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The preparation and properties of rf-plasma-anodized silicon dioxide thin films and aluminum-silicon… Reche, Jean Joseph Henri 1973

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THE PREPARATION AND PROPERTIES OF RF-PLASMA-ANODIZED SILICON DIOXIDE THIN FILMS AND ALUMINUM-SILICON SCHOTTKY PHOTODIODES by JEAN JOSEPH HENRI JOHN RECHE A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n 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 THE UNIVERSITY OF BRITISH COLUMBIA October 1973 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t c o p y i n g or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8 , Canada Date £LTL 11 /?73 ABSTRACT An experimental procedure which u t i l i s e s r f plasma anodization to grow SiO^ films on s i l i c o n i s described. The q u a l i t y of these films i s sui t a b l e f o r MOS technology and growth rates are p r a c t i c a l f o r i n d u s t r i a l manufacturing. The e l e c t r i c a l and p h y s i c a l propeties of the s i l i c o n dioxide films have been studied with comparisons being made, whenever p o s s i b l e , to r e s u l t s obtained with films grown by other methods. A novel method to determine the o p t i c a l properties of thin films from s i n g l e angle reflectance measurements has been devised i n order to accurately monitor i n - s i t u the growth of the thin films described i n t h i s work. Large-area aluminum-silicon Schottky photodiodes with wide spec-t r a l response have been manufactured using plasma anodization as a pro-cessing s»tep. -An aluminum ^-o-x-i'de coating drs- tused <for ;passivatdon, shaping -of the s p e c t r a l response and enhancement of the photoresponse throughout the spectrum of i n t e r e s t . The heights of the aluminum-p-type and -n-type s i l i c o n b a r r i e r s are reported and a comparison i s made between the e x p e r i -mental s p e c t r a l response and a t h e o r e t i c a l model. i TABLE OF CONTENTS Abstract i Table of contents i i List of Figures iv L i s t of tables ix Acknowledgement x I Introduction 1 II Thin Film Optics 4 2.1 Introduction 4 2.2 Reflectance and Transmittance of an Assembly of Thin Films 2.3 Program for Reflectance and Transmittance computation 6 2.4 Reflectance of the Surface of an Absorbing Film on an Absorbing Substrate * 10 III Plasma Anodization; Experimental Work 22 3.1 Introduction 22 3.2 Apparatus 24 3.2a Plasma Anodization Chamber 24 3.2b Sample Holder 26 3.2c Cathode 26 3.2d Sample Bias 29 3.2e Reflectance Analog Computer 29 ..v.3>.21f,^ Pho,toli,thc);gr,ap%hi c .Equipment t • 36 3.3 Anodization of Silicon '40 3.3a Sample Preparation 40 3.3b Anodization Procedure 42 3.3c Early Experiments 42 3.3d Later Experimental Growth of S i 0 2 43 3.3e Growth Characteristics 44 3.3f Effects of Current Density on Growth Characteristics 46 3.3g Stresses in Silicon Dioxide 50 3.3h Sputtering During Anodization 52 3.4 E l e c t r i c a l and Physical Properties of RF Plasma Grown Si02 54 3.4a C-V Measurements 55 3.4b Breakdown Field Strength 61 3.4c Insulating Properties 65 3.4d Index of Refraction 65 3.4e Etching Properties 68 3.4f Infrared Spectroscopy • 68 3.4g Nuclear Backscattering Spectrometry 71 3.5 Discussion 74 IV Anodization of Aluminum Covered Silicon 75 4.1 Aluminum-Silicon Schottky Photodiode with Plasma-Anodized Anti-Reflection Coating 75 4.1a Sample Preparation 75 4.1b. Film Growth 76 4.1c Simple Theoretical Models for a Front-Face illuminated Schottky Barrier 8 1 4.Id Monochromatic Photoresponse 89 4.1e Spectral Response 94 i i 4.2 Discussion * 117 4.3 Preliminary Work on A £ 2 0 3 - S i and A& 20 3 - S i 0 2 - S i Systems 119 4.3a Introduction 119 4.3b H i l l o c k s Formation During Anodization of Aluminum on S i l i c o n 123 4.3c Interpretation of the Defect Occurence 125 4.3d O p t i c a l Monitoring of the Growth 129 4.3e Nuclear Backscattering Spectrometry 135 4.3f Suggested Strategy f o r Further Research 135 V Conclusion 139 VI Appendix 140 6.1 Computer program to obtain the refle c t a n c e and transmittance of an assembly of thin films 141 6.2 Computer program to obtain the refle c t a n c e at the maxima and minima i n a s i n g l e - f i l m substrate system 144 6.3 Computer program to obtain the surface state density using the q u a s i - s t a t i c technique 145 VII References 148 i i i L I S T OF FIGURES . Page F i g . 2.1 Generalized system of s t r a t i f i e d thin films 7 2.2 Computed variation of sample reflectance with thin film thickness 11 n 2(S ±) = 3.86 - 10.017, <j> = 35.8°, X = 6328 A, (a) n± = 1.40, (b) n x = 1.40 - 10.05 11 2.3 Computed variation of reflectance difference between consecutive ex-trema with thin film refractive index, for the case of a transparent f l l m ' n 2(S ±) = 3.86 - 10.017, <f> = 35.8°, X = 6328 A. 13 2.4. Computed variation of reflectance difference between f i r s t and second extrema with thin film refractive index. n 2(S ±) = 3.86 - iO.017, <|> = 35.8°, X = 6328 A. 17 2.5 Computed variation of reflectance difference between f i r s t and third extrema with thin film refractive index. n 2(S ±) = 3.86 - iO.017, <f> = 35.8°, X = 6328 A. 18 2.6 Computed chart of AR^,and AR 2 (the reflectance difference between f i r s t and second and f i r s t and third extrema respectively) as func-tions of refractive index. n2(.S/) = 3.86 - iO.017, <j> = 35.8°, X = 6328 A. 2.7 Computed variation of AR^ and AR 2 with angle of incidence. n\ = 1.4 - i0.05, n„(S.) = 3.86 - i0.017, X = 6328 A. 1 2 x 19 20 3.1 Possible configurations obtained by stopping the anodization of a single deposited film over a substrate of various stages. 23 3.2 Schematic view of the plasma anodization chamber 25 3.3 Schematic view of the sample holder 27 3.4 Schematic view of the cathode 28 3.5 Schematic of the sample bias network and circuit monitoring 28 3.6 Reflectance measurement arrangement 30 3.7 Block diagram of the reflectance analog computer 33 3.8 Circuit diagram of the reflectance analog computer 35 3.9 Schematic view of f i r s t reduction pinhole camera 38 3.10 Schematic view of photoresist whirler 39 i v Page 3.11 Voltage across the oxide, V , versus thickness of the oxide. Sam-ox pie no. 68, p-type 1-1-1, n = 1.445, f i n a l oxide thickness = 1225 A, _2 anodization current ^ 12.2mA cm . 45 3.12 Thickness versus time f o r the growth of a p a r t i c u l a r SiO^ f i l m . Sample no. 88, p-type 1-1-1, n = 1.461, f i n a l oxide thickness = o _2 1350 A, anodization current ^ ll.lmA cm . 47 3.13 Voltage across the oxide, V q x , versus thickness^of the oxides. A l l samples n-type 1-1-1, anodization current d e n s i t i t e s = sample no. 101 -2 -2 -2 = 5.5mA cm , sample no. 97 = ll. l m A cm , sample no. 98 = 16.7mA cm , -2 -2 sample no. 99 = 22.2mA cm , sample no. 100 = 27.8mA cm . 48 3.14 Thickness versus time f o r the growth of n-type 1-1-1 samples. Ano-—2 d i z a t i o n current d e n s i t i e s : sample no. 101 = 5.5mH cm , sample -2 -2 no. 97 = l l . l m A cm , sample no. 98 = 16.7mA cm , sample no. 99 = 22.2mA cm"2, sample no. 100 = 27.8mA cm"2, ho. 101 = 5.5 mA cm - 2. 49 3.15 Scanning e l e c t r o n microscope micrographs of damage i n s i l i c o n dioxide f i l m s a-d) Sample no. 34, p-type 1-0-0, n = 1.425, f i n a l oxide t h i c k -ness ^ 1500 A, current density = 11.1 to 36.1 mA cm , damage caused by high current'dehsity 'in l a t t e r "part of the "growth. "Sample has been gold decorated f o r SEM. e-f) Sample no. 82, p-type 1-1-1, "n = 1.46, o _2 f i n a l oxide thickness ^ 1900 A, current density = 11.1 mA cm , damage caused by large thickness. B l i s t e r s show black because of secondary e l e c t r o n trapping under S i 0 2 f i l m : no m e t a l l i c decoration. 51 3.16 Scanning e l e c t r o n microscope of a S i 0 2 f i l m damaged by sputter i n g . Sample no. 4, n-type 1-1-1, n = 1.385 - i0.053, f i n a l oxide thickness = o _2 4060 A, current density = .55 mA cm * 53 3.17 E f f e c t s of oxide defects on C-V curve f o r a p-type semiconductor a) s h i f t of the curve due to f i x e d charges b) d i s t o r t i o n of the curve due to surface states c) hy s t e r e s i s of the curve due to i o n d r i f t d) h y s t e r e s i s of the curve due to trapping. 56 3.18 High-frequency C-V c h a r a c t e r i s t i c of r f plasma grown S i 0 2 . Sample no. 36, p-type 1-0-0, n = 1.452, oxide thickness = 1480 A, anodiza-_2 t i o n current density ^ 15mA cm , annealed at 400°C i n N 2 f o r 1 hour. 58 3.19 Schematic diagram of MOS capacitor measurements by the q u a s i s t a t i c method. C = MOS capacitor under t e s t . 60 3.20 C i r c u i t diagram of the instrumentation used i n measurements by the q u a s i s t a t i c method. 62 Page 3.21 C-V c h a r a c t e r i s t i c of r f plasma grown S i 0 2 obtained by the quasi-s t a t i c method. Sample no. 66, n-type 1-1-1, n = 1.45, oxide t h i c k -o _2 ness = 1060 A, anodization current density ^ 12.5mA cm , annealed at 450°C i n N 2 f o r 15 min. 63 3.22 Surface-State density f o r the r f plasma anodized S i - SiO,, system. Sample no. 66. 64 3.23 MOS capacitor - array with guard-rings a) Array as produced by f i r s t reduction camera b) Test array a f t e r second reduction (nega-t i v e ) . 66 3.24 Schematic diagram of MOS capacitor leakage current measurement with guard-ring» 67 3.25 Scanning e l e c t r o n microscope micrograph of etched s i l i c o n dioxide (thickness ^ 1000 A). . 6 9 3.26 T y p i c a l i n f r a r e d spectrum of r f plasma-grown s i l i c o n dioxide. 70 3.27 Nuclear backscattering spectrum f o r r f plasma-grown s i l i c o n dioxide at 2.0 MeV 4H + , sample no. 84, p-type 1-1-1, n = 1.46, oxide t h i c k -° e -2 ness = 1235 A, anodization current density = 11.1mA cm 72 4.1 Computed v a r i a t i o n of the transmittance and ref l e c t a n c e of aluminum anodized on a s i l i c o n substrate assuming an i n i t i a l aluminum thickness of 450 A. 77 '4.2 Experimental v a r i a t i o n of the re f l e c t a n c e of aluminum anodized on a o _ „ s i l i c o n substrate. Sample no. 41, i n i t i a l aluminum thickness = 450 A. <° 4.3 Schematic view of a Ai^O^ - AJl-Si photodiode a) without guard r i n g b) with S i 0 2 guard r i n g 79 4.4 J-V c h a r a c t e r i s t i c of a A£ 20„-A£-Si photodiode. Sample no. 41, p-o o type 1-1-1 s i l i c o n , thickness ^  534 A, Al thickness ^  65 A, 80 a r b i t r a r y l i g h t i n t e n s i t y increments. 80 4.5 Metal-semiconductor b a r r i e r f o r c o l l e c t i o n e f f i c i e n c y model. 83 4.6 Simple dc equivalent c i r c u i t f o r a Schottky b a r r i e r photodiode, R = s e r i e s resistance, R^ = load resistance, Rg^ = shunt r e s i s t a n c e . 88 4.7 Spectral response of S i p - i - n photodiode, Hewlett-Packard HP 4220 (from manufacturer's data sheet). 91 4.8 C i r c u i t diagram of the instrumentation used i n measurements of the ' s h o r t - c i r c u i t ' current of photodiodes operated i n the s o l a r - c e l l mode. 92 v i Page 4.9 Photocurre/it density versus irradiance at room temperature. 95 = 6328 A. 4.10 Open-circuit voltage versus i r r a d i a n c e at room temperature. 96 = 6328 A. 4.11 Block diagram of the experimental set-up to c a l i b r a t e the s p e c t r a l output of the monochromator. 98 4.12 Monochromator c a l i b r a t i o n curve, v i s i b l e spectrum (400 - 700 nm) , quartz-iodine source, f i l t e r : Corning cs 3-74. 99 4.13 Monochromator c a l i b r a t i o n curve, n e a r - i n f r a r e d (700 nm - 1300 nm), quartz-iodine source, f i l t e r : Corning cs 7-64. 100 4.14 Monochromator c a l i b r a t i o n curve, i n f r a r e d (1200 nm - 1600 nm), quartz-iodine source, f i l t e r : Corning cs 7-56. 101 4.15 Experimental s p e c t r a l response S i p - i - n photodiode Hewlett-Packard HP 4220. 102 4.16 Experimental s p e c t r a l response photodiode no. 40. 103 4.17 Experimental s p e c t r a l response photodiode no. 41. 104 4.18 Experimental s p e c t r a l response photodiode no. 45. 105 4.19 Experimental s p e c t r a l response photodiode no. 49. 106 •4.20 Fowler's p l o t : square root of the photoresponse per i n c i d e n t photon versus photo energy for-aluminum n-type s i l i c o n diode no. 45 and f o r aluminum p-type s i l i c o n diodes no. 40, no. 41 and no. 49. 108 4.21 V a r i a t i o n of r e f r a c t i v e index of aluminum with wavelength (from r e f . 87). 109 4.22 V a r i a t i o n of r e f r a c t i v e index of aluminum oxide with wavelength (see r e f . 88 and t e x t ) . 110 4.23 V a r i a t i o n of r e f r a c t i v e index of s i l i c o n with wavelength (from r e f . 89). I l l o 4.24 Reflectance and transmittance at aluminum-silicon i n t e r f a c e a) 50 A o o . aluminum on s i l i c o n b) 556 A of aluminum oxide and 50 A of alumxnum on s i l i c o n . 112 4.25 Quantum e f f i c i e n c y as a function of minority c a r r i e r l i f e t i m e -556 A A l 2 0 3 , 50 A A l , p-type 5ft -cm S i . 113 o 4.26 S p e c t r a l response as a function of minority c a r r i e r l i f e t i m e . 556 A Ah°3' 5 0 A A 1 ' P _ t y P e 5ft-cm S i . 114 v i i Page 4.27 E f f e c t of A^O., a n t i - r e f l e c t i o n coating on t h e o r e t i c a l s p e c t r a l response -a) 50 A A l , p-type 5 Q-cm S i b) 556 A Al 20g. 50 A A l , p-type 5 Q-cm S i . 115 o o 4.28 Spectral response for 556 A A^O-j, 50 A A l a) 5Acm p-type S i b) 5ilcm n-type S i . 116 4.29 Scanning e l e c t r o n microscope micrographs of aluminum h i l l o c k s f o r -mation, Sample no. 31, i n i t i a l aluminum thickness = 1650 A, anodization current = 16 mA -cm-2. 120 4.30 El e c t r o n probe microanalysis of anodized aluminum with h i l l o c k s formation. Sample no. 31 a) Backscattered e l e c t r o n image (to-pography) b) Aluminum x-ray image c) oxygen x-ray image d) S i l i c o n x-ray image. 121 4.31 Micrographs of sample no. 37 a) Scanning e l e c t r o n microscope b) e l e c t r o n probe microanalysis ( i ) backscattered e l e c t r o n image (topography) ( i i ) aluminum x-ray image. 122 o 4.32 Scanning e l e c t r o n microscope micrograph of 450 A vacuum evaporated aluminum (sample no. 32) before anodization. 123 4.33 Scanning e l e c t r o n micrograph of sample no. 31 showing h i l l o c k s d i s t r i b u t i o n on the sample. 126 "4.3*4 "Film on a 'substra'te •covered by 'another 'fi'lm-with lowex'•diffusion rate a) b i a x i a l stress forces c r e a t i n g a v e r t i c a l d r i f t force component at a vacancy s i t e b) Mass flow under compressive b i a x i a l s t r e s s c) Mass flow toward free surface a f t e r rupture of the upper f i l m . ' 128 4.35 Computed r e f l e c t i v i t y from anodization of aluminum deposited on s i l i c o n , the i n i t i a l aluminum thickness i s a) 450 A b) 550 A. 131 The s o l i d l i n e corresponds to A^O^ - SiO? - S i system and the dotted l i n e to an hypot h e t i c a l SiO^ - Al 203 - S i system. 4.36 Experimental v a r i a t i o n of the reflec t a n c e of aluminum anodized on a s i l i c o n substrate - Sample no. 90, i n i t i a l aluminum thickness ~ 450 A (sputtered*), anodizing current = 8.3 mA cm-^. 132 * Sputtering c a r r i e d out by Sloan Instruments, Santa-Barbara, C a l i f , on our wafers. 4.37 A 1 2 0 3 - Si0 2 - S i f i l m a f t e r h i l l o c k s formation. 133 4.38 Nuclear backscattering spectrum f o r r f plasma grown AI2O3 - Si02 _ S i system at 2.0 MeV H + , sample no. 91, i n i t i a l aluminum thickness -450 A. 6 135 4.39 Nuclear backscattering spectrum f o r r f plasma grown AI2O3 _ Si02 _ S i system at 2.0 MeV H + , sample no. 92, i n i t i a l aluminum thickness -450 A. 6 136 v i i i s 1 LIST OF TABLES Page I Comparison of reflectance and thickness values at the f i r s t three extrema as c a l c u l a t e d from eqn. 2.4.4 and by the approximation method described i n the text. 1 6 II F i r s t reduction pinhole camera c h a r a c t e r i s t i c s . 37 III S i l i c o n samples c h a r a c t e r i s t i c s . 41 IV Comparison of oxide r e f r a c t i v e index and thickness values as c a l c u l a t e d by the r e f l e c t a n c e technique and by e l l i p -sometry. 43 Summary of properties of r f plasma-anodized Si02< 74 ix ACKNOWLEDGEMENT During the course of this work the author became indebted to many individuals who provided helpful discussions, equipment or tech-nical help. I take this opportunity to express my gratitude to every-body who directly or indirectly contributed to this work. It i s a particular pleasure to acknowledge my supervisor Dr. D.L. Pulfrey for his continuous stimulating support and encouragement, and Dr. L. Young for his interest and many constructive suggestions. I wish especially to thank my wife for her assistance in many ways, including financial support during the past years. The financial support of the National Research Council of Canada is gratefully acknowledged. x 1 I. INTRODUCTION The, process of gaseous plasma anodization, which essentially consists of the growth of a thin film over a metal or semi-conductor by applying a bias between the substrate and a gaseous ionic source, has received considerable interest since Miles and Smith (1-2) f i l e d a US patent in 1963. Plasma anodization offers the potential advantage over many other thin film deposition techniques of being easily inte-grated in the chain of successive vacuum processes used in so l i d state device manufacturing. Its main features have been recently reviewed by several authors (3-5). Dc low pressure discharges have been used in most reported cases of plasma anodization but induced - r f , arc and microwave dis-charges have also been used and present certain practical advantages over dc plasmas e.g. higher thin film growth rates, possibly due to a larger concentration of some active oxygen ion species and, in the case of high frequency discharges, an elimination of the poss i b i l i t y of contamination of the sample from the electrodes sustaining the discharge. Despite these advantages there i s l i t t l e reported work on the use of high frequency discharges for plasma anodization (6-11). A program to study the plasma anodization of s i l i c o n in an r f (-1.0 MHz) electrodeless discharge (for details on the physics and h i s t o r i c a l reports of such a discharge see refs. 12-16) was started in this laboratory in 1969 and the progress made to early 1972 i s catalogued in refs. (10-11, 17-18). The work in this thesis is concerned with two main points: (i) the evaluation of the properties of plasma-grown Si02 films on Si and ( i i ) the investigation of the anodization of aluminum films 2 deposited on s i l i c o n . The former study was meant to ascertain whether plasma-grown SiO^ films offer any advantage over thermally-grown SiC^ films, which are almost exclusively used in present-day solid state device technology. The latter study was initia t e d to determine the fea s i b i l i t y of preparing relatively novel solid state devices (e.g. Schottky barrier photodiodes and double insulating layer memory devices) using plasma anodization for the insulating film processing steps. The results described i n this thesis indicate that (i) s i l i c o n dioxide films of quality suitable for MOS technology can be reproducibly grown in lengths of time that are practical for industrial manufacturing and ( i i ) novel large-area aluminum-silicon photodiodes with wide spec-t r a l response and aluminum oxide passivation can be produced. In carrying out the work described in this thesis i t was found necessary to construct equipment to enable accurate in - s i t u monitoring of the growth of thin films. This in turn required a knowledge of the theory of thin film optics and aspects relevant to this work are presen-ted in Chapter II. Computer programs used for the theoretical computa-tions are described and a method for determining both the complex index of refraction and the thickness of films from single-angle reflectance measurements i s reported for the f i r s t time. Chapter III i s concerned with the experimental details of the rf plasma anodization process. . The apparatus used or constructed speci-f i c a l l y for the experiments i s f i r s t described. The anodization of si l i c o n i s then reviewed in detail along with a discussion of the c r i t i c a l details necessary to obtain a successful film growth. The e l e c t r i c a l and physical properties of the resulting s i l i c o n dioxide are then studied with comparison being made whenever possible to results obtained with 3 films formed by other methods. Chapter IV details the preparation and properties of aluminum-sil i c o n Schottky photodiodes with plasma-anodized anti-reflection coatings. Simple theoretical models are presented in relation to experi-mental results and some useful information about the effects of plasma anodization on s i l i c o n i s extracted. The last part of the chapter presents some preliminary work on A^O^-Si and A^O^-Sif^-Si systems and attempts to define some of the parameters that need to be carefully controlled i n order to obtain consistently successful device fabrication. 4 II. THIN FILM OPTICS 2.1 Introduction In order to s u c c e s s f u l l y manufacture s i n g l e or m u l t i l a y e r devices i n a s i n g l e anodization i t i s imperative to obtain continuous information about the thickness of the growing f i l m . O p t i c a l measure-ments are s u i t a b l e since they can be performed without d i s t u r b i n g the anodization system. Automatic ellipsometry i s often used for t h i s pur-pose however the data a c q u i s i t i o n system, i . e . computer, attendant hardware and software and i n t e r p r e t a t i o n of the data, represents a considerable investment s u i t e d to research but questionable i n a p r a c t i c a l l y oriented environment. Reflectance measurements can be a s u i t a b l e a l t e r n a t i v e i n some circumstances (19) provided that the data a c q u i s i t i o n system i s automated to obtain continuous recording. This l a t t e r point i s es-p e c i a l l y important i f fast-occuring phenomena are to be observed and c o n t r o l l e d . 2.2 Reflectance and Transmittance of an Assembly of Thin Films The amplitude and phase of a beam of l i g h t r e f l e c t e d or trans-mitted by a system of t h i n films are determined by s e t t i n g up and s o l v i n g Maxwell's equations with the appropriate boundary conditions. In prac-t i c e the r e s u l t i n g equations are d i f f i c u l t to present c o n c i s e l y and at best d i f f i c u l t to i n t e r p r e t due to the preponderance of complex numbers. In 1937 Rouard (20) derived recursive equations by computing an equivalent r e f l e c t i o n c o e f f i c i e n t and equivalent phase change f o r a composite s t r u c -ture of the substrate and the f i l m next to it,then,working through to the top of the stack by successively adding one l a y e r . The scheme was fur t h e r r e f i n e d by Abeles (21) who introduced a compact matrix notation: Y = rSl cos <$ i s i n <5 /n r r i n s i n 6 cos 6 r r r 'n+l where: Y i s the o p t i c a l admittance of the f i l m assembly n i s the number of films i n the assembly 27i N d cos <j> r r r (2.2.1) i s the phase change i n the r t h f i l m n = N cos i> for s - l i g h t r r T r 6 N COS <j> f o r p - l i g h t <j>o i s the angle of incidence of the f i l m assembly and <j>r i s found by applying Snell's Law: N s i n d> = N s i n <j> o o r r ,d i s ..the thickness of .the .r.th f i l m • . r N i s the complex index of r e f r a c t i o n of the r t h f i l m , N = r r (n - i k ) v r r X i s the wavelength of the i n c i d e n t l i g h t . Some useful points can be derived using the matrix notation: The deter-minant of any number of these matrices i s unity. I f the phase change i n a f i l m i s 5 = n ^ n = 0, 2, 4, 6... .*. cos 6 = +1, s i n 6 = 0 then the c h a r a c t e r i s t i c matrix of t h i s f i l m becomes 1 0 0 1 which i s the unity matrix; consequently t h i s p a r t i c u l a r f i l m has no e f f e c t on the o p t i c a l admittance of the stack i . e . i t can be considered as being absent. The r e f r a c t i v e index N of the f i l m i s non-absorbing 6 (N = n a real number) since 6 must be real in order to obtain cos 5 = 1 , r r sin 6 = 0 . If 6 = n y n = 1,3,5,7... cos. 6 = 0, sin 6 = + 1 the matrix i s : 0 i/n " + i / n r o the admittance reaches a maximum and again the film must be non absorbing i n order to obtain this matrix. The amplitude of the reflected beam at the interface of a medium with admittance n Q and an assembly of admittance Y i s : *o " Y p = —rr o ,and the .reflectance, a measurable ^ quantity defined as the ratio of the input power to the power reflected at the interface of the film assembly i s : * R = p p where the asterisk indicates the complex conjugate. It follows that the reflectance of an assembly of films i s periodic i n nature, providing the absorption is not too large, due to the periodic solution for the optical admittance. It can also be shown that the transmittance, defined as the ratio of input to transmitted power of a stack is independent of the direction of propagation (front or back illumination) but this i s not true for the reflectance. 2.3 Program for Reflectance and Transmittance Computation The Rouard method was used to generate a computer program. We shall note that because matrix multiplication i s non-commutative the 7 2.1 Generalized system of s t r a t i f i e d thin films 8 major difference in Rouard's method and the matrix method resides in notation. The amount of computation performed is similar in both cases. An incidental advantage of Rouard's method comes from the manipulation of the equations which may yield more insight into the optical properties of an assembly of thin films. A generalized system of films is shown in figure (2.1). The films are assumed homogeneous. The following parameters must be known in order to carry out the computation: k = Number of films over the substrate. X = Wavelength of the incident monochromatic light.. <|> = Angle of incidence of the l i g h t w.r.t. the normal of the film assembly. n = Index of refraction of the medium, m n^ = "n^-ik^' - "index of refraction of "the kth film. n = n -ik = index of refraction of the substrate, s s s cl^ = thickness of the kth film. The complex angle at the kth interface (this angle is the angle of re-fraction only i f i t i s real) is computed using Snell's Law: cos <j>, = [1 - (=^) 2 s i n 2 * ] 1 / 2 (2.3.1) Yk n^ Tm then the change of phase in each film i s : 6k = "T C O S *k "k "*dk • (2.3.2) The program offers the option of working in s or p-light and can compute either the reflection or transmission properties. The Fresnel reflection coefficients at the kth interface are: 9 n. - cos A - n cos * , = / 1 , =£ (s-light) (2.3.4) k n k_ x cos ^  + A cos * k n. - cos $ • - n cos <j> r k = / ^ - (p-light) (2.3.5) K n, , cos <L + n. cos <L " ^ 6 k-1 k k k-1 In the case of transmitted light the Fresnel coefficients are: 2 n, , cos <J> . t, = = !L4 -4-^ — (s-light) (2.3.6) k n ^ cos ^ + n k cos <f>k 2 "k-1 C O S *k-l t == K ^ . - 1 . (p-light) (2.3.7) ^ ?k-l C O S *k + "k C O S + k - l The equivalent Fresnel coefficients at the kth interface, starting at the substrate interface are now computed from: -126, r k - l Pk e k Vl=7~ -126, <2'3'8> 1 + r k - l P k e k i n the reflection case and: t^_ x e " i 6 k - l V l = , + -126, , <2-3'9> 1 + r k - l pk 6 k " 1 in the case of transmitted li g h t . For the f i r s t iteration we evidently have p k = r f c and r k = t f c . The reflectance and transmittance are then respectively obtained from: R = pp (2.3.10) and T = n T T (2.3.11) m although caution must be exercised (22) i n using the latter expression when considering propagation into an absorbing medium since we are dealing 10 with the measurable energy r a t i o s f o r the r e f l e c t a n c e and transmittance and not merely the e l e c t r i c or magnetic vector amplitudes from which we s t a r t e d the above c a l c u l a t i o n s . The program was checked against gross errors by assigning various thicknesses but the same index of r e f r a c t i o n to the l a y e r s (up to 18 i n number) i n s and p - l i g h t . A zero thickness l a y e r with a high r e a l and imaginary part of the r e f r a c t i v e index was then i n s e r t e d at random p o s i t i o n s i n the stack from the top to bottom l a y e r then run as the f i r s t check. The bottom l a y e r , next to the substrate, was assigned the same index of r e f r a c t i o n as the substrate and the program again run as i n the f i r s t t e s t . F i n a l l y t h i s program output was checked against values derived i n c i d e n t a l l y from McCrackin 1s ellipsometry program (23). 2.4 Reflectance at the Surface of an Absorbing F i l m on an Absorbing ..,&ubs»t,r-ate,,(.2:4) In the course of our e a r l y experimental work on anodization of s i l i c o n substrates the recorded r e f l e c t a n c e curves i n d i c a t e d apparently absorbing oxide f i l m s , a f a c t previously overlooked using a manual bridge balancing method to measure the r e f l e c t a n c e of the specimen. If the f i l m and the substrate are allowed to become absorbing the equations are then generalized. A f t e r the a p p l i c a t i o n of S n e l l ' s law <j)^  becomes complex therefore one can write: c o s * k = a k + i \ The F r e s n e l c o e f f i c i e n t i s also a complex number , . . • 19. rk = 8k + 1 \ = Y k e k , 2 2.1/2 ^ . \ where Y k = ( g k + h f c ) , • tan 0fc - — LOG REFLECTANCE CO 3 I H -3 1 O o S c II ro II Pu LO • • *• 00 •I o ON H -03 1 1 r t H" H - H - O O O 3 • • o o O i-ti CO to -e- 9 II I—1 ro OJ • ro oo o ro o >• r t to II n ON ro OJ N> 00 r t > o 3 * r t /—N tr Pi 3 3 H i H -H ' II 0 o r t 3 * n 5" ro CO CO TT 12 When dealing with a single film on a substrate the reflected amplitude is given by: r i + r2 6 1 (2.4.1) where the change of phase <j>^  i s : 6 i = i r v d i c o s * i = ? d i <nriki> ( a i + l b i > AIT then - 2i5- = -(v + iu) where v = — d- (k a -n b ) and x A X JL 1 x X u = *x d i ( n i a i + W This enables us to put the reflected amplitude in the form: i6. , 16. - i u -v Y-, e l + y 9 e 2 e e p = — r^1 rr ^ — (2.4.2) ., , ie. ie„ - i u -v l + Y 1 e l Y 2 e 2 e e thus the reflectance becomes: 2 , 2 -2v , * Y l + Y 2 e + Y R = pp = -± ± -vf i[u-(6 -9 )] -i[u-(6 -6 ) ] ) 1Y2 I e Z X + e Z J - J - . 2 2 -2v , 1 + Y x Y 2 e + Y , Hu-o^e^] - i f u - o ^ e ^ ] ! XY 2 e 1 e + e J (2.4.3) or 2 , 2 -2v ^  „ -v A . Y N + Y , e + 2 Y , Y O e cos $. R = ~ 2 2 -2v ~ ( 2 ' 4 ' 4 ) 1 + Y - L Y 2 e + 2YjY 2 e cos $ 2 where ^ = u - (&2 - 8^, $ 2 = u - (8 2 + 8^ Figure (2.2) shows the computed variations of the reflectance for both a transparent and an absorbing film grown on a si l i c o n substrate, The light i s taken as having the E vector perpendicularly polarized to the plane of incidence ('s' l i g h t ) . J w „ ^»fiirtance difference between consecutive ex-film, JJ ( S I ) = 3 . 8 6 . - iO.017, <(> = 35.8°, X = 6328 A. For transparent films (non-absorbing) the damping terms exp (-v) and exp (-2v) reduce to zero thus the maximum and minimum values of the r e f l e c t i v i t y are independent of the thickness at which they occur. For absorbing thin films of refractive index n^ = n^-ik^ the maximum and minimum values of R w i l l decrease with increasing thickness through the damping terms in equation (2.4.4). In order to find the local maxima and minima of the reflectance with variations of the thickness d^ of the film one could use the deri-vative dR/dd^. Unfortunately due to the complexity of the equation this can only be done with a large computing time penalty. Instead the local maxima and minima are approximated by setting ^ = +1 i.e. u - (e2 - 6 1) = mir , m = 0, +1, +2, ... therefore mif + ,(0 - ,0 ) d n . rv z -\ X (2.4.5) lmax.min 4TT (n^a +k^b ) which gives for these values of d^: (k.a - n b ) . v - [ n n r + ^ - e p ^ + ^ 3 (2.4.6) The r e f l e c t i v i t y R can now be computed for the approximated local minima and maxima. The difference in reflectance AR between consecutive reflectance maxima and minima can be plotted as shown in figure(2.3)for the the case of a tranparent film. Using an experimentally-measured value of AR to compare with figure (2.3) enables the thin film refractive index to be determined and hence, by using this value of n^ i n equation (2.4.4) to generate the complete R versus d^ relation, the film thickness at a l l experimentally known values of reflectance can be obtained. 15 In the case of absorbing films n^ cannot be estimated i n such a simple manner as i t i s not f e a s i b l e to generate a s e r i e s of computed curves for various n^ and u n t i l the correct combination i s found to produce a reflectance v a r i a t i o n with thickness that matches the e x p e r i -mental data. Instead the method used r e l i e s on the fa c t that AR^ i s dependent mainly on and that AR^ i s dependent mainly on k^; where AR^ and hR^ a r e t n e values of the diff e r e n c e i n reflectance between the f i r s t and the second and f i r s t and t h i r d extrema r e s p e c t i v e l y (see fi g u r e 2.2). Figures (2.4) and (2.5) show the v a r i a t i o n of k^ with AR^ and AR^ r e s p e c t i v e l y with n^ taken as a parameter. The value of n^ and the range of n^ used here are intended to r e f e r to a S i C ^ - S i system. To obtain the computed values of AR^ and AR^ the values of d^ obtained from equation (2.4.5) were used. The v a l i d i t y of the approximation was checked by comparison with exact values of R d i r e c t l y from (2.4.4) and i s very good as shown i n table (2.1). The computed data can be p l o t t e d as shown i n f i g u r e (2.6) f o r convenience,then the value of n^ can be estimated i n one step. As the accuracy i n determining the experimental values of AR^ and ^^-p ( n e n c e w i l l be e f f e c t e d by the magnitude of AR.^ and AR^p a p l o t such as fi g u r e (2.7) could be used to optimize the angle of incidence employed. The sharp peak i n the AR^ curve follows from the v a r i a t i o n with 4> of the f i r s t r eflectance minimum; the l a t t e r passes through a minimum, at which the ref l e c t a n c e i s pr a c t i c a l ' l y zero, when the condition Y 1 / Y 2 = e x P (~v) i s s a t i s f i e d . The s e n s i t i v i t y of the. method f o r determining the r e f r a c t i v e index of an absorbing f i l m i s perhaps best i l l u s t r a t e d by reference to a p a r t i c u l a r example. For the case of a S i sample plasma anodized at Sample no. n l k l log f i r s t 3 reflectance extrema o Film thickness A at extrema using approxm. using equation using approxm. using equation (see text) (2.4.4) (see text) (2.4.4) 3 1.424 0.017 -0.375 -0.375 10 0 -1.144 -1.144 1230 1240 -0.420 -6.420 2450 2445 4 1.387 0.034 -0.378 -0.378 30 0 -1.142 -1.144 1290 1310 -0.474 -0.474 2540 2530 5 1.354 0.014 -0.376 -0.376 10 0 -0.974 -0.975 1310 1320 -0.418 -0.418 2600 2595 Table 2.1 Comparison of reflectance and thickness values at the f i r s t three reflectance extrema as calculated from eqn. 2.4.4 and by the approximation method described in the text. 70 20 30 40 50 Kr/10~3 2.5 Computed variation of reflectance difference between f i r s t and third extrema with thin film refractive index. ^ ( S ^ = 3.86 - 10.017, <j) = 35.8°, X = 6328 A. 2.6 Computed chart of AR-^and AR2 ( t h e reflectance difference between f i r s t and second and f i r s t and third extrema respectively) as func-tions of refractive index. n 2(S t) = 3.86 - 10.017, $ = 35.8°, \ = 6328 A. 0 10 30 50 70 90 f/DEGREES 2.7 Computed variation of AR.^  and AR2 with angle of incidence. n 1 « 1.4 - i0.05, n 2(S i) = 3.86 - i0.017, X = 6328. A. 21 75°C the values of AR.^ and-AR were 0.769-and 0.045 r e s p e c t i v e l y . Thus using figure (2.6) or figures (2.4) and (2.5) a value of n^ = 1.424 -i 0.017 i s i n d i c a t e d . The s e n s i t i v i t y to the .001 l e v e l i n both n^ and i s r e a d i l y a t t a i n a b l e . A f t e r e s t a b l i s h i n g the value of n^ equation (2.4.4) can be used to generate the dependence of R on f i l m thickness d and hence compare t h i s data with the experimental values of r e f l e c t a n c e to obtain the actual f i l m thickness at various stages of the growth process. I t can be seen from figure (2.2) that the most accurate deter-minations of d w i l l r e s u l t from refl e c t a n c e data on the steep parts of the curve and the l e a s t accurate from the data i n the regions of the ex-trema. The p r a c t i c e used i n t h i s work of taking the r e f l e c t a n c e of the "bare" s i l i c o n as the f i r s t reflectance extremum deserves some comment as, i n r e a l i t y , the substrate w i l l not be i n i t i a l l y f i l m - f r e e . For the case of S102 films on S i the e r r o r involved i n the above p r a c t i c e w i l l only be detectable ( i . e . a f f e c t the r e f l e c t a n c e by > .001) i f the i n i t i a l o o f i l m exceeds 70 A. Even for r e s i d u a l oxide thicknesses of 175 A, the r e f l e c t a n c e i s only changed from the f i l m - f r e e value by .01. 22 ' III. PLASMA ANODIZATION; EXPERIMENTAL WORK 3.1 Introduction Plasma anodization offers the direct realization of a wealth of possible thin film configurations other than the common die l e c t r i c -metal or dielectric-semiconductor configuration. For example a simple useful system can be obtained by anodization of a single thin metal film deposited over a semiconductor. By stopping the anodization at various stages one can obtain the four main useful configurations shown in f i g . (3-D. In (a) the anodization i s stopped before the complete anodization of the metallic film. A metal-semiconductor heterojunction is formed with automatic protection of the device brought by the dielectric encap-sulation. Furthermore the dielectric thin film can be optically matched as.ian anti-reflection ^ coating. i f .an .qp.to-electronic. .device is desired. When the anodization of the metallic film is completed (b), the simple dielectric-semiconductor configuration i s obtained but now the anodic film can be chosen for some desirable characteristic not obtain-able by direct anodization of the semiconductor. Further anodization brings another extremely useful double layer dielectric configuration (c) with applications i n non-volatile memory devices (MNOS, MA0S). In such devices charge tunneling through the thin dielectric II and trap-ping of the charges at the interface of dielectric I and II results in electrically-controllable hysteresis of the MOS structure. The last configuration (d) has direct applications in protection of the dielectric II by the effective sealing afforded by dielectric I. Radiation harden-ing of MOS devices could conceivably be achieved by such a structure. When the possibility of anodizing several deposited layers 23 dielectric metal semi conductor diel ectric semiconductor dielectric I thin dielectric U semiconductor dielectric I thick dielectric U semiconductor Possible configurations obtained by stopping the anodization of single deposited film over a substrate of various stages. 24 over a substrate i s contemplated the array of p o t e n t i a l l y u seful devices becomes extremely broad and t o t a l l y unexplored e s p e c i a l l y i n view of the fa c t that not only d i e l e c t r i c s but semiconducting layers could be obtained as w e l l . However before attempting anodization of m u l t i - l a y e r structures the anodization of a s i n g l e c r y s t a l metal or semiconductor has to be suc c e s f u l l y c o n t r o l l e d with high r e p r o d u c i b i l i t y , high oxide q u a l i t y and over reasonable periods of time. These requirements have never been previously met concurrently" to our knowledge f o r the SiO^-Si structure i n a gaseous plasma anodization system. The anodization of S i was inves-tigated because of i t s extreme importance to the current semiconductor technology due to i t s v i t a l r o l e as a d i f f u s i o n mask, t h i n d i e l e c t r i c or encapsulant. 3.2 Apparatus 3.2a Plasma Anodization Chamber Figure (3.2) shows the general configuration of the anodization chamber which i s a modified version of the chamber used i n previous work (17, 18). It e s s e n t i a l l y consists of a quartz tube 54 mm i n t e r n a l d i a -meter and 70 cm length mounted on A l flanges made s p e c i f i c a l l y f o r quick access to the sample. Two o p t i c a l l y f l a t windows ate a f f i x e d near the sample, at an angle of approximately 36° with respect to the tube a x i s , f o r i n - s i t u monitoring of the f i l m growth. The plasma chamber i s f i t t e d with a l i q u i d nitrogen-cooled sorption pump of 1 m i l l i t o r r nominal base pressure. A leak valve i s used to i n j e c t the discharge gas i n t o the chamber and also allows manual c o n t r o l of the pressure. The plasma d i s -charge i s sustained by a 1 MHz, 12 kW induction-furnace type r f generator. An adjustable coupling network serves to c o n t r o l the power fed to a 8 cm El ectrical Conn ecti on Coolin g Sample Cathode Plasma 3.2 Schematic view of the plasma anodization chamber 26 diameter two-turn c o i l wrapped around the discharge tube. A Tesla c o i l i s used to s t a r t the discharge. 3.2b Sample Holder The sample holder shown i n f i g . 3.3 i s the l a t e s t version i n a succession of holders that have been used during this experiment. The design of the sample holder must meet c o n f l i c t i n g requirements and i s complicated by the h o r i z o n t a l p o s i t i o n of the tube. While holding a sample of reasonable s i z e i t must present a low p r o f i l e to the discharge i . e . not disturb unduly the plasma. The sample bias wiring doubles as a thermocouple to monitor the back face temperature of the sample. A i r or l i q u i d cooling i s provided with quick connectors for easy dismantling. The e l e c t r i c a l contact at the back face of the sample i s e s t a -b l i s h e d through a 0.005" thick d u c t i l e tantalum washer. The tantalum has been gold plated to avoid i t s repeatedly "observed anodization, even though i t i s apparently completely shielded from d i r e c t exposure to the plasma where anodization would seem u n l i k e l y . The outer s h i e l d i s made of 0.005" thick aluminum l i n e d with mica to prevent e l e c t r i c a l contacts through the edges of the sample. Aluminum i s used because i t r a p i d l y coats i t s e l f with an oxide of low s p u t t e r i n g y i e l d thereby preventing contamination of the sample. 3.2c Cathode The p h y s i c a l make-up of the cathode has proved to be a major f a c t o r i n the s u c c e s s f u l anodization of s i l i c o n . A simple 1.5 cm diameter, 10 cm long aluminum rod was used i n the e a r l y part of the experiments. The voltage measurements then taken between the sample and the cathode were quite noisy and sometimes e r r a t i c , a f a c t a t t r i b u t e d to poor coupling between the cathode and the discharge. cooling duct exit, ent ranee stainless steel shield- retainer — W W -seal — aluminum shield • mica lining thermocouple sample tantalum washer quartz tube'' 3.3 Schematic view of the sample holder 28 3.4 Schematic view of the cathode 3.5 Schematic of the sample bias network and c i r c u i t monitoring V 29 The new cathode type is shown in f i g . (3.4). Its shape is designed to i n -crease i t s surface area exposed to the discharge while trapping the bulk of sputtered material in i t s grooves. Again the material is aluminum to minimize sputtering. The cathode must also retain some mechanical ri g i d i t y at the relatively high temperatures to which i t is subjected by the plasma. While the sample is at the edge of the plasma, -the cathode must penetrate into the plasma to present reasonably low impedance to the anodization current and thus can become hot enough to soften the metal. 3.2d Sample Bias Figure 0-5)shows the sample bias network and monitoring of the voltage between cathode and the sample. An rf choke has been placed -in the .cir.cuit,...to^minimize ..the .-rf.-.p.ower..coupled .„to ,the c i r c u i t . V i s measured with a high impedance electrometer (Keithley model 602) backed-off with a stable voltage source (Fluke model 407 DR) to provide over-range of the electrometer. The high impedance of the meter is unnecessary but the low-pass f i l t e r i n g of this particular meter is useful. 3.2e Reflectance Analog Computer (25) In order to monitor and record the r e f l e c t i v i t y of the samples undergoing anodization a small specialized analog computer was b u i l t with cost and simplicity regarded as important design factors while retaining an accuracy better than the 1% necessary to obtain the optical constants of a single thin film within an estimated + 1% accuracy. Fig. (3. 6) shows the experimental arrangement °used in measuring in - s i t u the reflectance of a sample being anodized. The l i g h t source was a 0.5 mW non-polarized He-Ne (A =6328 A) laser and linearly 30 SAMPLE n REFERENCE PHOTO DETECTOR / /XBEAM *SPL/TTER POLAR/ZER LASER REFLECTANCE ANALOG COMPUTER rag n iirrtC—i STRfP REFLECTANCE PHOTO DETECTOR 3.6 Reflectance measurement arrangement 31 polarized light (E vector perpendicular to the plane of incidence) was obtained by rotating the polarizer ('Polaroid sheet 1) until a maximum output was observed on the photodiode detectors. 's' ligh t was employed in this investigation in order to maximize the reflectance at the angle o of incidence (35.8°) used. Narrow band-pass ('Oriel*, 100 A band-pass) f i l t e r s were used in front of each detector to allow measurements to be made with the laboratory well-lighted and the sample immersed in a plasma. The output voltages e^, e.^ from the reference and reflectance photodiode amplifiers respectively are proportional to the intensity of the light incident on the photodiodes; i . e . e, = k.K, P and e„ = k„K_ RP (3.2.1) l l l e 2 2 2 e •whereR i s the samp le-.reflect an ce, P .the ..intensity of the polarized e laser light after passing through the polarizer, the K's are fixed optical constants of the respective optical paths and account for reflections and transmissions at the beam spl i t t e r and quartz windows of the anodi-zation c e l l , the k's are constants for the photodiode plus amplifier units and relate incident light intensity to output voltage. From the equations (3.2.1) we get e k K — = zr~^- R = CR (3.2.2) e l k l K l where C i s termed the optical constant of the system. Thus the ratio of photodiodes' output voltages i s directly proportional to sample reflectance and independant of any changes in laser light intensity. This lat t e r property i s important as the laser light intensity can be expected to vary during the length of time required to 32 c o l l e c t the complete reflectance data. Wr i t i n g (3.2.2) i n logarithmic form, i . e . : log (r^) = log R + l o g C (3.2.3) 1 puts the equation i n a s u i t a b l e form f o r the comparison of t h e o r e t i c a l and p r a c t i c a l r e f l e c t a n c e data as i t obviates the need to know the mag-nitude of C. To obtain a continuous automatic recording of the magnitude e2 of l o g R ( i . e . i n p r a c t i c e l o g ( — ) ) the si g n a l s e^ and e^ are fed i n t o a small analog computer and the output s i g n a l e Q i s p l o t t e d on a s t r i p chart-recorder (Hewlett-Packard model 7100 BM) . E l e c t r o n i c c i r c u i t : F i g . (3.7) shows a block diagram of the reflec t a n c e computer. The voltages generated by the r a d i a t i o n i n c i d e n t on the photodiodes can be characterized by the equations given i n ('3.2.1) where k^ and are given by: k = a Fz ; n = 1, 2 (3.2.4) n n where a i s the jun c t i o n area of the photodiode, F i s the photodiode -2 i r r a d i a t i o n response (measured i n uA/mW^ ' cm ) and z i s the impedance of the feedback loop i n the photodiode a m p l i f i e r . Eqn. (3.2.4) i s only v a l i d when the photocurrent i s much l a r g e r than the thermally-induced leakage current which i s common to any p-n j u n c t i o n (dark cur r e n t ) . In our case -2 -4 the dark current to photocurrent r a t i o v a r i e d from 10 to 10 depending on the sample r e f l e c t a n c e . The output of the logarithmic a m p l i f i e r s i s of the form: e . = TT l o g e, + CT out L ° i n L where the slope of the t r a n s f e r curve T and the a m p l i f i e r constant term 3.7 Block diagram of the reflectance analog computer 34 C T are both l i n e a r l y dependent on temperature. JL The l a s t stage of the system i s simply an i n v e r t i n g a m p l i f i e r serving as a b u f f e r to the chart recorder and also used to obtain an output voltage decreasing with decreasing r e f l e c t a n c e . Thus &q displayed on the chart recorder i s given by: e o = T s l o g (rf) + C g (3.2.5) where C represents the various constants i n the system and T i s given s s by: V T = A. A -~— s 4 3 q where A^ and A^ are the gain factors of the b u f f e r and d i f f e r e n t i a l am-p l i f i e r s r e s p e c t i v e l y , k i s Boltzmann's constant, T i s the absolute B temperature and q the e l e c t r o n i c charge = the term k^T/q a r i s e s from •the -expression «for-.<fehe- •collector" Gurrent^of 'the '."tnans-iS'tors -used inthe feedback loops of the logarithmic a m p l i f i e r s . By comparing (3.2.3) and (3.2.5) i t can be seen that e Q i s d i r e c t l y r e l a t e d to the required form of the sample re f l e c t a n c e , l o g R. A d e t a i l e d schematic of the c i r c u i t i s shown i n f i g . (3.8)• The operational amplifiers used i n the photodiode current to voltage con-verters were chosen f o r t h e i r high gain, t y p i c a l l y 3 x 10^, low noise and low d r i f t . The photodiodes were se l e c t e d for t h e i r low dark currents at the l i g h t l e v e l s of i n t e r e s t . The operational a m p l i f i e r s used i n the logarithmic amplifiers include f i e l d - e f f e c t t r a n s i s t o r i n the input stage to provide the required very low input o f f s e t current. The input r e s i s -tors and feedback t r a n s i s t o r s must be matched to allow e l i m i n a t i o n of the constants C,. and C „ by the d i f f e r e n t i a l a m p l i f i e r . Dual type t r a n s i s -tors are used to maintain the junctions at the same temperature. The 35 r 1Meg -AA /SELECT ) \FOR GAINl OFFSET ADJUST WOK' -AA—jl-10k ' SOpf <100k_ _ j */2-2N2639 f < Suf L -15 v REFLECTED _ J -o € OFFSET ADJUST "luf REFERENCE PHOTO - DIODE AMP LOG AMP 3.8 Circuit diagram of the reflectance analog computer 36 resistors of the operational amplifier must be matched to obtain a good common-mode signal rejection in this stage. Calibration: The system was calibrated by inserting various l i q u i d absorp-tion f i l t e r s in the path of the beam reflected from a sample of fixed optical properties (refractive index and thickness). Solutions to cover the transmittance range from 1 to 100% were prepared from copper sulfate and nickelous fluoborate solutions; each solution was independently calibrated using a CARY 16 spectrophotometer. The variation of the output voltage of the reflectance computer with the intensity of lig h t received at the reflectance photodiode after passing through the various f i l t e r s was such that a straight line drawn through the experimental points had a slope of 2.21V/decade transmittance. The deviation of any "partrciilar po'int Trom'the given straight line never exceeded 0.2% of the reflectance range covered by this instrument. This lat t e r range extends over the two orders of magnitude of reflectance which are of interest in this thesis. 3.2f Photolithographic Equipment Photolithographic techniques (26-29) have been used in'the course of our research to define patterns or masks in thin films or metal f o i l s . Typical commercial equipment had to be avoided in order to keep costs at a very low l e v e l . F i r s t Reduction Pinhole Camera As an alternative to expensive step-and-repeat cameras a pin-hole camera was manufactured in order to generate repetitive patterns necessary to make devices. This often-overlooked technique which was certainly known before i t s report by Ibn al Haitam in the year 1038 (30) i s quite effective despite i t s apparent simplicity. The limitations of the optics have been recently reviewed by Young (31) and applications 37 of pinhole cameras have been described by several authors i n c l u d i n g applications for integrated c i r c u i t manufacture (32). The camera i s schematically shown i n fig.(3.9) and was designed to f i t our requirements. The pinholes were etched i n beryllium-copper . sheet using photoresist techniques. The pinhole s i z e s were c a r e f u l l y matched since they sharply a f f e c t the e f f e c t i v e aperture and therefore the exposure received by each element of the array. The p i c t u r e s were formed on photolithographic glass plates to avoid the complication of a vacuum operated f i l m holder and to f a c i l i t a t e r e g i s t r a t i o n i n multimask systems. The data relevant to the operation of the camera i s shown i n table (3.1). To generate a set of several matching masks, the r e g i s t r a t i o n masks are simply incorporated by taking two photographs i n succession on the same pl a t e : one photograph of the photolithographic mask with "the four corner pinholes *bTo'cked-of f,' the second photograph of the r e g i s t r a t i o n mask with a l l pinholes but the four pinholes at the corners blocked-off. The second reduction was made i n a standard 20" x 24" photo-l i t h o g r a p h i c camera equipped with a high q u a l i t y apochromatic lens. Pinhole diameter . 4mm Pinhole p l a t e thickness .005" E f f e c t i v e aperture f/200 Array s i z e 45 (9x5) Reduction r a t i o 20:1 Photographic Plate Kodalith Ortho type 3, 4"x5", .060" thick Copyboard i l l u m i n a t i o n 250 W. u.v. "Sunlamp", no f i l t e r Copyboard - Lamp distance 18" Camera re s o l u t i o n ( t o t a l reduction 1:200) 30 urn (experimentally determined) Table 3.1 F i r s t reduction pinhole camera c h a r a c t e r i s t i c s . 3.9 Schematic view of f i r s t reduction pinhole camera Si wafer teflon platen screws pulley steel shaft bronze bearing vacuum hose s'prtn-g--ret amer vacuum 3.10 Schematic view of photoresist whirler 4Q Photoresist Whirler In photolithographic work not only the uniformity but the thickness of the photoresist determine the r e s o l u t i o n a t t a i n a b l e . Both must be reasonably w e l l - c o n t r o l l e d even for simple work. A simple w h i r l e r was constructed to hold the sample on a vacuum chuck, f i g . (3.10). The surface of the sample was flooded with ph o t o r e s i s t then the motor was turned on. The l i q u i d r e s i s t i s d i s t r i b u t e d evenly by the c e n t r i -f u g a l forces and the excess of material i s thrown-off the sample edges. The i n i t i a l a c c e l e r a t i o n , the f i n a l speed attained and the v i s c o s i t y of the r e s i s t determine i t s f i n a l thickness (33). The speed of the w h i r l e r was kept at 1250 rpm for mechanical s i m p l i c i t y but t h i s p r e c l u -ded the use of high v i s c o s i t y r e s i s t . Kodak KTFR negative-working r e s i s t was abandonned, due to d i f f i c u l t i e s i n c o n t r o l l i n g accurately the 'viscosi'ty 'by ••"•'d'i'l'ut±cn without' proper ins'trumentat-ion, i n "f avour of GAP M i c r o l i n e PR-102 p o s i t i v e r e s i s t which has a n a t u r a l low v i s c o s i t y . Films of approximately 0.17 um were c o n s i s t e n t l y obtained (n - 1.56, yellow-green interference colour) s l i g h t l y thicker than expected from thickness versus speed curves (34) but e n t i r e l y adequate f o r our work. 3.3 Anodization of S i l i c o n 3.3a Sample Preparation The s i l i c o n samples anodized were secured from the Western D i v i s i o n of Semimetals Inc. and had the c h a r a c t e r i s t i c s l i s t e d i n table (3.2). A l l samples had one face with a mirror f i n i s h , r e s u l t i n g from standard mechanical and chemical p o l i s h i n g treatments. The samples 2 were diamond-cut to f i t the sample holder with approximately 2.0 cm A l exposed f o r anodization. Some of the samples were provided with ohmic contacts on the back of the wafer, Au-Sb (1%) f o r the n-type and A l f o r the p-type. These metal films were vacuum evaporated then heated i n a furnace under a flow of nitrogen gas to the e u t e c t i c point, 560°C f o r the aluminum, 650°C f o r the gold-1% antimony a l l o y . Type Orientation Dopant R e s i s t i v i t y Diameter Thickness P 1-0-0 Boron 3-5ftcm 2" .016"-.018" P 1-1-1 Boron .6-3.5ftcm 1" .013"-.014" n 1-1-1 Phosphorus 3-5ftcm~1 2" .010"-.012" n 1-1-1 Phosphorus . 2-.7ftcm ^ 1" .006"-.0075" Table (3.2) S i l i c o n samples c h a r a c t e r i s t i c s A number of wafers was treated to a two-solution cleaning J:e,chnique (35) .devised <tq, remove ..organic, and .inorganic contaminants. The f i r s t solution,5-1-1 parts by volume H^O - ^2^2 ~ ^ 4 ^ ' removes the organic contaminants attacked by s o l v a t i o n i n the ammonium hydroxide and oxidized by the peroxide. The ammonium hydroxide also forms soluble complexes with some m e t a l l i c contaminants such as Cu, Ag, N i , Co and Cd. The second s o l u t i o n , 6-1-1 parts by volume 1^0 - ^2^2 ~ H < ^ » removes heavy metals and prevents r e p l a t i n g of the formed ions. The water used was d i s t i l l e d and deionized and the other chemicals were 30% u n s t a b i l i z e d . H2O2, 27% NH^OH, 37% HCl commercially-available e l e c t r o n i c grade reagents •Another cleaning technique was also used to remove any s i l i c o n dioxide present by etching i n buffered h y d r o f l u o r i c a c i d . The s o l u t i o n 3 3 (36) was prepared from 300 gm NH^F, 60 cm HF, 450 cm d i s t i l l e d and deionized ^ 0 . As no noticeable e f f e c t of the cleaning technique was recorded on the q u a l i t y of the subsequently-grown anodic oxide, the 42 wafers i n the l a t e r part of the experimental work were anodized as supplied from the manufacturer with no further preparation. Furthermore, some Auger spectroscopy evidence (37-38) has shown that many common cleaning techniques can i n f a c t be contamination sources, i n c l u d i n g the above methods to some extent. 3.3b Anodization Procedure Each run was c a r r i e d out following a routine procedure. The chamber was evacuated to the base pressure of the sorption pump i . e . approximately 1 mtorr, then flushed with oxygen which was l a t e r leaked i n t o the chamber so as to maintain a pressure of 30 mtorr. Small manual corrections could be made during a run whenever necessary. The discharge was then f i r e d and the o p t i c a l instrumentation was checked f o r alignment and p o l a r i z a t i o n of the l a s e r beam. The bias was applied from a constant current source adjusted to the desired l e v e l . With forced a i r cooling the temperature was found to be c o n s i s t e n t l y between 170°C and 210°C -2 depending on the bias current (0.5 to 25 mA cm ). The measured temper-ature i s representative of the back of the sample and a temperature gradient must e x i s t i n s i d e the sample, however the temperature diffe r e n c e can be considered small due to the thickness of the samples (.006" -.018") and the r e l a t i v e l y good thermal conduction of s i l i c o n . 3.3c E a r l y Experiments The oxide film? grown i n the e a r l y part of the experiment were found to be o p t i c a l l y absorbing. The o p t i c a l measurements were c a r r i e d out i n - s i t u using the method described e a r l i e r . As a check on the values of f i l m r e f r a c t i v e index determined by t h i s technique two SiO^ films were subjected to ellipsometry measurements. Readings i n two-zones were taken at an angle of incidence of 66.2° and the appropriate A , $ values 43 for each f i l m were determined. By generating computed A , \p curves i n the thickness region of i n t e r e s t the oxide thickness d and r e f r a c t i v e index n^ could be deduced. The data i s shown i n table (3.3). The discrepancies can be a t t r i b u t e d to the facts that the l a s e r beam used i n the ellipsometer measurements was of a d i f f e r e n t area to that used i n the r e f l e c t a n c e measurements and that some s l i g h t non-uniformity i n thickness i s to be expected. Sample No. 0 Oxide thickness (A) Refractive index from from from from reflectance ellipsometry re f l e c t a n c e ellipsometry n l k l n l k l 2 2965 3005 1.354 0.013 1.356 0.026 4 4000 4035 1.387 0.034 1.385 0.007 Table 3.3 Comparison of oxide r e f r a c t i v e index and thickness values as c a l c u l a t e d by the r e f l e c t a n c e technique and by ellipsometry. 3.3d Later Experimental Growth of SiO^ Good q u a l i t y s i l i c o n dioxide films were c o n s i s t e n t l y obtained a f t e r changing a few parameters i n the system. The sample holder was modified and brought to the form described e a r l i e r . E s s e n t i a l l y .the modifications enabled the anodization of l a r g e r samples and reduced pos s i b l e sputtering from the q u a r t z " s h i e l d by s u b s t i t u t i n g a low p r o f i l e aluminum s h i e l d . The cathode was changed from a p l a i n aluminum rod to the configuration described e a r l i e r . The anodization current was i n c r e a --2 -2 sed from the 0.25 to 2.5 mA cm range to the 5-30 mA cm range. One parameter at a time was changed i n the system i n c l u d i n g the coil-sample and coil-cathode distances. Nevertheless the d e f i n i t e improvement i n 44 oxide q u a l i t y could not be a t t r i b u t e d to any one sing l e f a c t o r although the current density appears to be p a r t i c u l a r l y important. Some of the modifications were made despite observations and conclusions drawn by e a r l i e r workers (39) i n dc discharges; v i z , the oxide thickness uniformity becomes poorer as the sample s i z e increases because of edge e f f e c t s i n c r e a s i n g the plasma perturbation. This does not seem to be the case i n the present system. 3.3e Growth C h a r a c t e r i s t i c s The temperature of the sample was again maintained i n the v i -c i n i t y of 180°C by a i r cooling. The bias current was applied as soon as the previously-mentioned routine checks were completed. The f u l l ano-d i z i n g current was suddenly applied since an increase i n small steps to i t s f i n a l value had no noticeable e f f e c t s on the growth or q u a l i t y of the oxicl'e. "A number of samples were anodized while supplied with ohmic contacts on the back, a few were also cleaned and/or etched, p r i o r to anodization with proper photoresist protection of the ohmic contacts whenever a p p l i c a b l e . Neither lowering of the impedance i n the anodization c i r c u i t , by providing ohmic contacts, nor the removal of the thi n oxide, naturally-grown on s i l i c o n exposed to a i r at room temperature, made any noticeable difference to the q u a l i t y of the f i n a l grown oxide. From observations of s l i g h t r i s e s i n the r e f l e c t i v i t y as the wafers were im-mersed i n the plasma while s t i l l unbiased i t i s be l i e v e d that an etching of. the naturally-grown oxide takes place hence the chemical cleaning procedure immediately p r i o r to anodization appears to be unnecessary. Figure (3.11) shows the voltage across the oxide V versus ox thickness of oxide for one p a r t i c u l a r sample. S i m i l a r p l o t s can be ob-tained f o r any of the 30 samples s u c c e s s f u l l y grown. V Q x i s obtained Sample no. 68 p-type 1-1-1 200 400 60Q 800 S1O2 (Angtroms) 1000 1200 U l 3.11 Voltage across the oxide, V , versus thickness of the oxide. Sam-O X pie no. 68, p-type 1-1-1, n = 1.445, fi n a l oxide thickness = 1225 A, anodization current ^ 12.2mA cm . 46 by subtracting the i n i t i a l voltage from the p o t e n t i a l d i f f e r e n c e recor-ded between the sample and the cathode. The voltage drop across the plasma and across the c i r c u i t resistance i s therefore implied to be constant during the growth at a f i x e d bias current. The thicknesses were obtained by the previously-described o p t i c a l method. Since the slope of a V versus thickness p l o t ( f i g . 3.11) ox i s constant the e l e c t r i c f i e l d i n the oxide must be constant. The f i e l d was computed to l i e between 1.4 and 2.0 mV cm \ depending upon the con-d i t i o n s p r e v a i l i n g during the growth, for a l l the experiments c a r r i e d out. A p l o t of the growth of one f i l m versus time i s shown i n f i g . (3.12). The r e l a t i o n was consistently l i n e a r from sample to sample beyond o o the f i r s t 300 A. Below 300 A the thickness measurements have poor ac-curacy "due "to *the" -broad"maximum "'in"the r e f l e c t i v i t y . ElTipsometric measurements would be required i n t h i s region for accurate measurements. 3.3f E f f e c t s of Current Density on Growth C h a r a c t e r i s t i c s Five n-type, 1-1-1 o r i e n t a t i o n , 3-5ftcm r e s i s t i v i t y samples -2 were successively anodized at 5.5, 11.1, 16.7, 22.2 and 27.8 mA cm r e s p e c t i v e l y . Figure (3.13) shows the voltage across the oxide versus thickness of the oxide f o r a l l f i v e samples. Apparently the f i e l d i n the oxide i s constant with respect to the current density and has a magnitude of 1.87 Mv cm corresponding to a s o - c a l l e d anodization ° -1 constant of 53.4 A V . A p l o t of thickness versus time i s shown i n f i g u r e (3.14). The growth rate increases sharply with the current density. I t must be 0 -1 noted that the f a s t e s t growth rate obtained, .878 A sec , was accompanied o by an e a r l y breakdown of the sample at 1270 A. For comparison purposes micro-Sample no. 88 400 800 1200 Thickness (A) 3.12 Thickness .versus time f o r the growth of a p a r t i c u l a r S i 0 2 f i l m . Sample no. 88, p-type 1-1-1, n = 1.461, f i n a l oxide thickness = o _2 1350 A, anodization current a. 11.1mA cm Si (Angstroms) 3.13 Voltage across the oxide, V , versus thickness'' of the oxides. A l l ox samples n-type 1-1-1, anodization current d e n s i t i t e s = sample no. 101 -2 - 9 -9 = 5.5mA cm , sample no. 97 = ll.lmA cm , sample no. 98 = 16.7mA cm , -2 -2 sample no. 99 = 22.2mA cm , sample no. 100 = 27.8mA cm . 2000 '. 4000 6000 8000 Tims (Sec) 3.14 Thickness versus time for the growth of n-type 1-1-1 samples. Ano-dization current densities: sample no. 101 = 5.5mA cm"2, sample -2 -2 no. 97 = ll.lmA cm , sample no. 98 = 16.7mA cm , sample no. 99 =» -2 -2 22.2mA cm , sample no. 100 = 27.8mA cm . 50 wave plasma anodization (6) has been reported with growth rates up to 1.66 ° -1 A sec (at higher temperature than these experiments) and the f a s t e s t dc plasma growth rate, to our knowledge, has been reported to be appro-° -1 ximately .11 A sec (40) (at lower temperatures). Analysis of the growth dynamics from the data c o l l e c t e d was not attempted owing to the lack of rigorous temperature co n t r o l (e.g. for anodization current d e n s i t i e s -2 -2 of 5.5 mA cm and 27.8 mA cm the sample temperature was estimated as 170°C and 210°C r e s p e c t i v e l y ) . A preliminary study of the growth k i n e t i c s of SIO^ on S i using an r f plasma and much lower anodizing currents than i n t h i s work has been made by P u l f r e y , Hathorn and Young (18). 3.3g Stresses i n S i l i c o n Dioxide Anodic films have been demonstrated to breakdown during growth beyond a c e r t a i n thickness. This ' c r i t i c a l thickness' depends upon the material and the growth conditions. Our experimental evidence points to a breakdown due to large stresses i n the s i l i c o n d i o x i d e . f i l m leading to s t r e s s r e l i e f by p l a s t i c flow followed by an eventual l i f t - o f f of the f i l m from i t s substrate. A current density-thickness product seems to l i m i t the growth, f o r -2 example at low current d e n s i t i e s , approximately 2mA cm , the f i l m can 0 -2 grow beyond 3000 A before breakdown while at 30 mA cm the breakdown w i l l occur around 1100 A. The e l e c t r i c f i e l d i n the oxide has been shown to be independent of current density (not allowing f o r temperature de-pendence on current density) and therefore does not appear to be the prime cause of breakdown i n our system. F i g . (3.15) shows scanning e l e c t r o n microscope micrographs of fi l m s i n the process of breakingdown. Stereoscopic views were taken i n order to ensure that the f i l m was e f f e c t i v e l y buckling up. Compressive 51 3.15 Scanning electron microscope micrographs of damage ln s i l i c o n diox-ide films a-d) Sample no. 34, p-type 1-0-0, n - 1.425, f i n a l oxide thickness ^ 1500 A, current density - 11.1 to 36.1mA cm , damage caused by high current density in latter part of the growth. Sample has been gold decorated for SEM. e-f) Sample no. 82, p-type 1-1-1, 9 -2 n = 1.46, f i n a l oxide thickness 'v- 1900 A, current density • ll.lmAcm damage caused by large thickness. Blisters show black because of secondary electron trapping under Si-0 film: no metallic decoration. 52 stresses are indicated by the micrographs which c l e a r l y show the forma-t i o n of ' b l i s t e r s ' . Two factors suggest that the very high stresses leading to the formation of the ' b l i s t e r s ' are p r e v a i l i n g mainly during the growth: ( i ) when the thickness i s large enough the f i l m breaks down i f the bias current i s switched o f f abruptly and ( i i ) some of the ' b l i s -t e r s ' i n the micrographs have collapsed. A sharp decrease i n the s t r e s s forces could cause shattering of the f i l m i f i t cannot accommodate t h i s change by sudden restructure. The collapse of the ' b l i s t e r s ' i n d i c a t e s that the compressive stresses decreased since t h e i r i n i t i a l formation under b i a s . 3.3h Sputtering During Anodization I t was commented upon e a r l i e r that sputtering of the sample apparently took place before any bias was applied. The r e f l e c t i v i t y i n -v a r i a b l y increased s l i g h t l y a f t e r immersion of the sample f o r a few min-utes i n the plasma but t h i s observation alone hardly constitutes a proof of sputtering since other factors could be involved such as a small change i n the r e f r a c t i v e index of the substrate due to temperature s t a -b i l i z a t i o n . However i f the growth of a sample i s stopped i n the region where changes i n r e f l e c t i v i t y are most s e n s i t i v e to thickness, a slow change of r e f l e c t i v i t y which can be i n t e r p r e t e d as a small decrease i n thickness takes place. Hence i t i s believed that the growth of the f i l m i s a dynamic balance between anodization and mild sputtering. Films grown at low anodic currents, i . e . low growth rat e s , were shown to be of poor q u a l i t y and have a small absorption c o e f f i c i e n t i n the r e f r a c t i v e index. Figure (3-16) shows a f i l m heavily damaged near the edge of the sample where the damage was usually worst. The type of damage i s obviously d i f f e r e n t from the s t r e s s damages shown e a r l i e r . i 53 3.16 Scanning electron microscope micrograph of a SiO^ film damaged by sputtering. Sample no. 4, n-type 1-1-1, n = 1.385 - i0.053, f i n a l oxide thickness - 4060 A, current density = .55mA cm -2 54 Irregular sputtering seems to have taken place leaving an extremely rough surface. The area where o p t i c a l monitoring was c a r r i e d out displayed only few i r r e g u l a r i t i e s , but even a small number of pinholes i n the f i l m exposing the substrate could explain the apparent o p t i c a l absorption over the area sampled by the l a s e r beam. The films d i s p l a y i n g good e l e c t r i c a l c h a r a c t e r i s t i c s were com-p l e t e l y featureless at magnifications as high as 10,000. Hence the sput-t e r i n g action of the plasma may be considered as i n c r e a s i n g only s l i g h t l y , i f at a l l , with increased current densities through the sample w h i l s t the anodization rate shows a strong dependence on current, f i g . (3.14). In the l i g h t of these observations further lengthy work on the dynamics of the f i l m growth seems unavoidable to c l a r i f y the r e s u l t s obtained. S i m i l a r observations have been made by Kraitchman (7) who introduced a constant sputtering rate i n t o h i s t h e o r e t i c a l growth model. Assuming that the growth rate i s large enough compared to the sput-t e r i n g rate, the continuous removal of surface material may be b e n e f i -c i a l by automatic e l i m i n a t i o n of some detrimental p o s i t i v e charges att r a c t e d to the surface. Sodium ions, H + or other p o s i t i v e mobile charges which have been demonstrated (41) to create i n s t a b i l i t y i n ther-mally grown oxides would be displaced to the surface of the f i l m and sputtered o f f . E f f e c t i v e l y no i o n i c i n s t a b i l i t y that could be detected by C-V h y s t e r e s i s has ever been observed i n any of the Si02 films grown i n t h i s system. Sputtering o f f during f i l m deposition has been shown to be b e n e f i c i a l i n another context (42). 3.4 E l e c t r i c a l and P h y s i c a l Properties of RF Plasma Grown Si0„ Test patterns c o n s i s t i n g of an array of aluminum dots were 55 deposited on the samples. The MOS capacitors formed were 0.12 mm radius with centres spaced 0.58 mm on a square matrix y i e l d i n g approximately 400 capacitors per sample giving an ample supply to check on uniformity of the r e s u l t s . Several defects detrimental to device applications can be asso-ciated with an oxide such as high leakage, low p e r m i t t i v i t y , surface sta t e s , f i x e d charges or p o l a r i z a t i o n . 3.4a C-V Measurements The MOS capacitance measurements r a p i d l y determine the usefulness of an oxide as gate i n s u l a t o r i n MOS t r a n s i s t o r s or charge-coupled devices. The defects i n metal-insulator-semiconductor systems have been extensively reviewed (43-45) and we s h a l l look only b r i e f l y at the main e f f e c t s . A capacitance versus bias voltage p l o t of a MOS capacitor .readily displays some of the problem areas as shown i n fig u r e (3.17) f o r a p-type semiconductor. Refering to the figure a f i x e d p o s i t i v e charge i n the i n s u l a t o r requires a more negative gate voltage to put the semiconductor surface i n accumulation and s i m i l a r l y a negative charge s h i f t s the curve i n the p o s i t i v e d i r e c t i o n . The surface states are defects l o c a l i z e d near the insulator-semiconductor i n t e r f a c e giving r i s e to l e v e l s i n the semiconductor band gap. The surface states d i s t o r t the C-V curve i n the depletion region and generally decrease i t s slope. The surface states influence the c a r r i e r mobility near the semiconductor .surface, provide recombination and generation centres and are a source of 1/f noise; a l l the above are undesirable factors i n p r a c t i c a l a p p l i c a t i o n s . The p o l a r i z a t i o n e f f e c t i s due to movement of charges. Mobile ions or traps i n the i n s u l a t o r can create hysteresis of the C-V curve f a t a l to the s t a b i l i t y of a device under b i a s . 56 i Wo JJ / \ „ \ a + ve charge _ J i \ \ -ve charge \ » accumulation V •*• depletion -*{ invertion-*-y v 3.17 E f f e c t s of oxide defects on C-V curve f o r a p-type semiconductor a) s h i f t of the curve due to f i x e d charges b) d i s t o r t i o n of the curve due to surface states c) h y s t e r e s i s of the curve due to i o n d r i f t d) h y s t e r e s i s of the curve due to trapping. 57 The as-grown plasma SiC^-Si system displayed a large positive charge shifting the flat-band voltage by as much as 25 volts. However these charges disappeared after annealing at relatively low temperatures and did not seem to be of further consequence. This phenomenon i s pos-sibly due to a build-up of trapped holes generated by the ionization ra-diation of the plasma (18). Ionic or electronic bombardment of the oxide can create the charge build-up. However the charge implanted by ionic bombardment (46) is linear with dose up to a saturation value and linear with thickness of oxide. The annealing-out of this radiation damage re-quires temperatures in excess of 600°C. In the electron bombardment case (47, 48) the charge build-up i s non-linear with either fluence, energy or thickness of oxide and the annealing can be carried out at low temperature (300°C). The non-linearity of the accumulated charge with respect to •"thickness ••'(18)*-^ and*'-l*he»-low-teemperat-uEe-^ nnealdflnig-nit-i'Msed in t-his»work suggest that the positive space charge is due to electron irradiation. With more electrons than holes leaving the oxide, because of the higher mobility-lifetime product of the electrons, a net positive charge is l e f t i n the oxide. The possibility of charge accumulation due to the ul t r a -violet radiation present in the discharge cannot be ruled out (49) since the effects are similar to the electron bombardment however, a p r i o r i , this effect would appear to be secondary. The high frequency capacitance measurements were carried out with the sample in a light-proof, shielded box using a Boonton 71A capa-citance meter having a 1 MHz, 15 mV rms fixed test signal. Fig. (3-18) shows an experimental curve obtained from ap'1-0-0 sample after a 1 hour anneal at 400°C in nitrogen with vacuum-evaporated aluminum counter-electrodes present. Similar curves were obtained by systematic testing 3.18 High-frequency C-V characteristic of rf plasma grown SiO^. Sample no. 36, p-type 1-0-0, n = 1.452, oxide thickness = 1480 k, anodiza-tion current density ^ 15mA cm , annealed at 400°C i n N_ for 1 hour. 59 across the samples in order to estimate the quality of the oxide over the entire anodized surface. Some samples were successfully annealed in a N2~H2 mixture (50) at 400°C. The variation of the flat-band voltage between capacitors on the the same wafer never exceeded .3 volt. Part of the displacement of the flat-band voltage from ideal must be attributed to the effect of the work function of the aluminum counterelectrode (51) and i s of course unrelated to fixed charges possibly present i n the oxide. The relative permittivity of the oxide was computed from the capacitance of the si l i c o n in deep accumulation (~ oxide capacitance) and the area of the aluminum counterelectrode and found to be approximately 4.3. This value compares well to the generally accepted (for the thermally-grown Si0 2) values of 3.84 to 4.4. Using the normalized theoretical minimum capacitance versus .iOxide- .;tehicknessv>eur.ve published by Goetzberger •(52) and -our"experimental values the si l i c o n doping concentration was found unchanged from the dop-ing concentrations before the anodization. Hence no redistribution of impurities nor uncontrolled doping through contamination has taken place, even though handling precautions taken were minimal. An immediate prac-t i c a l application follows in the determination of doping profiles by an anodic sectionning technique without running the risk of contamination brought by the wet anodization process normally used (53). The low-frequency response of the MOS capacitors was obtained by measurement of the quasi-static current which is directly proportional to the low-frequency capacitance (54). The basic c i r c u i t i s shown i n f i g . (3-19) and i s essentially an analog differentiator with the transfer function: V o(t) = - RC(t) V V N A R 3.19 Schematic diagram of MOS capacitor measurements by the quasistatic method. C = MOS capacitor under test. 61 Since V(t) i s a l i n e a r ramp the output i s d i r e c t l y p r o p o r t i o n a l to the capacitance. The instrumentation made for t h i s purpose i s shown i n f i g . (3-20). Detailed measurement procedure and surface state data e x t r a c t i o n have been published by several authors (55-56) . Figure (3-21) shows a q u a s i s t a t i c curve along with a high f r e -quency curve obtained from a n-type 1-1-1, 3.5 fi. cm sample annealed f o r 15 minutes i n dry ^ at 450°C. The surface state density d i s t r i b u t i o n across the s i l i c o n band-gap was computed from f i g u r e (3-21), using the procedure outlined by Kuhn (54) and a computer program k i n d l y supplied by Dr. C.A.T. Salama. The r e s u l t s are shown i n f i g . (3-22) and i n d i c a t e -11 2 a mid-gap surface state density of 5 x 10 states/cm -eV. A thermally-grown Si02 sample (using the same substrate material as f o r the plasma-grown fi l m ) was supplied by Bell-Northern'Laboratories and, f o r the same annealing treatment as above, y i e l d e d a mid-gap surface state density a f a c t o r of 10 l e s s than the plasma-grown f i l m . This probably i n d i c a t e s that the optimum annealing treatment for the plasma-grown fi l m s was not used. Ligenza and Kuhn ( 4) reported surface state d e n s i t i e s of 1-3 x lCT"* states/cm^-eV f o r dc arc-grown S1O2 f i l m s annealed i n at 350°C, 10 2 but the surface state density could be reduced to below 10 states/cm -eV by a 30 minute treatment i n at 1000°C. No such high temperature anneals were performed i n t h i s work although some improvement on the a l -ready-acceptable surface state density could be expected. 3.4b Breakdown F i e l d Strength The breakdown f i e l d strength was computed from the mean voltage required for catastrophic breakdown of approximately one hundred MOS ca-p a c i t o r s driven i n t o accumulation. Four d i f f e r e n t s i l i c o n dioxide samples ( RAMP " GENERA TOR) 0 CURRENT SOURCE INTEGRATOR DIFFERENTIATOR 3.20 Circuit diagram of the instrumentation used in measurements by the quasistatic method. O N u> Bias Voltage (V) 3 .21 C - V characteristic of rf plasma grown SiO„ obtained by the quasi-static method. Sample no. 66, n-type 1-1-1, n = 1.45, oxide thick-ness = 1060 A, anodization current density ^ 12.5mA cm , annealed at 450°C in N 0 for 15 min. 65 in the 1000 to 1200 angstrons thickness range were used. The average value found was 8.85 MV-cm with a .85 MV cm variance. Thermally grown oxides are reported to have a breakdown strength of approximately 6 MV cm - 1 (44). 3.4c Insulating Properties MOS capacitors with guard rings as shown in f i g . (3-23) were prepared by photolithographic etching techniques. The guard ring was maintained at the same potential as that of the capacitor as shown in f i g . (3-24) to avoid surface leakage currents. The bulk leakage current was measured with a Keithley model 602 electrometer. From the measured cur-rent the room temperature r e s i s t i v i t y of the oxide was found to be approx-16 ° imately 1.4 x 10 ftcm for samples in the 1000 to 2000 A thickness range. This value is comparable to the r e s i s t i v i t y of thermally grown oxides (-44). 3.4d Index of Refraction During the routine growth experiments the measured index of refraction always f e l l between the limits 1.455 and 1.465. The refrac-tive index generally reported for thermal oxides i s 1.45. to 1.47. From a l l the samples grown under various conditions i t was found that the refractive index of s i l i c o n dioxide i s somewhat related to the quality of the oxide; usually the lower the refractive index, the poorer the oxide. A small absorbing part appeared when the oxide was damaged as shown in section (3.3c). Similar observations have been made for related glass films (57-58). The reproducibility of the refractive index in routine growth is important since i t enables accurate determination of the thickness of films which have an optical thickness of less than a quarter wavelength, Electrometer 3.23 Schematic diagram of MOS capacitor leakage current measurement with guard-ring. MOS capacitor - array with guard-rings a) Array as produced by f i r s t reduction camera b) Test array after second reduction (negative). 68 i.e. i t obviates the necessity to grow transparent films to the f i r s t reflectance minima in order to compute refractive index and thickness. 3.4e Etching Properties Some anodic oxides have been reported to have poor etch-ing characteristics (57 and 59). A few samples were etched with a fine pattern and others used as guard rings for Schottky diodes. The etchant 3 was a standard buffered HF solution consisting of 300 gm NH^F, 60 cm 3 concentrated HF and 450 cm deionized ^ 0 . No adhesion problems were encountered and the etching character-i s t i c s appear good. Figure (3-25) shows a scanning electron microscope of a line cut in the oxide by the usual photolithographic techniques. 3.4f Infrared Spectroscopy Infrared spectroscopy can be useful in evaluating s i l i c o n oxides (57-58). In particular, impurities can be detected by their characteris-t i c absorption bands, e.g. absorbed water or hydrogen bonded hydroxyl groups show by absorption in bands near 3650 cm ^ (2.74u) and 3400 cm ^ (2.94u). The position of the Si-0 band near 1090 cm ^ and i t s half-width are strongly influenced by the bonding character, stochiometry, density or porosity of the film. Fig. (3-26) shows a typical spectrum obtained on a Perkin-Elmer _2 700 spectrophotometer. Samples anodized at currents from 5.5 to 27.7 mAcm yielded identical results. The band position at 1075 cm- ^ corresponds to values found by other workers for densified thermal oxides (57-58 and 60)> i t s half-width (85 cm ^) i s larger than for thermally grown oxide (73 cm ^) which may be an indication of strained bonding. For comparison purpose samples prepared by wet anodization (58) showed a shift i n band position (1040 cm ^) and large bandwidth (96 cm "*"). Reactively sputtered Si0„ films 69 3.25 Scanning electron microscope micrograph of etched s i l i c o n dioxide (thickness % 1000 A). No. PK 007-T051 REMARKS = a.a /*. O R I G I N S»lQi. i PURITY ; PHASE. CONCENTRATION. THICKNESS DATE AikL OPERATOR. t> flKaMM «uc SPECTRUM NO. . SAMPLE I * 9 8 S C - S C O - j SAMPLE 2_ 4000 3400 3200 2800 2400 FREQUENCY (CM') 2000 1800 1600 1400 1200 1000 800 650 i - / J / > f 1 ( 1 J. t •s 1 r >• ! < i 0 s. r 1 > 0 -• 1 z < z < 3.26 Typ i c a l i n f r a r e d spectrum of r f piasma-grown s i l i c o n dioxide. 71 or oxides obtained by the CO2 process (58) displayed nearly i d e n t i c a l spectra to the r f plasma anodized s i l i c o n . No absorbed water or other contamination was detected on any of the samples. I t can be concluded that i n f r a r e d spectroscopy of the r f plasma anodized samples revealed no defects or impurities and that the spectra obtained are nearly the same as that of thermally grown ox-ides. 3.4g Nuclear Backscattering Spectrometry To our knowledge the only non-destructive method that can pro-vide element i d e n t i f i c a t i o n as a function of depth i s the nuclear back-s c a t t e r i n g technique (61-62) . In t h i s method a p a r t i c l e a c c e l e r a t o r generates a collimated beam of helium ions i n the 1 to 3 MeV energy range and the target to be analysed i s bombarded i n an evacuated chamber. Some -atoms'of -the^beam <-are-'is'eatfcererl'backhand 'thei»r-'energies are analysed' :by s o l i d - s t a t e detectors. The signals produced have an amplitude p r o p o r t i o n a l to the energy of each backscattered p a r t i c l e . A p r e a m p l i f i e r and a pulse height analyser convert data f o r d i s p l a y , storage or further computer a n a l y s i s . The mass of the constituents, t h e i r depth d i s t r i b u t i o n and the c r y s t a l l i n i t y of the material can be determined. The depth r e s o l u t i o n i s l i m i t e d to 100 angstroms and the mass r e s o l u t i o n ranges from poor to good depending upon the mass of the elements present. Oxide grown from a 'p'-1-1-1 sample was analysed by t h i s technique (*). F i g . (3-27) shows the spectrum obtained. The spectrum has a step due to the s i l i c o n atoms i n the s i l i c o n dioxide layer then the backscat-(*) Spectrum obtained by Dr. M.A. N i c o l e t , C a l i f o r n i a I n s t i t u t e of Tech-nology, Pasadena, C a l i f o r n i a . HWo *> SO 100 150 Channel Number (Energy) 3.27 Nuclear backscattering spectrum for rf p-lasma-grown s i l i c o n dioxide 1 0 at 2.0 MeV 4H + , sample no; 84, p-type 1-1-1, n = 1.46, oxide thick-o e -2 ness = 1235 A, anodization current density = 11.1mA cm 73 tering yield increases due to the contribution of the underlaying s i l i c o n substrate but is shifted to lower energies due to the absorption of the over-lying layer. Because the substrate i s thick, this component of the spec-trum extends down to very low energies. The peak superposed on the s i l -icon spectrum corresponds to the backscattered yield from the oxygen atoms. The front of the oxygen peak is at lower energy than the front of the s i l i c o n step because of the lower mass of the oxygen atom. Since , the thickness of the oxide layer i s known from optical data, a depth scale can be attached to the s i l i c o n and oxygen signals. The two scales are slightly different because the stopping power is energy-dependent and the energy of the outgoing particles depends upon the nature of the scat-tering atom.. The widths labeled HW q and AE reflect the difference i n the value of the backscattering energy-loss parameter [S] and hence depth scale for the -two 'atomic'species. "The 'scattering "yield *R(d) , -at any depth d i n the oxide, is proportional to the local concentration. The concentration at any depth d i s determined through equation (8) of ref. (62 ): N (d) R (E)[S ]a . o N ' o v ' L o s i N .(d) R .(E)[S .]o s i v ' s i v L s i J o w h e r e = [ H W o ] [S g^] j- ^ j assuming a sharp interface between the oxide and the s i l i c o n substrate and homogeneous distribution of the atoms in the oxide the ratio of Rutherford scattering cross-sections a ./a i s ° s i o calculated (62) to be 3.08. The concentration ratio experimentally obtained i s approximately 2.0 indicating that the oxide i s stochiometric Si02 within the errors i n -volved in the process due to the s t a t i s t i c s in the number of counts per 74 channel. For comparison purposes solution-grown anodic oxide (62) was found to have a silicon-oxygen ratio dependent on water content; sput-tered oxide and oxide grown from SiH^ in 0^ atmospheres were found oxygen deficient with an oxygen/silicon ratio of 1.9 to 1.95 while thermally grown si l i c o n dioxide was stochiometric. 3.5 Discussion The characteristics of the rf plasma anodized SiO^ are summar-ised in the following table: Relative permittivity: Breakdown voltage Resistivity Infrared absorption band Stochiometry Index of refraction 4.3 -1 ^ 8.85 MV cm ,~16 > 10 ftcm 1075 cm"1 s i o 2 1.455 - 1.465 Mid-gap surface state density 5 x 10" states/cm - eV Flat-band voltage p-type 'v* - 1.7 volt (Al counter-electrode) n-type ^ - 1.7 volt Table V : Summary of properties of r f plasma anodized SiO, It has been shown that the Si - Si 0 2 system formed by r f plasma anodization can satisfy the high quality requirements needed for success-f u l MOS technology. Some benefits can be derived from this low temperature process such as reducing the stringent environment controls needed to avoid contamination in the currently standard thermal growth of Si 0 2 and avoid-ance of dopant redistribution. The growth rates and reproducibility of the results have been shown to be compatible with industrial manufacturing standards. Furthermore the system can easily be completely automatized 75 at low cost. IV ANODIZATION OF ALUMINUM-COVERED SILICON 4.1 Aluminum-Silicon Schottky Photodiode with Plasma-Anodized Anti-Re-flection Coating 4.1a Sample Preparation Thin films of aluminum were vacuum evaporated from tungsten c o i l filaments onto unheated s i l i c o n substrates at a base pressure of -4 approximately 4 x 10 torr. A shutter was used to avoid contamination while the aluminum was being heated to i t s vaporization temperature. The ° -1 deposition rate was approximately 100 A sec and the mass deposited was controlled by a quartz crystal oscillator used as a microbalance (63). For the 5 MHz AT-cut quartz crystal used the frequency shift-thickness relation was computed from Hartman's data (64). A Sloan angstrometer, *M-100, 'using'Fizeau-'Eitflti-be'amirttef'ferometry was used i n the early part of the experiment to estimate deposited-film thickness but abandoned i n favour of the quartz monitor due to insufficient resolution. The s i l i c o n wafers were subjected to a buffered HF etch immed-iately prior to evaporation then dried by pressurized ^ gas. A Si02 o film approx. 20 A thick, growing spontaneously by exposure to ai r , cannot be avoided by this procedure and, indeed, can only be satisfactorily re-moved by in-situ sputter cleaning. Some wafers were provided with ohmic contacts which were protected by photoresist during the cleaning etch. These ohmic contacts were supplied only for testing convenience after the growth of the oxide and did not appear to influence in any way the sub-sequent anodic film growth. 76 4.1b Film Growth The same routine procedure adopted for anodization of s i l i con was used. The anodization was again monitored opt ica l ly checking the exper-imental data on the chart recorder against theoretical data computed us-ing the thickness of aluminum obtained from the quartz monitor as a start-ing value. A set of typical experimental and theoretical curves i s shown in Figs. (4-1, 4-2). The anodization current was stopped before complete anodization of the deposited metal in order to leave a thin transparent aluminum fi lm which can then form a metal-semi-conductor recti fying bar-r i e r assuming no thin SiG^ i s present. The unavoidable thin SiO^ present before evaporation must be reduced by diffusion into the aluminum in order to form the necessary aluminum-silicon intimate contact. Because essentially no difference was noted between diodes subjected to a 400°C heat treatment ..•for -10.min,.prior -to...anodization, -as is.~done. to .manufacture good aluminum-s i l i con Schottky diodes (65), and diodes made without pre-anodization an-nealing, i t i s suggested that the anodization process provides the neces-sary SiC^ reduction by the aluminum. This phenomena i s not too surprising, even at the low temperatures under consideration in view of the p las t ic flows which are suggested to take place from evidence presented i n section (4.3.2). Photodiodes with and without guard rings are shown schematically i n f i g . (4.3). A l - S i recti fying barriers were found on both p and n type s i l i c o n . From a l i terature search (66-67) only one report of a p-type silicon-aluminum Schottky barrier was found (68) and this i n a photoemissive 2 cathode study. The large area (1.8 cm ) photodiodes formed in this fashion are self-protected by the aluminum oxide against atmospheric degradation without further encapsulation. No change in J-V characteristic f i g . (4.4) has been observed after s ix months exposure to the laboratory atmosphere Aluminum thickness, (Angstroms) A . l Computed v a r i a t i o n of the transmittance and r e f l e c t a n c e of aluminum anodized on a s i l i c o n substrate assuming an i n i t i a l aluminum thickness of A50 A. 78 Sample no. 41 Time (sec) 4.2 Experimental v a r i a t i o n of the r e f l e c t a n c e of aluminum anodized on a s i l i c o n substrate. Sample no. 41, i n i t i a l aluminum thickness = 450 A. 79 ( 3 ) A l 2 ° 3 Si j ( b ) 4.3 "Schematic view of a A £ 2 0 3 - AJl-Si photodiode a) without guard r i n g b) with SiO_ guard r i n g 80 4 . 4 J - V c h a r a c t e r i s t i c o f a A 5 . ? 0 _ - A £ - S i p h o t o d i o d e . S a m p l e n o . 4 1 , p -t y p e 1 - 1 - 1 s i l i c o n , AJt^O^ t h i c k n e s s ~ 5 3 4 A , Al t h i c k n e s s «v 6 5 A , a r b i t r a r y l i g h t i n t e n s i t y i n c r e m e n t s . 81 and a f t e r several immersions of the devices i n l i q u i d nitrogen with the ensuing heavy condensation of atmospheric water vapour while warming up to room temperature. The l a y e r of aluminum oxide can also be designed to modify the s p e c t r a l response of the photodiode as i s shown i n s e c t i o n (4.1e). 4.lc Simple T h e o r e t i c a l Models f o r a Front-Face Illuminated  Schottky B a r r i e r To-date no t h e o r e t i c a l d e r i v a t i o n of the s p e c t r a l response of front-face i l l u m i n a t e d Schottky b a r r i e r s appears to have been done to match s i m i l a r work i n p-n junction s i l i c o n s o l a r c e l l s (69) . In 1959 Gartner derived a model for the c a r r i e r generation i n f r o n t - i l l u m i n a t e d Schottky diodes under bias (70-71) but did not compute the e f f e c t s of the ai r - d e v i c e i n t e r f a c e . Later Schneider did some work towards modeling a ZnS a n t i r e f l e c t i o n coating on a g o l d - s i l i c o n diode (72) . Some i n t e r e s t i n a n t i - r e f l e c t i o n coatings was shown (74) f o r -Au-Cr a l l o y b a r r i e r metal s i l i c o n diodes but no model or relevant data was presented. More work has been done for back-illuminated Schottky b a r r i e r photodiodes (75-77) however t h i s mode of operation r e s t r i c t s the s p e c t r a l response to the ne a r - i n f r a r e d . L i et a l . (73) have recently presented a model i n c l u d i n g the e f f e c t s of the presence of an i n v e r s i o n l a y e r . A decrease of the quantum y i e l d i n the short wavelength response i s pre d i c t e d . 82 C o l l e c t i o n e f f i c i e n c y i n the semi-conductor The device under consideration i s schematically shown i n f i g . (4-5) disregarding the o p t i c a l e f f e c t s of the metal l a y e r , i t s a n t i - r e -f l e c t i o n coating and backcontacts f o r the moment. Thermal generation of c a r r i e r s w i l l be neglected and the bulk material doping w i l l be taken as p-type. The radiometric notation and un i t s adopted follow the IEEE recommendation (78) f o r the In t e r n a t i o n a l System. The photon f l u x <J>S at the s i l i c o n - m e t a l i n t e r f a c e i s assumed normal to the diode surface and to have a known wavelength dependence. For incident photons with energy l a r g e r than the energy gap (hv -• > Eg) the density of photons i n the semiconductor decreases exponentially due to rthe"absorption coe'f'fi'cient 'a. For 'the^monochromatic cond i t i o n the 3 -1 generation of electron-hole p a i r s per cm sec i s therefore: g(x) = <f> ae a x (4.1.1) s Assuming that recombination i s n e g l i g i b l e the current density i n the thi n depletion layer i s : J D R - q / g(x)dx - q * s ( l - e " a W ) (4.1.2) o A c a r r i e r concentration gradient i s provided by the e l e c t r o n -hole p a i r generation end thus the d i f f u s i o n equation f o r the p-type bulk region i s : 83 photo ns/cm^ / sec I depletion 1. p- fype bulk region I region 1 i \ 4 . 5 Metal-semiconductor barrier for collection efficiency model. 84 „ d n (n-n ) , -ax A D — r - - o' + a* e =0 n , 2 Ys dx T n (4.1.3) where D is the electron diffusion coefficient, x i s the electron l i f e -n ' n time and n Q the equilibrium electron density. Under short-circuit con-ditions the boundary conditions are: n = n at x = w and x = d o dn and the diffusion current density J,,,, = q D n -:— . J BR. n dx thus (69, 79): x=w JBR = q*s ae -aw a + (1/L ) n J 1 -. -d/L -adN  (e n - e ) L (a - 1/L ) sinh (d/L ) n n n (4.1.4) 1/2 where L = (D x ) is the diffusion length of minority carriers in the n n n bulk region and D r = un(KT/q) from Einstein's relationship between mobility and diffusion constants. If d >> the current density in the bulk region simplifies to: BR H S s ae -aw a + n" (4.1.5) Since the total current density i s : J T " JDR + JBR the simplified case yields: -aw J T " ^ s ' 1 " TT13r] n (4.1.6) It can be seen that with i n f i n i t e lifetime J m = qd> i.e. 100% conversion rs efficiency. 85 When an inversion layer i s present at the i n t e r f a c e between the metal and the semi-conductor because the b a r r i e r height of the diode exceeds one h a l f of the s i l i c o n forbidden gap, as i s the case here, the quantum y i e l d i s decreased p a r t i c u l a r l y i n the short-wavelength region. According to L i et a l . (73) the quantum y i e l d becomes: aL P a L n f 1 "I J m v q if [ — , n ,_ ] \ -exp (-ax.) + [1 ~ exp (-ax.)] r T H s laL + e/e L i ax. r i J n Where x^ i s the width of the inv e r s i o n layer and e i s the mean e l e c t r i c f i e l d strength within the i n v e r s i o n layer, i s the c r i t i c a l f i e l d , E = KT/qL . c P The f i r s t term of (4.1.7) i s due to the co n t r i b u t i o n from the 'inversion • iayex'-whi'le ' "the' *s'e cond --term '-represents the - c o n t r i b u t i o n - 'from both the depletion layer and- the bulk of the semi-conductor. I f x^ = 0 the equation (4.1.7) reduces to equation (4.1.6). In the case of a l u -minum-silicon Schottky diodes the contribution from the i n v e r s i o n l a y e r accounts to less than 1% of the quantum y i e l d at 400 nm. and decreases sharply as the wavelength increases. Therefore t h i s term can be ignored to give a s i m p l i f i e d expression: -aW J T . - q #8 [ e — i - (4.1.8) n In experimental work i t i s more convenient to measure the mono--2 chromatic power density H(W cm ) instead of the photon f l u x and measure the output current instead of the current density. Thus 86 I = & AH' he -aW •ax. _ e S 1 " 1+aL n. (A.1.9) where A is the junction area, h i s Planck's constant and c i s the velocity of light, (q/hc ^  .8065 \ i m ^ ) . It must be remembered that H1 repre-sents the power reaching the metal-semiconductor junction. The power H is illuminating the front-face of the device and thus: H' = HT, where T is the transmittance of the metal and any optics present. The response to an irradiation of known chromaticity follows by integration of the monochromatic response between the wavelength limits. Since no analytical expression exists for some parameters the response i s computed at various discrete wavelengths. The spectral response gen-erally plotted implies constant power input throughout the spectrum of . •int-eres't. Simple dc ci r c u i t model The J-V characteristic of a Schottky diode can, to a f i r s t order approximation, be obtained from: j = j ( e ^ V / K T - l) (4.1.10) o where J = A * V e " q * / K T (4.1.11) o ** A i s the effective Richardson constant. d> i s the junction barrier height. The c i r c u i t model of the photodiode i s shown i n figure (4-6). The only non-linear element i s the Schottky diode. The 'short-circuit' operation requires a very low external and 87 parasit ic impedance with respect to the diode impedance so that no s ign i -ficant light-generated current flows through the diode. Summing the cur-rents of figure (4-6): I = 1 + I e „ + IT = I [ e _ c l V / K T - l ] + ^ - + IT RSH L p SH L o which can be written as: (4.1.12) + R„ R SH + R s \ , exp( — ) - 1 KT -1 (4.1.13) The load current w i l l be approximately l inear i f the third term is negl igible, i . e . i f I (R^  + R ) << q_ KT thus I L „ K I p (4.1.14) (4.1.15) The 'open-circuit ' operation requires a load and series resist-*., "ance 'm'uCh'a'higher •''than. the• 'shunt-resi-st'ance. •<Under these conditions: V I p - I d + R therefore: SH I p - I o (e - 1) + — SH which can be rearranged as: (4.1.16) v = KT £ , _P q n I o *P *P V i f — » 1 and — » • o o o SH + 1] (4.1.17) then the output voltage V becomes approximately logarithmic with respect to the photocurrent. photo-current 4 . 6 Simple dc equivalent circuit for a Schottky barrier photodiode, R<, «= series resistance, R = load resistance, R c u = shunt resistance. 89 4.1.d Monochromatic Photoresponse Four Schottky diodes with parameters l i s t e d below were tested along with a commercial s i l i c o n PIN photodiode for which a manufacturer' data sheet was available. ** p-type samples no. 40, 41, 49 r e s i s t i v i t y 3-5ftcm orientation 1-0-0 thickness 16-18 mils. (> 400-450u) dopant boron 2 diode area 1.8 cm o Az thickness before anodization no. 40 450A 41 450A 49 425A. From anodization optical monitoring: A £ 2 0 3 thickness no. 40 598A. 41 5341 49 522A o AH thickness after anodization ho.40 20A 41 65A 49 50A ** n-type sample no. 45 r e s i s t i v i t y 3-5 P.cm orientation 1-1-1 thickness 10-12 mils. (> 250-300u) dopant phosphorus 2 diode area 1.8 cm o AZ thickness before anodization 450A 90 From anodization optical monitoring o ^2^2 thinness 540A o A£ thickness after anodization 62A ** Si p-i-n photodiode Hewlett-Packard HP 4220 (from manufacturer's specifications) 2 Irradiance response at 770 nm = 1.0uA./mW/cm typical 2 at 633 nm = .75uA/mW/cm typical -3 -2 sensitive area 2 x 10 cm spectral response f i g . (4-7) Photocurrent versus Irradiance The short-circuit current versus irradiance was measured using a He-Ne laser to avoid d i f f i c u l t i e s in controlling the spectral emittivity of a broadbanded source while varying the power level. Furthermore the optic al- eff ecfes^of .the '"anfei-re-f lection 'coating woul'd create 'non-linearities in the response i f non-monochromatic light was u t i l i s e d . A beam expander was used, to cover the active area of the diode, preceded by a circular linear-wedge f i l t e r to control the power. The diodes were set at several feet from the laser to avoid thermal effects. The power levels were mea-sured with a Jodon 450 B optical power meter; this instrument i s merely a calibrated s i l i c o n solar c e l l . The instrumentation used for the so-called short-circuit current measurement i s shown in f i g . (4.8). Since the diode is directly across the inverting and non-inverting inputs of the operational amplifier, which are at v i r t u a l ground potential, the effective voltage across the diode is limited to the offset voltage of the operational amplifier, i.e. 0.5 mV maximum according to the specification sheet of the particular JFET operational amplifier chosen. The current measured under these conditions is therefore a reasonable approximation to the short-circuit current of the device tested. 91 0 2 04 02 01 --> V -/ / / / \ \ \ -»v \ ELECTRO PHOTON i / \ \ \ \ \ \ \ \ I \ \ i \ \« \» \» /«A/; i t | .... -0.4 06 08 1.0 1.2 WWIWCTH (MICRONS! 4.7 S p e c t r a l response of S i p - i - n photodiode, Hewlett-Packard HP 4220 (from manufacturer's data sheet). 92 Rf switched to change range o - v V V v - o o-\ e 0 u r ~ 2 I R f 4 . 8 Circuit diagram of the instrumentation used in measurements of the 'short-circuit' current of photodiodes operated i n the s o l a r - c e l l mode. Fig. (4-9) shows the photocurrent density versus irradiance curves obtained at room temperature. The nonlinearities induced at high power levels are immediately noticeable, these can be traced to high series resistance in the diodes and can be eliminated by proper design commonly used i n solar c e l l s . The low power level regime can be used for comparison purposes since the curves are approximately linear in this region. The quantum efficiency i s very sensitive to the thickness of the aluminum as 93 expected from i t s transmittan.ee ( f i g . 4.1). Using the thickness of alum-inum computed by matching the experimental and theoretical r e f l e c t i v i t y data one would expect, a p r i o r i , device no. 40 to be the most eff i c i e n t o o since the aluminum is only 20 A, then no. 49 with 47 A. Devices no. 45 o and no, 41 have the thickest aluminum layer, 62 and 65 A respectively and therefore should have the same low response. Figii (4-9) indicates that this was not the case, and a possible explanation i s that films below o 100 A cannot reasonably be expected to behave as thicker films due to their microstructure (80) accompanied by changes in r e s i s t i v i t y and re-fractive index. Furthermore some aggregation of aluminum may have taken place as w i l l be shown in section (4.3a). Therefore the basic as-sumptions of homogeneity of the layers made to compute the theoretical r e f l e c t i v i t y and transmittance from which the thickness was obtained is-pTob-ably no Ionger• • a —va-lid -approximation. Scanning electron microscope micrographs of sample no. 41 under bias revealed no induced current contrast as would be expected i f the current flow was discontinuous over the sample surface but this does not constitute evidence of the continuity of the aluminum film since a depletion region can be formed between the aluminum discontinuities i f the spacing of the aluminum aggregates is close enough to form a natural grating (81). In the continuous areas of the film the sheet resistance can become very large as seems to be the case for no. 40 where nonlinear-i t i e s in the output current occur early. Surface recombination and bulk recombination which have been ignored in the simple model are also probably the source of nonlinearities at high illumination levels due to high carrier injection. The high efficiency of no. 41 at low levels can be attributed 94 to optical matching of the device to a i r by the aluminum oxide f i lm. From the 'knees' in the curve some estimate of the series resistance can be obtained, equation (4.1.12). On'short-circuit ' condition 1^ ^ 0 and as KT/q ^ 26 mV at room temperature, thus samples no. 40, 41 and 49 have series resistance in the order of lOKft, 500ft and 100ft respectively. Open-circuit voltage versus irradiance In f i g . (4-10) the effects of the low shunt resistance are part icularly obvious on devices no. 45 and 49. The maximum voltage obtainable from Schottky photodiodes i s l imited by the barr ier potentia l ; however, as for the p-n junction this value cannot be attained in prac-tice (82). The saturated photovoltage for device no. 41 was 285 mV. High shunt resistances are part icularly desirable in solar c e l l applica-tions.since only the maximum power output i s of interest . This can be obtained by proper design. •> 4.1e Spectral Response  Experimental The short-circuit current was obtained as a function of wave-length. These measurements required cal ibration of the spectral output of a monochromator. The monochromator had the following characterist ics : Make: Baush and Lomb, 'high-intensity' model entrance s l i t width 2.78 mm exit s l i t width 1.56 mm source tungsten (quartz-iodine) Vi s ib le spectrum (400-700 nm) grating 1200 grooves per mm 95 • " * .1 /. 10 Irradia nee (mw/cm<) 4.9 PhotocurrenJ: density versus irradiance at room temperature. « 6328 A. 96 4.10 Open-circuit voltage versus irradiance at room temperature. = 6328 A. 97 linear dispersion 7.4 nm/mm resultant bandpass ^ 11.5 nm f i l t e r Corning glass CS 3-74 (rejects most UV har-monics) Infrared spectrum grating 675 grooves per mm linear dispersion 12.8 nm/mm resultant bandpass 20 nm f i l t e r : 700 - 1300 nm C o r n i n g g l a s s n o . 9873 , C S 7 - 6 4 (rejects harmonics in v i s i b l e and U.V) 1200 - 1600 nm Corning glass no. 2540 , CS 7-56 (rejects harmonics below 900 nm) The experimental set-up i s shown in f i g . (4-11). A small synchronous mo-tor with suitable gear ratio was installed to drive the monochromator shaft at 1/2 rph. A silver-bismuth thermopile (Eppley no. 10657) with 2 -2 a calibrated emf of 55.5 nV/uW/cm at 84.3uW cm , according to the man-ufacturer, was used as detector. A lock-in amplifier with appropriate sensitivity (Princeton Applied Research model HR-8) was used to detect the thermopile signal buried in e l e c t r i c a l and optical noise. The synchron-ization signal was supplied by a photodiode and a 2 2/3 rph light chopper. Some of the d i f f i c u l t i e s associated with these measurements and attribut-able to the necessity ior f l a t response and very broadbanded detectors have been assessed in the literature (83). The calibration curves obtained are shown in figs. (4-12, 4-13, 4-l4). The photodiodes were then substituted for,the thermopile and Figs. (4-15 to 4-19) shows the spectral response of the photodiodes obtained Quartz-Iodine Source Filter Chopper signal Chart Recorder #»»« Lock-in Amp Thermopil e kg-.! Monochromator re/. Amp + Bias Photodiode 4.11 Block diagram of the experimental set-up to calibrate the spectral output of the monochromator. 4.12 Monochromator calibration curve, v i s i b l e spectrum (400 - 700 nm), ; quartz-iodine source, f i l t e r : c o r n i n g cs 3-74. 800 900 1000 1100 Wavelength (nm) 4.13 Monochromator calibration curve, near-infrared (700 nm - 1300 quartz-iodine source, f i l t e r : Corning cs 7-64. 1200 1300 UOO 1500 1600 Wavelength (nm) 4.14 Monochromator calibration curvfe, infrared (1200 nm - 1600 nm) , quartz-iodine source, f i l t e r : Cornirig cs 7-56. 102 Wavelength (nm) 4.15 Experimental spectral response Si p-i-n photodiode Hewlett-Packard HP 4220. 103 400 600 800 1000 1200 Wavelength (nm) 4 .16 Experimental spectral response photodiode no. 4 0 . 104 1 * • « • -400 600 800 1000 120C Wavelength (nm ) 4.17 Experimental spectral response photodiode no. 41. 105 106 107 from the recordings of the photodiode outputs and the s p e c t r a l c a l i b r a -t i o n of the monochromator. The photoresponse i n the i n f r a r e d was used to measure the bar-r i e r height (84) using Fowler's theory (85). At room temperature the e f f e c t i v e aluminum-silicon b a r r i e r height was found to be approximately .92 eV for n-type s i l i c o n and .98 eV f o r p-type s i l i c o n , f i g . (4.20). This compares reasonably w e l l with the figures of .83 + .02 eV (86) for A l on n-type S i and .92 eV for A l on p-type S i (68) since b a r r i e r heights quoted i n the l i t e r a t u r e are somewhat dependant upon the preparation tech-nique of the metal-semiconductor j u n c t i o n . T h e o r e t i c a l Spectral Response The t h e o r e t i c a l s p e c t r a l response was computed using equation (4.1.9) derived f o r the simple model. The transmittance was obtained with the computer ..program .described previously i n sec t i o n (2-3). The values f o r the indices of r e f r a c t i o n were derived with the help of pub-l i s h e d t h i n f i l m data. The r e f r a c t i v e index of aluminum (87) v a r i a t i o n with wavelength i s shown i n f i g . (4-21). Figure (4-22) shows the values f o r aluminum oxide from Hass (88) and our values modified on the basi s of e l l i p s o m e t r i c measurements c a r r i e d out on our f i l m s . The r e f r a c t i v e index of s i l i c o n (89) i s shown i n f i g . (4-23). Since t h i n films can change r e f r a c t i v e indices with many v a r i a b l e s such as thickness and the conditions and mode of deposition only i n d i c a t i v e values of transmittance can be obtained i n th i s manner. The absorption c o e f f i c i e n t i s r e l a t e d to the e x t i n c t i o n c o e f f i c i e n t of the index of r e f r a c t i o n (imaginary p a r t ) , i t s values f o r s i l i c o n were obtained from P h i l i p p (90). o Figure (4-24) shows the computed reflectance of 50 A aluminum o on a s i l i c o n substrate along with the reflectance of 50 A aluminum on 108 Energy per incident photon ( Ev) 4.20 Fowler's p lot : square root of the photoresponse per incident photon versus photo energy for n-type aluminum s i l i c o n diode no. 45 and,for p-type aluminum s i l i con diodes no. 40, no. 41 and no. 49. 4.21 Variation of refractive index of aluminum with wavelength (from ref. 87). 4.22 Variation of refractive index of aluminum oxide with wavelength ( ref. 88 and text). 112 I I 1 l I 400 600 600 1000 1200 Wavelength (nm) 4.24 Reflectance and transmittance at aluminum-silicon interface a) 50 A aluminum on s i l i c o n b) 556 A of aluminum oxide and 50 A of aluminum on s i l i c o n . 114 400 600 600 WOO 1200 Wavelengt h (nm) o 4.26 Spectral response as a function of minority carr ier l i fe t ime. 556 A Al-0_ , 50 A A l , p-type, 5ft-cm S i . 115 .31 , ' \s' ( b) « 6 o 2 b /( a) r / i/ w V * w •« 400 600 800 1000 Wavelength (nm) 1200 4.27 Effect of A^O., anti-reflection coating on theoretical spectral response a) 50 A A l , p-type 5 fi-cm Si b ) 556 A A1 20 3 > 50 A A l , p-type 5 ft-cm S i . 116 117 s i l i c o n with a 556 A A^O^ a n t i - r e f l e c t i o n coating r e s u l t i n g from anodi-o zing a 450 A aluminum l a y e r . The transmittance at the aluminum-silicon i n t e r f a c e computed from the same parameters exhibits from 90% transmittance increase i n the short-wavelength region down to 22% i n the i n f r a r e d region due to the A^O^ a n t i - r e f l e c t i o n coating. I t must be noted that the transmittance and other values l a t e r computed using the transmittance as a parameter must be considered u n r e l i a b l e near the o p t i c a l matching wavelength (-630 nm) due to probable breakdown of the equation (2.3.11) as pointed out i n section (2.3). However the reflectance computations, equation (2.3.10), are exact i n a l l cases. Figure (4.25) demonstrates the e f f e c t s of the minority c a r r i e r l i f e t i m e on the t h e o r e t i c a l quantum y i e l d . Low l i f e t i m e reduces the i n -frared quantum y i e l d d r a s t i c a l l y while the shorter wavelength y i e l d i s uneffected. 4.2 Discussion The general shape of the t h e o r e t i c a l curves agrees quite w e l l with the observed curves and explains the broader response i n the i n f r a -red with respect to p-n junctions i n terms of longer l i f e t i m e i n our de-v i c e s . The peak brought by the aluminum oxide l a y e r i s present but some-what wider i n the experimental response probably due to s l i g h t inhomogen-e i t i e s i n the oxide possibly i n the index of r e f r a c t i o n or the thickness or both. The major discrepancy happens i n the blue response which i s ob-served to be poorer than predicted by the model. Attempts were made to include i n the model e f f e c t s of surface recombination and bulk recombination i n the depletion l a y e r since d i s c r e p -118 ancles at short wavelength could imply losses i n photocurrent generated by the shallower penetrating r a d i a t i o n s . E f f e c t i v e l y these refinements i n the model can s l i g h t l y decrease the blue response. A probable cause of discrepancy i s believed to come from the transmittance due to sharp changes i n r e f r a c t i v e index of the aluminum at short wavelengths. This i s not unexpected since i t follows the general trend i n very thin f i l m s . The o p t i c a l model f o r computing the transmittance i s also expected to breakdown for very large absorption c o e f f i c i e n t s i n the r e f r a c t i v e index of the metal as in d i c a t e d i n sec t i o n (2.3) and r e f . (22). Further research could be made i n these areas i f enough i n t e r e s t i n the devices warran-ted i t . A l o s s i n o v e r a l l e f f i c i e n c y i s also apparent but this i s pos-s i b l y due to the p a r a s i t i c resistances present i n the experimental devices since no attempt was made to optimize the c e l l s i n these areas. An area of concern i n ap p l i c a t i o n s of s o l a r c e l l s and photo-detectors i s the ra p i d and pronounced d e t e r i o r a t i o n of standard p-n junc-t i o n devices exposed to r a d i a t i o n s . Reduction of l i f e t i m e due to the creat i o n of recombination centers decreases the response i n the i n f r a r e d , therefore decreases the o v e r a l l conversion e f f i c i e n c y (69) of any s o l a r c e l l . Because the l i f e t i m e i s estimated from the s p e c t r a l response to be i n the v i c i n i t y of 10u sec i n our devices we must conclude that the plasma anodization process does not appear to have detrimental e f f e c t s on l i f e -time. This may be due to low r a d i a t i o n fluence or to r a d i a t i o n hardening < a t r i b u t a b l e to the A^O^ (91-92) . Some research i n t h i s area must be under-taken due to i t s p r a c t i c a l i m p l i c a t i o n s . Although i t appears that the power output of the Schottky-bar-r i e r photodiodes cannot compete with the current p-n j u n c t i o n s o l a r c e l l s , 119 the broad spectral response and good potential quantum efficiency can be of interest in other applications such as photo-detection. The aluminum oxide thin film not only provides an effective physical protection to the diode but enables shifting of the response merely by changing the i n i t i a l aluminum thickness before anodization. This can be used to improve the quantum efficiency in a particular region of the spectrum. The poten-t i a l radiation-hardening effect of the A l ^ could be of much practical interest for special environments. The non-linearities observed i n the irradiance tests of the diodes can be eliminated by proper current collection grid design on the front face, by deposition of the aluminum film on s i l i c o n with an epitaxial layer of proper doping density on low r e s i s t i v i t y bulk and by providing a low r e s i s t i v i t y ohmic contact on the back of the wafer. A l l these tech-niques are standard in solar c e l l or Schottky diode manufacturing and should not present major d i f f i c u l t i e s in implementation. 4.3 Preliminary Work on Afl^O^ - Si and Al,,,0^  - SiO,, - Si Systems  4.3a Introduction Aluminum oxide as an insulator or passivating layer in semicon-ductor device manufacturing presents attractive characteristics due to a higher dielectric constant (^7.5) than S i 0 2 > greater resistance to radi-ation and the low inherent mobility of some impurities such as Na +. The aluminum oxide-silicon dioxide-silicon system has recently received some attention (93-97) due to i t s applications in MAOS (metal-alumina-oxide-silicon) memory devices. In a l l the reported devices the alumina has been formed by various means after growth of the thin SiO- film. Our work has 120 Scanning electron microscope microscope micrographs of aluminum h i l -locks formation. Sample no. 31, i n i t i a l aluminum thickness =1650 A, anodization current " 16mA cm-^. 121 ( * ) ( b) 20 pm 4 .30 Electron probe microanalysis micrographs of anodized aluminum with hillocks formation. Sample no. 31 a) Backscattered electron image (topography) b) Aluminum X-Ray image c) Oxygen X-Ray image d) S i l -icon X-Ray image. 122 4.31 Micrographs of sample no. 37 a) Scanning electron microscope b) Electron probe microanalysis (1) backscattered electron Image (topography) (11) Aluminum X-ray Image. 123 been orientated toward production of the double insulator layer in a sin-gle anodization run which appears to be the logical solution with the process used. Since no basic difference exists between the production of the aluminum Schottky barrier and the systems now under consideration, aside from stopping the anodization at different points, the sample preparation was the same as reported in section (4.1a). 4.3b Hillocks Formation During Anodization of Aluminum on  Silicon Failure in growing good quality aluminum oxide films was o 4.32 Scanning electron microscope micrograph of 450 A vacuum evaporated aluminum (sample no. 32) before anodization. 124 experienced regardless of the anodization depth at currents beyond ap--2 proximately 10 mA cm . Films grown, from i n i t i a l aluminum thicknesses o over approximately 1000 A were more sensitive to damages. A set of scan-ning electron microscope micrographs obtained from a sample i n i t i a l l y o _2 coated with 1650 A of aluminum and anodized at 16 mA cm i s shown in figure (4-29). In order to determine the nature of the extrusions some electron probe microanalysis (98) was performed on the same sample. The x-ray spectra excited from the sample are shown in f i g . (4-30) for qualitative analysis along with a backscattered electron image to indicate the topography of the area recorded. The four protrusions are indicated as having high aluminum content with l i t t l e or no oxygen or s i l i c o n present. The black horizontal t r a i l s to the right of the pro-trusions on the s i l i c o n recording are the result of shadowing effects „due„,to„the....low.,,angle ,pf.„the x-rays emitted by the s i l i c o n and must be disregarded. The microanalysis combined with the SEM photographs depict clearly the nature and the formation of the hillocks by plastic flow of aluminum. The same tests were carried' out on a sample anodized at the o same current density but starting with only 450 A of aluminum. The ano-dization was carried beyond a minimum in r e f l e c t i v i t y which would i n d i -cate a completion of the anodization of the aluminum and some anodization of the s i l i c o n as shown in f i g . (4-35 assuming homogeneous anodization. Figure (4-31) shows a resulting SEM and a set of electron probe micrographs. The aggregation of aluminum is clearly v i s i b l e , however a careful search had to be made to find extrusions such as the one shown. An aluminum film deposited at the same time as the previous sample was scanned to determine the uniformity of the aluminum deposit and proved to be feature-less, as shown in f i g . (4-32), and of very fine structure. The small 125 visible irregularities are much more closely spaced than the extrusions shown in a wider area of the previous sample ( f i g . 4.31). The aluminum oxide and aluminum were etched off several wafers in boiling phosphoric acid which reportedly grows s i l i c o n oxide on s i l i c o n ° -1 at rates of about 2 A min . Silicon dioxide was invariably found under the aluminum oxide when expected from interpretation of the r e f l e c t i v i t y data; however irregularities and small pits were present. The density of the pits suggest that these were occupied by aluminum lumps etched o away by the phosphoric acid. The thickness of the oxide, up to 600 A from interference colour interpretation, i s much too large to possibly grow irregularly in the acid etch in the short period involved, i.e. ap-proximately 10 minutes. In the thinner films grown, the aggregates of aluminum covered by aluminum oxide were easily v i s i b l e under an optical microscope as a misleading colourful grainy film structure presumably due to interference colours. This grainy structure was also reported by other workers (99) in dc plasma-anodized films when formed at high current densities; how-ever no explanation was offered as to the origin of the phenomenon since i t was not apparent once high current anodization was avoided. 4.3c Interpretation of the Defect Occurence Electromigration has been reported as a source of failure in 6 —2 integrated circuits where high current densities, beyond 10 amp cm , are present (100). However the mass transport i s effected i n the direc-tion of electron flow, and furthermore even i f the majority of current flow in the devices discussed above happened in the hillocks the current density would remain 10"* times too small from an estimate of the hillocks area in f i g . (4.33). Hence electromigration has been ruled out as the 126 4.31 Scanning electron microscope micrograph of sample no. 31 showing hillocks distribution on the sample. 127 mass transport cause. A more probable cause is high compressive stresses in the alum-inum film. A continuous distribution of infinitesimal defects in a thin film can create uniform stresses which have a d r i f t force component per-pendicular to the film whenever a vacancy exists (101) In the case of compressive biaxial stress in a film sandwiched between another film and a substrate the film w i l l attempt to relieve i t s elastic strain in the path of least resistance, i.e. push the covering film upward, f i g . (4-34). Although the covering film is i t s e l f l i k e l y to accomodate some deformation an eventual crack w i l l occur which then leaves a free path for strain re-l i e f by extrusion of the material toward the surface. This is not to imply that internal stresses in the aluminum film, originating in the evaporation process are alone responsible for the plastic flow of material, other factors such as temperature gradients, tensile stresses in the aluminum oxide film and e l e c t r i c a l stresses most certainly contribute toward the correct force senses to obtain mass flows. Nevertheless the formation of hillocks by internal stresses alone has been reported (102)in aluminum films. Since the stresses in thin films appear to be approximately inversely proportional to the grain diameter and that the structure of our films was revealed to be finely grained by the SEM, the internal stresses are l i k e l y to be high although not large enough to create the formation of whiskers without other contributions. As in the case of s i l i c o n dioxide, a current-thickness product relationship appears to exist in relation to stresses in the films. During the anodization, abrupt disturbances in the anodization current while the current i s high or the oxide i s thick, invariably results in disintegration of the films. This suggests that a precarious equilibrium exists between the various 128 4.34 Film on a substrate covered by another film with lower diffusion rate a) biaxial stress forces creating a ve r t i c a l d r i f t force component at a vacancy site b) Mass flow under compressive bi a x i a l stress c) Mass flow toward free surface after rupture of the upper film. 129 s t r a i n forces with collapse ensuing i f a sudden change i s applied. The s t r a i n forces, regardless of t h e i r exact o r i g i n , must be large and pre-v a i l only during the anodization process because no p l a s t i c flow i s ob-served a f t e r anodization, and also attempts to anneal stresses i n the aluminum f i l m before the anodization were i n n e f f e c t i v e i n r e l i e v i n g breakdowns during the growth. The aluminum oxide f i l m i s also l i k e l y to be under t e n s i l e stresses because shattered f i l m s leave very few spots attached to the substrate unlike s i l i c o n dioxide which has 'bub-ble s ' , the s t r a i n r e l i e f devices, bursting while the bulk of the f i l m s t i l l adheres to the substrate. Some s t r e s s a n a l y s i s of dc plasma-grown aluminum oxide was made by M i c h e l e t t i and a l . (59) by x-ray d i f f r a c t i o n and found to be s i m i l a r i n magnitude to AJ^O^ f i l m s deposited by pyrohy-d r o l y s i s of A l C l ^ at 925°C and decomposition of A&-isopropoxide at 500°C. aT-he-^strain •type, ''tensiOre-ror' compressive,>is not exp'TicitTy -reported but the authors mention the f e a s i b i l i t y of large i n t e r n a l forces due to the anodization f i e l d normal to the surface causing contraction i n the f i l m : t h i s suggests t e n s i l e s t r e s s . However we saw that, at l e a s t f o r SiC^, the f i e l d appears to be independent of current while stresses appear strongly dependent on anodizing current f o r both SiC^ and AJ^O^, therefore the e l e c t r i c f i e l d may be a con t r i b u t i n g f a c t o r , but not the sole responsible f a c t o r of high stresses during anodization. 4.3d O p t i c a l Monitoring of the Growth The anodization depth must be c o n t r o l l e d accurately so that anodization may be stopped p r e c i s e l y at the aluminum o x i d e - s i l i c o n i n t e r -face or at any desired s i l i c o n dioxide thickness. Approximately 400 angstroms of aluminum oxide was grown from a sample having an i n i t i a l o aluminum thickness of approximately 1250 A. This ensured that the aluminum 130 remaining on the wafer was vi r t u a l l y opaque to f a c i l i t a t e interpretation of the ellipsometric data from which both the index of refraction and the thickness of the aluminum oxide were obtained. Ellipsometry was preferred over the reflectance method to, compute the index of refraction because the ratio of maximum to minimum reflectance at quarter optical wavelength is very low, hence has poor accuracy, and also to avoid growing thicker films for which homogeneity could be doubtful. The index of refraction was found to be 1.77 as was earlier indicated for the Schottky barrier photodiodes. The aluminum oxide aluminum thickness ratio was assumed to be 1.4 pending the obtaining of a corrected figure once the anodization could be routinely stopped precisely at the aluminum oxide-silicon inter-face and the thicknesses measured by ellipsometry. A small rise in r e f l e c t i v i t y on conversion of a l l the AZ to AWjQ^ J* s "clearly v i s i b l e on "the* theoretical -curve computed i n f i g . (4-35) , This i s typical behaviour of the curves at least in the range of thickness of interest in this thesis. Detection of this small rise in the experi-mental work would accurately locate the aluminum oxide-silicon interface and give good control over the process. Effectively the interface can be easily detected on the chart recorder as shown in f i g . (4-36); however the location of the rise in r e f l e c t i v i t y occurs at higher r e f l e c t i v i t y than expected. The discrepancy originates with the formation of alumin-um hillocks within the sampling area of the laser beam because the re-f l e c t i v i t y remains high over the aluminum lumps. When the anodization i s carried beyond this point the minimum in r e f l e c t i v i t y i s never as low as expected for the same reason and the experimental curve i s distorted by the averaging process, f i g . (4-37). It follows that the optical monitor-ing could act as a valuable tool in assessing in - s i t u the homogeneity of the 200 400 Al?Oa (A) 600 200 400 Si 00 (A ) 4.35a Computed r e f l e c t i v i t y from anodization of aluminum deposited on s i l i c o n , the i n i t i a l aluminum thickness i s a) 450 A .b) 550 A. The s o l i d l i n e corresponds to A l j O ^ - S^Og ~ ^ i s v s t e m . the dotted l i n e to an h y p o t h e t i c a l SiO_ - AI2O3 - S i system. 1 3 2 0. OJ O C "4—• o OJ C D O 0 500 Time (sec ) 4.36 Experimental variation of the reflectance of aluminum anodized on a s i l i c o n substrate - Sample no. 90, i n i t i a l aluminum thickness - 450 A (sputtered^), anodizing current = 8.3 mA cm - 2. * Sputtering carried out by Sloan Instruments, Santa-Barbara, Calif, on our wafers. 133 A.37 A 1 2 0 3 - S i 0 2 134 growth, once the reasons for abnormal optical behaviour have been inter-preted. The r e f l e c t i v i t y data accumulated does not positively confirm that the s i l i c o n dioxide must be formed under the aluminum oxide as found by etching. Although the computed curves, f i g . (4-35), are different, the interpretation of inhomogeneous layers i s ambiguous. It must be noted that the formation of hillocks in preparing aluminum Schottky photodiodes does not present a major obstacle since their net effect i s to reduce the transmittance over only a very small total area. Nevertheless the hillocks disturb the r e f l e c t i v i t y , hence increase the d i f f i c u l t y in reliable optical monitoring of their formation. 4.3e Nuclear Backscattering Spectromety Backscattering spectra were obtained from two samples at d i f -ferent stages of anodization, f i g . (4-38, 4-39). Both samples were ano-dized beyond the interface-reflectivity rise; with sample no. 91 anodi-zation was stopped shortly after the rise and sample no. 92 was anodized further. The interpretation of the spectra is not easy because most of the details are obscured by the resolution of the detector. However i t can be ascertained that more oxygen is present in no. 92 and that the aluminum content has decreased with respect to sample no. 91 since the front peak is lower. These experimental results suggest that anodization of the aluminum hillocks takes place simultaneously to the anodization of si l i c o n and hence would eventually be completely used up i f the anodiza-tion was carried far enough. 4.3f Suggested Strategy for Further Research Most samples grown to date were formed at relatively large cur-rent densities while attempts were made to isolate the causes of discre-pancies between experimental and expected results. However, some encour-n O v. Q. O O 73 1C3 • • . • - • c c u o VO o <« OQ 5 0 7 0 0 Channel Number (Energy) 4.38 Nuclear backscattering spectrum for r f plasma grown AI2O3 - Si0"2 -Si system at 2.0 MeV H + , sample no. 9 l , i n i t i a l aluminum thickness -450 A. 6 Ln VO -t- (-*• C Ln n O CQ >oW cu • rt l-l O S M (tt (U O rt ?T W t o o . (JJ O rt rt K re ro M rc oo ro ro w o (tt rt S i ro Mi P o o H M VO l-h t o — *x3 CO 3 (tt 3 H-rt H-(tt 00 M H. O (tt § I—1 3 I > 3 K> C O a oo rt I 3* H- CO o H« O 3 to ro w I co Backscattering Yield (Counts per Channel) o o a-2» o So "I s — •vi V t ..» 9CT 137 aging results were obtained on a few samples grown at low currents; such samples displayed tractable MOS high frequency CV curves and an indica-tion of the expected MAOS switching behaviour. Unfortunately these sam-ples were destroyed i n attempts to establish a suitable annealing process. Aluminum oxide-silicon systems Have been obtained by several researchers using dc plasmas in an essentially low-current anodization process, there-fore useful AJZ^O-j-Si and A£20 3-Si02-Si systems are thought to be attainable in a single of anodization step i f the formation of hillocks can be pre-vented. Low anodization currents appear to be prerequisite, but other secondary factors may be involved which can only be revealed by further experimentation. The annealing process must also be solved by experiment-ation since no theoretical background i s available in this area. 138 V. CONCLUSION . It has been shown that s i l i c o n dioxide thin films on s i l i c o n suitable for MOS technology can be manufactured by rf plasma anodization. These films have proved to be of quality comparable to the best oxides currently manufactured. The fabrication technique used involves low temperature processing 200°C), resulting in a sharp decrease in the dangers of dopant redistribution and contamination. Furthermore, the method offers the advantage of a vacuum process compatible with other vacuum processing steps such as: sputter etching to clean the wafer, ion implantation to incorporate p-n junctions in a device, reactive sput-tering for insulator or encapsulation formation and metallization for the interconnecting layers needed to complete the devices. We therefore have the potential of MOS device manufacture entirely in a vacuum environment. The plasma anodization of aluminum., deposited .. on silicon„.yielded relatively novel Schottky photodiodes with potentially useful wide spectral response, self-encapsulation and probable radiation protection. Analysis of the spectral response showed that the plasma anodization process had no detrimental effect on the carrier mobility of s i l i c o n . Further research i s needed to solve d i f f i c u l t i e s with plastic flow of thin . aluminum films in order to then yield extremely useful multi-layer devices, such as MAOS memory devices, in a single anodization step. Some research i s also needed in optical modelling of the transmittance of absorbing thin films, a problem which has been, up to now, avoided probably due to lack of practical applications. 139 VI. APPENDIX 6.1 Computer program to obtain the reflectance and transmittance of an assembly of thin films 6.2 Computer program to obtain the reflectance at the maxima and minima in a s ingle-f i lm substrate system 6.3 Computer program to obtain the surface state density using the quasi-stat ic technique 6.1 Computer program to o b t a i n the r e f l e c t a n c e and t r a n s m i t - 140 tance of an assembly of t h i n f i l m s 81187 NULTJL6VER 1 »CBNPILE NOLIST.N.OWARN a ^NTCGEfi-T-I T fc f—f2 * ) - r *» * ' i » i T W J REAL LAYER,0, INC 4 COMPLEX N P , R F L » T R , D E L , R , T , C P H I . * DIMENSION- TAB(20) ,D<20), INC(20HM»-(4»-W)Pt<'21>rWa44^DEl.-M«-MI-U4 6 l ) , T ( 2 l ) , C P H I ( 2 1 ) 7 1 W R I T E ( 6 «2 ) T R AIT — i 6 WgA»<gT -»r^-NO°»0) T I T L E • 9 N R I T E C 6 , 3 ) T I T L E 1 0 W R I T E ( 6 , a ) T R A I T _ 1 4 R C A O < $ . , 5 ) ( . 4 Y £ B 1 8 K o I P I X ( L A Y E R 5 | K K « K * l IS 0 0 6 J u l . K - 4 - 4 U f l ^ W * P ( J > ° 0 , 0 1 I N C ( J ) n 0.0> N F ( J ) o ( 0 . 0 . 0 . 0 ) 1 5 - 6 D E L ( J5B(0.0,0,0) 1 6 00 T J J o l . K K -17 W J J ^ 4 ^ ^ r O 4 + T - W « » { © T 0 T « T 0 - > t R « . - W 4 > < ! ie T C P K I (jj)o(o.o,o,o) 1 9 C A L L M A I N C K , K K , D , I N C , T A B , N P , R , C P M I , T , R f L > T R , O E L ) _M : C O T O 1 -21 2 P O R M A T P l ' . S O A O ) 22 S PORMAT('0<,20A4) 8 J 4 PORMAT(iO',30Afl) -"20 S PCRMAT(FIO.O) 25 9 FORMAT (SOAa) - * 6 W-OONWNtfe : 1  27 8 STOP 28 END - 2 9 8 U B R CH> TIN e -W AI N—< K K , 0 , T C rT A fr, MP, R-rC Pt4 IrrT r* FVrYR-rD E H JO INTEGER S T , C A S E , TAB (K>,DIGIT ( 1 0 ) / ' H r 121 , • 3 L, 1411 • 5 <, 161 , «7 » , • ' • « » I . S l 1801 ,MOO'/,VP(9 ) / t ( lM l,« t I , I F 1 0 , I , » 1 , T •,», •» Si 2 ' F 1 0 | i ; w • SS REAL NM,P I /S .141593 / ,OPTION,0<K) , INC(K) ,LAMBDA 54 COMPLEX N S » N F C K ) » C S Q R T , R ( K K ) , C P H I ( K K ) « T ( K K ) « R F L ( K K ) « T R ( K K ) / D E L C K ) , • -35 1TEMP--36 1 R E A D ( 5 , 1 0 0 ) N L » P H 1 D G , N M , N S , O P T I O N IF ( W L . E Q . O . O ) W L « 6 3 2 6 , 0 -H— IF (NM.C(r r6 - r^v -^Mc- t rO • • 39 K R I T E ( 6 , i 0 1 ) H L » P H I D G , N M , N S 40 R E A D ( 5 , 1 0 2 ) 0 ( 1 ) , I N C ( I ) , N F ( 1 > , 8 T E P 41 — — — - J F - t K -( EQ-» 1) G O - T O - 3 ' 42 0 0 2 H l s 2 , K 43 R E A O C 5 , 1 0 3 ) 0 ( M 1 ) , I N C ( M 1 ) , N P ( M 1 ) - * 4 2 C-ONTINUE 45 3 DO 4 M2ot ,K 46 K R I T E ( » , ! 0 4 ) H 2 , N P ( M 2 } , D ( M 2 > - 4 ? 4 CONTINUE '• : 48 P H I ° P H I D G * P I / i e O , f L A M e O A a 2 , * P I / H L t N M M o N H * N M | S I N 2 « 8 I N ( P H I ) * * 2 49 e M P H I n C 0 S ( P H I ) » 3 T o I F I X ( S T E P » t . ) » C A S E « I F I X ( 0 P T I 0 N * l , ) -50 BO- 5 M3 -H-HS* 51' IP ( M 3 . E Q . K K ) GO TO 55 "52 C P H I ( M 3 ) o C S 0 R T ( 1 . 0 » ( ( N M M » S I N 2 ) / ( N F ( M 3 ) « N F ( M 3 ) ) ) ) - 5 5 GO-T-O-5— : ' : 54 55 ePHI< K K)»eS8RT ( I , 0 « ( ( N M H « 8 I N 2 ) / ( N 8 « N S)l) 55 5 CONTINUE - 5 * : 60-TO—tVrfer? , 6 , 7 , 7 ) , CfrSE-57 6 CALL 9 P 0 L A R ( C A 8 E , K , K K , N M , N F , N 8 , C M P M I , C P K I , R , T ) 58 N R I T E ( 6 , 1 0 5 ) 6 0 - T O - S • 60 7 CALL PPOLAR ( C A 8 E , K , K K , N M , N F , N 8 , C M P H I , C P M I , R , T > 61 N R I T E ( 6 , 1 0 6 ) -62 6 00 9 H f l s l . K — — ; : 63 9 0 £ L ( M a ) c L A M B D A » C P H ! ( N 4 ) * N F ( M 4 ) * D ( H 4 > 64 CALL COEF (K,KK,K,KK , R , T , C A 8 E , 0 E L » R F L . T R ) -65 6 0 - T O -( 1 Ot-I<-rl0 r l 1 T 11 r 10) t C A S E 1 66 10 - T E M P » R F L ( t ) 67 CALL P0NER(TEMP.RPOW,RLOO) ' -68 Wfl H E <6,107 >«PO» T»fcOG : 69 I F ( C A 3 E . E 0 . 2 . 0 R , C A 8 E , E S , 3 ) S 0 TO 12 70 11 T E M P s T R ( l ) 71 C * L L » P O « E R T — f T € # P r N M r N 6 r ? P O # T ? f c < > « 72 KRITE(4 ,108) TPOW/TLOO 73 12 KAsOtKCaO -74 6 0 - 1 4 - * SM- rK -75 I P ( I N C { M 5 ) , N E , 0 , 0 ) 6 0 TO 13 76 GO TO 14 77 » K A o M 5 f K C e K € * V f T - « ( * W » M 5 78 14 CONTINUE 79 I F ( K A , E Q , 0 ) G O TO 23 SO W t m^r+W CO I S Mftel .KC NRITE(6 ,110 )TABCM6) 1 5 CONTINUE N R I T E C f c . l l l ) I K B B K A * 1 | K D B K A : if ( K A , 6 T , 6 ) HO»B V P C 2 ) « D I G I T C K D ) 60 T O ( 1 5 1 , 1 5 2 , 1 5 2 , 1 5 3 , 1 S 3 , 1 5 1 ) , C A 8 E 151 V F <5 >oDIGIT < 9 > » VF-(-7 ) « 0 1 SI T J WRITE(6,vn < D ( I > , I B 1 , K D ) , R P 0 W , R L 0 S , T P 0 W , T L 0 Q 60 T O 15« - 1 5 2 Vf < 5 ) »W6 1 T (9 ) > VP-i7-HHHGffl^l WRITE ( 6 . V F ) C D < I ) , l B t , K D ) , R P O W , R L O Q CO T O 150 - W — - • V F < 5 ) B 0 I 6 I T « » > t V F < T - > » 0 I 6 I - H - » ) — W R I T E C 6 . V F ) ( D C I ) , I « 1 , K D ) , T P 0 W , T L 0 G 15a 00 22 U » l , 8 T , DO 17 H T » 1 , K A • D ( K 7 ) n O ( M 7 ) » I N C ( M T ) I F <OCM7) ,LT,0.e> 00 T O 16 60 TO-17 • 1 6 H R I T E ( 6 , 1 1 2 ) M7,0(M7) D ( H 7 ) o 0 . 0 —if O E L - W - > ° L - A W & A « C P H I (M7)*NF(M7)<>D(HT) : C A L L COEF C K , K K , K A , K B , R , T , C A S E , D E L » R F L » T R ) G O T 0 M 8 , 1 8 , 1 8 , 1 9 , 1 9 , 1 8 ) , C A S E —it fEMPoRFt-<+> CALL POWER C T E M P , R P O W , R L O G ) I F ( C A S E , E Q . 2 . 0 R , C A S E . E Q . 3 ) G 0 T O 20 —H> T £ - > 4 * » W - H r CALL POWERT <TEMP,NM,NS,TPOW,TLOG) I P C C A S E . E Q . a . O R . C A S E . E Q . S J G O T O 21 VF45)oDIGIT<94 • : — :  V F C 7 > » D I G I T C < I ) W R I T E C 6 , V F ) < D ( I ) , I » 1 , K D ) , R P 0 H , R L 0 G , T P 0 N , T L 0 6 / 60 T O 2 2 : — : 2 0 V F ( S ) B D I G I T { 9 ) V F C 7 ) o D I G I T ( 2 ) • — W Rimt - r V f f t M - 1 ) r I • 1 iKO) iRPOttrRL-Oft — ' O O T O 2 2 00 T O 2 2 —W V F ( S ) B O I G I T C 1 « — T ; : • V F(7 ) s O I G I T C 2 ) ' '-MRTTE'CG•,YF) CD'n me 1,KS)/TPewVTLCe1 -, 82 CONTINUE- = : '• 1 0 0 FORMAT <F9 ,0 ,5F10 ,0 ) 1 0 1 F O R M A T C ' O ' i J W A V E L E N G T H ' , T 2 9 , F 1 0 . U ' ANGSTROMS I , / ' A N G L E OF INCIDEN l C g ' , T a 9 , F l ( l,a, ' D E G R g E 8 ' , V ' I N 0 E X OF REFRACTION MEPIUM' , T 2 9 , F 1 0 .0,4 8 ' 8 U B 3 T R A T E ' , T 1 9 , ' I N D E X OF REFRACTION C F l O . a , ' , J ' , F 1 0 . fl,')' ) 102 - F O R M A T ( F 9 , 0 , « F 1 0 . 0 ) - . • 163 F0flH*-T-<^*T<>T-SF+«xe4^ : : 10a FORMATC , ' , ' P I L M N O . ' , 1 3 , T 2 0 , ' I N D E X O F REFRACTION ( " . F l O . a . l , J I l ,F tO,«,<)',T7e, ' TH ICKNESS • * F 1 0 . 1 » A N G S T R O M S ' ) —i«5 F-ORMAT {I 0 1 , 1 * * * * 8 'L IGHT POLARIZATION « « < n H ) : 1 1 0 6 FORMAT ( ' 0 ' , ' « » « » P - L I G H T POLARIZATION * * * • ' ) 107 F O R M A T C ' O ' , 'REFLECTANCE s ' , F 1 0 , 3 , T 3 0 , ' L O G . REFLECTANCE • I . F 1 0 . 3 ) 108 ' FORMAT( 1 0 1 , 1 TRAN&N^T-ANCE*-*-rF-l-0-r?T-TiO, 1 L 0 0 | TRANBMITANCE" 1 , F 10 ,3 ) 109 FORMAT ( ' 0 ' , ' V A R Y THICKNE88 PARAMETER O F l ' } 110 FORMAT( ' ' # ' F I L M N O , ' , 1 3 ) . —1-H FORKAT(<0 ' , 'TH ICKNESS OF FIRST 8 F1LH8 ' , / T S , ' F I L M 1 ' , T 1 S , ' F I L M 3 ' , 1 T 2 5 » ' F I L M 3 ' , T 3 5 , ' F I L M « ' , T f l 5 , ' F I L M 5 ' , T 5 5 , ' F I L M 6 ' , T 6 5 , ' F I L M T ' , T 8 7 5 , " F I L M 8 ' , T 8 3 , ' R E F L E C T , ' , T 9 3 , ' L O G . R E F L • # T t « 5 , ' T R A N S ' , T 1 1 2 , ' L 0 J O , T R A N S ' , / ) 1 1 8 F O R M A T ( ' 0 ' , ' F I L M N O . J f T J , ' H A S B E E N A S S I G N E D A T H I C K N E S S O F ' . F I O . l a , I A N G S T R O M S ' ) - C 5 R t H W N ;  E N D S U B R O U T I N E 8 P 0 L A R ( C A J E , K , K K , N M , N F , N S , C M F M I , C F H I , R , T ) tNTEGER—C-4SE • R E A L NM C O M P L E X NF(K ) ,N8,CPHI(KK ) ,T(KK ) ,R(Kr<) ,CMPLX,A,B oo a M B I I K W . ;  MMBHctt I F ( M , E 0 . 1 ) G 0 T O I WM re» j«««0-T<« : = A « N P C M N ) * C P H I ( N M ) f 8 » N F ( N ) « C P H I < M ) G O T O J . - 1 A B C H f > L » ( N M « C M P H I , 0 | 0 ) l B B N F ( l ) « C P H l ( l ) • G O T O J t A » N F ( H M ) « C P H I ( M M ) | B B N 8 * C F H I ( K K ) 142 1*1 162 16) i 6 s n n ( M } « s e » - 8 V ( » * B > — — IF ( C A S E , E O , 2 ) 6 0 TO a T ( M ) a ( 2 . 0 * A ) / ( * O B ) 16S 166 16T 168 169 . RETURN END SUBROUTINE PPOLAR < C A 8 E T * , K K , N M , N F , N 8 r C N P H l , C P M I r » r T ) INTEGER CASE REAL NM I rv i n 172 ITS ITfl ITS f T A t u n r t u l N r t M if N O l t r T I J i * Pr J fH I Hfv J - f Y ("fl 7 F * P O - " 1 1 """ "•' — 11 — 00 6 N s l . K K MMBMal I F ( C A 3 t , E 0 , 5 ) G 0 TO 7 -1F<M,EQ,1) GO TO 1 IF ( M . E 0 . K K ) GO TO 2 « ' u 1T7 ITS 179 • iee i a i 182 1 2 S n«uT>r j w n j « t r r t J O * F > j t ^ ~— 1 GO TO J A 8 N H * C P H I ( 1 ) » B « N F(1 ) « C M P H I GO T a S •. ' r -A o N F ( M M ) « C P M I ( M ) | B B N S * C P H I ( M M ) R ( H ) B ( A . B ) / ( A * B ) TT frAftr* P A 11 m Tft A 18S t e a , _ i88 166 187 186 7 0 1 r \ t j . 0 c | C U | I f r v ™ CONTINUE IF ( M , E 8,1 ) 6 0 TO A IP<H,EQ,KK)60 TO 5 T t M ) B ( 2 , 0 « N F ( M M ) i » C P H I ( M M ) ) / ( ( N F ( M M ) * C P H I ( M ) ) * ( N F ( M ) « C P M I ( M M ) ) ) GO TO 6 189 190 - 191 192 19S 19a 5 6 GO TO 6 T C M ) B ( 2 , 0 « N F ( N M ) » C P N I ( M M ) ) / ( ( N F ( M M ) * C P H I ( M ) ) * ( N S«ePHI ( M M ) ) ) •- CONTINUE : RETURN END flllRRfllJTTNF P O H P R f r f l E F P f i H ^ i o r p n u i • * ™ 195 196 197 198 .199 2 « « REAL L0GP0M COMPLEX COEF AROPoCABSKOEF-) : ; POMBAR0P*AR0P ..^tOGROWMfe'OO l'OfPC W ) RE-TURN . :  201 202 20S 20e 205 3tl Jfj. END SUBROUTINE POMERT (COEF,NM.N8,P0W,LOOPON) REAL L0GP0M.NM COMPLEX COEF.NS ' ' AROPBCABS(COEF) P A U n i n r i r t a A D n O a l t T P I I ' " « » 207 208 - 9 A O -LOGPOWSALOGIO(POW) RETURN r u n CWT 210 211 Pi > IND - — • ' SUBROUTINE COEF {K»KK,K»,KB ,R ,T ,CASE,DEL,RFL»TR) INTEGER CASE rnuo i cv «rrwo * _ it _T twn \ _0 tatt % _f \n 1 _PCI tftrfcri T» % ( L i t . 213 210 215 216 21T y%n t u n r ^ t * C C * ~ J • • O f f T \nrWf~\f*»* 7 f U C U * ~ 7 ? n r f T W v "™7 DO 2 M5B1.KA JBKB»M5| J J B J M IF<J ,E9.K) RFL<JJ )BR(JJ) A o R F L ( J J ) * CE X P C ( 0 . 0 , - 2 . 0 ) « D E L ( J ) ) BB1 , 0 * (R(J)*A) t r / f i t r ILA 1 ,nj> .p i f tp . r o . g x fln » n « . C i v 219 220 221 222 22S fta - i r r T C " 3 C • JBJUH <j L •> O C t t . V | ^ J t r v T v — X • • R P L ( J ) » ( R ( J ) « A ) / 9 . I F ( C A S E . E 0 . 2 , 0 R . C A S E.EB.S) GO T02 — CONTINUE •. : : I F ( J . E C . K ) TR(JJ )BT(JJ> TR{J )B (T(J)*TR(JJ)*CEXP((0.0,»1 , 0 ) »DEL(J)))/B r n w i 1 Miir 225 c vur* 1 i i u c • ~ 1 RETURN 226 END 227 —SOATA 228 SST0P END OF F I L E •81SNOFP - • — : 6.2 Computer program to obtain the reflectance at 143 maxima; i n a s i n g l e - f i l m substrate system SCOMPILE 5 ,000 C_ ; ; : 6 .000 C 7 ,000 C o — o T O COMPUTE THE REFLECTED POWER AT THE MAXIMA AND MINIMA IN A 8XBBB* 0 ,000 C — - « F I | . M o 3 U B 3 T R A T E 8YSTEM _j_000 " " C — " A B S O R B I N G OR NON ABSORBING PILM OR SUBSTRATE 10 ,000 C 11 ,000 C : : 12 .000 ,,_ O — . . D A T A CARDS. 13 ,000 Co.— .COMPLEX REFRACTIVE INOECES (N o j K) FILM AND 8U88TRATB 14 ,000 , C — — " P H I O G I ANGLE OF INCIOENCE IN DEGREES 15 ,000 C " ' " 16 ,000 C » » o . o 0 U T P U T l 17 ,000 C-T - " " IM A G I N A R Y PART OF FILM I N D E X , , REFLECTED PCHER AT MAX l .M IH 1 ,_MAX 2,MIN 2, 18 ,000 C o - . i - L W . OF R E F L , POWER AT MAX AND M J N , , PLOTTER OUTPUT IN CENTIMETER FOR 19,000 C 20 ,000 C __ 2 1 * 0 0 ? 1 R E A L G , ! N M , I N N , D l , R P 0 W , R L P # E O r t f 6 8 , O l 8 , k f 2 2 , 0 0 0 2 COMPLEX N M ,CM,SM,CMPLX,RM 2 3 , 0 0 0 3 DIMENSION DI ( 3 ) , R P 0 H ( 3 ) , R L P ( S ) , e 0 ( 4 ) , N H ( 3 ) , C M ( 3 ) , S M ( 3 ) , C(l ) t 0 S t a ) t 2 4 , 0 0 0 . 1Y<3) 25,000 4 READ (5 , 1 ) RNW,IWM,NM(3},PHI0S 2 6 , 0 0 0 5 1__ FORMAT (5F10.0) •_ ; 8 7 , 0 0 0 " b N H ( i ) - C M P L X C f , 0 » 0 , 0 ) : I 2370015 7 P l s 3 , 1 4 1 6 f P H I c P H I D G - P I / 1 8 0 , jCOnCOS(PHI) » 8 0 s 8 I N ( P H I . 2 9 , 0 0 0 11 S H ( 1 ) - C H P L X ( S 0,0 , 0 ) >CM ( l )eCHPLX ( C O , 0 , 0 ) : , 3 0 , 0 0 0 13 OO 100 K - 1 , 1 1 3 1 , 0 0 0 14 T E M P l - K / 1 0 0 , 0 1 RNNsRNM*TEMP1 12,000 lb WRITE ( 6 , 5 ) NH(_) ,PHIDO,RNN 33,000 17 " DO 100 k k s T . 5 1 " " " 34,000 16 T E M P 2 - K K / 2 0 0 0 , fINNalNM+TEMPJ jNM(2)oCMPLX(RNN, INN) 35,000 21 DO a 1 = 1,2 > : 36.000 22 H « I * 1 37,000 23 CALL 3'JELL (NMC1) ,NM(11 ) , 8M(1 ) ,SM(11 ) ,CM(II)) 38,000 . 24 CALL FRESNL (NM (I ) , N H (11) , C H ( I ) ,CM (11) , G (1) , T (I ) ) : ; 39,000 25 2 G G ( I ) 3 G ( T ) * G ( i ) f G 1 2 = G { l ) « G ( 2 ) « 2 , 0 40,000 27 A L l - K E A L ( N M ( 2 ) ) ) 4 l 3 R E A L ( C M ( 2 ) ) f K l o A I M A 0 ( N N ( 2 ) ) J B 1 0 A I M A O ( C M ( 2 ) ) fll.000 31 A A L a ( A l « A L l ) ° ( B 1 « K 1 > t AAHc( ( A 1«K 1) » ( A L 1 *B1 ) ) / A A L . 48.000 33 CALL FRESNL (NM(1),NM(3),CM(I),CM(3),G(3),T(3)) 43,000 34 R M A X s G ( 3 ) « G ( 3 ) | R L M A X a A L O G 1 0 ( R M A X ) 44,000 36 ' CO 7 M o l , 3 _ 45,000 17 P I M 0 ( M r * P ' l ) » ( T ( 2 T V T ( l ) ) |D l (M)o (P IM«6328,)/(4,0 *PX«AAL) f V P I M 6 A A H 467000 .40 " V 2 a 2 , 0 « V f E J V s g X P C V2) j E V = £ X P ( V) . 47,000 43 • Tr - (n ;Ea , - i ;c f i - ; 'HyEa i ; -3 ) -30 - ' 7 0 A - B • -48,0.09 — 4 4 RTW ( MT5T^ GTT)~*TG ' GT2T^ 497000 IV ) ) 30,000 43 GO TO 7 • 51,000 — 4 6 — — R ? o d ( M ) = i ( G O ( n » ( t c r m ^ e 2 v ) » ( G i 2 * e v ) > / ( i , o « ( S 6 ( n 0 6 6 ( 2 ) « g 2 V ) « ( a i a « E sTTora— IV ) ) 51,000 47 7 RLP(H)aALOGl0 (RPQW(M)) 54,000 ai c d O K o 2 , 2 « 2 S , o 55,000 49 E 0 ( 1 ) 9 C 0 0 K * ( R L M A X » R L P ( 2 ) ) |EO(2)t3 COOK*(RLMAXeRLP(1) > 9 6 , 0 0 0 St _ E O ( 3 ) s C O O K * ( R L P ( 2 V - J I L P C 1 ) ) >EO(4 )niCOOK*(RLP(2 ) -RLP(3 ) ) 9 7 , 0 0 0 53 NR'lfE ( 6 , 4 ) iNN;RNAX,RP"0NT71^N>X7~RLP,Eir " 5 8 , 0 0 0 54 100 CONTINUE 59 ,000 . 55 4 FORMAT ( 9 F 8,4 , 4 F 8 , 2 ) 6 0 , 0 0 0 56 5 FORMA? <iHt,T0"x7_0H INDEX OF SU93fRATE., B6.2,2H J , K 6 , » , /29H4NSLE ' 61,000 IOF INCIDENCE ( D E G R £ E 3 ) » » P 6 . 2 , /35HWAVELENGTH OF LASERS 6328 ANG3TR 6 2 , 0 0 0 20MS, /24HREAL PART INDEX OF F l L M o , F 6 , 3 # / / 1 9 X , 1 5 H R E P L E C T E D POWER,I 6 1 . 0 0 0 3 2 X , 3 0 M L 0 9 , REFLECTED POWER ,/U0H IM FILM M A X . l MIN,I WAX,2 6 4 , 0 0 0 4 MIN,2 MAX,1 MIN.l MAX,2 MIN,8 EO.t . 60,2 E0,3 69,000 • 3 E 0 . 4 /> 6 6 , 0 0 0 5 T To" STOP : 6 7 , 0 0 0 56 END 6 8 , 0 0 0 " 5 9 SUBROUTINE SNELL (NM1,NM,8M1,8M,CM) 6 9 , 0 0 0 60 COMPLEX NM1 ,NM,SM1,3M,CM,CSQRT 7 0 , 0 0 0 61 8 M ° ( N M 1 / N M ) « 3 H 1 • . 7 1 . 0 0 0 62 CMBCS8RTO , 0 « ( S M » 3 M ) > 7 2 . 0 0 0 61 RETURN 7 1 , 0 0 0 64 ZH0 . _ '. 7 4 . 0 0 0 65 SUBROUTINE FRESNL (NM1,NM,CM I , C M , G 1 , T I ) 7 3 , 0 0 0 66 COMPLEX^ HHUNM>CMl^CMiRJll* 13 '. 7 6 . 0 0 0 67 A»NN-*CM1 iB-NM-CM »RMa{A.B)/(A*B ) 77 ,000 70 GlaCASS(RM) f T 1 ° A T A N (A IHAG(RM) /REAL(RM)) 7 8 , 0 0 0 72 RETURN ; 7 9 . 0 0 0 71 END " ; : 8 0 , 0 0 0 -80ATA . - ' 6 1 . 0 0 0 144 6.3 Computer program to obtain the surface state density using . the quasi-static technique SCOMPI lE 1,000 C SURFACE STATE DENSITY USING THE OUASI STATIC TECHNIQUE 2 , 0 0 0 C REVISED BY R, C AV AN AGH JUNE 25/71 3 ,000 C 4 ,000 C NOTE - XITMIN THE BODY OF THIS PROGRAM NS3 REFERS TO SURFACE STATE 5 ,000 C DENSITY BUT 13 GIVEN AS NST ON ALL OUTPUT 6 ,000 C READ AND CALCULATE CONSTANTS 7 ,000 1 DIMENSION V ( 1 0 0 , 3 ) , C N ( 1 0 0 , 3 ) , M A X ( 3 ) , S Y t l O O , 3 ) , C T ( 1 0 0 ) , V T ( 1 0 0 ) 8 ,000 2 DIMENSION 3 Y P ( 1 0 0 ) . V M M ( 2 ) , C P ( 1 0 0 ) , V P < 1 0 0 ) , M A X N ( 3 ) • 9 ,000 3 COMMON U S , U B . L , B E T A , E P S I l , E P Z E R O , C I , O S C ( 1 0 0 ) , C 3 C ( 1 0 0 1 , N 3 S ( 1 0 0 » 3 > , 10 ,000 X E D S Y D V U O O , J ) , 0 11.000 4 REAL N D , N C , N V , N l , L f N S S 12,000 S REAL NSSP(100) .NSSMM(2) 13 ,000 6 INTEGER TEMP,THICK 14,000 . 7 5 R E A D ( 5 , 6 ) E R I N S , T E « P , N D , T H I C K 15,000 e 6 F O R M A T ( F 1 0 , 2 / 1 i / E l 0 , 2 / 1 5 ) 16 ,000 9 7 0=1 .6025E-19 17 ,000 10 8 E P Z E R 0 * 8 . 8 6 E - 1 4 18,000 11 9 T»TEMP 19 ,000 12 10 THICsTHICK 2 0 , 0 0 0 15 11 TH = T H I C M , 0 E - 0 8 2 1 , 0 0 0 14 12 B E T A » 1 , 0 / ( 8 . 6 2 E - 0 5 * T ) 2 2 , 0 0 0 15 13 N C a 5 , 3 < ) E * l 5 « T * * ( l , 5 ) 2 3 , 0 0 0 16 14 N V n 2 , 0 0 E * 1 5 * T * * ( l , b ) 2 4 , 0 0 0 17 15 N I = S O R T ( N C « N V * E X P ( - l , l l * B E T A ) ) 2 5 , 0 0 0 IS 16 UBaALOG(ND/NI) 26 ,000 19 17 E P S I L 3 1 1 . 7 2 7 , 0 0 0 20 18 L e S Q R T ( ( E P S I L * E P Z E R O ) / ( 2 , 0 » B E T A * Q « N I ) ) 2 8 , 0 0 0 21 19 E F o ( u B / B E T A ) + . 5 5 5 2 9 , 0 0 0 22 C I = E P l N S * E P Z E R O / T H 30 ,000 25 20 SYBaUB/BETA 31 ,000 24 21 WRITE(6 ,22) E P INS ,T E M P ,NO,T H ICK 3 2 , 0 0 0 25 22 F0RMAT(1H1,SHKI s ,F7 .3 ,5X14HTEMPERATURE « , f 3 , 7 H DfcG, K.5X5HND • 35 ,000 X , 1 P E B , 2 , 5 X 2 2 H I N S U L A T 0 H THICKNESS a , I 5 , 2 H A) 34 ,000 26 23 H R I T E ( 6 , 2 4 ) N C , N V , N I , U B , L r E F , S Y B ' 35 ,000 27 24 FORMAT(1H0,5HNC a ,1PE10,4,9X5HNV « ,t10,4,5X5HNI c , E 1 0 , 4 , / / 6 H UB 36 ,000 X « , 0 P F 7 , 3 , 5 X q H L « , 1 P E 1 0 , 4 , / / 6 H EF « , 0 P F 5 , 5 , 5 X 6 H 3 Y B « , F 5 , 3 ) 37 ,000 26 25 R E A D ( 5 , 2 6 ) VFB 38 ,000 29 26 " FORMAT (F 10,4 ) 59 ,000 30 40 C F B N s l , 0 / ( l , 0 * C I / 3 Q R T ( E P S I L * E P Z E R 0 * Q * B E T A * N D ) ) 4 0 , 0 0 0 ...C READ AND PREPARE C.,«.V OATA ' 41., 000 27 J » l 42 ,600 32 26 I » l 45 ,000 33 29 R E A D ( 5 , 3 0 ) C , V ( I , J ) 44 ,000 34 30 F O R M A T ( 2 F 1 0 , ~ 5 ) — " " " 45 ,000 -35 31 I F C C . E Q . 0 . 0 ) GO TO 57 4 6 . 0 0 0 56 52 I F ( I . E Q . l ) C l a C . 47 ,000 37 33 C N ( I , J ) « C / C 1 4 6 , 0 0 0 58 54 E D 3 Y D V ( I , J ) B ( 1 , 0 / C N ( I , J ) ) - 1 , 0 49 ,000 39 55 I " I » 1 5 0 , 0 0 0 40 36 GO TO 29 " ' ^ 1 , 0 0 0 <•! 57 I F ( I . E O . I ) GO TO 81 5 2 , 0 0 0 C CALCULATE VFB AND NFB 5 5 , 0 0 0 42 38 M A X ( J ) » I - 1 54 ,000 43 59 I F ( V F B , N E , 0 , 0 ) GO TO 55 5 5 , 0 0 0 44 41 H R I T E ( 6 , 4 2 ) CFBN 5 6 , 0 0 0 45 42 F0RMAT(1H0,7HCF8N • f F 6 , 4 ) 5 7 , 0 0 0 " 46 MAXJaMAX(J) 58 ,000 47 45 00 16 1*2 ,MAXJ 59 ,000 48 44 I F ( C N ( I , 1 ) , E Q , C F B N ) GO TO 51 60 ,000 49 45 I F C C N ( I , 1 ) , L T , C F B N ) CO TO SO 6 1 , 0 0 0 50 46 N F B « I + 1 6 2 , 0 0 0 51 47 K R I T E C 6 , 4 8 ) J 6 5 , 0 0 0 52 48 FORMAT(1H0,15HCANN0T F IND V F B , 5 X 4 H J • #12) 6 4 , 0 0 0 55 49 STOP 65 ,000 54 50 I F ( A B S ( C N ( N F B , 1 ) - C F B N ) , G T , A B S t C N ( N F B » 1 , 1 ) « C F B N ) ) NFB B NFB-1 6 6 , 0 0 0 55 51 V F B » V ( N F B , 1 ) 6 7 , 0 0 0 56 52 GO TO 62 6 6 , 0 0 0 C SEARCH FOR V ( I , J ) « V F 8 6 9 , 0 0 0 57 55 HAXJaMAX(J) 70 ,000 58 00 57 I o l , M A X J 71 ,000 59 54 N F B » I 72 ,000 60 55 I F ( V ( I , J ) , E Q , V F B ) GO TO 61 • 75 ,000 61 56 I F ( V ( I , J ) , L T , V F B ) GO TO 60. 74 ,000 62 57 CONTINUE " " ' " " 75 ,000 65 58 * R I T E ( 6 , 9 8 ) J 76 ,000 64 59 STOP 77 ,000 65 60 I F ( A B S ( V ( N F B , J ) - V F B ) , G T , A B 3 ( V ( N F B - 1 , J ) • V F B ) ) NFB«NFB»1 78 ,000 79 ,000 145 66 61 V F B » V ( N F B , J > 7 9 , 0 0 0 67 62 WRIT £ ( 6 , 63 ) V F B . N F B 8 0 , 0 0 0 6 8 6 3 FORMAT O H O , 6 H V F B s , F 6 , 3 , S X 6 H N F B o , I J ) 8 1 , 0 0 0 C C A L C U L A T E S U R F A C E P O T E N T I A L 8 2 , 0 0 0 . 69 64 N F B M l o N F B - l 8 3 . 0 0 0 70 6S NFBP1=NF6*1 84,000 71 66 S Y C N F B , J ) r . S Y B 85,000 72 • 67 DO 69 I = l , N F B M l 86,000 73 68 N=NFB» I 8 7 , 0 0 0 7a NP1SN+1 88,000 75 6 9 SY ( N , J ) = ( V ( N . J ) o V ( N P l , J ) ) « < ! , - , 5 * ( C N ( N , J ) » C N ( N P 1 , J ) ) ) * S Y ( N P 1 , J ) 89.000 76 MAXJsMAX(J) 90,000 77 70 DO 71 1 3 N F B P 1 ,MAXJ 91,000 78 IM lo I -1 92,000 7 9 71 S Y ( I , J ) = ( V ( I , J ) » V ( I M l , J ) ) * ( l , - , 5 * ( C N ( I , J ) * C N < I M l , J > » * S Y ( t M i , J > ^ 3 , 0 0 0 C GENERATE T H E O R E T I C A L DATA ANO NST 9 4 , 0 0 0 8 0 HAXJ lMAX ( J ) 9 5 . 0 0 0 et 72 DO 75 1=1,MAXJ r 96,000 8 2 7 3 U 3 3 B E T A * S Y ( I , J ) 9 7 , 0 0 0 8 3 74 C A L L T H E 0 R Y ( I , J ) 9 6 , 0 0 0 " 6 4 75 C O N T I N U E " 99,000 8 5 N S S ( N F B , J ) 3 ( N S S ( N F B P l , J ) * N 3 S ( N F B M 1 , J ) ) / 2 , 1 0 0 . 0 0 0 86 76 I F ( J . N E . l ) GO TO 7 9 1 0 1 . 000 c GENERATE T H E O R E T I C A L CV CURVE 102,000 87 MAX1=MAX(1) 1 0 3 , 0 0 0 8 8 TJ DO 78 I=1 ,MAX1 1 0 4 , 0 0 0 69 •VT(I)»"(0SC(157CT) •VT.8V(BETA«SY U , l ) * U B 5 / B E T A 1 0 5 , 0 0 0 " " 90 C T ( 1 ) B C S C ( 1 ) / ( C I * C S C U ) ) 1 0 6 , 0 0 0 91 I F C I . E O . N F B ) C T ( I ) s C F B N 1 0 7 , 0 0 0 - OJ 78 CONTINUE 108 ,000 9J 79 J B J * 1 1 0 9 , 0 0 0 94 8 0 GO TO 28 1 1 0 , 0 0 0 C OUTPUT DATA n r . OOF -95 81 W R I T E C 6 , 8 ' ) / 1 1 2 , 0 0 0 9 6 82 F O R M A T ( 1 H O , 1 7 H E X P E R I M E N T A L DATA) 1 1 3 , 0 0 0 9 7 J M l s J . l 114,000 "98 8 3 DO 88 J J n l . J M l 1 1 5 , 000 99 84 K R I T £ ( 6 , 6 5 > J J 1 1 6 . 0 0 0 "100 6 5 FORMAT ( 1 H 0 , iX i iHNCA P , 8x5HvOLTS ,9X2HSV, 10X3hN8T„, 10X4HJ, » , 1 2 , / / > 1 l7",.oo tr ^ 1 0 1 ' W R - I T E ( 6 , a " 6 ) * X N C i , ' J J ) , V t l , J J ) , 3 Y ( i r j J ) 118 ,000 102 86 F O R M A T ( I H , 2 X , F 8 , 6 , 3 X , F 1 0 , 5 , 4 X , F 8 , 5 ) 1 1 9 , 0 0 0 103 M A X J J B M A X ( J . J ) 120,000 104 00 BB I s 2 , M A X J J 1 2 1 , 000 1 0 5 W R I T E ( 6 , 8 7 ) C N ( I , J J ) , V ( I , J J ) , S Y C I , J J ) , N 3 S ( I , J J ) 122,000 106 87 FORMAT ( I H , 2 X , F 8 , 6 , 3 X , F 1 0 , 5 , 4 X , F 8 , 5 , 4 X , 1 P E 1 1 , 4 ) 1 2 3 , 0 0 0 107 88 CONTINUE 1 2 4 , 0 0 0 108 89 WRITE(6,90) 1 2 5 , 0 0 0 109 90 FORMAT(1H0,1 6 H T H E 0 R E T I C A L DATA) 1 2 6 , 0 0 0 I I S 91 W R I T E ( 6 , 9 2 ) 127,000 U l 92 F 0 R M A T ( 1 H 0 , 3 1 H NCAP VOLTS 8Y,/V) 128,000 112 MAXleMAX( l ) 1 2 9 , 0 0 0 113 DO 9 5 I » 1 , M A X 1 1 3 0 , 0 0 0 114 93 W R I T E ( 6 , 9 4 ) C T ( I ) , V T ( I ) , S Y ( I , 1 ) 1 3 1 , 000 1 1 5 94 FORMAT ( IH , 2 X F 8 , 6 , 3 X F 1 0 , 5 , 4 X F 6 , 5 ) 1 3 2 , 0 0 0 116 9 5 CONTINUE 1 3 3 , 0 0 0 117 STOP 1 3 4 , 0 0 0 .118 END 135,000 119 SUBROUTINE THEORY ( I , J ) 1 3 6 , 0 0 0 120 COMMON U S , U B , L , B E T A , E P S I L , E P Z E R O , C I , e S C ( 1 0 0 ) , C S C ( 1 0 0 ) , N S 3 ( 1 0 0 , 3 ) , 1 3 7 , 000 X E D S Y O V ( 1 0 0 , 3 ) , Q 1 3 8 , 0 0 0 121 REAL N S S , L 1 3 9 , 0 0 0 122 3 F t S Q R T ( A B S ( 2,0 * ( C 0 3 H ( U S ) » C 0 S H ( U B ) * ( U B » U S ) * S 1 N H ( U B ) ) ) ) 140,000 1 2 3 a Y=US»UB 1 9 1 , 0 0 0 124 S N Y B A 8 S ( Y ) / Y 1 4 2 , 0 0 0 125 6 E S s - S N Y « F / ( L « B E T A ) 1 4 3 , 0 0 0 126 7 O S C ( I ) s E P S I L * F P Z E R O * E S 144,000 127 C S C ( I ) = S N Y « ( ( F P S I L « E P Z E R 0 ) * ( S I N H ( U S ) » S 1 N H ( U B ) ) ) / ( L * F ) 1 4 5 , 0 0 0 128 9 T D 3 Y D V B C 1/CSC(!) 1 4 6 , 0 0 0 129 I F ( E O 3 Y D V ( I , J ) , E U , 0 , 0 > GO TO 1! 1 4 7 , 0 0 0 130 10 N S S ( I , J ) s ( ( T O S Y O V / E D S Y D V ( I , J ) ) - 1 , 0 ) « C 3 C < I J / Q 1 4 8 . 0 0 0 131 11 RETURN 1 4 9 , 0 0 0 132 END 150,000 SOATA 151,000 146 VII REFERENCES 1. 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