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UBC Theses and Dissertations

Continuous gas chromatography Wong, Ho Yew 1971

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SILICON THIN-FILMS I. LOW-TJ^iPERATURE-SUBLTMED SILICON FILMS ON SAPPHIRE AND SPINEL SUBSTRATES, I I . A FIELD EFFECT STUDY OF THE METAL-INSULATOR-SEMICONDUCTOR STRUCTURE AND ITS APPLICATIONS IN NOTCH NETWORKS. b y PETER HUNG-KEI WONG B. Eng.(Physics), McMaster University, 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF t'Labljjix. u r A i r J_IJ.IL JJ b L i h w o r . In The Department of E l e c t r i c a l Engineering We accept t h i s thesis as conforming to the required standard TEE UNIVERSITY OF BRITISH COLUMBIA October, 1972 In present ing th i s thes i s in pa r t i a l ful f i lrnent of the requirements fo r an advanced degree at the Un iver s i t y of B r i t i s h Columbia, I agree that the L ib ra ry sha l l make i t f r e e l y ava i l ab le fo r reference and study. I f u r the r agree that permission for extens ive copying of th i s thes i s for s cho l a r l y purposes rnay be granted by the Head of my Department or by his representat ives . It i s understood that copying or pub l i c a t i on of t h i s thes i s f o r f i nanc i a l gain sha l l not be allowed without my wr i t ten permiss ion. Department of ^ k ^ s / r ^ f l J^y?' 'AJ2J2^//^ The Un iver s i t y o f B r i t i s h Columbia Vancouver 8, Canada Date -f 7 ABSTRACT A s tudy o f the s t r u c t u r a l and e l e c t r i c a l p r o p e r t i e s o f l o w -t e m p e r a t u r e - s u b l i m e d s i l i c o n f i l m s i n d i c a t e s t h a t t h e y a r e c h a r a c t e r i z e d by a h i g h d e n s i t y o f g r a i n b o u n d a r i e s , hence c r y s t a l d e f e c t s . A t r a p p i n g mode l ha s been p r o p o s e d to e x p l a i n the e x p e r i m e n t a l l y o b s e r v e d t e m p e r a -t u r e - d e p e n d e n c i e s o f r e s i s t i v i t y and c a r r i e r c o n c e n t r a t i o n o f t h e s e f i l m s . The r e s u l t shows t h a t the d e f e c t d e n s i t y at the g r a i n b o u n d a r i e s i s o f 1 2 -2 the o r d e r o f 1 0 cm , and t h a t i t i s i n d e p e n d e n t o f the d o p i n g c o n c e n -t r a t i o n s i n the f i l m s . • I t has been shown t h a t the t h i n - f i l m m e t a l - i n s u l a t o r ^ s e m i -c o n d u c t o r (MIS) s t r u c t u r e can be r e d u c e d to a t r a n s m i s s i o n l i n e p r o b l e m by e x p r e s s i n g the e q u i v a l e n t c a p a c i t a n c e o f t h e s t r u c t u r e as a s e r i e s com-b i n a t i o n o f the d e p l e t i o n c a p a c i t a n c e and the i n s u l a t o r c a p a c i t a n c e . The v a r i a t i o n s o f b o t h the c a p a c i t a n c e and c h a n n e l c o n d u c t a n c e o f the MIS s t r u c t u r e have been u t i l i z e d t o make n o t c h f i l t e r s i n w h i c h t h e n o t c h f r e q u e n c y can be v a r i e d o v e r 2 0 0 % by an e x t e r n a l b i a s i n g v o l t a g e . In v i e w o f the need f o r m a i n t a i n i n g a c o n s t a n t n u l l d e p t h i n t h e s e m i c o n d u c t o r n o t c h f i l t e r under v a r i o u s b i a s i n g p o t e n t i a l s , a new n o t c h ne twork has been p r o p o s e d i n w h i c h the o p t i m a l n o t c h c o n d i t i o n . c o u l d be m a i n t a i n e d s i m p l y by d e s i g n i n g the r a t i o s o f the l e n g t h s and w i d t h s o f the MIS s t r u c t u r e t o the a p p r o p r i a t e v a l u e s . i TABLE OF CONTENTS Page ABSTRACT i TABLE OF CONTENTS . 1 1 LIST OF ILLUSTRATIONS iv ACKNOWLEGEMENT . . . . . . . v i i I. INTRODUCTION 1 1.1 Thin-Film S i l i c o n on Sapphire and Spinel Substrates . . . 1 1.2 S i l i c o n T h i n - f i l m D i s t r i b u t e d RC Structure 3 I I . VACUUM SUBLIMATION OF SILICON THIN-FILMS 5 2.1 Introduction • 5 2.2 Experimental Method 7 2.2*1 'Apparatus . 7 2.2.2 "Source and Substrate Preparation 10 2.3 Methods of Film Assessments 14 2.3.1 Deposition Rate and Film Thickness Measurements . 14 2.3.2 S t r u c t u r a l Properties . . . 15 2.3.3 E l e c t r i c a l Properties 16 III-. STRUCTURAL. AND,-. ELECTRICAL- PROPERTIES. 0E. LOWr-TEMPERATURE:-SUBLIMED.. SILICON THIN-FILMS 18 3.1 Introduction 18 3.2 S t r u c t u r a l Properties . 19 3.2.1 Surface Morphology 19 3.2.2 Growth Mechanism 22 3.2.3 L a t t i c e Imperfections i n Grown Films 26 3.2.4 A d d i t i o n a l Factors that May Influence the Structure of Sublimed S i l i c o n Films . . . 28 3.3 E l e c t r i c a l Properties 29 3.3.1 General 29 3.3.2 Temperature Dependence of R e s i s t i v i t y , H a l l M o b i l i t y and. E f f e c t i v e . C a r r i e r Concentration. . . . . . . . . . . . 32 3.3.3 Trapping Model f o r Semiconductor Films with. Defect Centers Locating at the Grain Boundaries 32 3.3.4 E f f e c t of Post-oxidation on the E l e c t r i c a l P r o p e rties :.'; of Low-Temperature-Sublimed S i l i c o n Films 41 IV. A THIN-FILM URC STRUCTURE 43 4.1 Introduction 43 4.2 Review of MIS Theory 45 4.2.1 Ideal C-V C h a r c t e r i s t i c s of MIS Structures . . . . . 45 4.2.2 MIS Structure Including Traps and Surface,States.. 45 4.3 Channel Conductance of Semiconductor Thin-Films- A f t e r Thermal Oxidation 46 i i 4.4 DC C h a n n e l C o n d u c t a n c e o f S e m i c o n d u c t o r T h i n - F i l m s i n a MIS S t r u c t u r e Page 49 4 .4 .1 C h a n n e l Conduc tance w i t h V =0 49 4 . 4 . 2 C h a n n e l C o n d u c t a n c e w i t h V ^ ^ O 53 4 . 4 . 3 S m a l l S i g n a l P a r a m e t e r s f o r T h i n - F i l m MIS S t r u c t u r e 55 4 . 4 . 4 D i s t r i b u t i o n of C h a n n e l p o t e n t i a l and t h e Shape o f Space Charge W i d t h A l o n g t h e C h a n n e l 56 4 .5 AC S m a l l S i g n a l M o d e l l i n g o f T h i n - F i l m URC S t r u c t u r e 61 4 .5 .1 E q u a t i o n o f S t a t e . . . . . 61 4 . 5 . 2 S i m p l i f y i n g t h e E q u a t i o n o f S t a t e .' . . . . . • • : 65 4.6 S m a l l S i g n a l A n a l y s i s o f a G e n r a l i z e d URC S t r u c t u r e . . . 67 4 .6 .1 S m a l l S i g n a l E q u a t i o n s 67 4 . 6 . 2 S o l u t i o n s o f t h e S m a l l S i g n a l E q u a t i o n s . . . . . 68 4 . 6 . 3 Common-Gate A d m i t t a n c e M a t r i x 70 V . APPLICATIONS OF URC STRUCTURES IN NULL NETWORKS 74 5.1 I n t r o d u c t i o n . . . . . 74 5.2 Rev iew 74 5.3 N o t c h F i l t e r C o m p r i s i n g a S e m i c o n d u c t o r URC S t r u c u r e . . . . 80 5.3.1 T h e o r e t i c a l T u n i n g C h a r a c t e r i s t i c s . . . 80 5 .3 .2 P r a c t i c a l C o n s i d e r a t i o n s i n D e s i g n O p t i m i a a t i o n . 82 5.4 A T u n a b l e N o t c h Network u s i n g D o u b l e URC S e c t i o n s . . . . 84 V I . EXPERIMENTS ON SEMICONDUCTOR THIN-F ILM URC NOTCH F ILTERS . . . 89 6.1 I n t r o d u c t i o n 89 6.2 F a b r i c a t i o n T e c h n i q u e s f o r a URC S t r u c t u r e . . . . . . . . 89 6.2.1 F a b r i c a t i o n P r o c e s s e s . . 89 6 .2 .2 C l e a n i n g t h e S i and S i 0 2 S u r f a c e 90 6 .2 .3 P h o t o r e s i s t T e c h n i q u e 90 6 .2 .4 H i g h T e m p e r a t u r e T r e a t m e n t s 92 6 .2 .5 F i l m T h i c k n e s s Measurements . . 92 6.3 C h a n n e l Conduc tance under N o n - u n i f o r m D e p l e t i o n L a y e r W i d t h 93 6.4 S i l i c o n T h i n - F i l m URC N o t c h F i l t e r 96 6.5 N o t c h F r e q u e n c y T u n i n g 99 V I I . CONCLUSION . . . . . . . . 103 APPENDIX A SPACE CHARGE AT THE SEMICONDUCTOR SURFACE OF A MIS STRUCTURE . 106 APPENDIX B SOLUTIONS OF LOSSLESS TRANSMISSION L INE EQUATIONS 108 REFERENCES 110) i i i LIST OF ILLUSTRATIONS Figure 2.1::; Schematic diagram of the sublimation chamber . 8 2.2 Sublimation chamber i n s i d e an Ultek TNB vacuum system . . 9 2.3 A schematic diagram of the H ^ - p r e f i r i n g apparatus . . . . 12 2.4 S i l i c o n films on Sapphire and s p i n e l substrates 14 2.5 Block diagram of the H a l l apparatus. 16 3.1 Photomicrographs of s i l i c o n f i l m s . . . . . 20 3.2 Electron-probe topographs of s i l i c o n films 21 3.3 R e f l e c t i o n electron d i f f r a c t i o n patterns of s i l i c o n films 24 3.4 X-ray Laue r e f l e c t i o n d i f f r a c t i o n patterns of s i l i c o n films 25 3.5 O p t i c a l micrograph of an etched s i l i c o n f i l m 27 3.6 Film r e s i s t i v i t y versus temperature 33 3.7 H a l l m o b i l i t y versus temperature. . , 34 3.8 E f f e c t i v e c a r r i e r concentration versus temperature . . . . . . 35 3.9 A one-dimensional in-homogeneous f i l m model 37 4.1 A schematic diagram of a t h i n - f i l m URC structure 44 4.2 Energy band diagrams of an MIS structure. 44 4.3 A URC st r u c t u r e with V rV 53 4.4-a T h e o r e t i c a l channel conductance of a Si-URC structure as function of 55 4.4. b T h e o r e t i c a l channel conductance as function of V . . . . 56 g 4.5. a D i s t r i b u t i o n of channel p o t e n t i a l s i n Si-URC str u c t u r e . 59 4.5.b Channel p r o f i l e i n Si-URC structure 60 4.6 An equivalent c i r c u i t for the subregion of a URC structure 66 4.7 A general representation of a Z-parameter equivalent c i r c u i t 72 4.8 An equivalent c i r c u i t of the generalized URC structure 72 i y 5.1 Distributed RC notch f i l t e r • 75 5.2 TT or T equivalent c i r c u i t s for the URC low-pass f i l t e r . . 76 5.3 Phase angle of and as a function of normalized . . frequency x = w R C t • • • • * -76 5.4 Theoretical notch characteristics of a simple URC i n series with an external r e s i s t o r R 79 n 5.5 Tunability factor n versus normalized space-charge width x j a as a function of the notch parameter £ -81 d 5.6 Optimal t u n a b i l i t y factor r\Q^ as a function of £ for devices operating i n mode 2 83 5.7 A notch network using double-URC sections - 85 5.8 Notch parameters a and 6 of the double-URC notch f i l t e r . .-. 88 5.9 Theoretical notch c h a r a c t e r i s t i c s of a double-URC notch f i l t e r having cx=3.0, £=6.674. -B8b 5.10 Effect of variations i n the notch parameters or and g on the notch c h a r a c t e r i s t i c s of a double-URC f i l t e r . . . . . . 88c 6.1 Photographic masks used for device f a b r i c a t i o n 91 6.2 A sample of the f i n a l device 93 6.3 Qualitative description of the channel under (a) deep-depletion at the drain, (b) accumulation at the drain. . . • 94 6.4 Ip-Vjj c h a r a c t e r i s t i c s of s i l i c o n t h i n - f i l m URC structures 95 6.5 A "bootstrapped" follower used i n the measurement of the amplitude response of URC notch f i l t e r s . . . . . 97 6.6 Amplitude response of a t h i n - f i l m semiconductor URC tunable notch f i l t e r 98 6.7 A display of the distorted waveform from a s t r u c t u r a l l y defective notch f i l t e r . . 99 6.8.a Notch frequency t u n a b i l i t y for sample 0 . . . . . . . 100 6.8.b Notch frequency t u n a b i l i t y for sample S 101 v 6.9.a Variations of notch r e s i s t o r R and C/C as function of n o of the biased voltage V i n the-tuning range of - sample 0 100 6.9.b Variations of notch r e s i s t o r R and C/C as function n o of the biased voltage V i n the tuning range of sample S 101 Cr v i ACKNOWLEDGEMENT The author wishes to thank h i s research supervisor, Dr. L. Young, for h i s guidance during the course of th i s work. Grateful acknowledgement i s given to Mr. J . Stuber f or b u i l d i n g the sublimation chamber, to Mr. A. Lacis f o r taking the electron-probe topographs, and to Mr. B. Cornish f o r taking the ellipsometer measure-ments. He also wishes to thank Messrs. C. Chang, P. P e l t i e r , and G. Oliv e for proof-reading part of the manuscript, and to Miss N. Duggan fo r typing t h i s t h e s i s . F i n a l l y , the author wishes to thank the National Research Council for f i n a n c i a l assistance i n the form of gran t - i n - a i d to h i s research supervisor. v i i Chapter 1 Introduction The topics of t h i s thesis are:-(a) materials r e s e a r c h i n s i l i c o n t h i n - f i l m s grown at low substrate temperatures, (b) a f i e l d - e f f e c t study on semiconductor t h i n - f i l m d i s t r i b u t e d RC elements, and (c) design, f a b r i c a t i o n and c h a r a c t e r i s t i c s of s i l i c o n t h i n - f i l m notch f i l t e r s . 1.1 Thin-Film S i l i c o n on Sapphire and Spinel Substrates ' Modern integrated c i r c u i t technology emphasizes high packing density as w e l l as low p a r a s i t i c capacitance i n order to a t t a i n a higher frequency performance of both the passive and active devices f a b r i c a t e d on a s i n g l e substrate wafer. In the monolithic integrated technology, the components are i s o l a t e d by reverse biased p-n junctions at the substrate-device i n t e r f a c e . Subsequently, the performance of such a c i r c u i t i s often l i m i t e d by undesirable high frequency coupling e f f e c t s and dc leakage at the junctions. With s i l i c o n devices on i n s u l a t i n g substrates, b e t t e r e l e c t r i c a l i s o l a t i o n i s ensured by the removal of excess s i l i c o n around each c i r c u i t component. Recently, t h i n - f i l m s i l i c o n devices on sapphire substrates have increased the operating frequencies of MOST d i g i t a l i n t e -grated c i r c u i t s beyond that of c i r c u i t s with conventional MOSTs"'". In a d d i t i o n , feedback capacitance of le s s than 0.02 pF/electrode has been 2 reported for MOS triodes and tetrodes which operate at 0.5-1 GHz. 3 Other advantages of s i l i c o n on i n s u l a t i n g substrates include : a) high strength and good heat conductivity, b) no p a r a s i t i c capacitance to the substrate, c) very high packing density (10^ complementary devices 1 per sq. i n . ) , d) fewer processing steps required for CMOS memory c e l l s as a resu l t of complete substrate i s o l a t i o n and no space charge spread into the substrate, etc. With chemical vapor deposition, e p i t a x i a l s i l i c o n on sapphire and magnesium-aluminum spinel substrates (SOS),, having a c a r r i e r concentra-1 7 - 3 tion of above 10 cm , can now be prepared with, state-of-art properties similar to those of bulk s i l i c o n ^ . However, an-increasingly poor c a r r i e r mobility i s observed at lower c a r r i e r concentration, with a maximum occurring at 16 17 ™3 the doping l e v e l of 10 -10 cm . Mobility degradation at higher car-r i e r concentration i s attributed to ionized impurity scattering s i m i l a r to that observed i n bulk s i l i c o n ; and that at lower c a r r i e r concentration i s caused by phonon scattering^ and possibly by an increase i n the space charge region around inhomogeneously di s t r i b u t e d defects^. At temperatures above 100.0°C, s i l i c o n attacks sapphire and spinel substrates re s u l t i n g i n aluminum contamination (autodoping^) of the grown f i l m . Direct correlation of mobility degradation at low ca r r i e r concentration with aluminum autodopihg can be deduced from the fact that the peak i n the hole mobility versus hole concentration re-lationship i s approximately an order of magnitude lower i n s i l i c o n on 8 spin e l as compared to s i l i c o n on sapphire , which i s consistent with 9 Robinson and Dumin's observation that autodoping i s an order "of magni-tude less i n s i l i c o n on spinel than i n s i l i c o n on sapphire. The techniques of growing s i l i c o n films by vacuum sublimation i s given i n chapter 2. An investigation on the st r u c t u r a l and e l e c t r i c a l properties of these films i s reported i n chapter 3. The stress has been on a low enough substrate temperature so that autodoping of the s i l i c o n films could be neglected. Consequently, t h e i r e l e c t r i c a l properties 3 should be dominated by the mechanism of f i l m growth as well as t h e i r s t r u c t u r a l properties rather than by substrate contaminations. 1.2 S i l i c o n Thin-film P i s t r i b u t e d RG Structures Since the inception of SOS technology by Manasevit et a l . " ^ 11-15 i n 1963, a number of active devices using e p i t a x i a l s i l i c o n films have been reported. A l l these devices, with the exception of the b i -polar t r a n s i s t o r s , u t i l i z e a thin layer of d i e l e c t r i c on top of the e p i t a x i a l semiconductor for f i e l d effect modulation. S i m i l a r l y , for device passivation, i s o l a t i o n (cross over technique), and f i e l d - e f f e c t enhanced R and C elements, the same configuration of an oxidized SiO layer on S i i s often employed. This gives r i s e to the semiconductor distr i b u t e d RC structure. The introduction of semiconductor into the sys-tem leads to a wide variety of problems which are non-existent i n the conventional d i s t r i b u t e d RC f i l t e r structure. These- problems-pertain to-the e l e c t r i c a l properties of semiconductor films and the insulator-semi-conductor interface. In chapter 4 a theoretical study has been made on the f i e l d effect of a t h i n - f i l m distributed RC structure based on the e x i s t i n g 16 theories of semiconductor surface physics . The emphasis i s on channel conductance i n the semiconductor f i l m . A detailed mathematical modelling of an i d e a l i z e d , homogeneous metal insulator-semiconductor t h i n - f i l m structure i s presented i n section 4.5. This i s followed by a small signal analysis of a t h i n - f i l m structure having a non-uniform space-charge layer. In chapters 5 and 6 the uniformly d i s t r i b u t e d RC (URC) struc-ture i s applied to notch networks. In contrast to the conventional t h i n -f i l m notch f i l t e r s , both capacitance and conductance variations have 4 been u t i l i z e d f° r notchr-frequency tuning. Device characteristics are derived i n section 5 .3 using the depletion layer approximation, and the experimental results are reported i n section 6 . 4 . In section 5 . 5 , a new notch network using double URC structures has been proposed. Such a c i r c u i t w i l l eliminate the v a r i a t i o n i n notch parameters during frequency tuning thereby maintaining a constant at-tenuation at the n u l l which i s unattainable with any of the known notch-.networks. The concluding remarks are presented In chapter* 7. CHAPTER 2 Vacuum Sublimation of S i l i c o n Thin-Films 2.1 Introduction In general there are 2 common methods for growing large areas of e p i t a x i a l s i l i c o n films on i n s u l a t i n g substrates:-21 (i ) In chemical vapour deposition (CVD) , s i l i c o n epitaxy can be 22 obtained by hydrogen reduction of s i l i c o n t e t r a c h l o r i d e ( S i C l ^ ) 23 or t r i c h l o r o s i l a n e (SiHCl^) > and by the p y r o l y s i s of s i l a n e 24 25 (SiH^) i n hydrogen or helium atmosphere. A water-cooled 26 reaction chamber i s used to provide a streamlined h o r i z o n t a l flow of the entering gas over the RF heated susceptor surface. The sub-s t r a t e s , r e s i d i n g on top of the pyrolytic-carbon coated pure carbon susceptor, are p r e f i r e d (to remove the mechanically damaged surface layer) i n a atmosphere 100-200°C above the deposition tempera-tures for 10-15 min., before the temperature i s lowered to that r e -quired for growth. A gas stream of the source materials i s then i n -troduced into the quartz r e a c t i o n chamber and s i l i c o n d e p o s i t i o n i s immediately obtained on the substrate surfaces. Impurity doping of the films i s accomplished by addition of pH._, B 2 H 6 ' ° r ^ s^3 t o t* i e gas stream during growth 20 ( i i ) In vacuum evaporation , the substrate and source materials (usually j u s t a piece of s i l i c o n ) can be heated separately by , , ' ^27,28 t, 29,30 _ ... , . ' e l e c t r o n bombardment or other means . Deposition or * • 17 Other a v a i l a b l e methods are:- u l t r a - t h i n a l l o y - z o n e - r e c r y s t a l l i z a t i o n 18 and temperature-gradient-zone—recrystallization . A summary of s i n g l e c r y s t a l f i l m formation i s given i n table 2 of f e f . 19, and that of the e p i t a x i a l technology i n r e f . 20. s 6 s i l i c o n i s , commenced, by r e t r a c t i n g , the., s h u t t e r l y i n g , between them. T h i s i s done i n s i d e a h i g h vacuum chamber where c o n t a m i n a t i o n s o f t he s i l i c o n vapour can be k e p t to a minimum. Dop ing o f the f i l m s can be a c h i e v e d by i n i t i a l l y p i c k i n g the ' r i g h t ' s o u r c e i m -p u r i t y c o n c e n t r a t i o n o r , i t can be i n t r o d u c e d by a s e p a r a t e e v a p o r -31 a t i o n o f the dopants a t the t ime o f f i l m growth . The s u b s t r a t e s can be c l e a n e d e i t h e r b e f o r e t h e i r i n s e r t i o n i n t o t h e vacuum sy s tem 22 by p r e - f i r i n g , o r t h e y can be h e a t e d up under vacuum t o a h i g h e r t e m p e r a t u r e , m inu te s b e f o r e the s t a r t o f e v a p o r a t i o n " * ^ . D e s p i t e the f a c t t h a t h i g h q u a l i t y e p i t a x i a l s i l i c o n f i l m s can now be grown by the t e c h n o l o g i c a l l y w e l l - i n n o v a t e d CVD method , t h e y s t i l l s u f f e r a ma jo r d raw-back i n the a p p r e c i a b l e a u t o d o p i n g ^ o f s u b s t r a t e i m p u r i t i e s i n t o the f i l m s a t t e m p e r a t u r e s above 1 0 0 0 ° C . R e c e n t l y , t he use o f v e r y h i g h d e p o s i t i o n . r a t e s had been p r o v e n s i g n i f i c a n t i n t h e s u p p r e s s i o n o f c h e m i c a l a t t a c k on i n s u l a t i n g s u b s t r a t e s by i m p i n g i n g s i l i c o n v a p o u r 34 a t the f i l m - s u b s t r a t e i n t e r f a c e . But i t i s a l s o known t h a t a l a r g e amount o f a u t o d o p i n g i n the f i l m s comes f rom the back s i d e o f t h e s u b s t r a t e s 35 th rough gas t r a n s p o r t . A n o t h e r new endeavour u n d e r t a k e n by ma jo r i n d u s -25 36 t r i a l r e s e a r c h c e n t e r s has been the use o f h e l i u m ambient ' i n s t e a d o f f o r p y r o l y s i s o f s i l a n e i n o r d e r to l ower the o p t i m a l growth t e m p e r a -t u r e by 1 0 0 - 2 0 0 ° C f r om the c o n v e n t i o n a l 1 0 5 0 - 1 2 0 0 ° C r a n g e . The g rowth o f good q u a l i t y e p i t a x i a l s i l i c o n f i l m s by no rma l vacuum t e c h n i q u e s i s e q u a l l y l i m i t e d by t h e need f o r h i g h s u b s t r a t e t e m p e r a t u r e s o f o v e r 1 0 0 0 ° C . A d d i t i o n a l advantages o f g row ing e p i t a x i a l s i l i c o n f i l m s a t , . t . • -, 35 ,37 l o w e r s u b s t r a t e t e m p e r a t u r e s a r e : - a d e c r e a s e i n c h e m i c a l r e a c t i o n 38 on the s u b s t r a t e s u r f a c e s , a r e d u c t i o n i n t h e r m a l s t r e s s r e s u l t i n g f r om different thermal expansions of the films and substrates, and a lower im-39 purxty contamination coupled with a minimized impurity d i f f u s i o n e f f e c t inside the grown films. Recent technological advancement i n low-temperature 40 4 deposited Si02 films together with organic and inorganic d i e l e c t r i c films has created much int e r e s t i n low-temperature device processings. The pre-sent investigation on low-temperature grown (centered about 800°C) s i l i c o n 42 thin-films i s a continuation of the work i n i t i a t e d by Weisberg for the growth of e p i t a x i a l s i l i c o n films by vacuum sublimation on sapphire and spinel substrates. 2.2 Experimental Method • 2.2.1 Apparatus The sublimation compartment was mounted inside an Ultek TNB vacuum system. Roughing of the vacuum chamber was accomplished i n 2 steps by 2 molecular sieve sorption pumps operating consecutively. F i n a l pumping was done by two 50 l i t r e / s e c ion pumps plus a T i sublimation pump rated at 3600 l i t r e / s e c for a i r . Vacuum inside the chamber was monitored by —8 using a Bayard Alpert ion gauge. A t y p i c a l vacuum of 4 xlO torr was ob-'-tained by f i r s t baking the system for 2-3 hours under roughing with 8-250W G.E. infra-red heat lamps supplying radiant heat into the chamber through the 14" DIA pyrex b e l l j a r , followed by continuous pumping with both the ion and sublimation pumps for 4-5 hours. The sublimation apparatus (shown schematically i n f i g . 2.1), with the exception of the substrate lamp holder which was i n type 306 stainless s t e e l , was made of high purity tantalum sheets. The s i l i c o n 1 3 source was i n the form of a rectangular bar, 1^" x ^" x 30ml thick. I t was r i g i d l y suspended between the 2 L-shaped supports.with 2 C-clamps separated by a distance of 1". The substrate, locating i n the re-cess of the substrate holder ( f i g . 2.2), could be externally rotated i n and out of the sublimation compartment v i a a magnetically coupled drive. Tp shutter : (•'nfeijral j^Qrt of theTa skelcQ RototobU 'substrate holder arm. (type 306 stainless steel) ^Upportinj f rame (to ground) W thick Ta s/ieet) rCCesS lor Substrate.. ~Ta C~ c lamps -fa S/i/e/c/ 2 m'iCQ sheet for electrical  /soldfjon 6efu/esn e/ec froc/es. F i g . 2.1 Schematic diagram of the vacuum sublimation chamber. 9 F i g . 2.2 Sublimation chamber inside an Ultek TNB vacuum system. Source to substrate spacing could be adjusted by r a i s i n g or lowering the substrate holder arm, and was usually maintained at 1/8" to 1/4" separations. Such close spacing was chosen not only because of the low vapour pressure of s i l i c o n during sublimation but also to avoid the wide departure from equilibrium conditions of the s i l i c o n vapour 43 over the substrate surface. N i c o l l asserted that i f the source-substrate spacing i s less than about 1/10 of the diameter of the source and substrate, the chemical transport conditions i n between are l a r g e l y independent of conditions elsewhere i n the system. In addition, close spacing of source-substrate also means d i r e c t transport of each component of the source material across the space. Substrate heating was created p a r t i a l l y by radiation from the 10 s i l i c o n source and, p a r t i a l l y by a DWY-650W Tungsten Halogen quartz lamp focused onto the substrate holder 3" below by a Ta parabolic r e f l e c -tor. The e l e c t r i c power delivered to the lamp was controlled by a variac The s i l i c o n bar was connected i n series with an external carbon r e s i s t o r , the conductance of which could be adjusted by changing- the pressure on the 80-odd pieces of carbon slab , each 1" square x 1/8" thick, through a tightening screw at one end. • Sublimation was obtained by passing 44 45 e l e c t r i c current ' through the s i l i c o n with a home-made transformer rated at 50A max current. In a t y p i c a l run, a s i l i c o n surface temperature of 1350 +20°C was maintained at the centre of the filament during sublimation. A tem-perature gradient of less than 50°C was observed from the centre portion to the two ends. This corresponds to a loss of about 20u per hour from the s i l i c o n filament, ...and.provided a -deposition rate of about 5u per hour on the substrate through a 20 ml thick quartz mask located at 1/4" from the source. Temperature of the source was monitored by a Hartman & Braun 46 Pyropto (optical pyrometer) corrected with the emissivity data of A l l e n but i t could also be calculated from the resistance of the s i l i c o n bar 47 with the knowledge of i n t r i n s i c s i l i c o n r e s i s t i v i t y vs. temperature The substrate temperature was obtained by a chromel-alumel thermocouple pressing on to the back of the 20ml thick, 1/2" dia. sapphire or spinel substrate. 2.2.2 Source and Substrate Preparation A s i l i c o n filament cut out from a lapped wafer was etched i n 1:1:2-HF (49%) :HNO3(70%) :C^H^ for 1/2 minute to remove roughly 0.5 ml from each surface and give the s i l i c o n a high p o l i s h . I t was then rinsed i n b o i l i n g d i s t i l l e d x^ater and two baths of deionized water p r i o r 11 to i n s e r t i o n into the sublimation system. Both the s t r u c t u r a l and e l e c t r i c a l properties of SOS have been shown to depend heavily on substrate preparation . Although various 48 chemical p o l i s h i n g techniques are a v a i l a b l e i n the l i t e r a t u r e , they often involve strong etching solutions l i k e the hot H^PO + H^SO^, or V 0 at high temperatures, and they do not often give a s a t i s f a c t o r y surface 49 p o l i s h . F i l b y claimed that s i l i c o n i n a s i l a n e and atmosphere can be used to p o l i s h (1102) alumina at a substrate temperature of 1380°C. I t i s now believed that heating sapphire or s p i n e l i n a ambient to a temperature 100-200°C above that used for e p i t a x i a l f i l m growth w i l l r e -move the work-damaged monolayer r e s u l t i n g from the mechanical p o l i s h " ^ and produce a smooth and fe a t u r e l e s s substrate surface. In t h i s i n v e s t i g a t i o n , p r e f i r i n g of sapphire and s p i n e l substrates f or .15 minutes at. a temperature as ..low as 9.5.0°.C .was found s u f f i c i e n t for s i n g l e - c r y s t a l l i n e growth of s i l i c o n at ~800°C. This was done i n s i d e a v e r t i c a l quartz chamber (shown schematically i n f i g . 2.3) using a P h i l i p s PH1012/16 RF generator operated at 1 MHz. P r i o r to ^ p r e f i r i n g , the as-received mechanically polished substrates were given a standard chemical r i n s e . They were then heated i n a ambient to 950°C f o r 15 minutes over the RF-heated carbon susceptor. Temperature was monitored by a chromel-alumel thermocouple sheathed i n s i d e the 1/4" d i a . quartz tube which also supported the carbon susceptor. Standard grade was made to pass through a dehydrated CuSO^ column before use. I t s flow rate of 30ml/min. was monitored by a RGI flowmeter. P o s i t i v e pres-sure i n s i d e the quartz cy l i n d e r was maintained by venting B.^ through a f l a s k containing ^ 0 . After p r e f i r i n g , the substrate temperature was. lowered to 300°C i n 1 minute and the substrate was allowed to c o o l by i t -> 12 self i n the atmosphere before d i r e c t insertion into the vacuum chamber for deposition of s i l i c o n . exhaust pure carbon  susceptor H2Q dehydrated F i g . 2.3 A schematic diagram of the H„-prefiring apparatus, 2.2.3 Sublimation Procedure The experiment was conducted' using source temperatures i n the range between 1300 and 1400°C, and substrate temperatures between 750-850°C. Various deposition rates were obtained by using d i f f e r e n t substrate-source separations, and source and substrate temperatures. A t y p i c a l run was as follows: —8 (1) After a vacuum of 5 x 10 t o r r had been attained, the substrate heater lamp was turned on to about 70% of the variac voltage (110-V maximum) which gradually heated the substrate up to about 500°C. At this time, the substrate was located l a t e r a l l y at 2" from the 13 filament. The background . pressure ..had now risen, to 9 x 10 to r r j and i t would stay at this l e v e l u n t i l the end of sublimation. 15-20V was'tapped from the autotransformer to feed the s i l i c o n filament i n series with the carbon r e s i s t o r (at ~5Q>). E l e c t r i c a l current i n the s i l i c o n filament was then gradually increased by adjusting the conductance of the carbon r e s i s t o r down to about i t s minimum of . 05J.. This was done at a rate which would give a tem-perature r i s e of ~100°C per 15 sec.to the filament. The f i n a l source temperature would be around 100°C below that required for deposition of s i l i c o n films. In about 5 minutes, the left-most portion of the substrate holder was rotated to d i r e c t l y above the filament. This brought the substrate to within a l a t e r a l displacement of only 1" away from the edge of the .source .-and yet, i t was cut off from the main stream of the s i l i c o n vapour by the Ta shutter right underneath i t ( f i g . 2.2). Temperature of the source was readjusted to that which would be used for deposition, and that of the substrate was raised to about 50°C higher than that used for f i l m grow:th. After 15 minutes, a steady deposition rate was assumed to have established as we l l as a homogeneously s i l i c o n - v a p o u r - f i l l e d ambient around the filament. Sublimation of s i l i c o n on to the substrate began when the l a t t e r was rotated to d i r e c t l y above the s i l i c o n source. Substrate temperature was co-ordinated simultaneously during substrate introduction by adjusting the e l e c t r i c power supplied to the heater lamp. Upon completion of f i l m deposition, the substrate was quickly retracted out of the chamber; i t s temperature was then lowered at 14 a rate of 200°C per minute down to 30Q°C, whence the f i l m would be annealed i n vacuum for 1/2-hour. F i g . 2.4 S i l i c o n films on sapphire and s p i n e l substrates; the f i l m at the l e f t was deposited through a quartz mask bearing a geometry for the Van 54 der Pauw H a l l and conductivity mea-surements . 2.3 Methods of Film Assessments Since the s t r u c t u r a l properties of grown films a f f e c t t h e i r e l e c t r i c a l properties, and since t h e i r e l e c t r i c a l properties w i l l deter-mine the c h a r a c t e r i s t i c s of any passive or active devices fabricated using them, an i n s i g h t into both these properties i s therefore e s s e n t i a l for p r a c t i c a l uses of t h i n - f i l m materials. These i n t e r e s t s w i l l be taken up i n d e t a i l f o r the sublimed s i l i c o n films grown at low substrate tem-peratures i n chapter 3. The following section i s to give a b r i e f account of the c r i t e r i a for semiconductor f i l m assessments and to outline the measuring techniques used i n this i n v e s t i g a t i o n . 2.3.1 Deposition Rate and Film Thickness Measurements Average deposition rate for each run could be determined by measuring the f i l m thickness and the deposition time. They varied from a maximum of lu/10min down to about 0.25y/hr. As mentioned above (section 2.2.3), the growth rate was con t r o l l e d by the temperatures of the source and substrate as we l l as t h e i r separation. The grown s i l i c o n -15 films were between. l-4u thick on Czochralski. 10001),. 60°, (1102)) sapphire and ((001), (111)) spinel substrates*. Their thicknesses were measured on a Sloan Angstrometer using a Na l i g h t source (X=5890 X). Accuracy of the Fizeau fringe displacement across the film-substrate step was es-o timated to be within + 150 A. 2.3.2 Structural Properties Eventhough no exis.ting theory s a t i s f a c t o r i l y explains and pre-dicts the e p i t a x i a l r e l a t i o n between a condensate and the substrate, i t i s believed"^ that q u a l i t a t i v e l y the phenomenon of epitaxy i s based on the nucleation of i n i t i a l l y oriented c r i t i c a l n u c l e i , or the growth of a dominant orientation resulting from the coalescence of the variously oriented c r i t i c a l n u c l e i . Direct observation of nucleation and growth of thin-films can be done by depositing films d i r e c t l y inside the elec-52 tron microscope or, to a lesser extent, by r e p l i c a electron microscopy. Study of surface morphology of the grown films by o p t i c a l microscopy and electron microprobe technique w i l l supply information as to the nature of f i l m growth — to see whether they are of the three dimensional growth or layer growth type. The i d e a l case, of course, i s a mirror-smooth, featureless surface f i n i s h . A metallurgical microscope of Union Bi-2395 series and a Hitachi JX3-3A electron microprobe analyser were used to observe the surface topography of the grown f i l m s . Further, c r y s t a l , structure i d e n t i f i c a t i o n s were done by r e f l e c t i o n - e l e c t r o n - d i f f r a c t i o n (RED) using a Hitachi HU-11B electron microscope at a camera constant of o 2.3198 A-cm, and by back-reflection Laue-diffraction on a X-ray machine using a molybdenum tube at 4.5 KV and 15A for 1/2 hr. Supplied by Union Carbide of Canada Ltd., Downsview, Ontario. 16 2.3.3 E l e c t r i c a l P r o p e r t i e s S i n g l e c r y s t a l semiconductor f i l m i s r e q u i r e d f o r the best 53 performance of a c t i v e devices f a b r i c a t e d on i t . In a d d i t i o n , f o r the purpose of r e p r o d u c i b i l i t y , a uniform t h i c k n e s s w i t h smooth su r f a c e f i n i s h and a homogeneous d i s t r i b u t i o n of i m p u r i t y c o n c e n t r a t i o n across t h surface of the grown f i l m i s d e s i r a b l e . In t h i s study, the m a j 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 type was iden t i f i e d by the standard thermal probe technique. C o n d u c t i v i t y and H a l l 54 . m o b i l i t y were measured using the Van der Pauw geometry ; such an r DC' Current Source 1 D -0 0— 1 A SAMPLE T 4. Current , Meter Q B 2 Null Detector Potentiometer PI Potent to metei P2 F i g . 2.5 Block diagram of the H a l l apparatus. For H a l l v o l t a g e measurement, set switch-connections: D - l , B-2, A-3, and C-4. For Van der Pauw c o n d u c t i v i t y measurement, set switch-connections: A - l , B-2, C-3, D-4, and set P2=0; repeat w i t h : A-2, D - l , B-3, C-4, and set P2=0. 17 apparatus had already been described i n d e t a i l elsewhere . The measur-ing c i r c u i t was given i n f i g . 2.5 and i s a modified version of that 5 6 designed by Fischer et a l . . Three Keithley model-602 electrometers were used as current meter and n u l l detectors. Noise l e v e l of the H a l l voltage i s t y p i c a l l y of the order of 0.05 mv, and the accuracy of the current and voltage measurements was at + 5% of the electrometers' f u l l scale readings. The -magnetic f i e l d was supplied by an Alpha 8500 elec-tromagnet powered by an Alpha P8500 power supply. A t y p i c a l f i e l d -2 strength of 0.42 weber-m was used. CHAPTER 3 Structural and E l e c t r i c a l Properties of Low-Temperature-Sublimed S i l i c o n Thin-Films 3.1 Introduction The f e a s i b i l i t y of e p i t a x i a l growth on a s i n g l e - c r y s t a l foreign substrate i s dependent on"^: (1) the amount of l a t t i c e m i s f i t between the substrate and the e p i -t a x i a l deposit — but small m i s f i t i s neither a necessary nor suf-f i c i e n t condition for the occurrence of epitaxy, (2) the degree of surface mobility of adatoms during the processes of nucleation, coalescence, and continuous f i l m growth, (3) the magnitude of the deposition rate at any Lgiven substrate temperature, and (4) contamination of the -ambient as w e l l as the perfection of -sub-strate surface. The present work was conducted at the lower l i m i t of the e p i -t a x i a l temperature range and was not intended to determine the estab-42 lishment of an optimal e p i t a x i a l growth condition. Weisberg et a l . pointed out that t h e i r results for films grown below 900°C were e r r a t i c and irreproducible. The object of this chapter, then, i s to look at such i r r e g u l a r i t i e s , and to explain the s t r u c t u r a l and e l e c t r i c a l properties of these low-temperature-grown s i n g l e - c r y s t a l l i n e s i l i c o n t h i n - f i l m s . Further, since the growth parameters 2-4 l i s t e d above would c r i t i c a l l y influence an e p i t a x i a l growth under the present condition, any s i g n i f i -cant, re s u l t introduced here would have to be derived from a large number of s i m i l a r runs. We s h a l l , therefore, only be interested i n the general features of f i l m growth at such a temperature rather than concentrating 18 19 on the i r i n d i v i d u a l s p e c i f i c a t i o n s . Although no p a r t i c u l a r attempt was made to es t a b l i s h the lowest substrate temperature for e p i t a x i a l s i l i c o n growth on sapphire and spinel substrates, s i n g l e - c r y s t a l l i n e s i l i c o n films of ly and less were i n fact obtained at substrate temperatures a s low as 750°C. 3.2 Structural Properties 3.2.1 Surface Morphology The majority of films grown at substrate temperatures near 800°C had a d u l l , metallic-grey surface f i n i s h , independent of the de-position rate i n the range from O.ly/min down to 0.25y/hr. A t y p i c a l photomicrograph of such a f i l m i s shown i n f i g . 3.1.a. The i r r e g u l a r surface-feature could be e a s i l y i d e n t i f i e d as the grain boundaries. Fig. 3.2.a shows an electron-probe topograph of a 2.ly thick f i l m grown at 800°C on (ll02) sapphire at a rate of Ay/hr from a boron-18 - 3 doped source (at 5 x 10 cm ). The measured H a l l mobility of such a f i l m was over 50% of bulk s i l i c o n with the same c a r r i e r concentration, and i t s r e s i s t i v i t y was about 35% higher than that of the source. I t had a mirror surface-finish and appeared s l i g h t l y reddish when viewed at a an angle. Under xlOOO magnification, i t s surface feature resembled the 58 e p i t a x i a l films grown by the pyrolysis of silane at 1050-1100°C. How-ever, i t i s interesting to note that such a surface feature does not look too diff e r e n t from that observed on a p o l y - c r y s t a l l i n e film, grown under similar substrate temperature- without the use of the H^ p r e f i r i n g treatment ( f i g . 3.2b). The effect of extremely fast deposition rate (flash, evaporation) was also studied. An i n i t i a l t h i n layer of s i l i c o n , estimated at about o 3000A thick, was grown on a 60° sapphire at a rate of 2y/hr at 780°C (c) (d) F i g . 3.1 Photomicrographs of s i l i c o n f i l m s on sapphire and spi n e l substrates (a,b,and c ) , and M o (d) of s i l i c o n filament a f t e r 5 hours of sublimation at ^1400°C. (c) (d) Fig. 3.2 Electron-probe topographs of s i l i c o n films on sapphire & spinel. 22 substrate temperature. This was followed by forcing an anomalous e l e c t r i c current through the s i l i c o n filament,thereby , creating instantaneously a large flux of high temperature s i l i c o n vapour. The source necked and burnt off i n roughly 2 seconds. The f i l m thus obtained was very shiny and appeared to have a continuous surface layer ( f i g . 5.2.c) despite heavy mechanical scratches on the sapphire surface,which are known to be good locations for generating p i t s and steps i n normal f i l m growth. Single c r y s t a l l i n e Laue and e l e c t r o n - d i f f r a c t i o n patterns were obtained from such a f i l m , but the film's r e s i s t i v i t y (-lO^-cm) was so high that e l e c t r i c a l measurement was almost impossible. I t s extremely high defect density was observed by S i r t l + etching i t for 15 minutes. 59 3.2.2 Growth Mechanism I t i s generally believed that f i l m growth usually begins with the .generation of three-dimensional nuclei"^-. -According to E h r l i c h et 60 a l . , each adatom has a f i n i t e l i f e t i m e before i t re-evaporates; and there exists a c r i t i c a l size of a c r y s t a l nucleus above which i t becomes energetically stable and takes up adatoms with the release of the heat of condensation. The maximum number of n u c l e i formed depends on the adsorption s i t e s , impurities and imperfections, e l e c t r o s t a t i c charges 61 present on the substrate surface, and the substrate temperature . The growth of a nucleus takes place p a r t l y by the capture of adatoms that diffuse across the substrate surface and s t r i k e i t s periphery, and p a r t l y 62 by the capture of adatoms that land d i r e c t l y upon i t . The stable n u c l e i 63 grow to form islands and eventually coalesce r e s u l t i n g i n a network structure which subsequently f i l l s up to obtain a continuous f i l m . + 3-g/CrO, 1 part HF, and 10 parts C^O,.. Ref: Z. Metallk, 52 , 529, (1961). 23 In th_e process of coalescence, the islands become elongated i n the d i r e c t i o n of preferred f i l m growth and are separated by long, i r r e g u l a r , 6 4 and narrow channels l i k e those found i n f i g . 3.1.b. In f a c t , the photo-micrograph of f i g . 3.1.b reveals some of the major stages of e p i t a x i a l f i l m growth ( f i l m i s at the left-handed side) on a chemically polished (111) s i l i c o n substrate. These are:- i s l a n d formation (nucleation stage i s somewhat phscured i n this p i c t u r e ) , coalescence, channel stage and con-tinuous f i l m growth. Observation of t h i s 'wide' film-substrate i n t e r f a c e was made possible by creating a narrow spacing between the surfaces of the substrate and a t h i n quartz mask at the time of deposition. The f a c t that such a l i q u i d - l i k e coalescence was not observed i n SOS q u a l i t a t i v e l y sup-ports the argument of poorer surface m o b i l i t y of deposit atoms over the substrate surfaces i n hetero-epitaxy vs homoepitaxy. 37 Yasudu et a l . discovered that 4 preferred o r i e n t a t i o n s were o present i n the i n i t i a l stage (-100A) of growth of S i on (0001) sapphire. This i s analogous to the LEED observations of a mixed S i (111)-7 and S i ( l l l ) - 5 s tructure developed during the i n i t i a l growth stage of homoepi-83 t a x i a l s i l i c o n by Thomas et a l . . In a d d i t i o n , a mixed (110), (001) S i was observed i n very t h i n films grown on (1102) sapphire by hydrogen reduction of silane^~*. S i m i l a r e l e c t r o n d i f f r a c t i o n patterns were also obtained from samples of the low-temperature-sublimed S i films on (0001) sapphire at f i l m thicknesses of up to l-2u ( f i g . 3 .3 .a). 37 With in c r e a s i n g f i l m thicknesses,. Yasudu et a l . , observed changes i n the structure of t h e i r films with the f i n a l o r i e n t a t i o n of (111) .// (0001)^^ Q . This change i n o r i e n t a t i o n s can be i n t e r p r e t t e d as: ( i ) an improvement i n the alignment of n u c l e i and i s l a n d s as growth proceeds, and ( i i ) p r e f e r e n t i a l growth of n u c l e i and i s l a n d s of one preferred o r i e n -t a t i o n at the expense of n u c l e i and i s l a n d s of other preferred o r i e n t a t -(a) (b) F i g . 3.3 Reflection electron d i f f r a c t i o n patterns of sublimed s i l i c o n f i l m s . 26 ions. For films grown at low substrate temperatures ( as i n our experi-ments), the reduction i n free energy of the islands by coalescing d i f f e r -ently oriented n u c l e i or islands to form one preferred orientation i s often severely impeded by low surface mobility of the adatoms, r e s u l t i n g i n a lack of r e c r y s t a l l i z a t i o n to focem a s i n g l e - c r y s t a l l i n e structure. 3.2.3 L a t t i c e Imperfections i n Grown Films The common st r u c t u r a l defects i n semiconductor films are stacking f a u l t s , twins., dislocations, and point-defect aggregations . Accommodation of l a t t i c e m i s f i t between substrate and overgrown f i l m 38 18 would be shared between interface dislocations and e.astic. strains ' i n the f i l m . Extended m i s f i t dislocations occur primarily during the channel and hole stage of growth. In addition, the coalescence of d i f -66 ferently oriented nuclei i s thought to give r i s e to twins . The lack of adequate surface d i f f u s i v i t y of the deposits at low subs'trate tempera tures impair p l a s t i c flow of adatoms between adjacent islands. As a r e s u l t , many small holes are generated at these boundaries, i n i t i a t i n g d i slocation loops, and other defects. Other mechanisms for the formation of l a t t i c e imperfections i n elude:-(1) propagation of substrate imperfection 3:yielding an anomalous - - 30 f i l m growth around the substrate defects ( f i g . 3.1.c), ,(2) production of stacking f a u l t s due to surface contaminations of the substrates by i m p u r i t i e s ^ . Further, with SOS, Heiman^ 8'"^ discovered that aluminum autodoping at the film/substrate interface had created a strongly ionizable 'glossy' layer which generated an inversion layer next to i t i n the s i l i c o n over growth. * See for example section 8.4 i n re f . 68, 27 One often finds a high degree of l a t t i c e imperfections i n 84 hetero-epitaxy because of (a) l a t t i c e mismatch hetween the nuclei of the deposit and the substrate, (b) difference i n expansion coefficients of the two materials, and (c) chemical changes, a s i n the reaction of s i l i c o n with sapphire. Fig. 3.5 Optical micrograph of an etched s i l i c o n f i l m after 15 minutes i n S i r t l etch, (magnification x400 ) Fig. 3.5 shows the o p t i c a l micrograph of an etched s i l i c o n f i l m , which was o p t i c a l l y f l a t before etching, formed on a spinel (111) surface after 15 minutes i n S i r t l etch. A high number of 'holes' or p i t s were observed on the etched surface characterizing the imperfect coales-cence and annihilation of grain boundaries during f i l m growth. The familiar triangular etched pattern which i s due to stacking faults on (111) s i l i c o n surface was not observed here. These, together with the irregular surface feature of f i g . 3.1.a suggests that the i n i t i a l , 28 3-dimerisional nucleatfon and growth pattern of the low-temperature-sub-limed s i l i c o n films p e r s i s t s even a f t e r the formation of a continuous f i l m . Subsequently, we conclude that the poor e l e c t r i c a l properties (see section 3.3) obtained from most of these films were e s s e n t i a l l y due to t h e i r high defect densities generated at the grain boundaries. 3.2.4 A d d i t i o n a l Factors that May Influence the Structure  of Sublimed S i l i c o n Films Layer or step growth pattern, s i m i l a r to those i d e n t i f i e d by 69 70 37 Abbink et a l . and others ' i n e p i t a x i a l s i l i c o n , was also observed i n a 2.5u thick p o l y c r y s t a l l i n e f i l m on 60° sapphire subs'trate grown at 740°C and at 3y/hr deposition rate ( f i g . 3.2.d). Film continuity was pinned down at defect s i t e s ( p i t s ) , which had i r r e g u l a r c r a t e r shapes and c r o s s - s e c t i o n a l areas but roughly the same depth. From the shadow of the dust p a r t i c l e casted on to the f i l m , we can estimate t h e i r depths to be i n the order of 5000 X t h i c k . I t therefore seems l o g i c a l to assume that such defects had been formed before a continuous l a y e r deposit, and that they were originated from surface contaminations of the substrates by impurities. Kikuchi l i n e s i n RED patterns, i n d i c a t i n g a high angular per-f e c t i o n i n the f i l m s , were obtained from S i on (001) and (111) s p i n e l substrates. This i s i n contrary to the RED patterns obtained from f i l m s on sapphire ( f i g . 3.3.b), thus conceding that f i l m s having smaller l a t -t i c e m i s f i t with t h e i r substrates normally have better c r y s t a l s t r u c t u r e s . Very often, when the substrate a f t e r f i l m deposition was not withdrawn fast enough from the sublimation compartment, the s i l i c o n vapour would condense on the cooler surface of the r e t r e a t i n g f i l m r e s u l t i n g i n a very t h i n layer of p o l y c r y s t a l l i n e overgrowth ( f i g . 3.3.c). This indicates that the substrate temperature (~750°C) used i n t h i s 29 experiment was close to the temperature l i m i t for e p i t a x i a l f i l m growth. Despite the fa c t that i t was extremely d i f f i c u l t to a t t a i n high q u a l i t y e p i t a x i a l s i l i c o n films grown at low temperatures, Kikuchi bands i n RED s i m i l a r to that of f i g . 3.3.d demonstrated that i t was not impossible to grow s t r u c t u r a l l y good e p i t a x i a l films at low substrate temperatures using the i n - s i t u s ublimiation technique • 3.3 E l e c t r i c a l Properties 3.3.1 General Table 3.1 shows a sample of the low-temperature-sublimed s i l i c o n films on sapphire and s p i n e l substrates. The e f f e c t i v e c a r r i e r concentration n given i n the l a s t column were derived from measured r e s i s t i v i t y P and H a l l mobility according to the formula n = l / C e ^ u ^ ) * . A few of t h e i r c h a r a c t e r i s t i c s which were summed up from measurements taken from 50 or more f i l m samples are as follows: 18 —3 (1) With s i l i c o n sources of high doping concentration (-5 x 10 cm ) the e f f e c t i v e c a r r i e r concentration i n the deposit films were, at the most, an order or so i n magnitude lower than the doping con-centrations of the source. However, as source impurity concen-18 —3 trationswere reduced to that below 10 cm , the f i l m s were i n v a r -i a b l y found to have higher r e s i s t i v i t y .'and much lower e f f e c t i v e c a r r i e r concentration (often 2-3 orders i n magnitude) than t h e i r source materials. We are to postpone the discussion of t h i s phen-omenal observation u n t i l a f t e r we have considered the trapping model proposed i n section 3.3.3. In f a c t , the d r i f t m o b i l i t y i s the primary quantity of i n t e r e s t . I t i s r e l a t e d to H a l l m o b i l i t y by a f a c t o r of (3/8) TT which i s found theo-r e t i c a l l y for acoustic-mode s c a t t e r i n g and other types of s c a t t e r i n g s 72 i n which the mean free path i s independent of v e l o c i t y . Table 3.1 Film Source Doping Cone, (cm - 3) Substrate .Temperature Substrate Type Film Type Film Thickness R e s i s t i v i t y (J.-cm) H a l l M o b i l i t y (cm2/V-sec) Carrier Cone, (cm -3) Q3 P - 5 x l 0 1 8 820° C (1102) P 2.2y 0.025 86 3 x l 0 1 8 Ml. t? n (100) P 4y 0.069 26 3.4x10 1 8 Q2 ii 800° C (111) P 1.5y 0.545 12.5 9x10 1 7 Ql I ! 820° C (100) P 1.7y 0.46 15.5 8.8xl0 1 7 016 I I i n i t i a l l y at 780°C, after 5min.used 820°C (0001) P 0.9y 1.2 6.2 8.4xl0 1 7 SEC-2 I I 780° C on etched P 0.9y 12.7 21".3 2.3xl01 6 Y14 I I 790° C (100) 60° P 1.3y 1.5 7.9 5.3xl0 1 7 X10 .p-3xl0 1 5 790° C I I P 1.5y 1.8 x l O 4 59 13 5.8x10 B12 n - 6 x l 0 1 6 750° C I I n 1.7y : 230 21 1.3xl0 1 5 PRI-14 n 770° C it n 2.3y 295 . 28 14 7.6x10 PLA01 'O'-free P J 0 1 6 800° C it P 0.9y 4.6xl0 4 39 13 3.5x10 31 (2) Varying the f i l m thicknesses between l-2u did not appreciably affect the e l e c t r i c a l properties of the deposit f i l m s . But, as th e i r thicknesses were increased to more than 2-3 p, a s l i g h t increase i n H a l l mobility and a decrease i n r e s i s t i v i t y were observed, r e -f l e c t i n g an improved c r y s t a l structure i n the thicker films. (3) Low oxygen content had been found by Weisberg^ and others^"*" to give r i s e to better s t r u c t u r a l and e l e c t r i c a l properties of grown films. But with the i n - s i t u sublimation apparatus, no ap-parent improvement i n the quality of films grown from the 10"'""' -17 -3 10 cm ' O'-free* sources was observed. This may mean that the effect of oxygen inclusion i n the films has j been diminished by other growth parameters at low substrate temperatures. (4) The effect of aluminum and magnesium autodoping from the sub-strates, which i s observed to predominate i n a l l high-temperature-grown s i l i c o n films (by CVD a s well as by vacuum deposition), was kept to a minimum. This made possible the growth of n-type films on sapphire at f i l m thicknesses of less than 2u and at a source doping l e v e l of -lO^^cm 3. 86 (5) The crystallographic relations between films and substrates were: (001) s i l i c o n // 60° or (1102) sapphire (111) s i l i c o n // .0° or (0001) sapphire (001) s i l i c o n // (001) s p i n e l (111) s i l i c o n // (111) spinel Supplied by Union Carbide of Canada Limited, Downsview, Ontario. 32 3.3.2 Temperature Dependence of R e s i s t i v i t y , H a l l M o b i l i t y and E f f e c t i v e C a r r i e r Concentration F i g . 3.6 to f i g . 3.8 show the v a r i a t i o n of r e s i s t i v i t y , H a l l m o b i l i t y and e f f e c t i v e c a r r i e r concentration.with temperature for 3 r e -presentative samples. Sample A represented a f i l m with 'good' s t r u c t u r a l and e l e c t r i c a l p r o p e r t i e s , samples B and C represented the majority of films grown from high and low doping s i l i c o n sources r e s p e c t i v e l y . For sample A, the v a r i a t i o n s of p and are r e l a t i v e l y small w i t h i n the given temperature range. the observation of a maximum i n 31 73 ' : H a l l m o b i l i t y agrees with that found by others ' . At low tempera-ture, defect s c a t t e r i n g predominates, and at high temperature, the decrease i n u i s caused by Coulombic s c a t t e r i n g s due to io n i z e d i m p u r i t i e s . The H v a r i a t i o n of r e s i s t i v i t y vs. temperature i n t h i s sample i s also consis-tent with the e l e c t r i c a l properties of h e a v i l y doped s i l i c o n studied 74 by Chapman et a l . . A marked exponential dependence of p and n with r e c i p r o c a l tem-perature was observed for samples B and C. This i s s i m i l a r to the ex-. i i - 73,5,37 , • A *. 7 5 » 5 5 perimental r e s u l t s on s i l i c o n and other semiconductor thm-films grown by other i n v e s t i g a t o r s . Q u a l i t a t i v e l y , one can a t t r i b u t e the r e l a t i v e l y rapid decrease, as compared to bulk s i l i c o n , of e f f e c t i v e c a r r i e r concentration with decreasing temperature to the i n t e r a c t i o n 73 of impurities with the defect structures . A q u a n t i t a t i v e model i s given i n the following s e c t i o n . 3.3.3 Trapping Model f o r Semiconductor Films with Defect Centers Locating at the Grain Boundaries. The presence of c r y s t a l l i n e defects a c t i n g as e l e c t r o n traps was demonstrated by Dumin et a l . ^ from measurement of the e l e c t r o n concentration i n films of constant donor density but varying d i s l o c a t i o n 33 F i g . 3.6 Film r e s i s t i v i t y versus temperature. Fig. 3.7 H a l l mobility versus temperature. F i g . 3.8 Effec t i v e c a r r i e r concentration versus temperature. 36 density. They noticed that n decreases as the defect density increases . - Analysis of data taken from both, p-type and n-type films 78 indicates that the Fermi-level i s pinned down by deep levels . These . 78 levels may occur at the grain boundaries , at the silicon-substrate i n -terface^ 8, or they may be uniformly distributed i n the f i l m . From o p t i c a l absorption 7^'^ 7 and photoconductivity 7 7'*^ 8 measurements, these donor and acceptor type traps appear to occur i n approximately equal density, 17 18 — with density as high as 10 -10 cm 3being deduced. Deep l e v e l s due to dislocations i n bulk s i l i c o n have been reported as well by Glaenzer et 80 a l . . The general theory, therefore, i s that these acceptor and donor 78 type traps are caused primarily by the dangling s i l i c o n bonds at grain boundaries and distorted l a t t i c e i n the neighbourhood of these 77 grain boundaries; and, they may also be associated with precipitates Optical conductivity measurements were . taken on a few of the low-temperature sublimed s i l i c o n films using a Bausch and Lomb monochromator i n the 0.7 - 1.5u range. The result showed q u a l i t a t i v e l y a gradual increase i n photoconductivity of the samples with increasing 60 incident photon energy, s i m i l a r to that observed by Heiman . The following trapping model i s based on 2 well-established experimental observations discussed above:- a) Fermi-level i s trapped deep inside the forbidden gap by ionized impurity centers, b) the majority of de-fects are located at the grain boundaries and, when ionized, they w i l l cause band bending. Let us assume that for an n-type semiconductor the surface den-s i t y of traps caused by defects at the grain boundaries i s Nfc, with a capture cross-section and a c h a r a c t e r i s t i c i o n i z a t i o n energy l e v e l E t measured from the conduction band edge. I f the surface density of f i l l e d traps i s ' n and the average electron v e l o c i t y i s v^, the rate 37 at which, electrons combine with traps w i l l he v o" (N -n )n/(l 1+l„), ^ n n t t 1 2 where n i s the average density of free electrons i n the irihomogeneous f i l m , and (1^+1^) i s the average grain s i z e . The i n t e r a c t i o n of trapping centers with c r y s t a l l a t t i c e releases electrons at the rate v o n n„/ n n t 2 ( l ^ + l ^ ) , where i s the density of electrons i n the conduction band when the Fermi-level i s at the trap l e v e l . The d i f f e r e n c e i n these 81 rates gives the net rate of change of trapped electrons , an -d t - \ n 5 — — = v a (N -n ) - v a n 3t n n t t ( 1 1 + 1 2 ) n n t 1 1 + 1 2 (3.1) n (Nfc - n t) = n t n 2 At equilibrium, the rate of change of trapped electrons has to be zero. (3.2) Next, we consider the one-dimensional inhomogeneous f i l m model of f i g . 3.9 . Here, we assume that the majority of the trapping Neutral Region Grain Boundary F i g . 3.9 A one-dimensional in-homogeneous f i l m model. centers are located at the grain boundaries. From the requirement of charge n e u t r a l i t y , a space charge region of opposite p o l a r i t y to that of the i o n i z e d traps i s generated. Its width of 1^ i s r e l a t e d to the number 38 of trapped carriers at the grain boundaries by _ ! ' • (3-3) n t -"ih ' where n^ i s the doping l e v e l and i s approximately equal to the free electron concentration i n the neutral region. Now.the number of free electrons at the top of the space charge b a r r i e r with respect to n^ i s ( E c - E F) - E f c n2 = n i 6 X P a n < i ^ 3'^ 95 according to the depletion approximation , the b a r r i e r height e<t) = (EQ -E-.) - E may be written as f t <Ec - V . - E t = ! r * ( ^ ) 2 ' ( 3 - 5 ) where e i s the electronic charge, and e i s the p e r m i t t i v i t y of the semi-conductor. Using the values' o f 12,;(3.3);, and e*. (3.5), we obtain n i n terms of as 2 2 n t e n t n = F=n~ n l 6 X P _ (8lkfnT) • ( 3- 6 ) t t 1 The negative exponential dependence of n on temperature as derived i n (3.6) i s consistent with both our experimental results and those of the others discussed i n section 3.3.2. By assuming that n^ and -\ n are both constant with temperature, and that n. i s approximately equal , t to the source impurity concentration, we obtain the values of n f c and N 11 -2 12 -2 11 -2 as 8 x 10 cm and 1 x 10 cm" for sample B and 2 x 10 cm and 3 x 1 2 - 2 10 cm for sample C. From these r e s u l t s we conclude that the density of defects N i s r e l a t i v e l y i n s e n s i t i v e to the source doping concentration (5 x lO^cm 3 for sample B vs. 6 x lO^cm 3 for sample C) . The immediate implication i s that the impurity segregation at the grain boundaries does not piay a major role i n defect generation, and that the apparently 39 poorer f i l m quality at lower c a r r i e r concentrations may be attributed to impurity compensation by ionizable s t r u c t u r a l defects. In f a c t , (3.6) t e l l s us more than j u s t the negative exponential dependence of n on T, i t also confirms and explains the puzzling experi-mental observation that the ef f e c t i v e c a r r i e r concentration deviated more from the actual impurity concentration of the source when the l a t t e r 73 was at a lower doping l e v e l than at a higher doping level:: . I f we as-VC sume that n varies slowly with d i f f e r e n t source doping l e v e l , then the exponential factor i n (3.6) w i l l be close to unity for large values of n^, and n w i l l d i f f e r from n^ by a factor of n f c/(N^-n^), which i s not too much smaller than unity. S i m i l a r l y , with low source doping l e v e l , and therefore n^, the exponential factor w i l l be much smaller than unity, and the measured value of n w i l l deviate more from that of n-^ * To obtain a s i m i l a r temperature-dependent expression for f i l m r e s i s t i v i t y , we proceed as follows: In a stationary f i e l d , the current density J wit h i n the inhomo-geneous f i l m should be the same for the neutral regions and at the grain boundaries. From Ohm's law J = = o 2E 2, (3.7) where o~^ , o"2 and the corresponding values of E^, E 2 are respectively . the conductivities and e l e c t r i c f i e l d s for the neutral regions, and at the grain boundaries. But according to our inhomogeneous f i l m model I t i s a reasonable assumption, since the function should have a stronger dependence on the growth parameters rather than on the segre-gation of impurities at the grain boundaries: the experimentally derived values of n f c and N confirm t h i s statement. 40 en-E2 " E l = ~ 2 T V ( 3 ' 8 ) Combining (3.7) and (3.8), and using (3.3) for the value of 1 2, we have a en 1 (o^-o^) 2e • But, we can also express (3.7) in terms of the c a r r i e r s ' mean l o c i t i e s ( v 1, v 2 > v) as ve J = n 1 ev 1 = n 2 e v 2 = n ev . (3.10) Using conservation of energy expression 1 2 1 2 I I 2 m e V l = 2 m e V2 " I 6 * ' ' where m i s the effec t i v e mass of the free electrons i n the conduction e band, we obtain the carrier's mean v e l o c i t y , averaged over the neutral region and the grain boundaries, as v = 1 I f I , (3.11) -m en ( — 2 - - — ) n2 n l Further, (3.7) and (3.10) allow us to write 1 _ _ E± = .5^  n e v . (3.12) Substituting the value of v from (3.11) into (3.12) and equating the value of i n (3.9) and (3.12), we have, after some algebraic s i m p l i f i c a t i o n , m e n l 1 p2 = P l + ~ 2 — ^2 ~ n i ^ ' (3.13) e e where and p 2 are respectively the r e s i s t i v i t i e s for the neutral region and at the grain boundaries. For n 2 << n ^ , 41 (3.. 14) 82 Equation (3.14) i s i n agreement with Volger's a s s e r t i o n that the grain boundary i s a region having higher r e s i s t i v i t y than that i n -side the grain. Using his q u a l i t a t i v e r e s u l t of the observed r e s i s t i v i t y p = + P 2 ^2^1 w e 0 b t a i n 3 1 1 expression for p which has an exponential temperature dependence s i m i l a r to the one observed i n the experiment. In addition, we can now understand why the measured f i l m r e s i s t i v i t y p at . low source c a r r i e r concentration n^ i s so much higher than that of P r 3.3.4 E f f e c t of Post-oxidation on the E l e c t r i c a l Properties  of Low-Temperature-Sublimed S i l i c o n Films For p r a c t i c a l device a p p l i c a t i o n , i t i s e s s e n t i a l that e l e c t -r i c a l properties of any semiconductor t h i n - f i l m should not change ap-34 p r e c i a b l y during the thermal oxidation used i n device processing P o s t - f i r i n g of s i l i c o n i n oxygen has been reported to remove acceptor-type impurities from the wafer and to push donor-type impurities back ,. 82 . , ... , . 65,76 . ... . .6 i n t o the wafer ; with silicon-on-sapphire . and s i l i c o n - o n - s p m e l , i t i s observed to remove aluminum impurity created by substrate auto-doping during s i l i c o n f i l m growth. This i s a t t r i b u t e d to the high d i f -f u s i v i t y of aluminum i n s i l i c o n and f o r i t s tendency to segregate i n the growing s i l i c o n oxide. However, appreciable e l e c t r i c a l changes could also r e s u l t from such a process. Ross et al."* imputed the m o b i l i t y degradation i n the s i l i c o n films to the i n t r o d u c t i o n of s c a t t e r i n g cen-te r s by the p r e c i p i t a t i o n of neutral aluminum-oxygen complexes. In t h i s experiment, thermal oxidation of s i l i c o n f i l m s was conducted i n s i d e a h o r i z o n t a l quartz tube (the d e t a i l e d set-up w i l l be 42 given i n section 6.2.4) at 1050°C for 15 minutes i n steam. The samples were subsequently annealed at 350°C i n atmosphere for ~ hr. before they were taken out of the reaction chamber. The oxide films were re-moved using 49% HF and then rinsed i n b o i l i n g d i s t i l l e d water. Ohmic contacts were applied, and the van der Pauw geometry was again used for both the. conductivity and H a l l mobility measurements. A few of the re-sult s are given i n table 3.2. Comparing the conductivity and H a l l mobility' measurements on the s i l i c o n films before and a f t e r thermal oxidation revealed only very minor changes i n e l e c t r i c a l properties of the low-temperature sub-limed s i l i c o n f i l ms. This suggests that aluminum autodoping, which i s commonly found i n films grown at higher substrate temperatures and which may often cause a- reduction i n c a r r i e r concentration up to an order or so i n magnitude a f t e r thermal oxidation., has been., kept to a n e g l i g i b l e amount by using low substrate temperatures for f i l m growth. Table 3.2 ' Film Thermal Treatment Substrate Type R e s i s t i v i t y (ft-cm) H a l l M o b i l i t y (cm2/v-sec Effective c a r r i e r )Conc.(cm - 3) Q3 as-deposited oxidized (1102) 0.025 0.026 86 83 3.1 x 1 0 1 8 3.1 x 1 0 1 8 KII as-deposited oxidized ( H I ) 0.65 0.69 20.5 19.8 4.7 x 1 0 1 7 4.5 x 1 0 1 7 PRI-14 as-deposited oxidized 60° 295 302 28 22 7.6 x 1 0 1 4 9.3 x-10. X10 as-deposited oxidized 60° 1.8x10^ 2.5x10 59 38 13 5.8 x 10 13 9 x 10 t See also f i g s . 3.6-3.8 for the variations of p, u, and n on temperature for the sample KII after thermal oxidation. CHAPTER 4 A Thin-Film U R C Structure 4.1 Introduction A t h i n - f i l m URC (uniformly distributed RC) structure normally consists of a d i e l e c t r i c layer sandwiched between a r e s i s t i v e layer and a highly conducting metal layer, a l l of which are deposited on an insu-l a t i n g substrate ( f i g . 4.1). 87 The r e s i s t i v e t h i n - f i l m can be made of (a) an a l l o y , e.g. nichrome, (b) a single metal, e.g. tantalum or chromium, (c) a cermet, e.g. Cr-SiO, or (d) a semiconductor. The method of preparation can be: vacuum deposition, electroless p l a t i n g , hydrolysis or p y r o l y s i s , etc. The most commonly used d i e l e c t r i c films are tantalum pentoxide, 88 aluminum oxide, and s i l i c o n oxide . Deposition methods include thermal, anodic or plasma oxidation, reactive or RF sputtering, vacuum evaporation, chemical decomposition, and polymerization. The substrate can be, for example, glass, alumina, quartz, or s p i n e l . However, i f a semiconductor i s chosen for the r e s i s t i v e com-ponent, the selection of substrate becomes c r u c i a l i f e p i t a x i a l semi-conductor i s needed: p o l y c r y s t a l l i n e semiconductors have r e s i s t i v i t i e s 5 6 89 of the order of 10 -10 fi-cm and are hence not i d e a l for use i n URC devices. I t i s the purpose of t h i s chapter to study the influence of semiconductor-insulator junction properties on a t h i n - f i l m URC structure. To comply with useful s o l i d state device dimensions, we s h a l l from now pn assume that the e p i t a x i a l semiconductor has a thickness of no more o than 2-3u, and no less than 1000A. In p a r t i c u l a r , we s h a l l use the . n-type s i l i c o n and the thermally grown Si02 for our i l l u s t r a t i o n s . 43 44 S-fi) (iv) OH) ( n ) (v) (a) (i)-D — A V (M (b) F i g . 4.1 A schematic diagram of a t h i n - f i l m URC s t r u c t u r e : (a) p h y s i c a l structure i n d i c a t i n g ( i ) ohmic contacts (S-source, D-drain), ( i i ) semiconductor channel, ( i i i ) d i e l e c t r i c l a y e r , (iv) h i g h l y conducting metal layer (gate), and (v) i n s u l a t i n g substrate; (b) e l e c t r i c a l symbol of a URC stru c t u r e . M MO "F i (a) 5 J Vg & (b) Electron Accumulation EP Channel Inversion t-F F i g . 4.2 Energy band diagrams of an MIS structure (n-type' semiconductor) showing d i f f e r e n t modes of operations: (a) the flat-band case, (b)' accumulation mode, and (c) deep-depletion into the i n -v e r s i o n mode. (c) Vg^O 45 4.2 Review of MIS Theory , 4.2.1 Ideal C-V Q i a r a c t e r i s t i c s of MIS Structures For a metal-insulator-semiconductor (MIS) system, i n which the metal and the semiconductor work functions are equal and there are no surface states at the semiconductor-insulator i n t e r f a c e , the energy-band diagrams (n-type semiconductor) are as depicted i n f i g . 4.2. When the gate i s made p o s i t i v e r e l a t i v e to the n-type semicon-ductor, electrons from the bulk semiconductor are a t t r a c t e d to form an accumulation l a y e r underneath the insulator-semiconductor i n t e r f a c e . The small s i g n a l ac capacitance measured across t h i s structure w i l l be G\ , the i n t r i n s i c i n s u l a t o r capacitor. However, i f the applied voltage V S i s negative, electrons w i l l be r e p e l l e d away from the same i n t e r f a c e and, a space charge region consisting of i o n i z e d donor impurities w i l l develop. The growth of this space charge l a y e r -gives r i s e -to an increasing-depletion l a y e r capacitance C^ - i n series with G\. Upon further decrease i n b i a s i n g p o t e n t i a l to a value such that the semiconductor surface p o t e n t i a l ^ g at the Interface i s numerically equal to, or greater than, twice the Fermi-p o t e n t i a l T\> , the semiconductor surface i s s a i d to be inverted and a very thin layer of p o s i t i v e charges begins to e f f e c t i v e l y s h i e l d the depletion region from any further increase i n e l e c t r i c f i e l d . The measured small s i g n a l capacitance for large negative values i n w i l l approach that of C\. But, for high frequency s i g n a l s , such that the minority car-r i e r s i n t r a n s i t i o n across the depletion l a y e r are short i n following, the s i g n a l , the s h i e l d i n g e f f e c t disappears and C w i l l l e v e l o f f at the minimum value of C. i n s e r i e s with C,. l d 4.2.2 MIS Structure Including Traps and Surface States In a r e a l MIS system, surface states together with impurity 46 and oxide traps play an important role i n determining the actual semi-conductor surface potential at the semiconductor-insulator interface. A few of the wel l established facts which are required for our analysis of a semiconductor U R C structure are l i s t e d below: (1) The amount and dis t r i b u t i o n s of surface states and oxide traps are determined primarily by the method of oxide preparation, the l a t t i c e orientation of the semiconductor, the contaminants i n t r o -duced during oxide growth, and the annealing treatments of the oxidized structure. (2) The interface states i n the oxide l i e very close to the semicon-ductor-insulator interface and can i n most p r a c t i c a l cases be re-garded as residing at the interface. (3) For a ca r e f u l l y prepared sample, charges that are trapped at the interface are almost independent of the biasing voltage. This allows one to determine the amount of surface states at the i n t e r -face (mainly the interface-trap density) by calculating from the flat-band voltage s h i f t i n the C-V c h a r a c t e r i s t i c . 4.3 Channel Conductance of Semiconductor Thin-Films After Thermal Oxidation I t i s well known that r e d i s t r i b u t i o n of impurities at the surfaces of semiconductors w i l l take place i n the process of thermal 83 11 oxide growth ' . The doping p r o f i l e underneath the interface of a thermally growth oxide had been shown to follow the normal d i f f u s i o n 83 theory . In this section we s h a l l look at the effect of thermal o x i -dation on the channel conductance of a semiconductor t h i n - f i l m r e s i s t o r . Let us assume that a homogeneous n-channel semiconductor t h i n - f i l m r e s i s t o r h i s after thermal oxidation a thickness a, width Z, 47 and length L. The r e d i s t r i b u t i o n of impurities casues a change i n Fermi-potential from the surface down to a depth of x' $ a.' The change i n r channel conductance of the r e s i s t o r can be calculated as follows: The channel conductance g = - J a(x) dx o = f f q u p(x) +n(x)] dx (4.1) where u , u are the effec t i v e c a r r i e r m o b i l i t i e s for electrons and n p holes with densities of p(x) and ri(x) respectively. Now, n(x) = n. exp-(u -u) l F p(x) = n. exp (u -u) , (4.2) where n j i s the i n t r i n s i c c a r r i e r concentration and u = £><J; i s the el e c t r o -s t a t i c p o t e ntial i n kT/q units.. Z ( a % So, g = - qy n (-f- exp (u -u) + exp-(u -u)') dx (4.3) Jo n We can separate the l a s t i n t e g r a l into two parts, one containing the surface region, and the other the homogeneous underneath layer with constant u„. Further, i f we introduce a change i n variable i n the f i r s t r i n t e g r a l from dx to l/(du/dx) with I dx = k S i n h U F + C O s h ^ UF~ U^ ~ C O S h "F-'2 » (4.4) •f £ S I 1/2 i n which = •(•---• qn^) i s the i n t r i n s i c Debye length (see Appendix A) , we get, * i— 92 The redistributed region i s l i m i t e d to 4/Dt from the interface , with D denoting the di f f u s i o n constant of the impurity, and c the time of oxidation. 48 g = M qu n [— exp (u -u) + exp -(u„-u)] du Z l'uF U n F F L / 1 s — j [u sinh u + cosh (u -u) - cosh u ] z f a y P + r / qu„ t — n exp (u ) + n exp -(u )] dx (4.5) The distance x' can be determined from (4.4) as fU: F U s J l [u sinh u-. + cosh (u -u) - cosh u . (4.6) r r c At room temperature, exp (-uJ)» t— exp (u„) , r U r n /Up []i /y^  exp (2u_.-u) + exp (u) ] d u Aence, f ~ = ~ 2 — ~ ' 172 S o yu g a ^ / ^ [u sinh Up + cosh (Up-u) - cosh Up] + a-x' a , (4.7) where = ZaaL .., i s the conductance of an equivalent semiconductor t h i n - f i l m r e s i s t o r having a uniform e l e c t r i c a l conductivity a and the same physical dimensions as ' the one considered above. Knowing what the bulk doping concentration CL i s for the semi-conductor, which i s almost the same as the homogeneous impurity concen-t r a t i o n of an unoxidized sample, we can f i n d the doping p r o f i l e i n the 93 83 ~ f i l m either experimentally or, by calculations based on the conditions of thermal oxidation. Then numerical evaluation of (4.6) and (4.7) w i l l give the change i n channel conductance as required. The above derivation has assumed that ohmic contacts to the semiconductor e x i s t at the 2 ends of the r e s i s t i v e element, so that both holes and electrons can be the e f f e c t i v e charge c a r r i e r s . This assump-By convention u i s negative for n-type semiconductor. 49 t i o n i s to he taken f o r a l l other s i m i l a r analyses contained i n th i s chapter. 4.4 DC Channel Conductance of Semiconductor Thin-Films i n a MIS Structure 4.4.1 Channel Conductance with V g = 0 For an e p i t a x i a l semiconductor grown on an i n s u l a t i n g sub-" 68 94 s t r a t e , the substrate-semiconductor i n t e r f a c e ' r e s u l t s i n an extra complication to the simple MIS st r u c t u r e . However, f o r most of the prac-t i c a l t h i n - f i l m devices, the f i e l d e f f e c t i s normally confined to a region close to the oxide-semiconductor i n t e r f a c e so that the space, charge e f f e c t generated at the film-substrate i n t e r f a c e can often be neglected i n the f i r s t order approximation of a n a y l s i s . We s h a l l now look at the v a r i a t i o n of channel conductance i n a MIS structure as a r e -s u l t of varying the surface p o t e n t i a l by an external b i a s i n g voltage. The e f f e c t of impurity r e d i s t r i b u t i o n a f t e r the oxide growth i s neglected. Further, we are to include only the i n t e r f a c e states i n t h i s a n a l y s i s . (1) Depletion Mode We s h a l l consider i n t h i s section the case i n which the source and drain regions have the same p o t e n t i a l with respect to the gate. In s t a t i c equilibrium, vG = v * s + ^ ( 4 - 8 ) QG - -Qs - Q s s (4.9) where V i s the p o t e n t i a l across the oxide, o A f a c t o r of 10 i n the r a t i o of surface to bulk impurity concentration w i l l a f f e c t the surface p o t e n t i a l by l e s s than one tenth of an e.v. at 123 room temperature 50 ^ i s the semiconductor p o t e n t i a l at the i n t e r f a c e , s i s the metal semiconductor work function difference, MS Qg, Q g and Q g s are r e s p e c t i v e l y the charges on the metal gate, i n the depletion region, and those i n the i n t e r f a c e s t a t e s . 95 Using the depletion layer approximation , and assuming no free charge 98 c a r r i e r s i n the depleted region, we have ND X d ' where q i s the e l e c t r o n i c charge N__ i s the donor density i n the semiconductor x^ i s the depletion l a y e r width measured with respect to the oxide-semiconductor i n t e r f a c e . Now, the e l e c t r i c , f i e l d . E g at... the., interface, is. given, by ( f i g . 4.2c) E = - ^ •8 dx n " " « - N D x d / e s ( 4 - 1 0 ) x=0 + so that, s o o sin c e , % = V o C o . Equation (4.11) can be reduced to an i d e a l MIS case when we r e -place V' f o r (V - + Q /C ) as the equivalent gate p o t e n t i a l . From G G JMo SS o con t i n u i t y of the displacement vector D 8u> £ s 9x n 1 9 x (4.12) x=0 where c and e_ are the d i e l e c t r i c p e r m i t t i v i t i e s of the semiconductor s I and the i n s u l a t o r r e s p e c t i v e l y . 51 Substituting (4.10) into (4.12) gives e q N n = e T — — (4.13) s D e I -x > s o and using ^ the value of ^ g from (4.11), we obtain the depletion l a y e r width x. as d x = — x + / ( — x )Z ^ - V ' (4.14) d E l ° V £ I ° q ND G ' The channel conductance can then be ca l c u l a t e d from g = g D (1 - Xd/a) (4.15) where g = aZa/L = Z q u N_ a/L. o n D (2) Accumulation and Inversion Modes In e i t h e r the inve r s i o n or the accumulation mode of operation, part of the c a r r i e r s responsible f o r conduction are confined to a region very close to the i n t e r f a c e . For enhancement mode, we can f i n d the en-~ 96 hanced conductance as follows: T o t a l charge/area i n the enhanced l a y e r i s £ I Q = - C V ' = - — V' (4.16) G x G o This charge d i s t r i b u t i o n can be represented by containing i t i n a u n i -form layer of thickness A and denisty n gy so that Q = -n X q. (4.17) Then the enhanced conductance i s g' = n g qu nA f - . e i V c T x f l T ; < 4 - 1 8 ) and the enhancement-mode channel conductance i s given by g/g D = 1 + g'/g o 52 However, pot e n t i a l V' cannot be increased i n d e f i n i t e l y , because the 5 97 e l e c t r i c f i e l d at avalanche breakdown i s about 5 x 10 V/cm for S i Another method for calculating surface conduction i s to account for 98 i t i n terms of surface potentials. To do t h i s , we find the number of holes or electrons per unit area i n the accumulation or inversion region r e s u l t i n g from a f i n i t e surface p o t e n t i a l . The inversion charges i n an n-type semiconductor are: / • U Q i n v = q I p ( x ) d x * ( 4 - 2 0 ) Jo So the change i n channel conductance i s f V y* exp (u -u) Agh = £ i n i rJ d u / d x — d u • <4-21> *^ u s * 99 where i s the effective hole mobility i n the inversion layer . The f i n a l expression for g i s obtained by -combining A^ g with -that value of g i n (4.15) at maximum depletion layer width x c j m a x (see Appendix A for x , ) j dmax; i . e . g. = g(x, = x, ) + Ag, , (4.22) inv d dmax bh * For operation i n accumulation mode, the enhanced conductance i s due to an accumulation of majority c a r r i e r (electrons) at the semiconductor surface, so that An = n ± [exp - (u p-u) - exp -u p] . (4.23) Hence, ' u * f F y exp - u (exp u - 1) Ag e , q « ± l m dn, (4.24) s * where y i s the electron surface mobility, n The actual channel conductance i s therefore given by gAcc = % + A g e ' 53 4.4.2 Channel Conductance with V ^ 0 U o In section 4.4.1, wehaveseen how the interface states and the metal-semiconductor contact potential difference can be taken care of by simply replacing the actual gate potential V with i t s equivalence of G V'. Henceforth, we s h a l l only consider the e l e c t r i c a l behavior of a G semiconductor channel having a n idea l C-V c h a r a c t e r i s t i c . me tal electrode insulator ^depletion region F i g . 4.3 A URC structure with V_ i V . JJ O A URC d i f f e r e n t i a l subregion i s defined by: y l < 7 < y2 ' y y 2 - y1 small < x < < z < a Z With V f 0 and V > 0, the second derivative of the channel Do G . potential W(y) at distance y from the source region i s not i d e n t i c a l l y equal to zero at the space charge boundary;here we have written W(y) 2 2 i n place of - ( V G S - V(y)). However, i f 8 W/3 y i s small compared to qNp/es, the one-dimensional approximation can be applied, and W(y) can be related to the space charge width by the same r e l a t i o n as i n the 54 case of V_„.= 0. Further, i f the e l e c t r i c f i e l d E varies much slower DS x than Ey at the space charge boundary with y, Shockley's gradual channel • I T , .,100 approximation can also be used The DC conduction current at y i s given by I D ( y ) = z f J D(x,y) dx (4.25) = -Z q y n J N ( x ) d x • ^  (4.26) Assuming constant doping p r o f i l e a l l through the depth of the f i l m , we integrate Ip(y) from y = 0 to y = L, o Now, the space charge width i s as given i n (4.14) 3 . XD _ , . E s Xo . 2 q ND „ r , £ s ,2 2 E s „ . I f -o I s I n D v. 2e — - V 1 [1+ c.p 2 -..3) <*•»> where I «.-y qN V ^ (4.29b) o n D D L • "If V ^ V , we can make use of the binomial expansion for the term i n square brackets, a n x j arrive at 1 1 3 X D _ , es V "2 1 . 2 £ s V " 2 . 1 , 2 £ s \ 2 " I n „ns • i " - 1 + t r * " X G ~ 4 x G + 24 fe-y) x G ( 4 - 3 0 ) o I D a D a ' 117 , , Q = 2.x 10'4cm Xo = .1 * 10°cm For n-tvpeS^with V<; = 0. -20 -m vg=ao ND-NA=W17 4.0 5D VD (volts) U l F i g . 4.4.a Theoretical channel conductance of a Si-URC s tructure as a function of V^. a = 2.x 104cm.; x0 = 7. x 105cm. .2 0 ,7 .2 .3 X . 5 ~S T 3 ~ 0 ..' _ VCAMAX F i g . 4.4.b Theoretical channel conductance as function of the gate p o t e n t i a l V . 57 where x G = (— — ) - ( — ~ ) I n D a (4.31) It can e a s i l y be shown that the r a t i o of I~/I i s i d e n t i c a l l y the same D o as g(V^,V G) / g Q(V D,0) ywhere g Q(Vp,0) i s the channel conductance under the f l a t band condition. 4.4-3 Small Signal Parameters for Thin-Film MIS Structure For a given channel p o t e n t i a l , the channel conductance i s given by (4.15) g(W) = Z qu n N Da/L (1 - x d(W)/a); (4.32) so we can rewrite (4.27) as GD XD = - g(W) dW. VGS From our d e f i n i t i o n of W(y) = ~ ( V G S - V(y)) (4.33) 3W GD 9W av -1, GD DS 3V. = 0. DS (4.34) The small s i g n a l source-drain conductance g^ g defined by 31. 'ds 9V. DS 9 V W G D  8 WGD 9 VDS V (4.35) xs 8ds = ^GJ? e x / e x „ 2e = ( i + _ ± _o _ /(_JL _°)2 + w I v I qN^a (4.36) S i m i l a r l y , we f i n d the small s i g n a l transconductance g^ of the channel as n D g(V D,V G) = I D S / V D S = -VV D' I n t h e f l a t- b a n d c a s e 8 0 ( V D ' 0 ) = ZW- N^ a / L - - I D / V D ; so g ( V D , V G ) / g o = ' y i o . 58 S m 9 VGS 9 WGS 9 VGS 9 WGD 9 VGS = g(W G S) - g(W G D) (4.38) 4.4.4 D i s t r i b u t i o n of Channel P o t e n t i a l and the Shape of . Space Charge Width Along the Channel To f i n d the d i s t r i b u t i o n of p o t e n t i a l along the channel, we use the expression •W W^ X g(W) dW -'  L r WGD g(W) dW (4.39) (4.40) W GS This w i l l give us the r a t i o of y/L f o r a given W $ W <: W . Go X GD To f i n d the channel p r o f i l e we f i r s t f i n d dx,/dy as a ^ = J i L 1 dW dy - qN D % dy ' . ( x d + ^ X o > then substitute dW/dy i n t o (4.26), assuming constant doping p r o f i l e a l l through the semiconductor f i l m , we have dx qN e VY ) = -Zq. nN D ^ ( x d + - ± x o) (a - x ^ _ (4.41) Integrating the above equation from y = 0 to y, whence x^ = x^s and res p e c t i v e l y , we f i n d the r a t i o I . qN £ - e x ' „ 2 e _o 1_ _L_D r x _s 7 X _ x ) + k n _ _£ -°) f x 2 _ x 2) _ L 1^  V„ e L x o e T U d X d s ; + 2 U e T a P U d W D D s I I X0 = I xW5cm. , a = 2. xl04cm. — ND = / . A - 7075 F i g . 4.5.a D i s t r i b u t i o n of channel potentials i n Si-URC structure. X„ = /. x 10*'cm. = 2. x tO cm. 61 where the value of I q i s as given by (4.29b). From (4.42) we can compute y/L for given values of -V , W and x^(y). 4.5 AC Small Signal Modelling of Thin-Film URC Structure 4.5.1 Equation of State 1 Our present task i s to come up with a small signal model"''^ ''" which w i l l f a c i l i t a t e the use of semiconductor distributed RC element as an e l e c t r i c c i r c u i t component. The basic postulates used i n the following analysis are: (1) The RC distributed structure i s assumed to have a uniform cross-section of width Z, a semiconductor layer of thickness a, and an oxide layer thickness x . / o (2) The terminal contacts to the semiconductor are ohmic. (3) For a n-type semiconductor, the number of mobile charge -3 ca r r i e r cm i s taken i d e n t i c a l l y equal to N^ ., the doping, concen-t r a t i o n of the f i l m . (4) The conducting channel i n the semiconductor i s assumed to have an eciui-potential surface perpendicular to the direc t i o n of flow of charge c a r r i e r s , and that the conducting current i n the channel has only a y-component. (5) The quasi-static approximation v a l i d at a l l points and at a l l time i s to be assumed, so that E(x,y,t) = VY(x,y,t). (6) The d i e l e c t r i c material i s assumed to be polarized uniformly and that i t contains no free volume charge. In other words, the d i e l e c t r i c i s l o s s l e s s , and that the current density i n i t i s zero. (7) We assume that E i s independent of x i n the d i e l e c t r i c , so x that E = E ( y , t ) . 62 (8) F i n a l l y , f o r easy mathematical manipulation, we assume that any net charges within the semiconductor appear as i n t e r f a c e states at the insulator-semiconductor j u n c t i o n . We s t a r t by taking a d i f f e r e n t i a l subregion of the device de-fined by ( f i g . 4 . 3 ) y l * y * y2 ' y = y2 ~ y l i s s m a 1 1 -x s x £ a o 0 £ z $ Z J and we. assume -that a space charge layer of depth 'd' e x i s t s . The e l e c t r i c current density enters and leaves the enclosed surfaces of the semiconductor sub-region only at y^ and y,,. Thus we can write = C) i . n dS ( 4 . 4 3 ) dt J ~ ~ 3 a fa = 'Z ! j (x,y (,t) dx - Z I j (x,y 2,t) dx ( 4 . 4 4 ) J ° 7 n) = i 1 ( t ) - i 2 ( t ) . (4.45) Since the d i e l e c t r i c i s assumed to be uniform, i t s volume charge density due to p o l a r i z a t i o n i s zero. Thus the charge density i n t r o -duced by Ci-^_12^ -*-s m a < ^ e t o confine within the space charge region only, and = Z - r / J P(x,y,t) dx dy . (4.46) Tt J J P ( J Now, (4.44) can be written as dq „ f a / , . 8v (x,y ,t) 9 V ( x , y 9 , t ) \ d F = z Jo (°(x'y.) 37 1 - °(*»y 2> "97 2 ) d x ( 4 , 4 7 ) which i s also equal to 63 f d z l t ) D r a r J o(x,y 2) [u(y 2,t) + w(x,y 2,t)] dx + Z -J^ ^ a ( x , y 2 ) d x | s r d i ( t ) — [ u ( y 2 > t ) + w(u 2 , y 2 , t ) ] | - Z J t r C x . y ^ | ^ l u C y ^ t ) + c ( x , y . ) dx -r- [u(y ,t) +w(u ,y ,t)] (4.48) ^ ( t ) y where the potentials u,v,w are as defined i n f i g . 4.3. If the steady state space charge width i s approximately uniform within the subregion, we can assume d^(t) = d 2 ( t ) = d(y,t). With the help of the following integration by parts relationship f2 £$• ( x ' y ' t } < f (x ,y ) dy = | i < x »y» t>-d ' ( x , y ) y2 1 • y l p ' y l 1^ 1^  dy (4.49) 9y 9y we can rewrite (4.48), which after equating to (4.46) w i l l give fd , , ' . rd f J-f d_9p (x,y,t) . f d f 92(u+w) 6 ( , 9a 3(u-HQ ^ Jo 9 t o^ I 9y 2 ' y 9 y 9 y i ri 1 "?^ 1 * ( x , y ) + * m^1} d x ' c4'3o) dx + where w' = w(d,y,t). So the equation of state becomes |/i£. (x,y,t) £_ (u+w) , . _ 9a(x,y) _9(u-rw) "\ _ Jol 9 t " 9 y 2 a ( x ) ^ y *y j " 64 For a semiconductor f i l m deposited uniformly on to the sub-strate a(x,y) - o(x); equation (4.51) can then be reduced to f d 9 , v 92(u+w) /• \ j / I F p ^ y * ^ 2 ~ ( x ) *'o 9y 3 92(u+w') , , , ... co>. — ^ - a(x) dx, (4.52) d 9y for any subregion at distance y from the source. Before going any further, i t i s demonstrative for us to see how the above result can be applied to a f a m i l i a r case -— a dis t r i b u t e d RC structure using metal r e s i s t o r s . Whence, w 0, d 0, and a(x) i s a constant for a l l regions inside the f i l m . In addition, the space charge layer i s often so thin that i t can be neglected;: so that fd ~ rd 9p (x,y,t) J IT d t = / i t d x = 91 P s < ° > ^ Jo Jo and .a o(x) dx = oa 'o Therefore, (4.52) i s reduced to dt . t 9y • Replacing a i i x s l .is. forpS-(y-t) x 9x o e x=0 the f a m i l i a r lossless transmission l i n e equation follows A c A r ^ f ^ - - i ^ H f c i t l (4.54) 9 t 3y 2 65 where ' Ar = — - — (4.55) aZa e Z and Ac = — ° - (4.56) x o • 4.5.2 Simplifying the Equation of State The i n t e g r a l f - g ^ p ^ X , y ' ^ dx i n (4.52) actually represents Jo the rate of change of t o t a l surface charge density i n the space-charge layer, as wel l as i n the interface states. I t should numerically be equal to the rate of change of surface charge density (Qs) ° n the metal gate since we had asserted no volume charge density inside the oxide by our postulate no. 6. Further, i f we adopt the d e f i n i t i o n dQ = C d(u+w) (4.57) S U where C„ i s the capacitance per unit area of the insulator and the space-charge layer i n serie s , equation (4-52) can be s i m p l i f i e d to L d 3£ A v - r JL(u+w) at d x " °t at o c a ii^si a ( x ) d x + r d i l ( u + v i a ( x ) d x ( 4 < 5 8 ) Jd 3y Jo 3y From the depletion layer approximation, the conductivity i n the space-charge region i s p r a c t i c a l l y zero, •d „2, , , r a 2 - ^ 1 <r (x) dx « f ^ 3y Jd 3y' fd 32(u+w) „.' . , „ fa 3 2 (u+w') , . , t, M , / — s CT (x) dx « I — j o(x) dx (4.59) o^ 3y . Jd 3y Further, i f we assume that a(x) i s a constant between d $ x $ a we arr i v e at the Kirchhoff's d i f f e r e n t i a l equation for the subregion y l * y * y 2 ' „ dW 32W v c t d T = - 2 ^ ( d " a ) , 3y 66 i . e . ct(y> t ( 7 ) ^ - - . i-p-3y (4.60) 1 1 where r(y) = — ^ a-^ 1 S t n e resistance per .unit length of the channel. An equivalent c i r c u i t for the subregion can be derived from (4.60) and i s depicted as i n f i g . 4.6. G G S cl V(yJ) Ay.Ct(w) cl V(y+&yf t) D Fig. 4.6 An equivalent c i r c u i t for the subregion of a URC structure. For channels having different depletion layer thicknesses along the length of the device, we can obtain the d i f f e r e n t i a l equation for such a structure i n much the same way as i f we were treating a non-uniform transmission l i n e case. The model i n f i g . 4.6 allows us to write i n the phasor space dV(s,y) dy Ks,y) G(y) f ( 3 ' y ) = - s C t(y) V(s,y) . Combining (4.61) and (4.62), we obtain (4.61) (4.62) d ZV(y) M d.ln.G(y) d v C t ( y ) , • . ^ 2 Y + d y - d y " ( s ' y ) ~SlHf) V ( S ' y ) = °' (4.63) which i s the R i c c a t i nonlinear d i f f e r e n t i a l equation. An a n a l y t i c a l solut-102 ion to (4.63) can only be obtained for a few exceptional cases 67 In the next section, however, we s h a l l use "the conventional j u n c t i o n 103 gate FET small s i g n a l model to a r r i v e at a small s i g n a l equivalent c i r c u i t f o r the URC structure having a non-uniform depletion layer thickness . 4.6 Small Signal Analysis of a Generalized URC Structure 4.6.1 Small Signal Equations We are to s t a r t from the equivalent c i r c u i t of a URC subregion ( f i g . 4.6). From Ohm's law AW(y,t) Ay G(W) = - I ( y , t ) , (4.64) and from the continuity equation AI(y,t) = at Q(W) Ay (4.65) The channel "to gate p o t e n t i a l W as -well as the channel'current I can be expressed as superposition of both dc and ac components W(y,t) = W'(y) + w(y,t) (4.66) I(y,t) = I'(y) + i ( y , t ) Expanding Q(W) and G(W) by Taylor's method, and neglecting a l l the second and higher order terms, we have i n the l i m i t as Ay -> 0 9W'(y) + t e ( y , t ) + 8G(W) 8 y 9 y aw ~ w w=w' J = -Ky) - <(y,t) (4.67) • 3 i'(y) + i l ( y , t ) .9y 9y | - C Q ( w ' ) + ^w )  3 t aw ~w] W-W' (4.68) One method of analyzing a non-uniform structure i s by considering HQ i t as an i n f i n i t e cascade of uniform s t r u c t u r e s . 68 R e c o g n i z i n g t h a t 3y G(W') » ^ - ° y ; |f = 0, - ^ Q ( W ' ) - 0 , and t h a t f o r s m a l l ac s i g n a l s , the c a p a c i t a n c e C (W) i s o n l y a f u n c t i o n o f t he dc component W' dW W=W'(y) we s i m p l i f y (4.67) and (4.68) t o (4.70) 3w 9y w dW dG(W) G(W') G(W') dy dW (4.71) W=W' and 9y- - - C t ( W > 9t" (4.72) T h i s l a s t s e t o f p a r t i a l d i f f e r e n t i a l e q u a t i o n i s r e p l a c e d i n L a p l a c e ' s t r a n s f o r m by two o r d i n a r y d i f f e r e n t i a l e q u a t i o n s . W i t h z e r o i n i t i a l c o n d i t i o n s and d W ( s , y ) G ( w I ) + dW dG(W) ^ ^ dW f i ( s ' y ) = - s C t ( W ' ) W ( s , y ) w ( s , y ) = - l ( s , y ) , W=W' (4.73) (4.74) 4.6.2 S o l u t i o n s o f t h e S m a l l S i g n a l E q u a t i o n s We a r e t o u s e the d e p l e t i o n a p p r o x i m a t i o n , and t h e n o t a t i o n b (W ' ) = [1 - x , ( W ' ) / a ] f o r t h e n o r m a l i z e d c h a n n e l t h i c k n e s s , d The dc c o n d u c t i o n c u r r e n t i s I =I '=G(W' =g b(W')^ • D dy too- dy The c a p a c i t a n c e C as d e f i n e d i n C4.70) c a n be w r i t t e n as (4.75) (4.76) Mak ing t h e a p p r o x i m a t i o n 69 db(W) dW _ d b C W ) „ db(W') 7 ? . dW W=W' (4.73) and (4.74) can Be written as r w , ) to,., - ^  » . D i f f e r e n t i a t i n g (4.78) with respect to b(W'), a £ - lbw.)«"^'j , C 4 - 8 Q ) and substituting the value of dW'/cly from (4.75) and from (4.78), we obtain , 2 T e x §-4 = k 2 I b ( l - b + (4.81) db^ e a , qN a 2Z where k 2 = - — ) 2 (4.82) C s XD Solutions for (4.$1) can be obtained by* using the generalized power series Kb) = Z A bP"*1 . ( 4 - 8 3 ) n=o n Substituting the value of I and i t s second derivative into (4.71), putting n=0 and at the same time demanding that A q i s not equal to zero, we a r r i v e at the i n d i c i a l equation p (p - 1) = 0 . (4.84) The roots are p = 0, or p = 1 . (4.85) The choice of p = 1 does not y i e l d an independent solution to (4.81), and i s discarded. So, the f i n a l solution for (4.81) i s K b ) = A QT(k,b) + AiR(k,b) (4.86) where AQ, AJ are a r b i t r a r y constants k 2 C o X n , k 2 b 4 i C M - I i - ^ t t + ^ ) » » + *T±-. , 2 E X . if e x . . i ' K -(1 + - J L ° ) 2 b 6 - A d + — ) C T \ + - h ^ 1 6.5.3.2 e^a 7.6 e-j-a 4.3 3.2 70 + kk b 8 8.7.4.3 + 0(.k6) ........ ] (4.87) R(k,b) - lb - ~ - ( l •+ - ^ S b 4 • . ex ( 1 + _ ^ ) 2 B 7 7.6.4.3 e a I _k^_bj 5.4 k" b 9 + ?:8X4 + 0 ( k b ) 8.7 E-j-a ' '5.4 4.3' (4.88) Very often, we are interested i n the channel voltage instead of the current, which can be obtained by d i f f e r e n t i a t i n g (4.86) with respect to b and substituting the resul t into (4.81) to get W(b) D 3T 3RX sqN DoZ za zb v"o3b 13b' (4.89) 4.6.3 Common-Gate Admittance Matrix We are now ready to represent the generalized URC structure by an equivalent 2-port network. The short c i r c u i t y-parameters In the common-gate configuration are: i '11 3g y21 sg V, =0 dg V, =0 dg '12 '22 V dg V =0 sg V =0 sg To evaluate y^and w e u s e t n e boundary conditions: (1) W=V , and b=b at the source, sg' s (2) W=0 , and b=b^ at the drain . S i m i l a r l y , for and y 22' t n e boundary conditions are: (1) W=VJ , and b ^ at the drain. , dg d '' (2) W=0 , and b=b at the source. s The value of I Q can be evaluated from (4.75) as J LI Ddy = J b d(Zoa3q N ^ ) b (1 - b• + ^ ) db ° ^ o (b? - b 2) e x b 3 - b 3 S i ) ] (4.90) (4.89b) 71 The y-parameters i n ma t r i x form i s s d s d " d R , d - Y V - T R 1 f "b ~ s s s d s —1 L*dJ (4.91) where where A = K (R* T' - T' R ' ) s d s d , K = - I D / ( s q N D a Z 2 a 2 ) . A f t e r some strenuous a l g e b r a , i t can be shown th a t 1 Y = (1+ST ) o (1 + S T ) 1 T = O e L 2 b 5  S _s a a 2 6 (1 + S T ) " 6<v" -5B 2 + 5B 3 --f- (1 + e x / ( c a ) ) 6 - s o l (1 '+ e x /(e_a) -^2 i - [1 - 3B 2 + 3B 4 - B&] (4.92) (4.93) (4V94) b 2 Cl ~ 7B 3 + 7B1* - B 7] , (4.95) T = 1 e L 2 -b3  s s a a 2 6 rz (1 + e x / ( e T a ) ) [ l - 3B 2 + 2B 3] s o I [1 - 4B 3 + 3B 4] (4.96) T = 2 e L 2 b 3 s s cr a 2 6 — i v 2 (1 + e x / ( e T a ) ) [ 2 - 3B + B 3] s o I B = b./b d s iJ = E b 2 - b 2 s d [3 - 4B + B 4] 2 <1+7JT> £ x ( b 3 - b 3 ) s o, s d (4.97) (4.98) (4.99) The corresponding open c i r c u i t impedance m a t r i x i s 1 Z = (1 + S T ) s ( T + T + S T T ) 1 2 1 2 0 1 g(w D G L (1 + S T ) 2 (1 + S T ) 1 (4.100) I 7> z a 72 3: ' D V2 F i g . 4.7 A general representation of a Z-parameter equivalent c i r c u i t , ii c ^3 0? v v v ^ — 1 | - •D z,4 7?, G • V2 R s _J_ 7 < 7 f ^ S G j rr, + t2; 7 " ( W g(WSG) R3 = (tj + r2)9(WSG)g(WDG) ; 9(wsc)-g(WDG) / zc " f 1 + st'srOM-G) 7 F i g . 4.8 An equivalent c i r c u i t of the generalized URC structure. 73 A T-network can be set up to represent the above matrix (4.100). 2 I f we neglect higher order terms i n s , i....e.. f o r low frequency approx-imation ?the lumped elements i n such a c i r c u i t ( f i g . 4.7) are: T (1 + S T ) , 2 - ° Z = "TT? >, 7 — T r (4.101) a g (W_ p ) (T + T ) SG 1 - 2 •> - 1 + S T Z = 4? ^ -T-T ? ' (4.102) b g(W c p) S ( T + T ) SG 1 2 1 _ f 8 ( W S G > g ( V ] + S [ ^ W V - V<V 1 (4.103) Z c S(.T + 0 g(W S Q) g(W D G) ( L + S T ) g(W ) - g(W ) •- . 7 = _?- £k £k f4 104) M S ( T +x ) g(W S G) g(W D G) _ ^ . 1 U<U Using the basic e l e c t r i c a l elements R, L, and C, i t can be shown that a se r i e s combination of R and L w i l l s a t i s f y Z &; and s i m i l a r l y f o r Z^ and Z^, the R, C combinations l i k e the ones .given i n the f i n a l equivalent c i r c u i t ( f i g . 4.8) are appropriate. CHAPTER 5 Applications of URC Structures i n N u l l Networks 5.1 Introduction D i s t r i b u t e d RC structures have many p o t e n t i a l a p p l i c a t i o n s as e l e c t r i c a l c i r c u i t components i n microminiaturization. In a monolithic i n -tegrated c i r c u i t , such structures are often produced u n i n t e n t i o n a l l y when reversed-biased p-n junction i s o l a t i o n i s used. For a ba s i c 3-layer r e s i s -104 tance-capacitance-resistance structure alone, Castro et a l . i l l u s t r a t e d that up to 13 non-redundant one-port and 21 non-redundant 2-port network functions a r e possible under various terminal connections. When used as a low-pass f i l t e r , a URC structure has an exponential c u t - o f f i n frequency response which i s more i d e a l than many conventional f i l t e r s using lumped \. parameters alone. A n u l l n e t w o r k " ^ " * } c a n be produced by connecting an appropriate lumped r e s i s t o r i n s e r i e s with a URC s t r u c t u r e . This narrow band r e j e c t i o n f i l t e r i s useful as a component i n high-Q tuned amplifiers"*"^ 7 oscillators"'""'" 3, and threshold transducers"*"^. For complex network functions modern synthesis techniques on distributed-lumped-active networks, i n c l u d i n g the use of optimization, can r e s u l t i n fewer components than comparable rea-n • • j ' i 1 0 8 ' l i z a t i o n using lumped elements alone I t i s the i n t e n t i o n of t h i s chapter to look at the physics of n u l l networks which, contain d i s t r i b u t e d RC sections that have used a semiconductor f o r the r e s i s t i v e component. 5.2 Review 106 In 1960, Kaufman proposed the f i r s t notch f i l t e r using a d i s -t r i b u t e d RC section with a lumped r e s i s t o r i n s e r i e s ( f i g . 5.1.a). I t s operation can be understood by noting that a sin g l e URC structure i s by i t s e l f a low-pass f i l t e r , and that i t s input impedance i s c a p a c i t i v e . 74 75 ft-p-type R,Ct V3 V2 o n - type SLlhstrot6 ^) An ac equivalent c i r c u i t of the nntr.h f i l t e r (a). (h) (a) C, n Fig. 5.1 (a) Monolithic distributed "*"^ .^ (c) An equivalent v V \ A RC notch f i l t e r notch f i l t e r using lumped capacitor C instead of R . n n (c) Given a network as i n f i g . 5.1.b, the voltage across the dis t r i b u t e d RC section lags the input V_^ , and the input current and hence lead V\ Now, the distributed section can produce more than 90° phase s h i f t , so i t i s possible to construct equal i n magnitude but opposite i n phase to that of by choosing an appropriate value for the lumped r e s i s t o r R^ . An equivalent n u l l network i s obtained by replacing the r e s i s t o r R with a lumped capacitor C i n p a r a l l e l with the distr i b u t e d RC low-n n pass f i l t e r as i n f i g 5.I.e. In fact^Wyndrum"'""^ showed that a whole class of notch networks can be produced by using combinations of R and C or, R and L i n place of R^ . To generalise, the mechanism of any n u l l net-work using distributed RC sections ± s as follows: By analogy with transmission l i n e theory, we can establish a ir or T equi-valent c i r c u i t ( f i g . 5.2). for an entire URC structure using the cascade of an i n f i n i t e number of the subregions .• derived i n section 4.5.2. 109 76 I Y. Z a a Z t 0 F i g . 5.2 IT and T equivalent c i r c u i t s f o r the URC low-pass f i l t e r . An admittance Y or a impedance Z can be con-P s nectcd to the USC for notch network formation. A zero of transmission w i l l occur when eit h e r an admittance Y =-Y„ i s p 2 placed i n p a r a l l e l with Y„ or an impedance Z --Z, i n s e r i e s with Z,. If we p l o t the phase angles of Y 2 and 2 --as a f u n c t i o n of normalized frequency X=toRCt ( f i g - 5.3) , with R as the r e s i s t a n c e and C t the capacitance of F i g . 5.3 Phase angle of Y. and Z. as a f u n c t i o n of normalized z b frequency x^RCj.. (After J . St e i n , r e f . 112). 77 the distributed section, we obtain* the phase requirement for either or Y . For instance, a n u l l i s produced at the normalized frequency x= P 11.19 when a r e s i s t o r i s placed i n series with Z^, and for the n u l l 112 to occur at x=30.84, a capacitor w i l l be required. The re s u l t i s sum-marized in table 5.1. TABLE 5.1 X=coRCt Z s Y P _ 0 <X< 11.19 R,L -G,C 11.19 R C 11.19 <X< 30.84 R,C G,C 30.84 C G 30.84 <X< 60.45 -R,C G,L 60.45 -R L 60.45 <X< 99.93 -R,L -G,L 99.93 L -G For x >99.93, the whole pattern repeats i t s e l f . Solutions for the d i f f e r e n t i a l equation (4.63) are straight f o r -ward when both G(y) and C t(y) are constants, as i s the case of a URC struc-ture with uniform depletion layer width from source to drain. The im-pedance matrix i s R Z =• — coth Y y — cosech Y Y cosech Y Y R ^ — coth y Y / where y= ^sRCt = /jx"' > with x= "RCt. (5.1) (5.2) For the notch network with lumped r e s i s t o r R^ i n series with the distributed section, the open c i r c u i t voltage transfer function i s 78 T = S-v. 1 v Z 0 1 — cosech Y + R 21 _ y n - — - — (5.3) 1=0 11 - coth Y + R 2 Y n A zero of transmission occurs when the numerator of T i s equal to zero, 1 , 6 4 - cosech v ^ T + R =0 (5-4> Y n Equating the r e a l and imaginary parts of this transcendental equation i n d i -v i d u a l l y to zero, we obtain: tanh /x/2 = - tan vyj2 , (5.5) and the notch parameter a = R/Rn = 2 v^Jl s i n vyjl cosh vx /2 . ' (5.6) Equation (5.6) has an i n f i n i t e set of solutions for x , denoted by ( X n ) . I t s fundamental solution i s at X-j^H• 1902. with the corresponding optimal notch parameter a^=17.786. 106 Kaufman also obtained a va r i a t i o n (tuning) i n the notch frequency of his n u l l network by adjusting the p-n junction capacitance C with an external biasing voltage VV, ( f i g . 5.1.a). In such a process, however, the D value of R i s also altered by the different space charge width extending into the semiconductor r e s i s t o r . Consequently, the optimal notch parameter a^, hence ' i n f i n i t e ' attenuation*is not obtained at a l l accessible values of the notch frequency. Similar imperfection occurs with the tunable notch network proposed by Golembeski"'""''4. One solution, l i k e that of Swart's 115 f i l t e r , i s to allow the distributed capacitance C to be adjusted independ-ently without any appreciable change i n the value of R. A layer of heavily doped semiconductor"'"''""', sandwiched between the r e s i s t i v e and the d i e l e c t r i c f ilms, can be used to house the space charge capacitance C g of C ., thereby preventing the semiconductor space charge region from spreading into the r e s i s t i v e f i l m . A new and simpler notch network i s proposed i n section 5.4, i n which an optimal n u l l i s maintained at a l l tunable frequencies. , 79 5.4 Theoretical notch c h a r a c t e r i s t i c s of a simple URC i n series with an external r e s i s t o r R n 30 5.3 Notch F i l t e r Comprising a Semiconductor URC Structure 5.3.1 Theoretical Tuning Characteristerics Consider the notch network obtained from a t h i n - f i l m semiconductor URC low-pass f i l t e r connected i n series with an external impedance Z^. I t i s assumed for the moment that Z^  can adjust i t s e l f automatically to give an optimal notch at any accessible value of the notch frequency. At the notch, (5.5) i s s a t i s f i e d , which means that x ="RC t i s a constant. If the t u n a b i l i t y factor n i s defined as the percentage change i n frequency to — (0 CO j . n = —— £ - -Jf - i • . (5.7) WF W F where the subscripts f and F denote flat-band and depletion cases respect-i v e l y , the r a t i o (RC^)_ /(RC ),. = to^ /aL w i l l offer a measure of the J t Fmax t f f Fmax range of t u n a b i l i t y under channel depletion of the URC structure. Using the depletion layer approximation, 1 1 ^ = (RCt\ ~ x • fa dmax-j fa ^  o dmax-j a ' ^  e x ' s o ^ t ^ m a x _ 1 1 e. T R C X " \ a x + 1 " x. x , . ( 5 ' 8 ) t f fa dmaxv fa + dmax 1\ e x s o The above function i s graphed i n f i g . 5.5 for a few £=-e a o In contrast to other tunable notch f i l t e r s using only depletion capacitance as a means for frequency selection (e.g. Swart's f i l t e r ) , the present network has a wider choice i n t u n a b i l i t y , above and below the semi-conductor flat-band frequency to^. We s h a l l elaborate t h i s point further i n the next section. The two operation modes are distinguished by n>0 i n mode 1 and n <0 i n mode 2. A few interesting c h a r a c t e r i s t i c s of n derived from f i g . 5.5 are noted below: as a function of the notch parameter 82 (1) Given a URC structure, thus Z, , v a r i a t i o n i n n follows the locus of con-stant £ from x =0 to x, d dmax (2) For a notch network having £ <^ 1 and, x d m a x / a > 5> the n u l l can be tuned to a frequency oi e i t h e r higher or lower than a) . The minima i n £, at r t x^/a = T; (1 - Q , pertain to maximum percentage changes i n the range of t u n a b i l i t y when the device i s made to operate i n mode 2. (3) From (5.8) we observe that the value of Z, depends e n t i r e l y on the rates of change of C and R under depletion. At f i r s t , the rate of change of C^ with respect to x^/a i s more rapid than R, then the trend i s reversed at x,/a = \ (1 - Q whence, the rate of increase i n R w i l l s t a r t to over-d J. take that of the decrease i n Beyond x^/a = £ , the change i n R w i l l become the dominating f a c t o r i n the con t r o l of n. 5.3.2 P r a c t i c a l Considerations i n Design Optimization An a p p l i c a t i o n engineer i s often more in t e r e s t e d to know the tradeoff i n h i s design for achieving a p a r t i c u l a r tuning c h a r a c t e r i s t i c and, the means of a t t a i n i n g the maximum t u n a b i l i t y f a c t o r for h i s n u l l network. According to f i g . 5.5, the optimal t u n a b i l i t y f a c t o r n f o r operation i n mode 2 under -op constant £ i s at x^/a = ^ (1 - 0, and i t can be approached i n e i t h e r one of the following two ways: (i) For a given doping concentration of the semiconductor f i l m , x d m a x i s a f i x e d value. To obtain n » one would have to choose the r a t i o op' x„ /a equal to ^  (1 - 0 • This value of n i s graphed i n f i g . 5.6. d max / op ( i i ) For the notch network to be fab r i c a t e d i n conjunction with other passive or active elements on the same chip, the freedom i n choosing f i l m thicknesses a and X q , hence £ , i s often severely hampered i n order to reduce the t o t a l number of processing steps to a minimum. Under such a circumstance, one would have to pick the impurity concentration of the semiconductor at a l e v e l which would r e s u l t i n n as close to n as op 83 _ 4 U f | - J } Fig. 5.6 Optimal t u n a b i l i t y factor n as a function of % for devices operating i n mode 2. possible. For optimal operation of the notch f i l t e r i n mode 1, the URC should-have the biggest possible values of £ and x., /a. dmax Physical . l i m i t a t i o n s i n the selection of parameters ' x^ m a x/ a a n c* £ can be i l l u s t r a t e d by using S i and i t s thermally grown oxide. Typical e p i -16 _3 t a x i a l s i l i c o n films have a doping concentration ~10 cm- , which corresponds -4 to a maximum depletion layer width of *"0.86 xlO cm. Also, commonly used epi-t a x i a l s i l i c o n films have thicknesses i n the range of 1-2 u, hence t h i n - f i l m s i l i c o n notch f i l t e r s can be ea s i l y implemented to give a x < j m a x / a r a t i o close to unity; and, i n r e a l i t y , can have a large percentage change i n notch f r e -quencies when they are made to operate i n mode 1. The trade-off i n cutting down appreciably the size of a conductive channel by designing a r e l a t i v e l y thick space charge layer w i l l be a large increase i n both the input and output impedances of the notch network. 84 Physical l i m i t a t i o n s on the values of £ are much more severe than those on x d m a x / a - * n f a c t , for s i l i c o n and i t s thermally grown oxide, £=.01 and £=1.0 correspond to oxide thicknesses of 70 A* and .7 u respectively for a 2-y thick semiconductor. Thin oxide films are avoided because of electronic conduction"*""^ through the oxide; and extremely th i c k oxides are not desirable 7because prolonged exposure to high temperature ambient during oxide growth may cause excessive impurity r e d i s t r i b u t i o n s i n the semiconductor. The accuracy of th i s theoretical tuning c h a r a c t e r i s t i c i s dependent on the precision of our d e f i n i t i o n of the space charge width x^. According to Lehovec et al."*""*"^, x^ i n i t s defining equation (A-9) a c t u a l l y corresponds to our terminology of x d m a x ' I f w e plot "the voltage-capacitance curve of a MIS structure using the depletion approximation and, superimpose on i t the 121 more accurate C-V curve arrived at by Grove et a l . , we would observe good agreements between the two curves i n the region of deep semiconductor surface depletion. Hence, we conclude that (5.8) i s at the least q u a l i -t a t i v e l y correct. Further, we are to expect a much larger deviation i n the tuning c h a r a c t e r i s t i c s from the above theory when the actual device i s made to operate i n accumulation or inversion mode. 5.4 A Tunable Notch Network using Double URC Sections To obtain high attenuation i n Kaufman's network"*"^, the notch para-meter a should be kept constant at a l l " values of the notch frequency. But such a requirement can be met only i f one i s prepared to adjust the external r e s i s t o r R at the same time as one changes C . The reason i s that the value n ° t of R i s altered with the space charge width i n the process of tuning. The following c i r c u i t , however, i s designed to eliminate the requirement of t h i s extra parameter of control. Consider two distributed sections connected i n series as shown i n f i g . 5.7.a. For R <<R, the channel to gate potentials for.the two URCs w i l l B 85 V. I - A A A -B c, -yV\/ F i g . 5.7 A notch network using double-URC sections; (a) c i r c u i t diagram, (b) ac equivalent, c i r c u i t be V B; which means that i f both the semiconductor and oxide f i l m thicknesses B are a l i k e , t h e i r space charge widths together with the i r conductive channel depths (a - x^) for a given external biasing voltage w i l l be the same. We s h a l l see the significance of such an arrangement i n the following analysis. Using the resu l t s of standard transmission l i n e solutions (Appendix B), we have for a 3-terminal URC structure Z ?= S coth y Z. „ = - cosech Y ; 12 Y (5.9) and a 2-terminal URC structureJ with i t s source and gate terminals connected together, U l 7* _ 7 Z  l l n *l2n Z l l n (5.9.b) For series connection of these two URC structures as i n f i g . 5.7.b, the open c i r c u i t voltage transfer function T Z,, + Z 12 n Z l l + Zn R/Y R /Y cosech y coth y + (R ly coth y ) - R 2/y 2 cosech 2 n \n n n n n n n n R / Y R / Y coth Y coth y + ( R ly coth y ) - R 2 / Y 2 cosech 2 Y n n 'n n n 'n n 'n n For zero transmission, the numerator of (5.10) should be zero, (5.10) 86 R R cosechzv - 1 n 'n Y sinh Y Y sinh y coshy n n 'n = 0. (5.11) If we adopt the following notations: R/R n(Y n/ Y) - a ., Y/Y n = 3 , y = / f t = (1 + j ) y , C5.12) where a = uRC t , y = yy/2 , equation (5.11) becomes ' 2 q + e x P ( 1 + 3>yn ~ e x P - d + j ) y exp (1 + j ) y - exp--(l + j ) y exp (1 + j ) y .+ exp-(l + j ) y = 0 n Equating the r e a l and imaginary parts separately to zero, we get (5.13) a (cos y) (sinh y) (cosh 2y n - s i n 2 y n ) + sinh y^cosh y ) (cosh 2y - cos 2y) = 0. . (5.14) a(sin y)(cosh y)(cosh 2y - s i n 2 y ) - cos y (sin y )(cosh 2y - cos 2y) n ^n -'n y n J ' • r = 0. (5'.15) This l a s t set of simultaneous equations can be solved by using Newton's 122 i t e r a t i o n method for a given value of a. Numerical solution for (5.14) and (5.15) was done using the r e l a t -ionship y ly - -y H ~ 1/3 • A sample of the re s u l t which i s within p r a c t i -n n r c a l range of the notch parameters a and 6 .. i s given i n table 5.2. Table 5.2 a .0.5 1.0 5.0 10.0 X l 11.21 11.29 13.17 16.7 3 1 35.74 18.08 4.57 2.92 X 2 149.28 149.28 149.28 3 2 0.69 x l O 5 0.345 x l O 5 0.69 x l O 4 If we combine (5.'14) and (5.15), we a r r i v e at the transcendental equation for the double URC network sinh 2y { : — 5 — } tanh y = - tan y . - -sin^y. n In the l i m i t as C goes to zero, sinh 2y / s i n 2 y goes to unity, and we have the trancendental equation (5.5) for series combination of a URC section with a lumped r e s i s t o r R . n 87 Similar to the properties of the trancendental equation (5.5), there are i n -f i n i t e sets of solutions for (x n '} a n d ^ o r a g l v e n value of a i n (5.14) and (5.15). But, due to the exceedingly rapid increase i n the order of mag-nitude of B, the second and higher order solutions are phy s i c a l l y impossible to implement i n a r e a l i s t i c device. Let us consider the notch parameters a and B i n s l i g h t l y more de-t a i l . According to our d e f i n i t i o n of a and B given i n (5.12), we .have R y /R- C - J2. = / 2. (5.16) R Y A / R C ' n v n Y Jt c3 = 7" = c~ C5.17) n n n . Since the two URC sections have the same semiconductor and oxide f i l m t h i c k -nesses (they are fabricated on the same chip through the same processing steps) and, because the dc gate to channel potential•would be the same i n both of them ( f i g . 5.7.a), the r a t i o s R-n/R> c „ / c are' s i m p l i f i e d to R J W n -t-n n R / W *• n C / W n "vn n (5,18) (5.19) C I W where £, 6 and W, W r are respectively the lengths and widths of the two URC sections. With these, we ar r i v e at the relationship , = ^ 3 - f - . (5.20) n In other words, to a t t a i n an optimal.null i n the tunable double-URCs notch network, we only need to design the lengths and widths of the 2 URC sections i n accordance to the values of a and 0 specified by (5.20). This w i l l allow us, then, the freedom to choose the semiconductor and the oxide f i l m thicknesses, as well as the impurity l e v e l i n the semiconductor for attaining a maximum percentage change i n tunable frequencies of the n u l l device. 88 A t y p i c a l design procedure for such a notch network is.:," (1) pick a convenient set of values a and 8, from f i g . 5.8 , (2) f i n d the corresponding normalized frequency x> a n c* design the lengths and widths of the distributed sections to give the notch frequency to, as desired; (3) then optimize the maximum t u n a b i l i t y factor according to the procedure outlined i n section 5.3.2 and, a r r i v e at the values for the semiconductor impurity concentration and the thicknesses a, and x^. In order to make the two distr i b u t e d sections more compatible i n size to each other, and the r a t i o of the length to width of each URC not too unreasonable, one would select the values of o<_ and £ ly i n g i n the neighborhood of point Q i n fig.5.8. On the other hand, i f the designer i s more interested i n compact miniaturization of the 2 URC sections, he would prefer to choose the set (a, B) given by point P i n f i g . 5.8, which corresponds to a minimum i n t o t a l surface area occupied by the 2 URCs. U 12 8 ' P(o(=3.0 ,&=67) Q 0 2 4 6 8 ... 10 wn ^ 7 7 7 F i g . 5.8 Notch parameters a and B of the W double-URCs notch f i l t e r . 88b Fi g . 5.10 Theorectical magnitude and phase response of a double URC notch f i l t e r (a=3.0, 3=6.67). 88c 5.10 "Effect of notch parameter va r i a t i o n s on the notch ch a r a c t e r i s t i c s of a double-URC f i l t e r (a=3.0, 6=6.74). CHAPTER 6 Experiments on Semiconductor Thin-Film URC Notch F i l t e r s 6.1 Introduction • E p i t a x i a l s i l i c o n on spinel was chosen for the. .experiments because: (a) high quality wafers were commercially av a i l a b l e , (b) con-v e n t i o n a l s i l i c o n technology can be used for the f a b r i c a t i o n processes, and (c) SIO2 can be readily prepared by thermal oxidation. The URC structure used i s si m i l a r to a coplanar-electrode TFT as introduced by Weimer"'""'"''. This configuration has the advantage of allow-ing the semiconductor to be processed at elevated temperatures, as i s required for thermal oxide growth, without the electrodes undergoing the same treatment. A t y p i c a l structure i s as shown i n f i g . 4.1. An external r e s i s t o r R was connected i n series with the URC to generate a n u l l net-n work ( f i g . 5.1.b). The leads between ground, R , and the gate electrode were made as short as possible to minimize the p a r a s i t i c inductance which affects the notch ch a r a c t e r i s t i c s (see section 3.3.2 i n r e f . 115). 6.2 Fabrication Technique for a URC Structure  6.2.1 Fabrication Processes The processing steps were:-(1) A rectangular mesa was etched out of the e p i t a x i a l f i l m i n a solution of 5HN03(75%):3HF(49%):3HAc by volume. I t was to bear the sane length and width as the f i n a l URC structure. (2) A thi n cap of thermally grown SiC^ was prepared by oxid i z i n g the s i l i c o n mesa i n steam at 1050°C. (3) An aluminum f i l m of 2-3 thousand X thick was vacuum evaporated to cover the entire substrate surface. (4) The r e s u l t i n g structure was annealed, i n a N 2 atmosphere at 400°C for 89 90 1/2 hr. (5) Photoresist masking was used to define the oxide region of the URC. The unwanted S i 0 2 over the source and drain regions were removed i n an etchant containing 3:1 by volume of HF with H^ O. This step was . preceeded by etching away the aluminum and the upper 200 X of S i 0 2 using a P-etch*, which was intended to remove any ions that were made to segregate at the aluminum/S102 interface by the annealing step....... (6) An approximately 2000 /? thick of Au f i l m doped with 0.1% Sb was vacuum deposited over the whole structure. I t was sintered into the semiconductor source and drain regions at 425°C i n a N 2 atmosphere, thereby forming ohmic contacts to the n-type channel. (7) F i n a l l y , the metal electrodes were defined using photoresist masking. 6.2.2 Cleaning the S i and S i 0 2 Surfaces An e p i t a x i a l s i l i c o n chip that had been cut "to about "twice "the size of a f i n a l URC structure was degreased i n an u l t r a s o n i c a l l y agitated trichloroethylene bath for 5 minutes. This was followed by r i n s i n g successively i n acetone and d i s t i l l e d water. The surface was subsequently dried by blowing a i r from a p l a s t i c squeeze b o t t l e over the e p i t a x i a l f i l m surface. 119 Before thermal oxidation, the s i l i c o n sample was cleaned i n a solution containing 1 part H 20 2, 1 part NH^ OH and 4 parts of H 20 by volume for 15 minutes. The sample was then rinsed i n 2 successive baths of u l t r a -s o n i c a l l y agitated d i s t i l l e d water, followed by 1 bath of deionised water. 6.2.3 Photoresist Technique Standard photolithography technique was used for device pattern formations. The photographic masks used i n the experiment were on a 2"x2" * P-etch constituents are:- 15ml 49% HF, 10ml 70% HN0 3 > and 300ml H 20. It has an etching rate for therfnally grown SiCL of 140A../min. 91 F i g . 6.1 Photographic masks used for device f a b r i c a t i o n ; from top to bottom, and l e f t to r i g h t : (1) for the s i l i c o n mesa, (2) for the SiC^ region, (3) for defining the metal-electrodes. The fourth mask has not been used, but i t i l l u s t r a t e s the source and drain regions of the 4 devices defined by (1). high res o l u t i o n glass s l i d e obtained from Shaw Studio*. The o r i g i n a l artwork, at 20x magnification, was made on Keuffel & Esser "Cut n 1 S t r i p " mylar-backed artwork sheet. Three masks were required:- one for defining the semiconductor mesa structure, one for the d i e l e c t r i c layer, and the t h i r d for i s o l a t i n g the contact electrodes ( f i g . 6.1). 5 drops of KTFR (diluted to a r a t i o of 4:5 with Kodak Thinner) was applied on to the sample spinning at 2000 rpm. The r e s i s t was applied through a syringe using a 0.45 M e t r i c e l f i l t e r . The sample was spun for at least 2 minutes before baking ? t 8" distance from a G.E. in f r a - r e d heat lamp ( r e s u l t i n g i n a temperature of about 75°C) for 15 minutes. After cooling, the dried sample was placed on to a micro-manupulator and the photomask, with the emulsified side facing down, was lowered on to d i r e c t contact with the r e s i s t f i l m . An exposure time of 6 minutes was used for a l y thick r e s i s t f i l m 6" underneath a Westinghouse 275W sun lamp. This was followed by developing i n Kodak Thin Film Developer for T^ - minutes and then r i n s i n g for 30 seconds i n Kodak Thin Film Rinser. An after-bake of 10 minutes was used. * Shaw Photogrammetric Services Ltd., Ottawa, Ontario. 92 6.2.4 High Temperature Treatments For thermal oxidation, SiO^ annealing i n atmosphere, and Sb-Au al l o y i n g with S i , a JMC e l e c t r i c furnance was used. The reaction chamber consisted of a 3' long, 2^" DIA quartz tube with the central portion sus-pended inside a S-288 element. A clean piece of l"x2" alumina wafer was used as sample holder. I t could be s l i d i n and out of the tube with the help of a DIA quartz tubing having a peg at one end. The wafer was sta -b i l i z e d by laying i t s face f l a t and by resting i t s two p a r a l l e l edges on the inner curved surface of the quartz tube. S i l i c o n oxidation was carried out at 1050°C i n a steam atmosphere, The temperature was registered by a chromel-alumel thermocouple inserted into the tube from one end. After about 10 minutes, a t y p i c a l oxide layer thickness of 2000 A* i s obtained. The steam was then cut-off, and ^ was introduced. The sample was retracted from the hot zone at a rate of l'/min. to one end of the tube where i t was allowed to cool down to the room temperature. A similar procedure was used for N 2 annealing and for Sb-Au a l -loying. Since Au has a high d i f f u s i v i t y i n s i l i c o n , the sample was never l e f t at the a l l o y i n g temperature for more than 30 seconds. 6.2.5 Film Thickness' Measurements For Si0 2> measurements were taken from an ellipsometer using a He/Ne laser (6328 R) and an incident angle of 60°. Optical constant of (3.86, 0.00452) was assumed for s i l i c o n . The oxide f i l m thicknesses were derived from matching the computed thicknesses with the S i 0 2 color chart. The error introduced by neglecting the substrate's r e f r a c t i v e index and the i n t e r -ference of l i g h t inside the S i 0 2 and S i films was. estimated to be less than 50 R, and was beyond the accuracy required. . S i l i c o n f i l m thicknesses were calculated from the o r i g i n a l e p i -93 t a x i a l layer thicknesses and the amount that had been transformed into the SiO„. F i g . 6.2 A sample of the f i n a l devices (this chip contained 2 devices having the same length but d i f f e r e n t widths). 6.3 Channel Conductance under Non-uniformed Depletion Layer Width For an n-type e p i t a x i a l s i l i c o n covered hy i t s thermally grown SiC^, the low temperature ^ annealing treatment so described i n section 6.2.1 for the URC structure produced a t h i n depletion layer at the Si-SiC^ i n t e r -face. The disappearance of donor surface states, which are normally present a f t e r thermal oxidation of s i l i c o n , i s confirmed by the flat-band voltage s h i f t i n the capacitance-voltage c h a r a c t e r i s t i c of such a sample. The v a r i a t i o n of channel conductance was observed on a Tetronix type-575 Transistor Curve Tracer. The gate was at f i r s t e l e c t r i c a l l y shorted to the drain; and by increasing the drain voltage (positive with respect to the source), a p a r t i a l accumulation of the channel at the source end could be obtained. Next, the gate was connected to the source; and, with p o s i t i v e drain voltage, a channel depletion into the inversion mode could be apprehended at the drain terminal. Now, by assuming that the o r i g i n a l channel had a uniform depletion layer width a l l the way from the source end to the drain end, the above arrangement would correspond to grounding the gate and the source, and varying the channel p r o f i l e by the dc voltage applied to the drain. The drain current 1^ and drain voltage character-i s t i c thus obtained would display the channel conductance under p a r t i a l accumulation, depletion, and inversion ( f i g . 6.3). The purpose of using at a l l time p o s i t i v e I and V i s to avoid misinterpretation of channel 94 conductance caused by non-uniformity of the s i l i c o n . f i l m , and by inhomogeous source and drain contacts with the channel. VD^0 J, Channel Spacey Charge Channel D k Inversion' -fa) V Accumulation (b) r F i g . 6.3 Qualitative description of the channel under (a) deep-depletion at the drain, (b) accumulation at the drain. The characteristic's of two URC samples are shown i n f i g . 6.4. The regions marked I , I I , I I I correspond to accumulation, depletion, and inversion at the drain terminal with the source and the gate both grounded ( f i g . 6.3). According to (4.29), the drain current for small magnitude of the drain voltage under channel depletion i s a li n e a r function of the dtain v o l -tage, such an effect can be observed around the o r i g i n of the Ip-V^ display i n f i g . 6.4. With increasing depletion layer width at the drain end, the channel conductance (from slope of the ^ "V^ curve) decreases u n t i l i t either saturates (due to channel pinch-off ( f i g . 6.4.a)), or approaches a constant value after the depletion layer width at the drain terminal reaches a maxi-mun ( f i g . 6.4.b). However, for increasing channel accumulation at the drain end ( f i g . 6.3.b), which correspondsto reducing the t o t a l space-charge region i n the channel, we observe, contrary to our predi c t i o n , a decrease rather than an increase i n the ov e r a l l channel conductance ( f i g . 6.4). This controversial observation may be attributed to charge r e d i s t r i b u t i o n at the silicon/sapphire 95 interface as a result of large horizontal e l e c t r i c f i e l d i n the channel »1 mA x = a .23\i .•5M 5 xlO^cm 96 6.4 S i l i c o n Thin-Film URC Notch F i l t e r s ^ A low-inductance v a r i a b l e r e s i s t o r R , e.g. a carbon r e s i s t o r , n was used i n series with the URC structure for notch f i l t e r formation. The voltage t r a n s f e r function of the f i l t e r was obtained by measuring i t s out-put voltage with the c i r c u i t shown i n f i g . 6.5. The bootstrapped follower had an o v e r a l l attenuation f a c t o r of 0.92 i n the frequency range of i n t e r e s t . A s i n u s o i d a l input s i g n a l of 100 mv was used. T y p i c a l amplitude response of the f i l t e r i s shown i n f i g . 6.6. Notch attenuation of 40-50 db was generally obtained. However, the measured notch c h a r a c t e r i s t i c s always d i f f e r from the t h e o r e t i c a l amplitude response ( f i g . 5.4) by as much as 20-30% i n i t s Q-value*. This discrepancy was mainly caused by the load r e s i s t o r that had been connected to the device, while the c h a r a c t e r i s t i c s of f i g . 5.4 were derived f o r the open-circuited voltage transfer function. In this work, a l a r g e r discrepancy was also observed for the value of R used i n comparison to that predicted by (5.6) — a deviation of n one order i n magnitude lower was common. A major contributor to t h i s d i s -crepancy comes from spreading resistances underneath the source and drain regions of the device. An improvement could be made using d i f f u s e d source and drain regions, and by f a b r i c a t i n g the device i n a cleaner atmosphere. Occassionally, when there are s t r u c t u r a l f a u l t s i n the semi-conductor or SiO^ t h i n - f i l m s , one would not only obtain l e s s attenuations at the notch frequencies, but also d i s t o r t e d output waveforms s i m i l a r . t o the one shown i n f i g . 6.7. But, i n t e r e s t i n g enough, one can s t i l l observe the 180° phase s h i f t at the notch frequency, as predicted by the theory. * The Q of the device as defined i n here i s f /Af, where f i s the o o notch frequency, and Af i s the notch gap at 25 db of attenuation. Source (S) ' Tetronix type-191 Constant Amplitude Signal Generator. + 20 V R,Ct 5 0 - f l > R, n 4.7 K 6.2M V\A-+ 2VL •6.2 M '210 K 3N159 1 IMPS 834 \4.7K >6.6K Philips PM 3250. F i g . 6.5 A "bootstrapped" follower used i n the measurement of the amplitude response of URC notch f i l t e r s . f (KHz) CO F i g . 6.6. Amplitude response of a t h i n - f i l m semiconductor URC tunable notch f i l t e r . 99 (a) (b) Fig . 6.7 A display of the d i s t o r t e d waveform from a s t r u c t u r a l l y defective notch f i l t e r ; the 180° phase s h i f t can be observed by comparing the two pictures taken at signal frequencies a l i t t l e below (a) and above (b) the notch frequency. 6.5 Notch Frequency Tuning F i g . 6.8 shows the range of t u n a b i l i t y of two devices using the c i r c u i t shown i n f i g . 5.1.a. These f i l t e r s had been designed to operate i n mode 1, and had a maximum t u n a b i l i t y of 200-300%. By comparison, a t h i n - f i l m notch f i l t e r tuned by using only capacitance v a r i a t i o n s i n the di s t r i b u t e d RC structure gives t u n a b i l i t y of only a few tens of per cent, e.g. the best notch f i l t e r fabricated by Swart had a tuning c a p a b i l i t y of 30% with a + 15V bias v o l t a g e 1 1 5 . F i g . 6.9 shows the value of R^ that was required to give an optimal n u l l at the tunable notch frequencies of the two devices. For sample S, the depletion capacitance saturated at a depletion layer width which was less than the semiconductor f i l m thickness. So, for a large negative gate potential,an inversion layer was developed at the Si/Si02 interface which lowered the t o t a l channel resistance R, hence R . Now, n according to the notch condition RC to = 11.19, and with C remaining almost 101 / to .8 £ .4 (MHz) 50 -40 -30 -20 -10 0 10 20 30 40 50 V~ (volts) F i g . 6.8.b Notch frequency t u n a b i l i t y for sample S. ^ 20r 7.5 7.0 .5 0 10 B .8 A -40 -30 -20 -10 0 10 20 30 40 50 VG (volts) g. 6.9.b Variations of notch r e s i s t o r R and C/C as function of n o the biased voltage V i n the tuning range of sample S. G 102 constant under channel i n v e r s i o n , the notch frequency to would have to i n -crease by the same amount as R has decreased, which i s what the experi-mental r e s u l t i n d i c a t e s i n f i g . 6.8.b. For sample Q under depletion, the channel pinched o f f before a maximum depletion l a y e r width had been attained. Consequently, f o r large negative gate p o t e n t i a l , the notch frequency l e v e l e d o f f to a constant value. The capacitance-voltage curves of f i g * 6.9 were obtained from a Booton model 71A Capacitance/Inductance Meter with the output displayed on a X-Y recorder. The measurement was done by connecting both the source and drain to the ground terminal of the meter. Since the Boonton Capacitance meter a c t u a l l y measures the reactive component of an impedance connected across i t s terminals, and because the channel conductance of the semicon-ductor t h i n - f i l m i s normally of the order of ten-thousandth of a mho, the readings recorded by the meter, therefore, does not give the exact capacitance of the URC structure. However, i t s normalized capacitance vs. voltage curve does q u a l i t a t i v e l y i n d i c a t e the regions of channel accumulation, depletion, and inv e r s i o n . CHAPTER 7 CONCLUSION The str u c t u r a l and e l e c t r i c a l properties of low-temperature sublimed s i l i c o n thin-films on sapphire and spinel substrates has been studied i n terms of their growth mechanisms and defect formations. The films were observed to have been formed by continuous nucleation and coalescence of the impinging s i l i c o n adatoms, irrespe c t i v e of the grown-f i l m thicknesses. Consequently, they were characterized by a high den-s i t y of grain boundaries which were also locations for defect generations. E l e c t r o n - r e f l e c t i o n - d i f f r a c t i o n patterns indicated that they consisted of singly oriented c r y s t a l l i t e s , with high angular perfections s i m i l a r to those obtained from e p i t a x i a l s i l i c o n f i l ms. Reduction i n aluminum autodoping i n films grown at low substrate temperatures was demonstrated by the growth of n-type films and by the suppression of changes i n the f i l m properties during post-deposition thermal oxidation. When compared to e p i t a x i a l s i l i c o n films grown at the optimal substrate temperatures, these films were observed to have lower c a r r i e r H a l l mobilities and higher f i l m r e s i s t i v i t i e s . However, they show.the same exponential dependence of r e s i s t i v i t i e s , m o b i l i t i e s , and c a r r i e r concen-t r a t i o n or temperature. From th i s we can i n f e r that while aluminum auto-doping does cause mobility degradation i n e p i t a x i a l s i l i c o n films grown on sapphire and spinel substrates at the optimal growth temperatures, car r i e r - s c a t t e r i n g by st r u c t u r a l defects i s s t i l l the predominant factor i n the control of f i l m q u a l i t i e s . By using various source doping concentrations but the same growth conditions, i t was found that the ef f e c t i v e c a r r i e r concentrations 103 104 deviated more from the source doping l e v e l when the l a t t e r was at a lower rather than at a higher impurity doping concentration. A defect scattering model using only a single i o n i z a -tion energy l e v e l inside the forbidden gap has been proposed. The result was foiind to be i n q u a l i t a t i v e agreement with experimental obser-vations. Using this model, the defect density was found to be i n -dependent of source doping concentrations, hence the impurity levels i n 12 -2 the grown films. They amounted to -10 cm i n films grown at ~800°C substrate temperature. The conductance of semiconductor r e s i s t o r s i n a distributed RC structure was studied under various channel biasing potentials. While the theory seemed to agree with experimental observations under channel depletion and inversion, a somewhat controversial r e s u l t was obtained for channel accumulation, the exact o r i g i n of which i s 'for the moment unknown. A detailed mathematical modelling of a URC structure using semiconductor for the r e s i s t i v e component has been made. By using the notation of C^ ="Q&/^ f° r t n e depletion layer capacitance the URC structure was shown to be analogous to that of a lossless trans-mission l i n e . An ac small -signal analysis of a URC structure having a non-uniform channel p r o f i l e was presented. • The result i s general enough that i t can also be used as an equivalent c i r c u i t for.a SOS deep-deple-tion MOST. The semiconductor URC structure was applied to frequency-tunable notch networks. Analysis based on the depletion approximation showed that both capacitance and conductance variations were incorporated 105 i n the process of notch frequency tuning.' Two d i s t i n c t operation modes are possible. They correspond to using predominantly either the capa-citance variations or the conductance vari a t i o n s . In contrast to the t r a d i t i o n a l tunable t h i n - f i l m notch f i l t e r s using only capacitance va-r i a t i o n s , the present configuration was shown to give a much better tuning capability of up to a few hundreds of per cent. A new notch network comprising of two URC sections has been proposed. I t i s characterised by i t s maintenance of an optimal notch at a l l tunable values of the notch freuqency. Consequently, i t makes possible the r e a l i z a t i o n of tunable semiconductor t h i n - f i l m notch f i l t e r s for p r a c t i c a l device applications. \ 106 APPENDIX A-Space Charge at the Semiconductor Surface of a MIS Structure For semiconductor, the space charge density p(x) i s given by p(x) = q (p - n + N D - N A) (A-l) where (N^ ~ ^ ) ^ s t n e n e t impurity l e v e l i n the semiconductor. In a non-degenerate case, n = n± exp -(u p-u) p = n. exp (u -u) (A-2) 1 r where u = q i^/kT, denotes the e l e c t r o s t a t i c p o tential r e l a t i v e to the i n t r i n s i c Fermi-level i n the bulk i n kT/q units. Now, charge n e u t r a l i t y has to be maintained i n the bulk semiconductor with IJJ = 0 and p(x) = 0. This gives N^ - N = 2 .n. -sinh .Ut, (A-3) D A x F Substituting (A-2) and (A-3) back into ( A - l ) , we can write the Poissons equation as d 2 u 2qn. —Tr [sinh (u -u) - sinh u ] (A-4) dx s Integrating once from x = 0 to x = 00, whereas u and du/dx are both zero, we have for an n-type semiconductor 1 d* = ~c£ ^ U S I N H U F + C O S ^ ^ U F - u * ~ G O s t l "p^ J (A-5) where T= bSr—^—]^ i s the i n t r i n s i c Debye-Length, 2p qn^ B kT By Gauss Law, the t o t a l charge per unit area within the semiconductor Q = - E s 1/2 s s B j- [u g sinh u F + cosh (up-u g) - cosh u^ , ] (A-6) 107 k.T .du, = e (-—) u s q Mx s The defining equation for depletion layer width i s Qs = QN + < * N D * d > (A-7) where i s the inve r s i o n layer charge given by F n. exp (u -u) 1 r du dx du , (A-8) The maximum depletion layer width i s assumed to occur at surface poten-t i a l = 2 For < < :Q S> w e f i n d x^ by i n t e g r a t i n g Poisson's equation twice; with p(x) = q.N , S F e , s J o 'Xdmax x dx = ^DXdmax 2 e. 4£ • N. so, x , = I • — — — In dmax v qN q D ) 2 . (A-9) (A-10) Ref.: Grove, A.S., B.E. Deal, E.H. Snow, C.T. Sah, "I n v e s t i g a t i o n of Thermally Oxidized S i l i c o n Surface Using Metal-Oxide-Semiconductor Structures", S o l i d State E l e c t r o n i c s , 8, pp. 145-163, 1965. 108 APPENDIX B Solutions of Lossless Transmission Line Equations For a lossless transmission l i n e of length X, the equations of state are: M | i t ) - _ r i ( z , t ) ( A - l l ) d Z 9 i ( z , t ) = _ i r ( z , t ) 3z 3t where r and c are respectively the distributed resistance and capacitance per unit length. Taking the Laplace's transform on both sides of ( A - l l ) and assuming zero i n i t i a l conditions, we have iY>,z) = _ r I ( } ( A _ 1 2 ) dz || ( S" Z ) = - s c V(s,z) . (A-13) Di f f e r e n t i a t i n g (A-12) w.r.t.z and substituting dl(s,z)/dz from . (A-13)>we get ^ ( 5 , 2 ) = G C R V ( S > Z ) ^ ( A _ U ) dz The f i n a l solution for (A-14) i s V(s,z) = A exp (az)+ B exp -(az) (A-15) where a = /src i s called the attenuation c o e f f i c i e n t . Using the boundary conditions . V(s,0) = V x, l(s,0) = I 1 , V(s,A) = V 2, V(s:,X) = I 2 , we obtain z,, = z__ = Z cothy (A-16) 11 22 o 109 Z12 = Z21 = Z 0 c o s e c h Y t where Z = / r / s c i s the c h a r a c t e r i s t i c impedance o / 2 / Y = Jscr = ysRC i s c a l l e d the complex propagation f a c t o r R = r.X = t o t a l s e r i e s resistance C = c.A = t o t a l capacitance »-In a T-network, ( f i g . 5.2) Z a = Z u - Z 1 2 (A-17) Z b = z 1 2 # (A-18) This 3-terminal URC structure can also be used as a two-terminal device by connecting terminals (s) and (D) or terminal (s) and (G) together. When the source and gate of the URC structure are connected together, the impedance of the r e s u l t i n g structure becomes a b 2 _ 2 Z l l Z12 Z l l Ref. Ghausi, M.S., J . J . K e l l y , "Introduction to D i s t r i b u t e d Parameter Networks", Holt, Rinehart and Winston, N.Y. , 1968. 110 REFERENCES 1. Wilcock, J.D., "MOST D i g i t a l Logic C i r c u i t s i n S i l i c o n Films Deposi-ted on Sapphire Substrates", Solid-State E l e c t r o n i c s , 14, 315, 1971. 2. Ronen, R.S., "Recent Advances i n Thin-Film S i l i c o n Devices on Sap-phire Substrates", Proc. IEEE, 59, 1506, 1971. 3. Mueller, C.W., "Thin Film Devices on D i e l e c t r i c Substrates", J. Vacuum S c i . Technol., ]_, 147, 1970. 4. A l l i s o n , J.F., D.J. Dumin, F.P. Heiman, C.W. Mueller, P.H. Robinson, "Thin-Film S i l i c o n : Preparation, Properties, -and Devices A p p l i c a -t i o n s " , Proc. IEEE, 57_, 1490, 1969. 5. Ross, E.C., G. Warfield, " E f f e c t of Oxidation on E l e c t r i c a l Charac-t e r i s t i c s of S i l i c o n on Sapphire Films", J. Appl. Phys., 40_, 2339, 1969. 6. Cullen, G.W., G.E. G o t t l i e b , C C . Wang and K.H. Zaininger, " E p i t a x i a l Growth and Properties of S i l i c o n on Alumina-Rich S i n g l e - C r y s t a l S p i n e l " , J. Electrochem. S o c , 116, 1444, 1969. 7. Dumin, D.J., P.H. Robinson, "Autodoping of S i l i c o n Films Grown E p i -t a x i a l l y on Sapphire", J. Electrochem, S o c , 113, 469, 1966. 8. Dumin, D.J., P.H. Robinson, G.W. Cullen, and G.E. G o t t l i e b , "Hetero-e p i t a x i a l Growth of Germanium and S i l i c o n on I n s u l a t i n g Substrates", RCA Rev., 31, 620, 1970. 9. Robinson, P.H., D.J. Dumin, "The Deposition of S i l i c o n on Single C r y s t a l Spinel Substrates", J . Electrochem. S o c , 115, 75, 1968. 10. Manasevit H.M., W.I. Simpson, "Single C r y s t a l S i l i c o n on a Sapphire Substrate", Amer. Phy. S o c Meeting, Aug. 1963, Edmonton, A l b e r t a , Canada. 11. Mueller, C.W., P.H. Robinson, "Grown-Film S i l i c o n T r a n s i s t o r s on Sapphire", Proc. IEEE, 52, 1487, 1964. 12a. Hofstein, S.R., "An Analysis of Deep Depletion Thin-Film MOS Trans-i s t o r s " , IEEE Trans. Electron Devices, ED-13, 846, 1966. 12b. Heiman, F.P., "Thin Film Silicon-on-Sapphire Deep Depletion Trans-i s t o r s " , IEEE Trans. Electron Devices, ED-13, 855, 1966. 13. Salama, C.A.T., L. Young, "Evaporated S i l i c o n Thin-Film T r a n s i s t o r s " , Solid-State E l e c t r o n i c s , 10, 473, 1967. 14. A l l i s o n , J.F., F.P. Heiman, and J.R. Burns, " S i l i c o n on Sapphire Complementary MOS Memory C e l l s " , IEEE Trans. S o l i d State C i r c u i t s , SC-2, 208, 1967. I l l 15. Heiman, F.P., P.H. Robinson, "Silicon-on-Sapphire E p i t a x i a l B i p o l a r T r a n s i s t o r s " , Solid-State E l e c t r o n i c s , 11, 411, 1968. 16. Many, A., Y. Goldstein, N.B. Grover, "Semiconductor Surfaces", . North-Holland Publishing Company, Amsterdam, 1965. 17. F i l b y , J.D., S. Nielson, "A New Technique for Producing E p i t a x i a l S i l i c o n Layers Using U l t r a Thin A l l o y Zones", Proc. 3rd In t e r n a t i o n a l Vacuum Congress, Stu t t g a r t , 1965. 18. Zakharov, V.P., Yu. A. Tevirko and V.N. Chugaev, Soviet Phys. Dok-lady English T r a n s l . , 11, 899, 1961. 19. Schloeterer, H. , "-Preparation -and Properties of Single •Crystal Semiconductor Films on Insulating Substrates", I n t e r n a t i o n a l Con-ference on Physics and Chemistry of Semiconductor Hetero-junction and Layer Structures, Budapest, Oct., 1970. 20. F i l b y , J.D., and S. Nielson, "Single C r y s t a l Films of S i l i c o n on Insulators", B r i t . J . Of Appl. Phys., 19_, 1357, 1967. 21. The l a t e s t , cpmprehensive review on the subject i s given by: Cullen, G.W.j "The Preparation and Properties of Chemically Vapor Deposited S i l i c o n on Sapphire and Sp i n e l " , J . of Cryt. Growth, 9_, 107, 1971. 22. Manasevit, H.M., and W.I. Simpson, "Single C r y s t a l S i l i c o n on a Sapphire Substrate", J. Appl. Phys., 35, 1349, 1964. 23. B i c k n e l l , R.W., J.H. Neave, B.A. Joyce, and G.V. Smith, "The Epitaxy of S i l i c o n on Alumina — S t r u c t u r a l E f f e c t s " , P h i l . Mag., 14_, 31, 1964. 24. Robinson, P.H., CW. Mueller, "The Deposition of Silicon-on-Sapphire Substrates", Trans. AIME, 236, 268, 1966. 25. Richman, D. and R.H. A r l e t t , "Preparation and Properties of Homo-e p i t a x i a l S i l i c o n Grown at Low-Temperature from Silane", 1st Int. Symposium on S i l i c o n M a t e r i a l Science and Technology, New York C i t y , May, 1969. 26. Richman, D., R.H. A r l e t t , "Low Temperature E p i t a x i a l Growth of S i n -gle C r y s t a l l i n e S i l i c o n from S i l a n e " , J . Electrochem. S o c , 116, 872 1969. 27. Salama, C.A.T., T.W. Tucker and L. Young, "Structure, Conductivity and H a l l E f f e c t of Electron Bombardment evaporated S i l i c o n Films on Sapphire", Solid-State E l e c t r o n i c s , 10, 339, 1967. 28. Reynolds, R.H., A.B.M. E l l i o t , "Vacuum Deposition of S i l i c o n on Corundum", Solid-State E l e c t r o n i c s , 10_, 1093, 1967. 112 29. Handelman, E.T., E.I. Dovilonis, " E p i t a x i a l Growth of S i l i c o n by Vacuum Sublimation", J. Electrochem. S o c , 111, 201, (1964). 30. Namba, S., A. Kawaza, and T. Maruyama, "Vacuum Deposited Single C r y s t a l S i l i c o n Films on Sapphire", Proc. 2nd Colloquim on Thin Films, 213, 1967. 31. Itoh, T., S. Hasegawa, and N. Kaminaka, " E l e c t r i c a l Properties of n-type E p i t a x i a l Films of S i l i c o n on Sapphire formed by Vacuum Evaporation", J. Appl. Phys., 39, 5310, 1968. 32. Naber, P., J. E. O'Neal, "Deposition of S i l i c o n on Sapphire i n U l t r a -high VAcuum", Trans. AIME, 24_2, 470,, 1968. 33. Itoh, T., S. Hasegawa, and N. Kaminaka, " E p i t a x i a l Films of S i l i c o n on Spinel by Vacuum Evaporation", J. Appl. Phys., 40_, 1206, 1969. 34. Cullen, G.W. , G.E. G o t t l i e b , C C . Wang, "The E p i t a x i a l Growth of S i l i c o n on Sapphire and Spinel Substrates: Suppression of Changes i n the Film Properties During Device Processing", RCA Review,31, 355, 1970. 35. Mercier, J . "Dopant Transfer i n H e t e r o e p i t a x i a l S i l i c o n Layers on Sapphire Substrates", J. Electrochem. Soc. 117, 812, 1970. 36. D. Richman, Chiang, Y.S., P.H. Robinson, "Low-temperature Vapour Growth of Tfomoepitaxial • S i l i c o n " , "RCA"Review '31, "613, 1970. 37. Yukio, Yasuda, and Y. Ohmura, " E p i t a x i a l Growth of S i l i c o n Films Evaporated on Sapphire", Japanese J . Appl. Phys., 8^, 1098, 1969. 38. Dumin, D.J., "Deformation of and Stress i n E p i t a x i a l S i l i c o n Films on Single C r y s t a l Sapphire", J . Appl. Phys., 36, Sc h l o t t e r e r , H., "Mechanical and E l e c t r i c a l Properties of E p i t a x i a l S i l i c o n Films on Spinel", Solid-State E l e c t r o n i c s , 10, 947, 1968. 39. Grove, A.S. , A. Roder, and C T . Sah, "Impurity D i s t r i b u t i o n ' i n E p i t a x i a l Grwoth", J..Appl. Phys., 36, 802, 1965. 40. Chu, T.L., " D i e l e c t r i c M aterials i n Semiconductor Devices", J. Vacuum S c i . and Tech., 6_, 25, 1969. 41. Szedon, J.R., " E f f e c t of Organic and Inorganic D i e l e c t r i c Films on Semiconductor Devices", IEEE Trans, on E l e c t r i c a l Insulation,. EI-5, 3, 1970. 42. Weisberg, L.R. , E.A. M i l l e r , "Vacuum Deposition of. Single Cry-s t a l l i n e S i l i c o n on Sapphire", Trans. AIME, 242, 479, 1968. 43. N i c o l l , F.H., "The Use of Close Spacing i n Chemical-Transport System for Growing E p i t a x i a l Layer of Semiconductors", J . E l e c -trochem. S o c , 110, 1165, 1965. 113 44. K i l g o r e , B.F., R.W. Roberts, "Preparation of Evaporated S i l i c o n Films", Rev. of S c i . Instr., 34, 11, 1963. 45. Widmer, H., " E p i t a x i a l Growth of S i l i c o n on S i l i c o n i n Ultra-high Vacuum", J. Appl. Phys., 5_, 108, 1964. Thomas, R.N., M.H. Francombe, "Low Temperature Epitaxy of S i l i c o n Junctions by Ultra-high Vacuum Techniques", Technical Report AIML-TR-68-355. 46. A l l e n , F.G., "Emissivity of .0.65 Micron of S i l i c o n and Germanium at High Temperatures", J. Appl. Phys., 28_, 1510, 1957. 47. Woif, H.F., "Semiconductors", Chapter 3-5, section 3, Wiley-Inter-science, 1971. 48. Reisman, A., M. Berkenblit, J. Crimo,, and S.A. Chan, "The Chemical P o l i s h i n g of Sapphire and MgAl S p i n e l " , J. Electrochem. S o c , 118, 1653, 1971. 49. F i l b y , J.D., "The Chemical P o l i s h i n g of Single C r y s t a l a - Alumina' Using S i l i c o n " , J. Electrochem. S o c , 113, 1985, 1966. 50. Reynolds, R.H., A.B.M. E l l i o t , "Etching Corundum with S i l i c o n " , P h i l . Mag., 13, 1073, 1966. 51. Chopra, K.L., "Thin Film Phenomena", se c t i o n 5.2.4, McGraw H i l l Company, N.Y. City, 1969. 52. Pashley, D.W., M.F. Stowell, "Nucleation and Growth of Thin Films as Observed i n the Electron Microscope", J. Vacuum S c i . and Tech., 3, 156, 1966. 53. Thornton, C.G., "New Trends i n Mi c r o - e l e c t r o n i c s F a b r i c a t i o n Tech-nology", Proc. NEC, 21, 31, 1965. 54. 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 Disc of A r b i t r a r y Shape", P h i l i p s Res. Report, 13, 1, 1958. 55. Yan, G. , "Studies of Sublimed GaAs Films, Anodic A^O-j Films, and A 1 2 ° 3 ^ G a A s I n t e r f a c e " » sections 4.5.2-4.5.4, Ph.D. D i s s e r t a t i o n , U n i v e r s i t y of B r i t i s h Columbia, 1970. 56. Fisher, G., D. Greig, and E. Mosser, "Apparatus f o r the Measurement of Galvanomagnetic E f f e c t s i n High Resistance Samples", Rev. S c i . Inst., 32, 842, 1961. 57. Pashley, D.W., "Hie Nucleation, Growth, Structure and Epitaxy of Thin Surface Films", Adv. Phys., 14, 327, 1965. 58. Hart, P.W., P.J. E t t e r , B.W. J e r v i s , and J.M. Flanders, " E l e c t r i c a l Properties of E p i t a x i a l S i l i c o n Films on a - alumina", B r i t . J . Appl. 114 Phys., 18, 1389, 1967. 59. A general review i s given i n : Neugebauer, C.A., "Condensation, Nucleation and Growth of Thin Films", Chapter 8, 'Handbook of Thin Film Technology', edited by L. Maissel, R. Gland, McGraw H i l l Book Company, N.Y. 1970. 60. McCarrol, B., G. E f r l i c h , "Condensation and Energy Transfer of C r y s t a l s " i n Condensation and Evaporation of S o l i d s , e d i t e d by E. Rutner, P. Goldfinger, and J.P. H i r t h , p. 521, Gordon and Breach, New York, 1962. 61. Pashley, D.W., "Hie Preparation of Smooth Single C r y s t a l Surfaces of S i l v e r by an Evaporation Technique", P h i l . Mag. 4, 316, 1959. 62. Matthews, J.W., "Evaporated Single C r y s t a l Films", Proc. 4th I n t e r . Vac. Congress, p. 479, Manchester 1968. ' 63. Chopra, K.L., M.R. Randett, "Influence of Deposition Parameters on the the Coalescence Stage of Growth of Metal Films", J . Appl. Phys., 39, 1874, 1968. 64. Pashley, D.W. M.J. Stowell, M.H. Jacobs, and T.J. Law, "The Growth and Structure of Gold and S i l v e r Deposits Formed by Evaporation Inside an Electron Microscope", P h i l . Mag. 10, 127, 1964. 65. Dumin, D.J., " E l e c t r i c a l Properties of S i l i c o n Films Grown E p i -t a x i a l l y on Sapphire", J . Appl. Phys., 38, 1909, 1967. 66. Nolders, R.L., D.J. K l e i n , D.H. Forbes, "Twinning i n S i l i c o n E p i -t a x i a l l y Deposited on Sapphire", J. Appl. Phys., 36_, 3444, 1965. 67. Batsford, R.O., D.J.D. Thomas, "Defects i n Vapour-grown S i l i c o n " , M i c roelectronics and R e l i a b i l i t y , 2_, 159, 1964. 68. Heiman, F.P., "Donor Surface States and Bulk Acceptor Traps i n SOS Films", Appl. Phys. L e t t e r s , 11, 132, 1967. 69. Abbink, H.C., R.M. Boudy, and G.P. McCarthy, "Surface Processes i n the Growth of S i l i c o n on (111) S i l i c o n i n U l t r a - h i g h Vacuum", J . Appl. Phys., 39, 4673, 1968. 70. Nielson, S., G.J. Rich, "Preparation of E p i t a x i a l Layers of S i l i c o n : 1. D i r e c t and Indirect Processes", M i c r o e l e c t r o n i c s and R e l i a b i l i t y , 3, 165, 1964. 71. Adamsky, R.F., " E f f e c t of Deposition Parameters on the C r y s t a l l i n i t y of Evaporated Germanium Films", J . Appl. Phys., 40, 3865, 1969. 72. McKelvey, J.P., " S o l i d State and Semiconductor Physics", pp 301ff, Harper and Row, New York, 1966. 115 73. Dumin, D.J., E.C. Ross, "Temperature Dependence of the H a l l M o b i l i t y and C a r r i e r Concentration i n Silicon-on-Sapphire Films", J . Appl. Phys., 41, 3839, 1970. 74. Chapman, P.W., O.N. Tufte, J.D. Zook, and D. Long, " E l e c t r i c a l Pro-p e r t i e s of Heavily Doped S i l i c o n " , J . Appl. Phys., 34, 3291, 1963. 75. Neugebauer, C.A., "Temperature Dependence of the F i e l d - E f f e c t Con-ductance i n Thin P o l y c r y s t a l l i n e CdS Films", J . Appl. Phys. 39_, 3177 1968. 76. Dumin, D.J., P.H.. Robinson, " C a r r i e r Transport i n Thin S i l i c o n Films", J . Appl. Phys., 39, 2759., 1968. 77. Dumin, D.J., "Deep Levels Within the Forbidden GAp of S i l i c o n - o n -Sapphire Films", Solid-State E l e c t r o n i c s , 13, 415, 1970. 78. Matukura, Y., "Grain Boundary States of S i l i o c n and Germanium", Japanese J . Appl. Phys. 2_, 91, 1963. 79. Meyer, M., M.H. Miles, and T. Ninomiya, "Some E l e c t r i c a l and O p t i c a l E f f e c t s of D i s l o c a t i o n s i n Semiconductor", J . Appl. Phys., 38, 4481, 1967. Dumin, D.J., P.H. Robinson, " E l e c t r i c a l l y and O p t i c a l l y Active De-fects i n Silicon-on-Sapphire Films", J . Crys. Growth, _3, 214, 1968. 80. Glaenzer, R.H., A.G. Fordan, "The E l e c t r i c a l Properties of D i s l o c a -tions i n S i l i c o n - I", Solid-State E l e c t r o n i c s , 1_2, 247, 1969. 81. O ' R e i l l y , T.J., " E f f e c t of Surface Traps on C h a r a c t e r i s t i c s of In-sulated-gate F i e l d E f f e c t T r a n s i s t o r s " , Solid-State E l e c t r o n i c s , _8, 267, 1965. 82. Volger, J . , "Note on the H a l l P o t e n t i a l Across an Inhomogeneous Conductor", Phys. Rev., 79_, 1023, 1950. 83. Grove, A.S., 0. L e i s t i k o J r . , C T . Sah, " R e d i s t r i b u t i o n of Acceptor and Donor Impurities During Thermal Oxidation of S i l i c o n " , J . Appl. Phys., 35, 2695, 1964. 84. Neumark, CP., "New Model f o r Interface.Charge-carrier M o b i l i t y : The Role of M i s f i t D i s l o c a t i o n s " , Phy. Rev. L e t t e r s , 2 1, 1252, 1968.' 85. Thomas, R.N., M.H. Francombe, "A LEED Study of the Homoepitaxial Growth of Thick S i l i c o n Films", Appl. Phys. L e t t e r s , 11, 108, 1967. 86. Nolder, R.L., I.B. Cadoff, "Heteroepitaxial Silicon-Aluminum Oxide Interface — I I . Orientation Relations of Single C r y s t a l S i l i c o n on Alpha Aluminum Oxide", Tech. Conf. on Solid-State Interfaces, Boston, Mass., 1964. Manasevit, H.M., D.H. Forbes, " S i n g l e - C r y s t a l S i l i c o n on S p i n e l " , J. Appl. Phys., 37, 734, 1966. 116 87. Maissel, L., "Thin Film Resistor", Ch. 18 i n 'Handbook of Thin Film Technology', edited by L. Maissel, and R Glang, McGraw H i l l , New York, 1970. 88. Gerstenberg, D., "Thin Film Capacitors", Ch. 19 i n 'Handbook of Thin Film Technology', edited by L. Maissel, and R. Glang, McGraw H i l l , New York, 1970. 89. Joseph, J.D., T.I. Kamins, " R e s i s t i v i t y of Chemically Deposited P o l y c r y s t a l l i n e - S i l i c o n Films", Solid-State E l e c t r o n i c s ( l e t t e r s ) , 15, 355, 1972. 90. Sze, S.M., "Physics of Semiconductor Devices", Wiley, New York, 1969. 91. Joyce, B.A., J.C. Weaver, and D.J. Maule, "Impurities R e d i s t r i b u t i o n Processes i n E p i t a x i a l S i l i c o n Wafers", J . Electrochem. S o c , 112, 1100, 1965. 92. Wolf, H.F., " S i l i c o n Semiconductor Data", Section 8.34, Pergamon Press, 1969. 93. Deal, B.E., A.S. Grove, E.H. Snow, and C T . Sah, "Observation of Impurity R e d i s t r i b u t i o n During Thermal Oxidation of S i l i c o n Using the MOS Structure", J . Electrochem. S o c , 112, 308, 1965. 94. Wrigley, C.Y., L.J. Kroko, "Properties of the Silicon-Sapphire •Interface i n Heteroepitaxy", *p. 325-329 i n 'Semiconductor S i l i c o n ' , edited by R.R. Haberecht, and E.L. Kern, Electrochemical S o c , Inc. 1969. 95. Lehovec, K., A. Slobodskoy, "Impedance of Semiconductor-Insulator-Metal Capacitors", Solid-State E l e c t r o n i c s , _7, 59, 1964. 96. Johnson, J.E., "Physical Processes i n Insulated Gate F i e l d E f f e c t T r a n s i s t o r s " , Solid-State E l e c t r o n i c s , ]_, 861, 1964. 97. Sze, S.M., G. Gibbons, " E f f e c t of Junction Curvature on Breakdown Voltages i n Semiconductors", Solid-State E l e c t r o n i c s , 9_, 831, 1966. 98. Kingston, R.H., S.R. Neustadter, " C a l c u l a t i o n of Space-charge, E l e c t r i c F i e l d , and Free C a r r i e r Concentration at Surface, of Semi-conductor", J. Appl. Phys., 26, 718, 1965. Garrett, C.G.B., W.H. B r a t t a i n , "Physical Theory of Semiconductor Surfaces", Phy. Rev., 99, 376, 1955. 99. L e i s t i k o , 0., A.S. Grove, and C T . Sah, "Electron and Hole M o b i l i t i e s i n Inversion Layers on Thermally Oxidized S i l i c o n Surfaces", IEEE Trans. E l e c t r o n Devices, ED-12, 148, 1965. 100. Shockley, W., "A Unipolar F i e l d E f f e c t T r a n s i s t o r " , P r o c IEEE, 40, 1365, 1952. 117 101. Lindholm, R.A., D.J. Hamilton, "A Systematic Modelling Theory f o r S o l i d State Devices", Solid-State E l e c t r o n i c s , 7_, 771, 1964. 102. Kaufman, W.M., S.J. Garrett, "Tapered D i s t r i b u t e d F i l t e r s " , IRE Trans, on C i r c u i t Theory, CT-9, 329, 1962. 103. See for Example: Cobbold, S.C., "Theory and Applications of F i e l d -E f f e c t Transistors", section 5.1, Wiley-Interscience, 1970. 104. Castro , P.S., W. Happ, " D i s t r i b u t e d Parameter C i r c u i t s and Micro-system E l e c t r o n i c s " , Proc. N a t l . E l e c t r o n i c Conf. , 1_6, 448, 1960. 105. Smith, A.B., "Rejection F i l t e r s with D i s t r i b u t e d R and C", Proc. 1960 E l e c t r o n i c s Components Conf., Washington, D.C, 1960. 106. Kaufman, W.M., "Theory of Monolithic N u l l Device and Some Novel C i r c u i t s " , Proc. IRE, 48, 1540, 1960. 107. F u l l e r , W.D., P.S. Castro, "A Micorsystern Bandpass A m p l i f i e r " , Proc. N a t l . E l e c t r o n i c s Conf., 16_, 139, 1960. 108. Haulsman, L.P., "The Distributed-Lumped-Active Network — I t s Ap-p l i c a t i o n s to F i l t e r i n g Problems", IEEE Spectrum, p. 51, Aug., 1969. 109. L i n , H.C, "Integrated E l e c t r o n i c s " , s e c t i o n V-7, Holden-Day, San Francisco, 1967. 110. Wyndrum, R.W., J r . , " D i s t r i b u t e d Notch Networks", Proc. IEEE (cor-resp.), 51, 374, 1963. 111. Dutta Roy, S.C, B.A. Shenoi, "Notch Networks Using D i s t r i b u t e d RC Elements", Proc. IEEE ( l e t t e r s ) , 54, 1020, 1966. 112. Stein, J . , "A New Look at D i s t r i b u t e d RC Notch F i l t e r s " , Proc. IEEE ( l e t t e r s ) , 58, 596, 1970. 113. Edson, W.A., "Tapered D i s t r i b u t e d RC Line f o r Phase S h i f t O s c i l -l a t i o n " , Proc. IRE, 49, 1330, 1961. 114. Golembeski, J . J . , " D i s t r i b u t e d RC Network Tuning", IEEE Trans. Solid-State C i r c u i t s CS-4_, 425, 1969. 115. Swart, P., "A Study of Evaporated Thin-Film Voltage-Controlled Tunable D i s t r i b u t e d R C - F i l t e r s " , Ph. D. D i s s e r t a t i o n , McMaster Univ., Hamilton, Ontario, Canada, 1971. 116. Meyerhofer, D., "Conduction Through I n s u l a t i n g Layers", Ch. 3 i n ' F i e l d - E f f e c t T r a n s i s t o r s , Physics, Technology and A p p l i c a t i o n s ' , edited by J.T. Wallmark, H. Johnson, P r e n t i c e - H a l l , Englewood C l i f f , N.J., 1966. 117. Weimer, P.K., "The Insulated-Gate Thin-Film T r a n s i s t o r " , p. 147-192, i n 'Physics of Thin Films', Vol 2, Academic Press, New York, 1963. 118 118. Glang, R. , L.V. Gregor, "Generator of Patterns i n Thin Films", Chapter 7, i n 'Handbook of Thin Film Technology', edited by L.I. Maissel, R. Glang, McGraw H i l l , New York, 1970. 119. Henderson, R.C., " S i l i c o n Cleaning with Hydrogen Peroxide Solutions", J. Electrochem. S o c , 119, 771, 1972 . Kern, W., D. Puotinen, "Cleaning Solutions based on Hydrogen Peroxide for Use i n S i l i c o n Semiconductor Technology", RCA Rev., 31, 187, 1970. 120. C h i r l i a n ., P.M., "Integrated and Active Network Analysis and Synthe-s i s " , p. 134-139, P r e n t i c e - H a l l , Englewood C l i f f s , N.J., 1967. 121. Grove, A.S., B.E. Deal, E.H. Snow, C T . Sah, "Inv e s t i g a t i o n of Thermally Oxideized S i l i c o n Surface Using Metal-Oxide-Semiconductor Structures", Solid-State E l e c t r o n i c s , 8, 145, 1965. 122. H e n r i c i , P., "Elements of Numerical A n a l y s i s " , pp. 105-107, Wiley, New York, 1964. 123. Grove, A.S., "Physics and Technology of Semiconductor Devices", p. 104, Wiley, New York, 1967. 

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