for recombination-generation current in pGe-nZnSe heterojunctions analogous to those for homojunctions by considering the net recombination rate of electrons from n-type' ZnSe and holes from p-type Ge at the same interface states. -Since barriers for electrons and holes are usually different in heterojunctions, i t is possible that electrons and holes reach the interface states by different transport mechanisms. The important transport mechanisms by which c a r r i e r s can reach the i n t e r f a c e s t a t e s are the f o l l o w i n g : 1) Capture: The c a r r i e r s are captured by the i n t e r f a c e s t a t e s from the conduction or valence band edges at the i n t e r f a c e of the two semi-conductors . 2) Tunneling: The c a r r i e r s can tunnel from the d e p l e t i o n regions through the b a r r i e r i n t o i n t e r f a c e s t a t e s . 3) Capture t u n n e l i n g : Since there i s a p o s s i b i l i t y of having i m p u r i t y centers i n the semiconductors of the h e t e r o j u n c t i o n , the c a r r i e r s may be f i r s t captured by the i m p u r i t y centers i n the d e p l e t i o n regions and from the i m p u r i t y centers they may tunnel i n t o the i n t e r f a c e s t a t e s . C o n s i d e r a t i o n of these three b a s i c mechanisms f o r c a r r i e r s gives a t o t a l of nine processes by which recombination-generation of e l e c t r o n s and holes can occur. They are given i n Table 2.1. Table 2.1: Recombination-generation processes i n pSCl-nSC2 h e t e r o j u n c t i o n s Holes from V.B. of p-type SCI E l e c t r o n s from C.B. of SC2 1 Capture Capture 2 Capture Tunneling 3 Tunneling Capture 4 Tunneling Tunneling 5 Capture Capture t u n n e l i n g 6 Capture t u n n e l i n g Capture 7 Tunneling Capture t u n n e l i n g 8 Capture t u n n e l i n g Tunneling 9 Capture t u n n e l i n g Capture t u n n e l i n g The energy band diagrams of pSCl-nSC2 h e t e r o j unctions., i n which Ay t i s greater.or l e s s than zero are shown i n f i g s . 2.3(a) and (b) r e s p e c t i v e l y . The Ay i s defined as AX = X - X , narrow wide I t can be seen from F i g . 2.3 that the energy range i n which i n t e r -face s t a t e s e x i s t i s d i f f e r e n t f o r AX > 0 and AX < 0,and b a r r i e r s f o r e l e c t r o n s from nSC2 and holes from pSCl are d i f f e r e n t i n the two cases. The recombination-generation mechanism may be d i f f e r e n t i n the two cases. To d e r i v e an expression f o r the recombination-generation r a t e of the c a r r i e r s i n g e n e r a l , only the conduction band edge of nSC2 and the valence band edge of pSCl are considered. The energy range of i n t e r f a c e s t a t e s w i l l be decided by the s p e c i f i c h e t e r o j u n c t i o n . AX = X - X > 0 AX = X - x 2 < 0 Energy Range of I n t e r f a c e States. = E Energy Range of I n t e r f a c e States = E -|Ax | •c2 v2 F i g . 2,3 Energy band diagrams of pSCl-nSC2 h e t e r o j u n c t i o n s The expressions f o r recombination-generation r a t e s f o r a l l the nine processes are de r i v e d . I t i s assumed that only one recombination-generation process takes place i n a h e t e r o j u n c t i o n . F i g . 2.4 shows the important parts of the energy band diagrams f o r these processes. The expressions f o r nSCl-pSC2 h e t e r o j u n c t i o n s are e a s i l y obtained by changing t n e s u f f i x or s u f f i x e s and symbols i n the expressions f o r pSCl-nSC2. L i s t of the symbols used f o r Recombination-generation r a t e s i n pSCl-nSC2 •heterojunctions : The top s u f f i x (n or p) G f any symbol ( f , k, J , t , etc) i s f o r the type of the c a r r i e r , and bottom s u f f i x e s ( t l , t 2 , I I , I I , etc) f o r every symbol are explained below. The bracket ( ) f o l l o w i n g the symbol contains v a r i a b l e s or values of the v a r i a b l e s at which the symbol i s considered. SC: semiconductor C.B.: conduction band V.B.: valence band E^: i n t e r f a c e s t a t e l e v e l E t ^ : trapping l e v e l (or trap) i n SCI Et^' trapping l e v e l (or trap) i n SC2 : density of i n t e r f a c e s t a t e s E^ N. N t l = d e n s : * - t y °f t r a p p i n g l e v e l E ^ i n SCI N t2* den s i t y of t r a p p i n g l e v e l E ^ i n SC2 P f j . ( E ^ . ) : s t a t i s t i c a l f i l l i n g of i n t e r f a c e - s t a t e E^ . by a hole f j ( E ) : s t a t i s t i c a l f i l l i n g of i n t e r f a c e s t a t e E by an e l e c t r o n P f , (E , ) : s t a t i s t i c a l f i l l i n g of trap E . by a hole t l t l t l n f t 2 ( E t 2 ) : s t a t i s t i c a l f i l l i n g of trap E by an e l e c t r o n Pk-,(E T)=k : capture r a t e of a hole from V.B. of SCI by i n t e r f a c e s t a t e E n l i p . . . . . ] occupied by an e l e c t r o n n (E T) = k^: capture r a t e of an e l e c t r o n from C.B. of SC2 by i n t e r f a c e s t a t e E occupied by a hole P k | ( E t l ) = k^: capture r a t e of a hole from V.B. of SCI by trap E t l n k ' ( E ) = k': capture r a t e of an e l e c t r o n from C.B. of SC2 by trap E 2 t2 n t l P e (E ) = e : emission r a t e of a hole from i n t e r f a c e s t a t e E i n t o V.B. P of SCI 1 ne„(E ) = e : emission r a t e of an e l e c t r o n from i n t e r f a c e s t a t e E i n t o 2 1 n C.B. of SC2 P e ' ( E n) = e': emission r a t e of a hole from trap E n i n t o V.B. of SCI 1 t l p t l n e ' ( E „) = e': emission r a t e of an e l e c t r o n from trap E „ i n t o C.B. of SC2 2 t2 n t2 p^(-O): density of holes i n the V.B. of SCI at the i n t e r f a c e p 1 ( - x 1 ) : density of holes i n the V.B. of SCI at x=-x^ from the i n t e r f a c e density of e l e c t r o n s i n the C.B. of SC2 at the i n t e r f a c e density of e l e c t r o n s i n the C.B. of SC2 at x=x^ from the i n t e r f a c e n 2(+0) n 2 ( x 2 ) P | ( - O ) density of holes i n V.B. of SCI when E ^ = E j a t the i n t e r f a c e p | ( - x ^ ) : density of holes i n V.B. of SCI when E = E t ^ at x=-x^ from the i n t e r f a c e n 2(+0): de n s i t y of e l e c t r o n s i n C.B. of SC2 when E^=E^ at the i n t e r f a c e n 2 ( x 2 ) : . d e n s i t y of e l e c t r o n s i n C.B. of SC2 when E^ = E ^ at x=x 2 from the i n t e r f a c e P t l I ( ' X l ' ' E b l ) = t l I ( x l ) : t u n n e l i n g r a t e of a hole from V.B. of SCI to an I n t e r f a c e s t a t e E occupied by an e l e c t r o n through a b a r r i e r of height K and width x^ P t T 1 (]x |,E, .. ) = t (x ) : tunneling r a t e of a hole from an i n t e r f a c e s t a t e E l l l D l l l l „ I to V.B. of SCI through a b a r r i e r of height E. ., and width IxnI b l 1 P t 3 I ( |x11 ' E b 3 ) = t 3 I ( x 1 ) '• t u n n e l i n g r a t e of a hole from a trap E ^ to an i n t e r -face s t a t e E occupied by an e l e c t r o n through a b a r r i e r of height E, „ and width x, b j 1 P t I 3 ( [x^| , E b 3 ) = t I 3 ( jx^j^l) : tunneling r a t e of a hole from an i n t e r f a c e s t a t e to a trap E and widt 2 . occupied by an e l e c t r o n through a b a r r i e r of height E, „ - ^ k I b 3 °t„ (kJjE „)=t. (x„): tu n n e l i n g r a t e of an e l e c t r o n from C.B. of SC2 to an 21 ' 2' b2 21 2 i n t e r f a c e s t a t e E j occupied by a hole through a b a r r i e r of he i g h t and width | ^21 ntT„(|x:J,E1 0)=t T„(x„) : tun n e l i n g r a t e of an e l e c t r o n from an i n t e r f a c e s t a t e E I 2 ' 2 ' b 2 I 2 2 i to C.B. of SC2 through a b a r r i e r of height E ^ a n d width j x ^ f n t . T (IxJ.E ', ) =t. T (x 0) : t u n n e l i n g r a t e of an e l e c t r o n from a trap E _ to an 41 1 I b4 41 2 t2 i n t e r f a c e s t a t e E^ occupi height E ^ and. width |x 2 i n t e r f a c e s t a t e E^ occupied by a hole through a b a r r i e r of n t ( l xo ! >E,/ ) = t T / ( x 9 ^ : t u n n e l i n g r a t e of an e l e c t r o n from an i n t e r f a c e s t a t e E^ to a trap E ^ occupied by a hole through a b a r r i e r of • he i g h t E ^ and width | | 1. Capture-Capture The e l e c t r o n s are captured from the C.B. of SC2 and holes from the V.B. of SCI by the i n t e r f a c e s t a t e s E (see F i g . 2.4). The p r o b a b i l i t y of occupation of an i n t e r f a c e s t a t e l e v e l E by an e l e c t r o n i s 1 n f ( E ) = : (2.57) I I 1 . (E T-Ej-) 1 + exp I £' kT and by a hole i s P f (E ) = (2.58) 1 + exp 1 1 kT and n f I ( E ] . ) + ^ ( E j ) = 1 (2.59) I f r (+0) i s the capture r a t e of e l e c t r o n s from C.B. of SC2 by i n t e r f a c e s t a t e s E. a I r (+0) i s the emission r a t e of e l e c t r o n s from i n t e r f a c e s t a t e s E T to C.B. of SC2 b I r (-0) i s the capture r a t e of holes from V.B. of SCI by i n t e r f a c e s t a t e s E^ . r (-0) i s the emission r a t e of holes from i n t e r f a c e s t a t e s E T to V.B. of SCI. d 1 r (+0) = k n„(+0) N T P f T a n z I I = k n (+0) N T ( l - n f T ) n l 1 1 r, (+0) = e N n f T b n i l r (-0) = k P l ( - 0 ) N T n f c p i I I r d ( - 0 ) = e p N I P f i = e p N l ( l - n f i ) At e q u i l i b r i u m : r (+0) = r, (+0) a b or k no(+0) N P f T = e N n f T n 2 I I n I I E „(+0)-ET 1 M c2 I or e = k N „exp -n n c2 kT where e = k n!(+0) n n 2 E (+0)-E nl(+0) = N exp - — — . kT and r (-0) = r (-0) c a or k p (-0) N f = e N / f p i I I p I I E I - E v l ( " 0 ) or e = k N nexp -p p v l kT = k p P ; ( - o ) E r E v i ( _ 0 ) where p'(-0) = N exp-V kT 9n (+0) - ~ = {r (+0) - r,(+0)} + i V . j (+0) = 0 (2.70) dt a D e n2 3P,(-0) • . , — - = ( r (-0) - r d ( - 0 ) } - -V.J ,(-0) = 0 (2.71) 3 t c a e p i where {r (+0)-r n (+0)} i s net r a t e of recombination of e l e c t r o n s a b {r (-O)-r.(-O)} i s net r a t e of recombination of holes c d J^C+O) i s e l e c t r o n c u r r e n t f l o w i n g from C.B. of SC2 to i n t e r f a c e s t a t e s J ,(-0) i s hole cu r r e n t f l o w i n g from V.B. of SCI to i n t e r f a c e s t a t e s E p l I For recombination c u r r e n t , e l e c t r o n and hole f l u x e s must be equal J n 2 / ( - e ) = J p l / ( e ) (2.72) or {r (+0) - r, (+0) } = {r (-0) - r ,.(-0) } (2.73) a b c d using (2.60) to (2.66), (2.72) and (2.73) k N T(l- nf T)n„(+0)-k n l ( + 0 ) N T n f T = k p _ ( - 0 ) N n f - k p ' ( - 0 ) N _ ( l - n f _ ) (2.74) n l i z n z 1 1 p l l l p l 1 1 k n (+0) + k p (-0) n 2 (2.75) or f = k {n o(+0)+nI(+0)} + k {p (_0)+p'(-0)} n z z P 1 1 S u b s t i t u t i n g t h i s value of n f T i n {r (+0)-r, (+0)} the net recombination r a t e l a b » i s given by u = N I k n k p { n 2 ( + 0 ) p 1 ( - 0 ) - n 2 ( + 0 - ) P ; ( - 0 ) } ( 2 > ? 6 ) k n(n 2(+0)+n 2(+0)} + k {p 1(-0)+ PJ(-0)} The holes are captured by the i n t e r f a c e s t a t e s from the V.B. of SCI and e l e c t r o n s from the d e p l e t i o n region of SC2 tunnel through the b a r r i e r to the i n t e r f a c e s t a t e s (see F i g . 2.4). The p r o b a b i l i t y of occupation of an i n t e r f a c e s t a t e l e v e l E by an e l e c t r o n i s given by equation (2.57) and a hole by equation (2.58). I f r £ ( x 2 ^ t' i e t u n n e l i n g r a t e of e l e c t r o n s n^(x^) from C.B. of SC2 i n t o i n t e r f a c e s t a t e s E r^(x^) i s the tun n e l i n g r a t e of e l e c t r o n s from i n t e r f a c e s t a t e s E^ to C.B. of SC2 r (-0) i s the capture r a t e of holes from V.B. of SCI by i n t e r f a c e s t a t e s E e ' . 1 r , (-0) i s the emission r a t e of holes from i n t e r f a c e s t a t e s E to V.B. of SCI a I Then these r a t e s are r g ( x 2 ) = n 2 ( x 2 ) N ^ f j t 2 ] [ ( x 2 ) (2.77) . = n 2 ( x 2 ) N j d ^ f j ) t n ( x 2 ) (2.78) r f ( x 2 ) = N i n f I ( N c 2 - n 2 ( x 2 ) } t I 2 ( x 2 ) For non-degenerate semiconductors with the c o n d i t i o n ^ c 2 > > n 2 ( x 2 ^ r f ( x 2 ) - N ] . n f I N c 2 t I 2 ( x 2 ) (2.79) r (-0) = k p ( - 0 ) N T n f T (2.80) e . p 1 1 I r d ( - 0 ) = e pN./ f l = e N T ( l - n f T ) (2.81) p I I At e q u i l i b r i u m : r (x.) = r f ( x 9 ) (2.82) e 2 r 2 n 2 ( x 2 ) N j d ^ f j ) t 2 I ( x 2 ) = ^ " f j N ^ t ^ U p t T , ( x . ) - exp - W " E l ' 2 I ^ > ( 2 ' 8 3 ) kT and r (-0) = r,(-0) (2.84) c d E r Evi^-°) or e = k N ,exp -P P v l k T • e p = V i ( - 0 ) ( 2 , 8 5 ) where p' (-0) = N exp - b^l^L • • (2-86> 1 V l kT At steady s t a t e : the c o n t i n u i t y equations f o r e l e c t r o n s and holes are 3n 2(x 2) = ( r ( } _ r ( x ) } + I v . J n 2 ( x ) = 0 (2.87) e 2 f 2 e n z 2 at 3p 1(-0) 9 t = {r (-O)-r.(-O)} - - V . J p i ( - O ) = 0 (2.88) where J „ i s the e l e c t r o n c u r r e n t from the C.B. of SC2 to the i n t e r f a c e s t a t e s n2 v i a t u n n e l i n g J , i s the hole cu r r e n t from the V.B. of SCI to the i n t e r f a c e s t a t e s E T p l I v i a c a p t u r i n g For the recombination current J , e l e c t r o n and hole f l u x e s must be equal J p l ' = Jn2 (2.89) e (re) or { r e ( x 2 ) - r f ( x 2 ) } =' { r c ( - 0 ) - r d ( - 0 ) } (2.90) Using (2.78) to (2.81), (2.83), (2.85) and (2.90) n 2 ( x 2 ) N T ( l - n f I ) t 2 I ( x 2 ) - N i n f i N c 2 t 2 l ( x 2 ) exp - " \ = k P l ( - 0 ) N n f - k p ' ( - 0 ) N ( l - n f T ) (2.91) p l l l p l l l S u b s t i t u t i n g ^(x^ = N c 2 exp - E c 2 ( x 2 ) ~ E I (2.92) kT n f = k p PJ<-°> + W t 2 I ( x 2 ) (2.93) 1 k p.{p 1(-0)+pj L(-0)} + t 2 I ( x 2 ) { n 2 ( x ) + n 2 (x 2)} S u b s t i t u t i n g n f ^ i n the net recombination r a t e equation i s U = r (x„) - r , ( x ) = r (-0) - r (-0) e 2 r 2 c a N I k t 2 I ( x 2 ) { P 1 ( - ° ) n 2 ( x 2 ) " p i ( " 0 ) n 2 ( x 2 ) } k p { p 1 ( - 0 ) + P | ( - 0 ) }+ t 2 ] . ( x 2 ) { n 2 ( x 2 ) + n 2 ( x 2 ) } (2.94) 3. Tunneling-Capture The e l e c t r o n s are captured by the i n t e r f a c e s t a t e s E from the C.B. of SC2 and holes tunnel from the V.B. of SCI to i n t e r f a c e s t a t e s E where they recombine w i t h the e l e c t r o n s . F o l l o w i n g the procedure of Capture-Tunneling, the expression f o r the net r a t e of recombination i s N I k n t n ( - x 1 ) { n 2 ( + 0 ) p 1 ( - x 1 ) - n 2 ( t O ) P ; ( - x 1 ) } ( 2 > 9 5 ) u — k (n 2(+0)+ n 2(+0) }+t 1 ].(-x 1) { p 1 ( - x 1 ) + p | ( - x 1 ) } The expressions f o r the next s i x processes are d e r i v e d and given i n t a b l e 2.2. x=o 33 E v l 'I CAPTURE-CAPTURE X=0 CAPTURE - TUNNELING X=0 TUNNELING - TUNNELING X=0 ZAPTURE TUNNELING - CAPTURE X=0 ZAPTURE TUNNELING -TUNNELING X=0 TUNNELING - CAPTURE X=0 CAPTURE - CAPTURE TUNNELING X=0 TUNNELING - CAPTURE TUNNELING CAPTURE ~ CAPTURE T UNNELIN G TUNNEL ING F i g . 2.4 D i f f e r e n t recombination-generation- processes i n pSCl-nSC2 Table 2.2 Expressions for net recombination rate of c a r r i e r s i n pSCl-nSC2 h e t e r o j u n c t i o n s Recombination-Generation process- N e t recombination ra t e V • . Njk k { n 2 ( + 0 ) P l ( - 0 ) - n 2(+0)pj_(-0)} Capture - Capture k^n^+O) + n 2(+0)} + k {p^-0) + pj(-O)} N I k p t 2 I ( x 2 ) { n 2 ( x 2 ) p l ( - 0 ) - n 2 ( x 2 ) p l ( - ° ) } Capture-Tunneling { n ^ + n ' C x ^ } + k p { P ] L ( - 0 ) 4 p •<-<)) } Tunneling-Capture N I k n t l I ( " X l ) { n 2 ( + ° ) p l ( ~ X l ) " n 2 ( + 0 ) p l ( " X l ) } k n{n 2(+0)+n 2(+0)} + t n (-x^ { p ^ - x ^ + P^(-x ]_)} N ] [ t 2 I ( x 2 ) t 1 I ( - x 1 ) { n 2 ( x 2 ) p 1 ( - x 1 ) - n ^ ( x 2 ) p j ( - x 1 ) } Tunneling-Tunneling j — r r 7 , . , , 7 r-7 ^ — r — r ? r-i t 2 I ( x 2 ) { n 2 ( x 2 ) + n 2 ( x 2 ) } + t 1 I ( - x 1 ) { p (-x ) + p^(-x )} Capture-Capture N I N t 2 k p k n t 4 l ( x 2 } ^ n 2 ( x 2 ) p l ( " 0 ) ~ n 2 ( x 2 ) p l ( " 0 ) }  t u n n e l i n g t . (x )[k'N { n (x )+n'(x„)} + {k N o (-0)+k' N_p'(-0)}] + k k'[{n„(x„)+nl(x„)}{Pl (-0)+p'(-0)} ] 41 2 n t2 2 2 2 2 p l l p l l p n 2 2 2 2 1 1 N N k k'f (-x_){n ( + 0 ) P l ( - x )-n!(+0)p'(-x )} 1 t l n p .31 1 Z 1 1 / 1 1 Capture y _ p t - — — tunn e l i n g a P U r e k k'[{n„(+0)+nI(+0)}{Pl(-x.)+p'(-x_)}] + t , T ( - x . )[k'N {p (-x >fp 1(-x.)}+{k N n o(+0)+k N.nl(H n p z Z l i l l j l l p t / l l l l n I 2 n l z Cont'd. Co -E-Recombination-Generation process i n PSCl-nSC2 r - N J , k ' t 1 T ( - x . ) t / T ( x , ) i ' { n . ( x )p (-k ) - n I ( x . ) p ' ( - x )} Tunnelmg-Capture I t z n l l 1 41 2 2 2 1 1 2 2 1 1 tun n e l i n g [ k U n ^ x ^ + n ^ x ^ J i p ^ - x ^ + p ^ - x ^ l ^ ^ - x ^ ] + t ^ C x ^ [ k U n ^ x ^ + n ^ x ^ i N ^ + t ^ - x ^ N ^ p ^ - x ^ ^ C -r _ • , N k N 1k't„ T(-x 1){n„(xJp 0(-x 1)-n;(x 9)p'(-x )} Capture }-Tunneling I n t i p 31 1 2 2 2 1 2 2 1 1 tun n e l i n g t 2 I ( x 2 ) < V X 2 } ^ 2 ( x 2 } H V ^ l ^ l / ' V } k + t 3 I ( _ x l ) ^ ' { p ^ - x ^ + p j C - x ^ } +^21^2) In^x^+n^) }} Capture ' j _ ^Capture N I k ; k p N t 2 t 4 l ( x 2 ) t n 2 ( x 2 ) p 1 ( - x 1 ) - n 2 ( x 2 ) p ' ( - x x ) } t u n n e l i n g ' 1 t u n n e l i n g k ^ k ' { n 2 ( x 2 ) + n 2 ( x 2 ) Hpj^C-x^+p^C-x^}+ k ^ 2 ( i 9 + n 2 ( x 2 ) } N I t 3 I ( " X l ) + k J { p l ( " X l ) + P i ( " X l ) } N I t « ( x 2 ) process (equation 2.77) i s very s i m i l a r to the expression d e r i v e d by Sah et al.. (1957) f o r homojunctions. The p r i n c i p a l f eatures of the recombination -generation current can be obtained by making some assumptions. • ( i ) k = k = K n p ( i i ) The a p p l i e d forward b i a s v o l t a g e i s e q u a l l y d i v i d e d between SCI and SC2 ( i i i ) The Fermi l e v e l at e q u i l i b r i u m passes through the i n t e r f a c e s t a t e energy l e v e l The net recombination r a t e (equation 2.77) reduces to E o(+0)-E f E -E (-0) r eV c2 f •„ f v l I exp — -1] N I K N c 2 £ X p - kT N v l £ X P ~ kT k T U = r» E c 2 ( + 0 ) - E f n , V E v l ( - 0 ) ] [ e x P f - - l ] C N c 2 e x p kT + N v l e X P ~ — k T 2 k T (2.96) For the h e t e r o j u n c t i o n s i n which AXpX -X . , 1 > 0, the f o l l o w i n g V narrow wide/ equations may be considered to c h a r a c t e r i z e a t h i r d semiconductor Eg3 = E(J°)-Evl(-0) N c 3 = N c 2 f (2.97) • N v 3 = N v l „ 2 vj M E c 2 ( + Q ) - E v l ( - Q ) (2.98) a n d n i 3 = N c 2 N v l 6 X p ~W The expression (2.96) reduces to 2 KN n U = 1 X 3 [exp | J +1] (2.99) V P 3 The maximum value of U i s obtained when n^ = p^> i . e . n 3 = P 3 = n i 3 a n d or \ a x = — ^ + ( 2 - 1 0 0 ) ' K N U - ~ ~ n.. exp ~ V (2.101) max 2 i 3 2 k l or U a n.„ (2.102) max i 3 a N (2.103) a exp ^  (2.104) The net recombination r a t e of c a r r i e r s i n a h e t e r o j u n c t i o n i s equ i v a l e n t to the net recombination r a t e of c a r r i e r s i n a homojunction made of semiconductor 3 whose p r o p e r t i e s are defined by the semiconductors of which h e t e r o j u n c t i o n i s made (equation 2.97). The p r o p e r t i e s of semiconductor 3 w i l l be s l i g h t l y d i f f e r e n t i n pSCl-nSC2 and nSCl-pSC2 h e t e r o j u n c t i o n s because of d i f f e r e n t values of. the products N . N „ and N .. N „. c l v2 v l c2 The net recombination r a t e i s p r o p o r t i o n a l to the d e n s i t y of i n t e r -face s t a t e s and i n h e t e r o j u n c t i o n s w i t h a l a r g e l a t t i c e mismatch between i t s semiconductors, the net recombination r a t e of the c a r r i e r s at i n t e r f a c e s t a t e s might be very l a r g e and dominate over the recombination r a t e of the c a r r i e r s i n the two n e u t r a l regions. The t h i r d important f a c t o r i s that the recombination r a t e at i n t e r -eV eV face s t a t e s i s p r o p o r t i o n a l to exp - r — • r a t h e r than exp — — i n the n e u t r a l Z K. 1 K1 regions of the two semiconductors. 3.3 Recombination-generation current The recombination-generation current can be obtained from the net recombination-generation r a t e (U) of the c a r r i e r s . S u b s t i t u t i n g the value = U(x) + — V . J = 0 (2.105) 3t e n2 9 P 1 1 — - = U(x) - - V.J = 0 (2.106) e p i dt Let J be the recombination cu r r e n t J = J „ = J . rg rg n2 p i J = / e U(x) dx (2.107) rg w where 5J i s the width of the j u n c t i o n . In the above expression U(x) was the recombination generation r a t e due to the i n t e r f a c e s t a t e energy" l e v e l E of d e n s i t y N . I f the i n t e r f a c e s t a t e s are u n i f o r m l y d i s t r i b u t e d throughout the range E i n which i n t e r f a c e s t a t e s e x i s t and d e n s i t y of s t a t e s i s uniform (N^) throughout the energy range E, the expression f o r recombination-gneeration current i s J = f f e U(x) dx dE (2.108) r§ E W I f traps are- assumed to e x i s t i n both the semiconductors and they are a l s o u n i f o r m l y d i s t r i b u t e d , the most general expression f o r the recomb-i n a t i o n - g e n e r a t i o n current i s J r g = i ± i 2 EW e U(x).dx.dE dE t l.dE t 2 (2.109) where E^ i s i n t e g r a t i o n energy range f o r traps E ^ E^ i s i n t e g r a t i o n energy range f o r traps E 2 E i s i n t e g r a t i o n energy range f o r i n t e r f a c e s t a t e E^ W i s i n t e g r a t i o n range f o r the d e p l e t i o n regions Equation (2.109) may be solved f o r p a r t i c u l a r case w i t h some assumptions and approximations. The t o t a l c urrent i n a h e t e r o j u n c t i o n i s the sum of the d i f f u s i o n (equation 2.55) and recombination c u r r e n t s (equation 2.109). J , = J + J (2.110) T o t a l D i f rg The recombination-generation current at the im p u r i t y centers i n the d e p l e t i o n regions i s a l s o i n c l u d e d i n the J term of equation (2.110), r g 5. Summary and conclusions The theory of anisotype h e t e r o j u n c t i o n s (without i n t e r f a c e s t a t e s ) has been discussed on the b a s i s of m i n o r i t y c a r r i e r i n j e c t i o n . The expression f o r b u i l t - i n v o l t a g e i s q u i t e s i m i l a r to that f o r a homojunction except i t has AE -AE N c 2N N c 2 N v l the a d d i t i o n a l terms — — - and in — — . The term In kT N N _ N N 0 c l v2 c l v2 i s due to d i f f e r e n t e f f e c t i v e masses of e l e c t r o n s and holes i n the two AE -AE V c semiconductors and — — i s due to d i s c o n t i n u i t y i n band edges at the rC JL i n t e r f a c e . I f N = N N =N . and AE = AE = 0 , the two a d d i t i o n a l terms c l c2 v l v2 c v i n the expression f o r b u i l t - i n v o l t a g e reduce to zero and the expression i s the same as that f o r a homojunction. The forward b i a s c u r r e n t - v o l t a g e r e l a t i o n i s very s i m i l a r to that of homojunctions. I t i s a l s o shown that the current i n h e t e r o j u n c t i o n s i s u s u a l l y dominated by the i n j e c t i o n of one type of c a r r i e r , i . e . e i t h e r i n j e c t i o n of e l e c t r o n s i n t o p-type from n-type or i n j e c t i o n of holes i n t o n-type from p-type. The cu r r e n t v o l t a g e r e l a t i o n i n h e t e r o j u n c t i o n s a l s o reduces to the w e l l known r e l a t i o n of the homojunction by s u b s t i t u t i n g AE = AE = 0 and N 1 = N 0 , N 1 = N „ . J J c v e l c2 v l v2 The i n t e r f a c e s t a t e s and traps play an important r o l e i n hetero-j u n c t i o n s and the recombination-generation current at the i n t e r f a c e s t a t e s and traps may dominate over the m i n o r i t y c a r r i e r i n j e c t i o n c u r r e n t . Since the b a r r i e r s f o r the e l e c t r o n s and holes are d i f f e r e n t i n h e t e r o j u n c t i o n s , the e l e c t r o n s and holes may reach the i n t e r f a c e s t a t e s by d i f f e r e n t t r a n s p o r t mechanisms. The three mechanisms (1) capture, ( i i ) t u n n e l i n g , ( i i i ) capture t u n n e l i n g are proposed and nine d i f f e r e n t models f o r recombination-generation r a t e s are considered. The expressions of recombination-generation r a t e s of the c a r r i e r s i n each case are d e r i v e d . The s i m p l i f i e d expression f o r recombination generation r a t e shows that the r a t e i s p r o p o r t i o n a l to ( i ) d e n s i t y of i n t e r f a c e eV s t a t e s ( N j ) , ( i i ) exp and ( i i i ) i n t r i n s i c c a r r i e r c o n c e n t r a t i o n of a t h i r d semiconductor whose p r o p e r t i e s are defined by the two semiconductors of which the h e t e r o j u n c t i o n i s made. The recombination-generation current can be obtained from the r a t e by i n t e g r a t i n g over d i f f e r e n t l i m i t s of energies and d e p l e t i o n l a y e r widths. III. ZnSe FILMS DEPOSITED UNDER NEAR-EQUILIBRIUM CONDITIONS 1. Introduction The II-VI compounds are used for numerous applications such as cathodoluminescence phosphors (in C.R.O. Tubes, T.V., electron microscopes), photoconductors, photovoltaic devices, f i e l d effect transistors and electro-luminescent devices (Vecht, 1966). For most of their applications, they are required in film form. Originally II-VI compounds were used mostly for phosphor purposes and films were deposited on some insulating amorphous substrate like glass. These films were either made by a spray technique or vacuum evaporation methods. Although recent advances in the f i e l d of d.c. electroluminescence (Fischer 1966, Aven 1967), especially the fabrication of heterojunctions of non-amphoteric II-VI compounds with other semiconductors, have led to the study of epitaxial II-VI compounds layers on other semiconductors, there are s t i l l relatively few studies on the epitaxy of II-VI compounds. The important point to consider in making good films of II-VI compounds is the maintenance of the stoichiometric ratio in the elements of the deposited films. The optical and e l e c t r i c a l properties of II-VI films are very much dependent upon the stoichiometry of their constituent elements (Albers 1967, Devlin 1967). Ge, GaAs and ZnSe have similar crystal structures, and l a t t i c e matching in these three semiconductors is very good (Appendix 1). The hetero-junctions made by these semiconductors are expected to have a low interface state density. Since single crystal wafers of Ge and GaAs with specific doping are easily available compared to that of ZnSe, i t was decided to deposit ZnSe films on Ge and GaAs substrates to make ZnSe-Ge and ZnSe-GaAs heterojunctions. The properties of ZnSe films were studied by depositing ZnSe films on mica. Holt (1966) and Cusano (1967) reviewed the study of II-VI films deposited on amorphous and ordered s u b s t r a t e s . There i s some l i t e r a t u r e a v a i l a b l e on the f i l m s of I I - V I compounds such as CdTe, CdSe, CdS, ZnTe and ZnS but r e l a t i v e l y l i t t l e work has been done on ZnSe f i l m s . The I I - V I compounds d i s s o c i a t e on heating i n vacuum ( G o l d f i n g e r et a l . 1963 and Wosten et a l . 1962) and no evidence f o r the exi s t e n c e of any I I - V I gas molecule has been found. Therefore, the f i l m s always have to be r e c o n s t i t u t e d from the i n d i v i d u a l vapor c o n s t i t u e n t s and s p e c i a l techniques f o r making I I - V I f i l m s are used. Some of the methods that have been used are the f o l l o w i n g : 1. F l a s h evaporation 2. Diode s p u t t e r i n g 3. Three temperature method 4. Vapor phase e p i t a x y and close-spaced t r a n s p o r t methods 5. Sublimation under n e a r - e q u i l i b r i u m c o n d i t i o n s The f i r s t f our methods have been discussed i n ' a book e d i t e d by J . C. Anderson (1966). Hudock (1967) deposited CdS f i l m s from powder and -c r y s t a l s on sapphire by employing a s u b l i m a t i o n technique at n e a r - e q u i l i b r i u m c o n d i t i o n s i n an u l t r a h i g h vacuum. The o r i e n t e d CdS f i l m s on sapphire were of good q u a l i t y (high m o b i l i t y ) . 2 . Survey of literature of ZnSe films on ordered substrates A brief description of the published literature on the ZnSe films deposited on ordered substrates is given here. Most of the films were depos-i t e d by vacuum deposition and vapor transport methods. Goodman (1969) deposted ZnSe films on quartz and sapphire sub-—5 -6 strates in a Vacuum of the order of 10 -10 torr at substrate temperatures from 400° to 670°C. The films were deposited in a special type of closed she l l , and two separate sources, one for ZnSe and the other for NaCl (doping impurity) were used. The highly oriented films were obtained on suitably clean sapphire at substrate temperatures of about 670°C. He l i s t e d some un-resolved questions concerning the epitaxy, e l e c t r i c a l properties and possible applications of ZnSe films. Calow et a l . (1968) deposited ZnSe on Ge sub-strates in a special type of evaporation assemply. The ZnSe-powder source was kept in a quartz tube and the Ge substrate was kept at the exit of the tube. The source and substrates were heated separately. The vacuum was of the —6 o order of 10 torr. The films were deposited at substrate temperatures of 250 C. and above. The e l e c t r i c a l properties of the films were not measured but the I-V characteristics of nZnSe-pGe heterojunctions were reported. The I-V characteristics were dominated by space-charge-limited currents. Dhere et a l . (1969) deposited films on rock salt and mica in a vacuum of the order of, -4 o 10 torr at a substrate temperature of 450 C but the e l e c t r i c a l properties of the films were not measured. Several vapor phase transport methods have been used for the epitaxy of ZnSe. Baczewski (1965) deposited ZnSe on GaAs in an open tube HC1 process. The source and substrate temperatures were in the ranges 600°-740°C and 570°-610°C, respectively. The optimum substrate temperature for e p i t a x i a l f i l m s was 585°C. The e l e c t r i c a l p r o p e r t i e s of the f i l m s were not measured. A r i z u m i et a l . (1966) deposited ZnSe f i l m s on Ge by the i o d i n e d i s p r o -p o r t i o n a t i o n method at high s u b s t r a t e temperatures (about 825°C)and observed et c h i n g of the Ge s u b s t r a t e . Hovel et a l . (1969) deposited ZnSe on (111) o r i e n t e d s u b s t r a t e s of Ge, GaAs and ZnSe, using a close-spaced HC1 tr a n s p o r t process. S i n g l e c r y s t a l l a y e r s of 1-350u i n thickness were obtained at su b s t r a t e temperatures of 550°-680°C. Both surface appearance and growth r a t e were found to depend s t r o n g l y on the s u b s t r a t e m a t e r i a l . The ZnSe l a y e r s grown on Ge cracked i f the c o o l i n g r a t e was not low enoughs.',. R e s i s t i v i t y 3 4 2 of the f i l m s between 10 and 10 ohm-cm and m o b i l i t y between 50 and 100 cm / •volt-sec were obtained. In t h i s chapter, the d e p o s i t i o n of ZnSe f i l m s on Ge , GaAs and mica i s described. The f i l m s were made by Hudock's method (1967) of sub-l i m a t i o n under n e a r - e q u i l i b r i u m c o n d i t i o n s . The s t r u c t u r a l p r o p e r t i e s of the f i l m s were s t u d i e d by an e l e c t r o n microprobe, X-ray d i f f r a c t i o n and o p t i c a l microscopy. The photo H a l l - m o b i l i t y and r e s i s t i v i t y of the f i l m s deposited on mica were measured under i l l u m i n a t i o n and the r e s u l t s are explained using a mosaic f i l m model. 3. The p r i n c i p l e of n e a r - e q u i l i b r i u m c o n d i t i o n s sublimation and i t s a p p l i c a t i o n  to the s u b l i m a t i o n of ZnSe on Ge, GaAs and mica In t h i s process, the source (compound m a t e r i a l ) and s u b s t r a t e are both kept i n an e s s e n t i a l l y closed volume (Yan 1970). The se p a r a t i o n between source and s u b s t r a t e v a r i e s from a few mm to. a-few. cm.depending;, on the c o n d i t i o n s . A temperature gra d i e n t between the source and s u b s t r a t e i s a p p l i e d . When the source m a t e r i a l i s heated, the vapor of the source c o n s i s t s of i t s c o n s t i t u e n t s only and not of the compound m a t e r i a l . I f these vapors are enclosed near the source m a t e r i a l , the vapors of the c o n s t i t u e n t s come i n t o e q u i l i b r i u m w i t h the source m a t e r i a l at that temperature. Under t h i s e q u i l i b r i u m c o n d i t i o n , the atomic r a t i o of the c o n s t i t u e n t s i n the vapor, is the same as the r a t i o i n a s o l i d source.Therefore, the s t o i c h i o m e t r i c r a t i o of the c o n s t i t u e n t s i s maintained i n the vapor. Since the source i s at s l i g h t l y h i g her temperature than the s u b s t r a t e , there i s a net flow of s t o i c h i o m e t r i c a l l y maintained vapor from source to s u b s t r a t e . These vapors recombine at the s u b s t r a t e kept at a suitable temperature, and form a f i l m of the source m a t e r i a l having the same s t o i c h i o m e t r i c r a t i o of i t s c o n s t i t u e n t s as. i n the source m a t e r i a l . In d e s c r i b i n g t h i s p r i n c i p l e , i t i s assumed that the vapor pressure of the s u b s t r a t e m a t e r i a l i s much l e s s than that of the source m a t e r i a l at that temperature. The p r i n c i p l e of s u b l i m a t i o n under n e a r - e q u i l i b r i u m c o n d i t i o n s was used to deposit ZnSe on Ge, GaAs and mica. The source ZnSe was kept i n the temperature range .400°-550°C and the s u b s t r a t e i n the range 300°-500°C. The f i r s t c o n d i t i o n f o r the s u b l i m a t i o n under n e a r - e q u i l i b r i u m i s (P ) » (P ,) (3.1) source ^ s u b . ^ where P and P , are the vapor pressures of the source and the su b s t r a t e , source sub. r e s p e c t i v e l y } a n d T^ i s the s u b s t r a t e temperature. The exact values of the vapor pressures of ZnSe, Ge, GaAs and mica are not known i n the range of temperatures described above but an approximate r a t i o of the vapour pressures of the source and the s u b s t r a t e c l o s e to the d e p o s i t i o n temperature can be found. According to Korneeva et a l . (1960) the vapor pressure of ZnSe o -4 at 600 C i s about 10 t o r r and according to Arthur (1967) the vapor pressure -10 of GaAs at the same temperature i s about 10 t o r r . The e x t r a p o l a t e d v a l u e of the vapor pressure of Ge (Grove 1967) at 600°C i s about 10 t o r r so the r a t i o s of the vapour pressures are P 8 P 6 , ZnSe. - 10 and . ZnSe. - 10 l-j? ) (p > G e 600°C GaAs 6 Q Q o c and equation (3.1) i s s a t i s f i e d . I t i s expected that equation (3.1) i s s a t i s f i e d i n . t h e temperature range of d e p o s i t i o n . For mica, t h i s c o n d i t i o n i s d e f i n i t e l y s a t i s f i e d due to i t s very low vapor pressure. -4 The vapor pressure of ZnSe at the source temperature i s in the 10 t o r r range and i f the ZnSe f i l m s are deposited i n a vacuum u n i t w i t h a back-ground pressure of 10 ^ t o r r , then the sublimed f i l m s w i l l be contaminated by the r e s i d u a l gases i n the vacuum u n i t . To make f i l m s which w i l l •  have p r o p e r t i e s very s i m i l a r to the source m a t e r i a l , the vapor pressure of the source should be much higher than the r e s i d u a l gas pressure i n the vacuum u n i t , i . e . , (P ) » (P . , ,) (3.2) source r.esioual 1 Let (P ) _ source Ti „ ^Q-> ( P - A i> r e s i d u a l and s u b s t i t u t i n g the value of (P_ _ ) i n the above equation the approximate ZnSe T -9 value of P . , • i s 10 t o r r , i . e . , an u l t r a high vacuum (U.II.V.) i s needed r e s i d u a l ' to make good sublimed f i l m s of ZnSe on Ge and GaAs. 4. Design and f a b r i c a t i o n of the apparatus f o r n e a r - e q u i l i b r i u m c o n d i t i o n s s u b l i m a t i o n The f o l l o w i n g were the main c r i t e r i a f o r design c o n s i d e r a t i o n s : (1) Background pressure of the vacuum system should be of the order of 10 t o r r , i . e . , an u l t r a high vacuum u n i t . (2) R e s i d u a l gases should be analyzed at d i f f e r e n t stages of. s u b l i m a t i o n . (3) Source and s u b s t r a t e should be i n an enclosed volume i n a U.H.V. system. (4) Substrate should be cleaned i n s i t u . (5) Source and s u b s t r a t e temperatures should be independently c o n t r o l l e d and measured. These p o i n t s are discussed i n d e t a i l w i t h the d e s c r i p t i o n of the U.H.V. system and s u b l i m a t i o n assembly. 4.1 U.H.V. system F i g . 3.1 shows the schematic diagram of the U.H.V. system. The vacuum system was made of standard components (ULTEK high vacuum Corp.) w i t h the exception of the water cooled s u b l i m a t i o n chamber. The s o r p t i o n pump was used f o r roughing and the i o n pump f o r u l t r a high vacuum. The. r e s i d u a l gas analy z e r (R.G.A. U l t e k , Quad 150) was kept near the s u b l i m a t i o n assembly to analyze the r e s i d u a l gases. The s u b l i m a t i o n assembly was kept i n a water cooled chamber about 10cm in diameter and 15cm in l e n g t h . Ceramic to- metal feed-throughs were used f o r e l e c t r i c a l connections at one of the por ' of'..the cross. An i s o l a t i o n v a l y e was used to i s o l a t e the s o r p t i o n pump from the r e s t of the system and a bakeaHe v a l v e was used to i s o l a t e the -3 -11 system w h i l e baking. The low pressures (10 to 10 t o r r ) were measured by a Bayard-Alpert type i o n gauge. The system,along w i t h the r e s i d u a l gas analyzer (R.G.A.),was baked up to 250°C. Copper gaskets were used to j o i n d i f f e r e n t p a r ts of the system. The vacuum u n i t was assembled on a t h i c k asbestos sheet r i g i d l y f i x e d on a movable rack. RESIDUAL GAS ANALYSER CHAMBER F i g . 3.1 Schematic diagram of the u l t r a high vacuum system SUBSTRATE HEATER a U A R T Z MASK SUBSTRATE SUBSTRATE SOURCE HEATER s 0 / r - r IRON ENCLOSED IN QUARTZ TANTALUM REFLECTOR V ^ PURITY1 jMPURiTY HEATER 'FHERMO COUPLE hUARTZ RODS °FOR SUPPORT Fig- 3.2 Schematic diagram ° f the s o b l i g a t i o n assembly QUARTZ PLME OF THICKNESS 0.3mm DIAMETER 12mm ^EFCE%CLOSED % QUARTZ SHELL QUARTZ PLATE THICKNESS 1mm VAN DER PAW QEQMETERY Fig. 3 . 3 A sketch of the quartz m a s k and s h u t t e r 4 . 2 Sublimation assembly The s u b l i m a t i o n assembly was made of c l e a r fused quartz and i s shown i n F i g . 3.2. I t had a source chamber f o r ZnSe powder and a s m a l l tube on the s i d e of the source chamber f o r an i m p u r i t y to dope the f i l m s . The s u b s t r a t e was he l d i n a hole through the top p l a t e . The source, s u b s t r a t e and i m p u r i t y were heated by r a d i a t i o n from s e p a r a t e l y c o n t r o l l e d tungsten w i r e heaters and t h e i r temperatures were measured by chromel7alumel thermocouples. Heat l o s s e s were reduced by usi n g tantalum r a d i a t i o n s h i e l d s . A s h u t t e r was kept between the source and s u b s t r a t e through a s l o t i n the main chamber near the s u b s t r a t e . The sh u t t e r was made of quartz p l a t e w i t h a piece of s o f t i r o n completely enclosed i n a quartz tube on i t s end ( F i g . 3.3(b)) and was opened using a magnet ou t s i d e the s u b l i m a t i o n chamber. A quartz mask ( F i g . 3.3(a)) was used to d e f i n e p a t t e r n s f o r H a l l e f f e c t and thickness measurements. The source and s u b s t r a t e were i n an almost c l o s e d volume about 5 mm apart. A l l the leads f o r heaters and thermocouples were i n s u l a t e d by p u t t i n g e i t h e r pyrex or quartz sleeves over them. Two quartz rods were attached to the bottom p l a t e of the s u b l i m a t i o n assembly and these rods were r i g i d l y f i x e d to a support attached to the i n s i d e of the c r o s s . The whole s u b l i m a t i o n assembly was r i g i d l y f i x e d to the vacuum u n i t . A f t e r p u t t i n g the s u b s t r a t e , source and s h u t t e r i n t o the s u b l i m a t i o n assembly, the s t a i n l e s s s t e e l chamber was made to s l i d e over the s u b l i m a t i o n assembly manually and attached to the vacuum u n i t w i t h screws and nuts. To open the system, the above procedure was reversed. 4.3 Performance of U.H.V. system A t y p i c a l pressure versus time c h a r a c t e r i s t i c of the system i s shown i n F i g . 3.4. The system was baked at 250°C ov e r n i g h t , g i v i n g a vacuum i n the 10 1 0 t o r r range. The t y p i c a l power r a t i n g s f o r the source and s u b s t r a t e TIME (MINUTES) F i g . 3.4 A t y p i c a l pressure versus time c h a r a c t e r i s t i c of the U.H.V. 5. Experimental procedures 5.1 Source p r e p a r a t i o n Sevac grade ZnSe powder (Semi-Elements, Inc.) was used as source m a t e r i a l . Both doped and undoped types of ZnSe were t r i e d . Z i n c and indium were used f o r doping. According to Aven et a l . (1962), z i n c and indium f i l l up the Zn vacancies and ZnSe becomes low r e s i s t i v i t y n-type. A cleaned quartz tube was f i l l e d w i t h ZnSe and the re q u i r e d amount of i m p u r i t y . The tube was evacuated, sealed and kept at 900°C f o r 4-5 days. The undoped ZnSe was out-gassed at 600°C i n another vacuum u n i t i n the 10 ^  t o r r range. 5.2 Substrate p r e p a r a t i o n ' Mica: A c i r c u l a r piece of s i n g l e c r y s t a l mica was cut to f i t i n t o the s u b s t r a t e h o l d e r and a t h i n sheet of about 30y thic k n e s s was cleaved j u s t before l o a d i n g i n t o s u b l i m a t i o n assembly. Germanium: S i n g l e c r y s t a l pGe (p-0.5 ohm-cm, thic k n e s s 1/15"» obtained from Semi-Elements,Inc.) was cut such that i t could be placed i n the s u b s t r a t e h o l d e r . The Ge s l i c e s were mechanically p o l i s h e d , f i n i s h i n g w i t h 0.05 y alumina powder and the damaged su r f a c e was removed by chemical p o l i s h i n g i n a s o l u t i o n of CP-4A (3HF(48%):5HN0 3(70%):3CH 3COOH(100%) by volume}. G a l l i u m Arsenide: S i n g l e c r y s t a l GaAs (p-type and very h i g h r e s i s t i v i t y , 1/15" t h i c k , obtained from Monsanto,Inc.) was cut and mechanically p o l i s h e d s i m i l a r to the Ge. The chemical p o l i s h i n g s o l u t i o n was 7H 2SO^(96%): 1H 20 2(30%):1H 20(100%) by volume(Yan (1970)). A l l p o s s i b l e care to remove wax, grease, e t c . from the su b s t r a t e s was taken by c l e a n i n g w i t h t t i c h l o r o e t h y l e n e , acetone, a l c o h o l and dei o n i z e d 5.3 Sublimation of ZnSe A t y p i c a l s u b l i m a t i o n schedule i s given below. (1) Vacuum i n the 10 ^  t o r r range was ob t a i n e d , (2) R.G.A. reading was taken when the source and s u b s t r a t e were at room temperature. (3) The source and su b s t r a t e temperatures were increased s l o w l y u n t i l the re q u i r e d source temperature was obtained. The su b s t r a t e temperature was kept higher than that of the source (see F i g . 3.5). (4) The source temperature was kept constant at the re q u i r e d temperature but the su b s t r a t e temperature was increased to cl e a n i t the r m a l l y . A f t e r c l e a n i n g the su b s t r a t e t h e r m a l l y , i t s temperature was lowered to the re q u i r e d v a l u e . (5) A f t e r the re q u i r e d source and su b s t r a t e temperatures had s t a b i l i z e d , the s h u t t e r was opened by a magnet from o u t s i d e the s u b l i m a t i o n chamb er. (6) R.G.A. reading was taken at d i f f e r e n t times during s u b l i m a t i o n . (7) A f t e r o b t a i n i n g the re q u i r e d t h i c k n e s s of the f i l m , the source power was q u i c k l y reduced to stop the s u b l i m a t i o n . (8) The su b s t r a t e temperature was brought to room temperature at a s u i t a b l e c o o l i n g r a t e . (9) The R.G.A. reading was taken again at room temperature. F i g . 3.5 shows the d e t a i l s of a t y p i c a l s u b l i m a t i o n procedure. The background pressure was about 7 x 10 ^ " t o r r and the pressure during s u b l i m a t i o n was 1.3 to 2.5 x 10 t o r r . The s u b s t r a t e and source temperatures were about 435°C and 520°C,respectively. In t h i s run, the su b s t r a t e was mica and was not cleaned thermally. 01 . i i • I 0 40 SO 120 160 200 240 F i g . 3.5 A t y p i c a l v a r i a t i o n of source temperature, s u b s t r a t e temperature and pressure wit h time during s u b l i m a t i o n F i g . 3.6 shows a c h a r a c t e r i s t i c spectrum of the gases present i n the vacuum u n i t at d i f f e r e n t stages of s u b l i m a t i o n . Helium (peak 4 a.m.u.) was the major gas i n the background pressure of the vacuum system and was due to the i n e f f i c i e n t pumping a b i l i t y of the i o n pump f o r i n e r t gases. During s u b l i m a t i o n , the gases n i t r o g e n (peak 14 and 28), water vapor (peak 16 and 17) and carbon monoxide (peak 28) were the major contents. The water vapor and n i t r o g e n presumably came from.the ZnSe powder and carbon monoxide was produced by carbon i n the tungsten w i r e and the oxygen from the water vapor or some other source. At higher source and s u b s t r a t e temperatures carbon d i o x i d e (peak 44) was a l s o detected which had the same o r i g i n as carbon monoxide. Oxygen was perhaps evolved from' the quartz ( S i 0 2 ) at hig h temperatures. 6. S t r u c t u r a l properties of the f i l m s 6.1 ZnSe f i l m s on mica The e l e c t r o n microprobe topographs of the ZnSe f i l m s (as grown) deposited on mica at d i f f e r e n t s u b s t r a t e temperatures are shown i n F i g . 3.7. The average c r y s t a l l i t e s i z e as a f u n c t i o n of substrate, temperature was estimated from F i g . 3.7 and i s given i n Table 3.1. Table 3.1 V a r i a t i o n of c r y s t a l l i t e s i z e w i t h s u b s t r a t e temperature Sample Source Substrate C r y s t a l l i t e s i z e No. Temp.(°C) Temp.(°C) (u) 33 460 ' 3 3 0 < 1 32 530 365 = 1 29 530 435 6 to 9 34 550 500 10 to 14 R A N G £ Q_SQ -EMISSION CURRENT 1.0 m A RUN No 29 SCALE 50mV//NCH SUBSTRATE: MICA (a) BEFORE TURNING ON SOURCE AND SUB. HEATERS (PRESSURE 7.8x10~WTORR ) (c) AFTER SUBLIMATION (PRESSURE 2.1x10  9 TORR) 4 _ i : i 1— : , '. : J 4 14 A.M.U. 28 60 ^ F i g . 3.6 R.G.A. spectrum at d i f f e r e n t stages of su b l i m a t i o n o Fig. 3.7 E l e c t r o n microprobe topographs of the ZnSe f i l m s deposited at d i f f e r e n t s u b s t r a t e temperatures An a n a l y s i s of the e l e c t r o n microprobe r e s u l t s f o r the s i n g l e c r y s t a l bulk ZnSe and the ZnSe f i l m s deposited on mica showed that there was a d e f i c i e n c y of Zn and an excess of Se i n the f i l m s as compared to the bulk composition. I t was not p o s s i b l e to determine e x a c t l y the d e f i c i e n c y of Zn and excess of Se. The d e f i c i e n c y • o f Zn was found i n the f i l m s deposited at a l l temperatures ( i . e . , 300° to 500°C) . At h i g h e r s u b s t r a t e temperatures (above 400°C), the hexagonal h i l l o c k - s t r u c t u r e was observed. S i m i l a r types of h i l l o c k s were observed by I g a r o s h i (1969) i n CdS f i l m s deposited on GaAs. As the temperature was inc r e a s e d , the s i z e of the hexagonal h i l l o c k s a l s o increased (see F i g . 3.7 (c) and (d)). The f i l m s deposited at higher temperatures cracked i f the c o o l i n g r a t e was not low enough ( F i g . 3.7(d)). This c r a c k i n g was due to the d i f f e r e n c e i n thermal expansion c o e f f i c i e n t s between s u b s t r a t e (mica) and f i l m . Hovel et a l . (1969) a l s o found c r a c k i n g i n ZnSe f i l m s deposited on Ge and GaAs. Laue b a c k - r e f l e c t i o n p a t t e r n s of the f i l m s showed that the f i l m s were o r i e n t e d . Laue b a c k - r e f l e c t i o n p a t t e r n s of the f i l m s deposited at • low s u b s t r a t e temperatures (365°C)had r i n g s only but the f i l m s deposited at high temperatures (400°C and above) had symmet r i c a l l y discontinuous r i n g s . The s i z e of the X-ray beam (chromium t a r g e t ) was q u i t e l a r g e (about 500y) and the maximum observed c r y s t a l l i t e s i z e was about 15U f o r the f i l m deposited at 500°C. Thus the X-ray beam f e l l on approximately- 330 sm a l l c r y s t a l l i t e s . In order to get maximum i n f o r m a t i o n ' from the ZnSe f i l m s and minimum from the s u b s t r a t e , long wavelength X-ray r a d i a t i o n (chromium t a r g e t , average wave-o leng t h 2.291 A ) was used. The ab s o r p t i o n c o e f f i c i e n t of ZnSe f o r t h i s Iwavelength i s high (about 1160 cm \ C u l l i t y 1959). For example i f the angle between the i n c i d e n t and the back s c a t t e r e d beam i s taken to be 135 then 90% of the s c a t t e r e d beam i n t e n s i t y i s due to a l a y e r of thickness 15u. 6.2 ZnSe f i l m s on GaAs The ZnSe f i l m s deposited on GaAs ( i l l ) at s u b s t r a t e temperatures higher than 380°C were s i n g l e c r y s t a l s and f i l m s deposited at 340°C were p o l y c r y s t a l l i n e . F i g . 3.8 shows the X-ray d i f f r a c t i o n p a t t e r n of a ZnSe f i l m deposited at 380°C on GaAs (111). Since the thickness of the deposited f i l m was about 7u, the d i f f r a c t i o n p a t t e r n had spots both from the ZnSe f i l m and from the GaAs s u b s t r a t e . By comparing w i t h the d i f f r a c t i o n spots of the GaAs s u b s t r a t e , the spots a r i s i n g from the ZnSe f i l m s were recognized. Due to the f a i r l y s m a l l t h i c k n e s s of the f i l m , the ZnSe spots were of lower i n t e n s i t y (see F i g . 3.8). These spots (of ZnSe) were compared w i t h the spots of a t h i c k ZnSe f i l m deposited on Ge (111) by Hovel et al.(1969) and .an agreement was found. The non-coincidence i n the d i f f r a c t i o n p a t t e r n s of (111) o r i e n t a t i o n of ZnSe and GaAs i s perhaps due to the d i f f e r e n t c r y s t a l symmetry (Appendix 1) of these two compounds. Since Ge, GaAs and ZnSe have almost the same l a t t i c e constants and c r y s t a l s t r u c t u r e (cubic) . i t i s expected that t h e i r mutual e p i t a x i a l behaviour would be q u i t e s i m i l a r . Davey and Pankey (1968) s t u d i e d the e p i t a x y of GaAs on Ge and found that s i n g l e c r y s t a l f i l m s were observed, at s u b s t r a t e temperatures of about 400°C. Calow et a l . (1968) s t u d i e d e p i t a x y of ZnSe on Ge and found that the e p i t a x i a l temperature v a r i e d between 270° to 400°C depending on the o r i e n t a t i o n of Ge s u b s t r a t e and pressure. Epitaxy F i g . 3.8 Laue X-ray b a c k - r e f l e c t i o n p a t t e r n of ZnSe f i l m (about 7y t h i c k ) on GaAs (111), the spots marked w i t h arrow are due to ZnSe l a y e r (specimen No. 25) ,i Fig. 3.9 Electron microprobe scanning results of ZnSe fi l m deposited on GaAs substrate (specimen No. 22) of ZnSe on GaAs at 380 C i s very compatible w i t h the ep i t a x y of the other members of t h i s group. The i n t e r f a c e between the ZnSe f i l m and the GaAs su b s t r a t e was observed by scanning an e l e c t r o n microprobe along the cleaved edge. F i g . 3.9(a) shows the e l e c t r o n microprobe topograph of the boundary. The t r a n s -i t i o n from ZnSe to GaAs was q u i t e sharp. The Zn f o r ZnSe and Ga f o r GaAs were scanned across the boundary and t h e i r X-ray images are shown i n F i g . 3.9(b) and (c), r e s p e c t i v e l y . 6.3 ZnSe f i l m s on Ge The ZnSe f i l m s deposited on Ge at s u b s t r a t e temperatures higher than 300°C were not adherent and the f i l m s deposited at 300°C and below were p o l y c r y s t a l l i n e (see F i g . 3.10). I t seems that the r a t e of d e p o s i t i o n of the f i l m s on Ge was much higher than on GaAs under the same source and s u b s t r a t e temperature c o n d i t i o n s . 6.4 F i l m t h i c k n e s s measurement Since the thi c k n e s s of the deposited f i l m s was i n the range of 5 to 20u, the usu a l Angstrometcr method could not be used. The thi c k n e s s of the f i l m s was measured by the T a l y s u r f method. In t h i s method, a mechanical s t y l u s i s moved across.the step and the mechanical movement of the s t y l u s w i t h respect to a reference plane i s a m p l i f i e d , recorded and c a l i b r a t e d . The s u b s t r a t e plane was used as the reference plane. The l i m i t a t i o n on the T a l y -s u r f method i s that the thicknesses of the f i l m at a. d i s t a n c e g r e a t e r than the s t y l u s - t o - h e e l d i s t a n c e (about 2 mm) from the f i l m - s u b s t r a t e step can not be measured s i n c e the hee l w i l l r i d e on the f i l m r a t h e r than remain on the reference plane. Since the deposited f i l m dimensions were l e s s than 4 mm from one edge to'the other, the f i l m t h i c k n e s s could be measured F i g . 3.10 Laue b a c k - r e f l e c t i o n - p a t t e r n of ZnSe f i l m on Ge d e p o s i t e d a t 300°C at any p o s i t i o n on the f i l m . The t h i c k n e s s of the f i l m was measured a t s e v e r a l p l a c e s by scanning the step at d i f f e r e n t p o s i t i o n s . The a c c u r a c y o f the T a l y s u r f me thod i s ±3% of the f u l l s c a l e i n the range 0.5 t o lOOu f u l l s c a l e . F o r example, the t h i c k n e s s of sample 29 was about 1 5VJ ±1.5U. The r o u g h n e s s o f the top s u r f a c e of the f i l m i t s e l f was of the o r d e r o f ab o u t l u and so the f i l m t h i c k n e s s c o u l d not be determined more a c c u r a t e l y t h a n t h i s . The e l e c t r i c a l p r o p e r t i e s of ZnSe f i l m s deposited on mica through a quartz mask of Van der Pauw geometry ( F i g . 3.2(b) were measured under i l l u m i n a t i o n . 7.1 Ohmic C o n t a c t s and specimen holder 'Ohmic contacts to ZnSe f i l m s were made by d e p o s i t i n g indium (59 grade) i n a Veeco 400 vacuum u n i t (vacuum 10 ^ to' 10 t o r r ) through a s u i t -able mask such that Van der Pauw e l e c t r o d e s were made only on the circum-ference of the f i l m . The indium was a l l o y e d to the ZnSe f i l m i n a hydrogen atmosphere at 300°C f o r 5-10 minutes (Aven et a l . 1963). Indium makes ohmic contacts to nZnSe because (1) indium i s a donor i n ZnSe and n +ZnSe l a y e r i s formed near the e l e c t r o d e , (2) the reported work f u n c t i o n of indium (<f>_ ) i s about In 4.1 eV and the e l e c t r o n a f f i n i t y of ZnSe ( X Z n g e ) i s 4.1 eV (Swank, 1967) so that (j) -X ~ 0 and there i s l i t t l e or no b a r r i e r f o r e l e c t r o n s i n j e c t e d In ZnSe from the indium e l e c t r o d e to ZnSe. The contacts to p-type Ge were made by a l l o y i n g indium spheres i n a hydrogen atmosphere and to p-GaAs by d e p o s i t i n g a f i l m of Zn-Au e u t e c t i c and a l l o y i n g i n a hydrogen atmosphere. The d e t a i l s of the specimen h o l d e r are shown i n F i g . 3.11. Since the mica s u b s t r a t e was very t h i n , the ZnSe f i l m (deposited on mica) was kept i n a r i g i d perspex holder to prevent i t from being bent. The Van der Pauw el e c t r o d e s A'B'C' and D'were t r a n s f e r r e d to A',B',C' and D' on the perspex holder w i t h the help of .002" Au w i r e and t h i c k s i l v e r paste. The H a l l e f f e c t probe holder was made of t e f l o n and contacts A',B' ,C' and D' were t r a n s -f e r r e d to A"', B", C'"and through 0.002" Au wire) .'•• From there they were sent to the measuring apparatus. • ^ f F I L M /HOLDER* TEFLON BLOCK TO MEASURING CIRCUITS V 7 ALUMINUM TUBE ALLOYED INDIUM INSULATED LEADS TO CIRCUITS • ' . SUPPORT TO HOLD SPECIMEN RIGIDLY MICA SUBSTRATE F i g . 3,11 Specimen holder f o r H a l l e f f e c t measurements 7.2 Photo H a l l e f f e c t measurement^ The setup f o r measuring the photo H a l l e f f e c t of the ZnSe f i l m i s shown i n F i g . 3.12. A tungsten halogen lamp ( S y l v a n i a DVY 47-24) was used f o r i l l u m -i n a t i o n . The l i g h t was passed through a l i g h t pipe and the specimen was i l l u m i n a t e d by keeping a plane m i r r o r between the l i g h t beam and the specimen The l i g h t pipe was clamped to the specimen h o l d e r . The magnetic f i e l d was s u p p l i e d by an Alpha 8500 e l e c t r o magnet powered by an Alpha P8500 power supply. The s i z e of the pole pieces was about 4 inches i n diameter and the gap about 2 inches.. The b l o c k diagram of the measuring c i r c u i t f o r the H a l l v o l t a g e i s shown i n F i g . 3.13 and has been discussed i n d e t a i l by Tucker (1966). A Fluke d.c. d i f f e r e n t i a l voltmeter was used f o r measuring cu r r e n t i n the c i r c u i t w h i l e K e i t h l e y 600A and 602 ZnSe FILM AND PHOTO DIODE SPECIMEN HOLDER WINDOW LAMP LIGHT PIPE (FIBRE OPTICS) CLAMP PLANE MIRROR POLE PIECES OF ELECTROMAGNET F i g . 3.12 Setup f o r measuring photo H a l l e f f e c t of ZnSe f i l m s D.C. CURRENT SOURCE D.C DIFFERENTIAL VOLTMETER FLUKE 881A B KE/THLEY 600 E.M. KE/THLEY 602 E.M. COMPENSATING] PO TEN TIOM E TER2 F i g . 3.13 Block' diagram of R a i l v o l t a g e measuring, c i r c u i t electrometers were used f o r n u l l d e t e c t i o n and H a l l v o l t a g e measurements. With the help of a f u n c t i o n a l s w i t c h , the i n t e r c o n n e c t i o n s between the four Van der Pauw el e c t r o d e s and the four leads going to the c i r c u i t could be change Let the r e s i s t a n c e R be the p o t e n t i a l d i f f e r e n c e V -V between A D , C D D L the contacts D and C per u n i t c u r r e n t through the contacts A and B and the r e s i s t a n c e R^  be the p o t e n t i a l d i f f e r e n c e V.-V between the contacts A 736, DA A D and D per u n i t c u r r e n t through the contacts B and C. Then r e s i s t i v i t y p i s given by (Van der Pauw,1958) R ~f* R R 1 T i d AB.CD BC,DA c AB, CD . O N p = » . f ( ^ ) ( 3.3) Zn2 2 ^ DA where d i s the th i c k n e s s of the f i l m and •n AB CD f (•;-—1 ) i s a f a c t o r which depends on the r a t i o of the two BC DA r e s i s t a n c e s and i t s value i s obtained from Van der Pauw's paper r e f e r r e d to above. The H a l l m o b i l i t y i s determined by measuring the change of r e s i s t a n c e R ^ when a magnetic f i e l d B i s a p p l i e d perpendicular to the . AC,BD & v v sample. The H a l l m o b i l i t y i s given by d A RAC,BD = 2£n2 A RAC,BD . B P " * B <RAB,CD-4*BC,DA) and c a r r i e r d e n s i t y i s given by 1 P e y H The parameters i n equations (3.3) to (3.5) are expressed i n M.K.S. u n i t s n = ~~~~ (3.5) The r e l a t i v e i n t e n s i t y of i l l u m i n a t i o n was changed by v a r y i n g the input v o l t a g e to the lamp. The r e l a t i v e i n t e n s i t y of i l l u m i n a t i o n was c a l i b r a t e d a g a i n s t the curr e n t of a Hoffman 58-CL photo diode at zero v o l t a g e . The photo diode was placed at the p o s i t i o n of the ZnSe f i l m during i n t e n s i t y c a l i b r a t i o n s . 7.3 Accuracy of measurements The accuracy of the K e i t h l e y electrometers used f o r measurements was -3% of f u l l s c a l e . The meters were l e f t on f o r s e v e r a l hours to reduce the d r i f t e r r o r . The accuracy of the c o n d u c t i v i t y measurements w a s " l i m i t e d by the thickness, measurement. Since the accuracy of thic k n e s s measurement was about * 10% due to roughness of the f i l m surface measured by the T a l y -s u r f method, the estimated accuracy of c o n d u c t i v i t y measurements i s ^15%. The noise s i g n a l w h i l e measuring the photo H a l l v o l t a g e was q u i t e high (about 0.5 mV) . The photo H a l l v o l tage was i n the range of 1.5 to 8 raV depending on the photocurrent and magnetic f i e l d . The percentage inaccuracy was high at low photocurrents and low magnetic f i e l d s . To minimize the e r r o r i n measured H a l l v o l t a g e s , mean of s e v e r a l readings was taken. The p o l a r i t i e s of the photo cu r r e n t and the magnetic f i e l d were reversed and f o r each value of photo cu r r e n t and magnetic f i e l d , three readings were taken. Thus the H a l l v o l t a g e was the mean of 12 readings. The H a l l v o l t a g e was a l s o measured at d i f f e r e n t magnetic f i e l d s and was found prop-o r t i o n a l to the s t r e n g t h of the magnetic f i e l d . The value of the m o b i l i t y at each photo i n t e n s i t y was obtained from 24 readings. The estimated accuracy i n the m o b i l i t y measurement i s about -40% at low photo i n t e n s i t i e s and improves to ^ 20% at high photo i n t e n s i t i e s . The accuracy i n c a r r i e r d e n s i t y i s estimated from equation (3.5) and v a r i e s from ^55% to ^ 35% w i t h the in c r e a s e of i n t e n s i t y . The f i n i t e s i z e , n o n - c i r c u m f e r e n t i a l contact e r r o r s and s h o r t i n g , e f f e c t s were neglected. 7.4 E l e c t r i c a l p r o p e r t i e s of ZnSe f i l m s on mica The photo H a l l e f f e c t could not be measured i n the dark due to the very low c o n d u c t i v i t y of the f i l m s . The minimum p h o t o c o n d u c t i v i t y at -8 -1 which the photo H a l l e f f e c t could be measured was around 6 x 10 (ohm-cm) The photo H a l l e f f e c t s were measured under i l l u m i n a t i o n i n t e n s i t i e s f o r which the r a t i o of the c o n d u c t i v i t y under i l l u m i n a t i o n to the c o n d u c t i v i t y i n the dark v a r i e d from 10 to 50. F i g . 3.14(a) and (b) show the measured photo H a l l v o l t a g e a g a i n s t photo c u r r e n t . The e f f e c t s of r e v e r s i n g the p o l a r i t i e s of photo cu r r e n t and magnetic f i e l d are a l s o shown i n F i g . 3.14(a) and (b). The s i g n of the photo H a l l v o l t a g e always agreed w i t h the n-type behaviour of ZnSe. The H a l l v o l t a g e versus photo cu r r e n t c h a r a c t e r i s t i c s are q u i t e sym-m e t r i c a l about the o r i g i n . The photo H a l l v o l t a g e was measured at d i f f e r e n t 2 stre n g t h s of magnetic f i e l d s ( F i g . 3.14(a) f o r 0.32 weber/m and F i g . 3.14(b) 2 f o r 0.44 weber/m } a n c [ w a s found p r o p o r t i o n a l to the s t r e n g t h of the magnetic f i e l d . The photo H a l l v o l t a g e increased as the photo cu r r e n t increased at low i n t e n s i t i e s but at higher i n t e n s i t i e s i t began to s a t u r a t e . This type of behaviour was observed at a l l the magnetic f i e l d s t r e n g t h values from 0.15 to 0.55 weber/m 2 F i g . 3.15 shows the v a r i a t i o n of photo H a l l m o b i l i t y , photo cond-u c t i v i t y and photo e l e c t r o n d e n s i t y w i t h photo i n t e n s i t y . The photo c o n d u c t i v i t y , photo H a l l m o b i l i t y and photo e l e c t r o n d e n s i t y were c a l c u l a t e d from expressions (3.3), (3.4) and (3.5), r e s p e c t i v e l y . I t i s important to note that the photo-H a l l m o b i l i t y i s independent of t h i c k n e s s i n expression (3.4). The photo H a l l m o b i l i t y increased almost l i n e a r l y w i t h photo i n t e n s i t y at medium i n t e n s i t i e s but showed a k i n d of s a t u r a t i o n at low and high i n t e n s i t i e s . F i g . 3.14(a) Photo- H a l l v o l t age versus photo current at-magnetic f i e l d of v a l u e 0.32 weber/m -v o F i g . 3.14 (b) Photo H a l l v o l t a g e versus photo current at magnetic f i e l d of value 0.44'"'weber/m 30 20 10 20x10 8 x 5^  43x10" 10x10 o o o o o 7 8 6x10 10 15x10 10 o UJ Uj 0 7 2 RELATIVE PHOTO INTENSITY (ARBITRARY UNITS) F i g . 3.15 V a r i a t i o n of p h o t o c o n d u c t i v i t y , photo H a l l m o b i l i t y and photo e l e c t r o n d e n s i t y w i t h r e l a t i v e photo i n t e n s i t y 8 2 5 - ° I o °^ 20.0 - J 3 o I o I-— o 0 . 15.0 10-0 5.0 0 3-0x10 10 JO 4.0x10'" 5.0x10 PHOTO ELECTRON DENSITY 10 6.0x10 10 7.0x10 10 (cm-3) F i g . 3.16 V a r i a t i o n of photo H a l l m o b i l i t y w i t h photo e l e c t r o n d e n s i t y The photo e l e c t r o n d e n s i t y d i d not i n c r e a s e w i t h photo i n t e n s i t y at low i n t e n s i t i e s but s t a r t e d i n c r e a s i n g r a p i d l y at higher i n t e n s i t i e s . . The p h o t o c o n d u c t i v i t y increased q u i t e n o n - l i n e a r l y w i t h i n t e n s i t y . F i g . 3.16 shows the v a r i a t i o n of photo H a l l m o b i l i t y w i t h photo e l e c t r o n d e n s i t y . The photo H a l l m o b i l i t y increased r a p i d l y as the photo e l e c t r o n d e n s i t y was increased i n the i n i t i a l stages but at higher photo e l e c t r o n d e n s i t i e s , the photo H a l l m o b i l i t y s a t u r a t e d . . This type • of c h a r a c t e r i s t i c was observed by Bube et a l . (1961) i n s i n g l e c r y s t a l cadmium s u l p h i d e . • - -The measured m o b i l i t y of the ZnSe f i l m s ranged from 12 to 31 2 1 0 - 3 cm / v o l t - s e c and the c a r r i e r d e n s i t y from 3.8 to 6.0 x 10 cm depending on the r e l a t i v e i l l u m i n a t i o n i n t e n s i t y . 7.5 ZnSe f i l m s deposited on p-type Ge and GaAs The c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of nZnSe-pGe at d i f f e r e n t temperatures were measured. The cu r r e n t was due to h e t e r o j u n c t i o n s up to 0.1 v o l t and above 0.1 v o l t i t was space charge l i m i t e d . F i g . 3.17 shows 2 the I -versus V c h a r a c t e r i s t i c s f o r pGe-nZnSe (No. 17) and s t r a i g h t - l i n e s are observed at higher v o l t a g e s . -The I versus V c h a r a c t e r i s t i c f o r forward b i a s i s shown i n F i g . 3.18, • Assuming a c u r r e n t - v o l t a g e r e l a t i o n l = 1 o ( « P (3,21) where the symbols have t h e i r u s u a l meanings, the val u e of n was about 1 .9 (up to 0.1 v o l t ) showing that the cu r r e n t was mainly due to a recombination-generation mechanism. The r e c t i f i c a t i o n r a t i o of the nZnSe-pGe devices was not hig h and h e t e r o j u n c t i o n s made by t h i s method were not of good q u a l i t y . F i g . 3.17 Forward current versus (voltage) c h a r a c t e r i s t i c s of pGe-nZnSe h e t e r o j u n c t i o n at s e v e r a l temperatures 10 -2 10 -3 UJ Uj CL UJ * TO' o 10 -5 \=19 TRANSITION REG/ON JUNCTION LIMITED SPACE-CHARGE LAW 0-0 0.1 0.2 0.3 0.4 FORWARD BIAS VOLTAGE 0.5 0.6 (VOLTS) F i g . 3.18 Forward c u r r e n t versus v o l t a g e c h a r a c t e r i s t i c of pGe-nZnSe at room temperature The p o l y c r y s t a l l i n e . f i l m i s composed of grains ( c r y s t a l l i t e s ) separated by some grain boundaries ( i n t e r - c r y s t a l l i n e region). The s i z e of the c r y s t a l l i t e s i s usually i n the range 0.05u to few microns depending on' • the deposition condi t i o n s . The s i z e Q f the i n t e r c r y s t a l l i n e region i s assumed to be o f - the order of 5°A. to 100°A. The r e s i s t i v i t y of the i n t e r c r y s t a l l i n e region- i s assumed to be much higher than the r e s i s t i v i t y of the c r y s t a l l i t e s . The cause of the high r e s i s t i v i t y of the i n t e r - c r y s t a l l i n e region may be due to . var i a t i o n s i n stoichiometry, existence of d i s t i n c t separate phases at g r a i n boundaries or i n t e r n a l stresses due to d i f f e r e n t o r i e n t a t i o n s of the neighbouring c r y s t a l l i t e s (Waxman et a l . , 1965). Volger (1950) proposed a model for p o l y c r y s t a l l i n e f i l m s and several authors ( P e t r i t z 1956, Waxman et a l . 1965, Salama et a l . 1967, Bube 1968) developed Volger's model . fur t h e r and discussed many e f f e c t s observed i n semiconductor p o l y c r y s t a l l i n e f i l m s . Volger's mosaic f i l m model i s shown i n F i g . 3.19(a). I t consists of c r y s t a l l i t e s (square) of dimensions of r e s i s t i v i t y (n-type) separated by i n t e r - c r y s t a l l i n e regions ' f l ^ ' °f r e s i s t i v i t y (n-type). The photoconductivity and photo H a l l e f f e c t s of p o l y c r y s t a l l i n e f i l m s are governed by three major factors ( P e t r i t z 1956). ( i ) Space charge e f f e c t s i n the c r y s t a l l i t e s ( i i ) Inter - c r y s t a l l i n e b a r r i e r s -( i i i ) C a r r i e r density Since the c a r r i e r density i n the c r y s t a l l i t e s i n ZnSe fil m s i s 10 3 low (-10 /cm ), the space charge length i s of the order of 500 u. Since the average s i z e of the c r y s t a l l i t e s i s 0.05-15y, the v a r i a t i o n i n the neglected. I f the c a r r i e r d e n s i t y i n the c r y s t a l l i t e s had been of the order 18 3 of 10 /cm (as i s the case w i t h PbS f i l m s ) , the space charge length would have been about 300°A and w i t h the c r y s t a l l i t e s i z e of O.ly the v a r i a t i o n i n c a r r i e r d e n s i t y i n the c r y s t a l l i t e s due to the space charge e f f e c t s would have been a major f a c t o r governing the p h o t o c o n d u c t i v i t y ( S l a t e r 1956). The i n t e r - c r y s t a l l i n e b a r r i e r s are assumed to be due to the d i f f e r e n t c a r r i e r d e n s i t i e s i n the c r y s t a l l i t e s and i n t e r c r y s t a l l i n e r e g i o n s . Since the width of the i n t e r - c r y s t a l l i n e r e g i o n i s much sm a l l e r than the c r y s t a l l i t e s i z e , there i s no ap p r e c i a b l e change i n the c a r r i e r d e n s i t y of the c r y s t a l l i t e s . F i g . 3.19(b) shows the e q u i l i b r i u m energy band diagram of the i n t e r - c r y s t a l l i n e r e g ion between two c r y s t a l l i t e s assuming uniform band gap. The b a r r i e r height <(> expressed i n terms of c a r r i e r d e n s i t i e s i n the two regions i s given by JSA £n -A ( 3 > 6 ) q n 2 where n^ i s the d e n s i t y of e l e c t r o n s i n the region 1 and n^ i s the d e n s i t y of e l e c t r o n s i n the region 2. Fol l o w i n g Waxman (1965) and P e t r i t z (1956) , the curr e n t d e n s i t y due to a n a p p l i e d v o l t a g e V across the b a r r i e r r e g i o n i s given by d 3 , qV • J = 4 4 n l V t h e X p ( - k T ° , ( 6 X P _ 1 } ( 3 * ? ) where J i s the e l e c t r o n current d e n s i t y across the b a r r i e r , v . i s the thermal v e l o c i t y of the c a r r i e r s th J- » q i s the e l e c t r o n i c charge, k i s the Boltzmann constant, and T i s the temperature.. CRYSTALLITES INTER -CRYSTALLINE REG ION F i g . 3.19 (a) Mosaic model f o r p o l y c r y s t a l l i n e f i l m INTER-CRYSTALLINE REGION F i g . CRYSTALLITES 3.19 (b) E q u i l i b r i u m energy band diagram of c r y s t a l l i t e -r e g i o n — c r y s t a l l i t e , s t r u c t u r e - i n t e r c r y s t a l l i n e I f V i s the a p p l i e d v o l t a g e between the e l e c t r o d e s separated by d i s t a n c e L, and i s the number of b a r r i e r s per u n i t l e n g t h i n the f i l m . t h e n V V, = —2- (3.8) q V d For low voltages,. < < : 1, and equation (3.7) can be expressed as kT J * n ^ 2 v t h exp(- A j - J L — . (3.9) The macroscopic e l e c t r i c f i e l d E and c o n d u c t i v i t y a are defined as E = V D/L (3.10) (3.11) J = aE The expression of a i s obtained from equation; (3.9) to (3.11), as 2 0 = n i SjkY- - . ( 3-1 2 ) D e f i n i n g y = V t h q (3.13) 4N kT Equation (3.12) becomes o = qn y exp - ^ (3.14) X K. X The term exp (- "^ Tjr) i n c provides the e s s e n t i a l c h a r a c t e r i z a t i o n of the b a r r i e r . Equation (3.14) can be w r i t t e n i n two ways: ( i ) a = n^qy* where y * = y exp - — (3.15) * * cb ( i i ) a = qp where n^ = n^ exp - -Q^ (3.16) Equation (3.15) can be i n t e r p r e t e d as e l e c t r o n s i n c r y s t a l l i t e s t a k i n g p a r t i n the conduction process but w i t h effective m o b i l i t y y and n* equation (3.16) as only _1 of the c r y s t a l l i t e c a r r i e r s t a k i n g p a r t i n the n l conduction process, but w i t h the m o b i l i t y y . For photo e f f e c t s , equation The change i n c o n d u c t i v i t y of the f i l m due to i l l u m i n a t i o n can be due to a change i n the d e n s i t y of c a r r i e r s and from a change i n e f f e c t i v e m o b i l i t y . For a s m a l l change i n r e l a t i v e i n t e n s i t y A l , the change i n con-d u c t i v i t y i s obtained from equation (3.15), as Aa = qy*An x + q n ^ y * (3.17) . The change i n c o n d u c t i v i t y due to a', u n i t change i n r e l a t i v e i n t e n s i t y i s given by The f i r s t term on the R.H.S. i s due to an i n c r e a s e i n the c a r r i e r c o n c e n t r a t i o n w h i l e the second term i s due to an in c r e a s e i n the e f f e c t i v e m o b i l i t y . This i n c r e a s e i n m o b i l i t y i s perhaps due to b a r r i e r modulation. Sometimes, the e f f e c t of an i n c r e a s e i n c o n d u c t i v i t y due to an i n c r e a s e i n m o b i l i t y i s much more than the in c r e a s e i n c a r r i e r concentration,and to c h a r a c t e r i z e the r e l a t i v e e f f e c t s of the two processes, a parameter A i s defined as A = (-^- ) / ( — i ) (3.19) • u* n l and s u b s t i t u t i n g A i n equation (3.18), = qy* (1 + A) ^  (3.20) I f A - 0, the change i n c o n d u c t i v i t y i s only due to the change i n c a r r i e r d e n s i t y and i s c a l l e d " c a r r i e r l i m i t e d " , A>> 1, the change i n c o n d u c t i v i t y i s only due to the change i n e f f e c t i v e m o b i l i t y and i s c a l l e d " b a r r i e r l i m i t e d " and A ~ 1, the change i n c o n d u c t i v i t y i s due to both the change i n c a r r i e r c o n c e n t r a t i o n and the e f f e c t i v e m o b i l i t y and i s c a l l e d " c a r r i e r -b a r r i e r l i m i t e d " . The r e s u l t s of F i g . (3.15) are explained by equation (3.20). The r e l a t i v e i l l u m i n a t i o n i n t e n s i t y range i s d i v i d e d i n t o three r e g i o n s : (I) Low i n t e n s i t i e s ( l<2), ( i i ) M e d i u m i n t e n s i t i e s (2 < I < 3.5), ( i i i ) High i n t e n s i t i e s ( I > 3.5). Values of A were obtained f o r the three regions and they are Low i n t e n s i t i e s A - 7.30 Medium i n t e n s i t i e s A - 2.06 High i n t e n s i t i e s A - 0.19 The p h o t o c o n d u c t i v i t y i s " b a r r i e r l i m i t e d " at low i n t e n s i t i e s , and at high i n t e n s i t i e s i t i s " c a r r i e r l i m i t e d " , w h i l e at medium i n t e n s i t i e s i t i s " c a r r i e r - b a r r i e r " l i m i t e d . F i g . 3.16 was obtained from F i g . 3.15 and r e s u l t s of F i g . 3.16 could be exp l a i n e d by a d i s c u s s i o n s i m i l a r to that given f o r F i g . 3.15. Bube et a l . (1961) explained t h i s k i n d of c h a r a c t e r i s t i c i n s i n g l e c r y s t a l CdS by assuming that the m o b i l i t y at low e l e c t r o n d e n s i t y was l i m i t e d by the pos-i t i v e l y charged donors. As the photo e l e c t r o n d e n s i t y was increased the e l e c t r o n s were captured by the p o s i t i v e l y charged donors and the donor centers became n e u t r a l . The m o b i l i t y was not l i m i t e d by the n e u t r a l i m p u r i t y centers and at high i n t e n s i t i e s a l l the centers were n e u t r a l and the m o b i l i t y saturated w i t h i n t e n s i t y . The t r a n s i t i o n from low m o b i l i t y to high m o b i l i t y regions took place through the f i l l i n g of the charge c e n t e r s . He used t h i s method to f i n d the energy of the center and i t s capture c r o s s - s e c t i o n . I f i t i s assumed that i n the ZnSe f i l m s , the low m o b i l i t y to high m o b i l i t y t r a n s i t i o n takes place through the f i l l i n g of a center,then the f o l l o w i n g two conclusions can be made'. ( i ) The donor center has to be about 0.43 eV below the conduction band edge. ( i i ) The centers are empty ( p o s i t i v e l y • charged^)at a c a r r i e r d e n s i t y o f about 3.8 x 10 cm and are completely f i l l e d ( n e u t r a l ) when the c a r r i e r i n 1 0 -3 densxty becomes about 5 x 10 cm These two conclusions are not i n agreement w i t h the known i m p u r i t y canters i n ZnSe. There has not been any i m p u r i t y center reported at 0.43 eV below the conduction band edge and the f a c t that the centers are empty at a 10 -3 10 -3 c a r r i e r d e n s i t y of 3.8x 10 cm and f i l l e d at 5 x 10 cm does not look reasonable. The i h t e r - c r y s t a l l i n e b a r r i e r l i m i t e d theory seems more reason-able f o r the f£lms s t u d i e d • compared to Bube's im p u r i t y center l i m i t e d theory. 9. Summary and :conclusion ZnSe f i l m s were deposited on Ge, GaAs and mica by Hudock's method of s u b l i m a t i o n under n e a r - e q u i l i b r i u m c o n d i t i o n s i n an u l t r a h i g h vacuum u n i t (background pressure = 10 t o r r ) . The r e s i d u a l gases were analyzed at the d i f f e r e n t stages of d e p o s i t i o n by a r e s i d u a l gas a n a l y z e r . Helium was the major content i n the background pressure w h i l e n i t r o g e n , carbon monoxide, water vapour and carbon d i o x i d e were detected during s u b l i m a t i o n . The ZnSe f i l m s were deposited on mica at s u b s t r a t e temperatures from 330° to 500°C. The c r y s t a l l i t e s i z e i n the f i l m s increased as the s u b s t r a t e temperature was increased and c r y s t a l l i t e s i z e up to 15^ was observed at a s u b s t r a t e temperature of 500°C. The hexagonal h i l l o c k s were observed at high s u b s t r a t e temperatures. P h o t o c o n d u c t i v i t y and photo H a l l e f f e c t measure-ments showed that the p h o t o c o n d u c t i v i t y was ' b a r r i e r l i m i t e d ' at low i n t e n -s i t i e s and ' c a r r i e r l i m i t e d 1 at high i n t e n s i t i e s . The m o b i l i t y increased 2 2 1 0 - 3 from 12 cm / v o l t - s e c to 31 cm / v o l t - s e c and c a r r i e r d e n s i t y from 3.8 x 10 cm 1 0 - 3 to 6 x 10 cm as the r e l a t i v e i n t e n s i t y was i n c r e a s e d . The p h o t o c o n d u c t i v i t y and photo H a l l e f f e c t r e s u l t s were expl a i n e d using a mosaic model f o r p o l y -c r y s t a l l i n e f i l m s . E p i t a x i a l ' ZnSe f i l m s on GaAs were grown at s u b s t r a t e temperatures around 380°C. The films deposited on Ge at substrate temperatures below 300°C were polycrystalline and above 300°C were not adherent. The el e c t r i c a l properties of nZnSe-pGe were recombination-generation limited up to 0.1 volt and space charge limited at higher voltages. The nZnSe-pGe and nZnSe-pGaAs heterojunctions were not of good quality due to the improper doping of the ZnSe films. The measured electron mobility in bulk (single crystal) ZnSe is 2 300-400 cm /volt-sec. The ratio of the mobility in bulk ZnSe to the maximum measured effective mobility in ZnSe films i s of the order of 10 which is f a i r l y good compared to the results of other semiconductor films deposited by vacuum evaporation methods. ZnSe films deposited on mica having 2 f a i r l y good mobility (31 cm /volt-sec) and low carrier density could be used for making thin film transistors. I n t r o d u c t i o n Since wide band gap I I - V I compounds are non-amphoteric, e l e c t r o -luminescence by adouble i n j e c t i o n process i n homojunctions of these compounds i s u n a t t a i n a b l e . Aven (1967) and F i s c h e r (1966) discussed the p o s s i b i l i t y of o b t a i n i n g electroluminescence i n I I - V I compounds. Schottky diodes and h e t e r o j u n c t i o n s have been made w i t h these compounds w i t h the aim of g e t t i n g electroluminescence. ZnTe i s a I I - V I compound w i t h band gap energy 2.26 eV ( D e v l i n 1967). I t can only be made i n t o a low r e s i s t i v i t y p-type semiconductor. There has been c o n s i d e r a b l e i n t e r e s t to o b t a i n electroluminescence i n ZnTe at room . temperature. Devices made of ZnTe can be c l a s s i f i e d i n t o two types: (A) Indium (Aluminium and G a l l i u m a l s o ) - pZnTe s t r u c t u r e (B) n-type semiconductor - pZnTe h e t e r o j u n c t i o n s (A) Indium (Aluminium and Gallium) - pZnTe s t r u c t u r e Although much e f f o r t has been devoted to t h i s type of de v i c e , the r e s u l t s and i n t e r p r e t a t i o n s given by s e v e r a l authors [Watsncbe(1964), Watanab e et a l . (1964), M i k s i c et a l . (1964), Eastman et a l . (1964), Crowder et a l . (1966), Kennedy et a l . (1967), B o r t f e l d et a l . (1968), Morehead et a l . (1968), Radautsan et a l . (1970) and Donnelly et a l . (1970)] are very d i f f e r e n t . (B) n-type semiconductor - pZnTe h e t e r o j u n c t i o n s : There has not been much work done on t h i s type of dev i c e . Aven et a l . (1964) observed double i n j e c t i o n behaviour i n nCdS-pZnTe h e t e r o j u n c t i o n s . Tsujimoto et a l . (1967) s t u d i e d nZnSe-pZnTe heterojunctions-and obtained electroluminescence. Kot et a l . (1967) s t u d i e d nSi-pZnTe and Serreze et a l . (1968) reported nGaSb-pZnTe h e t e r o j u n c t i o n s without any i n t e r e s t i n e l e c t r o -luminescence. Recently Takahashi et a l . (1969) reported l i g h t e m i t t i n g nlnAs-pZnTe h e t e r o j u n c t i o n s . InAs and ZnTe together form a good p a i r of semiconductors f o r h e t e r o j u n c t i o n s and t h e i r p r o p e r t i e s are given i n Table 4.1. This chapter d e s c r i b e s n-type InAs-pZnTe h e t e r o j u n c t i o n s made by the i n t e r f a c e a l l o y i n g technique. The e l e c t r i c a l p r o p e r t i e s ( c u r r e n t - v o l t a g e , capacitance-voltage) of these h e t e r o j u n c t i o n s were measured and t h e i r theory i s di s c u s s e d . These h e t e r o j u n c t i o n s emitted l i g h t under reverse b i a s c o n d i t i o n s . The i n t e n s i t y , r i s e and f a l l times, and s p e c t r a l p r o p e r t i e s of the emitted l i g h t were s t u d i e d . A band model i s proposed to e x p l a i n the d i f f e r e n t f e a t u r e s of the observed spectrum. 2. F a b r i c a t i o n and contacts 2.1 F a b r i c a t i o n of devices The i n t e r f a c e a l l o y i n g technique (Rediker et a l . (1965)) was used to make j u n c t i o n s between n-InAs* and pZnTe^. The manufacturer's s p e c i f i c -a t i o n s of the compounds are given below. n-InAs p -0.0025 ohm-cm 4 2 y -2.2 x 10 cm / v o l t - s e c . n n - 1.1 x 1 0 1 7 /cm 3 p-ZnTe p - 1.0 ohm_cm minimum Assuming y p ^ 100 c m 2 / v o l t - s e c . , th p,- 6.2 x 10"^ /cm3 p u r i t y b e t t e r than 99.999% A w i r e saw was used to cut 0.4 to 0.8 mm t h i c k s l i c e s from the ZnTe chunk and the InAs p l a t e . These s l i c e s were p o l i s h e d mechanically and f i n i s h e d w i t h 0.05u alumina powder. The ZnTe s l i c e s were cut to approximately 2 2 2 x 2 mm and the InAs s l i c e s to 1 x 1 mm pieces by a s i l i c o n carbide s c r i b e r . These pieces were washed thoroughly i n b o i l i n g t r i c h l o r e t h y l e n e , f o l lowed S i n g l e c r y s t a l n-InAs was obtained from Cominco L t d . , T r a i l , B.C., Canada. ^ S i n g l e c r y s t a l p-ZnTe chunk was obtained from Semi-elements, Inc., Saxon-burg, Pa., U. S. A. Table 4.1 P r o p e r t i e s of InAs and ZnTe Property InAs* ZnTe* 1) L a t t i c e constant 6.0585°A 6.1037°A 2) S t r u c t u r e Zincblende Zincblende 3) Symmetry Tj -F43 m d T2-F43'm d 4) Density' 3 5.66 gm/cm 5.7 gm/cm^ 5) M e l t i n g p o i n t 942°C 1295°C 6) Coeff. of l i n e a r Expan. -5.9 x 1 0 ~ 6 / d e g _ 1 -8.29 x 10~ 6 deg" 7) R e l . P e r m i t t i v i t y ( S t a t i c ) 14.0 8.26 8) Band gap (Eg) 0.34 eV 2.26 eV 9) dEg/dT -4.5 x 10~ 4 eV/C° -6.0 x 10~ 4 eV/C° 10) E l e c t r o n a f f i n i t y 4.9 eV 3.5 eV 11) m e /m0 0.025 0.15-0.20 12) mh*/m0 0.4 0.6 13) 2 23,000 cm / v o l t - s e c . 2 350 cm / v o l t - s e c . 14) 2 200 cm / v o l t - s e c . 2 100 cm / v o l t - s e c . 15) Normal nature Amphoteric Non-amphoteric, p only Most of the data from "Physics of I I I - V Compound1,' 0. Madelung, John Wiley and Sons (1964). . ^Most of the data from "Physics and Chemistry of I I - V I Compounds", E d i t o r s , M. Aven and J . Prener, North-Holland Pub. Comp., Amsterdam (1967). by u l t r a s o n i c c l e a n i n g i n acetone and d e i o n i z e d water. P r i o r to a l l o y i n g the ZnTe was c h e m i c a l l y p o l i s h e d i n a 0.5% bromine-methanol s o l u t i o n (Strehlow 1969) and the InAs i n a CP-4 s o l u t i o n . These pieces, were r i n s e d f i n a l l y i n d e i o n i z e d water. A g r a p h i t e or molybednum•strip was used as a heater. The two ends of the s t r i p were r i g i d l y f i x e d i n copper s t r i p e l e c t r o d e s which were con-nected to a high c u r r e n t transformer. The a l l o y i n g was done e i t h e r i n a vacuum (-10-.^ t o r r ) or i n a hydrogen atmosphere. A b i n o c u l a r microscope (X 20) was used to observe a l l o y i n g and a chromel-alumel thermocouple was used to measure the temperature. F i g . 4.1(a) shows a schematic diagram of the apparatus used f o r making devices. To prevent the InAs from moving during a l l o y i n g , a depression 3 of 2 x 4 x 0.5 mm was made i n the g r a p h i t e boat. The ZnTe wafer was kept i n s i d e the depression ( F i g . 4.1(b)) so that i t was f l a t and not able to move. The InAs wafer was kept over ZnTe i n such a way that the p o l i s h e d s i d e s o f ZnTe and InAs x^ere f a c i n g each other. A current of about 70 amps was passed through the g r a p h i t e heater. A temperature g r a d i e n t was produced such that the ZnTe was at a higher temperature than the InAs. As the temp-era t u r e was r a i s e d , the lower face of the InAs began to melt (melting p o i n t s of InAs and ZnTe are 942°C and 1295°C r e s p e c t i v e l y ) . As soon as the lower face of the InAs s t a r t e d to melt the he a t i n g current was turned o f f . The melted p o r t i o n of the InAs r e c r y s t a l l i z e d on c o o l i n g and was a l l o y e d to the InAs. The e n t i r e a l l o y i n g c y c l e was completed w i t h i n , one. minute. Since the vapor pressure of a r s e n i c i s much higher than that of indium near the mel t i n g p o i n t of InAs, a r s e n i c s t a r t e d subliming from the bulk InAs and a l a y e r of In was always l e f t on the outer surface of the InAs. This In l a y e r made an In-ZnTe s t r u c t u r e r a t h e r than an InAs-ZnTe j u n c t i o n . GLASS PLATE 0 RING-CONTROL VALVE •HYDROGEN .OR ARGON THERMO COUPLE p r — 1 AIR INLET VALVE TO ROTARY PUMP • METAL CHAMBER HIGH CURRENT FEED-THROUGH F i g . 4.1 (a) Schematic diagram of the sytem used f o r making nlnAs-pZnTe h e t e r o j u n c t i o n s ZnTe InAs POLISHED SURFACE GRAPHITE BOAT —I I— F i g . 4.1 (b) Sketch of the g r a p h i t e boat w i t h InAs and Znte This l a y e r of In was removed by d i s s o l v i n g i n h y d r o c h l o r i c a c i d or by using an a b r a s i v e . 2.2 Contacts Ohmic contacts to p-semiconductors are made by high work f u n c t i o n metals. The valence band of ZnTe i s about 5.76 eV below the vacuum l e v e l (Swank 1967) which i s out of reach of the work f u n c t i o n of any metal. The work f u n c t i o n of gold i s about 4.8 eV (Sze 1969) and i t i s a l s o an acceptor i m p u r i t y i n ZnTe w i t h an a c t i v a t i o n energy of 0.22 eV ( D e v l i n 1967). Never-t h e l e s s gold has been found to make good ohmic contacts (Aven and Swank 1968) w i t h pZnTe. Gold was evaporated from a tungsten boat i n a vacuum i n the 10 ~* t o r r range i n a Veeco vacuum d e p o s i t i o n system. The bottom of the conduction band of InAs i s about 4.9 eV below the vacuum l e v e l , so a metal w i t h a work f u n c t i o n l e s s than 4.9 eV could make ohmic contact w i t h nlnAs. T i n (work f u n c t i o n 4.4 eV) was soldered d i r e c t l y to the InAs and made good ohmic contact. The Au-Ge e u t e c t i c (12% Ge) which a l l o y e d to InAs at 450°C a l s o formed good ohmic c o n t a c t s . The diodes were mounted on TO-5 t r a n s i s t o r headers. The header was placed i n a g r a p h i t e strip heater by p u t t i n g the leads of the heater through two holes i n the g r a p h i t e s t r i p . A s m a l l p i e c e of t i n (cut from wire) was kept on the p l a t e of the header and a c u r r e n t was passed through the g r a p h i t e heater. As soon as the t i n s t a r t e d to melt, the InAs s i d e of the InAs-ZnTe h e t e r o j u n c t i o n was g e n t l y rubbed on the melted t i n and the c u r r e n t through the heater was turned o f f . S p e c i a l care was r e q u i r e d w h i l e rubbing the h e t e r o j u n c t i o n on the melted t i n to avoid the p o s s i b i l i t y of melted t i n making contact w i t h ZnTe. The gold w i r e (.002") was bonded to a l e a d of the header by an u l t r a s o n i c bonder ( K u l i c k e and S o f f a , model 484). The gold w i r e was soldered to the evaporated gold contact on the ZnTe s i d e by t i n w i t h a low v o l t a g e s o l d e r i n g i r o n . The contacts to the InAs-ZnTe hetero-j u n c t i o n s were f a i r l y r i g i d and were able to stand mechanical shocks. 3. Experimental procedures 3.1 Current-voltage c h a r a c t e r i s t i c s The c u r r e n t v o l t a g e c h a r a c t e r i s t i c s were stud i e d w i t h a T e k t r o n i x 575 curve t r a c e r and p o i n t by p o i n t measurements of current and v o l t a g e . A d i f f e r e n t i a l voltmeter (Fluke model 881AB) was used to measure the v o l t a g e across the diode and a K e i t h l e y 150A ammeter f o r the c u r r e n t . A Statham temperature c o n t r o l l e r was used f o r measuring c h a r a c t e r i s t i c s at d i f f e r e n t temperatures. In order to avoid condensation of water, the devices were kept i n a s m a l l copper box.' .A chromel-alumel thermocouple was placed very near to the device to measure the temperature. The accuracy of the K e i t h l e y 150 A ammeter was w i t h i n 3% of the f u l l s c a l e reading on a l l ranges and the accuracy of the d i f f e r e n t i a l v o l t -meter operating under n u l l c o n d i t i o n s up to 10 v o l t s was b e t t e r than -.01%. 3.2 Reverse b i a s capacitance Reverse b i a s capacitance and a.c. conductance of nlnAs-pZnTe hetero-j u n c t i o n s were measured usi n g a Boonton 75C (frequency range from 5 to 500 KHz) capacitance b r i d g e . This bridge i s a modified transformer arm r a t i o b ridge and i s equipped w i t h i t s own s i g n a l generator, d.c. supply and n u l l d e t e c t o r . The d i r e c t capacitance (three t e r m i n a l method) was measured i n order to avoid s t r a y capacitance. C o - a x i a l cables were used to connect the sample ( i n a grounded box) to the b r i d g e . The reverse b i a s v o l t a g e was measured by a Fluke d.c. d i f f e r e n t i a l v o l tmeter (model 881AB). A l l the measurements were done i n a i r ambient and at room temperature. Accuracy: f o r m u l t i p l i e r range C = 1, R = 10 on the b r i d g e , C = C + ( 0 . 2 5 % + ~ ^ pf + .2 pf) meas. R P R = R ± (10% + T^r % + -~r % ) meas. 500 1 0 4 where R i s the eq u i v a l e n t p a r a l l e l r e s i s t a n c e of the t e s t i n ohms. P . Q = ^ = 2Trf CR where C i s the t e s t specimen capacitance i n pf f i s the frequency i n MHz R i s the specimen r e s i s t a n c e i n M ohms Approximate accuracy: 0.5% f o r capacitance and 10% f o r r e s i s t a n c e . 3.3 Electroluminescence 3.3.1 I n t e n s i t y The electroluminescence p r o p e r t i e s were s t u d i e d by usi n g e i t h e r an R.C.A. 931A (S-4 response) or a P h i l i p s 150 CVP ( S - l response) photo-m u l t i p l i e r . The standard w i r i n g c i r c u i t (R.C.A. datasheet -3, 11-69) w i t h a load r e s i s t o r of 470K ohms was used. A Hewlett-Packard 214A pulse generator was used to b i a s the nlnAs-pZnTe j u n c t i o n . Pulse lengths from l y sec to 1 m sec at an approximate r a t e of 100 pulses/sec were used. The current i n the diode was determined by measuring the v o l t a g e drop across a standard r e s i s t o r of 100 ohms. The output of the p h o t o m u l t i p l i e r across the load r e s i s t o r and the v o l t a g e across the standard r e s i s t o r i n the diode c i r c u i t were measured simultaneously by using a 3 A l dual a m p l i f i e r p l u g - i n o s c i l l i s c o p e . The r i s e and f a l l times of the pulse generator were about 30 nanoseconds. F i g . 4.2(a) shows the setup used f o r measuring r e l a t i v e e l e c t r o -luminescent i n t e n s i t y versus the j u n c t i o n current c h a r a c t e r i s t i c . The diode, WOn RESISTANCE TEFLON SPECIMEN HOLDER PYREX DEWAR \3A1 DUAL AMI \PLUG IN. 470 K^. LOAD RESISTOR IN PHO TOMUL TIPLIER . CIRCUIT F i g . 4.2 (a) Schematic diagram f o r measuring i n t e n s i t y versus diode c u r r e n t c h a r a c t e r i s t i c INSULATED LEADS To-5 TRANSISTOR HEADER • U? TEFLON HOLDER THERMO COUPLE LIGHT EMISSION F i g . 4.2 (b) Sketch of the t e f l o n h o l d e r w i t h a device mounted on a t e f l o n holder ( F i g . 4 . 2 ( b ) ) , was kept i n a pyrex dewar to measure electroluminescence at low temperatures. A chromel-alumel thermo-couple was kept near the device to measure i t s temperature. 3 . 3 . 2 Rise and f a l l times The r i s e and f a l l times of the l i g h t pulse were studied with the 9 3 1 A photomultiplier with a modified load c i r c u i t . The'time constant of the photomultiplier c i r c u i t with a load r e s i s t o r of 4 7 0 K ohms was very high ( 2 5 usee). The time constant of the c i r c u i t was reduced by changing the load r e s i s t o r from 4 7 0 K ohms to 2 . 2 K ohms. The time constant was further reduced by connecting the output of the photomultiplier (across 2 . 2 K ohms) to an emitter follower stage with output resistance of 8 2 ohms. The time constant of the c i r c u i t was checked against a standard l i g h t emitting diode (XP - 1 0 F e r a n t i GaP diode) having a r i s e time of 2 5 nanoseconds. 3 . 3 . 3 Spectrum of the emitted l i g h t A J a r r e l l - A s h 8 2 - 4 0 0 monochromator was used to study the spectrum of emitted l i g h t from the ju n c t i o n . A ruled grating (blaze 6 0 0 0°A) was used. The wavelength range of the monochromator was from 1 9 0 0°A to 9 0 0 0°A. The spectrum was scanned by a motor at the rate of l - 6°A/sec. The manu-f a c t u r e r ' s s p e c i f i c a t i o n s f o r the monochromator are Focal length 0 . 2 5 meter Resolution 2°A with 2 5 micron s l i t s (half band width) 3°A with 75 micron s l i t s 5°A with 1 0 0 micron s l i t s F i g . 4 . 3 shows the block diagram of the setup used for measuring the spectrum. A negative pulse from 5 to 6 0 v o l t s (pulse length = 1 0 - 5 0 0 u sec. and pulse rate=about 1 0 0 pulses/sec) was used to reverse bias (-ve voltage to ZnTe) the diode. The photomultiplier was mounted d i r e c t l y at the e x i t FLUKE HIGH VOLT. POWER SUPPLY MOD. 405B o o o U] - 3 : JARREL-ASH MONO CHROMA TOR 82-400 931A PHOTO MULTIPLIER REFERENCE SIGNAL STANDARD RESISTANCE 214 A PULSE GENERATOR PRINCETON LOCK IN AMPLIFIER JB-5 MOSELEY 7100 BM STRIP CHART RECORDER TRIGGERING INPUT TO SCOPE F i g . 4.3 Block diagram of the setup used f o r measuring e l e c t r o -luminescence spectrum s l i t of the monochromator. The output of the p h o t o m u l t i p l i e r was given to a JB-5 l o c k - i n a m p l i f i e r ( P r i n c e t o n ) . The l o c k - i n a m p l i f i e r was used i n the " s e l e c t e x t e r n a l mode" and the reference s i g n a l was obtained from the pulse generator. The output of the l o c k - i n a m p l i f i e r was given to a Moseley 710.0 BM s t r i p chart recorder. The p h o t o m u l t i p l i e r s were used at almost max-imum s e n s i t i v i t y . 3.3.4 C a l i b r a t i o n of the monochromator. The monochromator was c a l i b r a t e d against the standard mercury l i n e s . A mercury lamp was placed at the entrance, s l i t ( 2 5y). The monochromator. was scanned u n t i l the green l i n e was v i s i b l e . The counter was set at,5460 and " s i n e bar" of the monochromator was adjusted such that the g r e e n . l i n e and 5460 reading of the counter c o i n c i d e d . The monochromator was checked w i t h the other l i n e s of mercury a l s o . The counter readings were w i t h i n 2°A of the standard l i n e s of mercury. 3.3.5. S p e c t r a l width ( h a l f band width) gap s l i t (lOOOy) or no s l i t (the 2000y gap of the s l i t adapter) was used to get a reasonably d e t e c t a b l e s i g n a l . The green l i n e of a standard mercury lamp was used as a source. The h a l f s p e c t r a l width f o r the entrance s l i t s of d i f f e r e n t gaps were measured and they are: Since the i n t e n s i t y of l i g h t from the diode was very s m a l l , a wide Monochromator scanning r a t e 6 A/sec Entrance s l i t width H a l f s p e c t r a l width 100 U 1000 y 200 M 100°A 110°A 125°A no s l i t The h a l f s p e c t r a l w i d t h was i m p r o v e d by s c a n n i n g t h e monochromator a t l o w r a t e s . 4. R e s u l t s 4.1 C u r r e n t - v o l t a g e c h a r a c t e r i s t i c s The c u r r e n t v o l t a g e c h a r a c t e r i s t i c o f a t y p i c a l n l n A s - p Z n T e h e t e r o -j u n c t i o n (No. 36) o b t a i n e d by t h e c u r v e t r a c e r i s shown i n F i g . 4.4. F i g . 4.4 C u r r e n t - v o l t a g e c h a r a c t e r i s t i c o f n l n A s - p Z n T e h e t e r o j u n c t i o n (No.36) S c a l e : x - a x i s 1 v o l t / d i v a n d y - a x i s 2 mA/div. 4.4.1 F o r w a r d b i a s Fig. 4.5 shows I v e r s u s V p l o t o f t h e n l n A s - p Z n T e j u n c t i o n f o r s e v e r a l t e m p e r a t u r e s ( f r o m 235°K t o 368°K) i n f o r w a r d b i a s c o n d i t i o n s . I t can be s e e n f r o m t h e p l o t t h a t a t h i g h e r v o l t a g e s (more t h a n 0.6 v o l t s ) , t h e s l o p e o f the 1 - V c h a r a c t e r i s t i c i s i n d e p e n d e n t o f t e m p e r a t u r e . The c u r -r e n t v o l t a g e r e l a t i o n c o u l d be e x p r e s s e d as I = I„ exp AV (4.1a) 0 2 OJ 0^6 lh8 10 12 14 FORWARD BIAS VOLTAGE (VOLTS) F i g . 4.5 Forward b i a s c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of nlnAs-pZnTe h e t e r o j u n c t i o n at va r i o u s temperatures where I i s the diode c u r r e n t , V i s the a p p l i e d v o l t a g e , A i s a constant independent of temperature and I Q i s the e x t r a p o l a t e d value of the cur r e n t f o r v o l t a g e equal to zero. The value of A(A =2.3 1 ) f o r d i f f e r e n t temperatures i s given i n F i g . 4.5 and i s almost constant w i t h temperature. At lower v o l t a g e s (about 0.1 v o l t ) , there i s a co n s i d e r a b l e v a r i a t i o n of A w i t h temperature. The values of A at d i f f e r e n t temperatures f o r low volta g e s are a l s o shown i n F i g . 4.5. At lower v o l t a g e s equation (4.19) can be w r i t t e n as 1 = 1 exp — (4.1b) ° n k T where k i s the Boltzmann constant T i s the temperature e i s the e l e c t r o n i c charge h i s a constant From equation 4.1b, the values of f) were c a l c u l a t e d (A = — ) n k l and n v a r i e d from 2.38 to 3.22 i n the temperature range from 235°K to 368°K. The temperature independence of A at higher v o l t a g e s suggests that the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s are dominated by a t u n n e l i n g mech-anism and values of n c l o s e to 2 at lower v o l t a g e s i n d i c a t e that the cur-rent i s due to a recombination-generation mechanism. 4.1.2 Reverse b i a s F i g . 4.6 shows I versus V c h a r a c t e r i s t i c s under reverse b i a s c o n d i t i o n s at s e v e r a l temperatures. The c u r r e n t - v o l t a g e r e l a t i o n could be expressed by I = KV n (4.2) where V i s the a p p l i e d v o l t a g e I i s the current K i s a constant and n i s a parameter which changes from low v o l t a g e s to high v o l t a g e s . 70-71 ^_ 1 :—i 1 o.07 o.i 1.0 no REVERSE BIAS VOLTAGE (VOLTS) F i g . 4 . 6 Reverse b i a s c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of nlnAs-pZnTe h e t e r o j u n c t i o n at v a r i o u s tenmeratures At low v o l t a g e s the value of n i s between 0.76 and 0.87. This can be approximated by a l i n e a r r e l a t i o n s h i p between current and v o l t a g e (n = 1). At higher v o l t a g e s the value of n i s observed to be about 2.5 at a l l temperatures. 4.2 Reverse, b i a s capacitance-voltage c h a r a c t e r i s t i c s The r e v e r s e b i a s c a p a c i t a n c e - v o l t a g e c h a r a c t e r i s t i c s f o r a t y p i c a l diode (No. 36) are shown i n F i g . 4.7. The capacitance was measured from 5 to 500 KHz. The capacitance decreased w i t h the a p p l i e d v o l t a g e but d i d not s a t u r a t e . F i g . 4.8 shows the capacitance versus frequency c h a r a c t e r i s t i c s . Capacitance decreased w i t h an i n c r e a s e i n frequency. There was a c o n s i d e r -able drop i n capacitance i n the frequency range 5 to 50 KHz and above 50 KHz the capacitance decreased m o n o t o n i c a l l y . F i g . 4.9 shows the l / C 2 versus reverse b i a s v o l t a g e c h a r a c t e r i s t i c s obtained from F i g . 4.7. The v a r i a t i o n was a s t r a i g h t l i n e up to 2 v o l t s at frequencies above 40 KHz. The cap-a c i t a n c e d i d i n c r e a s e w i t h forward b i a s but accurate measurements of the c a p i c i t a n c e were not p o s s i b l e due to the high conductance of the j u n c t i o n s . The higher l i m i t of reverse b i a s v o l t a g e was once again l i m i t e d because of the high conductance which made — >R where to i s the frequency, Q i s the wC P p p-capacitance and R p i s the p a r a l l e l a.c. r e s i s t a n c e of the j u n c t i o n at that frequency. F i g . 4.10 shows the p a r a l l e l a.c. r e s i s t a n c e of the j u n c t i o n during capacitance measurements ( F i g . 4.7). The p a r a l l e l a.c. r e s i s t a n c e increased up to 0.3 v o l t s and then decreased f o r the higher reverse b i a s • v o l t a g e s . 4.3 Electroluminescence 4.3.1 I n t e n s i ty A t y p i c a l l i g h t i n t e n s i t y versus reverse b i a s current c h a r a c t e r i s t i c at room temperature f o r specimen No. 36 i s shown i n F i g . 4.11. The minimum values of v o l t a g e and current at which l i g h t could be detected by the photo-10 2.0 3.0 40 F i g , 4 . 7 Reverse biasvcapacitance versus voltage c h a r a c t e r i s t i c s of nlnAs-pZnTe h e t e r o j u n c t i o n at v a r i o u s frequencies to 50~ lob ISO 200 250 300 350 400 450 FREQUENCY [KHz ) F i g . 4.8 Reverse b i a s capacitance as a f u n c t i o n of frequency at d i f f e r e n t reverse b i a s v o l t a g e s 3.0 2.0 1.0 0.0 1.0. 2.0 3-0 4.0 5 BIAS VOLTAGE ' . (VOLTS) F i g . 4.9 1/C versus reverse b i a s v o l t a g e c h a r a c t e r i s t i c s a t var i o u s frequencies o i i i . : i _ 0.0 7.0 2.0 3.0 4.0 REVERSE BIAS VOLTAGE (VOLTS) F i g . 4.10 V a r i a t i o n of a.c. r e s i s t a n c e versus reve r s e b i a s v o l t a g e at v a r i o u s frequencies m u l t i p l i e r (931A) were about 6 v o l t s and 1 mA. L i g h t could be seen w i t h the unaided eye i n a dark room at about 20 v o l t s . When the j u n c t i o n was observed under a microscope, the emission of l i g h t was only from the j u n c t i o n and not from the bulk semiconductors. There was no de t e c t a b l e emission under forward b i a s c o n d i t i o n s up to 70 mA. The l i g h t i n t e n s i t y v a r i e d super-l i n e a r l y w i t h the c u r r e n t . The approximate f u n c t i o n a l r e l a t i o n s h i p between the measured l i g h t i n t e n s i t y and current i n the range 1 mA to 60 mA was 1 5 B = constant I (4.3) where B i s the i n t e n s i t y of l i g h t and I i s the reverse b i a s current. 4.3.2 Rise and f a l l times The o s c i l l o g r a m s of the simultaneous l i g h t and current pulses are shown i n F i g . 4.12(a) and 4.12(b). In F i g . 4.12(a), the output of the p h o t o m u l t i p l i e r c i r c u i t having a load r e s i s t o r of 470K ohms was fed s t r a i g h t to the o s c i l l o s c o p e w h i l e i n F i g . 4.12(b), i t was passed through the emitt e r f o l l o w e r , discussed i n s e c t i o n 3.3.2 of t h i s chapter. The r i s e and f a l l times of the l i g h t pulse could not be measured a c c u r a t e l y because of the upper l i m i t of the r i s e and f a l l times of the c i r c u i t . However, i t can be seen from F i g . 4.12(b) that the r i s e and f a l l times of the l i g h t pulse were l e s s than 0.2p sec. 4.3.3 Electroluminescence spectrum The spectrum of the emitted l i g h t was observed a t d i f f e r e n t reverse biased c u r r e n t s (from 3 mA to 60 mA). F i g . 4.13 shows the electroluminescence spectrum f o r currents 3, 6, 10, 30 and 60 mA. The spectrum was c o r r e c t e d f o r the r e l a t i v e p h o t o s e n s i t i v i t y of the 931 A p h o t o m u l t i p l i e r . The s p e c i a l f e a t u r e s of the spectrum were: ( i ) the photons of energy g r e a t e r than the band gap energy of e i t h e r of the semiconductors were observed and F i g . 4.11 L i g h t i n t e n s i t y versus reverse b i a s c u r r e n t c h a r a c t e r i s t i c at room temperature (a) F i g . 4.12 Simultaneous l i g h t (upper trace) and current (lower pulses for reverse bias nlnAs-pZnTe heterojunction Scale: x-axis, lusec/div. and y-axis, 500 mA/div. 3500 4000 4500 5000 5500 6000 6500 7000 WAVELENGTH IN °A . F i g . 4.13 Electroluminescence s p e c t r a of the l i g h t emitted from a reverse b i a s nlnAs-pZnTe h e t e r o j u n c t i o n at v a r i o u s currents at room temperature ( i i ) the s p e c t r a l h a l f width of the peaks was very l a r g e (more than 1000°A). These two fe a t u r e s are the c h a r a c t e r i s t i c s of the reverse b i a s e l e c t r o -luminescence i n homojunctions. At low currents (6 mA), peaks were observed at energy 2.28, 2.20, 2.12, 2.04 eV and a band i n energy range 1.69 eV to 1.94 eV. At high c u r r e n t s (60 mA), only one peak at energy 2.04 eV was observed. 5. D i s c u s s i o n 5.1 Current-voltage c h a r a c t e r i s t i c s 17 3 The e l e c t r o n c o n c e n t r a t i o n i n the n-type InAs was 1.1 x 10 /cm 16 • 3 and the hole c o n c e n t r a t i o n i n the p-type ZnTe was 6.2 x 10' /cm . The p o s i t i o n of the f e r m i l e v e l s i n the two semiconductors was c a l c u l a t e d . In nlnAs the fe r m i l e v e l c o i n c i d e d w i t h the bottom of the conduction band edge ( i . e . , E - j ^ f i ~ 0) a n d i n p-type ZnTe i t was about 0.15 eV above the top of the valence band edge ( i . e., E£- -E _ = 0.15 eV). F i g . 4.14(a) shows the f2 v2 energy band diagram of nlnAs and pZnTe i n i s o l a t e d c o n d i t i o n s and F i g . 4.14(b) shows the energy band diagram of nlnAs-pZnTe h e t e r o j u n c t i o n at e q u i l i b r i u m assuming that the d e n s i t y of i n t e r f a c e s t a t e s i s low and does not d i s t u r b the bending of the bands i n the two semiconductors. 5.1.1 Forward b i a s F i g . 4.14(c) shows the energy band diagram of the h e t e r o j u n c t i o n under forward b i a s c o n d i t i o n s . The p o s s i b l e e l e c t r o n and hol e c u r r e n t d e n s i t i e s are the f o l l o w i n g : J i s the hole current d e n s i t y from ZnTe to InAs ( n e u t r a l region) i 'P by i n j e c t i o n - The e l e c t r o n current d e n s i t y J n from InAs to ZnTe i s n e g l i g i b l e compared to Jp due to the l a r g e value of AE c-J,£ i s the hol e c u r r e n t d e n s i t y from the V.B. of ZnTe to the V.B. of InAs through the b a r r i e r due to t u n n e l i n g . I l l VACUUM LEVEL Xj=4-9Q lX2=3.5 c / _ l c2 \F1 0.36 •F2 2.26 J-Ev2 0.15 nlnAs pZnTe (a) ISOLATED •c2 cl vl ==XJrg J T v2 Jr nlnAs-pZnTe HETEROJUNCTDN\ (c) AT FORWARD BIAS VACUUM LEVEL % = 4.90 vl AEV=0.5 nlnAs -pZnTe HETEROJUNCTION (b) AT EQUILIBRIUM EcL Ev2 nlnAs -p ZnTe (d) AT REVERSE BIAS F i g . 4.14 Energy band diagrams of nlnAs-pZnTe h e t e r o j u n c t i o n at d i f f e r e n t c o n d i t i o n s J i s the recombination-generation current d e n s i t y due to the rg t u n n e l i n g of e l e c t r o n s from InAs through the b a r r i e r w i t h the holes from the V.B. of pZnTe at the i n t e r f a c e s t a t e s . There w i l l be some recombination-generation c u r r e n t due to centers i n the d e p l e t i o n regions of the two semiconductors. Recombination of the i n j e c t e d c a r r i e r s at the i n t e r f a c e s t a t e s can take place through the centers i n the two semiconductors ( f o r d e t a i l s see Chapter 2) but the behaviour of the recombination-generation c u r r e n t by traps w i l l be s i m i l a r to the behaviour of J . The t o t a l c urrent d e n s i t y i s given by J = J + J T + J (4.4) p T rg The expressions f o r these three currents are discussed below. J p : The band diagram of nlnAs-pZnTe ( F i g . 4.14(c)) i s s i m i l a r to the band diagram of ,nSCl(narrow)-pSC2(wide) ( F i g . 2.1(b)) and the e x p r e s s i o n f o r J p can be obtained from equation 2.47 and i s given by j _fpl N A 2 ! v l exp ( AV e VD ) [ e x p f - 1 ] (4.5) P Vl N v 2 kT where D „ i s the d i f f u s i o n c o e f f i c i e n t of holes i n InAs p i L i s the d i f f u s i o n l ength of holes i n InAs r N,„ i s the acceptor c o n c e n t r a t i o n i n ZnTe A2 N , & N „ are the d e n s i t y of s t a t e s i n the V.B. of InAs and ZnTe v l v2 AE^ i s the d i s c o n t i n u i t y i n the valence band edge i n nlnAs-pZnTe h e t e r o j u n c t i i V Q i s the t o t a l b u i l t - i n v o l t a g e i n nlnAs-pZnTe^heterojunction e i s the e l e c t r o n i c charge of an e l e c t r o n k i s the Boltzmann constant T i s temperature JP = J P o C e x p i - 1 ] ( 4 - 6 ) 1^1 N A ? N v l exp<AVeV (4.7) where J = ~T— A2 — — — po L • N p l v2 kT J ^ : The hole t u n n e l i n g c u r r e n t d e n s i t y ( F i g . 4.14(c)) i s analyzed on the b a s i s of Zeidenberg's model (1967) and i s given by T B r 4 , m* £2 , ^ Z 2 Y (v - V ) ] (4.8) J = B exp [- - ( T T - F 2 ) ] 2 v D A 2 n where m* i s the e f f e c t i v e mass of the tu n n e l i n g c a r r i e r s i s the d i e l e c t r i c constant of ZnTe i s the net acceptor c o n c e n t r a t i o n i n ZnTe B i s an appr o p r i a t e constant i s the b u i l t - i n v o l t a g e Y 2 i s the f r a c t i o n of the a p p l i e d v o l t a g e that appears across ZnTe The above expression can be reduced to a simple form: J T = J T Q exp AV (4.9) , m*e , where J T 0 = B e x p [" 3 ( V ( 4 - 1 0 ) NA2* 4 m*£2 1/2 A = -| ( — ) L ' 1 Y (4.11) N -ft A2 J : The expressions f o r d i f f e r e n t p o s s i b l e cases of recombination-generation r a t e s i n pSCl(narrow)-nSC2(wide) h e t e r o j u n c t i o n s were de r i v e d i n chapter 2. The expressions f o r nSCl(narrow)-pSC2(wide) h e t e r o j u n c t i o n s are e a s i l y obtained by changing n f o r p and p f o r n i n those d e r i v a t i o n s . The recombination-generation r a t e i n nlnAs-pZnTe h e t e r o j u n c t i o r s f o r the Tunneling-Capture process i s given by k t . _ ( - x )N {p (+0) n (-x )-p!(-K))n'(-x )} / N P I I 1 I Z 1 1 Z 1 1 f t T O N u K ) = ~^ (4.12) k p{p 2(4-0) + P 2(+0)} + t n ( - x 1 ) { - n ^ - x ^ n ^ - y ^ ) } where k = a v . i s the capture r a t e of a hole from the V.B. of ZnTe by an p p th . • * . i n t e r f a c e s t a t e E occupied by an e l e c t r o n o i s the capture c r o s s - s e c t i o n f o r holes by the i n t e r f a c e s t a t e s E^ .  . . P 1 ' v , i s the thermal v e l o c i t y of the holes i n ZnTe th J t ^ j ( - x ^ ) i s the t u n n e l i n g r a t e of an e l e c t r o n from the C.B. of InAs (at p o s i t i o n x^ of the d e p l e t i o n l a y e r ) to the i n t e r f a c e s t a t e E^ . Nj. i s the d e n s i t y of i n t e r f a c e s t a t e E P 2(+0) i s the d e n s i t y of holes i n the V.B. of ZnTe at the i n t e r f a c e (x = 0) P 2(+0) i s the d e n s i t y of holes i n the V.B. of ZnTe when E^ = E^ . at the i n t e r f a c e n^(-x^) i s the d e n s i t y of e l e c t r o n s i n the C.B. of InAs at x - -x^ n|(-x^) i s the d e n s i t y of e l e c t r o n s i n the C.B. of InAs when E^ = E at x = -Assuming that the i n t e r f a c e s t a t e s are uniform l y d i s t r i b u t e d w i t h a constant d e n s i t y N T throughout the range E.„, then the recombination-I AB generation r a t e i s given by l U-x^ = / u ( - x 1 ) d E I (4.13) EAB The net recombination current due to the e l e c t r o n s tunneling from the d e p l e t i o n r e g i o n of InAs and recombining w i t h the holes from ZnTe at a l l the i n t e r f a c e s t a t e s i s given by rg = q I dll / / E u(-x^) dE^dx^ (4.14) AB where |d^| i s the d e p l e t i o n width i n SCI. S u b s t i t u t i n g the value of u(-x ) from equation 4.12 i n t o equation (4.14) l Q l l J = q / / rg k p t 1 I ( - x 1 ) N T { P 2 ( - H ) ) n 1 ( - x 1 ) - P 2(+0) n ^ ) } . i i o k p{p 2(+0) + P 2(+0)} + t 1 I ( - x 1 ) { n 1 ( - x 1 ) + n j ( - X l ) } (4.15) This i n t e g r a l i s not easy to sol v e because u depends upon t ^ j ( - x - ^ ) and 'ri^(-x ) which depend upon the d i s t a n c e x^ i n a complicated manner. However, the important f e a t u r e s of the r e s u l t s can be obtained by making the same assumptions and approximations as were made i n chapter 2. Equation (4.12) can be approximated by 2 N t (-x ) k ^ n -,(-x ) u ( - x l } - 1 1 1 1 P 1 3 1 ( e x p ^ + 1 ) (4.16) { k p P 3 + t l I ( - X l ) n 3 ( " X l ) } where p^, n^ and n ^ a r e the p r o p e r t i e s of a t h i r d semiconductor defined as n i 3 = N c l N v 2 6 X P E c & ^ ~ E v 2 ( + 0 ) kT p 3 = N v 2 exp VE v 2 ( + 0 ) kT (4.17) n 3 = N c l exp - ^ l ^ l ^ f kT N = N and N = N c3 c l v3 v2 The recombination-generation current i n terms of semiconductor 3 i s g iven by „ ^ d l ^ q L t ( - x j k n2„(-x_) T , qV I T \ r r 1 I I 1 P i 3 1 dE Tdx. J r g = ( e x p 2kT 1 } 7 1 ~ 1 1 ° EAB { V 3 + t 1 I ( - x 1 ) n 3 ( - x 1 ) } (4.18) or J = J (exp -9^ + 1 ) (4.19) rg rgo 2 f c T I d I 2 l l qN t , T ( - x )k n (-x ) . , T r r I I I 1 p i 3 1 dEdx.. (4.20) where J = J J c I 1 o EAB k P P 3 + t n ( - x 1 ) n 3 ( - x 1 ) The t o t a l c u r r e n t d e n s i t y from equations (4.4),(4.6), (4.9) and (4.19) i s J a JP o ( e x p S - 1 } + JT0 6 X P A V + J r g o ( £ X p 2 k f + 1 } ( 4 - 2 1 ) For a forward b i a s v o l t a g e V such that exp > > x a n d f o r con-s i d e r i n g the temperature and v o l t a g e dependences equation (4.21) can be w r i t t e n i n a more general form J " J o 6 X P ^kT + JT0 6 X P A V ( 4 ' 2 2 ) where n i s between 1 and 2. The e x p e r i m e n t a l l y observed I-V c h a r a c t e r i s t i c s showed t h a t , at eV lower v o l t a g e s , the current i s dominated by J and J which has an exp — — P rg * nkT dependence. At higher v o l t a g e s , the b a r r i e r f o r the holes going from ZnTe to InAs decreases and the t u n n e l i n g current dominates. This i s f u r t h e r confirmed by the i n v a r i a n c e of the slope of the l o g I versus V c h a r a c t e r i s t i c s at higher v o l t a g e s . Rediker et a l . (1964) a l s o observed s i m i l a r t u n n e l i n g dominated currents i n GaAs-GaSb h e t e r o j u n c t i o n s . 5.2.2 Reverse b i a s F i g . 4.14(d) shows the energy band diagram of the nlnAs-pZnTe h e t e r o j u n c t i o n under the reverse b i a s c o n d i t i o n s . For sm a l l reverse b i a s v o l t a g e s , the current w i l l be due to the recombination-generation of c a r r i e r s at the i n t e r f a c e s t a t e s and other centers i n the d e p l e t i o n r e g i o n . The current w i l l be mainly due to the recombination-generation of the c a r r i e r s i n the d e p l e t i o n r e g i o n u n t i l the bottom of the C.B. of SCl(InAs) i s i n l i n e (at the same energy) w i t h the top of the V.B. of SC2 (ZnTe). As the vo l t a g e i s increased f u r t h e r , t u n n e l i n g of e l e c t r o n s from the V.B. of SC2 to the unoccupied s t a t e s i n the C.B. of SCI w i l l take p l a c e . At higher v o l t a g e s , the current w i l l be mostly due to t u n n e l i n g of e l e c t r o n s from the V.B. of SC2 to the unoccupied s t a t e s i n the C.B. of SCI The t u n n e l i n g current d e n s i t y w i l l be given by (Sze. 1969) J m = A T / E l e c t r o n ' de n s i t y i n the V.B of SC2 •J I Tunneling P r o b a b i l i t y unoccupied s t a t e d e n s i t y i n the C.B. . of SCI / \ Tunneling v P r o b a b i l i t y e l e c t r o n d e n s i t y ' i n the C.B. of SCI / unoccupied s t a t e d e n s i t y i n the V.B of SC2 (4.23) where A i s an appr o p r i a t e constant and assumed to be same f o r both the terms i n the R.H.S. of eq. 4.23. Since the a p p l i e d reverse v o l t a g e s are q u i t e h i g h , the t u n n e l i n g of e l e c t r o n s w i l l take place from deep w i t h i n the V.B. of SC2 to the un-occupied s t a t e s deep w i t h i n the C.B. of SCI. The d e n s i t y of s t a t e s v a r i e s w i t h energy i n the conduction and. the valence bands. The current d e n s i t y due to t u n n e l i n g of e l e c t r o n s i n an energy range dE at energy E i s given by d J T = dJ 2 ]_ - d J 1 2 = A V [ { N v 2 ( E ) - p 2 ( E ) } T 2 1 ( E ) { N c l ( E ) - n ] L ( E ) } - - n 1 ( E ) T 1 2 ( E ) p 2 ( E ) ] dE (4. where dJ,_ i s the current d e n s i t y due to tu n n e l i n g of e l e c t r o n s from the 12 . C.B. of SCI to the empty s t a t e s i n the V.B. of SC2 c l J ^ l i s the current d e n s i t y due to tu n n e l i n g of e l e c t r o n s from the V.B. of SC2 to the empty s t a t e s i n the C.B. of SCI N _ i s the d e n s i t y of s t a t e s i n the V.B. of SC2 v2 N .. i s the d e n s i t y of s t a t e s i n the C.B. of SCI c l P 2 i s the hole c o n c e n t r a t i o n i n the V.B. of SC2 n^ i s the e l e c t r o n c o n c e n t r a t i o n i n the C.B. of SCI T^ 2 i s the tunneling p r o b a b i l i t y f o r the e l e c t r o n s i n the C.B. of SCI to the V.B. of SC2 T 2^ i s the tu n n e l i n g p r o b a b i l i t y f o r the e l e c t r o n s i n the V.B. of SC2 to the C.B. of SCI v i s the number of e l e c t r o n o s c i l l a t i o n s per second and i s assumed to be the same f o r both SCI and SC2. The t o t a l c u r r e n t d e n s i t y due to the a p p l i e d v o l t a g e V i s Ev2< d2> J T = A / v [ { N v 2 ( E ) - p 2 ( E ) } T 2 ]_(E) { N c l ( E ) - n i ( E ) } - r ^ ( E ) T ^ ( E ) p ? (E) ] dE (4.25) B c l ( " d l ) where |d^| and |d 2| are the d e p l e t i o n region lengths i n SCI and SC2 under reverse b i a s c o n d i t i o n s . This i n t e g r a l can be s i m p l i f i e d by making some assumptions and approximations. Let T 1 2 ( E ) = T 2 1 ( E ) ( 4 , 2 6 ) T h e n V• (A \ E c 2 ( d 2 ) J T = A / v [ N v 2 ( E ) N c l ( E ) T 2 1 ( E ) - n 1 ( E ) N v 2 ( E ) . T 2 1 ( E ) - p 2 ( E ) N c l ( E ) T 2 1 ( E ) ] d E For non-degenerate semiconductors (4.27) P 2(E) N c l ( E ) + n^(E) N v 2 ( E ) « N v 2 ( E ) N c l ( E ) and equation (4.27) becomes J T - A / V ^ v N _(E) N (E) T-.(E) dE (4.28) E ( -d ) V 2 C l 2 1 c l 1 S u b s t i t u t i n g the values of N c l ( E ) and N^ 2(E) (Sze 1969, p. 26) i n equation (4.28) 2 3/2 2 m 3/2 E v 2 ( d 2 ) 1 / 2 J = A (—y 2- ) ( — ~ ) 1 ? / v T (E) {E-E , ( - d 1 ) } 1 1\ 1i (2ir ) E (-d ) Z 1 C 1 1/2 { E v 2 ( d 2 ) - E } dE (4.29) where m, „ i s the e f f e c t i v e mass of holes i n SC2 h2 m ., i s the e f f e c t i v e mass of e l e c t r o n s i n SCI e l "h = _h and h i s the Planck constant 2TT According to Riben (1966) •3/2 1/2 2m* E (E) T 2 1 ( E ) = exp [- \ (~2 ) ] "ft qF where m* i s the e f f e c t i v e mass of the t u n n e l i n g c a r r i e r s E^(E) i s the b a r r i e r f o r e l e c t r o n s of energy E i n the V.B. of SC2 w h i l e t u n n e l i n g to empty s t a t e s i n the C.B. of SCI at energy E, F i s the f i e l d i n the t r a n s i t i o n r e g ion of the h e t e r o j u n c t i o n E b(E) = E g l + AE v + {E-E c l(-0)} (4.31) Substituting the value of E^(E) in equation (4.30) 3/2 4 2m* 1 / 2 -IE + AE + {E-E (-0)}] , } T 2 1(E) = exp - | <^-) — ^ ^ ^ qF Making the s u b s t i t u t i o n E " E c l ( ~ d 1 ) = e (4.33) and assuming | q v D 1 | << E ^ + AE^, equation (4.29) becomes 2 ^ 3 / 2 2n,el 3 / 2 E v 2 W 2 ) - E c l ( - d l ) 1/2 J t ' A ( ^ ) S 2 0 ' V el/2(Ev2W2>-Ecl<-dl'->-3/2 . {E +AE +e} , 4 . 2m* . g l v de exp - - (-y- ) — 5  i i qF (4.34) but E v 2 ( d 2 ) - E c l ( - d 1 ) = qV-q(V n+V p) = E ^ s a y ) (4.35) where qV = E -E._ and qV = E - E „ i n bulk semiconductors, n c l f p f v2 2m 3 / 2 2m 3 / 2 2 EA , ^ 2 T ~ A f h 2 ^ / e l \ . / J _ i r 1/2. J / 2 4. 2m* N T " — 2 ~ ~ — 2 ~ — 2 v e ^ A~ e^ e x p ~ — 2 ' "h "h 2ir • o "h 3/2 . {E +AE +e} — £ i v — — de (4.36) This i s the b a s i c equation of the tu n n e l i n g c u r r e n t i n reversed b i a s n-p h e t e r o j u n c t i o n s . Bates (1961) and Karlovsky (1962) attempted to so l v e t h i s type of equation f o r forward b i a s tunnel diodes (homojunctions) They assumed constant t u n n e l i n g p r o b a b i l i t y ( i . e . e = o for. the e x p o n e n t i a l f a c t o r i n equation 4.36). Riben (1966) d i d not consider the v a r i a t i o n of the d e n s i t y of s t a t e s w i t h energy i n the conduction and valence bands and a l s o assumed t h a t the t u n n e l i n g p r o b a b i l i t y was constant w i t h the a p p l i e d f i e l d . The i n t e g r a l i n eq. (4.36) was solved by making the f o l l o w i n g assumptions: (1) The f i e l d F does not change a p p r e c i a b l y w i t h the a p p l i e d v o l t a g e and can be taken as a constant. The e l e c t r o n o s c i l l a t i o n frequency according to McAfee (1951) i s given by v = where a i s the l a t t i c e constant. (2) The a p p l i e d f i e l d i s s m a l l such that e < E + A E and the g l v approximation ( E . + A E + e ) 3 / 2 = ( E . + A E ) 3 / 2 {1 + — — } (4.37) s g V 2 ( E . . + A V ) i s v a l i d . With the above approximations, equation (4.36) becomes 2m. . 3/2 2m . 3/2 2 k ^ 1/2 (E. j+AE ) 3 / 2 JT A h C * ; ( ^2 > ( 2 7 T2> 3 * q F EA / e 1 / 2 ( E A - E ) 1 / 2 exp g e .d e (4.38) o „ 1/2 ( E + A E ) 1 / 2 where 3= 1/2 ( — ) (4.39) qF The i n t e g r a l i n equation (4.38) has to be solved n u m e r i c a l l y . The main f e a t u r e s of the J-V c h a r a c t e r i s t i c s can be obtained by p u t t i n g .$= 0 i n eq. (4.38) which i s eq u i v a l e n t to saying that the t u n n e l i n g p r o b a b i l i t y does not change w i t h the f i e l d . v 2m,, 3 / 2 2m... 3/2 2 1/2 (E .+AE ) 3 / 2 J T A A ^ Hr> H r } (-^ ) e x p - f (25T> - £ L - Z — - h ^ I T 2TTZ 3 1T qF E / A l / 2 , _ 1/2 , £ (\~e) & (4.40) 2m. 3 / 2 * , 3 / 2 , ,. * / 2 tt.W'2 A £il f J l l i / e l \ 1 4 ,2m*x g l v „2 ... A V ^ ^ - 3 ( ^ " ^ F — • A 2m, . 3 / 2 2m 3 / 2 . , . . 1/2 (E 1 + A E ) 3 / 2 C£F h2 _ e l _J_ _ A (-2m* gl - v 1i (2TT ) t i qF . .[q{V-(V +V ) } ] 2 (4.42) n p Equation (4.42) gives the approximate c u r r e n t - v o l t a g e r e l a t i o n s h i p s f o r reverse b i a s e d h e t e r o j u n c t i o n s . The f i e l d F can be. w r i t t e n as 1/2 F = H(V d + V) (4.43) ' 1 / 2 q (N • e +N e ) N N where H - [ D 1 1 A 2 2 D 1 A 2 1 < 4" 4 4 ) 2 e i E 2 < ND1 + NA2 ) and the symbols have t h e i r usual meanings. J^, can be w r i t t e n as 1 / 9 2m, . 3/2 2 m 3/2 2 1/2-T ~ A _9iL u/,T I T T N 1/ 2 / h2 ^ , e l . 1 4. 2m* JT A h H (V V ) (~X") ('T2_ } ( T 2 ) 6 X P " 3 ( ~ 2 } •n n 2TT -ft 3/2 ( E g l + A E v ) [q{V-(V + V ) } ] 2 (4.45) 1/2 • P qH (V+V) ' o r R 2 A / T T I T T \ 1/ ^  1 -[V-(V+V )] J - A (V +V) exp - , n p (4.46) d where 3/2 2 3 2m 5 1 1 2m J / Z 1 q(N e+N e )N N 1/2 , 7, q a / h2 \ / eiN , x , DI 1 A2 2 DI A2 i (4.47) A = ) (_^) ( } [ ] h "h /h 2ir . 2z z ( N - + N ) 1 2 DI A2 3/2 1/2 B = i t ( 2 ^ ) 1 / 2 ( \ l + A E v ) t 2 £ 1 £ 2 ( N D 1 + N A 2 ) j (4.48) 1 3 ^ q q ( N D l £ l + NA2 £2> ND1 NA2 In eq. 4.46, i f B. = 0, V >> V + V and V >> V J then 1 n p d J a V 2 , 5 (4.49) T P u t t i n g B-^  - 0 i n equation (4.46) i s eq u i v a l e n t to making the tu n n e l i n g p r o b a b i l i t y equal to 1. J : The recombination-generation c u r r e n t under reverse b i a s c o n d i t i o n s can be obtained by making n 1(-x 1)«ri^(-x 1) and -p 2(+0)«p 2(+0) i n equation- (4 .15) and i s g i ven by J r g =' q V l I ( - X l ) N I P 2 ^ ) n i ( - X l ) d E ^ (4.50) ° EAB k pl(+0) + t . f - x J n U - x . ) p 2 II 1 1 1 F o l l o w i n g s i m i l a r assumptions as i n forward b i a s c o n d i t i o n s J r g I d ! 2 I l l qN t (-x ) k n (-x ) , / / I H I P _ i l _ _ J _ _ dE ] [dx 1 (4.51) ° EAB { k p P 3 + t 1 I ( - X l ) n 3 ( ^ 1 ) } j ~ j r g rgo where p^, n^, n^^ and J' Q a r e defined i n equation (4.17) and (4.20). The t o t a l r e v e r s e b i a s current d e n s i t y i s given by J = J + J f {V-(V +V )} rg T n p' J +-A 1(V,+V) 1 / 2[V-(V +V ) ] 2 exp " 1 rgo 1 d n p ( V d + V ) l / 2 f{V-(V +V )} (4.52) n p where f{(V-(V +V )} = 0 f o r V < (V +V ) n p n p f{V-(V +V )} = 1 f o r V > (V +V ) n p n p F i g . 4.6 shows the I-V curve on a l o g - l o g s c a l e under reverse b i a s c o n d i t i o n s f o r s e v e r a l temperatures (from 235°K to 368°K). The almost l i n e a r behaviour at low v o l t a g e s i s due to the recombination-generation c u r r e n t . The c u r r e n t v o l t a g e c h a r a c t e r i s t i c s are more temperature dependent at lower v o l t a g e s than at higher v o l t a g e s . This agrees w i t h the t h e o r e t i c a l p r e d i c t i o n s of equation (4.52). The value of n, equal to 2.5 i n equation (4.3) i s observed f o r a l l temperatures at higher b i a s v o l t a g e s showing that the current t r a n s p o r t mechanism i s r e l a t i v e l y temperature independent. The approximate t h e o r e t i c a l v a l u e . o f n i s 2.5. S i m i l a r I-V c h a r a c t e r i s t i c s have been observed i n nGe-pGaAs h e t e r o j u n c t i o n s (Riben 1966). The capacitance of a reverse b i a s n-p h e t e r o j u n c t i o n i s given by (chapter 2) C r q N D l N A 2 e i £ 2 1 ^ c = = f j ( 4 . 5 3 ) 2 ( £ 1 N D 1 + E2 NA2> D where the terms on the R.H.S. of the expression (4.53) have t h e i r u s u a l meanings and A i s the area of the j u n c t i o n c i s the j u n c t i o n capacitance per u n i t area C i s the measured capacitance of the j u n c t i o n . A decrease i n capacitance w i t h reverse b i a s v o l t a g e ( F i g . 4.7) i s expected from equation (4.53). The a.c. r e s i s t a n c e of the j u n c t i o n ( F i g . 4.10) inc r e a s e d r a p i d l y w i t h v o l t a g e u n t i l the bottom of the C.B. of SCI l i n e d up w i t h the top of the V.B. of SC2. The decrease of the a.c. r e s i s t a n c e at v o l t a g e s higher than t h i s (at which the bands l i n e up) i s due to tunneling-of e l e c t r o n s from the V.B. of SC2 i n t o unoccupied s t a t e s i n the C.B. of SCI. The v o l t a g e at which the bands l i n e up i s expected to be independent of frequency and i s c l e a r l y shown i n F i g . 4.10 (about 0.3 v o l t s ) . The v a r i a t i o n of capacitance w i t h frequency i n F i g . 4.8 can be expla i n e d on the b a s i s of the time constants of the i m p u r i t y l e v e l s and the i n t e r f a c e s t a t e s (Hovel 1968). These l e v e l s can be charged and discharged (w i t h a p p l i e d s i g n a l ) so they e f f e c t i v e l y add to the j u n c t i o n capacitance. The a d d i t i o n a l capacitance due to traps and i n t e r f a c e s t a t e s w i l l depend on t h e i r time constants and hence on the frequency of the a p p l i e d s i g n a l . At low frequencies the traps can f o l l o w the s i g n a l and t h e r e f o r e r e s u l t i n a l a r g e value of C, but at high frequencies only traps w i t h short time constants can f o l l o w , and the capacitance i s s m a l l . In F i g . 4.8, there i s a sharp decrease of capacitance from 5 KHz to 40 KHz. There i s not much change of capacitance above '40 KHz showing that m a j o r i t y of traps have time constant i n the range of .025 to.2 m sec. Equation (4.53) can be w r i t t e n as 1_ = 1_ 2 ( £ 1 N D 1 + £ 2 N A 2 (V^-V) C 2 ~ A 2 q N D l G l N A 2 £ 2 and d i f f e r e n t i a t i n g w.r.t. V D 1^  C z _ 1 ""1"D1'C'2"A2/ (4.54) d 7 7 -, 2(e 1N T^+e„N A O) d(-V) A 2 q N D l E l N A 2 E 2 or . N = (4.55) e o A l l d ( l / C 2 ) - f 2 2 d(-V) , £]_ N M 17 3 S u b s t i t u t i n g the values of E 2 = 8.3 e Q , = 14.5 E q , N = 1.1 x 10 /cm , 1 -2 2 d C2" A = 1.27 x 10 cm , and from F i g . 4.9, the values of N are d(-V) k l c a l c u l a t e d f o r d i f f e r e n t frequencies and are given i n Table 4.2. 2 Table 4.2 The values of N' 2 at d i f f e r e n t frequencies obtained from the 1/C versus V c h a r a c t e r i s t i c s Frequency NA2 5 KHz 1.0 x 1 0 1 5 / cm 40 KHz 14 5.5 x 10 t i 100 KHz 5.0 x 1 0 1 4 I I 200 KHz 4.5 x 1 0 1 4 i t 400 KHz 14 4.0 x 10 i t From the s u p p l i e r ' s data, i t was known that pZnTe had a minimum r e s i s t i v i t y of 1 ohm-cm but no data was s u p p l i e d on c a r r i e r m o b i l i t y . Assuming 2 that the room temperature m o b i l i t y of holes i n ZnTe i s about 100 cm / v o l t - s e c 16 3 (Aven 1967), a value of N 2 < 6.2 x 10 /cm was estimated. This value was hig h e r than the ex p e r i m e n t a l l y observed ones given i n Table 4.2 . I f i t i s 16 3 assumed that N - 6.2 x 10 /cm the d e v i a t i o n . o f experimental values from the assumed value might be due to the s m a l l a c t u a l area of the j u n c t i o n . When InAs i s a l l o y e d to ZnTe, the InAs i s not uni f o r m l y a l l o y e d to ZnTe which causes the a c t u a l j u n c t i o n area to be smaller than-the geometrical measured area. The other p o s s i b l e reason f o r the sm a l l values of N 2 from 2 the 1/C versus V c h a r a c t e r i s t i c s i s the tr a p p i n g of c a r r i e r s i n the i n t e r -face s t a t e s and t r a p s . The values of b u i l t - i n v o l t a g e at v a r i o u s frequencies 2 ( F i g . 4.9) obtained from the 1/C versus V c h a r a c t e r i s t i c s are higher than 2 the expected v a l u e s . Large values of b u i l t - i n v o l t a g e from 1/C versus V c h a r a c t e r i s t i c s have been observed i n many h e t e r o j u n c t i o n s (Hovel 1968, Hi n k l e y 1967). 5.3 Reverse b i a s electroluminescence L i g h t emission i n reverse b i a s homojunctions has been observed i n S i by Chynoweth et a l . (1956), i n Ge by Chynoweth et a l . (1960), i n GaAs by M i c h e l et a l . (1964), i n GaP by Logan et a l . (1962) and i n SiC by Kholuyanov (1962). L i g h t emission i n h e t e r o j u n c t i o n s has been reported by s e v e r a l authors i n forward b i a s c o n d i t i o n s [ Thornton (1967), Aven et a l . (1964), Takahashi et a l . (1969), Tsujimoto (1967), Razi (1968)] and i n reverse b i a s c o n d i t i o n s notably by Shewchun (1963) in. Ge-Si, Tsujimoto (1967) i n ZnSe-ZnTe, Krause et a l . (1969) i n Ge-GaAs and A l f e r o v et a l . (1970) i n A l x G a T _ x A s - G a A s . F i g . 4.15(a) shows the energy band diagram of an nlnAs-pZnTe hetero j u n c t i o n under s t r o n g l y reverse b i a s c o n d i t i o n s . There are four major pro-cesses by which c a r r i e r s can be created i n the d e p l e t i o n regions of the two semiconductors. (a) I n j e c t i o n of m i n o r i t y c a r r i e r s : The holes from the b u l k nlnAs are i n j e c t e d i n t o the d e p l e t i o n r e g i o n of InAs. S i m i l a r l y , e l e c t r o n s from the bulk pZnTe are i n j e c t e d i n t o the d e p l e t i o n r e g i o n ofZnTe. (b) Thermal generation of c a r r i e r s at i n t e r f a c e s t a t e s and recombination-generation c e n t e r s : The c a r r i e r s generated at the i n t e r f a c e s t a t e s and the i m p u r i t y centers may come to the conduction band of InAs and the valence band of ZnTe by d i f f e r e n t processes ( t u n n e l i n g , capture e t c ) . (c) I n t e r n a l f i e l d emission: E l e c t r o n - h o l e p a i r s can be created i n ZnTe and InAs by i n t e r n a l f i e l d emission. E l e c t r o n - h o l e p a i r s can a l s o be created by the e l e c t r o n s t u n n e l i n g f rom the V.B. of ZnTe to the C.B. of InAs and thus l e a v i n g holes i n ZnTe and e l e c t r o n s i n InAs. (d) Avalanche mechanism: M a j o r i t y c a r r i e r s (holes i n ZnTe and e l e c t r o n s i n InAs) are a c c e l e r a t e d by the a p p l i e d f i e l d and g a i n s u f f i c i e n t energy so that when they c o l l i d e w i t h the l a t t i c e (or unionized centers) they produce e l e c t r o n -hole p a i r s (or i o n i z e the c e n t e r s ) . To f i n d out the dominant process, one must take i n t o account the nature of the semiconductors, the technique by which the devices are made, the i m p u r i t y c e n t e r s , the temperature and other c o n d i t i o n s . and q u a n t i t a t i v e forms and Gershenzon (1966) has discussed reverse b i a s electroluminescence i n p-n homojunctions of d i f f e r e n t semiconductors. The 4 processes (a) and (b) w i l l dominate at low f i e l d s ( < 10 volt/cm) but at high f i e l d s (10~*-10^ volt/cm) the processes (c) and (d) are more important. For each of these processes, the primary c a r r i e r s must have energies g r e a t e r than some t h r e s h o l d energy, which i s the b a s i c c o n d i t i o n f o r simultaneous c o n s e r v a t i o n of both energy and momentum f o r these m u l t i -p a r t i c l e i n t e r a c t i o n s . A f t e r the c a r r i e r s are c r e a t e d , the e l e c t r i c f i e l d tends to separate the e l e c t r o n s and h o l e s , d r i v i n g e l e c t r o n s towards the n-side of the j u n c t i o n s and holes towards the p-side. These e x t r a gen-erated e l e c t r o n s and holes recombine r a d i a t i v e l y and produce photons i n the j u n c t i o n r e g i o n . The important r a d i a t i v e recombination processes are ( Thornton 1967) (a) Recombination of thermal e l e c t r o n - h o l e p a i r s by c o l l i s i o n . (b) Recombination v i a i m p u r i t y centers (c) T r a n s i t i o n s between nearby i m p u r i t y centers (d) R a d i a t i v e recombination of e x c i t o n s Recombination of hot e l e c t r o n - h o l e p a i r s by c o l l i s i o n w i l l produce photons of energy l a r g e r than the band gap energy of the semiconductor i n which the recombination takes p l a c e . The high energy l i m i t w i l l depend on the sum of the r e s p e c t i v e p a i r - p r o d u c t i o n t h r e s h o l d energies of e l e c t r o n s and holes i n the wide band gap semiconductor. The lower l i m i t of r a d i a t i o n w i l l depend on the i m p u r i t y - i m p u r i t y r a d i a t i v e recombination process i n e i t h e r of the two semiconductors, depending upon which semiconductor has that i m p u r i t y - i m p u r i t y p a i r t r a n s i t i o n . The important n o n - r a d i a t i v e processes are Auger and multiphonon processes. F i g . 4.15 (a) The d i f f e r e n t processes by which c a r r i e r s are created i n the d e p l e t i o n regions of the two semiconductors of a reverse b i a s e d nlnAs-pZnTe h e t e r o j u n c t i o n As y e t , r a d i a t i v e recombination at the i n t e r f a c e s t a t e s has not been obtained. In the event of such a p o s s i b i l i t y , the h e t e r o j u n c t i o n s would become important e l e c t r o l u m i n e s c e n t d e v i c e s . 5.3.1 I n t e n s i t y The i n t e n s i t y versus current v a r i a t i o n ( F i g . 4.11) at room temp-erature was given by B = k^I"'""' (equation 4.3). S i m i l a r r e l a t i o n s have been observed by Aven et a l . (1964) i n forward b i a s Cu2Se-ZnSe hetero-j u n c t i o n s . Measurements of the quantum e f f i c i e n c y were not t r i e d but i t i s expected to be low. The i n t e n s i t y - c u r r e n t c h a r a c t e r i s t i c was measured 2.25 at l i q u i d temperatures and the r e l a t i o n found was B = Vi^l . By v i s u a l comparison of the b r i g h t n e s s at room temperature and at l i q u i d N temperatures, i t seems that the quantum e f f i c i e n c y i s much l a r g e r at l i q u i d temperatures. 5.3.2 Rise and f a l l times The r i s e and f a l l times of the l i g h t pulses depend on the process of r a d i a t i v e recombination. Since the exact r i s e and f a l l times could not be measured, the d i f f e r e n t r a d i a t i v e recombination processes could not be d i s t i n g u i s h e d . However, s i n c e the r i s e and f a l l times are l e s s than 0.2p sec, one expects that a f a s t l i g h t pulse source can be made. No p u b l i s h e d data are a v a i l a b l e concerning the r i s e and f a l l times of the l i g h t pulses from a reverse b i a s e d anisotype heterojunct-'on. East-man et a l . (1964) d i d some measurements on reverse b i a s e d In-ZnTe diodes and found that the l i g h t output waveforms f o l l o w e d the input c u r r e n t and • v o l t a g e waveforms without delay. Since d i f f e r e n t peaks were observed i n the electroluminescence s p e c t r a of the reversed b i a s e d h e t e r o j u n c t i o n , the recombination of the c a r r i e r s must be through centers. The electroluminescence due to the r e -combination of the c a r r i e r s i n InAs w i l l be i n the f a r i n f r a r e d r e g i o n and hence i s not very important f o r v i s i b l e l i g h t . I t i s very important to consider the d i f f e r e n t i m p u r i t y centers i n ZnTe i n order to study the spectrum of the emitted l i g h t . D e v l i n et a l . (1967) gave a l i s t of acceptor centers i n ZnTe w i t h t h e i r i o n i z a t i o n energies and they are: vl~ .05 eV Zn \>l~ .14 eV Zn Cu .15 eV Ag .11 eV Au .22 eV F i s c h e r (1964) made high r e s i s t i v i t y n-type ZnTe by doping w i t h A l but i t s a c t i v a t i o n energy i s not known. The low r e s i s t i v i t y p-type ZnTe can be converted to high r e s i s t i v i t y p-type by doping w i t h group I I I ( I n , A l , Ga) elements. I t i s expected that the i m p u r i t i e s of group I I I act as compensated donors i n pZnTe. D e i t z et a l . (1962) observed a compensated donor or acceptor l o c a t e d about 0.4 eV below the conduction band minima i n ZnTe. The p r e c i s e nature of t h i s center i s not yet known. Since group I I I elements are s u b s t i t u t e d f o r Zn and act as donors, i t i s reasonable to assume that t h i s center i s a compensated donor i n pZnTe. With the above f i v e acceptor l e v e l s and a deep compensated donor l e v e l , the energy band diagram of ZnTe w i t h d i f f e r e n t i m p u r i t y centers i s shown i n F i g . 4.16. The f o l l o w i n g are the models by which recombination of the c a r r i e r s can take place ; 1. Band to Band Recombination model 2. Schon-Klasens Recombination model 3. Lambe-Klick Recombination model 4. Prener-Williams Recombination model . i i .048 .11 .14 .15.22 • 35-.40 2.26eV F i g . 4.16 Energy band diagram of ZnTe w i t h d i f f e r e n t acceptor and donor centers During the f a b r i c a t i o n of nlnAs-pZnTe h e t e r o j u n c t i o n s by the i n t e r f a c e a l l o y i n g technique, some In from the InAs i s d i f f u s e d i n t o the ZnTe. Since the i n t e r f a c e a l l o y i n g time i s very s h o r t , the d i f f u s e d In i s very near to the i n t e r f a c e i n ZnTe. F i g . 4.13 showed the spectrum of the emitted l i g h t at d i f f e r e n t reverse b i a s c u r r e n t s . The energy of the emitted photons was i n the range 1.7 to 3.5 eV depending on the diode c u r r e n t . At low currents (3 to 10 mA) the electroluminescence spectrum had the f o l l o w i n g peaks. ( i ) 5430°A e q u i v a l e n t to 2.28 eV ( i i ) 5640°A equ i v a l e n t to 2.20 eV ( i i i ) 5740°A eq u i v a l e n t to 2.12 eV ( i v ) 6070°A eq u i v a l e n t to 2.04 eV (v) A band 6400°A to 7300°A e q u i v a l e n t to 1.94 eV to 1.69 eV. At higher currents (30&60 mA) , there was one major peak at 6070°A (equiva-l e n t 2.04 eV)and a shoulder at. 5740°A (eq u i v a l e n t to 2.12 eV) . The d i f f e r e n t spectrum c h a r a c t e r i s t i c s at low and high currents can be expl a i n e d on the b a s i s of the energy band model of ZnTe shown i n F i g . 4.16. Thermal as w e l l as hot c a r r i e r s are created i n the d e p l e t i o n r e g i o n of the semiconductors due to the a p p l i e d f i e l d . At low f i e l d s , the thermal c a r r i e r s dominate and the recombination of thermal c a r r i e r s through a p a r t -i c u l a r center w i l l y i e l d photons of the energy corresponding to that recomb-i n a t i o n center. The peak at 2.28 eV i s due to the band to band recombination of c a r r i e r s i n ZnTe (band gap 2.26 eV). The peaks 2.20 eV, 2.12 eV and 2.04 eV are.due to recombination of the thermal e l e c t r o n s from the C.B. w i t h the thermal holes i n acceptor centers (.05 eV from the V.B.), 2-V Z n ( ° - 1 4 e V f r o m t h e v - B - ) > A u Z n (-22 e V from the V.B.) r e s p e c t i v e l y . The band i n the energy range 1.94 eV to 1.69 eV i s due to recombination of e l e c t r o n s ' 1— ? — from In center (.-35 to .4 eV from the C.B.) to holes i n the V , V , Ag A n Zn Zn Zn and Au centers. The minimum energy t r a n s i t i o n i s between In and Au ^ n Zn Zn centers and the energy of t h i s t r a n s i t i o n i s approximately given by h v ^ E g 2 - ( E I n + E A u ) • (4.56) where hv is energy of the emitted photons Eg^is the band gap energy of ZnTe E T is the ionization energy of the In center below the C.B. of ZnTe In Zn E i s the ionization energy of the Au center above the V.B. of ZnTe Au Zn 2 -3— i s the exciton energy bound to In -Au„ donor-acceptor pair r e 2 Zn Zn r i s the distance between the donor-acceptor pair &2 is the dielectric constant of ZnTe q is the electronic charge The activation energy of the In center is not exactly known but is expected to be in the range of 0.35-0.40 eV (see Fig. 4.17). Substituting the other values into equation 4.56 gives hv = 2.26 - {(0.35-0.40) + 0.22} -.02 hv =1.62 - 1.67 eV (4.57) The observed value of minimum energy is about 1.69 eV and is very close to the value estimated from equation (4.57). At high currents, the generated carriers are hot and recombination of hot carriers yields photons of energy larger than the corresponding energy of the transition. The energy distribution of the hot carriers i s usually smooth and this gives a smooth spectral distribution of emitted photons as seen in Fig. 4.13. The peak at 2.04 eV is due to the deepest acceptor center Au with activation energy 0.22 eV. The upper energy limit of electroluminescence depends on the threshold energy of the carriers to produce electron-hole pairs. The most energetic photons w i l l be due to the recombination of hot holes and hot electrons. The maximum photon energy w i l l be twice the threshold energy for pair prod-uction plus. band gap energy (assuming that the threshold energy for pair p r o d u c t i o n i s the same f o r e l e c t r o n s and h o l e s ) . The p r o b a b i l i t y of t h i s recombination i s exceedingly s m a l l (Chynoweth et a l . 1956). The maximum photon energy observed e x p e r i m e n t a l l y i s due to the recombination of one hot c a r r i e r and one thermal c a r r i e r and i s equal to the t h r e s h o l d energy f o r p a i r - p r o d u c t i o n plus band gap energy. The assumption of recombination of one hot and one thermal c a r r i e r i s w e l l j u s t i f i e d f o r Schon-Klasens and Lambe-Klick recombination processes. The maximum energy of the observed electroluminescence was 3.5 eV which gives about 1.26 eV f o r the t h r e s h o l d energy f o r p a i r p r o d u c t i o n i n ZnTe. The reported maximum energy photons i n reverse biased p-n homo-j u n c t i o n s i n S i and GaP are 3.4 and 3.0 eV, r e s p e c t i v e l y and the observed valu e of 3.5 eV f o r ZnTe i s q u i t e compatible w i t h these v a l u e s . 6. Summary and c o n c l u s i o n ZnTe ( I I - V I compound) and InAs (HI-V compound) have almost the same l a t t i c e constant and c r y s t a l s t r u c t u r e , and are a good p a i r of semi-conductors f o r a h e t e r o j u n c t i o n . The nlnAs-pZnTe h e t e r o j u n c t i o n s were made by the i n t e r f a c e a l l o y i n g technique. These h e t e r o j u n c t i o n s were mounted on t r a n s i s t o r headers w i t h proper ohmic c o n t a c t s . The c u r r e n t - v o l t a g e , c a p a c i t -ance-voltage and reverse b i a s electroluminescence c h a r a c t e r i s t i c s were measured. The forward b i a s c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s were s t u d i e d at d i f f e r e n t temperatures. At low v o l t a g e s (- 0.1 v o l t ) the curr e n t i s given eV by I = I 0 exp where n v a r i e s from 2.38 to 3.22 as the temperature i s nkT increased from 235°K to 368°K. At higher v o l t a g e s (- 1 v o l t ) the r e l a t i o n i s I >= I 0 exp AV where A v a r i e s from 2.13 to 1.90. The values of n and A suggest that the current i s dominated by a recombination-generation mechanism ( i n the t r a n s i t i o n region) at lower voltages, and at higher voltages the current i s due to the tunneling of c a r r i e r s . In reverse bias conditions the current i s approximated by a power law I = KV n. The value of n varies from about 1 to 2.5 as the voltage i s increased. The value of n - 2.5 i s observed at a l l temperatures (235°K to 368°K) but the voltage at which n 2.5 i s observed to be higher at high temperatures. An energy band model with i n t e r f a c e states i s proposed for nlnAs-pZnTe heterojunctions. Expressions f o r the forward bias current-voltage r e l a t i o n s were derived on the basis of the theory discussed i n chapter II and the general nature of the expressions i s very s i m i l a r to the experimentally observed behaviour of the current-voltage r e l a t i o n discussed above. The reverse bias current voltage r e l a t i o n s were derived on the basis of tunneling of electrons from the ZnTe valence band to the InAs conduction band and the f i n a l expression i s of the form of a power law with n = 2.5. Capacitance-voltage (along with a.c. conductance-voltage) charact-e r i s t i c s were measured i n the frequency range 5 — 500 kHz. The capacitance 2 decreased with reverse bias voltage and the 1/C versus V c h a r a c t e r i s t i c s 2 were s t r a i g h t l i n e s . The c a r r i e r density i n ZnTe as measured from the 1/C versus V c h a r a c t e r i s t i c s was l e s s than the assumed c a r r i e r density and the b u i l t - i n voltage was higher than the expected value. The low c a r r i e r density 2 from the 1/C versus V c h a r a c t e r i s t i c s could have been caused by i n t e r f a c e states or non-uniformity of the j u n c t i o n . The reason for the large b u i l t - i n voltage i s not understood. Light emission was observed at the heterojunctions under the reverse bias conditions. The l i g h t emission threshold detected by the photomultiplier was at • about 6 v o l t s and 1 mA and there was no detectable l i g h t up to 70 mA under forward bias conditions. The reverse biased emission i n t e n s i t y versus c u r r e n t r e l a t i o n at room temperature was approximately given by B = constant I''""' w h i l e the r e l a t i o n was of higher power at l i q u i d temperatures. The r i s e and f a l l times of the l i g h t pulses were s t u d i e d by modifying the out-put c i r c u i t of the p h o t o m u l t i p l i e r and were found to be l e s s than 0.2p sec. The reverse b i a s spectrum was observed at d i f f e r e n t c u r r e n t s from 3 mA to 60 mA. S e v e r a l peaks were observed at low currents (3 to 10 mA) but at h i g h c u r r e n t s (30 mA and above) only one peak at 2.04 eV was observed. The observed peaks were i d e n t i f i e d w i t h the known i m p u r i t y centers i n ZnTe reported i n d i f f e r e n t papers and a complete model f o r the i m p u r i t y centers i n ZnTe was proposed. The lower energy l i m i t of the emitted photons obtained from the model i s i n good agreement w i t h the e x p e r i m e n t a l l y observed l i m i t . V. pGe-CdS (PHOTOSENSITIVE) HETEROJUNCTIONS 1. I n t r o d u c t i o n This chapter d e s c r i b e s the p r e p a r a t i o n , p r o p e r t i e s and theory of pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n s . The p h o t o s e n s i t i v e p r o p e r t i e s of I I - V I compounds have been the subject of much study f o r a long time (Ray 1969). A systematic under-standing of the p r o p e r t i e s r e l a t e d to t h e i r e l e c t r o n i c s t r u c t u r e has how-ever been spurred only r e c e n t l y w i t h the advance of s i n g l e c r y s t a l growth techniques f o r I I - V I compounds (Bube 1960 and 1967). The CdS i s a good p h o t o s e n s i t i v e semiconductor but i t can only be made i n t o n type w i t h low r e s i s t i v i t y . There i s no s e l e c t i v e evidence of p type CdS but Spear et a l . (1963) measured the low d r i f t m o b i l i t y of holes i n h i g h r e s i s t i v i t y samples. Homojunctions of CdS.-have not been made and most of the photo-s e n s i t i v e devices made w i t h CdS are e i t h e r photoconductors or hetero-j u n c t i o n s w i t h some other low r e s i s t i v i t y p type semiconductor. Cu2S-CdS h e t e r o j u n c t i o n s have been s t u d i e d e x t e n s i v e l y ( G i l l et a l . 19 69, S e l l e et a l . 1967 and Cusano 1967) w i t h c o n s i d e r a t i o n f o r t h e i r p h o t o v o l t a i c p r o p e r t i e s i n e f f i c i e n t s o l a r energy conversion. The other reported h e t e r o j u n c t i o n s o f CdS are: PbS-CdS (Watanabeet a l . 1970), CdS-CdTe (Dutton et a l . 1968 and A d i r o v i c h et a l . 1969), CdS-ZnTe (Aven et a l . 1963), CdS-CdSe (Kandilovou et a l . 1965), CdS-SiC ( Salkou 1965) and CdS-Si (Okimura 1970, Okimura et a l . 1967 and Brojdo et a l . 1965) and Ge-CdS (Okimura 1968). The Ge-CdS j u n c t i o n s s t u d i e d by Okimura were n-n type. There have not been any previous r e p o r t s on pGe-CdS h e t e r o j u n c t i o n s . The pGe-CdS h e t e r o j u n c t i o n s were made by the a l l o y i n g technique? and t h e i r c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s and capacitance at d i f f e r e n t i l l u m i n a t i o n - i n t e n s i t i e s were s t u d i e d . The energy band model, eq u i v a l e n t c i r c u i t and theory of the h e t e r o j u n c t i o n s are d i s c u s s e d . 2. Sample p r e p a r a t i o n and contacts The pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n s were made by a l l o y i n g p type Ge on p h o t o s e n s i t i v e CdS. The Ge and CdS s l i c e s were p o l i s h e d and cut i n t o pieces as described i n chapter IV. Since the photo-s e n s i t i v e p r o p e r t i e s of I I - V I compounds change when annealed, a l l o y i n g was achieved i n such a way that the CdS was kept at r e l a t i v e l y low temperatures. A gra p h i t e boat of s p e c i a l shape was made as shown i n F i g . 5.1. I t had a c a v i t y w i t h two depressions AB and CD carved i n the. boat (Dimensions i n mm) Fig., 5.1 A sketch of the gr a p h i t e boat w i t h Ge and CdS (a) Top view (b) Side view AB. The Ge and CdS were kept crosswise as shown i n F i g . 5.1 ( a ) . The depth of depression CD was equal to the t h i c k n e s s of the Ge s l i c e so that the p o l i s h e d surfaces of Ge and CdS were touching each other. Approximate dimensions of the boat are shown i n the f i g u r e . The other a l l o y i n g c o n d i t i o n s were the same as those mentioned i n chapter IV. The current through the g r a p h i t e heater was turned o f f as soon as the Ge s t a r t e d to melt. The r e s i s t i v i t y of the p type Ge was about 0.5 ohm-cm and that of the p h o t o s e n s i t i v e CdS^ was g r e a t e r than 2 x 10^ ohm-cm i n the 2 dark. Assuming a h o l e m o b i l i t y i n Ge of 1200 cm / v o l t - s e c and an 2 e l e c t r o n m o b i l i t y i n CdS of 110 cm , / v o l t - s e c (Bube 1960), the h o l e 16 3 c o n c e n t r a t i o n i n the p type Ge was 6.9 x 10 /cm and the e l e c t r o n 10 3 c o n c e n t r a t i o n i n the CdS was not greater than 3 x 10 /cm . Indium was a l l o y e d to make ohmic contacts to the p type Ge as w e l l as to the CdS (Smith 1955). Indium i s a shallow acceptor i m p u r i t y + i n Ge and makes i t p Ge at the contact. Indium i s a l s o a donor i m p u r i t y i n CdS. The work f u n c t i o n of indium (<bT' ) i s about 4.1 eV and the e l e c t r o n Y I n a f f i n i t y of CdS ( X P J Q ) 1 S about 4.5 eV (see s e c t i o n 5 of the current chapter). The d i f f e r e n c e ( ^ T n ' X r j d s ^ "'"S n e S a t l v e a n <* indium makes ohmic contacts w i t h CdS. The devices were mounted on TO-5 t r a n s i s t o r headers. 3. Experimental procedures 3.1 Current-voltage c h a r a c t e r i s t i c s The c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of the devices were studied p type Ge obtained from Semi-Elements , Inc., Pa. ^ P h o t o s e n s i t i v e CdS obtained from E a g l e - P i c h e r , Miami, Oklahoma. by using a T e k t r o n i x 575 curve t r a c e r and a l s o by t r a c i n g c u r r e n t - v o l t a g e graphs on a Moseley (model 135) x-y r e c o r d e r . The f u n c t i o n generator 202A (Hewlett _ Packard) w i t h t r i a n g u l a r output at 0.01 Hz was used as a v o l t a g e source and a K e i t h l e y ammeter (150A) f o r cur r e n t measurements. 3.2 Capacitance The capacitance and a.c. conductance of the pGe-CdS h e t e r o j u n c t i o n s were measured by G.R. 1615A bri d g e w i t h G.R. 1210C s i g n a l generator and G.R. 1232A tuned a m p l i f i e r and n u l l d e t e c t o r . The capacitance was measured i n the frequency range 1 to 100 kHz. Reverse b i a s capacitance versus v o l t a g e c h a r a c t e r i s t i c s were measured by a m o d i f i c a t i o n i n the b r i d g e c i r c u i t . The br i d g e accuracy f o r capacitance measurements was w i t h i n +5%. A l l the capacitance measurements were done by the three t e r m i n a l method. 3.3 R e l a t i v e i l l u m i n a t i o n i n t e n s i t y A tungsten halogen lamp ( S y l v a n i a DVY 47-24) was used as an i l l u m i n a t i n g source. The r e l a t i v e i l l u m i n a t i o n i n t e n s i t y was v a r i e d by Kodak n e u t r a l d e n s i t y f i l t e r s (No. 96). F i l t e r s of n e u t r a l d e n s i t y 3.00 to 0.10 were used to o b t a i n r e l a t i v e i l l u m i n a t i o n i n t e n s i t y i n the range of 0.1% to 80%. I l l u m i n a t i o n without any f i l t e r was taken as 100% and i t i s denoted by I i n the subsequent s e c t i o n s . The l e v e l of I was o . o changed by c o n t r o l l i n g the input v o l t a g e of the i l l u m i n a t i n g lamp. The lamp was cooled by a fan and i t s l i g h t was passed through water to absorb heat r a d i a t i o n . The CdS s i d e of the devices faced the light beam (unfocussed) from the lamp. A l l the measurements were made i n a darkroom. 4. Results 4.1 Current-voltage c h a r a c t e r i s t i c s • . F i g . 5.2 shows the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of a t y p i c a l pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n at v a r i o u s i l l u m i n a t i o n i n t e n s i t i e s . I0 : INTENSITY FROM THE SOURCE OPERATING AT 90 VOLTS ID : NO ILLUMINATION h < 0. 001 0.001 0.01 h h - 0.10 MP 0. IS h - A, h - 0-40 0.80 h Uj CURR • 2.0 -15 -10 -0.5 REVERSE 0.5 1.0 1.5 2. •100 FORWARD Fig. VOLTAGE (VOLTS) 5.2 Current-voltage c h a r a c t e r i s t i c s of a pGe-CdS (photosensitive) heterojunction at various r e l a t x v e i l l u m i n a t i o n i n t e n s i t i e s (source voltage 90 v o l t s ) M F i g . 5.3 Current-voltage c h a r a c t e r i s t i c s of a pGe-CdS (photosensitive) heterojunction at ^ various r e l a t i v e i l l u m i n a t i o n i n t e n s i t i e s (source voltage 35 v o l t s ) to CL g JO -4 10 -5 INT. A to ' 5.60 h 5.J5 h 5-35 T3 4.73 J4 4. 42 VALUES OF A AT DIFFERENT INTENSITIES W 0.0 0.1 0.2 0.3 0.4 0-5 0.6 0.7 0.8 0.9 1.0 FORWARD BIAS . (VOLTS ) 1.1 1.2 1.3 1.4 Fig. 5.4 Current-voltage characteristics of a pGe-CdS (photosensitive) heterojunction at various illumination intensities (source voltage 90 volts) CD CAPACITANCE fPICO: FARADS) Kj Co CD CD 1— CD H-OP m • V o fD &) rt T3 (0 ff> H • O O H1-<_J. r t C n o CD ti o < 3 ft) H 0 01 fD e CO CO C i-S H fD fD M Cu P> Pi rt < fD(-» O K-O P S rt a N fD 2 C"-i CO w H-rt O Ml CO h3 O fD I 1 o CO O fD ^ 3 cn r rt < fD \ \ CAPACITANCE (PICO FARADS) CD ~ i — en c 3 n O 3 NO 0.01 0.10 UOO 10.00 100.00 RELATIVE INTENSITY (ARBITRARY UNITS) F i g . 5.6 (a) A.C. conductance (lOOKHz) and r e c t i f i c a t i o n r a t i o (D.C.) versus r e l a t i v e i n t e n s i t y of a pGe-CdS (ph o t o s e n s i t i v e ) h e t e r o j u n c t i o n • ; M F i g . 5.6 (b) A.C. c o n d u c t a n c e (lOOKHz) versus r e l a t i v e I n t e n s i t y o f a pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n • r n l] = NORMAL ROOM LIGHT A' 12 - -063 J0 ' 13 = .020 rG i4 - -ow i0 TD NO ILLUMINATION (DARK) RELATIVE RELATIONS IB>I1> I2 >I3>I4>ID Tn ILLUMINATION FROM THE LAMP OPERATING AT 35 VOLTS IR ILLUMINATION FROM THE LAMP OPERATING AT 90 VOLTS o.o 0.20 0.40 0.60 REVERSE BIAS 0.80 TOO 1.20 VOLTAGE (VOLTS) 1.40 1.60 F i g . 5.7 Reverse b i a s capacitance versus v o l t a g e c h a r a c t e r i s t i c s of pGe-CdS (ph o t o s e n s i t i v e ) h e t e r o j u n c t i o n at v a r i o u s r e l a t i v e i n t e n s i t i e s 1,50 100 0-50 REVERSE 0.00 0.50 1.00 FORWARD (VOLTS) 1.50 2.00 F i g . 5.8 1/C versus V c h a r a c t e r i s t i c s of a pGe-CdS ( p h o t o s e n s i t i v e ) hetero-The l i g h t i n t e n s i t y was increased from I to 1^ and the r e l a t i o n s between d i f f e r e n t r e l a t i v e i n t e n s i t i e s are shown i n the f i g u r e . I n t e n s i t y I corresponds to no i l l u m i n a t i o n and I to the i n t e n s i t y of the lamp operating at 90 v o l t s without any i n t e n s i t y reducing f i l t e r . F i g . 5.3 shows the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of the same j u n c t i o n at a sm a l l e r v a l u e of I (lamp o p e r a t i n g at 35 v o l t s ) . The forward b i a s e d c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of F i g . 5.2 at high i n t e n s i t i e s (1^ to I ) are p l o t t e d i n a semi-log p l o t i n F i g . 5.4. At lower v o l t a g e s the c u r r e n t - v o l t a g e r e l a t i o n can be expressed as J = J exp AV o where, V i s the a p p l i e d v o l t a g e , A i s a parameter, i s the e x t r a p o l a t e d value of J at V = 0, and J i s the current The values of A f o r d i f f e r e n t i n t e n s i t i e s were obtained from the slopes of the c h a r a c t e r i s t i c s and are shown i n F i g . 5.4. 4.2 Capacitance and a.c. conductance F i g . 5.5 (a) shows the capacitance versus l o g ( r e l a t i v e i l l u m i n a t i o n i n t e n s i t y ) c h a r a c t e r i s t i c f o r the pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n s . The capacitance increased r a p i d l y at low i l l u m i n a t i o n i n t e n s i t i e s but s t a r t e d s a t u r a t i n g at higher v a l u e s . This i s c l e a r i n F i g . 5.5 (b) where capacitance versus r e l a t i v e i l l u m i n a t i o n i n t e n s i t y i s p l o t t e d f o r the same diode. F i g . 5.6 (a) shows a.c. conductance versus l o g ( r e l a t i v e I l l u m i n a t i o n i n t e n s i t y ) c h a r a c t e r i s t i c . The a.c. conductance of the devices shown i n F i g . 5.6 (a) was measured along x<?ith the capacitance shown i n F i g . 5.5 ( a ) . The a.c. conductance increased w i t h i n t e n s i t y at i n t e n s i t i e s (I to I_) and again s t a r t e d i n c r e a s i n g at very high i n t e n s i t i e s (above I ). This behaviour of a.c. conductance at low i n t e n s i t i e s can be seen much b e t t e r i n the conductance versus r e l a t i v e i l l u m i n a t i o n c h a r a c t e r i s t i c i n F i g . 5.6 ( b ) . F i g . 5.5 (a) shows a l s o the v a r i a t i o n of r e c t i f i c a t i o n r a t i o B w i t h the r e l a t i v e i n t e n s i t y obtained from F i g . 5.2. The r e c t i f i c a t i o n r a t i o B at a p a r t i c u l a r i n t e n s i t y i s defined as B = reverse forward where, R i s the d.c. r e s i s t a n c e of the j u n c t i o n under a reverse reverse b i a s of 1.0 v o l t , and R„ , i s the d.c. r e s i s t a n c e of the j u n c t i o n under a forward forward b i a s of 1.0 v o l t . The r e c t i f i c a t i o n r a t i o B was approximately equal to u n i t y up to i n t e n s i t y I ( F i g . 5.6 (a)) and s t a r t e d i n c r e a s i n g at higher i n t e n s i t i e s . A r e c t i f i c a t i o n B r a t i o of up to 20 was obtained. Fig.; 5.7 shows the reverse b i a s capacitance versus v o l t a g e charac-t e r i s t i c s measured at 100 kHz f o r v a r i o u s values of r e l a t i v e i l l u m i n a t i o n i n t e n s i t i e s . The f o l l o w i n g are the important o b s e r v a t i o n s . a) There was no change of capacitance w i t h v o l t a g e i n the dark (I i n F i g . 5.7). b) The capacitance was found to i n c r e a s e w i t h the i l l u m i n a t i o n i n t e n s i t y . c) For a p a r t i c u l a r i l l u m i n a t i o n i n t e n s i t y , the capacitance decreased w i t h the i n c r e a s e c f a p p l i e d reverse b i a s v o l t a g e i n i t i a l l y but at higher i n t e n s i t i e s , i t s value s a t u r a t e d . d) I t was also f ound that the variation -of capacitance w i t h v o l t a g e i s more prominent at higher i n t e n s i t i e s . Furthermore the v o l t a g e at which capacitance s t a r t e d to s a t u r a t e increased w i t h the i n t e n s i t y . 2 F i g . 5.8 shows the 1/C versus V c h a r a c t e r i s t i c s ( 1 ^ , I ^ , I ^ 2 and I ). The 1/C versus V c h a r a c t e r i s t i c s were p l o t t e d f o r low reverse lj b i a s voltages where an a p p r e c i a b l e decrease i n capacitance was observed.. 5. . D i s c u s s i o n 5.1 I-V C h a r a c t e r i s t i c s I t may be noted from F i g . 5r2 and 5.3 that the pGe-CdS (p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n i s n o n - r e c t i f y i n g i n the dark and at low i l l u m i n a t i o n i n t e n s i t i e s , but becomes r e c t i f y i n g as the i l l u m i n a t i o n i n t e n s i t y i s i n c r e a s e d . In F i g . 5.6 ( a ) , the a.c. conductance inc r e a s e s from g 4 to g„ as the i n t e n s i t y i s increased from I. to L but the j u n c t i o n A B J • A B J i s s t i l l n o n - r e c t i f y i n g .As the i n t e n s i t y i s increased above I , the B a.c. conductance drops and the j u n c t i o n becomes r e c t i f y i n g . The r e c t i -f i c a t i o n r a t i o i n c r e a s e s w i t h the i l l u m i n a t i o n i n t e n s i t y and at very h i g h i n t e n s i t i e s i t s a t u r a t e s (not shown i n . the f i g u r e ) . E l e c t r o n - h o l e p a i r s are generated i n CdS due to i l l u m i n a t i o n . The holes are captured by s e n s i t i z i n g centers immediately a f t e r the c r e a t i o n of the e l e c t r o n - h o l e p a i r s w h i l e e l e c t r o n s remain i n the conduction band (Bube 1967). The e l e c t r o n s spend more time i n the conduction band as compared to the time spent by the holes i n the valence band of CdS before they are trapped. The approximate values of these times are 10 m sec f o r e l e c t r o n s and lusec f o r holes (Ray B r a i n 1969). The steady s t a t e - e l e c t r o n d e n s i t y (n) and h o l e d e n s i t y (p.) created i n CdS due to the i l l u m i n a t i o n are given by n = f x n (5.1) p = f T p (5.2) T r is the time spent by the photo generated electrons in the conduction band before recombining, T is the time spent by the photo generated holes in the v&lence band before trapping, and f i s the electron-hole pair generation rate due to illumination i n CdS. Since T >> x , i t is seen that n>>p and the photosensitive n p CdS under illumination behaves as n type provided the photo generated electron density n is greater than the carrier density of CdS in the dark. The pGe-CdS (photosensitive) structure becomes a pGe-nCdS_ heterojunction under illumination. The r e c t i f i c a t i o n ratio depends on the density of the carriers in CdS under steady state conditions. The steady state electron density increases with the illumination intensity but i t saturates at very high intensities. The saturation of the steady state electron, density with intensity is perhaps due to.the f i l l i n g of the sensitizing centers with holes. No illumination The electron a f f i n i t y of the two semiconductors must be known for drawing energy band diagrams of the heterojunction, but the electron a f f i n i t y of CdS is not exactly known. The reported values of the latter range between 4.0 and 4.8 eV (Okimura et a l . 1970, Swank et a l . 1967, Brojdo et a l . 1965 and Aven et a l . 1963) but a value between 4.5 and 4.8 eV is more acceptable. The values of E..-E for p type Ge and of E -Er f v ' J t f . • Q f for photosensitive CdS were calculated from the manufacturer's specifications and they are: 0.16 eV and 0.47 eV, respectively. F i g . 5.9 (a) shows an energy band diagram of the two i s o l a t e d semiconductors and F i g . 5.9 (b) shows the energy band diagram of the h e t e r o j u n c t i o n at e q u i l i b r i u m . Accumulation l a y e r s are formed i n the Ge and CdS at the i n t e r f a c e , a n d an excess of e l e c t r o n s ( m a j o r i t y c a r r i e r s ) i n the CdS and of holes ( m a j o r i t y c a r r i e r s ) i n the Ge form a d i p o l e l a y e r at the i n t e r f a c e . The accumulation l a y e r i n p type Ge r e s u l t s i n a d e p l e t i o n of e l e c t r o n s near the i n t e r f a c e i n the Ge. Since there i s a l a r g e b a r r i e r f o r the holes going from the valence band of Ge to the valence band of CdS and there are r e l a t i v e l y no holes a v a i l a b l e i n the CdS to go i n t o the valence band of Ge, the c u r r e n t w i l l be mostly due to the t r a n s p o r t of e l e c t r o n s from the conduction band of CdS to Ge and v i c e v e r s a . At e q u i l i b r i u m , the number of e l e c t r o n s going from the CdS to the Ge and v i c e v e r s a are ..equal and the net current i s zero. , For forward b i a s i n j e c t i o n l e v e l s i n which the i n j e c t e d e l e c t r o n d e n s i t y from the CdS to the Ge i s l e s s than the e l e c t r o n d e n s i t y i n the Ge, the j u n c t i o n w i l l behave l i k e an n-n h e t e r o j u n c t i o n . Since the d i s c o n t i n u i t y i n the conduction bands at the i n t e r f a c e i s s m a l l (AE^-0.25 eV), the c u r r e n t v o l t a g e c h a r a c t e r i s t i c s w i l l be ohmic. The e l e c t r o n d e n s i t y i n 8 3 10 3 Ge i s 5 x 10 /cm. and t h a t i n CdS i s 3 x 10 /cm i n the b u l k m a t e r i a l s . In t h i s h e t e r o j u n c t i o n , Ax(where, Ax= Xp ~ Xpjc) 1 5 negative (see F i g . 5. 9 ( a ) ) . Hence higher v o l t a g e s w i l l be r e q u i r e d to i n j e c t e l e c t r o n s from the CdS conduction band to the Ge conduction band. Due to low e l e c t r o n d e n s i t i e s i n the conduction bands of Ge and CdS, the c u r r e n t d e n s i t y i s very low i n the dark. Under i l l u m i n a t i o n : The e l e c t r o n d e n s i t y i n the p h o t o s e n s i t i v e CdS under i l l u m i n a t i o n can be represented by a.quasi Fermi l e v e l i n the band diagram. As the VACUUM LEVEL X] = 4.25 X2=4.50 Xj nGe=5xW8 10 •cl Ef. ^9 '.ill'15 V 1 nCdS=3*10 Ec2 •c2 .47 -F JGe = 1.2x1016 E. vl g2=2.4 v2 Ge CdS (PHOTOSENSITIVE) (a) AE, c2 v2 pGe- CdS (PHOTOSENSITIVE) (b) F i g . 5 . 9 Energy band diagram of pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n VACUUM LEVEL VACUUM LEVEL — VACUUM LEVEL x> Xi X, X 2 •f v! •ch :c2 :v2 fa) LOW INTENSITY Ev1 > I Er c2 Evf E, v2 (b) MEDIUM INTENSITY 1^2 v2 (c) HIGH INTENSITY F i g . 5.10 Energy band diagram of pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n at low, medium and high i n t e n s i t i e s i n t e n s i t y , of i l l u m i n a t i o n i s i n c r e a s e d , the quasi Fermi l e v e l f o r e l e c t r o n s i n the p h o t o s e n s i t i v e CdS moves towards the conduction band. In the dark and at low i l l u m i n a t i o n i n t e n s i t i e s ( l e s s than I i n F i g . 5.6 ( a ) ) , the quasi Fermi l e v e l i n CdS i s below the Fermi l e v e l i n Ge as shown i n F i g . 5.9. Furthermore, the i n j e c t e d e l e c t r o n d e n s i t y from the CdS to the Ge under forward b i a s c o n d i t i o n s i s much l e s s than the e l e c t r o n d e n s i t y i n Ge. The I-V c h a r a c t e r i s t i c s of the pGe-CdS are n o n - r e c i t i f y i n g . As the i n t e n s i t y i s increased (to approximately I ), the q u a s i Fermi l e v e l i n CdS l i n e s up w i t h the Fermi l e v e l i n pGe, and the bands i n the band diagram of the h e t e r o j u n c t i o n are f l a t as shown i n F i g . 5.10 ( a ) . There i s no d i p o l e l a y e r at the i n t e r f a c e . The i n j e c t e d e l e c t r o n d e n s i t y from CdS to Ge under forward b i a s c o n d i t i o n s , and that from Ge to CdS under reverse b i a s c o n d i t i o n s , are of the same order ( s t i l l l e s s than the e l e c t r o n d e n s i t y i n Ge), and the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of pGe-CdS are s t i l l n o n - r e c t i f y i n g . As the i l l u m i n a t i o n i s increased f u r t h e r to medium i n t e n s i t i e s ( i . e . , above I but below I ) is L the CdS becomes more n type and the quas i Fermi l e v e l i n the CdS moves above the Fermi l e v e l i n the Ge. At t h i s stage, the d e p l e t i o n regions are formed i n the two semiconductors at the i n t e r f a c e and a b u i l t - i n v o l t a g e i s developed ( F i g . 5.10 ( b ) ) . At medium i n t e n s i t i e s , the d e n s i t y of e l e c t r o n s i n j e c t e d i n t o pGe from the CdS i s comparable to the d e n s i t y of e l e c t r o n s i n the Ge, and the r e c t i f i c a t i o n r a t i o s t a r t s i n c r e a s i n g ( F i g . 5.6 ( a ) ) . As the i n t e n s i t y i s increased f u r t h e r ( i . e . , above I , to high i n t e n s i t i e s ) , the steady s t a t e e l e c t r o n d e n s i t y i n CdS becomes con s i d e r a b l y high ( F i g . 5.10 ( c ) ) . The d e n s i t y of the i n j e c t e d e l e c t r o n s from the CdS to the Ge i s much more than the d e n s i t y of e l e c t r o n s i n Ge and a high r e c t i f i c a t i o n r a t i o i s obtained. At very high i n t e n s i t i e s (not shown i n the F i g . 5.6 ( a ) ) , the time spent by the holes i n the valenceband of CdS incr e a s e s due to f i l l i n g of the s e n s i t i z i n g c e n t e r s . The steady s t a t e d e n s i t y of the holes i s reasonably high (but s t i l l l e s s than that of e l e c t r o n s ) . Under reverse b i a s c o n d i t i o n s , the holes and e l e c t r o n s are separated by the f i e l d and the reverse b i a s c u r r e n t i s h i g h , which l i m i t s the r e c t i f i c a t i o n r a t i o to low v a l u e s . The expression f o r the cur r e n t d e n s i t y i n the pGe-nCdS hetero-j u n c t i o n s at a p a r t i c u l a r i n t e n s i t y I i s -given by ( s e c t i o n 2.2 of chapter I I , assuming ^ c i ~ ^ c 2 ^ e n 2 ( I ) e V D ( I ) + A E C E V J N ( D = — J exp[-{ ^ }]{exp^ -1} n where, n 2 ( I ) i s the steady s t a t e e l e c t r o n d e n s i t y i n the CdS at i n t e n s i t y I , V Q ( I ) i s the b u i l t - i n v o l t a g e i n pGe-nCdS at i n t e n s i t y I , T i s the l i f e t i m e o f . e l e c t r o n s i n the pGe, n V i s the a p p l i e d forward b i a s , and e, T and A E have c t h e i r u s u a l meanings. T CTv e n 2 ( I > " A E c E V » ( I ) / E V - I T . n eV For a p p l i e d v o l t a g e s such that exp—~—>>1, the above equation kT reduces to where, J n< 1 > = J n o ( I ) 6 X P f ( 5- 3> A E C - e V D ( I ) J n o ( I ) = 7 n n 2 ( I ) E X P " I T E X P — W The recombination-generation c u r r e n t at the i n t e r f a c e s t a t e s and i m p u r i t y centers i n the t r a n s i t i o n r e g i o n w i l l be of the form (from chapter 2 ) , . J r g ( I ) • J r g o ( D « P f T (5.4) and the t o t a l c u r r e n t at a particular i n t e n s i t y I w i l l be J ( I ) - J o ( I ) exp ^ (5,5) or J ( I ) - J (I) exp AV (5.6) where e A n k T Here n and A are the constants independent of i l l u m i n a t i o n i n t e n s i t y . The values of A f o r d i f f e r e n t values of i l l u m i n a t i o n i n t e n s i t i e s were found from l o g (c u r r e n t ) versus v o l t a g e c h a r a c t e r i s t i c s . F i g . 5.4 shows that the valu e of A v a r i e d from 5.35 to 5.6 as the i n t e n s i t y was changed from 0.401 to I . At a lower, i n t e n s i t y of 0.101 , the v a l u e "• o o o* of A was found to be about 4.42. The s m a l l e r v a l u e of A was perhaps due to the high r e s i s t i v i t y of the b u l k CdS.. For higher i n t e n s i t i e s , the value of A was almost constant. 5.2 Equivalent c i r c u i t The e q u i v a l e n t c i r c u i t s of pGe-CdS ( p h o t o s e n s i t i v e ) devices under d i f f e r e n t i n t e n s i t i e s of i l l u m i n a t i o n corresponding to F i g . 5.10 ( a ) , 5.10 (b) and 5.10 (c) are shown i n F i g . 5.11 ( a ) , 5.11 (b) and 5.11 ( c ) , r e s p e c t i v e l y . C, LOW Cj(I) Cj LAA J Gj (I) Gj MEDIUM Cj(I) LAA J Gj(I) HIGH F i g . 5.11 Equivalent c i r c u i t of pGe-CdS ( p h o t o s e n s i t i v e ) at low (and d a r k ) , medium and high i l l u m i n a t i o n i n t e n s i t i e s With r e f e r e n c e to F i g . 5.6 ( a ) , the r e l a t i v e i n t e n s i t y range i s d i v i d e d i n t o three regions and they are: Low, I , to I ; Medium, I„ & j ' A B B to I ; High, higher than I . Under dark and low i n t e n s i t i e s ( u n t i l the bands become f l a t ) , the Ge makes ohmic contact w i t h CdS and the measured capacitance (C-j.) and conductance (G^) are those of bulk CdS as shown i n F i g . 5.11 (a). The in c r e a s e . o f capacitance and a.c. conductance from dark to i n t e n s i t y I i s due to an i n c r e a s e i n the capacitance and conduc-B tance of the bulk CdS. At medium i n t e n s i t i e s (I to I ), the j u n c t i o n B C i s formed and i t i s i n s e r i e s w i t h the bulk CdS and the eq u i v a l e n t c i r -c u i t i s a s e r i e s combination of the e q u i v a l e n t c i r c u i t s of the j u n c t i o n and the bulk CdS as shown i n F i g . 5.11 (b). The capacitance and conduc-tance of the j u n c t i o n are denoted by C^(I) and G^(I) r e s p e c t i v e l y . Here the capacitance and conductance of both j u n c t i o n and bulk are f u n c t i o n s of i l l u m i n a t i o n i n t e n s i t y . At higher i n t e n s i t i e s , the bulk CdS becomes l e s s r e s i s t i v e so that the e f f e c t of i t s c a p a c i t a n c e - i s n e g l i g i b l e compared to i t s conductance. Hence the e q u i v a l e n t c i r c u i t of the device i s that of the j u n c t i o n i n s e r i e s w i t h conductance of b u l k CdS as shown i n F i g . 5.11 ( c ) . 5.3 Capacitance The v a r i a t i o n of capacitance w i t h i l l u m i n a t i o n i n t e n s i t y ( F i g . 5.5 (a) and (b)) can be obtained from the e q u i v a l e n t c i r c u i t s drawn at d i f f e r e n t i n t e n s i t i e s . I n the dark and at low i n t e n s i t i e s , the capacitance i s due to bulk CdS. The capacitance of the b u l k CdS i n c r e a s e s r a p i d l y w i t h i n t e n s i t y . At medium i n t e n s i t i e s , the t o t a l capacitance i s a s e r i e s combination of the j u n c t i o n capacitance and the b u l k CdS capacitance ( F i g . 5.10 ( b ) ) . At high i n t e n s i t i e s , the CdS becomes l e s s r e s i s t i v e and the capacitance i s only that of the j u n c t i o n . Since the e l e c t r o n d e n s i t y i n CdS s a t u r a t e s at very high i n t e n s i t i e s , so does the capacitance. The v a r i a t i o n of capacitance w i t h reverse b i a s v o l t a g e ( F i g . 5.7) i s a l s o explained by the e q u i v a l e n t c i r c u i t s . Since capacitance i n the dark i s due to b u l k C dS, . i t does not vary w i t h reverse b i a s v o l t a g e . At high i n t e n s i t i e s , the capacitance i s due to the formed j u n c t i o n and a v a r i a t i o n of the capacitance w i t h v o l t a g e i s observed. At medium i n t e n s i t i e s , due to the v a r i a t i o n of the j u n c t i o n capacitance, the t o t a l capacitance v a r i e s w i t h the v o l t a g e but t h i s v a r i a t i o n i s observed only f o r very s m a l l v o l t a g e s . Since j u n c t i o n capacitance i s observed only at h i g h i n t e n s i t i e s , 2 the 1/C versus V c h a r a c t e r i s t i c s are expected to be s t r a i g h t l i n e s only at high i n t e n s i t i e s , assuming that the steady s t a t e e l e c t r o n d e n s i t y i n 2 CdS due to the i l l u m i n a t i o n i s uniform. Fig..5.8 shows the 1/C versus V c h a r a c t e r i s t i c s f o r a few high i n t e n s i t y capacitance versus v o l t a g e measure-ments (obtained from F i g . 5.7). The reverse b i a s capacitance (per u n i t area) of p-n he t e r o -junctions i s given by (chapter 2) 1/2 m r e N A l N D 2 ( I ) £ 1 £ 2 - ' 1 1 °* " L 2 { £ l N A i + £ 2 N D 2 ( I ) } V I ) + V • ( } where S u b s c r i p t 1 r e f e r s to Ge and 2 r e f e r s to CdS and i s the i o n i z d d acceptor c o n c e n t r a t i o n i n the pGe, N ^ ( I ) i s the e f f e c t i v e i o n i z e d donor c o n c e n t r a t i o n i n the CdS a t i n t e n s i t y I , V D ( I ) i s the b u i l t - i n v o l t a g e i n the h e t e r o j u n c t i o n at i n t e n s i t y I , and z^ are the p e r m i t t i v i t i e s of Ge and CdS, V i s the a p p l i e d reverse b i a s v o l t a g e , and e i s the e l e c t r o n i c charge. Since e ; j ^ l > > E : 2 ^ D 2 ^ ' e v e n a t v e r v high i l l u m i n a t i o n i n t e n s i t i e s , equation (5.7) becomes eN ( T ) e 1/2 C j C D - [ (5.8) I f A i s the area of the h e t e r o j u n c t i o n then i t s capacitance Cj ( I ) i s given by C (I) eN (I)e 1 / 2 Hence, 1/2 1/2 2 — ? ] {V (I)+V} (5.10) K 1 / 2 ( I ) [ V d ( I ) + V ] 1 / 2 (5.11) K ( I ) = ——=• (5.12) e N D 2 ( I ) £ 2 A At medium i n t e n s i t i e s , the t o t a l capacitance (obtained from the measurements) i s a s e r i e s combination of j u n c t i o n capacitance (Cj) and bulk CdS capacitance (CT)• Hence (5.13) c M ( i ) c . ( i ) c I or . 1 1 _ _1 c . d ) " c M ( i ) - c T From equations (5.11) and (5.13), 1 1 1 /*> T/2 — A — _ _L_ * K - ' - C I ) [ V n ( I ) + V ] i / Z (5.14) On squaring both sides of the above equation 1 + 1 ? . K ( I ) [ V ( I ) ] (5.15) C M ( I ) C I 2 V ^ I " At medium i n t e n s i t i e s , the bulk capacitance C^'is expected to be more than the measured capacitance C^. Assuming C M(I)< C j , i t i s seen that - ~ — > >~^' » an<^ ~h i - s n e g l i g i b l e as compared w i t h ~^ cJ(D c 2 c 2 t£(I) i n the l e f t hand s i d e of equation (5.15). Hence 1 « K - ( I ) [ V + { V n U ) + _ _ 2 _ _ } ] ( 5 . 1 6 ) C 2 ( I ) ° C M ( I ) C I K ( I ) At high i l l u m i n a t i o n i n t e n s i t i e s , the measured capacitance i s only that of the j u n c t i o n hence K ( D [V+V f l ) ] (5.17) Equation (5.16) shows that at medium i n t e n s i t i e s , the i n t e r c e p t 1 1 of the r2. . versus V curve at 2. . = 0 w i l l g i v e a higher value of b u i l t - i n v o l t a g e by an a d d i t i o n a l term of 2 . At medium 2 % ( ! ) < ( ! ) i n t e n s i t i e s , the t e r m —— T T T — T y r - may be q u i t e l a r g e compared to V (I) I M ) k ' (see 1^ i n F i g . 5.8). As the i n t e n s i t y i s i n c r e a s e d , V (I) in c r e a s e s but r .j\—TTTT- decreases (see I„ i n F i g . 5.8). The V (I) can be determined only at high i n t e n s i t i e s . The e l e c t r o n c o n c e n t r a t i o n i n CdS at higher i n t e n s i t i e s can be determined from the slope of the — ~ — versus V c h a r a c t e r i s t i c s which M gives a value of K ( I ) = „ .2 . The steady s t a t e e l e c t r o n concen-e N D 2 ( I ) e 2 A y t r a t i o n i n CdS and the b u i l t - i n v o l t a g e at va r i o u s i n t e n s i t i e s are obtained from the F i g . 5.8 and are given i n Table 5.1. Table 5.1 B u i l t - i n v o l t a g e i n the pGe-nCdS h e t e r o j u n c t i o n and steady s t a t e e l e c t r o n d e n s i t y i n the CdS f o r various i n t e n s i t i e s obtained from F i g . 5.8. R e l a t i v e Value of i n t e r c e p t d ( - ~ — ) / d ( - V ) Steady s t a t e i n t e n s i t y • .. - « /r2 _ 'C ( I ) e l e c t r o n d e n s i t y . . .at • 1/C =0 M „ . . ( i n i n c r e a s i n g order) , M ,-2 ( v o l t s ) ( f a r a d I 3 2.4 1.57 x I 2 2.1 1.38 x l 1 1.95 1.17 x I L 1.95 0.84 x v o l t Y ) i n CdS - 3. (cm ) 22 10 2. 13 20 x 10 22 10 2. 13 38 x 10 22 10 2. 13 80 x 10 22 10 3. 13 88 x 10 The. hig h values of b u i l t - i n v o l t a g e f o r medium i n t e n s i t i e s (T_2 and I^) are due to the bulk capacitance of the CdS. The valu e of b u i l t - i n v o l t a g e at h i g h e r i n t e n s i t i e s (1^ and 1^) i s about 1.95 v o l t . This v a l u e seems to be high compared w i t h that of other h e t e r o j u n c t i o n s . Such high values of b u i l t - i n v o l t a g e have been observed i n other h e t e r o -j u n c t i o n s (discussed i n chapter I V ) . The steady s t a t e c a r r i e r d e n s i t y i n the CdS increases w i t h the i n t e n s i t y , but the i n c r e a s e seems to be l e s s than the expected v a l u e . The capacitance was measured at d i f f e r e n t f requencies (1 to 100 KHz range) and was observed to be higher at low fr e q u e n c i e s . The v a r i a t i o n of capacitance w i t h frequency i s due to the presence of i n t e r f a c e s t a t e s and traps (Hovel et a l . 1968) i n the t r a n s i -t i o n r e g i o n . These traps and i n t e r f a c e s t a t e s may be the cause of the disagreement between the expected and the e x p e r i m e n t a l l y observed values. 6. Summary and c o n c l u s i o n pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n s were made by a l l o y i n g Ge on CdS. Ohmic contacts to pGe and CdS were obtained by a l l o y i n g indium and the devices were mounted on t r a n s i s t o r headers. The current versus v o l t a g e c h a r a c t e r i s t i c s were found to be n o n - r e c t i f y i n g at low i n t e n s i t i e s and r e c t i f y i n g at high i n t e n s i t i e s . The capacitance of the devices was a l s o measured at d i f f e r e n t i l l u m i n a t i o n i n t e n s i t i e s . The capacitance was observed to i n c r e a s e r a p i d l y at low i n t e n s i t i e s and a s a t u r a t i o n was found at h i g h i n t e n s i t i e s . The a.c. conductance increased at low i n t e n s i t i e s but decreased a f t e r a p a r t i c u l a r i n t e n s i t y . The reverse b i a s capacitance of the devices was constant w i t h the v o l t a g e a t low i n t e n s i t i e s but decreased w i t h the v o l t a g e at h i g h i n t e n s i t i e s . These measurements showed that the behaviour of the pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n was q u i t e d i f f e r e n t at low and high i n t e n s i t i e s . . The energy band diagrams f o r pGe - CdS h e t e r o j u n c t i o n s w e r e developed f o r d i f f e r e n t i n t e n s i t i e s of i l l u m i n a t i o n . The steady s t a t e e l e c t r o n d e n s i t y i n the CdS was represented by a quasi Fermi l e v e l . At low i n t e n s i t i e s , the quasi Fermi l e v e l i n the CdS was lower than the Fermi l e v e l i n the Ge and accumulation l a y e r s were formed at the j u n c t i o n r e s u l t i n g i n an ohmic c o n t a c t , between pGe and CdS. At higher i n t e n s i t i e s , the quasi Fermi l e v e l i n the CdS was above the Fermi l e v e l i n pGe and a j u n c t i o n ( d e p l e t i o n regions i n pGe and nCdS at t h e i r i n t e r f a c e ) was formed between pGe and nCdS and the cu r r e n t v o l t a g e c h a r a c t e r i s t i c s were r e c t i f y i n g . E q u i v a l e n t c i r c u i t s of the pGe-CdS ( p h o t o s e n s i t i v e ) h e t e r o j u n c t i o n were developed f o r d i f f e r e n t i l l u m i n a t i o n i n t e n s i t i e s and the r e s u l t s of the measured capacitance f o l l o w e d from the eq u i v a l e n t c i r c u i t s . The 2 1/C versus V c h a r a c t e r i s t i c s were s t r a i g h t l i n e s at high i n t e n s i t i e s . From 2 the 1/C versus V c h a r a c t e r i s t i c s the b u i l t - i n v o l t a g e i n the h e t e r o j u n c t i o n s and the steady s t a t e e l e c t r o n d e n s i t y i n the CdS were determined to be 1.95 v o l t s 13 3 and 3.28 x 10 /cm , r e s p e c t i v e l y . H e t e r o j u n c t i o n s of wide band gap non-amphoteric I I - V I compounds w i t h other semiconductors were s t u d i e d w i t h c o n s i d e r a t i o n f o r t h e i r a p p l i c a t i o n s as l i g h t e m i t t i n g and p h o t o s e n s i t i v e devices. Expressions f o r b u i l t - i n v o l t a g e and c u r r e n t - v o l t a g e r e l a t i o n s were d e r i v e d f o r anisotype h e t e r o j u n c t i o n s on the b a s i s of m i n o r i t y c a r r i e r i n j e c t i o n . I t was shown that the b u i l t - i n v o l t a g e was a f u n c t i o n of the d i s c o n t i n u i t y i n the band edges at the i n t e r f a c e and the e f f e c t i v e mass'of the c a r r i e r s i n the two semiconductors. The recombination-generation r a t e s of the c a r r i e r s at the i n t e r f a c e s t a t e s of the h e t e r o j u n c t i o n s were considered f o r three d i f f e r e n t c a r r i e r t r a n s p o r t mechanisms, v i z . , 1) Capture, (11) Tunneling and (111) Capture t u n n e l i n g . I t was a l s o shown that the recombination-generation r a t e of the c a r r i e r s i n a h e t e r o j u n c t i o n could be considered to be that of a homojunction whose p r o p e r t i e s are c h a r a c t e r i z e d by the two semiconductors of which the h e t e r o j u n c t i o n i s made. ZnSe f i l m s were deposited on p type Ge, GaAs and mica by the s u b l i m a t i o n under n e a r - e q u i l i b r i u m c o n d i t i o n s method i n an u l t r a high vacuum. The f i l m s deposited on mica at the s u b s t r a t e temperature higher than 400°C showed hexagonal h i l l o c k s t r u c t u r e . The s i z e of the c r y s t a l l i t e s i n the f i l m s increased w i t h the s u b s t r a t e temperature w i t h a maximum value of about 15y at 500°C. Ep i t a x y of ZnSe on GaAs (111) was observed around 380°C. The photo H a l l m o b i l i t y of the c a r r i e r s 2 2 increased w i t h i l l u m i n a t i o n i n t e n s i t y from 12 cm / v o l t - s e c to 31 cm / v o l t -sec. The p h o t o c o n d u c t i v i t y of the f i l m s was analyzed using a mosaic model and i t was found that the p h o t o c o n d u c t i v i t y was b a r r i e r l i m i t e d at low i n t e n s i t i e s but c a r r i e r l i m i t e d at high i n t e n s i t i e s . The c u r r e n t -v o l t a g e c h a r a c t e r i s t i c s of pGe-nZnSe were spac e - c h a r g e - l i m i t e d . The i n t e r f a c e a l l o y i n g technique was used to f a b r i c a t e nlnAs-pZnTe h e t e r o j u n c t i o n s . Under forward b i a s c o n d i t i o n s , at low v o l t a g e s the c u r r e n t t r a n s p o r t mechanism i n these h e t e r o j u n c t i o n s was due to the recombination-generation of the c a r r i e r s i n the d e p l e t i o n r e g i o n s , w h i l e at high v o l t a g e s i t was due to the t u n n e l i n g of c a r r i e r s . The nlnAs-pZnTe h e t e r o j u n c t i o n s emitted l i g h t under reverse b i a s c o n d i t i o n s and r a d i a t i o n from the j u n c t i o n could be seen w i t h eye i n a dark room. The t h r e s h o l d v o l t a g e and current f o r the d e t e c t i o n of emitted l i g h t using a photomultiplier. were about 6 v o l t s and 1mA. The r i s e and f a l l times of the l i g h t pulse were l e s s than 0.2usec. The s p e c t r a of the emitted l i g h t were i n the range of 1.69 eV to 3.5 eV. A number of peaks i n the s p e c t r a and photons of energy higher than the band gap energy of e i t h e r semiconductor i n d i c a t e that the recombination-generation of the hot c a r r i e r s through i m p u r i t y centers i s i n v o l v e d . An energy band diagram of ZnTe w i t h d i f f e r e n t i m p u r i t y centers was developed. The d i f f e r e n t peaks, the low energy l i m i t and the high energy l i m i t of the emitted l i g h t were i n agreement w i t h the proposed model. The p h o t o s e n s i t i v e pGe-CdS h e t e r o j u n c t i o n s were made by a simple a l l o y i n g technique. The c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s of the h e t e r o j u n c t i o n were n o n - r e c t i f y i n g i n the dark but r e c t i f y i n g under i l l u m i n a t i o n . The study of t h i s h e t e r o j u n c t i o n at d i f f e r e n t i n t e n s i t i e s showed that pGe makes ohmic contact w i t h p h o t o s e n s i t i v e CdS i n the dark and low i n t e n s i t i e s , but at high i n t e n s i t i e s pGe-nCdS h e t e r o j u n c t i o n i s formed. The concept of steady s t a t e Fermi l e v e l i n CdS under i l l u m i n a t i o n was used to e x p l a i n the behaviour of the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s . The energy band diagrams and e q u i v a l e n t c i r c u i t s of the pGe-CdS (photo-s e n s i t i v e ) h e t e r o j u n c t i o n s were developed. L i g h t e m i t t i n g and p h o t o s e n s i t i v e h e t e r o j u n c t i o n s of I I - V I compounds w i t h other semiconductors can be made by simple a l l o y i n g techniques. The h e t e r o j u n c t i o n s made by d e p o s i t i n g f i l m s of I I - V I . compounds by vacuum evaporation methods should be improved. A complete i n v e s t i g a t i o n of the f i l m s of I I - V I compounds of c o n t r o l l e d q u a l i t y i s needed to make s u c c e s s f u l h e t e r o j u n c t i o n s of I I - V I compounds. APPENDIX 1 SELECTION OF PAIRS OF SEMICONDUCTORS FOR HETEROJUNCTIONS Some of the b a s i c requirements f o r s e l e c t i n g a p a i r of semiconductors f o r a h e t e r o j u n c t i o n are that they should have almost the same l a t t i c e constant , c r y s t a l s t r u c t u r e , thermal expansion c o e f f i c i e n t e t c . But w i t h the e x i s t i n g semiconductors, there are not many semiconductor-p a i r s a v a i l a b l e which s a t i s f y t h i s c o n d i t i o n . Some of the semiconductor-p a i r s which could r e s u l t i n good h e t e r o j u n c t i o n s ( i . e . , having low i n t e r f a c e s t a t e d e n s i t y ) • i f made by appropriate techniques, are Ge-GaAs, Ge-ZnSe, GaAs-ZnSe, InSb-CdTe and InAs-ZnTe. There w i l l a l s o be some a d d i t i o n a l c r i t e r i a about the f e a s i b i l i t y of the h e t e r o j u n c t i o n s on the b a s i s of t h e i r u s e f u l n e s s and f a b r i c a t i o n techniques. The semiconductors of group IV, I I I - V and I I - V I compounds are c l a s s i f i e d i n t o a few c a t e g o r i e s according to closeness i n t h e i r c r y s t a l s t r u c t u r e , l a t t i c e match,etc. Heterojunctions formed between the two semiconductors of the same group have a high p o s s i b i l i t y of forming good devices. Some data of the semiconductors, u s e f u l , f o r making h e t e r o j u n c t i o n s , are given i n subsequent t a b l e s (see t a b l e 4.1 f o r units).- Since there i s c o n s i d e r a b l e v a r i a t i o n i n the data obtained from d i f f e r e n t sources, those given i n these t a b l e s should not be taken as being standard. The f o l l o w i n g are the major sources f o r the data; 1. S e l e c t e d Constants R e l a t i v e to-Semiconductors, P.A. A i g r a i n and M. B a l k a n s k i Perg amon Press (1961). 2. Physics and Chemistry of I I - V I Compounds, M. Aven and J.S. Prener ( E d i t o r s ) North-Holland P u b l i s h i n g Company, - Amsterdam (1967). ' 4. Semiconducting II-VI, IV-VI and V-VI Compounds, N.K. Abrikosov . et a l . , Plenum Press, New York (1969). 5. Photoconductivity of Solids, R.H. Bube, John Wiley Inc., 2nd printing (1967). 6. Physics of III-V Compounds, 0. Madelung, John Wiley Inc. (1964). 7. Physics of Semiconductor Devices, S.M. Sze, John Wiley Inc. (1969). Table A l . l Classification of semiconductors for making heterojunctions Seaaicond. Category No. No. 1 2 3 4 5 6 1 Ge a-Sn+ - InAs Si InP HgS 2 GaAs InSb GaSb A T A #' AlAs CdS HgSe 3 ZnSe CdTe CdSe GaP AlSb # HgTe 4 ZnTe A1P« 5 ZnS t a-Sn i s a semi-metal.. Alsb, AlAs and A1P are not stable in air. P r o p e r t i e s Ge GaAs ZnSe 1) L a t t i c e constant 2) C r y s t a l s t r u c t u r e 3) Symmetry 4 ) Dens i ty 5) M e l t i n g p o i n t 6) Coeff. of l i n e a r expans, 7) R e l a t i v e p e r m i t t i v i t y 8) Band gap (Eg) 9) dEg/dT 10) E l e c t r o n a f f i n i t y 11) m /m e o 12) m*/m h o 13). u 14) y h 15) n 16) N c 17) N v 18) Normal nature 5.6575 Diamond 0^-fd3m n .5.32 937 5.75 x 10 16 .67 -1.2 x 10 4.25 -4 m7 m. _ i = 1 . 6 , — m m o o •k m m - i - .04 A m m o o 3800 1820 .082 = .3 2.5 x 10 13 1.04 x 10 '6.1 x 1 0 1 8 19 -4 5.6534 Zincblende C4- -F43m 6v 5.307 1238 5.9 x 10" 6 10.9 1.35 -5.1 x 10 3.71-4.07 .068 .12 6000 400 1.1 x 10' 4.7 x. 10 7 x 1 0 1 8 17 -6 5.6687 Zincblende T,2-F43m d 5.42 1515 9.44 x 10 .8.85 2.7 -7.2 x 10 4.1 .17 .60 150 30 = x 10 -4 18 both n & p types both n & p types 1.0 x 10 19 1.3 x 10 * only n type Table A1.3 Some p r o p e r t i e s of InSb and CdTe Property InSb CdTe 1) L a t t i c e constant 6.47877 6.481 2) C r y s t a l s t r u c t u r e Zincblende C Ziocblende')-, '1 W u r t z i t e J 3) Symmetry T^-F43m 2 -Td-F43m 4) Density 5.7751 6.06 5) M e l t i n g p o i n t 530 1098 6) Coeff. of l i n e a r expansion 4.7 x 10" 6 7) R e l a t i v e p e r m i t t i v i t y 18.7 9.65 8) Band gap (Eg) .167 1.44 9) dEg/dT -2.9 x 10~ 4 ' -4.1 x 1 0 ~ 4 10) E l e c t r o n a f f i n i t y 4.3 11) m*/m e o .013 .14 12) m*/mo .6 .35+ .05 13) y e 78,000 1050 14) 750 80 15) n. •' '-• I 16) N c 17) N v 18) Normal nature both n & p types both n & p t Table A1.4 Some p r o p e r t i e s of InAs, GaSb, CdSe and ZnTe InAs GaSb CdSe ZnTe 1) L a t t i c e constant 6.0585 6.0954 | 6.084 \e 4.2985,7.0150) .1037 2) C r y s t a l s t r u c t u r e Zincblende Zincblende ( ZincblendeKzincblende ~? L W u r t z l t e J l w u r t z i t e 3 3) Symmetry T2-F43m d C4v-F43m 0 l|-F43m l e 4 -P6„mc ^ cv . 3 Td2-F43m 4) Density 5.66 5.619 5.68 5.7 5) M e l t i n g p o i n t 942 706 1258 1295 6) —6 Coeff. of l i n e a r expans. 5.9 xlO 6.9 x 10~6 8.29 x 10~ 6 7) R e l a t i v e p e r m i t t i v i t y 14 15 e«C 9.25 ElC 8.75 9.67 8) Bandgap (Eg) ..35 .67 1.67 2.26 9) dEg dT -4.5 x 10~4 -4.1 x 10~ 4 -4.6 x 10~ 4 -6.0 x 10~ 4 10) E l e c t r o n a f f i n i t y 4.9 4.9 3.5 11) m*/m e o .025 .047 .13 m h -T- ~ .15-.20 4m o .'. 12) m «/ m " o .4 .5 .45 .6 1 3 ) y e 23,000 4,000 650 350 14) y h 200 750 50 100 15) n i 14 3.55 x 10 1.161 x 10° 16) N c 9.2 x 1 0 1 6 6.68 x 1 0 1 8 17) N V 3.2 x 1 0 1 8 19 1.07 x 10 18) Normal nature- both n & p types both n & only n type only p type p types Table A l . 5 Some p r o p e r t i e s of S i , GaP and ZnS Property S i GaP 1) L a t t i c e constant 5.4308 5.4508 2) C r y s t a l s t r u c t u r e Diamond Zincblende 3) Symmetry 0^-Fd3m n 4 0,, -F43m 6v A) Density 2.328 5) M e l t i n g p o i n t 1420 1467 6) Coeff. of l i n e a r expansion 2.6 x 10" 6 5.3 x 10" 6 7) R e l a t i v e p e r m i t t i v i t y 11.8 10 8) Bandgap (Eg) 1.11 2.24 9) d E g / dT -5.4 x 10~ 4 10) E l e c t r o n a f f i n i t y 4.05 11) m' /m e o m j=. 9 7 mt = .19 .34 12) m. /m h o m =.16 m = 1 t .5 •5 13) y e 1500 110 14) % 600 75 15) n. l 1.6 x 1 0 1 0 16) N c 19 2.8 x 10 * 17) N V 19 1.02 x 10 18) Normal nature bothn and both n and p ZnS 5.4093 { Zincblende W u r t z i t e T2-F43m d 4.079 1830 6.2 x 10 8.1 3.6 -5.3 x 10' 3.9 .25 .5-1.0 140 5 -6 n type o n l p types types Table A1.6 Some p r o p e r t i e s of InP and CdS Property InP CdS 1) L a t t i c e constant 5.86S7 2) C r y s t a l s t r u c t u r e Zincblende 3) Symmetry 2 -Td-F43m 4) Density 4.787 5) M e l t i n g p o i n t 1058 6) Coeff. of l i n e a r expansion 4.5 x 10~ 6 7) R e l a t i v e p e r m i t t i v i t y 12.1 8) Eandgap (Eg) 1.26 9) dEg/dT -4.6 x 10~ 10) E l e c t r o n a f f i n i t y 11) m*/m e o .07 12) m*/m h o .4 13) M e 4600 14) % 150-650 15) n i 16) N c 17) N V 18) Normal nature both n and 5.820 4.1368, 6.7163 Zincblende I W u r t z i t e J I T^-F^m / Ci„ - P6^mc b v 4.820 1750 11.6 2.41 4.8 .204 300 15 only n type APPENDIX 2 In-pZnTe DIODES' In-pZnTe diodes were made by the same method as that of nlnAs-pZnTe except that the temperature of a l l o y i n g was lower (about 500°C). The current voltage c h a r a c t e r i s t i c of a t y p i c a l In-pZnTe diode i s shown i n F i g . A2.1 and A2.2. Fig. A2.1 Current-voltage c h a r a c t e r i s t i c of In-pZnTe diode Scale: x-axis 1 volt/div and y-axis 5 mA/div. The capacitance decreased with the reverse biased voltage and a decrease i n capacitance with frequency was also found.' The a.c. resistance increased with reverse bias voltage up to 0.1 v o l t and started decreasing 2 above this value (similar to F i g . 4.10). The 1/C versus V c h a r a c t e r i s t i c s were straight l i n e s with b u i l t - i n voltage about 1.4 to 1.6 volts as shown in Fig. A2.3. 10 -3 Rio-4 K. (J) irT-0 10 -6 V / FORWARD BIAS - © 1 L J _L REVERSE BIAS J L J L J I 0-0 0.2 0.4 0.6 0-8 10 1.2 1.4 16 18 2.0 2.2 VOLTS 2.4 2.6 2.8 A. 2.2 Cur r e n t - v o l t a g e c h a r a c t e r i s t i c s of In-pZnTe diode -FORWARD 1.5 10 0.5 0-0 0-5 10 BIAS VOLTAGE (VOLTS) 1.5 F i g . A2.3 1/C versus reverse b i a s v o l t a g e c h a r a c t e r i s t i c s of In-ZnTe diode at v a r i o u s frequencies Fig. A2.4 Electroluminescence s p e c t r a of the l i g h t emitted from a reverse b i a s In-ZnTe diode at v a r i o u s currents a t room temperature Electroluminescence was obtained under reverse b i a s c o n d i t i o n s . The devices were observed under a microscope and i t was found that the orange l i g h t was emitted from some random spots i n the bulk ZnTe. The e l e c t r o -luminescence was a l s o observed i n the forward b i a s c o n d i t i o n s at very high v o l t a g e s i n In-pZnTe h e t e r o j u n c t i o n s , u n l i k e nlnAs-pZnTe h e t e r o j u n c t i o n s . The i n t e n s i t y of l i g h t was much grea t e r i n In-pZnTe diodes i n comparison w i t h nlnAs-pZnTe h e t e r o j u n c t i o n s . F i g . A2.4 shows the electroluminescence spectrum ( c o r r e c t e d f o r the r e l a t i v e p h o t o s e n s i t i v i t y of the p h o t o m u l t i p l i e r ) at d i f -f e r e n t c u r r e n t d e n s i t i e s . There are a few major d i f f e r e n c e s between the reverse b i a s e d spectrum of nlnAs-pZnTe h e t e r o j u n c t i o n s ( F i g ; 4.13) and In-pZnTe diodes ( F i g . A2.4): ( i ) t h e r e i s only one i n t e n s i t y peak at 2.04 eV i n the spectrum of In-pZnTe at low c u r r e n t s , and ( i i ) there i s no e l e c t r o -luminescence i n In-pZnTe diodes below 5350°A, i . e . , no photons of energy greater than the band gap energy of ZnTe are detected. The common f e a t u r e s • of the spectrum of the two devices are ( i ) at higher c u r r e n t s , the peak i n t e n s i t y i s at 6100°A(i.e2.04 eV) and ( i i ) the t a i l s of the spectrum at hig h e r wavelengths (6500°A to 7000°A) are very s i m i l a r at higher c u r r e n t s . I t was' found that i f the In l a y e r formed on nlnAs-pZnTe hetero-j u n c t i o n s was not removed by d i s s o l v i n g i n HC1 or by an a b r a s i v e , then the electroluminescence spectrum of nlnAs-pZnTe h e t e r o j u n c t i o n s was s i m i l a r , to that of In-pZnTe diodes, and electroluminescence was a l s o observed under forward b i a s c o n d i t i o n s . F i g . A2.5(b) shows the energy band diagram of an In-pZnTe diode. The expected value of b u i l t - i n v o l t a g e i s about 1.5 eV and the value obtained 2 from the 1/c versus V c h a r a c t e r i s t i c s i s between"1.4 to 1.6 eV. This i s very c l o s e to the expected value-A comparison of f i g u r e s 4.14(b) and A2.5(b) shows that the b a r r i e r f o r e l e c t r o n s going from In to ZnTe i s much l e s s than the b a r r i e r f o r e l e c t r o n s going from InAs to ZnTe under forward b i a s fa) (b) ISOLATED EQUILIBRIUM F i g . A2.5 (a) Energy band diagram of In and pZnTe ( i s o l a t e d ) (b) Energy band diagram of In-pZnTe diode c o n d i t i o n s . -Hence electroluminescence i s observed i n In-pZnTe diodes under forward b i a s c o n d i t i o n s and not i n nlnAs-pZnTe h e t e r o j u n c t i o n s . The forward bias e d electroluminescence i n In-pZnTe diodes has been reported by s e v e r a l authors ( B o r t f e l d et a l . (1968), Komatsu et a l . (1964)). Electroluminescence i n In-pZnTe i s from the bulk ZnTe and any r a d i a t i o n of energy g r e a t e r than the band gap energy (2.26 eV) w i l l be absorbed i n b u l k ZnTe. This i m p l i e s then that no r a d i a t i o n of energy gre a t e r than 2.26 eV can be detected i n the In-pZnTe diodes. In the case of nlnAs-pZnTe, the r a d i a t i o n comes from the j u n c t i o n only and photons of energy greater than the band gap energy can be detected. BIBLIOGRAPHY A d i r o v i c h , E . I . , Y.M. Yuabov and G.R. Yagudaev, " P h o t o e l e c t r i c E f f e c t s i n F i l m Diodes w i t h CdS-CdTe H e t e r o j u n c t i o n s " , Sov. Phys. -Semicond. 3_» 61 (1969) . A l b e r s , A., " P h y s i c a l Chemistry of D e f e c t s " , Physics and Chemistry of I I - V I Compounds, M. Aven and J.S. Prener ( E d i t o r s ) , North H o l l a n d , Amsterdam (1967). A l f e r o v , Z.A. and O.A. Ninua,"Electroluminescence A l Ga 1 As-GaAs Hetero-" x 1—x j u n c t i o n s under Avalanche Breakdown C o n d i t i o n s " , Sov. Phys. -Semicond. _4, 296 (1970) . Anderson, J.C., "The Use of Thin Films i n P h y s i c a l I n v e s t i g a t i o n s " , ( E d i t o r ) . Academic P r e s s , New York (1966). Anderson, R.L., "Ge-GaAs H e t e r o j u n c t i o n s " , IBM J . Res. and Dev. j i , 283 (1960). Anderson, R.L., "Experiments on Ge-GaAs H e t e r o j u n c t i o n s " , S o l i d State E l e c t r o n i c s 5_, 341 (1962). A r i z u m i , T., T. Nishinaga and M. Kakehi, "Thermodynamics of Vapor Growth of ZnSe-Ge-I System i n Closed Tube Process", Japan J . Appl. Phys. _5, 588 (1966) . A r t h u r , J.R., "Vapor Pressures and Phase E q u i l i b r i a i n the Ga-As System" J . Phys. Chem. S o l i d s _28, 2257 (1967). Aven, M. and H.H. Woodbruy, " P u r i f i c a t i o n of I I - V I Compounds by Solvent E x t r a c t i o n " , A p p l i e d Phys. L e t t e r s _1, 53 (1962). Aven, M. and W. Garwacki, " E p i t a x i a l Growth and P r o p e r t i e s of ZnTe-CdS H e t e r o j u n c t i o n " , J . Electrochem. Soc. I l l , 401 (1963). Aven, M. and B. S e g a l l , " C a r r i e r M o b i l i t y and Shallow Impurity States i n ZnSe and ZnTe", Phys. Rev. 130, 81 (1963). Aven, M. and D.A. Cusano, " I n j e c t i o n Electroluminescence i n ZnS and ZnSe", General E l e c t r i c Research Laboratory Report No. 64-RL-3596G (1964). Aven, M. , "Electroluminescence i n I I - V I Compounds", I I - V I Semiconducting Compounds, D.G. Thomas ( E d i t o r ) , I n t e r n a t i o n a l Conference, W.A. Benjamin, Inc., New York, 1232 (1967). Aven, M., " M o b i l i t y of Holes and I n t e r a c t i o n between Acceptor Defects i n ZnTe" J . Appl. Phys. 38, 4421 (1967). Aven, M. and R.K. Swank, "Ohmic Contacts to Wide Band Gap Semiconductors" Extended A b s t r a c t s of Electrochem. 17_, No. 2, A b s t r a c t No. 493, p. 444, Montreal Meeting , (1968). Baczewski, A., " E p i t a x i a l Growth of ZnSe on GaAs", J . Electrochem. Soc. 112, 577 (1965). Bates, C.W., "Tunneling Current i n E s a k i Diodes", Phys. Rev. 121, 1070 (1961). B a r t f e l d , D.P. and H.P. K l e i n k n e c h t , " I n j e c t i o n Electroluminescence i n A l l o y e d ZnTe J u n c t i o n s " J . Appl. Phys. 39, 6104 (1968). Brojdo, S., T.J. R i l e y and G.T. Wright, "The H e t e r o j u n c t i o n T r a n s i s t o r and the Space-Charge-Limited T r i o d e " , B r i t . J . Appl. Phys. 16, 133, (1965). Bube, R.H., " P h o t o c o n d u c t i v i t y of S o l i d s " , John Wiley I n c . , New York, 2nd P r i n t i n g (1967). Bube, R.H., " P h o t o c o n d u c t i v i t y " , P h y s i c s and Chemistry of I I - V I Compounds, M. Aven and J.S. Prener ( E d i t o r s ) , North H o l l a n d , Amsterdam, (1967) Bube, R . H . , " I n t e r p r e t a t i o n of H a l l and Photo-Hall E f f e c t s i n Inhomogeneous M a t e r i a l s " , A p pl. Phys. L e t t e r s 13, 136 (1968). Calow, J.T., P.J. Deasley, S.J.T.'Owen and P.W., Webb, "A Review of Semi-conductor H e t e r o j u n c t i o n s " , J . M a t e r i a l s Science 2_, 88 (1967). Calow, J.T., S.J.T. Owen and P.W. Webb, "The Growth and E l e c t r i c a l C h a r a c t e r i s t i c s of E p i t a x i a l Layers of ZnSe on p-Type Germanium", Phys. S t a t . S o l . 213, 295 (1968). Calow, J.T., D.L. K i r k , S.J.T. Owen and P.W. Webb "The E l e c t r i c a l and P h o t o e l e c t r i c a l C h a r a c t e r i s t i c s of Ge-ZnSe Heterodiode", I n t e r n a t i o n a l E l e c t r o n Device (IEEE) Meeting, Washington, Paper No. 23.1 (1970). Chang, L.L., "The Conduction P r o p e r t i e s of Ge-GaAs P n-n H e t e r o j u n c t i o n s " , S o l i d State E l e c t r o n i c s j3, 721 (1965). 1 x x Chang, L.L., "Comments on J u n c t i o n Boundary Conditions f o r H e t e r o j u n c t i o n s " , J . Appl. Phys. 37_, 3908 (1966). Chynoweth, A.G. and K.G. McKay, "Photon Emission from Avalanche Breakdown i n S i " , Phys. Rev. 102, 369 (1956). Chynoweth, A.G. and H.K. Gummel, "Photon Emission from Avalanche Breakdown i n Ge p-n J u n c t i o n " J . Phys. Chem. S o l i d s 1_6, 191 (1960). Crowder, B.L., F.F. Morehead and P.R. Wagner, " E f f i c i e n t I n j e c t i o n E l e c t r o -luminescence i n ZnTe by Avalanche Breakdown", Appl. Phys. L e t t e r s 8,148 (1966). Cusano, D.A., "Thin F i l m s Studies and E l e c t r o - O p t i c E f f e c t s " , Physics and Chemistry of I I - V I . Compounds" M. Aven and J.S. Prener ( E d i t o r s ) , North H o l l a n d Amsterdam, . (1967). Dale, J.R., " A l l o y e d Semiconductor H e t e r o j u n c t i o n s " , Phys. S t a t . S o l . 16, 351 (1966). Davy, J.E. and T. Pankey " E p i t a x i a l GaAs Films Deposited by Vacuum Evaporation", J . Appl. Phys. 39, 1941 (1968). D e v l i n , S.S., "Transport P r o p e r t i e s " , Physics and Chemistry of I I - V I Compounds,M. Ayen and and J.S. Prener ( E d i t o r s ) , N o r t h - H o l l a n d , Amsterdam (1967). D e i t z , R.E. and D.C Thomas, " M i r r o r Absorption and Fluorescence i n ZnTe", Phys. Rev. L e t t e r s 8, 391 (1962). Dhere, N.G. and A. Goswami, "An E l e c t r o n D i f f r a c t i o n Study of ZnTe and ZnSe Films',' Thin S o l i d Films 3_, 439 (1969). . Dolega, V., "Theory of the p-n H e t e r o j u n c t i o n Between Semiconductors w i t h D i f f e r e n t C r y s t a l L a t t i c e s " , Z« N a t u r f o r s c h , 18, 653 (1963). Donnelly, J.P. and A.G. M i l n e s , "Current/ Voltage C h a r a c t e r i s t i c s of p-n Ge-Si and Ge-GaAs H e t e r o j u n c t i o n s " , Proc. IEE 113, 1468 (1966). Donnelly, J.P., A.G. Foyt, W.T. L i n d l e y and G.W. Iseler,"MIS E l e c t r o -luminescent Diodes i n ZnTe", S o l i d State E l e c t r o n i c s 1_3, 755 (1970). Durupt, P., J.P. Raynaud and G. Mesnard /'Heterojunctions Ge p- SinObtenues Par E p i t a x i e Sous Vide", S o l i d State E l e c t r o n i c s 12_, 469 (1969). Dutton, R.W., and R.S. M u l l e r , ' T h i n F i l m CdS-CdTe H e t e r o j u n c t i o n Diodes" S o l i d State E l e c t r o n i c s 11_, 749 (1968). E s a k i , L., W.E. Howard and J . Heer,"The I n t e r f a c e Transport p r o p e r t i e s of Ge-GaAs H e t e r o j u n c t i o n s " , Surface Science .2, 127 (.1964). Eastman, P.C., R.R. Haering and P.A. B a r n e s , " I n j e c t i o n Electroluminescence i n Metal-Semiconductor Tunnel Diodes", S o l i d State E l e c t r o n i c s 7_, 879 (1964) . F i s c h e r , A.G., J.N. Carides and J . Dresner, " P r e p a r a t i o n and P r o p e r t i e s of n type ZnTe", S o l i d State Communications J2> 157 (1964) . F i s c h e r , A.G., "Electroluminescence i n I I - V I Compounds", Luminescence of Inorganic S o l i d s , P. Goldberg ( E d i t o r ) , Academic Press, New York (1966), Gershenzon, M., "Electroluminescence From p-n J u n c t i o n i n Semiconductors" Luminescence i n Inorganic S o l i d s P- Goldberg ( E d i t o r ) , Academic Press, New York.(1966). G i l l , W.D. and R.H. Bube, " P h o t o v o l t a i c P r o p e r t i e s of Cu ?S-CdS Hetero-j u n c t i o n s " , I n t e r n a t i o n a l P h o t o c o n d u c t i v i t y Conference, Palo A l t o (1969) G o l d f i n g e r , P. and M.. Jeunehomme, "Mass Spectrometric and Knudsen-cell V a p o r i z a t i o n Studies of Group 2B-6B Compounds", Tr a n s a c t i o n of the Faraday Society 59.2851 (1963). Goodman,, A.M., " E l e c t r i c a l l y Conducting Photoluminescent ZnSe Film s " J . Electrochem. Soc. 116,364 (1969). Grove, A.S., "Physics and Technology of Semiconductor Devices", John Wiley, New York (1967). H o l t , D.B. , "Defects i n E p i t a x i a l Films of Semiconducting Compounds w i t h S p h a l e r i t e S t r u c t u r e " , J . M a t e r i a l s Science 1, 280 (1966). H i n k l e y , E.D.and R.H. Rediker,"GaAs-InSb Graded-G a P H e t e r o j u n c t i o n " , S o l i d S t a t e E l e c t r o n i c s TO, 671 (1967). Hovel, H.J. and A.G. M i l n e s - "The E l e c t r i c a l C h a r a c t e r i s t i c s of nZnSe-pGe Heterodiodes" I n t . J . E l e c t r o n i c s 25, 201 (1968). Hovel, H.J. and A.G. M i l n e s , "The Epitaxy of ZnSe on Ge, GaAs and ZnSe by an KCl Close-spaced Transport Process", J . Electrochem. S o c i e t y 116, 843 (1969). Hudock, P., " H i g h - M o b i l i t y PbS and CdS Films Deposited under U l t r a High Vacuum E q u i l i b r i u m C o n d i t i o n s " , Transactions of the M e t a l l u r g i c a l S o c i e t y of AIME 239_, 338 (1967). K a n d i l a r o v , B. and R. An d e r y t c h i n , " P h o t o v o l t a i c E f f e c t s i n CdS-CdSe H e t e r o j u n c t i o n s " Phys. S t a t . S o l . 8_, 897 (1965). K a r l o v s k y , J . , "Simple Method f o r C a l c u l a t i n g the Tunneling Current of an E s a k i Diode", Phys. Rev. 127_, 419 (1962). Kot, M.V. and L. J . Panasyuk, " P r i n c i p a l R e l a t i o n s h i p s Governing the E l e c t r i c a l C h a r a c t e r i s t i c s of Some Hete r o j u n c t i o n s and T h e i r Band Schemes", Sov. Phys.-Semicond. 1, 155 (1967). Kennedy, D.I. and M.J. Russ, "Room Temperature Electroluminescence i n . S e m i - i n s u l a t i n g ZnTe", S o l i d State E l e c t r o n i c s 10, 125 (1967). Kennedy, D.I. and M.J. Russ, "New El e c t r o l u m i n e s c e n t Spectrum i n ZnTe R e s u l t i n g from Oxygen I n c o r p o r a t i o n " , J . Appl. Phys. J38, 4387 (1967) Kholuyanov, G.F., " L i g h t Emission A s s o c i a t e d w i t h Breakdown i n SiC p-n J u n c t i o n " , Sov. P h y s . - S o l i d State 3, 2405 (1962). Korneeva, I.V., V.V. Sokolov and A.V. Novoselova, "Saturated-vapor Pressure . of Zinc and Cadmium Selenides i n the S o l i d S t a t e " , Russ. J . Inor-ganic Chemistry 5_, 117 (1960). Krause, P.W., S.T. L i u , R.G. Schulze and S.R. Peterson, "Avalanche Breakdown i n nGe-pGaAs H e t e r o j u n c t i o n s " , J . Appl. P h y s . 4_0, 5401 (1969). Kroemer, H., "Theory of a Wide-Gap Emitter f o r T r a n s i s t o r s " , Proc. I.R.E. 45, 1535 (1957). Kumar, R.C., "Current Transport i n Isotype H e t e r o j u n c t i o n s " , I n t . J . E l e c t r o n i c s 25, 239 (1968). Kumar, R..C. , '".Diffusion Theory of Current Transport i n Anisotype Hetero-j u n c t i o n s " , I n t . J . E l e c t r o n i c s 27, 185 (1969). Logan, R.A. and A.G. Cheynoweth, "Charge M u l t i p l i c a t i o n i n GaP p-n J u n c t i o n s " J . Appl. Phys. 33, 1649 (1962). Marinace, J.C., "Tunnel Diodes by Vapor Growth of Ge on Ge and on GaAs", IBM J . of Res. and Dev. 4-,. 280 (1960). McAfee, K. B., E.J. Ryder, W. Shockley and M. Sparks, "Observations of Zener Current i n Germanium p-n J u n c t i o n s " , Phys. Rev. _83, 650 (1951). M i k s i c , M.G., G. Mandel, F.F. Morehead, A.A. Onton and E.S. S c h l i g , " I n j e c t i o n Electroluminescence i n p-type ZnTe", Phys. L e t t e r s 11,202 (1964). Morehead, F.F. and B.L. Crowder, "Photo-n-p J u n c t i o n s i n ZnTe", IBM J . Res. and Dev. 12, 458 (1968) . Mroczkowski, R.S., M.C. Lavine and E.G. Gatos, " M e t a l l u r g i c a l Aspects of I n t e r f a c e A l l o y e d GaAs-Ge H e t e r o j u n c t i o n s " , Trans, of the M e t a l l u r -g i c a l Soc. AIME _233, 456 (1965). Okimura, H., M. Kawakami and Y. S a k a i , " P h o t o v o l t a i c P r o p e r t i e s of CdS-pSi H e t e r o j u n c t i o n C e l l s " , Japan J . Appl. Phys. b_, 908 (1967). Okimura, H., "Anomalous Breakdown i n CdS (CdSe)-nGe J u n c t i o n s " , Japan J . Appl. Phys. 7_> !297 (1968). Okimura, H. and R. Kondo, " E l e c t r i c a l and P h o t o v o l t a i c P r o p e r t i e s of CdS-Si J u n c t i o n " , Japan J. of A p p l . Phys. 9_, 274 (1970). Oldham, W.G. and A.G. M i l n e s , "n-n Semiconductor H e t e r o j u n c t i o n s " , S o l i d S tate E l e c t r o n i c s jS, 121 (1963). Oldham, W.G. and A.G. M i l n e s , " I n t e r f a c e States i n Abrupt Semiconductor H e t e r o j u n c t i o n s " , S o l i d State E l e c t r o n i c s 7_, 153 (1964). P e t r i t z , R.L., "Theory of P h o t o c o n d u c t i v i t y i n Semiconductor F i l m s " , Phys. Rev. 104,1508 (1956). Radautsan, S.I. and A.E. Tsurkan, "Some P r o p e r t i e s of Recombination R a d i a t i o n i n p-n j u n c t i o n s of ZnTe", Phys. S t a t . S o l . (a) 1, 545 (1970). Ray, B., " P h o t o c o n d u c t i v i t y and A s s o c i a t e d Behaviour", I I - V I Compounds, Pergaman Pr e s s , Edinburgh (1969). R a z i , S., " I n j e c t i o n Luminescence i n Rare-Earth Doped CdS H e t e r o j u n c t i o n s " , Trans, of the M e t a l l u r g i c a l Soc'. of AIME 242, 448 (1968). Rediker, R.H., S. Stopek and J.H.R. Ward, " I n t e r f a c e - A l l o y E p i t a x i a l H e t e r o j u n c t i o n s " , S o l i d State E l e c t r o n i c s 7_> 621 (1964). Rediker, R.H., S. Stopek and E.D. H i n k l e y , " E l e c t r i c a l and E l e c t r o - O p t i c a l P r o p e r t i e s of I n t e r f a c e - A l l o y H e t e r o j u n c t i o n s " , Trans, of M e t a l l u r g i c a l Soc. of AIME 233, 463 (1965). Riben, A.R. , and D.L. Feucht, "nGe-pGaAs H e t e r o j u n c t i o n s " , S o l i d State E l e c t r o n i c s £, 1055 (1966). Riben, A.R., and D.L. Feucht, " E l e c t r i c a l Transport i n nGe-pGaAs Hetero-j u n c t i o n s " , I n t . J . E l e c t r o n i c s 20, 583 (1966). Sah, C.T., R.N. Noyce and W. Shockley, " C a r r i e r Generation and Recombination i n P-N'Junctions and P-N J u n c t i o n C h a r a c t e r i s t i c s " , Proc. I.R.E. 45, 1228 (1957). Salama, C.A.T., T.W. Tucker and L. Young, " S t r u c t u r e , C o n d u c t i v i t y and H a l l E f f e c t of E l e c t r o n Bombardment Evaporated S i l i c o n Films on Sapphire", S o l i d State E l e c t r o n i c s 10, 339 (1967). Salkov, E.A., "Some P r o p e r t i e s of p(SiC)-n(CdS) J u n c t i o n s " , Sov. Phys. S o l . State ]_, 227 (1965). S e l l e , B., W. Ludwig and R. Mach, "Photovoltaic Response of Cu„S-CdS p-n H e t e r o j u n c t i o n s " , Phys. State S o l . _24, K149, (1967) . . Serreze, H., S. F i s c h l e r and D. Sawyer "GaSb-ZnTe H e t e r o j u n c t i o n " , J . Appl. Phys. _39, 5330 (1968). Shockley, W., "The Theory of p-n Ju n c t i o n s i n Semiconductors and p-n J u n c t i o n T r a n s i s t o r s " , B e l l System T e c h n i c a l J o u r n a l 28, 435 (1949). Shockley, W., " E l e c t r o n s and Holes i n Semi-conductors", D.Van Nostrand Co. Inc. (1950). Shockley, W., " C i r c u i t Element U t i l i z i n g Semiconductive M a t e r i a l " , U.S. Patent 2,569,347 (1951). Shewchun, J . , "Ge-Si Heterojunctions",Ph.D. T h e s i s , The U n i v e r s i t y of Waterloo, Waterloo (1963). S l a t e r , J.C., " B a r r i e r Theory of P h o t o c o n d u c t i v i t y of Lead Sulphide", Phys. Rev. 103, 1631 (1956). Smith, R.W., " P r o p e r t i e s of Ohmic Contacts to CdS S i n g l e C r y s t a l s " , Phys. Rev. S_7, 1525 (1955). Spear, W.E. and J . Hart, " E l e c t r o n and Hole Transport i n CdS C r y s t a l s " , Proc. Phys. Soc. (London) 21, 130 (1963). Strehlow, W.H., "Chemical P o l i s h i n g of I I - V I Compounds" J . Appl. Phys. 40, 2928 (1969). Swank, R.K., "Surface P r o p e r t i e s of II^-VI Compounds", Phys. Rev. 153, 844 (1967). Sze, S.M., "Physics of Semiconductor Devices", W i l e y - I n t e r s c i e n c e (1969). Takahashi, K., W.D. Baker and A.G. M i l n e s , "ZnTe-InAs H e t e r o j u n c t i o n s " , I n t . J . E l e c t r o n i c s 27, 383 (1969). Tansley, T.L., "Forward Bi a s Current-Voltage C h a r a c t e r i s t i c s f o r a Hetero-j u n c t i o n i n which Tunneling Dominates", Phys. S t a t . S o l . 18, 105 (1966). Thornton, P.R.,"The Physics of E l e c t r o l u m i n e s c e n t Devices", E. and F.N. Spon L t d . , London (1967). Tsujimoto,Y. and M. Fukai, "Electroluminescence from ZnSe-ZnTe H e t e r o j u n c t i o n Diodes", Japan. J . Appl. Phys. 6_, 1024 (1967). Tucker, T.W., "The E l e c t r i c a l P r o p e r t i e s of Evaporated S i l i c o n F i l m s " M.A.Sc. T h e s i s , The U n i v e r s i t y of B r i t i s h Columbia, Vancouver (1966) Van der Pauw, L . J . , "A Method of Measuring S p e c i f i c R e s i s t i v i t y and H a l l E f f e c t of D i s c s of A r b i t r a r y Shape", P h i l i p s Res. Repts. 13, 1 (1958). Van Opdorp, C. and H.K. Kanerra, "Current-Voltage C h a r a c t e r i s t i c s and Capacitance of Isotype H e t e r o j u n c t i o n s " , S o l i d State E l e c t r o n i c s 10, 401.., (1967). Vecht,A. "Methods of A c t i v a t i n g and R e c r y s t a l l i z i n g Hhin F i l m s of I I - V I Compounds", Physics of Thin F i l m s , G. Hass and R.E. Thun ( E d i t o r s ) , • _3, 165,Academic Press,New York (1966). V o l g e r , J . , "Note on the H a l l P o t e n t i a l across an Inhomogeneous Conductor", Phy. Rev. 87, 1023 (1950). Warner, R.M. and J.N. Fordemwalt, " I n t e g r a t e d C i r c u i t s Design P r i n c i p l e s and F a b r i c a t i o n " , ( E d i t o r s ) McGraw-Hill Co. (1964). Watanabe,N., S. Usui and Y. Kanai, " I n j e c t i o n Luminescence i n ZnTe Diodes", Japan J . Appl. Phys. _3, 427 (1964). Watanabe,N., "Forward and Reverse Biased Electroluminescence i n A l l o y e d ZnTe Diodes", Japan. J . Appl. Phys. 5_> 12 (1964). Watanabe,S. and Y. M i t a , "CdS-PbS H e t e r o j u n c t i o n s " , J . Electrochem. Soc. 116, 989 (1970). Wosten, W.J. and M.G. Geers, "The Vapor Pressure of ZnSe",J. Phys. Chem., 66, 1252 (1962). Waxman, A., V.E. Henrich, F.V. S h a l l c r o s s , H. Borkan and P.K. Weimer, "Electron M o b i l i t y Studies i n Surface Space-Charge Layers i n Vapor Deposited CdS F i l m s , " J . Appl. Phys. 36, 168 (1965). Yan, G., "Studies on Sublimed GaAs F i l m s , Anodic A 1 2 0 3 Films and A1„0 /GaAs I n t e r f a c e s " , PhD. T h e s i s , The U n i v e r s i t y of B r i t i s h Columbia, Vancouver (1970). Zeidenberg, G. and R.L. Anderson, "Si-GaP H e t e r o j u n c t i o n s " , S o l i d State E l e c t r o n i c s fo 113 (1967). 

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