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Studies on plasma anodization in a DC glow discharge Olive, Graham 1973

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STUDIES ON PLASMA ANODIZATION IN A DC GLOW DISCHARGE by Graham Ol i v e B.Sc, Brunei U n i v e r s i t y 1965 M.A.Sc., U n i v e r s i t y of B r i t i s h Columbia 1970 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of E l e c t r i c a l Engineering We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 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 of the requirements fc an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree tha" 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 of 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 g r a n t e d 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 copying 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 a l l o w e d w i t h o u t my v w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date ABSTRACT The phenomenon of anodization i n the plasma of a dc low pressure oxygen glow discharge i s i n v e s t i g a t e d , both from the viewpoint of the mechanisms involved and f o r p o t e n t i a l a p p l i c a t i o n s . Aspects studied include the e f f e c t of discharge conditions on anodization r a t e , the s i g n i f i c a n c e of negative oxygen ions i n the plasma, the i o n i c current-f i e l d strength r e l a t i o n i n the oxide, and the anodization of metal f i l m s on s i l i c o n f o r MIS devices. I t was found that the process does not u t i l i z e gaseous negative ions from the n e u t r a l plasma, and that species transport through the oxide i s by high f i e l d i o n i c conduction. The v a r i a t i o n of anodization rate with discharge conditions was a t t r i b u t e d p r i n c i p a l l y to a dependence of the oxide f i e l d strength on the e l e c t r o n energy d i s t r i b u t i o n and density i n the plasma. Double oxide layer MIS s t r u c t u r e s were f a b r i c a t e d , and charge storage e f f e c t s were i n v e s t i g a t e d . i TABLE OF CONTENTS ABSTRACT Page i TABLE OF CONTENTS i i LIST OF ILLUSTRATIONS v LIST OF TABLES x ACKNOWLEDGEMENT x i 1. INTRODUCTION 1 2. REVIEW OF PREVIOUS WORK ON PLASMA ANODIZATION 4 3. COMPARISON OF PLASMA- AND SOLUTION-ANODIZATION 7 3.1 General Features of Solution Anodization 7 3.2 The High F i e l d Ionic Conduction Process -C l a s s i c a l Theory 9 3.3 General Features of Plasma Anodization 12 4. THEORETICAL ASPECTS OF PLASMA ANODIZATION 17 4.1 Introduction 17 4.2 Plasma Sheath Theory 17 4.2.1 General 17 4.2.2 The Plasma Anodization Case 20 4.3 The Metal/Oxide/Space Charge Sheath/Plasma System . . . 20 4.4 The Formation of Gaseous Negative Ions 26 4.5 The Low Pressure Cold Cathode Glow Discharge i n Oxygen ' 29 5. PROBE TECHNIQUES IN PLASMA DIAGNOSTICS 35 5.1 Introduction 35 5.2 S i m p l i f i e d Treatment of the Langmuir Probe Method . . . 35 5.3 The E f f e c t of Negative Ions on Langmuir Probe Measurements 40 6. THE APPLICATION OF ELLIPSOMETRY TO ANODIZATION STUDIES . . . . 42 6.1 Introduction *. 42 6.2 P r i n c i p l e s of Ellipsometry 43 6.2.1 R e f l e c t i o n of a Plane Wave at an Interface Between Two I s o t r o p i c Media and at a Film-Covered Surface . . . . . . . . . . . 43 6.2.2 The Poincare" Sphere Representation of E l l i p -c a l l y P o l a r i z e d L i g h t 45 i i Page 6.2.3 Theory and Operation of the Ellipsometer 49 6.2.4 The Analysis of Ellipsometry Data 54 7. EXPERIMENTAL CONSIDERATIONS 58 7.1 The Discharge Tube and Vacuum System - Design and F a b r i c a t i o n 5.8 7.2 The O p t i c a l System 65 7.2.1 The Automated Ellipsometer 65 7.2.2 Ellipsometer Alignment 69 7.2.3 Treatment of Errors i n i n s i t u E l l i p s o m e t r y . . . 76 8. INVESTIGATION OF DISCHARGE PARAMETERS AFFECTING RATES OF ANODIZATION 82 8.1 Introduction 82 8.2 Sample Preparation 82 8.3 Measurements and Results 84 8.3.1 O p t i c a l Constants of the Substrates 84 8.3.2 Oxygen Flow Through the C e l l 90 8.3.3 Plasma Density 91 8.3.4 Gas Pressure 98 8.3.5 Discharge Current 105 8.3.6 Sample Current Density . . . . . . . . . . . . . . 106 8.4 Discussion 112 9. THE ROLE OF PLASMA NEGATIVE IONS 121 9.1 Introduction 121 9.2 E l e c t r o n F i l t e r Experiments 122 9.3 Modulation of the Negative Ion Flux to a Sample by the Simultaneous A p p l i c a t i o n of r f and dc Biases . . . . 128 9.3.1 Constant dc Voltage Approach . 128 9.3.2 Constant dc Current Approach 132 9.3.3 Experiment and Results 135 9.3.4 Discussion 138 10. THE RELATION BETWEEN OXIDE GROWTH RATE, ELECTRIC FIELD STRENGTH IN THE OXIDE AND OXIDE TEMPERATURE DURING PLASMA ANODIZATION 140 10.1 Introduction 140 10.2 The Estimation of F i e l d Strengths i n the Oxide 141 10.3 V a r i a t i o n of Voltage with Time at Constant T o t a l Current 145 10.4 Voltage vs. Thickness f o r Steady-state Conditions . . . 147 10.5 Thickness and Oxide P o t e n t i a l Difference vs. Time During a Formation 147 i i i Page 1 0 . 6 V a r i a t i o n of Ionic Current with Estimated Oxide F i e l d 1 4 7 1 0 . 7 Dependence of Ionic Current on Temperature 1 5 5 1 0 . 8 Discussion 1 6 2 1 1 . THE PRODUCTION OF DIELECTRIC FILMS FOR METAL-INSULATOR-SEMI CONDUCTOR DEVICES 1 6 5 1 1 . 1 Introduction 1 6 5 1 1 . 2 D i e l e c t r i c M aterials f o r Gate I n s u l a t i o n . . . . . . . . 1 6 6 1 1 . 3 B r i e f Review of Recent Work on Metal Oxide Thin Films Useful f o r Gate I n s u l a t i o n 1 6 8 1 1 . 4 Plasma Anodization of Metal Films on S i l i c o n 1 6 9 1 1 . 4 . 1 Introduction 1 6 9 1 1 . 4 . 2 E l l i p s o m e t r i c Considerations 1 7 0 1 1 . 4 . 3 C(V) Measurements 1 7 3 1 1 . 4 . 4 Experimental 1 7 7 1 1 . 4 . 5 Results 1 7 9 1 1 . 5 Discussion 1 8 8 1 2 . CONCLUSIONS 1 9 2 'REFERENCES 1 9 5 APPENDICES 2 0 1 Appendix A: V e l o c i t y and Energy D i s t r i b u t i o n s 2 0 1 Appendix B: Mean Free Path Lengths and Sheath Thickness 2 0 2 Appendix C: The 'Sounding Probe' Method of Determining Plasma P o t e n t i a l 2 0 5 Appendix D: Summary of i n s i t u E llipsometry Results f o r the Plasma Anodization of Niobium and Tantalum . 2 0 7 i v LIST OF ILLUSTRATIONS Pa^e Fig. 3.1 Supposed potential energy of ion versus distance with and without an applied f i e l d 11 Fig. 3.2 Biasing arrangements for plasma anodization . . . . 14 Fig. 4.1 One-dimensional electron energy band diagram for an oxide-covered metal sample drawing a current density less than ( j £ g + J+s^ ' a n <^ n e a r b y floating probe 21 Fig. 4.2 Electrostatic f i e l d and potential distributions in the metal/oxide/space charge sheath/plasma system, neglecting potential gradients i n plasma . 23 Fig. 4.3 The space charge, e l e c t r i c f i e l d and potential distributions i n the dc cold cathode glow discharge 30 Fig. 5.1 Ideal current-voltage characteristics of a Langmuir probe 37 Fig. 6.1 Reflection and refraction at an interface . . . . . 44 Fig. 6.2 The locus of the e l e c t r i c vector for e l l i p t i c a l l y polarized l i g h t i n a plane normal to the direction of propagation 46 Fig. 6.3 Representation of polarized l i g h t on the Poincare sphere 48 Fig. 6.4 Arrangement of the ellipsometer 50 Fig. 6.5 Poincare sphere representation of an ellipsometer n u l l 52 Fig. 6.6 Computed ellipsometry curves for single f i l m (N-|_ = 2.25) on niobium (N 2 = 3.6 - J3.6) at 0^ = 65° and X = 5461A i n a i r and water 55 Fig. 6.7 Two layer model 56 Fig. 7.1 Schematic of anodization c e l l and pumping station (system B) 59 Fig. 7.2 The water-cooled adjustable sample holder 61 Fig. 7.3 Discharge and sample biasing circuits . 64 v Page F i g . 7.4 Schematic of c o m p u t e r - c o n t r o l l e d e l l i p s o m e t e r system 66 F i g . 7.5 Angle o f i n c i d e n c e (A.I.) z e r o e r r o r d e t e r m i n -a t i o n . . . 71 F i g . 7.6 C a l i b r a t i o n of the p o l a r i z e r and a n a l y z e r s c a l e s ( s h a f t encoder o u t p u t s ) 73 F i g . 8.1 Schematic of d i s c h a r g e system used by Lee e t a l . 1970 (system A) 83 F i g . 8.2 E l l i p s o m e t r y d a t a f o r Ta„0 on Ta I n a i r used t o o b t a i n the o p t i c a l c o n s t a n t s o f Ta a t X = 6328A . 86 F i g . 8.3 C i r c u i t used to m o n i t o r sample and probe p o t e n t i a l s . . . . . 89 F i g . 8.4 Sample c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s : x g o l d -p l a t e d sample i n n e g a t i v e glow o f system A, 1^ = 10mA, p = 55 m t o r r ; o suspended n i o b i u m sample i n p o s i t i v e column of system B, 1^ = 40 mA, p = 60 mtorr;»as o exc e p t mounted on sample h o l d e r 94 F i g . 8.5 L o c a t i o n o f c o n s t r i c t o r s : (a) s t a i n l e s s s t e e l 'top h a t ' , (b) b o r o s i l i c a t e f u n n e l 95 F i g . 8.6 E f f e c t o f c o n s t r i c t o r on probe c h a r a c t e r i s t i c s . . 97 F i g . 8.7 R i n g cathode-base p l a t e anode plasma a n o d i z a t i o n system 100 F i g . 8.8 (a) Cur r e n t e f f i c i e n c i e s v e r s u s p r e s s u r e f o r a n o d i z a t i o n of sample Ta2 at I = 0.1 mA, 0.2 mA and 0.3 mA i n the p o s i t i v e column (b) E l e c t r o n d e n s i t y and mean e l e c t r o n energy v e r s u s p r e s s u r e 102 , F i g . 8.9 C u r r e n t - v o l t a g e c h a r a c t e r i s t i c s f o r g o l d - p l a t e d sample i n the p o s i t i v e column at v a r i o u s p r e s s u r e s 103 F i g . 8.10 E l e c t r o n c u r r e n t - v o l t a g e c h a r a c t e r i s t i c o b t a i n e d from 60 m t o r r curve o f F i g . 8.9, and e l e c t r o n and p o s i t i v e i o n c u r r e n t s to g o l d b a l l probe used as a 'sounding probe' 104 F i g . 8.11 Oxide t h i c k n e s s and grox^th r a t e d u r i n g c o n s t a n t 2 c u r r e n t a n o d i z a t i o n o f n i o b i u m sample Nb5 at 1mA/cm , 1^ = 5mA, p = 60 mtorr (system A n e g a t i v e glow) . 107 vi Page F i g . 8.12 Ellipsometer readings obtained during anodization of sample Ta2 i n p o s i t i v e column of system B . . . 108 F i g . 8.13 Oxide growth during anodization of Ta2 at 0.1 mA and 0.3 mA i n p o s i t i v e column I l l F i g . 8.14 V a r i a t i o n of oxide growth rate (expressed as i o n i c current density) with t o t a l current to sample Ta2 i n p o s i t i v e column of system B at pressures of 60, 100 and 150 mtorr 113 F i g . 8.15 Electron energy diagram f o r anodizing sample drawing current density l e s s than (j + j ), showing e f f e c t of plasma e l e c t r o n energy d i s t r i -b ution 117 F i g . 9.1 Electron f i l t e r 123 F i g . 9.2 C i r c u i t used f o r e l e c t r o n f i l t e r experiments . . . 124 F i g . 9.3 Dependence of the current-voltage c h a r a c t e r i s t i c s of a gold-plated sample on the dc and r f voltages V , and V applied to the g r i d 126 gdc grf F i g . 9.4 V a r i a t i o n of sample current at f i x e d sample voltage with g r i d r f voltage, f o r d i f f e r e n t g r i d dc voltages . 127 F i g . 9.5 (a) C i r c u i t for simultaneous a p p l i c a t i o n of dc and r f biases to a sample (b) I-V r e l a t i o n s f o r sample subject to dc and dc+ r f bias conditions at a pressure of 60 mtorr . . . 129 F i g . 9.6 Current decay through aluminum sample (from O'Hanlon and Pennebaker 19 71) 131 F i g . 10.1 Estimation of oxide f i e l d from sample-probe poten-t i a l and oxide thickness data 143 F i g . 10.2 T y p i c a l v a r i a t i o n of sample p o t e n t i a l with respect to a f l o a t i n g probe during a constant current formation 146 Fi g . 10.3 V a r i a t i o n of sample-probe voltage with thickness for a niobium sample (Nbl) as recorded at the end of four formations at the same constant t o t a l current of 0.5 mA 148 Fig. 10.4 V a r i a t i o n of oxide thickness and estimated v o l -tage across oxide during anodization of a v i i Page 2 niobium sample (Nb5) at 1 mA/cm i n the nega-t i v e glow of system A . . . . , 149 Fi g . 10.5 Ionic current versus estimated oxide f i e l d (Tafel p l o t ) for anodization of sample Nb2 at 30°C i n the negative glow of system A, showing data uncorrected, ,and corrected f o r factors 150 F i g , 10.6 Io n i c current (from incremental growth rates) versus estimated oxide f i e l d during a p a r t i c u l a r constant current formation on sample Nb5 152 F i g . 10.7 Ionic current density versus oxide f i e l d f o r the anodization of sample Ta2 at 30°C i n the p o s i t i v e column of system B at d i f f e r e n t pressures . . . . . 153 Fi g . 10.8 Ellipsometry data f o r the anodization of evaporated aluminum (sample A l l ) i n the negative glow of system B 157 F i g . 10.9 Io n i c current d e n s i t i e s and estimated oxide f i e l d s f o r the anodization of sample A l l (negative glow, system B) at 40°C and 70°C 159 Fi g . 10.10 Rates of anodization of s i l i c o n at various tempera-tures i n the dc and r f discharges 161 F i g . 11.1 Computed ellipsometry curve f o r the anodization of 0 an 800A evaporated aluminum f i l m on s i l i c o n to 1280A of AI2O3 and the subsequent growth of an i n t e r -mediate f i l m of SiO^ 172 Fi g . 11.2 Computed ellipsometry curve f o r the anodization o of a 450A sputtered tantalum f i l m on s i l i c o n o to 1071A of Ta20^ and the subsequent growth of an intermediate f i l m of SiO^ 174 Fi g . 11.3 Form of high frequency capacitance-voltage curve f o r an i d e a l MIS capacitor (n-type semiconductor) . 176 Fig . 11.4 Probe f o r i n s i t u capacitance measurements 178 Fi g . 11.5 Ellipsometry data f o r the anodization of an eva-porated aluminum f i l m on a s i l i c o n substrate (sample A l - S i l ) i n the negative glow of system B 180 Fi g . 11.6 High frequency capacitance-voltage curves obtained i n s i t u at point Y i n F i g . 11.5 182 v i i i Page F i g . 11.7 Ellipsometry data f or the anodization of a 200A evaporated aluminum f i l m on s i l i c o n (sample A l - S i 2 ) , system B, negative glow) 184 F i g . 11.8 High frequency capacitance-voltage curves f o r A^O^-SiO^-Si sample (A1-S12) anodized to point Y i n F i g . 11.7 obtained with evaporated gold counterelectrode 186 F i g . 11.9 High frequency capacitance-voltage curve f o r gold electrode on sample A l - S i 2 adjacent to MIS diode of F i g . 11.8, showing l a r g e r h y s t e r e s i s 187 F i g . 11.10 High frequency capacitance voltage curves f o r sample A l - S i 2 a f t e r annealing f o r 30 minutes at 300°C i n nitrogen and then f o r one hour at 350°C i n hydrogen 189 F i g . 11.11 High frequency capacitance-voltage curve f o r sample S i l anodized i n the p o s i t i v e column of system B 190 F i g . C l Sounding probe current versus reference probe voltage for various values of sounding probe bias . ' 206 LIST OF TABLES Page Table 8.1 Rates of anodization f o r various experimental configurations . . . . . 92 Table 8.2 V a r i a t i o n of growth rate w i t h p o s i t i o n i n the negative glow 9 8 Table 8.3 Oxide growth rates obtained on a tantalum sample at d i f f e r e n t pressures and current d e n s i t i e s . . . . 101 Table 9.1 Tbe e f f e c t of the r f bia s on the oxide growth rate and f i e l d strength 137 Table 9.2 Comparison of expected change i n j . on a p p l i c a t i o n of r f b i a s , with that measured by e l l i p s o m e t r y . . . 139 x ACKNOWLEDGEMENT The author wishes to express his gratitude for the encourage-ment and guidance received from his research supervisor Dr. L. Young and also from Dr. D.L. Pulfrey during the course of this work. The author also thanks Messrs. J. Stuber, C. Chubb, A. Mac-Kenzie and H. Black for their valuable technical assistance, and Miss N. Duggan for her patience i n typing the manuscript. F i n a l l y the f i n a n c i a l support of the United States A i r Force under contract no. F33615-71-C-1886, and l a t e r the National Research Council of Canada under operating grant no. NRC A-3392 i s gra t e f u l l y acknowledged. 1. INTRODUCTION The production of t h i n i n s u l a t i n g f i l m s by the anodic ox i d a t i o n of c e r t a i n metals and semiconductors i n various l i q u i d e l e c t r o l y t e s has been studied f o r many years. The d i e l e c t r i c properties of these f i l m s are w e l l documented, and indeed such fi l m s on tantalum and aluminum are ex-te n s i v e l y u t i l i z e d i n the f a b r i c a t i o n of capacitors. More recently, develop-ments i n s o l i d state e l e c t r o n i c devices have produced s p e c i a l requirements f o r t h i n d i e l e c t r i c f i l m s and the methods by which they are f a b r i c a t e d which leave much room f o r improvement over present r e a l i t i e s . For instance, whereas anodization i n aqueous e l e c t r o l y t e s i s s t i l l used i n the f a b r i c a t i o n of tantalum t h i n f i l m RC m i c r o - c i r c u i t s , t h i s process i s a source of i o n i c contamination and i t would be advantageous i f the d i e l e c t r i c f i l m were produced by a vacuum technique, i n common with other process stages. The most widely used d i e l e c t r i c i n the ac t i v e device f i e l d i s s i l i c o n dioxide produced by thermal oxida t i o n , but the high o x i d a t i o n temperatures r e -quired create several problems, and the r e s u l t i n g f i l m s are r e l a t i v e l y poor b a r r i e r s to i o n i c contaminants. This l a t t e r property reduces the effectiveness of S102 f o r surface p a s s i v a t i o n , and together wi t h a low p e r m i t t i v i t y and poor r a d i a t i o n resistance renders i t f a r from i d e a l i n the important a p p l i c a t i o n of the gate d i e l e c t r i c i n i n s u l a t e d gate f i e l d e f f e c t devices. The process of plasma anodization studied here i s an a l t e r n a -t i v e method of f a b r i c a t i n g t h i n i n s u l a t i n g f i l m s that i s p o t e n t i a l l y a p p l i c a b l e to the above-mentioned areas. I t i s s i m i l a r to anodization i n i o n i c l i q u i d solutions except- that the l i q u i d e l e c t r o l y t e i s replaced by a gaseous oxygen plasma, which may be produced by any of several types 2 of e l e c t r i c a l discharge, e.g., dc low pressure glow, dc arc, r f or micro-wave. A t t r i b u t e s common to both processes are that oxidation can be ca r r i e d out without high temperatures, and that o x i d a t i o n rates and oxide thicknesses are e l e c t r i c a l l y c o n t r o l l e d . Being a vacuum technique, the plasma method has the important advantage of freedom from e l e c t r o l y t e i o n i c contamination, and i t can be used to produce fi l m s of materials which are soluble i n l i q u i d e l e c t r o l y t e s . There has been considerable i n t e r e s t i n the technique, and i t has been u t i l i z e d i n the experimental f a b r i c a t i o n of t h i n f i l m c a pacitors, metal-oxide-semiconductor t r a n s i s t o r s (MOST's) and Josephson junct i o n s . The use of alumina produced by plasma anodization as gate i n s u l a t o r i n s i l i c o n MOST's has r e s u l t e d i n improved performance over thermal SiO„ i n s u l a t e d devices i n the areas of r a d i a t i o n resistance and long term s t a b i l i t y ( M i c h e l e t t i et a l . 1970). However, a p p l i c a t i o n of the process has as yet been r e s t r i c t e d to these e x p e r i -mental i n v e s t i g a t i o n s , i n which c o n t r o l was achieved i n a l a r g e l y empi-r i c a l manner. This can be a t t r i b u t e d i n part to a l i m i t e d understanding of the nature of the phenomenon, and a p o r t i o n of the present work i s aimed at improving t h i s s i t u a t i o n by studying the k i n e t i c s of the process, that i s the dependence of the oxide growth rate on measurable parameters. Related to t h i s aspect of the work i s the question of whether the oxygen atoms incorporated i n the oxide o r i g i n a t e d as negative ions i n the plasma as has been assumed by many i n v e s t i g a t o r s , and s p e c i f i c experiments were devised to resolve t h i s p o i nt. The production of t h i n i n s u l a t i n g f i l m s of metal oxides on s i l i c o n i s also i n v e s t i g a t e d f o r MOS device a p p l i c a t i o n s . To f a c i l i t a t e the task of r e l a t i n g anodization rates to conditions i n the plasma, the r e l a t i v e l y w e l l documented dc cold cathode glow discharge was selected f o r the plasma source, and an automated 3 ellipsometer was used f o r continuous i n s i t u monitoring of the thickness of the growing oxide. The t r a n s i t i o n metals tantalum and niobium were used predominantly as sample materials since they e x h i b i t consistent ano-d i z a t i o n behaviour i n aqueous e l e c t r o l y t e systems. The remainder of the thesis i s di v i d e d up as f o l l o w s . The next chapter i s a review of previous work on plasma anodization, chapter 3 compares the o v e r a l l features of the process with those of s o l u t i o n anodization, and chapter 4 examines some t h e o r e t i c a l aspects of plasma-s o l i d i n t e r f a c e s and gas discharge phenomena. Chapters 5 and 6 deal r e s -p e c t i v e l y w i t h the techniques of Langmuir probe diagnostics and e l l i p -sometry as applied to anodization s t u d i e s , and experimental considerations are given i n chapter 7. Chapters 8 to 10 describe experimental i n v e s t i -gations i n t o three aspects of plasma anodization: the e f f e c t of d i s -charge conditions; the r o l e of plasma negative i o n s ; and the i o n i c current-oxide f i e l d r e l a t i o n . The a p p l i c a t i o n of the process i n the f a b r i c a t i o n of i n s u l a t e d gate devices i s considered i n chapter 11, and conclusions are presented i n chapter 12. 4 2. REVIEW OF PREVIOUS WORK ON PLASMA ANODIZATION Observations on the oxidation of the surface of a metal sample i n e l e c t r i c a l contact with the anode of an e l e c t r i c a l discharge i n oxygen have been made f o r many years (Ignatov 1946, 1957), and the phenomenon was also observed with s i l i c o n and germanium (Nazarova 1962). However, Miles and Smith 1963 appear to have been the f i r s t to u t i l i z e the process f o r the c o n t r o l l e d production of oxide f i l m s by l o c a t i n g and b i a s i n g the sample separately from the discharge anode. These workers were able to anodize a wide v a r i e t y of metals and semiconductors ( A l , Ta, Mg, Cr, Sb, B i , Be, Ge, Si) and the method has since been applied to other materials by T i b o l 1965 ( T i ) , Whitmore and Vossen 1965 ( L a - T i ) , Weinrich 1966 (GaAs) Ramasubramanian 1970 (Zr, z i r c a l l o y ) , Lee et a l . 1970 (Nb) , N o r r i s and Zaininger 1970 (Hf), O'Hanlon 1970 (La, Mo, W), Simpson and Lucas 1970 (Y, Gd, Y-Fe, Gd-Fe) and Husted et a l . 1971 (V). The l i t e r a t u r e on plasma anodization up to 1970 has been reviewed r e c e n t l y by Dell'Oca et a l . 1971 and w i l l be dealt with only b r i e f l y here. Much of the e a r l y work was concerned with the a p p l i c a t i o n of anodization i n the negative glow region of the dc discharge to the production of t h i n f i l m capacitors (Miles et a l . 1963; T i b o l and H u l l 1964; T i b o l and Kaufmann 196 4; Johnson 1964) and l a t e r to MOS t r a n s i s t o r f a b r i c a t i o n (Waxman and Mark 1969 ; M i c h e l e t t i et a l . 1970). Other methods of producing the plasma have been i n v e s t i g a t e d , i n c l u d i n g r f induced (Woorledge and White 1967; Mik-h a l k i n and Odynets 1970; Scholtz 1971) and microwave exc i t e d (Ligenza 1965; Kraitchman 1967; Skelt and Howells 1967) discharges, and more r e -cently a hot cathode dc arc discharge (Ligenza and Kuhn 1970). A l l of these methods of plasma anodization y i e l d e d very low values of current 5 e f f i c i e n c y , i . e . , the f r a c t i o n of the sample current which i s i o n i c (oxide producing), these values u s u a l l y being l e s s than 5% i n contrast to up to 99% att a i n a b l e i n s o l u t i o n anodization. However, the ac t u a l o growth rates v a r i e d considerably, from a few A/min i n dc cold cathode o discharges (Lee et a l . 1970) to up to 400 A/min i n dense microwave plasmas (Kraitchman 1967), although the r e l a t i v e i n f l u e n c e of plasma parameters and sample temperature on these rates was not c l a r i f i e d . In t h i s respect, i t should be pointed out that most workers have not attempted to c o n t r o l substrate temperature, and very few have used i n s i t u methods of oxide thickness determination (Locker and Skolnick 1968,,Lee et a l . 1970) and even these were not continuous monitoring systems. Thus while many experiments on plasma anodization have been described, the data sheds l i t t l e l i g h t on the mechanisms involved, a be.tter understanding of which i s important f o r improved c o n t r o l and optimum a p p l i c a t i o n of the process. For instance, i t has been l a r g e l y assumed that the oxide growth process was analogous to that occurring i n s o l u t i o n anodization, with the forming voltage across the oxide simply given by the bias voltage applied to the sample. In more recent s t u d i e s , Ol i v e et a l . 1970, Ramasubramanian 1970, Lee et a l . 1970 and O'Hanlon 1970 have attempted to c l a r i f y t h i s s i t u a t i o n . Some of t h i s work i s reviewed i n more d e t a i l i n sections 4.2 and 10.2. Also Miles and Smith's o r i g i n a l postulate (1963) that the negative ions i n the plasma were the source of the oxygen incorporated i n the oxide appears to have been gen-e r a l l y accepted. This point was in v e s t i g a t e d recently by O'Hanlon and Pennebaker 1971, but t h e i r conclusions (which supported Miles and Smith's postulate) are shown i n secti o n 9.3 to be u n j u s t i f i e d , and i n fa c t i n c o r -rect , 6 D i e l e c t r i c f i l m s produced by plasma anodization have been found to have s i m i l a r properties to f i l m s of the respective materials produced by s o l u t i o n anodization, f o r instance Waxman and Zaininger 1968 obtained A^Og films having a r e l a t i v e p e r m i t t i v i t y of 7.6 and l o s s f a c t o r of 2% @ 1 kHz, which are comparable w i t h wet-anodic A^O^, and Lee et a l . 1970 found plasma-grown Ta^O^ and Nb^O^ f i l m s to have p e r m i t t i v i t i e s of 17 and 34 r e s p e c t i v e l y , and loss f a c t o r s around 1% @ 1 kHz. The l a t t e r p e r m i t t i v i t y values are somewhat lower than the respective values of 21 and 42 f o r solution-grown oxides of Ta and Nb, and t h i s was supported by lower values of r e f r a c t i v e index as determined by el l i p s o m e t r y . Plasma anodization of s i l i c o n i n a dc arc discharge (Ligenza and Kuhn 1970) has provided oxides with high d i e l e c t r i c strengths and very s t a b l e i n t e r -face properties equal to the very best reported f o r thermal oxides. 7 3. COMPARISON OF PLASMA- AND SOLUTION-ANODIZATION 3.1 G e n e r a l F e a t u r e s o f S o l u t i o n A n o d i z a t i o n Oxide f i l m s may be grown on many me t a l s and some group IV and I I I - V semiconductors by immersing the m a t e r i a l and a'cathode i n a s u i t a b l e e l e c t r o l y t e s o l u t i o n and b i a s i n g the m a t e r i a l a n o d i c a l l y (Young 1961). The t r a n s p o r t o f m e t a l and/or oxygen i o n s i n the f i l m , w hich must o c c u r f o r the f i l m to grow, i s a i d e d by the e l e c t r i c f i e l d e s t a b l i s h e d i n the f i l m by t h e a p p l i e d v o l t a g e , the e l e c t r o l y t e s e r v i n g as a c o n d u c t i n g medium and s o u r c e of oxygen. The t o t a l c u r r e n t through the o x i d e , as r e g i s t e r e d i n the b i a s i n g c i r c u i t , i s found t o be almost e n t i r e l y i o n i c f o r many m a t e r i a l s , e.g., Ta, Nb and A l , the e l e c t r o n i c component b e i n g v e r y s m a l l . I f the c u r r e n t d e n s i t y through the o x i d e i s m a i n t a i n e d con-s t a n t by the b i a s i n g c i r c u i t r y , t h e n the f i l m w i l l grow at a c o n s t a n t r a t e , and any d e s i r e d t h i c k n e s s D can be o b t a i n e d s i m p l y by t e r m i n a t i n g the c u r r e n t a f t e r a c e r t a i n time when the a p p r o p r i a t e charge Q has been pa s s e d . For an o x i d e of f o r m u l a M 0 whose d e n s i t y i s p, Q i s g i v e n by Faraday's x y law: o f e l e c t r o l y s i s as Q = 2ypFDA/mn (3.1) where A i s the sample a r e a , F i s the Faraday, m i s the m o l e c u l a r w e i g h t of the o x i d e and n the c u r r e n t e f f i c i e n c y , i . e . , the p r o p o r t i o n o f charge used on o x i d e growth. D u r i n g f o r m a t i o n a t c o n s t a n t c u r r e n t d e n s i t y , the v o l t a g e i n c r e a s e s l i n e a r l y w i t h t h i c k n e s s to m a i n t a i n the o x i d e f i e l d c o n s t a n t . I n making f i l m s f o r a p p l i c a t i o n s , i t i s u s u a l t o form at c o n s t a n t c u r r e n t u n t i l a c e r t a i n v o l t a g e i s reached, and then h o l d the a n o d i z a t i o n c e l l a t t h i s c o n s t a n t v o l t a g e f o r a f i x e d time o f some h o u r s . D u r i n g 8 t h i s period the f i l m continues to grow, but at a continuously decreasing rate due to the decreasing oxide f i e l d , and the current decays with time towards leakage (non film-forming) l e v e l s . I t i s be l i e v e d that weak spots i n the f i l m may be. 'patched' during t h i s f i n a l constant voltage p e r i o d , producing f i l m s with lower leakage currents. The anodization constant or f i l m thickness-voltage r a t i o obtained f o r the above method i s often r e f e r r e d t o , and i s sometimes i n t e r p r e t e d as the r e c i p r o c a l of the oxide f i e l d strength at the end of the formation process, but s t r i c t l y t h i s implies formation at constant voltage to a f i x e d current l e v e l (indepen-dent of voltage) rather than f o r a f i x e d time. During both constant current and constant voltage formation the r e l a t i o n between i o n i c current density JL , mean oxide f i e l d i n t e n s i t y E and temperature T i s found to be approximated by the e m p i r i c a l equation J ± = A exp(BE) (3.2) where A = J exp(-W/kT) o B = C/T, k i s Boltzmann's constant and J , W and C are independent of T and E. o In a r r i v i n g at such a dependence, the f i e l d E i s generally obtained from the o v e r p o t e n t i a l , defined as the excess of the c e l l v o l -tage over the t h e o r e t i c a l r e v e r s i b l e value, corrected f o r any ohmic p o t e n t i a l differences i n the s o l u t i o n . The f i e l d strengths required to produce i o n i c current d e n s i t i e s i n the range of .10 ^  to 10 1 A/cm^ are usual l y i n the range 10^ to 10^ V/cm, and the maximum f i l m thicknesses a t t a i n a b l e by s o l u t i o n anodization are generally l i m i t e d by the voltage across the f i l m exceeding some break-down threshold, e i t h e r at flaws i n the f i l m or at the film/masking m a t e r i a l 9 i n t e r f a c e . C o n s i d e r a b l e q u a n t i t i e s o f e l e c t r o l y t e s p e c i e s may be i n c o r -p o r a t e d i n t o s o l u t i o n grown f i l m s , p a r t i c u l a r l y w i t h more c o n c e n t r a t e d s o l u t i o n s ( e . g . , o f E^SO^ o r H^PO^), as has been shown by t r a c e r (Ran-d a l l e t a l . 1965) and a c t i v a t i o n s t u d i e s (Amsel e t a l . 1969). These i m p u r i t i e s , and perhaps a l s o those from the m e t a l s u b s t r a t e i f the l a t t e r i s a s p u t t e r e d f i l m , a p p r e c i a b l y a f f e c t p r o p e r t i e s o f the o x i d e such as r e f r a c t i v e i n d e x , p e r m i t t i v i t y and i o n i c c o n d u c t i v i t y , as was shown i n a r e c e n t s t u d y u t i l i z i n g e l l i p s o m e t r y ( D e l l ' O c a 1969). The pr e s e n c e o f such i o n i c and p o t e n t i a l l y m o b i l e i m p u r i t i e s i s s t r o n g l y a t v a r i a n c e w i t h the requirements of i n s u l a t i n g f i l m s f o r a c t i v e s o l i d s t a t e d e v i c e s . Another phenomenon which causes changes i n the o x i d e p r o p e r t i e s i s t h a t of p h o t o s t i m u l a t e d growth under u l t r a - v i o l e t i r r a d i a t i o n ( D e l l ' O c a 1969). D u r i n g t h i s p r o c e s s , i n a d d i t i o n t o the presence of a p h o t o e l e c t r o n i c c u r -r e n t , the i o n i c c u r r e n t a t a g i v e n f i e l d s t r e n g t h i s enhanced, and the r e s u l t i n g photogrown m a t e r i a l has o p t i c a l p r o p e r t i e s v e r y d i f f e r e n t from those o f the normal o x i d e . 3.2 The H i g h F i e l d I o n i c C o n duction P r o c e s s - C l a s s i c a l Theory W i t h some n o t a b l e e x c e p t i o n s , t h e k i n e t i c s o f s o l u t i o n a n o d i -z a t i o n as e x p r e s s e d by Eqn. 3.2 are w e l l accounted f o r by t h e o r i e s o f h i g h f i e l d i o n i c c o n d u c t i o n ( D e l l ' O c a e t a l . 1971). I n the c l a s s i c a l p i c t u r e o f i o n i c c o n d u c t i o n , which was o r i g i n a l l y a p p l i e d t o the motion of d e f e c t s ( i . e . i n t e r s t i t i a l i o n s o r vacant l a t t i c e s i t e s ) i n a c r y s t a l -l i n e . s o l i d , t he p o t e n t i a l energy o f an i o n i s taken to be a t i m e - i n d e p e n -dent p e r i o d i c f u n c t i o n of the c o - o r d i n a t e s of the i o n . The a p p l i c a t i o n of a f i e l d E (the m a c r o s c o p i c f i e l d i n the d i e l e c t r i c ) i s supposed to 10 add a term (~qxE), where x i s the coordinate of the ion resolved in the direction of E and q i s the charge on the ion (Fig. 3.1). Thus to a f i r s t approximation, i f a i s the distance between the positions of minima and maxima of the potential energy, the energy b a r r i e r opposing a jump from one s i t e to the next i s reduced from W to W-qaE. The ion i s treated as a nearly independent harmonic o s c i l l a t o r whose loose coupling to the l a t t i c e at temperature T causes i t to have a chance of having the a c t i -vation energy W-qaE equal to exp-[(W-qaE)/kT]. If the frequency of v i -bration of the ion about i t s mean position i s v, and the concentration of defects i s n, then at f i e l d s high enough to make jumps against the f i e l d unlikely the i o n i c current density i s J ± = 2qanv exp-[(W-qaE)/kT] (3.3) While this equation i s c l e a r l y of the experimentally observed form 3.2, the application of this theory to anodic oxides i s complicated by the fact that a range of activation energies and distances would be expected i n such amorphous films. Another problem i s that the c l a s s i c a l theory sug-gests that one type of ion, either metal or oxygen, should dominate i n the conduction process through a lower activation energy, whereas with tantalum, niobium, tungsten and aluminum both metal and oxygen ions are mobile (Davies et a l . 1965), and to about equal extents for aluminum and tantalum (Randall et a l . 1965). Precise work over a wide range of currents using o p t i c a l methods of thickness measurement on tantalum (Young 1960a) and niobium (Young and Zobel 1966) has shown that the results are more exactly described by a quadratic dependence of log on f i e l d E: J. = J exp -[(W-aE+(3E2)/kT] l o I : Distance F i g . 3.1 Supposed p o t e n t i a l energy of i o n versus distance w i t h and without an applied f i e l d . 12 Explanations of t h i s nonlinear dependence have been proposed,e.g. by Young and Zobel 1966 i n terms of a channelling model of i o n i c conduction, and by Ord et a l . 1972 i n terms of v a r i a t i o n s i n the l o c a l e f f e c t i v e f i e l d / a pplied f i e l d r a t i o due to a f i e l d dependence of the r e l a t i v e p e r m i t t i -v i t y which has been observed experimentally. F i n a l l y , the c l a s s i c a l approach can be extended to account f o r some (but not a l l ) types of t r a n s i e n t behaviour by in t r o d u c i n g the idea of f i e l d - a s s i s t e d thermal a c t i v a t i o n of ions from l a t t i c e s i t e s into-i n t e r s t i t i a l s i t e s to create Frenkel defects (Bean et a l . 1956). This gives a mechanism which causes a delayed change i n the concentration of mobile species on changing the f i e l d , and q u a l i t a t i v e l y explains such e f f e c t s as the f i e l d going through a maximum when the current i s increased from one constant value to another. 3.3 General Features of Plasma Anodization The term plasma ano.dization i s here r e s t r i c t e d to the process i n which an oxide f i l m i s made to grow on the surface of a m a t e r i a l ex-posed to an e l e c t r i c a l discharge i n oxygen by e x t e r n a l l y b i a s i n g the sample so that i t draws a p o s i t i v e current from the discharge*. As a consequence of the properties of gaseous plasmas (Engel 1965, Cobine 1958) the s u b s t i t u t i o n of an oxygen plasma f o r the s o l u t i o n e l e c t r o l y t e gives r i s e to various departures from s o l u t i o n anodization conditions: Oxides can be formed by exposure of a mat e r i a l to a plasma without drawing a net current from the l a t t e r v i a an external b i a s i n g source, and the growth i s reported to follow e i t h e r a logarithmic law i n dc d i s -charges (Miles and Smith 1963), or a parabolic law i n microwave discharges (Kraitchman 1967). 13 (1) The method of b i a s i n g the sample w i l l depend on whether or not the discharge i s e x c i t e d v i a i n t e r n a l e lectrodes, as shown i n F i g . 3.2. For instance i n the dc discharges (hot or cold cathode, glow or arc) the anode provides a convenient p o t e n t i a l reference, usu a l l y grounded, and the sample may be biased w i t h respect to t h i s reference. In discharges e x c i t e d by an e x t e r n a l l y induced r f or microwave f i e l d , an a d d i t i o n a l electrode must be introduced to com-pl e t e the dc c i r c u i t , and t h i s arrangement i s perhaps more analogous to s o l u t i o n anodization. (2) In s o l u t i o n anodization c e l l s , the p o t e n t i a l drop through the e l e c t r o l y t e i s t y p i c a l l y of the order of a v o l t and i s s t a b l e , but i n the plasma systems the p o t e n t i a l drop though the discharge from the reference electrode to the v i c i n i t y of the sample may be much l a r g e r , and v a r i a b l e with time. In the dc discharge t h i s p o t e n t i a l difference can be as large as 100 V, depending on the pressure, discharge current, configuration and condition of the electrodes and the sample l o c a t i o n . This,'together w i t h space charge sheath regions u s u a l l y present at plasma/solid i n t e r f a c e s , can lead to large errors i n estimating the p o t e n t i a l d i f f e r e n c e across the oxide f i l m , as w i l l be pointed out i n secti o n 4.1. (3) An important difference from s o l u t i o n anodization conditions i s that l i q u i d e l e c t r o l y t e s contain few, i f any, free e l e c t r o n s , whereas the plasmas involved here have large concentrations of electrons 7 13 -3 (10 - 10 cm ) with mean energies of a few e l e c t r o n - v o l t s . Many of these electrons are able to enter the oxide, and t h i s coupled with the much lower energies of the various i o n i c species may be the major cause of the large e l e c t r o n i c f r a c t i o n of the t o t a l current 14 <» H V o-u__ Q ®— BIAS SUPPLY (a) dc DISCHARGE RF OR MICROWAVE COUPLER - o ® BIAS SUPPLY (b) hf - EXCITED DISCHARGE F i g . 3.2 Bia s i n g arrangements f o r plasma anodization. 15 density i n plasma anodization. (4) As mentioned i n s e c t i o n 3.1, l i q u i d e l e c t r o l y t e s act as a source of contaminant species f o r the oxide f i l m , whereas the e l e c t r o l y t e i n the gaseous system contains only oxygen. Thus the plasma-anodized oxides can be expected to be purer than those formed by wet anodiza-t i o n ( i n p r a c t i c e there may be contamination from the discharge cham-ber w a l l s or ele c t r o d e s ) . (5) L i q u i d e l e c t r o l y t e s generally have some degree of solvent a c t i o n , which may hinder the formation of oxides on c e r t a i n m aterials such as Ge, GaAs and V. The plasma e l e c t r o l y t e enables oxide f i l m s to be grown on these m a t e r i a l s , as reported i n chapter 2. However, during plasma anodization the oxide surface i s c o n t i n u a l l y bombarded by various charged and uncharged p a r t i c l e s , and under c e r t a i n con-d i t i o n s s p u t t e r i n g of the oxide f i l m by energetic species can occur (Locker and Skolnick 1968), and compete with the anodization process i n a manner somewhat s i m i l a r to oxide d i s s o l u t i o n . (6) Whereas sample temperatures i n s o l u t i o n anodization do not normally exceed the 0 - 100°C range, a much wider range i s p o s s i b l e i n plasma anodization, but temperature c o n t r o l and measurement i s generally more d i f f i c u l t . (7) The plasma i s a continuous source of uv r a d i a t i o n , absorption of which during oxide growth may lead to s t r u c t u r a l d i f f e r e n c e s from ordinary anodic oxides (see sec t i o n 3.1). In s p i t e of the major complications represented by (2) and (3) above, the gross behaviour of anodic oxide growth i n low pressure dc discharges i s s i m i l a r to s o l u t i o n anodization. Thus, when the current drawn by the sample i s maintained constant, the oxide grows at a constant 16 rate and the sample p o t e n t i a l r i s e s approximately l i n e a r l y w i t h time, whereas with a constant voltage applied to the sample the growth rate and current both decrease with time. In view of the extremely low current e f f i c i e n c i e s , however, these observations alone are not s u f f i c i e n t evidence f o r i d e n t i c a l mechanisms i n the two processes. The anodization of s i l i c o n i n a h i g h l y i o n i z e d microwave d i s -charge has been found to follow a p a r a b o l i c growth law i n d i c a t i v e of d i f f u s i o n c o n t r o l (Ligenza 1965; Kraitchman 1967), but i n t h i s case both the sample temperature and discharge pressure were r e l a t i v e l y high, about 400°C and 500 mtorr r e s p e c t i v e l y . 17 4. THEORETICAL ASPECTS OF PLASMA ANODIZATION 4.1 Introduction In attempting to formulate an understanding of the plasma ano-d i z a t i o n process, various questions of a fundamental nature need to be dealt with. For instance, what i s the p r i n c i p a l mechanism by which the oxide-forming species are transported through the oxide f i l m , and what are the roles of the plasma and i t s various constituent species? To i n v e s t i g a t e whether a high f i e l d i o n i c conduction mechanism i s operative i n the plasma oxide as i n s o l u t i o n anodization, some estimate of the e l e c t r o s t a t i c f i e l d i n the oxide must be made from measurements of the p o t e n t i a l of the sample being anodized. This requires cognizance of cer-t a i n plasma p r o p e r t i e s , i n p a r t i c u l a r the behaviour of sheath regions, as o u t l i n e d i n the f o l l o w i n g s e c t i o n . In the subsequent s e c t i o n i t i s shown that across-the-sheath transport of plasma negative ions could account for the observed dependence of anodization rate on estimated oxide f i e l d , and i n the f i n a l two sections the production of gaseous negative ions and the plasma properties of the low pressure cold cathode dc glow discharge i n oxygen are examined. 4.2 Plasma Sheath Theory 4.2.1 General A gaseous plasma i s a c o l l e c t i o n of p o s i t i v e , negative and n e u t r a l p a r t i c l e s having only a small or zero net charge density. In discharges i n e l e c t r o p o s i t i v e gases the charged p a r t i c l e s c o n s i s t of electrons and p o s i t i v e ions, whereas oxygen plasmas also contain the s i n g l y charged negative ions 0 and 0^. Since the plasma electrons d i f f u s e much more r a p i d l y than the heavier ions, any surface exposed to 18 the plasma but drawing no net c u r r e n t from the l a t t e r a c q u i r e s a n e g a t i v e charge and a b a l a n c i n g sheath o f p o s i t i v e space charge develops o v e r the s u r f a c e , such t h a t the p o t e n t i a l d i f f e r e n c e V , a c r o s s t h i s s h e a t h sh r e p e l s a l l e l e c t r o n s except a f l u x which w i l l recombine e x a c t l y w i t h the f l u x o f p o s i t i v e i o n s r e a c h i n g the s u r f a c e . To a f i r s t a p p r o x i m a t i o n the e l e c t r i c f i e l d i n the sheath decreases to zero a t i t s o u t e r boundary w i t h the e l e c t r i c a l l y n e u t r a l plasma, so t h a t the p a r t i c l e s c r o s s t h i s boundary by v i r t u e o f t h e i r random therm a l v e l o c i t i e s . The r e s u l t i n g f l u x o f p o s i t i v e i o n s i s t h e r e f o r e independent of V g^, and c o n s t i t u t e s the random p o s i t i v e i o n c u r r e n t d e n s i t y to the s u r f a c e g i v e n by (see Appendix A) 3 + g = n +ev +/4 (4.1) where e i s the magnitude of the e l e c t r o n charge ( i o n s assumed s i n g l y c h a r g e d ) , v + i s the mean random v e l o c i t y o f the i o n s and n + t h e i r number d e n s i t y . The e l e c t r o n c u r r e n t t o the s u r f a c e i s g i v e n by those e l e c t r o n s c r o s s i n g the o u t e r sheath boundary from the plasma which overcome the r e t a r d i n g p o t e n t i a l V ^ . I f i t i s assumed t h a t .due t o r a n d o m i s i n g c o l l i s i o n s the plasma e l e c t r o n s are i n t h e r m a l e q u i l i b r i u m and have a Maxwell d i s t r i b u t i o n of v e l o c i t i e s w i t h temperature T g (see Appendix A ) , then the f r a c t i o n h a v i n g an energy g r e a t e r than eV i s g i v e n by the Boltzmann f a c t o r , e x p r - e V g h / k T e ] , and so i n the absence o f c o l l i s i o n s i n the sheath r e g i o n the e l e c t r o n c u r r e n t d e n s i t y r e a c h i n g the s u r f a c e i s ^e = ( _ n e 6 v e / 4 ) e x p [ " e V s h / k T e ] = j exp[-eV ,/kT ] (4.2) J e s sh e 19 where n and v a r e the number density and mean random v e l o c i t y of the e e electrons respectively. For the e l e c t r i c a l l y i s o l a t e d surface, the sheath space charge i s such that V , gives j = - i , . In this s i t u a t i o n V , sh b J e +s sh i s t y p i c a l l y a few v o l t s , being a measure of the higher electron energies i n the plasma, and the surface i s said to be at ' f l o a t i n g ' or 'wall' potential V^. In the case of the surface of a metal electrode, V , can be sh increased or decreased by external biasing so that j as given by Eqn. 4.2 no longer balances j + g > and a net current i s drawn from the plasma. If the electrode i s biased p o s i t i v e l y with respect to (as i n plasma anodization), more electrons are able to overcome the reduced retarding potential V , and a net electron current i s drawn from the plasma. This r sh r electron current increases with increasing positive bias u n t i l V ^ = 0, at which point the positive sheath disappears and the surface draws the saturation value of electron current i defined i n Eqn. 4.2 i n addition Jes to i , . The metal surface i s now removing the same number of each species as would cross from one side of an imaginary plane replacing the surface, and the electrode i s considered to register plasma po t e n t i a l V , i n that the rest energy of an electron i s constant at i t s bulk plasma l e v e l up to the surface. Further positive biasing produces a negative space charge sheath and a potential b a r r i e r which repels positive ions, so that Eqns. 4.1 and 4.2 no longer apply and the net current to the electrode increases by decreasing the positive ion current j + . As j is reduced to zero the net current should saturate at j but in practice i t continues to increase by the attraction of electrons from further regions of the plasma and by impact ionization i n the sheath f i e l d . 20 4.2.2 The plasma anodization case The plasma anodization case of an oxide-covered metal sample electrode drawing a current density l e s s than (j + from the plasma i s represented by the e l e c t r o n energy diagram of F i g . 4.1, which also shows an a u x i l i a r y f l o a t i n g electrode located nearby. For a known oxide thickness, estimation of the mean e l e c t r o s t a t i c f i e l d i n the oxide requires the determination of V , the d i f f e r e n c e i n p o t e n t i a l between ox two points j u s t i n s i d e the inner and outer oxide surfaces. I t i s evident that the measurable p o t e n t i a l d i f f e r e n c e , i . e . , the d i f f e r e n c e i n the metal Fermi l e v e l s , includes p o t e n t i a l drops across sheath regions i n a d d i t i o n to gradients i n the bulk plasma and work function d i f f e r e n c e s , and the sample sheath pd i s a function of sample current. 4.3 The Metal/Oxide/Space_Charge Sheath/Plasma System In previous'work i n v o l v i n g ellipsometry and plasma probe measurements which recognized the complications mentioned i n the pre-ceding s e c t i o n , evidence of an exponential dependence of i o n i c current on estimated oxide f i e l d strength was obtained f o r the anodization of tan-talum and niobium i n the negative glow of a dc cold cathode discharge (Olive 1969; Lee et a l . 1970). On the other hand, Thompson 1961a (see 2 section 4.5) had estimated a random current density of 1.8 pA/cm due to negative ions from the plasma of a cold cathode oxygen glow discharge, which i s s i m i l a r to the oxide i o n i c currents obtained i n the above ano-d i z a t i o n studies. I t i s possible then, that the oxygen ions incorporated i n the oxide o r i g i n a t e d as negative ions i n the plasma, and f o r t h i s reason the transport of negative ions and electrons across the sheath and the p o t e n t i a l d i s t r i b u t i o n i n the metal/oxide/space charge sheath/plasma METAL OXIDE SHEATH PLASMA SHEATH METAL (SAMPLE) (PROBE) F i g . 4.1 One-dimensional e l e c t r o n energy band diagram f o r an o x i d e - c o v e r e d m e t a l sample drawing a c u r r e n t d e n s i t y l e s s than ( j £ S + J + g ) > a n <^ nearby f l o a t i n g probe. E = Fermi energy l e v e l ; 0g = samnle m e t a l work f u n c t i o n ; y = e l e c t r o n a f f i n i t y o f the o x i d e ; V = p o t e n t i a l d i f f e r e n c e a c r o s s ox ox the o x i d e ; V , = p o t e n t i a l d i f f e r e n c e a c r o s s sample s h e a t h ; Vc , = p o t e n t i a l d i f f e r e n c e a c r o s s f l o a t i n g sh J - S U ^ probe sheath; 0 = probe m e t a l work f u n c t i o n . M 22 system s h o u l d be examined. The expected e l e c t r o s t a t i c f i e l d and p o t e n t i a l d i s t r i b u t i o n s i n t h i s system d u r i n g plasma a n o d i z a t i o n , i n the absence of o x i d e space charge, a r e shown i n F i g . 4.2. A f i n i t e e l e c t r i c f i e l d e x i s t s i n the o x i d e , and the e l e c t r o n c u r r e n t d e n s i t y a c r o s s the sheath j exceeds the s a t u r a t e d p o s i t i v e i o n c u r r e n t j _ j _ s s s o t h a t i n the absence o f any s e c o n -dary e m i s s i o n or r e f l e c t i o n of e l e c t r o n s , a n e t e l e c t r o n c u r r e n t d e n s i t y o f J = j + J _ L < j + j • (4-3) J e  J+s es J+s e n t e r s the o x i d e , where j and j + s are g i v e n by e q u a t i o n s 4.2 and 4.1 r e s p e c t i v e l y . I t would seem t h a t once e l e c t r o n s from the plasma have o v e r -come the r e t a r d i n g p o t e n t i a l V and reached the o x i d e s u r f a c e , t h e r e S h i s no energy b a r r i e r a g a i n s t e n t r y i n t o the o x i d e . E l e c t r o n t r a n s p o r t through the o x i d e i s thus l i k e l y to be determined by a b u l k mechanism such as the f i e l d - a s s i s t e d t h e r m a l e x c i t a t i o n of t r a p p e d e l e c t r o n s i n t o the c o n d u c t i o n band ( P o o l e - F r e n k e l e m i s s i o n ) . I f the P o o l e - F r e n k e l e f f e c t i s o p e r a t i v e , the dependence of e l e c t r o n c u r r e n t on o x i d e f i e l d E r ox i s g i v e n (Goruk et a l . 1966) by J = G E exp[(-e/kT) ($ - /eE '/TTE ) ] (4.4) o ox o x o x where <j> i s the depth of the t r a p p o t e n t i a l w e l l , e i s the ( h i g h f r e -B quency) p e r m i t t i v i t y of the o x i d e , and G q i s a c o n s t a n t * . T h i s e x p r e s s i o n * A s i m i l a r dependence has been observed i n wet anodic T a ^ , N b ^ and A l 0 by Jaeger et a l . 1972 f o r e l e c t r o n i c c u r r e n t d e n s i t i e s up to 10mA/cm i n j e c t e d w i t h the a i d of a s e m i c o n d u c t i n g o x i d e l a y e r o ver the v a l v e m e t a l o x i d e . Fig. 4.2 E l e c t r o s t a t i c f i e l d and potential distributions i n the metal/oxide/space charge sheath/plasma system, neglecting p o t e n t i a l gradients in plasma. 24 e o-1/2 w i l l be dominated by the exponential dependence on ( E o x ) • I t may b argued that i n the steady state the surface charge density located at thouter oxide surface has a value such that V , and E y i e l d e l e c t r o n sh ox currents given by Eqns. 4.3 and 4.4 which are equal. This i s equi-valent to assuming that the f i e l d In the oxide i s determined s o l e l y by the e l e c t r o n i c conduction mechanism i n the bulk of the oxide and the e l e c t r o n i c current c o n t i n u i t y requirement. Now i f the negative ions i n the plasma have a Maxwellian v e l c i t y d i s t r i b u t i o n with an equivalent temperature T_, then the negative ion f l u x across the sheath to the oxide surface w i l l be given by a r e l a t i o n s i m i l a r to Eqn. 4.2: j = j exp t-eV ,/kT 1 (4.5) -s sh where j _ g i s the random negative ion current density i n c i d e n t on the outer sheath boundary. Equations 4.2 and 4.5 give l n j _ = ( T e / T _ ) [ l n j e - l n j e g ] + l n j _ g (4.6) Furthermore, f o r p r a c t i c a l l e v e l s of anodizing current, j + s can be ne-glected i n 4.3, so that using 4.4, equation 4.6 becomes 1 /? = ( T e / l _ ) [ l n E o x + (e/kT) ( e E ^ / r c e ^ ) i / + A ] + l n j _ s (4.7) where A i s independent of j _ . This can be re w r i t t e n as j _ = B ( E o x ) T e / T - exp [(T e/T_) (e/kT) ( e E o x / T r e o x ) 1 / 2 ] where B i s independent of E . That i s , f o r large oxide f i e l d s the current r ox of negative ions reaching the oxide from the plasma i s exponentially de-pendent on the square root of the oxide f i e l d . Thus, i f the supply of negative oxygen ions from the plasma was the rate determining step i n plasma anodization, an exponential dependence of oxide growth rate on 25 (E ) might be. expected . In examining experimental growth rate-oxide f i e l d data for a souare law or linear dependence of Inj . on E , the 4 X ox range of the data should be considered. Furthermore, the measured values for E are only estimations, given by for example V / D where ox ' ° J 1 sp D i s the oxide thickness (determined by ellipsometry) and V ^ i s the metal sample potential measured with respect to a fl o a t i n g reference electrode (probe) located just outside the space charge sheath of the sample. Referring to Fig. 4.2 and neglecting work function differences, V = V - V , + V . , (4.8) sp ox sh fsh where V^ g^ i s the potential drop across the sheath of the f l o a t i n g probe, and from equation 4.7, V q x = a [ I n ( j _ / C ) ] 2 (4.9) w h e r e a = (kT/e) 2 (ire D/e) and InG = (T e/T_) [ l n G o E Q x - l n j e s - (e^/kT)] - l n j _ s Also i f the sheath pd of the sample when the l a t t e r i s e l e c t r i c a l l y i s o -lated, i . e . when j £ = j , i s equal to the f l o a t i n g probe sheath pd V £ s ^ 5 then equation 4.2 becomes 3 +s = ^es e ^ - e V f s h / k T e ] <4-10> and equations 4.2 and 4.10 y i e l d V f s h - V s h = ( k V e > l n < V V ( 4 - 1 1 } It i s interesting to note that a simila'r dependence, deduced from a channeling model of ioni c conduction analogous to the Poole-Frenkel ef-fect, accounted reasonably well for the curvature i n log J^~E data ob-tained from solution anodization of tantalum and niobium. (Young and Zobel 1966). 26 F i n a l l y u s i n g 4.6, 4.9 and 4.11 i n 4.8, V s p = a [ l n ( j _ / C ) ] 2 + ( k T _ / e ) l n ( j _ / j _ s ) + ( k T e / e ) l n ( J e s / j + s ) = a ( l n j _ ) 2 + 3 1 n j _ + y (4.12) where B = kT_/e - 2alnC. Thus depending on the magnitude o f the c o e f f i c i e n t s a and 8, the c u r r e n t of n e g a t i v e i o n s a c r o s s the sheath may v a r y a p p r o x i m a t e l y e x p o n e n t i a l l y 1/2 w i t h e i t h e r (V ) or V , and i t i s p o s s i b l e t h a t n e g a t i v e i o n t r a n s -sp sp 1 b p o r t a c r o s s the sheath c o u l d g i v e r i s e to a r a t e o f a n o d i z a t i o n exponen-t i a l l y dependent on e s t i m a t e d o x i d e f i e l d s t r e n g t h as o b s e r v e d by Lee e t a l . 1970 i f the oxygen i n c o r p o r a t e d i n the o x i d e o r i g i n a t e d as nega-t i v e i o n s i n the plasma. I f the l a t t e r were the case, then an a d d i t i o n a l i o n i z a t i o n s t a g e would have t o be i n v o l v e d , s i n c e the p r o c e s s o f m e t a l o x i d e c o n s t r u c t i o n u t i l i z e s doubly charged oxygen, 0 , whereas o n l y s i n g l y charged n e g a t i v e i o n s (0 , 0^ ) are c o n s i d e r e d t o e x i s t i n gaseous plasmas (McDaniel 1964). T h i s f u r t h e r i o n i z a t i o n might o c c u r a t the o x i d e s u r f a c e o r at the f i n a l l o c a t i o n i n the o x i d e , and i t would not p r e c l u d e the p o s s i b i l i t y o f sheath t r a n s p o r t b e i n g the r a t e - d e t e r m i n i n g s t e p i n the growth p r o c e s s . 4.4 The Formation of Gaseous N e g a t i v e Ions A n e g a t i v e i o n i s an atom o r molecule w i t h a n e t n e g a t i v e charge, which i n the gaseous s t a t e i s always a s i n g l e charge. The f o r -* The c o e f f i c i e n t a can be e v a l u a t e d by assuming a t y p i c a l h i g h frequency d i e l e c t r i c c o n s t a n t f o r the o x i d e , but the e v a l u a t i o n of 6 i s f r u s t r a t e d by the P o o l e - F r e n k e l f a c t o r G q i n InC which i s not u s u a l l y known e x p l i -c i t l y . 27 m a tion of n e g a t i v e i o n s i n the i n e r t gases i s v e r y i m p r o b a b l e , s i n c e the o u t e r e l e c t r o n s h e l l s a re c o m p l e t e l y f u l l and the b i n d i n g energy of h i g h e r quantum number s t a t e s i s s m a l l . However, i n the e l e c t r o n e g a -t i v e gases such as the halogens and oxygen w i t h one o r two v a c a n c i e s i n the o u t e r s h e l l , the o u t e r e l e c t r o n s have v e r y l i t t l e e f f e c t i n s h i e l d i n g an a p p r o a c h i n g e l e c t r o n from the a t t r a c t i v e f i e l d o f the n u c l e u s , and a n e g a t i v e i o n i s l i k e l y . For s t a b i l i t y , the b i n d i n g energy of the ne-g a t i v e i o n must be g r e a t e r than t h a t o f the o r i g i n a l n e u t r a l atom, the energy d i f f e r e n c e b e i n g termed the e l e c t r o n a f f i n i t y . N e g a t i v e i o n s can be formed by a number of mechanisms i n the gaseous s t a t e . M a c D a niel 1964 l i s t s the f o l l o w i n g : (a) r a d i a t i v e c a pture by a n e u t r a l atom o r m o l e c u l e (b) capture by an atom o r m o l e c u l e w i t h a t h i r d body t a k i n g up the energy (c) c a p t u r e by a molecule t o g i v e an e x c i t e d i o n , d e - e x c i t a t i o n by a t h i r d body c o l l i s i o n (d) d i s s o c i a t i v e attachment by a m o l e c u l e (e) i o n - p a i r p r o d u c t i o n , or non-capture d i s s o c i a t i o n of a m o l e c u l e ( f ) charge t r a n s f e r c o l l i s i o n s (g) s u r f a c e r e a c t i o n s e.g. s p u t t e r i n g by p o s i t i v e i o n s , A e r m i o n i c e m i s s i o n or s u r f a c e i o n i z a t i o n A c c o r d i n g to McDaniel p r o c e s s e s (b) and (d) are i m p o r t a n t t o n e g a t i v e i o n focrmation i n oxygen. The three-body p r o c e s s (b) o f c a p t u r e by an oxygen mo l e c u l e e + 0 2 + X -> + X + ( k i n e t i c energy) depends on the a v a i l a b i l i t y (and s u i t a b i l i t y ) of t h i r d b o d i e s X, and so dominates at h i g h e r p r e s s u r e s p, or more p r e c i s e l y , at v a l u e s of 28 reduced f i e l d E/p < 3V/cm-torr, where E i s the e l e c t r i c f i e l d strength i n the gas. This i s equivalent to average e l e c t r o n energies l e s s than leV, and t h i s process has a peak attachment c o e f f i c i e n t at O.leV. The e l e c t r o n a f f i n i t y of the 0^ molecule i s approximately 0.46eV, being a measure of the s t a b i l i t y of the 0^ i o n , and the attachment c o e f f i c i e n t 2 i s p r o p o r t i o n a l to p . Although process (b) i s i n s i g n i f i c a n t at low pressures, 0^ ions can s t i l l be produced from 0 ions by a charge ex-change process (Thompson 1961b): 0~ + o2 ->• o2~ + 0 The two-body process (d) of d i s s o c i a t i v e attachment, e + 0„ 0„ -)-0 + 0 + ( k i n e t i c energy) where 0^ i s an exc i t e d v i b r a t i o n a l s t a t e , dominates f o r E/p > 3V/cm/torr. The attachment c o e f f i c i e n t i s p r o p o r t i o n a l to p, and the process has a peak cross-section at 6.7eV. The ele c t r o n a f f i n i t y of the oxygen atom Is approximately 1.5eV, so that the atomic ion i s l e s s susceptible than the molecular ion to destruction mechanisms. The l a t t e r p o s s i b i l i t i e s include the thermodyna-m i c a l l y reverse equivalents of (a) to ( f ) , and i n the presence of p o s i -t i v e i o n s , (g) three-body recombination (h) r a d i a t i v e recombination ( i ) mutual n e u t r a l i z a t i o n through charge exchange and e x c i t a t i o n ( j ) detachment by c o l l i s i o n s with surfaces. At pressures l e s s than a few t o r r process (g) can be neglected compared with the two-body processes (h) and ( i ) , of which (h) may be neglected (except at extremely low pressures) compared with ( i ) : 29 + ' — ft ft 0 +0 -> 0 +0 0 1 o2+ + o~ 0 + 0 + 0 Although c o l l i s i o n s of negative ions with surfaces (j) provide the most eff e c t i v e means of a l l of electron detachment i f the work function of the surface exceeds the electron a f f i n i t y , the plasma sheath potential b a r r i e r w i l l normally prevent negative ions from reaching such surfaces i n s i g n i f i c a n t quantity. 4.5 The Low Pressure Cold Cathode Glow Discharge i n Oxygen As mentioned before, both high frequency and dc gas discharges have been u t i l i z e d i n plasma anodization studies. According to Francis I960, discharges sustained by high frequency excitation can contain 13 -3 higher electron densities (-10 cm ) and higher gas temperatures than dc discharges. However, the l a t t e r are also of interest i n that they possess s p a t i a l l y separated regions of widely different species content, and can generate large volume plasmas. The main regions of the dc cold cathode discharge between -plane, p a r a l l e l electrodes at pressures of the order of 1 torr are shown i n Fig. 4.3, together with the space charge, e l e c t r i c f i e l d and potential distributions. Electrons are emitted from the cathode mainly by positive ion bombardment (Cobine 1958) and form a negative space charge close to i t s surface, but they are then accelerated by the e l e c t r i c f i e l d , some of them causing excita-tion of gas molecules which results i n the cathode glow. The high density of positive ions attracted to the cathode results in a large net positive space charge i n the Crookes dark space, and electrons accelerated by the associated potential gradient produce intense ionization and mu l t i p l i c a t i o n . Towards the end of the Crookes dark space the electron density increases 30 CATHODE GLOW NEGATIVE GLOW CR00KES DARK PACE FARADAY DARK SPACE POSITIVE COLUMN 31 so much that the net p o s i t i v e space charge decreases sharply and the f i e l d becomes very small or even reverses. The electrons now consist of two groups: a f a s t group which o r i g i n a t e d at or near the cathode and have not suffered many c o l l i s i o n s i n the dark space, and a l a r g e r group which were created i n the dark space and are r e l a t i v e l y slow, having energies below the i o n i z a t i o n l e v e l . Thus i n t h i s next region most of the electrons lose energy by e x c i t a t i o n c o l l i s i o n s , g i v i n g the negative glow. As the electrons are slowed down fur t h e r the space charge reaches a negative maximum, the e x c i t a t i o n decreases and the Faraday dark space begins. The e l e c t r o n density decreases by recombination and d i f f u s i o n i n the dark space u n t i l the space charge i s reduced to zero and the f i e l d r i s e s to a constant small value, a c c e l e r a t i n g the electrons once more to e x c i t a t i o n and i o n i z a t i o n energies, and producing the p o s i t i v e column. The f i e l d i n the l a t t e r assumes a value j u s t s u f f i c i e n t to maintain along the length of the column the degree of i o n i z a t i o n required to carry the discharge current. The phenomena occurring at or near the cathode, i n c l u d i n g the Faraday dark space, are e s s e n t i a l to the discharge, whereas the p o s i t i v e column merely serves to maintain a conducting path f o r the current. Thus on reducing the pressure, the negative glow and Faraday dark space expand at the expense of the p o s i t i v e column, which eventually disappears completely. S i m i l a r l y , i f the distance between the electrodes i s v a r i e d at constant gas pressure and current, the region from the ca-thode to and i n c l u d i n g the Faraday dark space moves as a body and i s un-a l t e r e d i n length while the length of the p o s i t i v e column v a r i e s . Further-more, the negative zones w i l l move with a r o t a t i n g cathode as i f they were f i x e d to the l a t t e r . These observations i n d i c a t e that the motion of the charged p a r t i c l e s i n tbe negative zones i s of a beam-like nature, 32 whereas in the positive column the motion must be essentially random. Consequently, there should be l i t t l e influence from the walls of the discharge tube i n the cathode region, while i n the positive column the light emitted and.the potential distribution depend on the tube diameter: decreasing the l a t t e r increases the potential gradient. The positive column i s often divided up into d i s t i n c t a l t e r -nating bright and dark s t r i a t i o n s , which are associated with variations i n e l e c t r i c f i e l d strength and species concentrations. The phenomenon appears to occur when the energy distribution of the electrons leaving the Faraday dark space consists of two d i s t i n c t l y separate groups of electrons (Twiddy 1961). If a c y l i n d r i c a l hollow cathode (Engel 1965) i s used instead of a plane electrode, the cathode f a l l region follows the internal geometry of the cathode and the negative glow i s also partly compressed inside the cylinder. The radial e l e c t r i c f i e l d i n the Crookes dark space contributes to increased ionization, and the ult r a - v i o l e t radiation of the negative glow i s more e f f i c i e n t l y u t i l i z e d for photo-emission from the cathode, so that for a given cathode f a l l voltage the discharge current density i s increased. Also a discharge with a positive column can be obtained within a shorter discharge tube. Both the negative glow and positive column can be said to con-st i t u t e plasmas, although the space charge neutrality condition i s not as well s a t i s f i e d i n the negative glow region. The electron and ion 11 -3 concentrations i n the negative glow may be as high as 10 cm , compared 8 10 —3 with around 10 to 10 cm i n the positive column. At levels of dis-charge current 1^ in' the abnormal glow region, when the cathode Is com-pletely covered with the cathode glow, then these carrier densities 33 increase with I and pressure. The electrons have considerably higher energies than the charged or neutral p a r t i c l e s , and numerous e l a s t i c c o l l i s i o n s have a randomising effect giving the electrons an equilibrium energy d i s t r i b u -tion which can approach Maxwellian form with an associated temperature T £ that may be around 50,000°K. The ion temperature i s close to that of the gas, which i s seldom over 100°C i n the positive column. In the l a t t e r region, T^ decreases with increasing Rp, the product of discharge tube radius and pressure, but i n molecular gases i t i s r e l a t i v e l y inde-pendent of 1^. The cold cathode dc glow discharge in oxygen has been i n v e s t i -gated i n d e t a i l by Thompson 1961a using sophisticated current probe techniques and an r f mass spectrometer probe. Thompson reported that i n his discharge between c y l i n d r i c a l hollow S w e d i s h iron electrodes the negative glow was green and the positive column consisted of blue grey s t r i a t i o n s . At a pressure of 40 mtorr he found the negative glow and Faraday dark space to be v i r t u a l l y f i e l d free, but that i n the positive column steps of potential of about 11V occurred at each s t r i a t i o n head (cathode end). By measuring the second derivative of probe current-voltage characteris-t i c s , Thompson determined the energy distributions and concentrations of the charged p a r t i c l e s for a discharge current of 4 mA, and the mass spectrometer probe provided some information on the r e l a t i v e abundance of various ions. The negative glow and Faraday dark space were found to be characteristic of an electropositive' plasma of positive ions and electrons, with very few negative ions present. In the positive column, however, positive and negative ions were present in almost equal concen-8 —3 trations of about 4 x 10 cm , with mean energies of 0.15eV, compared 34 w i t h an e l e c t r o n d e n s i t y of 2 x 10'cm J and mean energy around 4eV. The i o n s of g r e a t e s t abundance were 0^ and 0 . The l a t t e r were assumed to be produced by d i s s o c i a t i v e attachment (process ( d ) , s e c t i o n 4.4) and t h e i r d e n s i t y was h i g h e s t at the head of a s t r i a t i o n on the d i s c h a r g e tube a x i s . The n e g a t i v e i o n random c u r r e n t d e n s i t y j _ near a s t r i a t i o n 2 t a i l was 1.8 uA/cm . Thompson 1961b a l s o deduced t h a t the n e g a t i v e i o n d e n s i t y i s p r o p o r t i o n a l to the 2/3 power of the d i s c h a r g e c u r r e n t 1^ between 0 and 10 mA, and t h a t the n e g a t i v e i o n to e l e c t r o n r a t i o o f 20 a t 1^ = 4 mA would decrease w i t h i n c r e a s i n g 1^ a c c o r d i n g to n /n a I , - e d r e a c h i n g a v a l u e of 2 at 1^ ~ 9 mA, a t which p o i n t the plasma ceases t o be e l e c t r o n e g a t i v e i n c h a r a c t e r . Above 10 mA the p o s i t i v e column be-haved as a weakly i o n i z e d e l e c t r o p o s i t i v e plasma w i t h n + p r o p o r t i o n a l t o 1^ b u t the n e g a t i v e i o n d e n s i t y was not determined. 35 5. PROBE TECHNIQUES IN PLASMA DIAGNOSTICS 5.1 Introduction This chapter deals with the a p p l i c a t i o n of e l e c t r i c a l probes to the measurement of various plasma parameters, such as e l e c t r o s t a t i c f i e l d strength, f l o a t i n g p o t e n t i a l , plasma p o t e n t i a l , and charge c a r r i e r concentrations and temperatures. A number of other diagnostic t e c h n i -ques are a v a i l a b l e , f o r instance microwave transmission, r e f l e c t i o n or cavity resonance measurements, o p t i c a l interferometry, o p t i c a l spectro-scopy, and mass spectrometer a n a l y s i s , but the Langmuir probe technique i s p a r t i c u l a r l y appropriate since the anodization sample i t s e l f can be considered as a large plane probe-. Much of the theory applicable to probes has already been introduced i n se c t i o n 4.2.1. The use of the Loeb e l e c t r o n f i l t e r and the simultaneous a p p l i c a t i o n of r f and dc bias to a probe are dealt with separately i n chapter 9. 5.2 S i m p l i f i e d Treatment of the Langmuir Probe Method The theory of the flow of charge c a r r i e r s to an e l e c t r i c a l probe can be extremely complex, and has been treated i n some d e t a i l by Swift and Schwar 1970. An elementary theory applicable to low pressure plasmas found i n a glow discharge at pressures below 100 mtorr i s presen-ted here, with the following assumptions: 1. Negative ions are absent, and electron and p o s i t i v e i o n concen-t r a t i o n s are equal (see secti o n 5.3 f p r the e f f e c t of negative i o n s ) . 2. Electron and ion mean free paths are much l a r g e r than the probe dimensions (see Appendix B). 3. The probe dimensions are much lar g e r than the Debye length (see 36 Appendix B ) . 4. There i s a M a x w e l l i a n d i s t r i b u t i o n of e l e c t r o n and p o s i t i v e i o n v e l o c i t i e s (see Appendix A ) . 5. The e l e c t r o n temperature T i s much g r e a t e r than the p o s i t i v e i o n temperature T, . The c i r c u i t shown i n F i g . 3.2(a) r e p r e s e n t s a Langmuir probe c i r c u i t i f the e l e c t r o d e marked '•sample' i s a s p h e r e , c y l i n d r i c a l w i r e o r p l a n e d i s c of u n r e a c t i v e m e t a l . I f t h i s probe i s b i a s e d so as t o draw zero net c u r r e n t from the d i s c h a r g e , then the probe r e g i s t e r s the f l o a t i n g p o t e n t i a l f o r t h a t plasma l o c a t i o n . A s e r i e s o f such f l o a t i n g probes can y i e l d an e s t i m a t e of the e l e c t r o s t a t i c f i e l d s t r e n g t h i n the plasma. By v a r y i n g the p o t e n t i a l of the s i n g l e probe w i t h r e s p e c t t o the anode, an I-V c h a r a c t e r i s t i c o f the g e n e r a l form shown i n F i g . 5.1 w i l l be o b t a i n e d , (a) S t r o n g l y n e g a t i v e probe As the probe i s b i a s e d n e g a t i v e l y from i t s f l o a t i n g p o t e n t i a l V^, p r o g r e s s i v e l y more e l e c t r o n s w i l l be r e p e l l e d by the i n c r e a s i n g e l e c t r i c f i e l d i n the space s u r r o u n d i n g the probe u n t i l e v e n t u a l l y the c u r r e n t drawn i . i s e n t i r e l y due t o p o s i t i v e i o n s . +s I n s e c t i o n 4.2(a) i t was assumed t h a t the whole of the p o t e n -t i a l v a r i a t i o n i n the r e g i o n s u r r o u n d i n g a n e g a t i v e s u r f a c e was c o n f i n e d t o the p o s i t i v e i o n space charge sheath. However, between the space char^ sheath and the u n d i s t u r D e d plasma t h e r e i s a q u a s i - n e u t r a l t r a n s i t i o n r e g i o n i n which i o n s and e l e c t r o n s are p r e s e n t i n almost e q u a l q u a n t i t i e s but a c r o s s which a s m a l l p o t e n t i a l drop occurs due to the w i t h d r a w a l o f p o s i t i v e i o n s to the probe. The sheath begins when the e l e c t r o n concen-t r a t i o n s t a r t s to decrease a p p r e c i a b l y , so t h a t V , the pd a c r o s s the POSITIVE SPACE CHARGE SATURATED~7lON CURRENT xPROBE AT PLASMA POTENTIAL NEGATIVE SPACE CHARGE SATURATED ELECTRON CURRENT PROBE CURRENT 0 In i. .PROBE VOLTAGE .PROBE VOLTAGE RELATIVE TO ANODE F i g . 5.1 Ideal current-voltage c h a r a c t e r i s t i c s of a Langmuir probe. Co 38 t r a n s i t i o n r e g i o n , must be j u s t l a r g e enough t o p r e v e n t a s i g n i f i c a n t f r a c t i o n of the e l e c t r o n s i n the d i s c h a r g e from e n t e r i n g the s h e a t h , i . e . eV^ - kT^/2. However, s i n c e the mean i o n energy i s much s m a l l e r than the mean e l e c t r o n energy, even t h i s weak f i e l d p e n e t r a t i n g the t r a n s i t i o n r e g i o n g r e a t l y d i s t o r t s the random i o n mo t i o n , and i n e f f e c t g i v e s the i o n s at the sheath edge a d i r e c t e d v e l o c i t y v towards the probe: v t = ( 2 e V t / m + ) 1 / 2 where m + i s the i o n i c mass. Now the e l e c t r o n c o n c e n t r a t i o n n a t the sheath boundary i s g i v e n by Boltzmann's law: n = n exp[-eV /kT ] t e t e where n i s t h e c o n c e n t r a t i o n i n the u n d i s t u r b e d plasma. S i n c e the i o n e and e l e c t r o n c o n c e n t r a t i o n s at the sheath edge are s t i l l a p p r o x i m a t e l y e q u a l we have f o r the i o n c u r r e n t i + g to the probe i + s = A e ( 2 e V t / m + ) 1 / 2 n e e x p [ - e V ^ k T j P where A^ i s the a r e a o f the probe. R e p l a c i n g e V t by kT g/2 we o b t a i n , -i n s t e a d o f Eqn. 4.1, i , = 0.607 A en (kT /m.) 1 / 2 = 0.607 A en,(kT / m j 1 / 2 +s p e e + p + e + Thus the i o n c u r r e n t to the probe i s a f u n c t i o n of the mean e l e c t r o n energy r a t h e r than the mean i o n energy, so t h a t the l a t t e r cannot be o b t a i n e d from t h i s i o n c o l l e c t i o n r e g i o n o f the c h a r a c t e r i s t i c . (b) Probe b i a s e d p o s i t i v e l y from f l o a t i n g p o t e n t i a l When the p o t e n t i a l d i f f e r e n c e a c r o s s the space between the prob and plasma i s decreased, as e x p l a i n e d i n s e c t i o n A.2.1 e l e c t r o n s b e g i n 39 to reach the probe i n increasing numbers u n t i l the retarding f i e l d d i s -appears and the probe i s at plasma potential V . Throughout this region the probe draws a constant positive ion current ( i ) and the velocity -rS d i s t r i b u t i o n of the electrons \d_ll determine, the variation of to t a l probe current with potential. Assuming a Maxwellian d i s t r i b u t i o n and a pressure low enough for c o l l i s i o n s i n the sheath to be unimportant (according to assumptions (2) and (3)), the electron current to the probe i s given by Eqn. 4.2 as i = i exp[-eV ,/kT ] (5.1) e es sh e where i s the retarding potential between the probe and the plasma, and i i s the electron current to the probe when the l a t t e r i s at plasma es potential (V ^  = 0). This random electron current i s given by i = -(l/4)n v eA = -n eA (kT /2iTm ) 1 / Z (5.2) es e e p e p e e where v g i s the mean thermal speed of an electron (see Appendix A). The measured potential V of the probe with respect to the s anode Is given by V = -V - V , s as sh where V includes the potential drop through the discharge from the •3.S anode to the probe, and the work functions of the probe and anode metals. Thus under constant discharge conditions, Eqn. 5.1 gives l n ( - i ) = l n ( - i ) + eV /kT + const. x e es s e and a graph of l n ( - i ) versus probe voltage i n this region i s l i n e a r , having a slope (e/kT ) from which the electron temperature T & can be obtained. The value of i i s obtained from the t o t a l probe current e by correcting for the positive ion contribution as indicated i n Fig. 5.1. 40 F u r t h e r p o s i t i v e b i a s i n g o f the probe causes i o n s to be r e p e l -l e d and produces an a c c e l e r a t i n g f i e l d f o r the e l e c t r o n s so t h a t the law g o v e r n i n g the i n c r e a s e o f e l e c t r o n c u r r e n t changes. T h i s i s m a n i f e s t by a b reak a t V p i n the I-V c h a r a c t e r i s t i c , which s h o u l d then r e a c h a s a t u r a t i o n c u r r e n t due o n l y to e l e c t r o n s . However, impact i o n i z a t i o n commences i n the sheath f i e l d , i n c r e a s i n g the c u r r e n t t o the p r o b e , and the l a t t e r may become a s u b s i d i a r y anode. Knowledge of the e l e c t r o n c u r r e n t 1^ r e a c h i n g the probe at plasma p o t e n t i a l V enables n to be found from Eqn. 5.2 s i n c e T i s p e ^ e now known. However, the sharpness o f the break i n the c h a r a c t e r i s t i c at Vp depends markedly on d i s c h a r g e c o n d i t i o n s . I t i s o f t e n l o c a t e d by e x t r a p o l a t i n g the l i n e a r p a r t of the l n i g v e r s u s V g c h a r a c t e r i s t i c t o meet the b e s t s t r a i g h t l i n e o b t a i n e d from the e l e c t r o n a c c e l e r a t i n g r e g i o n as shown i n F i g . 5.1. Another method f o r d e t e r m i n i n g V , p r o -posed by Dote e t a l . 1966, depends on the charged p a r t i c l e d e n s i t y i n the sheath r e g i o n becoming a maximum when plasma p o t e n t i a l i s r e a c h e d , and i n v o l v e s the use of a v e r y s m a l l sounding probe l o c a t e d c l o s e t o a l a r g e r r e f e r e n c e probe (see Appendix C). T h i s e l e c t r o d e arrangement c o r r e s p o n -ded t o the sample and probe combination u t i l i z e d i n the p r e s e n t work, and the method was i n v e s t i g a t e d as r e p o r t e d i n s e c t i o n 8.3.4. 5.3 The E f f e c t of N e g a t i v e Ions on Langmuir Probe Measurements I f , as can o c c u r i n the p o s i t i v e column of the oxygen glow d i s c h a r g e , n e g a t i v e and p o s i t i v e i o n s are p r e s e n t i n much l a r g e r numbers than e l e c t r o n s ( n _ / n g can be as l a r g e as 20 i n oxygen - see s e c t i o n 4.5), then c l e a r l y the r a t i o of the e l e c t r o n and p o s i t i v e i o n s a t u r a t i o n c u r r e n t s w i l l g r e a t l y decrease, and more care i s r e q u i r e d i n e l i m i n a t i n g the p o s i t i v e 41 ion c o n t r i b u t i o n to the probe current as mentioned above. However, since the r a t i o of the negative ion and e l e c t r o n s a t u r a t i o n currents i s given (see Eqn. 5.2) by i / i = (n /n )(m T /m T ) 1 / 2 -s es - e e - - e 1/2 then provided n_/n g << (m_Te/meT ) the negative i o n current w i l l always be small compared with the el e c t r o n current. For an 'active' discharge 3 ( i . e . T g >> T + - T ) i n oxygen t h i s condition approximates n_/n& « 10 , and so el e c t r o n concentration and temperature can s t i l l be obtained from the e l e c t r o n c o l l e c t i o n part of the probe c h a r a c t e r i s t i c by the methods of sec t i o n 5.2 as i f negative ions were absent. Furthermore, Boyd and Thompson 1959 have shown that f o r an electronegative plasma with n_/n £ >> 2, the p o s i t i v e i o n current c o l l e c t e d i s the random current across the 1/2 sheath edge, i . e . (1/4) n.e (8kT,/TOI,) as i n Eqn. 4.1. Thus i n both e l e c t r o p o s i t i v e and electronegative plasmas the i o n current i s a func-t i o n of ion density, i . e . the plasma density. 42 6. THE APPLICATION OF ELLIPSOMETRY TO ANODIZATION STUDIES 6.1 Introduction A method of determining the thickness of the anodic oxide f i l m as a function of time i s c l e a r l y e s s e n t i a l to the study of the k i n e t i c s of the plasma anodization process. The method should preferably be r a p i d and non-destructive and should i d e a l l y be an i n s i t u measurement, that i s , i t should be possible to determine the f i l m thickness from readings taken while the sample i s being anodized. Methods which might be c o n s i -dered include (a) i n t e n s i t y r e f l e c t i v i t y of l i n e a r l y p o l a r i z e d l i g h t (Masing et a l . 1961); (b) minimum r e f l e c t i v i t y spectrophotometry (Dignam et a l . 1965) and (c) ellipsometry (Winterbottom 1955; Archer 1962; McCrackin et a l . 1963; Pa s s a g l i a et a l . 1963). The spectrophotometric and e l l i p s o m e t r i c methods of examina-t i o n are generally the most accurate, provided that accurate information i s a v a i l a b l e f or the o p t i c a l constants of the substrate, and recent devel-opments (Ord 1969) have considerably improved the speed of ellipsometer measurements. Other advantages of ellipsometry are that i t i s a n u l l detection method, and a s i n g l e n u l l measurement y i e l d s two parameters of the o p t i c a l system i f a l l others are known. As w i l l become evident l a t e r i n t h i s chapter, studies of the growth and o p t i c a l properties of anodic oxide f i l m s are a near i d e a l a p p l i c a t i o n f o r ellipso m e t r y , and the technique has 1 een used extensively i n t h i s area (Barrett 1963; Kumagai and Young 1964; Young and Zobel 1966; Dell'Oca and Young 1969; Ord et a l . 1972). Method (a) has been u t i l i z e d recently i n a study of the plasma anodization of s i l i c o n i n an r f induced discharge (Hathorn, P u l f r e y and Young, unpublished; Pulfrey and Reche 1973). 43 6.2 P r i n c i p l e s o f E l l i p s o m e t r y 6.2.1 R e f l e c t i o n of a plane wave at an i n t e r f a c e between two i s o -t r o p i c media and a t a f i l m - c o v e r e d s u r f a c e The study o f the o p t i c a l p r o p e r t i e s o f s u r f a c e s and s u r f a c e f i l m s by e l l i p s o m e t r y i n v o l v e s measuring the changes i n the s t a t e o f p o l a r i z a t i o n of a beam of e l l i p t i c a l l y p o l a r i z e d monochromatic l i g h t w h ich o c c u r when the beam i s r e f l e c t e d by the s u r f a c e . By e l l i p t i c a l l y p o l a r i z e d l i g h t i s meant l i g h t whose e l e c t r i c ( o r magnetic) d i s t u r b a n c e can be r e s o l v e d i n t o two l i n e a r l y p o l a r i z e d v i b r a t i o n s d i f f e r i n g I n o r i e n t a t i o n and phase - the l o c u s o f the end of the e l e c t r i c v e c t o r i n a p l a n e p e r p e n d i c u l a r t o the d i r e c t i o n of p r o p a g a t i o n i s then an e l l i p s e . The case of e l l i p t i c a l l y p o l a r i z e d l i g h t i n c i d e n t on the boun-dary s e p a r a t i n g two i s o t r o p i c media, each c h a r a c t e r i z e d by a complex r e -f r a c t i v e i n d e x o f the form N = n - j k , i s c o n s i d e r e d f i r s t ( F i g . 6.1). The problem i s most c o n v e n i e n t l y d e a l t w i t h by examining the e f f e c t on the components E and E of the e l e c t r i c v e c t o r of the i n c i d e n t p s p l a n e wave i n and normal t o the p l a n e o f i n c i d e n c e r e s p e c t i v e l y : E = a cos(wt - k . r + 6 ), E = a cos(wt - k . r + 6 ) p p v p s s s where |k| = 2-rrNo/X, N q b e i n g the complex r e f r a c t i v e i n d e x o f the f i r s t medium. The s t a t e of p o l a r i z a t i o n of the wave can be s p e c i f i e d by the ft amplitudes a and a and the phase d i f f e r e n c e 6 - <5 o f these components . ^ p s p s I n g e n e r a l , the pro c e s s of r e f l e c t i o n has d i f f e r e n t e f f e c t s on the a m p l i -* For i n s t a n c e , i f 6 - 6 = m i where m = 0,1,2,..., the wave i s l i n e a r l y P s a P s p o l a r i z e d , whereas i f "6 - & = mrr/2 where m = 1,3,5,..., and a p - s • the wave i s c i r c u l a r l y p o l a r i z e d . 44 F i g . 6.1 R e f l e c t i o n and r e f r a c t i o n a t an i n t e r f a c e between two i s o t r o p i c media, tudes and the phases o f the d i f f e r e n t components, so t h a t a f t e r r e f l e c -t i o n they become E' = r E = a' cos(wt - k . r + 6' ) , E' = r E = a 1 cos(wt - k . r + 6' ) p p p p p s s s s s where r and r are the F r e s n e l r e f l e c t i o n c o e f f i c i e n t s f o r p and s l i g h t p s r e s p e c t i v e l y . The r e l a t i v e a m plitude r e d u c t i o n , tanijj, and r e l a t i v e phase change A which c h a r a c t e r i z e the changes i n . t h e s t a t e of p o l a r i z a t i o n on r e f l e c t i o n are found as the modulus and argument o f the complex r e -f l e c t a n c e r a t i o , p : 45 r E 1 /E a' /a' P = -E- = - r ^ T ^ = — £ 7 - ^ - exp j f (6' - 6 ) - (6' - 6 ) ] r E ' / E a / a ^ J L V p p' v s s y j s s s p s d - t a n ^ exp j A U s i n g the boundary c o n d i t i o n s on phase and a m p l i t u d e o f the e l e c t r i c f i e l d components g i v e s r and r as p s N., cos d> - N cos 6. N, cos 4. - N cos i> 1 0 0 1 , _ __1 1 o _o_ p N, cos 6 + N cos d). ' s N, cos + N cos <j> 1 o o 1 1 1 o o where the s u b s c r i p t s r e f e r to the media and <j> and <j> are the angles of i n c i d e n c e and r e f r a c t i o n r e s p e c t i v e l y , , Thus the q u a n t i t i e s A and IJJ which are measured by e l l i p s o m e t r y are f u n c t i o n s of the r e f r a c t i v e i n d i c e s and angle of i n c i d e n c e . For r e f l e c t i o n from a f i l m - c o v e r e d s u r f a c e , A and ip a l s o be-come f u n c t i o n s of the r e f r a c t i v e i n d e x o f the f i l m , i t s t h i c k n e s s d^, and the wavelength A, through the t o t a l r e f l e c t i o n c o e f f i c i e n t s and R which i n c l u d e the c o n t r i b u t i o n s o f r e f l e c t i o n s from b o t h i n t e r f a c e s : . s R p = t a n ij> exp jA = —^- (6.1) S and each R i s o f the form „ r o l + r 1 2 6 x p _ 2 j 6 l 1 + r o l r 1 2 6 x p " 2 j 5 l where 6^ = (2"rrN^d^coscf>^)/A and i s now the r e f r a c t i v e i n d e x o f the f i l m , the F r e s n e l r e f l e c t i o n c o e f f i c i e n t s u b s c r i p t s r e f e r r i n g to the sequence i n which the wave encounters the media. 6.2.2 The P o i n c a r e sphere r e p r e s e n t a t i o n o f e l l i p t i c a l l y p o l a r i z e d l i g h t To understand how the q u a n t i t i e s ifi and A are measured by e l l i p -sometry, a r e p r e s e n t a t i o n f o r e l l i p t i c a l l y p o l a r i z e d l i g h t i s r e q u i r e d . 46 As already mentioned, the p o l a r i z a t i o n can be s p e c i f i e d by the amplitudes a and a and the phase difference 6 = 6 - 6 of l i n e a r l y p o l a r i z e d com-p s p s r ponent v i b r a t i o n s i n and perpendicular to a reference plane. A l t e r n a t i v e l y , the representation may be made i n terms of the e l l i p s e traced out by the e l e c t r i c vector ( F i g . 6.2), using the r a t i o of the semi-axes — and the azimuth <f>, i . e . the i n c l i n a t i o n of the major axis a. with the reference plane. F i g . 6.2 The locus of the e l e c t r i c vector f o r e l l i p t i c a l l y p o l a r i z e d l i g h t i n a plane normal to the d i r e c t i o n of propagation A comprehensive notation f o r the representation i s the Stokes vector (s o> s^, s^, Using the a u x i l i a r y angles a and x defined by s , b tana = — , tanx = , a ^ a P i t can be shown (Born and Wolf 1959) that the two forms f o r the vector r e l a t i n g to the two sets of q u a n t i t i e s above are 47 l = s i o cos2a = s 1 = cos2xcos2({> (6.2) sin2acosS = s2 = cos2xsin2<j> sin2asin6 = = sin2x normalized so that the i n t e n s i t y parameter s =1. I t can be seen that o S Q = 1, 2<£>, 2x are the s p h e r i c a l co-ordinates equivalent to c a r t e s i a n co-ordinates s^, s^, s^, that i s , the state of p o l a r i z a t i o n can be repre-sented by a point C on a sphere of un i t radius . This sphere, c a l l e d the Poincare sphere, i s shown i n F i g . 6.3. The i n t e r s e c t i o n I of the p o s i t i v e s^ axis with the equator represents the l i n e a r l y p o l a r i z e d component i n the reference plane. The longitude of the point measured clockwise from I represents twice the azimuth <j>, and the l a t i t u d e of the point twice the e l l i p t i c i t y , x« Thus points on the equator, X = 0, represent l i n e a r p o l a r i z a t i o n s of various azimuths from 0 to ir, and the poles, x = - 45°, represent c i r c u l a r l y po-l a r i z e d l i g h t . By convention, the northern hemisphere i s associated w i t h left-handed e l l i p s e s , the southern with right-handedness. The opposite end S of the diameter through I represents a l i n e a r p o l a r i z a t i o n of a z i -muth given by 2<j> = IT, i . e . the other component v i b r a t i o n i n the plane perpendicular to the reference plane. Returning to the expressions for s^, s^ and s^, equations 6.2, we have ^ = tan6 = ^ £ • ( 6, 3 ) s^ sm2(|) and i t can be seen that the angle between the perpendicular from C to the diameter IS and the equ a t o r i a l plane i s the phase angle between the l i n e a r l y p o l a r i z e d components of C represented by I and S. Thus r o t a t i o n 48 F i g . 6.3 Representation of p o l a r i z e d l i g h t on the Poincare sphere. 49 of C about the diameter IS i s equivalent to changing the phase d i f f e r e n c e 6 between the components I and S. Also S2 — = tan2a cos6 = tan2d> S l so that IOC = 2a, using the above r e s u l t f o r 6. .'. CSI = a (isosceles A CSO) a and CJ_ = tana = — /A / \ cs a P ( 6 - 4 ) Thus i n the t r i a n g l e formed by C and the. component diameter the amplitude r a t i o of the components i s given by the length r a t i o of the t r i a n g l e sides opposite the respective component po i n t s . Movement of C along a great c i r c l e containing I , C and S i s therefore, equivalent to changing the r a t i o a /a of the components I and S. p s The operation of the ellipsometer can now be considered, i n p a r t i c u l a r the e f f e c t s of a b i r e f r i n g e n t p l a t e and r e f l e c t i o n on the state of p o l a r i z a t i o n of the l i g h t beam. 6,2.3 Theory and operation of the ellipsometer The usual ellipsometer arrangement ( F i g . 6.4) consists of a monochromatic l i g h t source(S), c o l l i m a t o r ( C ) , l i n e a r p o l a r i z e r ( P ) , quarter wave plate(Q), t e s t surface(T), analyzer(A) (another l i n e a r p o l a r i z e r ) and detector(D). E l l i p t i c p o l a r i z a t i o n i s produced by passing a l i n e a r l y p o l a r i z e d beam through the quarter wave p l a t e , which i s a b i r e f r i n g e n t p l a t e of thickness such that the phase difference introduced between the compo-nents of the beam p a r a l l e l to the fa s t and slow axes of the p l a t e i s IT/2. On the Poincare sphere t h i s operation i s represented by r o t a t i o n 50 through an angle of TT/2 about an e q u a t o r i a l diameter passing through the doubled azimuths of the fa s t and slow axes. I t can be seen that t h i s combination of a p o l a r i z e r and a quarter wave pla t e can produce l i g h t of any e H i p t i c i t y and azimuth. The r e f l e c t i o n of the e l l i p t i c a l l y p o l a r i z e d l i g h t at the t e s t surface introduces an a d d i t i o n a l phase di f f e r e n c e A between the p and s Fi g . 6.4 Arrangement of the ellipsometer components, and changes the r a t i o of t h e i r amplitudes by a f a c t o r tanijj. This i s represented by r o t a t i o n about an e q u a t o r i a l diameter passing through the doubled azimuths I and S of the planes of incidence and of the surface through an angle A, and movement of the res u l t a n t point C along a great c i r c l e through I and S u n t i l the r a t i o of the chords 01/CS has changed by the factor tanifj. For a measurement, the ellipsometer i s n u l l e d by varying the parameters of the incident e l l i p t i c p o l a r i z a t i o n u n t i l the r e f l e c t e d 51 p o l a r i z a t i o n i s l i n e a r and can therefore be extinguished by the (crossed) analyzer A. I f t h i s parameter v a r i a t i o n i s accomplished by r o t a t i n g the p o l a r i z e r P with the quarter wave pla t e f a s t axis at exactly + TT/4 a z i -muth, the c a l c u l a t i o n of A and tan^ from the e x t i n c t i o n azimuths of P and A i s greatl y s i m p l i f i e d , as can be seen on the Poincare" sphere shown i n F i g . 6.5. A l l azimuths are measured from the plane of incidence I , and we consider the quarter wave pla t e f a s t axis azimuth set at -TT/4, as represented by the point Q^ . At n u l l , a point on the equator represen-t i n g the l i g h t emerging from the p o l a r i z e r must be t r a n s l a t e d by the com-bined e f f e c t of the wave pla t e and surface r e f l e c t i o n to another point on the equator ( i . e . l i n e a r p o l a r i z a t i o n ) f o r complete e x t i n c t i o n by the analyzer. Assume that the p o l a r i z e r has an azimuth between zero (point I) and +TT/4 (point Q ) so that the l i g h t emerging from i t i s represented by P i n F i g . 6.5. The i n t r o d u c t i o n of a TT/2 phase d i f f e r e n c e by the quar-te r wave pla t e rotates P over the sphere about the diameter Q^Qg through an angle TT/2 to R on the great c i r c l e through and Q . Now since the phase difference A introduced by r e f l e c t i o n causes a r o t a t i o n about the diameter IS which i s perpendicular to Q^Qgj and since the f i n a l point must be on the equator i r r e s p e c t i v e of the magnitude of tan if, t h i s ro-t a t i o n must move the point from R around the great c i r c l e to Q^ , so that angle ROQ^ = A. The r e l a t i v e amplitude reduction on r e f l e c t i o n causes a movement around the equator from u n t i l the r a t i o of the chords sub-tended at I and S has changed by the facto r tantjj. However, since at Q,£ the chords Q^I and Q^ S are equal, the chord r a t i o at the f i n a l point T, TS/TI, i s simply equal to tantjj, and angle SIT = i>. Fig, 6.5 Poincare sphere representation of an e l l i p -someter n u l l . The r e f l e c t e d l i g h t represented by T i s extinguished by the analyzer In an o r i e n t a t i o n denoted by A, and i t can be seen that angle AOI = 2ty. Thus the angle i s given by the azimuth A of the analyzer at n u l l . Also angle POQ^ = angle ROQ^ = A, so that the phase change A i s given by A = angle Q 01 + angle IOP = TT/2 + 2P ( 6- 5) where P i s the p o l a r i z e r azimuth at n u l l . In the above example depicted i n F i g . 6.5, the analyzer a z i -muth A i s l e s s than TT/2. For the quarter wave p l a t e f a s t axis at —IT/4 azimuth, there i s a second combination of p o l a r i z e r and analyzer azimuths (apart from those d i f f e r i n g by T T ) , i n which A > ir/2, that also r e s u l t s i n a n u l l , but which has d i f f e r e n t - A and A - P r e l a t i o n s h i p s . These two sets of P and A values are termed zones, and are numbered 1 and 3 r e s p e c t i v e l y . S i m i l a r l y a quarter wave pla t e set at +ir/4 gives two more zones, numbered 2 and 4, making four independent sets of P and A readings i n a l l . I d e a l l y , the A , i|/ values obtained from measurements i n a l l four zones should be i d e n t i c a l , ' but due to various imperfections i n the o p t i -c a l components and the alighment of the ellipsometer, the d i f f e r e n t zones y i e l d s l i g h t l y d i f f e r e n t values f o r the angles A and i>. The subject of instrumental errors and ellipsometer alignment i s treated i n chapter 7. Returning to s e c t i o n 6.2.1, Eqn. 6.1, i t i s seen that values of A and obtained from one ellipsometer measurement enable the r e a l and imaginary parts of Eqn. 6.1 to be solved for two unknown q u a n t i t i e s of the film-substrate system, such as the thickness and r e f r a c t i v e i n -dex of the f i l m , i f the l a t t e r i s homogeneous and non-absorbing. I f there are more than two unknowns, for instance i f the f i l m i s absorbing and/or o p t i c a l l y non-uniform (e.g. layered), or i f the substrate o p t i c a l 54 constants are not known, then a number of ellipsometry measurements must be used i n a curve f i t t i n g procedure. These measurements may be obtained as a function of angle of incidence or of the immersion medium, but i n anodization studies they are most ea s i l y obtained as a function of chan-ging f i l m thickness from in s i t u measurements during the oxide growth process. 6.2.4 The analysis of ellipsometry data As a homogeneous non-absorbing f i l m (N^ = n^) on a thick sub-strate (N 2 = n2 ~ increases in thickness, a curve i s traced out i n the A-ijj plane which recyles continuously. The curve may be an open or a closed loop, depending on the r e l a t i v e magnitudes of the o p t i c a l con-stants of the substrate, f i l m and ambient medium, and t y p i c a l examples are shown i n Fig. 6.6. The recycling can be understood from the expres-sion for the r e f l e c t i o n coefficients R and R i n Eqn. 6.1, which are of p s ^ the form R(x), where x = S^mod T T , 6^ being the phase retardation for a single passage through the fil m . If the f i l m i s absorbing (k^ ^ 0) then the curve does not re-trace i t s e l f on successive cycles but instead tends to lower values of i|> with increasing thickness. Alternatively, i f the f i l m consists of two uniform layers of oxide as shown i n Fig. 6.7, growing at constant rates, then in general the ellipsometry curve does not retrace i t s e l f after one cycle, although i f both layers are non-absorbing approximate retracing does occur after two cycles. In the l a t t e r case, depending on whether n^ i s less than or greater than n^, the second cycle moves to higher or lower <|J values than the f i r s t cycle respectively. Thus by curve f i t t i n g computed A, tj; values for an assumed theo-r e t i c a l model to experimental A, values obtained at various stages 55 56 INCIDENT LIGHT REFLECTED LIGHT E0 Eo Nj =nr}kj INDEX OF REFRACTION OF i'n MEDIUM <f; ^TNjDjCOS PHASE RETARDATION OF I th FILM F i g . 6.7 Two l a y e r model. 57 during the growth of an anodic oxide f i l m , the o p t i c a l s t r u c t u r e of the f i l m can be determined. A computer program for analysis of ellipsometer measurements i s a v a i l a b l e from the U.S. National Bureau of Standards (McCrackin 1969) which among other things w i l l compute A, 4> values f o r s i n g l e or m u l t i -l a y e r f i l m s , but which can analyze only s i n g l e A, \p experimental p a i r s . Tliis program was obtained and modified f o r use on the U.B.C. IBM 360/67 computer. A program to f i t to m u l t i p l e experimental A, if) values has been w r i t t e n by Dell'Oca 1969. I t was o r i g i n a l l y designed f o r the a n a l y s i s of ellipsometry data on the anodization of tantalum i n aqueous e l e c t r o -l y t e s , and could employ a m u l t i - l a y e r f i l m model with each l a y e r growing so as to be a constant proportion of the t o t a l f i l m thickness. In the present work the f i t t i n g strategy of t h i s program was modified to accom-modate closed A, curves with sharp turning points such as are obtained f o r f i l m s of Al^O^ growing on aluminum, and the program was used on the U.B.C. computer to cal c u l a t e values of oxide f i l m thickness and r e f r a c -t i v e index, and i n some cases to determine the substrate r e f r a c t i v e index where t h i s was not known at the l a s e r wavelength used. 58 7. EXPERIMENTAL CONSIDERATIONS 7•1 The Discharge Tube and Vacuum System .-^Design and Fabrication The purpose of selecting the dc cold cathode glow discharge as a plasma source was to permit an investigation of the anodization pro-cess as a function of plasma conditions. To f a c i l i t a t e this investiga-tion, i t was decided to base the p r i n c i p a l dimensions of the anodization c e l l on the discharge tube used by Thompson 1961a, so that his detailed studies on p a r t i c l e concentrations and energy distributions i n oxygen re-ported i n section 4.5 could be applied as a guide to the plasma condi-tions used here. Furthermore, the process of high f i e l d i o n i c conduction in anodic oxides has a strong temperature dependence (see Eqn. 3.3) so that i n any attempt to determine the importance of this process r e l a -tive to other mechanisms associated with plasma conditions, the sample temperature must be closely controlled. The equipment was therefore designed according to the following c r i t e r i a : (a) To reproduce the experimental configuration used by Thompson 1961a where p r a c t i c a l , and to permit anodization i n di f f e r e n t regions of the discharge. (b) To provide ease of o p t i c a l alignment of the system for e l l i p s o -metry. (c) To enable control of sample temperature. (d) To minimize contamination by impurities, especially those de-trimental to MOS applications, such as sodium ions. (e) To provide ease of sample replacement. The anodization c e l l , shown in Fig. 7.1, consisted of a quartz tube 10 cm i n diameter and 60 cm long, f i t t e d with stainless steel end F i g . 7.1 Schematic of a n o d i z a t i o n c e l l and pumping s t a t i o n (system B). 60 caps each sealed by three neoprene '0' r i n g s . Teflon rings of f l a t r ec-tangular cross-section were provided to cushion the end faces of the quartz tube. A hollow cathode (C) made of aluminum (for i t s low spu t t e r -ing rate) was mounted on the end of an i n s u l a t e d l i n e a r motion feedthrough i n one of the end caps, and the other end cap (A) served as grounded anode and connected the c e l l to a pumping system assembled from standard s t a i n -l e s s s t e e l components. The anode surface was gold p l a t e d by vacuum eva-poration to reduce oxide formation and associated plasma p o t e n t i a l v a r i a -tions . An adjustable sample holder (H) e l e c t r i c a l l y i s o l a t e d from ground entered the discharge tube c o - a x i a l l y through the pumping port i n the anode. The holder, shown i n F i g . 7.2, consisted of a hollow 2.6 cm diameter s t a i n l e s s s t e e l block j o i n e d v i a s t a i n l e s s s t e e l bellows to a pyrex tube (T) which was mounted on a standard vacuum flange. Water could be c i r c u l a t e d v i a t e f l o n tubes through the block, which had a chromel-alumel thermocouple (TC) embedded i n the back of the sample mounting face. The block, bellows and pyrex tube were covered by a two-part t u -bular quartz s h i e l d (Q) held by springs, f o r i s o l a t i o n from the discharge, and together with a mica mask (M) t h i s s h i e l d served to hold the sample ( S ) i n contact with the temperature-controlled block. The e n t i r e sample holder assembly could be extracted through the pumping port f o r sample replacement. Except i n e a r l y experiments, a l i n e of s i g h t b a f f l e (B) also made of quartz was attached to the front of the cathode to reduce the p o s s i b i l i t y of sputtered aluminum depositing on the sample . An i n v e s t i g a t i o n of the anodized surface of a tantalum sample with an electron probe microanalyzer did not detect any aluminum impurity, but minor p a r t i c u l a t e contamination present on the oxide surface was found to be r i c h i n s i l i c o n , and was a t t r i b u t e d to the mica mask. Y .AAAAA^ V . r. TC WATER >— EPOAY 3 / Q ALIGNMENT T _ ALIGNMENT LB_n CONTROLS [ h i 1 R :3 F i g . 7.2 The water-cooled adjustable sample holder. 62 In order to avoid hydrocarbon contamination from d i f f u s i o n pumps a sorption pump (SP) - ion pump (IP) combination was used i n the pumping s t a t i o n . The sorption pump (Varian 941-6002) was c o n t r o l l e d by a v a r i a b l e leak valve ( G r a n v i l l e P h i l l i p s model 203) and the 20&/sec d i f f e r e n t i a l i o n pump (Ultek) was provided with an i s o l a t i o n valve ( G r a n v i l l e P h i l l i p s type C model 202). A s t a i n l e s s s t e e l gas feed l i n e connected a c y l i n d e r of 99.999% oxygen (Matheson research grade) v i a another leak valve to the cathode end cap. Overnight pumping with the ion pump enabled a base pres--7 sure of 2 x 10 t o r r to be reached. The pressure range around 100 mtorr used f o r operation of the discharge was obtained by continuous sorption pumping of oxygen from the c y l i n d e r , to minimize impurity build-up. The pressure could be maintained w i t h i n -3% of a desired value (as i n d i c a t e d ft by the amp l i f i e d s i g n a l from a thermocouple gauge displayed on a chart recorder) by manual c o n t r o l of the oxygen i n l e t and pump leak valves. With p e r i o d i c inspection of the chart trace and appropriate valve adjus-tment, the pressure could be held constant f or the periods of several hours sometimes required to produce the desired oxide thicknesses. D i f f e r e n t regions of the discharge could be located around the sample by moving the cathode v i a i t s l i n e a r motion feedthrough, and various probes mounted on pyrex tubes could be brought i n front of the sample by means of double '0' r i n g feedthroughs i n the anode end cap. These consisted of a simple 0.5 mm diameter gold b a l l probe, a t r i p l e probe assembly of three platinum wires with 5 mm spacing f o r f i e l d meas-urements, an electron f i l t e r array of 0.08 mm diameter tungsten wires with 1 mm spacing and an indium-coated gold b a l l probe which was sp r i n g -This gauge, an Ultek model VT 6, was c a l i b r a t e d against an absolute gauge of the McLeod type. 63 loaded f o r MOS capacitance measurements. The discharge and sample b i a s i n g c i r c u i t s are shown i n F i g . 7.3. The high voltage supply (Hewlett Packard model 6525A) was provided with a current l i m i t c o n t r o l and ammeter, which were used to maintain the discharge current constant under varying conditions. The current gene-ra t o r (Northeast S c i e n t i f i c model R l 233) could supply constant currents from 10 uA up to 225 mA. The discharge tube was f i t t e d with 2.5 cm diameter p l a n e - p a r a l -l e l quartz windows W ( F i g . 7.1) on short side arms to allow entry and e x i t of the ellipsometer l i g h t beam before and a f t e r r e f l e c t i o n from the sample surface. The arms were mounted f o r an angle of incidence of 70° at the sample . The discharge tube and pumping system were mounted on a car-riage f i t t e d with r o l l e r bearings and running on a twin r a i l system. The ellipsometer stood on a rotatable p l a t e also mounted on the heavy s t e e l base of the r a i l system. The discharge tube could be moved i n t o p o s i t i o n between the ellipsometer arms, and aligned by means of various f a c i l i t i e s on the carriage u n t i l the ellipsometer l i g h t beam passed at normal i n c i -dence through the tube windows. Alignment of the sample was accompli-shed by tensioning two sets of threaded rods, one set attached i n s i d e the holder at the j o i n t between the hollow block and i t s bellows, the other attached to the flanges of a l a r g e r bellows D which connected the This angle was selected on the basis of the s e n s i t i v i t y of the e l l i p -someter measurement to the thickness of films of Nb^ O^ - on Nb and S i 0 2 on S i , obtained from computer c a l c u l a t i o n s using l i t e r a t u r e values of the r e f r a c t i v e i n d i c e s . 64 4kv VARIABLE SUPPLY + \ 12-5 C AT MODE SAMPLE ANODE 1 c CONS TAN I CURRENT GENERATOR T77T7T F i g . 7.3 Discharge and sample b i a s i n g c i r c u i t s . 65 holder to the system (rods not shown i n F i g . 7.1). 7.2 The O p t i c a l System 7.2.1 The automated ellipsometer The b a s i c ellipsometer was a Rudolph model 200E. A 1 mW He-Ne l a s e r (Spectra-Physics model 133, not l i n e a r l y polarized) was used as a ft l i g h t source and a ph o t o m u l t i p l i e r (RCA 931A tube with Kepco regulated voltage source) as a detector. A p r o t e c t i v e ground glass d i f f u s e r was o o placed over the ph o t o m u l t i p l i e r window, and a 6328A f i l t e r (100A bandwidth) was>located i n front of the d i f f u s e r . The l a s e r and f i l t e r combination enabled measurements to be made i n the presence of normal room l i g h t i n g , and more importantly, i n the presence of the emission from the glow o discharge. The Rudolph 5461A quarter wave p l a t e was replaced i n i t i a l l y o by a 6328A mica quarter wave p l a t e , and l a t e r by a quartz S o l e i l - B a b i n e t type compensator (Gaertner model L-135) mounted on the Rudolph wave p l a t e drum and set f o r quarter wave reta r d a t i o n at 6328A. A D i g i t a l Equipment Corp. PDP-8/E minicomputer was used to operate the ellipsometer i n the fol l o w i n g automated system, depicted i n F i g . 7.4. The p o l a r i z e r and analyzer mounts were each driven v i a gear t r a i n s by separate stepping motors (IMC Magnetics Corporation //PIN 008-008), one step producing .01° r o t a t i o n , and t h e i r azimuthal p o s i t i o n s were detected to 0.01° by shaft encoders (Decitrak TR 511-CW/D). The encoder output u n i t converted the angles fo binary-coded decimal form * a l l r e f r a c t i v e indices determined i n t h i s study p e r t a i n to the o He-Ne l a s e r wavelength of 6328 A. 66 s PDP8E COMPUTER TELETYPE F i g . 7.4 Schematic of computer-controlled e l l i p s o m e t e r system 67 (BCD) for input to the computer v i a an i n t e r f a c e , which was l a r g e l y comple-ted independently of t h i s study. The motor drive c i r c u i t s were also con-t r o l l e d v i a t h i s i n t e r f a c e . The p h o t o m u l t i p l i e r e r r o r s i g n a l , a f t e r a m p l i f i c a t i o n by a va-r i a b l e gain a m p l i f i e r with an adjustable zero c o n t r o l , was monitored as one of four analog inputs multiplexed i n the i n t e r f a c e to a s i n g l e analog-t o - d i g i t a l converter (DEC A811) with an accuracy of 0.1% F.S. The e r r o r s i g n a l was also displayed on a meter connected to the input of the A/D converter, to permit manual n u l l i n g and alignment of the ellipsometer. The BCD output from a d i g i t a l voltmeter could be fed to the i n t e r f a c e , which also contained a clock c o n s i s t i n g of a d i v i d e - b y - s i x counter that was t r i g g e r e d by a 60 Hz s i g n a l , g i v i n g a b a s i c u n i t of 0.1 seconds, and the 10 Hz pulses were fed to a second counter which was used to obtain s p e c i f i e d i n t e r v a l s between successive balances of the e l l i p -someter . The strategy employed i n automatic balancing of the ellipsometer was based on the p r i n c i p l e that the l i g h t i n t e n s i t y at the detector (error s i g n a l ) varies symmetrically with p o l a r i z e r (or analyzer) r o t a t i o n about i t s minimum value for small excursions from the minimum (Archer 1962). Furthermore, the p o l a r i z e r i s adjusted f i r s t since i t s true e x t i n -c t i o n s e t t i n g i s independent of the exact s e t t i n g of the analyzer for small deviations of the l a t t e r , whereas the converse i s not true (Archer 1962). In i t s balancing routine, the computer program determines which way the p o l a r i z e r motor must be stepped to reduce the p h o t o m u l t i p l i e r error s i g n a l , and then steps the motor i n that d i r e c t i o n , taking e r r o r s i g n a l readings a f t e r each step. The readings for a c e r t a i n number of steps (e.g. 64) are summed, and stepping i s continued so that the e r r o r 68 s i g n a l eventually goes through a minimum arid begins to increase again. The program then calculates a second sum of the same number of readings and continuously updates t h i s sum to contain only the 64 most recent readings. When t h i s second sum equals the f i r s t sum obtained on the other side of the minimum, the balance p o i n t , i . e . the mid-point between the two equal sums, i s calculat e d and the p o l a r i z e r i s stepped to that p o s i t i o n . Then the analyzer i s adjusted by the same routine. P r o v i s i o n i s made f o r the p o l a r i z e r or analyzer s t a r t i n g i n t h e i r (previously) balanced p o s i t i o n by d r i v i n g the motors away from the balance point p r i o r to proceeding as above, and a check f o r any er r o r due to gear backlash or missed or gratuitous motor steps was made by comparing the change i n p o s i t i o n of the shaft encoder before and a f t e r a balance with the net number of steps taken by the respective motor. A f t e r the analyzer and p o l a r i z e r have both been balanced, t h e i r encoder s e t t i n g s , the minimized e r r o r s i g n a l , the clock time and the d i g i t a l voltmeter output are read and stored to await output on a t e l e -type operated on an i n t e r r u p t b a s i s . The time required to balance the ellipsometer (from a condition close to balance) was about 2 to 3 seconds, and p r i n t i n g the data by the teletype required 5 or 6 seconds. These times presented no problem i n the present st u d i e s , f o r which the e l l i p -someter was balanced at one minute i n t e r v a l s . To obtain readings-in other ellipsometer zones (see secti o n 6.2.3), i t was necessary to manually preset the ellipsometer components. In . p r i n c i p l e the system could be programmed to alternate readings be-tween two zones not r e q u i r i n g r o t a t i o n of the quarter wave p l a t e , although the time required to step the p o l a r i z e r and analyzer from one zone to the other may be excessive for c e r t a i n applications. 69 The computer was not used to c a l c u l a t e A and from the e x t i n c -t i o n s e t t i n g s of the p o l a r i z e r and analyzer due to i t s l i m i t e d memory and a r i t h m e t i c c a p a b i l i t i e s . The corrections required f o r quarter wave plat e imperfections i n these c a l c u l a t i o n s are dealt w i t h i n s e c t i o n 7.2.3. 7.2.2 Ellipsometer alignment Proper alignment of the ellipsometer i s c r i t i c a l i f meaningful measurements using the f u l l s e n s i t i v i t y of the instrument are to be ob-tained. This i s e s p e c i a l l y true of automated measurements i n one zone only. Errors which may be present i n a misaligned instrument include ( i ) zero e r r o r i n angle of incidence scale ( i i ) v a r i a t i o n of the plane of incidence with angle of incidence ( i i i ) zero errors i n the p o l a r i z e r , analyzer and quarter wave p l a t e azimuth scales. Various methods of alignment have been described. McCrackin et a l . 1963 favoured the use of a metal r e f l e c t i n g surface, and presented a method which was independent of any small e l l i p t i c i t y i n the p o l a r i z e r prism. Aspnes and Studna 1971, however, pointed out that the use of a transparent r e f l e c t i n g surface eliminated the e f f e c t of f i r s t order e l l i p -t i c i t i e s i n e i t h e r prism, and t h i s approach was adopted. The o v e r a l l alignment procedure was as follows. (a) Collimator focusing Although a la s e r was used as a l i g h t source, the c o l l i m a t o r was retained since i t s input pinhole conveniently defined the p o l a r i z e r arm a x i s . Focusing was necessary since a condensing lens concentrated the l a s e r beam on t h i s input pinhole. The c o l l i m a t i n g lens p o s i t i o n was adjusted u n t i l the e x i t beam was sharp when viewed through an 70 a u x i l i a r y telescope previously focussed on i n f i n i t y (the Rudolph analyzer arm eyepiece o p t i c s could not be focused on objects more than 2 or 3 feet d i s t a n t ) . (b) Alignment of l a s e r beam with p o l a r i z e r arm axis A mounting f a b r i c a t e d for the l a s e r was adjusted u n t i l a maxi-mum i n t e n s i t y was transmitted through the stopped down quarter wave p l a t e e x i t i r i s diaphragm. This maximum was detected by the p h o t o m u l t i p l i e r with the analyzer arm i n the s t r a i g h t through p o s i t i o n but with no aper-tures to r e s t r i c t the l i g h t beam's passage to the ground glass d i f f u s e r . (c) Determination of zero e r r o r i n angle of incidence scale With the quarter wave pla t e i r i s stopped down as above, and the analyzer arm axi s defined by small apertures at the entrance and also immediately i n front of the photo m u l t i p l i e r f i l t e r , the analyzer arm was rotated i n .01° steps through the p o s i t i o n of maximum detector s i g n a l , noting the err o r s i g n a l meter d e f l e c t i o n at each point. The d i s t r i b u t i o n curve thus obtained was reasonably symmetrical, see F i g . 7.5, and the angle of incidence scale e r r o r was determined from the peak s i g n a l p o s i t i o n to be -0.05°. (d) Determination of the zero e r r o r i n the p o l a r i z e r and analyzer a z i -muth scales . The purpose of t h i s procedure i s to determine the analyzer and p o l a r i z e r scale readings P and A when the planes of transmission of t h e i r prisms are p a r a l l e l to the plane of incidence. The l a t t e r i s defined by the d i r e c t i o n s of propagation of the inc i d e n t and r e f l e c t e d beams The t h e o r e t i c a l basis for t h i s p o rtion of the alignment procedure i s given by Aspnes and Studna 1971. 71 F i g . 7.5 Angle of incidence (A.I.) zero e r r o r determination, and so may move with angle of incidence i f e i t h e r of the p o l a r i z e r or analyzer arm axes i s not perpendicular to the axis about which the analy-zer arm p i v o t s . Since the Rudolph ellipsometer i s not provided with t i l t adjustment on the arms, the procedure should be performed with the analyzer arm at the angle of incidence to be used i n subsequent measure-ments. An extra i r i s diaphragm aperture was mounted at the e x i t of the p o l a r i z e r assembly to permit the establishment of the plane of incidence, with the quarter wave plate assembly removed, as foll o w s . A f t e r s e t t i n g the desired angle of incidence of 70° (allowing f o r the zero error determined i n ( c ) ) , with the compensator removed and with P z A = 90° a thick o p t i c a l l y f l a t quartz plate was mounted as a 72 d i e l e c t r i c r e f l e c t o r and i t s p o s i t i o n adjusted u n t i l a maximum detector s i g n a l was obtained. This adjustment i s purely geometric and indepen-dent of component imperfections. With the plane of incidence established i n t h i s way, the analy-zer was allowed to n u l l near A = 0° f o r d i f f e r e n t set values of P about 90° to obtain a s t r a i g h t l i n e p l o t of A versus P (here the outputs from the shaft encoders). Then the p o l a r i z e r was allowed to n u l l near P = 0° for d i f f e r e n t set values of A about 90° to obtain another s t r a i g h t - l i n e p l o t of P versus A. The r e s u l t s of a t y p i c a l c a l i b r a t i o n are shown i n F i g . 7.6. At the point of i n t e r s e c t i o n the transmitted f i e l d vectors of the p o l a r i z e r and analyzer prisms are p a r a l l e l (or perpendicular) to the plane of incidence. The shaft encoder outputs were corrected by f i r s t s e t t i n g the p o l a r i z e r and analyzer so that the outputs read the i n t e r s e c -t i o n values, and then adjusting the shaft encoder p o s i t i o n s i n t h e i r mountings u n t i l the encoder outputs read 0.00° (or 90.00°). I t should be noted that the usefulness of t h i s alignment de-pends on the r e p r o d u c i b i l i t y with which any sample r e f l e c t i n g surface can be positioned by maximizing the i n t e n s i t y of l i g h t transmitted through the ellipsometer. This point i s dealt with f u r t h e r i n s e c t i o n 7.2.3. (e) Determination of the zero e r r o r i n the quarter wave pla t e azimuth s c a l e . With the p o l a r i z e r and analyzer crossed at 0.00° and 90.00° i n the s t r a i g h t through p o s i t i o n , the quarter wave pla t e (QWP) assembly was re-inserted and i t s azimuth adjusted u n t i l minimum transmission was again obtained. In t h i s condition the fa s t axis of the QWP was p a r a l l e l to the p o l a r i z e r transmission a x i s , i . e . 0.0° azimuth, and the QWP scale 73 P (DEC) F i g . 7.6 C a l i b r a t i o n of the p o l a r i z e r and analyzer scales (shaft encoder outputs). o-o balancing p o l a r i z e r with analyzer stationary near 90°. x-x balancing analyzer with p o l a r i z e r stationary near 90°. 74 error could be determined. (f) Calibration and tuning of a Soleil-Babinet Compensator for use as a near-ideal quarter wave plate. Ellipsometer measurements made i n the f u l l y automated mode were r e s t r i c t e d to a single zone. In the calculation of A and ip from such measurements, serious errors can be introduced by quarter wave plate imperfections, i . e . deviations of the r e l a t i v e phase retardation A and transmittance ratio T from the ideal values of 90.0° and 1.0 c c respectively (see section 7.2.3). It i s therefore very desirable to have as perfect a QWP as possible, and i n the present study a very care-f u l l y adjusted quartz Soleil-Babinet compensator (SBC) was used. This device consists of two wedges of quartz arranged to s l i d e re l a t i v e to each other so that they form a p a r a l l e l plate of variable thickness, mounted on a second p a r a l l e l plate of fixed thickness. The optic axes of the two plates are i n the plane of the plates but mutually perpendicular, so that when l i g h t passes through the two plates, a phase difference i s introduced between the two components p a r a l l e l to the axes whose magnitude can be varied by changing the thickness of the s l i d i n g wedge plate. The Gaertner model L-135 SBC used here was provided with a micrometer screw for wedge movement. The parameters A and T are strong functions of angle of i n -c c cidence, which i n turn may be a function of compensator azimuth Q (see section 7.2.3), and so the calibration and tuning were carried out with the SBC fast axis at the azimuth of 315° (=-45°) required for subsequent measurements in zone 1 (selected for i t s simple A, P and , A re l a t i o n s ) . F i r s t the approximate micrometer setting for 90° retardation (or —-where n i s an odd integer) for the laser l i g h t was determined by mounting 75 the SBC with i t s f a s t axis at approximately 3 1 5 ° between p o l a r i z e r and analyzer crossed at 0 . 0 ° and 9 0 . 0 ° i n the s t r a i g h t through p o s i t i o n , and noting the micrometer readings which gave e x t i n c t i o n at the detector. These are the set t i n g s producing 0 , 2TT, 4TT, ... r e t a r d a t i o n , i . e . the difference between successive s e t t i n g s represents 2TT r e t a r d a t i o n and nTi should be constant. The —j r e t a r d a t i o n condition i s obtained by adding one quarter of t h i s difference to any of the above n u l l s e t t i n g s . With t h i s approximate quarter wave s e t t i n g , the SBC f a s t axis azimuth was set to exactly 3 1 5 . 0 ° by adjusting f o r a n u l l with P = 3 1 5 . 0 ° , A = 4 5 . 0 ° (equivalent to (e) above). The f i n a l tuning of the SBC micrometer screw was accomplished by minimizing the differences between readings i n zones 1 and 3 obtained with a c a r e f u l l y aligned polished metal surface as r e f l e c t o r (the quartz surface could not be used since i n the A, P and , A r e l a t i o n s the compensator imperfection parameters have c o e f f i c i e n t s of sinA, which equals zero f o r d i e l e c t r i c s ) . A glass s l i d e coated w i t h Inconel having a m i r r o r - l i k e f i n i s h was used as the r e f l e c t o r , and aligned by maximi-zing the l i g h t r e f l e c t e d at 7 0 ° with the SBC assembly removed and p e A - 9 0 ° . The alignment was checked and considered good by f i n d i n g that P balanced at 0 . 0 + 0 . 0 1 ° when A was set at 9 0 . 0 ° . The compensator was then replaced and by very c a r e f u l adjustment of the micrometer, the follo w i n g minimal spread readings were obtained: P A Zone 1 1 6 . 8 2 ' 3 2 . 7 5 Zone 3 1 0 6 - 7 5 1 4 7 . 2 2 Using these readings i n the A,P and IJJ,A r e l a t i o n s , programmed by McCrackin 1 9 6 9 , gave the tuned compensator constants as A £ = 9 0 . 0 4 ° , 76 T c = s o t h a t A a n d ^ C 0 U 1 Q D e obtained to a good approximation (+0.1%) from e i t h e r zone 1 or zone 3 measurements using the f o l l o w i n g simple * r e l a t i o n s , p r o v i d i n g there were no errors due to c e l l windows or t i l t of the sample surface (see next s e c t i o n ) : f A = 90° + 2P , 135° % P >, -45° -\ (7.1a) Zone 1 < 1 1 V Q = -45° I i|) = A x , 90° >, A± ? 0° J (7.1b) f A = 2P - 90° , 225° * P, * 45° ) (7.1c) Zone 3 < J V Q = -45° I = 180° - A 3 , 180° 5 A 3 >, 90° J (7.Id) 7.2.3 Treatment of errors i n i n s i t u e l l i p s o m e t r y The a n a l y s i s and correction of errors i n ellipsometry has been the subject of a number of recent papers, f o r instance McCrackin 1970, Aspnes 1971, Azzam and Bashara 1971. A b r i e f discussion of some of the more important errors w i l l be presented here, (a) P o l a r i z a t i o n of the l i g h t source I d e a l l y the l i g h t incident on the p o l a r i z e r should be i s o t r o p i c , with no l i n e a r preferences. This condition was checked f o r the Spectra-Physics l a s e r used here by i n s e r t i n g a c i r c u l a r p o l a r i z e r a f t e r the l a s e r and noting any change i n the n u l l P and A s e t t i n g s f o r r e f l e c t i o n from a surface. The changes observed were n e g l i g i b l e f o r two d i f f e r e n t angles of incidence and d i f f e r e n t o r i e n t a t i o n s of the c i r c u l a r p o l a r i z e r , and the l a s e r was assumed to be s u f f i c i e n t l y unpolarized. * The i d e a l ellipsometer r e l a t i o n s for the other two zones are: f * = - 2V 135° * P2 * "45° \ Q . + 4 5 c Z ° n e 2 \ , = A 2 . . 9 0 ° . , A 2 , 0 ° J f A = 90° - 2P 4, 45° % P 4 * -225° 20116 4 U = 180° - A 4, 180° * A 4 * 90° Q = +45' 77 (b) P o l a r i z e r and analyzer prism imperfections These include leakage, i . e . the transmission of l i g h t not p o l a r i z e d p a r a l l e l to the transmitted f i e l d vector of the prism, and de p o l a r i z a t i o n . The degree of p o l a r i z a t i o n of a p a r t i a l l y p o l a r i z e d beam of l i g h t i s the i n t e n s i t y of the p o l a r i z e d part as a f r a c t i o n of the t o t a l i n t e n s i t y . In terms of the Stokes parameters i t i s given by ( S l 2 + s 2 2 + s 3 2 ) 1 / 2 / S ( ) . P o l a r i z e r prism leakage can be checked by n u l l i n g the e l l i p -someter, i n s t r a i g h t through operation withthe compensator removed, f o r various o r i e n t a t i o n s of the p o l a r i z e r with respect to a p a r t i a l l y p o l a r -i z e d l i g h t source. I f the r e l a t i v e azimuth A-P i s i n v a r i a n t under t h i s operation, then p o l a r i z e r leakage i s n e g l i g i b l e . This was found to be the case f o r the Rudolph p o l a r i z e r , and Aspnes 1971 found that leakage was i n general undetectable i n e l l i p s o m e t e r - q u a l i t y c a l c i t e prisms. He also showed that averaging measurements over four zones would cancel the e f f e c t of leakage i f the compensator was pe r f e c t . Azzam and Bashara 19 71 showed that p o l a r i z e r d e p o l a r i z a t i o n would a f f e c t the c a l c u l a t i o n of ^  and would not be cancelled by four-zone averaging - a 1% depolarization could give an e r r o r of 0.15° i n a ip of 22.5° . A l l analyzer prism imperfections are cancelled by j u s t two-zone averaging, so that the better prism should be used as p o l a r i z e r , (c) Compensator imperfections The two major imperfections are, as mentioned i n se c t i o n 7.2.2, deviations o f t h e retardation A c and r e l a t i v e transmittance T^ from 90.0° and unity r e s p e c t i v e l y . Holmes 1964 and Oldham 1967 have pointed out that due to multi p l e i n t e r n a l r e f l e c t i o n interference phenomena, A c and 78 T £ are both o s c i l l a t i n g functions of compensator pl a t e thickness, and also strong functions of angle of incidence. The l a t t e r means that i f the compensator axis of r o t a t i o n i s not w e l l aligned with the d i r e c t i o n of propagation of the l i g h t , then A c and T^ w i l l be functions of QWP azimuth Q. The mica quarter wave pla t e used i n i t i a l l y i n t h i s work showed both of these e f f e c t s - computer c a l c u l a t i o n s (McCrackin 1969) from four zone measurements on a c a r e f u l l y aligned Inconel surface gave the f o l l o w -ing values: Q T A c c 45° 1.041 91.58 -45° 1.033 92.33 On the Poincare sphere (Fig. 6.5) i t may be seen that small deviations i n A^ mainly a f f e c t \j>, and those i n T^ a f f e c t A. McCrackin 1970 has shown that f o r a quarter wave p l a t e with small imperfections set at Q = -45° the r e l a t i o n s between P, A, A, \JJ and the imperfections t = T - 1 and a = A = 90° are c c r P = (A - 90° - tsinA)/2 135° >, P-L 5 -45° Zone 1 \ L A± = i> - (asinAsin2i(j)/2 90° >, A± >, 0° (7.2) T P = (A + 90° + tsinA)/2 225° * P 3 >, 45° Zone 3 3 I A = 180° - if> - (asinAsin2^)/2 180° >, A^ >, 90 x3 Thus i f both these imperfections are small, they may be can-c e l l e d by two-zone averaging. The errors are maximum f o r a surface w i t h A - 90° and i}i - 45°, which implies that a r e f l e c t i n g surface with these values should be chosen f o r the evaluation of these errors or f o r t h e i r minimization by compensator tuning. This was reasonably s a t i s f i e d by the Inconel surface (A = 123°, i> - 33°) used i n section 7.2.2(f). 79 Other i m p e r f e c t i o n s which may be p r e s e n t i n the compensator are s t r a i n b i r e f r i n g e n c e and o p t i c a l a c t i v i t y , Aspnes 1971 found the former t o be absent i n q u a r t z components, and the e f f e c t s o f b o t h a r e expected to be c a n c e l l e d by a v e r a g i n g o v e r a l l f o u r zones (Azzam and Bashara 1971). (d) C e l l windows S t r a i n b i r e f r i n g e n c e i n the c e l l windows may be a major source of e r r o r i n i n s i t u measurements. The e f f e c t can be a n a l y z e d by t r e a t i n g each window as a wave p l a t e of f i x e d azimuth and s m a l l r e l a t i v e r e t a r d a -t i o n . I f the compensator i s n e a r - i d e a l , the s m a l l compensator and w i n -dow c o r r e c t i o n s w i l l add a l g e b r a i c a l l y , and McCrackin 1970 has shown t h a t t h e i r combined e f f e c t on vp i s c a n c e l l e d by two-zone a v e r a g i n g , b u t the two-zone-averaged A must be c o r r e c t e d by a window c o r r e c t i o n f a c t o r w which i s independent of A. The e q u a t i o n s 7.2 become f P = [A - 90° - t s i n A - (a 2/tan2i|0 + w]/2 (7.3a) Zone 1 •{ I A± = i> + ( a 1 - a) (sinAsin2i|))/2 (7.3b) f P = [A + 90° + t s i n A + (o<2/tan2ij/) + w]/2 (7.3c) Zone 3 -j I A 3 = 180° - i> + (a± - a) (sinAsin2i}0/2 (7.3d) w i t h the same r e s t r i c t i o n s on the range of P and A, and where c^, and w are the window c o r r e c t i o n parameters. The v a l u e of w can be determined from measurement of P^ and P f o r a s u r f a c e w i t h and w i t h o u t the c e l l windows i n p o s i t i o n , the change 3 i n t he sum (?1 + 7 ) b e i n g e q u a l t o w . Measurement of w f o r the windows of the d i s c h a r g e tube d e s c r i b e d i n s e c t i o n 7.1 gave v a l u e s between 1.5° and 2°, depending on the e x a c t r e -g i o n of the windows u t i l i z e d . Furthermore, the two-zone-averaged \p v a l u e s o b t a i n e d w i t h and w i t h o u t the windows were always e q u a l w i t h i n .05°, c o n f i r m i n g the s m a l l n e s s of the b i r e f r i n g e n c e and the v a l i d i t y o f McCra-c k i n 1 s treatment. 80 I f automated s i n g l e zone i n s i t u measurements are to be cor-rected, assuming a and t have been determined f o r t h i s zone s e t t i n g of the quarter wave p l a t e , and a can be evaluated from equations 7.3 by using measurements on the surface i n a i r f o r the values of A and ty. The e r r o r terms i n 7.3(a) and 7.3(b) could thenbe estimated f o r any P^, measured i n s i t u , using the i d e a l r e l a t i o n s (Equations 7.1 a) and 7.1 b) to f i n d sinA, s i n 2\IJs and tan 2ty, with i t e r a t i o n i f desired. The c e l l windows should be as th i n as p r a c t i c a l (without pro-ducing excessive s t r a i n birefringence due to pressure d i f f e r e n t i a l s ) and should be aligned close to normal to the l i g h t beam, to minimize the path length i n the windows and hence the bi r e f r i n g e n c e e f f e c t s and also alignment problems caused by l a t e r a l displacement of the l i g h t beam (by r e f r a c t i o n ) . Other window Imperfections, such as o p t i c a l a c t i v i t y , have been shown to be cancelled by two-zone averaging (Azzam and Bashara 1971). (e) T i l t of the sample surface Although a l l samples should be aligned by the method used i n section 7.2.2(d), i t i s possible that the sample surface may be t i l t e d with respect to the surface Which was used f o r e s t a b l i s h i n g the plane of Incidence. The main e f f e c t of a small r o t a t i o n of the sample surface by an angle T about the axis formed by the surface and the o r i g i n a l plane of Incidence i s to change the readings of the p o l a r i z e r , QWP and analyzer azimuths by the same angle T, i . e . P x = P 1' + T , A± = A x ( + x P 3 = P3< - f x , A 3 - A 3' + x Q = Q' + x where P^', A^', P A 3' amd Q' are the actu a l azimuth readings and P^, 81 A^, P^, A^ and Q are the true azimuths which would be measured i f the instrument and surface were properly aligned. I t i s clear from Eqns.7.1 that whereas averaging measurements over four zones can correct for T i n P and A, the error i n the QWP azimuth i s not corrected by averaging. For measurements i n a i r , McCrackin 1969, 197 0 has shown that x can be ca l c u l a t e d from P ', A,', P„', A ' and Q' i f T and A are 1 1 3 3 c c known, and his program w i l l make the necessary corrections to a l l sub-sequent readings f o r the sample and ca l c u l a t e A and TJJ with the corrected values. For measurements made on a sample with t i l t i n a c e l l , the c e l l window corrections to P^ , A^\7^ , A^' must be made f i r s t using previously determined values of w, and.a^, then T computed as above. The readings are then f u r t h e r corrected for x, and f i n a l l y averaged to cancel the com-pensator imperfections t and a and y i e l d A and ty. Thus samples i n a c e l l should be adjusted c a r e f u l l y to eliminate t i l t i f p o s s i b l e . 82 8. INVESTIGATION OF DISCHARGE PARAMETERS AFFECTING RATES OF ANODIZATION 8.1 Introduction The anodization of niobium i n a dc cold cathode discharge was studied with in s i t u ellipsometry i n e a r l i e r work (Lee et a l . 1970). In the system used for that study, denoted system A and shown in Fig. 8.1, the b o r o s i l i c a t e glass discharge tube was 5 cm i n diameter, and the e l -lipsometry measurements could only be made between oxide formations with o the plasma extinguished. Mean growth rates of from .04 to 3.4 A/min were obtained for t o t a l current densities to the sample of 0.1 to 1.5 2 mA/cm respectively. The work was extended by using phase-sensitive detection of ellipsometer n u l l s , which enabled oxide thickness estimates to be made pe r i o d i c a l l y while anodization was i n progress, and some re-sults of these measurements are included here. However, the above studies were r e s t r i c t e d to anodization i n the negative glow with gas pressures around 60 mtorr and discbarge currents not greater than 10 mA. The main investigations were performed i n the 10 cm diameter quartz system B described i n section 7.1, and were aimed at complementing the e a r l i e r studies with measurements i n the positive column while s a t i s -fying the requirements detailed i n section 7.1. The samples consisted mainly of electropolished polycrystalline tantalum and niobium, and the parameters varied were plasma density, location \vdthin the plasma region, gas pressure, and discharge and sample currents. 8.2 Sample Preparation Samples about 1.5 cm square were cut from 1.6 mm thick Fansteel capacitor grade niobium or 99.99% tantalum and mechanically abraded on CAPACITOR MANOMETER ION GAUGE LEAK VALVE SERVO LEAK VALVE SORPTION PUMP FROM OXYGEN FEED SYSTEM ELLIPSOMETER AXIS -DISCHARGE ELECTRODE 00 Co F i g . 8.1 Schematic of discharge system used by Lee et a l . 1970 (system A). 84 emery papers to 4/0 grade. They were then e l e c t r o p o l i s h e d i n a Teflon c e l l with a platinum electrode to give a good o p t i c a l r e f l e c t i n g surface. For niobium the e l e c t r o l y t e was 2 parts by volume of 48% HF, 4 parts 98% H 2S0 4 and 5 parts 85% l a c t i c a c i d (Pelleg 1967) and f o r tantalum i t was one part 48% HF and 9 parts 98% H„S0,. Current d e n s i t i e s of be-2 4 2 tween 100 and 150 mA/cm were used f o r several minutes with p e r i o d i c i n s p e c t i o n . Both e l e c t r o l y t e s were c i r c u l a t e d and used warm. A f t e r p o l i s h i n g , the samples were rinsed thoroughly i n d i s t i l l e d water, dipped i n 48% HF f o r 10 seconds and then rinsed again. 8.3 Measurements and Results 8.3.1 O p t i c a l constants of the substrates Before any i n s i t u ellipsometry data on the plasma anodization of niobium and tantalum could be analyzed, i t was necessary to determine the o p t i c a l constants of these metals at the He-Ne l a s e r wavelength of o 6328A. This was accomplished by s o l u t i o n anodizing a sample of each metal i n stages, making ellipsometry measurements at each oxide thickness u n t i l at l e a s t one complete cycle of A, if) values had been obtained, and then curve f i t t i n g to t h i s data . The samples were prepared as i n section 8.2, except that a metal stub was provided f o r e l e c t r i c a l contact purposes. Anodization was c a r r i e d out i n d i l u t e (0.2N) ^SO^ s o l u t i o n i n order to obtain a homogeneous non-absorbing oxide (Young and Zobel 1966) and so s i m p l i f y The o p t i c a l constants cannot be obtained from a measurement of A and if) f o r the unanodized substrate because the .A, if; values are affected by the few tens of angstroms of oxide present a f t e r e l e c t r o - p o l i s h i n g . In the curve f i t t i n g procedure, the unknown r e f r a c t i v e index of t h i s pre-e x i s t i n g f i l m i s taken to.be that of the anodic oxide, but. the method i s s t i l l v a l i d since A and if) are r e l a t i v e l y i n s e n s i t i v e to r e f r a c t i v e index of very t h i n f i l m s ( i n contrast to f i l m t hickness). 85 the c u r v e - f i t t i n g . The constant current density of about 1 mA/cm2 was int e r r u p t e d at various predetermined times and the sample removed from the e l e c t r o l y t e , rinsed i n d i s t i l l e d water and blown dry with nitrogen gas f o r the ellipsometry measurements. Alignment was maintained by mounting the sample i n a f i x t u r e which r e g i s t e r e d i n the aligned mounting j i g of the ellipsometer. An angle of incidence of 70° was used, and readings were taken i n a l l four zones using a mica quarter wave p l a t e as compensator. ft The A, vjj values obtained for the tantalum sample are shown o i n F i g . 8.2. The l a s t of the 32 points (oxide thickness = 3307A) over-lapped i n t o the 3rd c y c l e , and i t can be seen that the i n i t i a l loop i s retraced on subsequent cycles. This establishes that the oxide f i l m i s a s i n g l e homogeneous non-absorbing l a y e r , and the s o l i d curve shown was f i t t e d to the experimental points on t h i s b a s i s using Dell'Oca's program (see sec t i o n 6.2.4). The r e f r a c t i v e indices of the f i l m and tantalum substrate which gave the best f i t were N^ = n^ = 2.185 and = 2.46 - J2.56 re s p e c t i v e l y . The f i t t i n g was accomplished by varying n^ i n steps of .005 and and i n steps of .01. The above value of n^ i s i n good agreement with the value of o 2.19(5) f o r anodic tantalum pentoxide at 6328A predicted by the Hartmann equation reported by Young 1958: n x(X) = 2.14 + 0.292 [(X/10 3A) - 2.305]" 1' 2 S i m i l a r c u r v e - f i t t i n g to the data obtained on the niobium * The work on s o l u t i o n anodization of tantalum was e a r n e d out rn con-iunction with w. Cornish - see Cornish 1972. A s i m i l a r procedure was also i s e d l a t e r to determine the o p t i c a l constants of a sample of sput-tured tantalum supplied by.the Northern E l e c t r i c Co. These were round to be 2.99 - 2.82J at 6328A. 86 360t 340 320 300 2Q0] 2.60 240 CO 220 Uj C j 200 < Fig. 8.2 Ellipsometry data for l ^ O ^ on Ta i n a i r used to obtain the op t i c a l constants of QTa at X = 6328A. The numbers alonj the curve are fi l m thicknesses i n A. The word 'bare' i d e n t i f i e s the f i r s t measurement on the unanodized sample, o f i r s t cycle • x .'2nd cycle Q 3rd cycle 87 sample y i e l d e d ^ = = 2.32 for the oxide and N £ = 3.5 - J3.75 f o r the niobium substrate. Again the oxide index i s i n reasonable agreement O with the value ^ = 2.34(1) at 6328A c a l c u l a t e d from the expression nx(x) = 2.26 + 0.398 [(x/10 3l) - 2.56]" 1* 2 previously reported by Young 1960b. Recently, Ord et a l . 1972 have published data obtained by i n s i t u e llipsometry on the anodization of tantalum and niobium i n d i l u t e s ulphuric a c i d . They found ^ = 2.20 and N 2 = 3.02 - j2.57 f o r tantalum, and n^ = 2.30 and 3.03 - J3.61 for niobium. The values of the two oxide indices are close to the r e s u l t s presented here, but the substrate i n d i c e s , p a r t i c u l a r l y the r e a l parts n^, are not i n agreement. I t has been r e -ported by B e l l i n a et a l . 1972 that the amount of oxygen absorbed i n niobium can change the o p t i c a l constants of that metal, and both the r e s u l t s found here for niobium and those of Ord et a l . are w i t h i n the range c a l c u l a t e d by B e l l i n a et a l . This absorbed oxygen e f f e c t may apply f o r tantalum also. A l i t e r a t u r e search f a i l e d to reveal other determinations of o the o p t i c a l constants of these metals at 6328A, except f o r suspect niobium values obtained by neglecting the oxide f i l m present a f t e r e l e c -t r o p o l i s h i n g (Golovashkin 1969 - r e f e r also to Burge and Bennett 1964). For the actual plasma anodization s t u d i e s , the polished samples were (unless otherwise noted) soldered to the water-coolable sample holder with indium for good thermal contact and covered with a mica mask and the quartz cap so as to expose a ~lcm square of the sample surface. The l a t t e r was aligned with respect to the ellipsometer for measurements both before and a f t e r discharge c e l l assembly and evacuation, to obtain the window correction (section 7.2.3(d). 88 The general anodizing procedure was as f o l l o w s : (1) The system was evacuated with the sorption pump and then pum-ped overnight using the ion pump to a base pressure of about 2 x 10 t o r r (as in d i c a t e d by the pump cu r r e n t ) . (2) The ion pump valve was closed and the pumping function was returned to the sorption pump i n order to operate the system i n a dynamic flow mode at the desired pressure i n the 50-200 mtorr range by allowing oxygen to c o n t i n u a l l y leak i n t o the system and monitoring the thermocouple gauge output. (3) With the leak valves adjusted to maintain the required pressure, the substrate holder temperature c o n t r o l l e d by water c i r c u l a t e d from a thermos tat t e d bath, and the ellipsometer c o n t r o l system programmed to balance at one minute i n t e r v a l s , the discharge was struck and i t s current 1^ adjusted to the required l e v e l , u s u a l l y 40 mA. The discharge was q u a l i t a t i v e l y s i m i l a r to that described by Thompson 1961a, operating i n the hollow ca-thode mode (section 4.5) with well-defined s t r i a t i o n s i n the p o s i t i v e column. However, the l i g h t emitted from the negative glow was w h i t i s h with only a s l i g h t green ti n g e , and the s t r i a t i o n s were i n i t i a l l y pink, only becoming b l u i s h a f t e r some time. (4) I s o l a t e d high input impedance electrometers (Keithley model 602) were used i n the c i r c u i t shown i n F i g . 8.3 to monitor the p o t e n t i a l of the sample with respect to a small gold b a l l probe located nearby, and the p o t e n t i a l of t h i s f l o a t i n g probe with respect to the discharge anode. When the discharge had stab-i l i z e d , as evidenced by the constancy of these p o t e n t i a l s and - H V 1 S A M P L E P P O B E A N O D E J O CONSTANT CURRENT GENERATOR + 40v V A R I A B L E SUPPLY EL 7 R VOLTMETER \ / y + 1 kv VARIABLE S U P P L Y 7 / / D V M INTERFACE 7777"" I S O L A T I O N A M P L I F I E R R E C O R D E R ^ F i g . 8.3 C i r c u i t used to monitor sample and probe p o t e n t i a l s . oo vo 90 the r e l a t i v e infrequency of f l u c t u a t i o n s i n the emitted l i g h t , the constant current supply was switched to the sample and anodization commenced . Diagnostic measurements were also made by using a dummy sample, o coated by vacuum evaporation with a -5000A th i c k gold f i l m , i n place of the anodization sample. Current-voltage c h a r a c t e r i s t i c s obtained f o r these gold-plated samples were analyzed as f o r an i d e a l plane Langmuir probe. Four-zone ellipsometer readings were taken at the end of every period of anodization. A f t e r several formations, on a given sample, oxide thicknesses could be obtained by curve f i t t i n g to the A , T|I values calcul a t e d from these readings. The curve f i t t i n g was accomplished by varying the parameters of a s i m p l i f i e d model of the oxide f i l m , and usu a l l y a model of two-non-absorbing layers growing simultaneously was found to be appl i c a b l e (see also Dell'Oca et a l . 1971). Except as otherwise noted, the sample temperature was main-tained at 30°C, and the anodization rates quoted i n the fo l l o w i n g sec-tions are mean oxide growth r a t e s , given by the" increase i n oxide t h i c k -ness as determined from ellipsometry readings before and a f t e r the f o r -mation divided by the time the anodizing current was applied. 8.3.2 Oxygen flow through the c e l l In the e a r l i e r work (Lee et a l . 1970) using system A the pressure In the discharge tube was maintained by admitting oxygen at a point An important advantage of anodizing at constant current as opposed to constant voltage i s that the conditions i n the plasma, s p e c i f i c a l l y the p o t e n t i a l d ifference across the sheath region, should also remain con-stant (ignoring such e f f e c t s as work function f l u c t u a t i o n s ) . Maintain-ing the voltage across the oxide constant during growth i s not a s t r a i g h t -forward matter, and i s c e r t a i n l y not achieved by applying, a constant sam-ple bias with respect to the anode (see section 4.2.2). 91 between the tube and the s o r p t i o n pump (see F i g . 8.1). T h i s system was su b s e q u e n t l y m o d i f i e d so t h a t the oxygen flowed c o n t i n u o u s l y through the a c t i v e r e g i o n o f the c e l l , and as can be seen from Table 8.1 t h i s r e s u l t e d i n about a t h r e e f o l d i n c r e a s e i n const a n t c u r r e n t growth r a t e on a p o l y c r y s t a l l i n e n i o b i u m sample. S i m i l a r r e s u l t s (not shown i n Table 8.1) were o b t a i n e d w i t h a s i n g l e c r y s t a l n i o b i u m sample when the e a r l i e r s t a t i c c o n d i t i o n s were approximated by r e s t r i c t i n g the t h r o u g h -put w i t h the s o r p t i o n pump and oxygen i n l e t v a l v e s . S i n c e t h e r e were no obvious s i g n s o f any change i n plasma c o n d i t i o n s (e.g. as r e g a r d s l i g h t e m i s s i o n o r p o t e n t i a l d i f f e r e n c e r e q u i r e d f o r the 5 mA d i s c h a r g e c u r r e n t ) , the i n c r e a s e was thought t o be due to a r e d u c t i o n i n the b u i l d up o f i m p u r i t i e s from the d i s c h a r g e tube w a l l s and e l e c t r o d e s . Such an i m p u r i t y e f f e c t may a c t through changes i n the energy d i s t r i b u t i o n and d e n s i t y o f the e l e c t r o n s i n the plasma (see s e c t i o n 8.4). 8.3.3 Plasma d e n s i t y I n i t i a l attempts t o anodize t a n t a l u m samples i n the 10 cm d i a -meter d i s c h a r g e o f system B r e s u l t e d i n v e r y low growth r a t e s i n the ne-g a t i v e glow, and no d e t e c t a b l e growth i n i the p o s i t i v e column as measured by the r a t e o f change o f p o l a r i s e r n u l l s e t t i n g dP-^/dt, f o r d i s c h a r g e c u r r e n t s 1^ up to 40 mA and a n o d i z a t i o n c u r r e n t s t o the sample I g o f be-tween 0.1 and 2 mA at a p r e s s u r e o f 60 mtorr (see Table 8.1). The growth r a t e s i n the n e g a t i v e glow c o u l d be i n c r e a s e d s l i g h t l y by p o s i t i o n i n g a b a f f l e c o n s i s t i n g o f a 3 cm diameter n i o b i u m d i s c on the tube a x i s about 2 cm i n f r o n t o f the sample, s u g g e s t i n g a p o s s i b l e i n f l u e n c e from h i g h energy e l e c t r o n s emanating from the h o l l o w cathode (Thompson 1961a). However, mounting a q u a r t z b a f f l e on the cathode as d e s c r i b e d i n s e c t i o n 7.1 d i d n ot enable a n o d i z a t i o n to occur i n the p o s i t i v e column, and i n Table 8.1 Rates of anodization for various experimental configurations. C e l l configuration Sample Location and orientation System A: 5cm dia. pyrex c e l l , inverse brush cathode, no baffles. 11. no through flow of oxygen 2. oxygen flowed through c e l l System B: 10cm dia. quartz c e l l , hollow cathode. 1. no baffle on cathode (a) no baffle near sample (b) fixed Nb f o i l b a f f l e 1.5 cm i n front of sample (c) movable Ta f o i l b a f f l e 3cm in front of sample on axis off axis 2. quartz b a f f l e on cathode (a) movable Ta baffle 2.8-8 cm i n front of sample on axis (b) sample on rotatable holder, f no baffle (c) rotatable sample holder, constrictor 2 cm i n front of sample (d) regular sample holder, constrictor 2 cm in front Nb3,px,ep Nb5,px,ep Ta,pxf,cp Nb4,sx,ep I I Nb3*,px,ep! rag, fa ng,fa pes,fc ng,fc ng,fc ng,fc pes,fc pes, f c pes, fa pes,f c pes,fa pes, f c P (mtorr) 60 60 60 60 60 60 70 65 65 62 62 60 Id (mA) 20-40 20 20 20 20-30 30 30 40 40 40 Is (mA) dP-L/dt (deg/min) 1 1 0.1-2.0 0.4 0.4 0.4 0.1-3.0 0.2 0.2 1.0 1.0 0.2 <0.005 -0.01 -0.06 <0.005 <0.005 -0.005 -0.007 0.11 0.10 Me Growth an rate(A/min) 1.5 4 - 6 0.045 0.06 -3 ~3 chemical po l i s h , f: f o i l , Key px: polycrystalline, sx: single c r y s t a l , ep: electropolished, cp: ng: negative glow, pes: positive column s t r i a t i o n , f a : facing anode, f c : facing cathode Oxide grown previously i n system A removed with ammonium fluoride-buffered HR. 93 f a c t moving the ni o b i u m d i s c from an o f f - a x i s p o s i t i o n i n the Faraday dark space onto the tube a x i s caused the f i r s t s t r i a t i o n to be s h i f t e d f orwards t o a l o c a t i o n i m m e d i a t e l y b e h i n d the d i s c , which demonstrates t h a t the main i o n i z i n g e l e c t r o n s i n the Faraday dark space a re s t i l l on the tube a x i s , even w i t h the b a f f l e d cathode. N e v e r t h e l e s s , these e l e c -t r o n s were not the o n l y reason f o r l a c k o f o x i d e growth, s i n c e a n i o b i u m sample o r i e n t e d w i t h i t s exposed s u r f a c e f a c i n g the anode by suspending i t from a t h i n q u a r t z tube w i t h the u s u a l sample h o l d e r r e t r a c t e d d i d no t a n o d i z e e i t h e r . A comparison o f the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s o b t a i n e d f o r t h i s f r e e l y suspended sample (both w h i l e f a c i n g the cathode and anode) and f o r a g o l d - p l a t e d sample i n the 5 cm d i a . system A r e v e a l e d t h a t the plasma d e n s i t y (as i n d i c a t e d by the p o s i t i v e i o n c u r r e n t ) was much lower i n the 10 cm system, even w i t h e q u a l d i s c h a r g e c u r r e n t d e n s i t i e s through the t u b e s , and was lower i n the p o s i t i v e column than I n the n e g a t i v e glow. The c h a r a c t e r i s t i c s f o r the two extremes, namely the n e g a t i v e glow o f s y s -tem A and the p o s i t i v e column o f system B, are shown i n F i g . 8.4. I t can be seen t h a t the samples behave as Langmuir p r o b e s , the c h a r a c t e r i s t i c s e x h i b i t i n g the u s u a l p o s i t i v e i o n and e l e c t r o n c o l l e c t i o n r e g i o n s . A l t h o u g h the i o n c u r r e n t magnitudes are v e r y d i f f e r e n t , the e q u a l d i s c h a r g e c u r r e n t d e n s i t i e s do r e s u l t i n s i m i l a r e l e c t r o n ' s a t u r a t i o n ' c u r r e n t s . The lower s l o p e o f the curve f o r the 10 cm system can be p a r t l y accounted f o r by t h i s sample not b e i n g g o l d - p l a t e d (the areas o f the n i o -2> 2 bium and g o l d - p l a t e d samples were 1.1 cm and 1.0 cm r e s p e c t i v e l y ) . F urthermore, the e l e c t r o n c u r r e n t drawn by the ni o b i u m sample when mounted on the s t a n d a r d 3 cm diameter h o l d e r was e s p e c i a l l y low, as i n d i c a t e d by the t h r e e s o l i d p o i n t s i n F i g . 8.4. T h i s shows t h a t the sample h o l d e r 94 10. POSITIVE ION CURRENT REGION ELECTRON AND NEGATIVE ION CURRENT REGION 20 30 F i g 8.4 Sample c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s : x g o l d - p l a t e d sample i n n e g a t i v e glow of system A, I d = 10mA, p -= 55 m t o r r ; o suspended niobium sample i n p o s i t i v e column of system B, I d = 40 mA, p = 60 mtorr; • as o except mounted on sample h o l d e r . 95 assembly p e r t u r b s the plasma and e f f e c t i v e l y lowers the plasma d e n s i t y near the sample f a c e by d i v e r t i n g the plasma. I t was found p o s s i b l e t o l o c a l l y i n c r e a s e the plasma d e n s i t y i n the p o s i t i v e column of the 10 cm system by the i n t r o d u c t i o n of a plasma c o n s t r i c t o r , and i n t h i s way a n o d i z a t i o n r a t e s comparable to those f o r the 5 cm system c o u l d be a c h i e v e d . Two types o f c o n s t r i c t o r were t e s t e d , w i t h s i m i l a r r e s u l t s : one was i n the form of a 'top h a t ' made from s t a i n l e s s s t e e l shim; the b r i m of the hat was 9.5 cm o.d., and the 3.5 cm d i a m e t e r , 4 cm l o n g c e n t r a l f u n n e l was open ended. The o t h e r con-s t r i c t o r c o n s i s t e d of a 10 cm diameter c o n i c a l b o r o s i l i c a t e g l a s s f i l t e r f u n n e l w i t h the stem sawn o f f and l e g s added f o r s u p p o r t . The s m a l l e r end ( ' e x i t ' ) of e i t h e r c o n s t r i c t o r was u s u a l l y p o s i t i o n e d 2 t o 3 cm i n f r o n t o f the sample ( F i g . 8.5). Both arrangements produced an o p t i c a l l y dense plasma ahead o f the sample, and i n c r e a s e d the i o n and e l e c t r o n TO CATHODE (a) TO CATHODE s\ (b) F i g . 8.5 L o c a t i o n of c o n s t r i c t o r s : (a) s t a i n l e s s s t e e l 'top h a t ' , (b) b o r o s i l i c a t e f u n n e l . 96 currents to the 0.5 mm diameter gold b a l l probe located i n t h i s plasma as shorn i n F i g . 8.6. Although the mean elec t r o n energy as obtained from the el e c t r o n r e t a r d a t i o n region had not changed s i g n i f i c a n t l y , being 3.5 eV at t h i s pressure of 60 mtorr, the p o s i t i v e i o n current had increased by a f a c t o r of mo approximately, and i n the electron 'saturation' region the increase was a f a c t o r of three. This means that with the c o n s t r i c t o r present a given current drawn from the plasma requires a smaller p o t e n t i a l drop across the sheath region. As an example, i t was found that to draw an 2 (anodizing) current of 0.2 mA from the p o s i t i v e column, a 1 cm gold-pla t e d sample required a bias of less than 1 V above plasma p o t e n t i a l with tbe c o n s t r i c t o r compared with -10 V without i t , and f o r t h i s current density the growth rate on an unplated' niobium sample with the c o n s t r i -ct ctor positioned 2 cm i n front was approximately 1 A/min. The s i g n i f i c a n c e of the p o s i t i o n of the c o n s t r i c t o r r e l a t i v e to the sample holder was not inv e s t i g a t e d i n d e t a i l , since movement of the c o n s t r i c t o r caused a t r a n s i t i o n period during which the growth ra t e always decreased, perhaps while the tapered edge of the oxide f i l m near the mica mask adjusted i n thickness to a new p o t e n t i a l d i s t r i b u t i o n . However, i t was observed that with the c o n s t r i c t o r 2 cm from the sample holder, a sample current of 0.4 mA was w i t h i n the elec t r o n saturation region and the sample anodized normally, but when the c o n s t r i c t o r was moved 5 cm away the same current caused a v i s i b l e glow i n front of the sample, and the rate of anodization decreased considerably. This glow i s analogous to the luminous sheath or anode glow which i s present on the main anode of a glow discharge, and i t s occurrence i n d i c a t e d that the extrac t i n g f i e l d of the sample was accelerating electrons to e x c i t a t i o n 97 1000r F i g . 8.6. E f f e c t of c o n s t r i c t o r on probe c h a r a c t e r i s t i c s : o w i t h o u t c o n s t r i c t o r , x w i t h c o n s t r i c t o r . Broken curves are c o r r e c t e d f o r p o s i t i v e i o n c u r r e n t . I d = 40mA, p = 60 m t o r r . 98 and i o n i z i n g energies. A p o s i t i o n dependence was also found f o r the anodization rate of a niobium sample i n the negative glow of system A. The sample was s h i f t e d from the cathode end to the Faraday dark space end of the glow by moving the inverse brush cathode, and the growth rate increased as shown i n Table 8.2. Over t h i s same period, the e l e c t r i c f i e l d strength i n the oxide was estimated to have increased by 20%. These r e s u l t s may be compared with the f a c t , mentioned i n se c t i o n 4.5, that electrons are slowed down through the negative glow region, and t h e i r density increases towards the Faraday dark space. Using the c o n s t r i c t o r with the suspended niobium sample i n the absence of the usual holder, i t was found that t h i s sample anodized at the same rate at constant current whether facing the c o n s t r i c t o r or the anode. Cathode - sample Growth rate separation (mm) (A/min) 56 1.0 67 1.3 86 2.9 96 5.0 Table 8.2 V a r i a t i o n of growth rate with p o s i t i o n i n the negative glow (system A, p o l y c r y s t a l l i n e niobium sample). 8.3.4 Gas pressure V a r i a t i o n of the gas pressure i n a dc glow discharge i s accom-panied by changes i n the dimensions of the d i f f e r e n t glow and dark space regions, caused by changes i n the elec t r o n mean free path. This presents a d i f f i c u l t y i n attempts to determine the e f f e c t of system pressure on rate of anodization. Variations i n the anodization rate with pressure 99 r e p o r t e d (e.g. O'Hanlon 1971) f o r e l e c t r o d e c o n f i g u r a t i o n s w i t h a l a r g e anode-to-cathode a r e a r a t i o , such as the r i n g cathode and b a s e - p l a t e anode system shown i n F i g . 8.7, may have been caused i n p a r t at l e a s t by movement of the d i s c h a r g e r e g i o n s r e l a t i v e t o the sample, p a r t i c u l a r l y s i n c e these c o n f i g u r a t i o n s g i v e d i s c h a r g e s which are l e s s w e l l - d e f i n e d s p a t i a l l y than the c y l i n d r i c a l tube d i s c h a r g e . I n t h i s c o n t e x t i t was somewhat f o r t u i t o u s t h a t the c o n s t r i c t o r used t o i n c r e a s e the plasma d e n s i t y a l s o had the e f f e c t of c o n s t r a i n i n g a p o r t i o n o f the d i s c h a r g e , u s u a l l y a p o s i t i v e column s t r i a t i o n , to remain l o c a l i z e d at the c o n s t r i c -t o r i r r e s p e c t i v e of p r e s s u r e v a r i a t i o n s w i t h i n c e r t a i n l i m i t s , so t h a t the dependence of the a n o d i z a t i o n r a t e on p r e s s u r e c o u l d be determined f o r the p o s i t i v e column. For t h i s s t u d y two p o l y c r y s t a l l i n e t a n t a l u m samples were f i r s t o a n o d i z e d i n d i l u t e s u l p h u r i c a c i d to produce a 3000.A t h i c k o x i d e mask over t h e i r e l e c t r o p o l i s h e d f r o n t s u r f a c e s except f o r a c e n t r a l 8.5 mm diameter c i r c u l a r a r e a on each, and then a g o l d l a y e r was vapour d e p o s i t e d through a m e t a l mask on the unanodized a r e a of one o f the samples. These o x i d e masks were p r o v i d e d to reduce such u n d e s i r a b l e e f f e c t s as h i g h sheath f i e l d s and c u r r e n t leakage a t the mica mask edge, which were thought to have caused d e c r e a s i n g growth r a t e s w i t h t h i c k n e s s on p r e v i o u s samples. The masks were f a b r i c a t e d by p r o t e c t i n g the c e n t r a l sample a r e a from ano-d i z a t i o n w i t h a d i s c of adhesive e l e c t r i c a l I n s u l a t i o n tape ( S c o t c h b r a n d ) . By p o s i t i o n i n g the c o n s t r i c t o r w i t h i t s e x i t 2 cm i n f r o n t of the sample h o l d e r , the sample plane was p l a c e d i n the f i r s t s t r i a t i o n f o r the p r e s s u r e range from 60 to 150 mtorr and a d i s c h a r g e c u r r e n t of 40 mA. Constant c u r r e n t s of 0.1, 0.2 and 0.3 mA were used, and Table 8.3 shows the growth r a t e s o b t a i n e d i n u n i t s of A/min. Cu r r e n t e f f i c i e n c i e s 100 F i g . 8.7 Ri n g cathode-base p l a t e anode plasma anodi z a t i o n system: (a) anode base p l a t e (b) r i n g cathode (c) sample (d) probe and (e). q u a r t z s h i e l d s f o r e l e c t r i c a l i n s u l a t i o n . 101 \\ p(mtorr) J \ 60 100 150 s \ 2 (mA/cm ) .18 0.10 0.23 0.17 .35 0.32 0.64 0.50 .53 0.60 1.1 0.8-1.3 Table 8.3 Oxide growth rates O (A/min) o ined on a tantalum sample at d i f f e r e n t pressures p and sample current d e n s i t i e s J g (system B) . ri were c a l c u l a t e d from these values by assuming that the oxide produced was s t o i c h i o m e t r i c with the same density as wet anodic T^Oj. (8.0 gm/cm , Young 1958), g i v i n g the r e s u l t s shown i n F i g . 8.8(a). F l o a t i n g t r i p l e probe measurements showed that i n c r e a s i n g the pressure p from 60 mtorr to 150 mtorr caused the reduced f i e l d E/p, which i s p r o p o r t i o n a l to the average energy aquired by an el e c t r o n along a mean free path i n the f i e l d d i r e c t i o n , to decrease from 60 to -40 v/cm-torr, The I-V c h a r a c t e r i s t i c s of the gold-plated sample i n the same l o c a t i o n as the Ta sample f o r pressures from 60 to 200 mtorr are shown i n F i g . 8.9. These curves were corrected for p o s i t i v e ion components to y i e l d the elect r o n current-voltage c h a r a c t e r i s t i c s , such as the one f o r 60 mtorr shown i n F i g . 8.10 i n semilogarithmic form. The dashed curves i n t h i s f i g u r e are the electron and p o s i t i v e ion currents I and I to the ° pe p+ small gold b a l l probe used as a 'sounding'probe' (see appendix C), and provide a check on the determination of plasma p o t e n t i a l by the e x t r a -p o l a t i o n method. I t can be seen that the maxima i n the sounding probe currents (corresponding to a maximum c a r r i e r density near t h i s probe) 102 50 100 150 p(mtorr) F i g 8 8 (a) Cu r r e n t e f f i c i e n c i e s v e rsus p r e s s u r e f o r a n o d i z a t i o n of simple Ta2 at I 8 = O.lmA(x), 0.2mA(o) and 0.3mA(A) i n the p o s i t i v e column. (b) E l e c t r o n d e n s i t y (o) and mean e l e c t r o n energy (x) versus p r e s s u r e . 103 104 F i g 8 10 Electron current-voltage c h a r a c t e r i s t i c ob-tained from 60 mtorr curve of F i g . 8.9, and electron and p o s i t i v e ion currents (broken curves) to gold b a l l probe used as a 'soundxng probe 105 coincide on the sample voltage scale with the i n t e r s e c t i o n of the e x t r a -polated l i n e s . This supports the use of the i d e a l Langmuir probe a n a l y s i s even though one e x t r a p o l a t i o n i s based on a rather short p o r t i o n of the electron a c c e l e r a t i n g region of the c h a r a c t e r i s t i c where the current i s not perturbing the plasma too severely. Values of the mean elec t r o n energy kT £ and e l e c t r o n density n g obtained from the e l e c t r o n current at the i n t e r s e c t i o n points of the electron current-voltage c h a r a c t e r i s t i c s (according to s e c t i o n 5.2) are shown i n F i g . 8.8(b). These c h a r a c t e r i s t i c s also i n d i c a t e d that as the pressure was increased the l a r g e r energies of the e l e c t r o n d i s t r i b u t i o n , as given by the p o t e n t i a l difference V -V r, decreased from 9eV to ~6eV p f with the l a r g e s t change occurring between 60 and 100 mtorr, and the net current f l u x to the sample at plasma p o t e n t i a l also decreased, p a r t i c u -l a r l y between 100 and 150 mtorr. 8.3.5 Discharge current The e f f e c t of the current through the discharge on the anodi-zation rate was not as c l e a r as the pressure e f f e c t , and was dependent on the anodizing current l e v e l and the stage of anodization. For a con-stant current of 0.2 mA drawn by a tantalum sample at a pressure of 70 mtorr, increasing the discharge current from 10 mA to 40 mA i n 10 mA steps during the i n i t i a l stages of anodization was accompanied by a two-f o l d growth rate increase, but at a l a t e r stage, when the sample had an oxide of ~500A and was being anodized at 100 mtorr, reducing the discharge current i n one step from 40 mA to 10 mA had no apparent e f f e c t on the oxide growth rate. At higher sample currents, however, reducing the discharge current as above could r e s u l t i n the same phenomenon that was produced 106 by r e t r a c t i n g the c o n s t r i c t o r away from the sample, namely the appearance of a luminous glow over the sample accompanied by a decrease i n the ano-d i z a t i o n rate. 8.3.6 Sample current density Preliminary ellipsometry measurements made during anodization i n the negative glow of system A by using phase-sensitive detection r e -vealed that the oxide growth rate varied with time even though the cur-rent to the sample was maintained constant. F i g . 8.11 shows r e s u l t s for a p a r t i c u l a r formation on a p o l y c r y s t a l l i n e niobium sample at a current 2 density J g of 1 mA/cm , i n which the growth rate decreased by a f a c t o r of four as the formation progressed. The i n i t i a l rate of growth was 2 es p e c i a l l y high f o r another 1 mA/cm formation which followed an hour-long 2 ° low current (0.2 mA/cm ) formation, being 20 A/min (see section 10.5). During t h i s e a r l y work i t was found that the i n i t i a l a p p l i -cation of the current to the sample caused an almost instantaneous change i n the o p t i c a l behaviour of the sample surface, i n a d i r e c t i o n which ap-peared to i n d i c a t e a decrease i n oxide f i l m thickness before net growth occurred. This e l e c t r o - o p t i c e f f e c t was observed much more c l e a r l y with the automated ellipsometer used on system B, and while i n i t s e l f a phenomenon worthy of study (see f o r example Ord et a l . 1972, Cornish 1972), i t c o nstituted an a d d i t i o n a l complication to instrumental imperfections i n the analysis of the single zone ellipsometry measurements made during anodization. Zone 1 p o l a r i z e r and analyzer n u l l readings taken at one minute i n t e r v a l s both during and between anodizations on tantalum sample Ta2 are shown i n F i g . 8.12. The i n i t i a l s h i f t s on applying a bias to the sample a c t u a l l y move the n u l l readings onto a curve of lower oxide r e f r a c -t i v e index, i n agreement with the r e s u l t s of Ord et a l . 1972 for s o l u t i o n n1050 t (min) F i g . 8.11 Oxide t h i c k n e s s (o) and growth r a t e (x) d u r i n g c o n s t a n t c u r r e n t a n o d i z a t i o n of n i obium sample Nb5 at 1mA/cm , I , = 5mA, p = 60 m t o r r (system A n e g a t i v e g l o w ) . A 811 "to 87.0 80-5 g E H c x F 130 J x 125 120 P', Ueg) P * 0 s x 115 Q O 03 F i g . 8.12 E l l i p s o m e t e r r e a d i n g s o b t a i n e d d u r i n g a n o d i z a t i o n of sample Ta2 i n p o s i t i v e column of system B-see key on n e x t page. 109 Key f o r F i g . 8.12 . : zone 1 readings x : four-zone-averaged values AB : end p o r t i o n of a 0.2 mA formation BC : 0.2 mA switched o f f CD : 50 uA switched on EF : 50 uA " o f f FG : 50 yA " on HIJ : 50 uA " o f f JK : 0.1 mA " on KL : formation at 0.1 mA LM : 0.1 mA switched o f f MN : exposure to plasma f o r ~2 hours NOP : 0.1 mA switched on PQ : formation at 0.1 mA 110 anodization. Rather than correct f o r the deviations of the s i n g l e zone readings from the four-zone-averaged values (also shown i n F i g . 8.12), estimates of oxide thickness (equivalent ' f i e l d - f r e e ' thickness) were obtained as follows. A quadratic was f i t t e d to the r e l a t i o n between ft oxide thickness D and s i n g l e zone p o l a r i z e r n u l l s e t t i n g P^ ( f i e l d applied) f o r two consecutive formations: D = a Q + a 1 P 1 + a 2 P x 2 (8.1) The three constants a^, a^, were evaluated by a s s o c i a t i n g P^ values at the beginning and end of the formations with the D values obtained from the f i t to the four-zone-averaged ellipsometry readings taken at the end of every formation ( f i e l d o f f ) . This method assumes that the r e l a t i o n 8.1 i s not af f e c t e d by any changes with P i n the deviation of s i n g l e zone readings from the four-zone average, or changes i n the oxide f i e l d due to current l e v e l changes. Values of D obtained i n t h i s way f o r 0.1 and 0.3 mA formations 2 on sample Ta2 (area = 56.5 mm ) i n the p o s i t i v e column are shown as a function of time i n F i g . 8.13. For p o s i t i v e column anodization at these 2 current d e n s i t i e s (0.18 to 0.53 mA/cm ), the rate of oxide growth was f constant with time a f t e r an i n i t i a l t r a n s i e n t , i n contrast to the growth Analyzer s e t t i n g s A^ were used i f these were changing f a s t e r than 7 with growth. The i n i t i a l decrease i n thickness shown i n F i g . 8.13 i s a r e s u l t of the approximate treatment of s i n g l e zone readings o u t l i n e d above. The t r a n s i t i o n NOP i n F i g . 8.12, which l a s t e d two minutes, appears to sug-gest a r e f r a c t i v e index decrease followed by a thickness decrease. However, comparison with contours of constant thickness confirms that point P corresponds to a s l i g h t l y t h i c k e r f i l m (of lower index) than that at p oint N, i n agreement with the r e s u l t s of Ord et a l . 1972 and Cornish 1972. 0 500 WOO 1500 2000 t (sec) F i g . 8.13 Oxide growth during anodization of Ta2 at (a) 0.1mA and (b) 0.3mA i n p o s i t i v e column (p = 150 mtorr). 112 rate variation associated with formation current history reported above. The variation of anodization rate with t o t a l sample current density J g at various pressures is given i n Fig. 8.14 in the form of l°g versus log J . The values of ionic current density j . here are x s i calculated from mean growth rates, i . e . growth rates obtained from the D values at the beginning and end of each formation. It can be seen that log j . increases approximately l i n e a r l y with log J up to J ~0.5 s s mA, above which peaks and then decreases. 8.4 Discussion The results of section 8.3.3 concerning anodization rates i n the positive column, and negative glow and the effect of a constrictor imply that certain plasma conditions have a strong influence on the anodization of metals such as tantalum and niobium. Considering f i r s t the suggestion of a number of researchers that the bulk plasma acts as the source of the negative oxygen ions u t i l i z e d i n the oxide growth pro-cess, one might expect the positive column to sustain higher oxidation rates than the negative glow, i n accordance with the higher negative ion density as determined by Thompson 1961a and Whitlock and Bounden 1961. In fact, as found i n this study and also reported by Nilson and McKay 1971, the reverse i s true. Regarding the constrictor, since i t s introduction caused the positive ion density to increase and since Thompson 1961a found positive and negative ions to be present i n approximately equal numbers i n the oxygen positive column, i t can be assumed that the negative ion density was also increased l o c a l l y . However, although this would result i n an increased flux of negative ions to the sample, i t would not necessarily increase the ratio of negative ion flux to electron flux, since the 113 10r 0.1 I i i i i i 0.05 0.1 0.2 0.5 1.0 2.0 J s (ma/cm^) F i g . 8.14 V a r i a t i o n of o x i d e growth r a t e ( e x p r e s s e d as i o n i c c u r r e n t d e n s i t y ) w i t h t o t a l c u r r e n t to sample Ta2 i n p o s i t i v e c o l u n n of system B at p r e s s u r e s of 60 mtorr (©)> 100 mtorr (x) and 150 mtorr ( o ) . 114 e l e c t ron density had also increased. The p o s i t i v e ion and e l e c t r o n density changes are also possible causes of the increased growth rates i n the presence of the c o n s t r i c t o r . Ligenza and Kuhn 1970 r e f e r to the formation of the n a t u r a l l y occurring oxide ion 0 ~ from p o s i t i v e and ne-gative ions implanted i n the oxide surface, and i n t h i s manner the p o s i t i v e ion and e l e c t r o n d e n s i t i e s may both be important. Studies of such a model have been c i t e d (Ligenza 1971), but not published i n d e t a i l . An a d d i t i o n a l way i n which the plasma e l e c t r o n density could be important, together with the e l e c t r o n energy d i s t r i b u t i o n , w i l l be o u t l i n e d l a t e r i n t h i s s e c t i o n . The E/p values reported i n s e c t i o n 8.3.4 i n d i c a t e that negative ion formation i n the p o s i t i v e column i s by the two-body process of d i s -s o c i a t i v e attachment (section 4.4 process (d)). The attachment c o e f f i c i e n t fo r t h i s process i s proportional to pressure p, so that an increase i n negative ion density with p could be expected^ On the other hand. F i g . 8.8 shows that as p was increased above 100 mtorr, the anodization rate decreased. O'Hanlon 1971 has i n f e r r e d a s i m i l a r peak i n the growth r a t e -pressure dependence from observations of the anodic current decay during anodization of aluminum i n the negative glow at constant bias voltage. C l e a r l y the experimental observations are not consistent w i t h the theory that plasma negative ions are d i r e c t l y involved i n the anodi-z a t i o n process, and i n the next chapter i t w i l l be shown that the nega-t i v e ion f l u x from the plasma to the sample does not have any major i n -fluence on the constant current anodization rate. The pressure v a r i a t i o n r e s u l t s displayed i n F i g . 8.8(a) and (b) show the growth rates i n c r e a s i n g as the mean energy of the electron energy d i s t r i b u t i o n decreased and the electron density increased s l i g h t l y . When the l a t t e r decreased however, the growth rates also f e l l , suggesting that high electron densities and 115 low e l e c t r o n energies are conducive to higher anodization rates. The decrease i n growth rates which occurs at higher sample current d e n s i t i e s (see F i g . 8.14) i s thought to be associated with the onset of i o n i z a t i o n i n the e x t r a c t i n g f i e l d of the sample. At 150 mtorr the decrease occurs at lower sample currents than at 60 mtorr, which i s consistent with the increase i n the slope of the log I-V c h a r a c t e r i s t i c at around 0.6 mA at the higher pressure compared with 1 mA i n F i g . 8.10. This sheath i o n i -zation phenomenon, which was also obtained when the c o n s t r i c t o r was r e -tracted or the discharge current reduced s u f f i c i e n t l y during constant current anodization, i s again dependent on the energy d i s t r i b u t i o n and the density of electrons i n the plasma. When the e x t e r n a l l y applied sample current density exceeds the random f l u x of electrons to the sample, the sheath f i e l d may increase to impact i o n i z a t i o n values and increase the energy range of electrons reaching the oxide surface. The f o l l o w i n g i s of f e r e d as a p o s s i b l e explanation of the influence of e l e c t r o n energy d i s t r i b u t i o n and density on the anodization rate. The electrons i n the plasma have a d i s t r i b u t i o n of energies, which means that those electrons which traverse the sheath region and reach the oxide surface must also have a d i s t r i b u t i o n of energies. Any of these electrons which enter the oxide w i l l i n i t i a l l y be hot electrons •k because of the e l e c t r o n a f f i n i t y of the oxide , and w i l l have a f i n i t e penetration depth. In experiments with beam-deposited e l e c t r o n s , P i c k a r 1970 has found that even electrons a r r i v i n g with zero k i n e t i c energy pene-o t r a t e to a depth of 50A i n wet-anodic S i 0 2 before they lose the e l e c t r o n a f f i n i t y of 0.9 eV by o p t i c a l phonon emission and become thermalized. _ . ~ Processes competing with t h i s electron 'capture' by the oxide might be capture by adsorbed oxygen atoms to form negative ions, or recombin-ati o n with adsorbed p o s i t i v e ions. 116 Some electrons w i l l be incident with a f i n i t e v e l o c i t y component i n t o the oxide, and these w i l l penetrate f u r t h e r before reaching the conduction band edge. Thus the mean oxide f i e l d necessary to produce a c e r t a i n net current density through the oxide to the metal substrate w i l l be a ft function of the v e l o c i t y d i s t r i b u t i o n of the incident electrons . This d i s t r i b u t i o n w i l l i n turn depend on the magnitude of the net current density drawn from the plasma r e l a t i v e to the random e l e c t r o n f l u x . For sample currents l e s s than the random e l e c t r o n f l u x , the energy d i s -t r i b u t i o n at the oxide w i l l be an appropriate p o r t i o n of the high energy t a i l of the plasma d i s t r i b u t i o n as shown i n F i g . 8.15. Above plasma po-t e n t i a l , the plasma electrons w i l l be accelerated across the sheath and the d i s t r i b u t i o n w i l l be s h i f t e d to higher energies, w i t h correspondingly deeper penetration depths i n the oxide. I f the plasma electron density were increased, then the same current across the sheath would require a lower sheath a c c e l e r a t i n g p o t e n t i a l , but the r e s u l t i n g lower i n c i d e n t energies would necessitate a higher p o t e n t i a l drop across the oxide to maintain the net current to the substrate, which could mean an increase i n the growth rate i f the oxide-producing r e a c t i o n was i o n i c conduction-l i m i t e d . I f the e x t e r n a l l y applied current density were to exceed the random elec t r o n f l u x so much that the e x t r a c t i n g p o t e n t i a l across the sheath reached i o n i z a t i o n l e v e l s , then the r e s u l t a n t electrons with v e l o c i t i e s d irected at the oxide and t h e i r associated penetration depths could conceivably lead to a decrease i n p o t e n t i a l difference across the This dependence was not taken i n t o account i n the analysis of sec-t i o n 4.3. 117 Fig. 8.15 Electron energy diagram for anodizing sample drawing current density less than ( J e s + j ), showing e f f e c t of plasma electron energy d i s t r i b u t i o n . 118 oxide and a f a l l i n the growth rate . Another observation made during the course of these studies which may have some bearing on the s i g n i f i -cance of electron energies i s that the application of a magnetic f i e l d (from a bar magnet) p a r a l l e l to the surface of a sample being anodized at constant current caused the growth rate to increase by about a fac-tor of s i x at the. point monitored by the ellipsometer. However, the oxide growth also became very non-uniform over the sample surface, and the effect was not pursued further. The above explanation of certain experimental observations can be summarized into a number of postulates, which constitute a rudimentary model for plasma anodization in the cold cathode glow discharge i n oxygen: (a) The oxide-producing process i s rate-limited by species trans-port through the oxide. (b) The ion flux i n the oxide at a given temperature i s determined by the e l e c t r i c f i e l d strength i n the oxide. (c) The mean e l e c t r i c f i e l d strength i n the oxide i s related to the electronic flux through the oxide (~ t o t a l current density) and the electron energy d i s t r i b u t i o n and density i n the plasma. A refinement of the model would include the s p a t i a l d i s t r i b u t i o n of ne-gative space charge due to trapped electrons near the outer oxide surface, as determined by the electron energy di s t r i b u t i o n (through the penetra-A different interpretation of anodization rates f a l l i n g (even to zero) at higher sample currents has been made by Slawecki 1969. Slawecki stated that the rates f a l l because the destruction of negative oxygen ions by f i e l d - s t r i p p i n g of electrons occurs in the high sheath f i e l d s , and that the v i s i b l e glow i s due to subsequent electron-positive ion recombination, rathe than decay of impact-excited atoms. However, the emission of l i g h t due to recombination i s in general small (Engel 1965, Llewellyn-Jones 1966), and the unimportance of plasma negative ions i s demonstrated in the next chap ter. 119 t i o n depth). Tliis approach a t t r i b u t e s the low current e f f i c i e n c i e s i n plasma anodization to the presence of electrons with a wide range of energies i n the plasma, which give large e l e c t r o n i c currents through the oxide at the f i e l d strengths necessary f o r i o n i c transport. On t h i s ar-gument, the plasma best s u i t e d to anodization would be one i n which the electrons a l l have r e l a t i v e l y low energies but are present i n s u f f i c i e n t numbers to maintain the conductivity of the plasma. One p r a c t i c a l ap-proximation to t h i s case i s the plasma of a dc arc discharge with a ther-mionic cathode. Ligenza and Kuhn 1970 have used such a discharge system, modified to allow prolonged operation i n the presence of oxygen, and they o reported growth rates for the anodization of s i l i c o n of around 50A/min at room temperature, i . e . almost two orders of magnitude higher than those obtained i n t h i s study. However, analysis of t h e i r r e s u l t s suggests that the current e f f i c i e n c i e s were s t i l l quite low, l e s s than 1%. No estimations of oxide f i e l d strengths were given. Recently, high anodization rates have been obtained i n the plasma of an r f e x c i t e d discharge (on S i by P u l f r e y and Reche 1973, on Ta by Mikhalkin and Odynets 1971 and on Nb by Makara et a l . 1971), and i n these cases a r e l a t i o n between growth rate and oxide f i e l d was found. I t ap-pears that with t h i s discharge, as with the hot cathode arc, large current d e n s i t i e s can be drawn to the sample without d i s t u r b i n g the e l e c t r o n There i s a v a r i e t y of other evidence showing that large e l e c t r o n i c current d e n s i t i e s can be passed through normally i n s u l a t i n g oxides w i t h -out damage (see Pickar 1970, N i c o l l i a n and Berglund 1970, Jaeger et a l . 1972). Destructive breakdown e f f e c t s (Shousha et a l . 1972) occur when the stored energy associated with the charge on a large area conducting electrode i s d i s s i p a t e d i n a few l o c a l i z e d low resistance paths, but i f current i s uniformly i n j e c t e d i n the absence of such an electrode, these flaws w i l l not sustain damage. 120 energy d i s t r i b u t i o n so much that electrons are incident on the oxide with high k i n e t i c energy. The contention that the observed variations i n anodization rate with conditions i n the discharge arise p r i n c i p a l l y through a depen-dence of e l e c t r i c f i e l d strength i n the oxide on the energy d i s t r i b u t i o n and density of electrons i n the plasma would be strengthened by demon-str a t i n g the following: (a) That the supply of negative oxygen ions from the plasma i s not essential to plasma anodization. (b) That the ionic current obtained from anodization rates i s a function of oxide f i e l d strength. These points w i l l be dealt with i n the next two chapters. 121 9. THE ROLE OF PLASMA NEGATIVE IONS 9.1 Introduction I t has often been considered that the negative oxygen ions i n tbe plasma are the source of the oxygen i n the plasma-anodic f i l m . I f th i s were so then the production of negative ions i n the plasma and t h e i r transport across the sheath region to the sample might be r a t e - l i m i t i n g steps i n the anodization process, and i t i s possible that improvements could be made i n the usually inconveniently low oxide growth rates. The measured random p o s i t i v e ion current densities to the sample of about 5 to 10 uA/cm can be used as an i n d i c a t i o n of the possible magnitude of the negative ion f l u x , and these current d e n s i t i e s are indeed s i m i l a r to the values of i o n i c current density i n the oxide calcul a t e d from measured growth rates (see F i g , 8.14). To obtain information on the importance of negative ions i n the plasma, the f o l l o w i n g experimental approaches might be considered: (a) To measure the actual f l u x of negative ions reaching a sample being anodized, by removing a l l electrons from the p a r t i c l e f l u x from the plasma. (b) To change the value of the negative i o n f l u x reaching the sample i n a c o n t r o l l e d manner while monitoring the oxide growth rat e . (c) To vary the density of negative ions In the plasma. Approach (a) c a l l s f or a device such as the Loeb e l e c t r o n f i l t e r , and (b) should be possible with the simultaneous a p p l i c a t i o n of s u i t a b l e dc and r f sign a l s to the sample. Methods of varying the elec t r o n temperature i n the plasma (e.g. Alexeff and Jones 1966, MacKenzie et a l . 1971) could 122 make approach (c) possible through the dependence of the cross-section f o r negative i o n production on e l e c t r o n energy. The use of magnetic f i e l d s could also be considered f o r a l l three methods - f o r instance a magnetic f i e l d applied p a r a l l e l to the sample surface to d e f l e c t electrons could be used i n (a) and (b), and a magnetic f i e l d applied l o n g i t u d i n a l l y to the c y l i n d r i c a l discharge would reduce the e l e c t r o n temperature f o r approach ( c ) . However, the necessity to confine these f i e l d s makes the magnetic methods more d i f f i c u l t . The methods mentioned i n i t i a l l y f or approaches (a) and (b) were chosen f o r i n v e s t i g a t i o n since they were the most d i r e c t . 9.2 Electron F i l t e r Experiments The e l e c t r o n f i l t e r r e f e r r e d to here i s a device developed by Loeb (seeLoeb 1955 and McDaniel 1964) f o r removing electrons from a mixed swarm of electrons and negative ions d r i f t i n g through a gas i n an e l e c -t r i c f i e l d . I t consists of a plane g r i d of p a r a l l e l wires mounted per-pendicular to the d r i f t d i r e c t i o n , a lternate wires being connected to opposite sides of a high-frequency o s c i l l a t o r . For an a l t e r n a t i n g f i e l d of appropriate frequency (1 to 10 MHz) and s u f f i c i e n t amplitude established between alternate wires, a l l electrons attempting to pass through the g r i d should be captured on i t , but the much heavier negative ions are transmitted since they respond only slowly to the r a p i d l y changing f i e l d . The device used i n t h i s study was constructed of sixteen .003 inch diameter tungsten wires cemented with 1 mm spacing on a 3 cm square . mica frame with a 12 mm square aperture as shown i n F i g . 9.1. The two leads from the alternate sets of wires were in s u l a t e d i n quartz tubing and sealed with low outgassing epoxy cement i n t o the end of a boro-s i l i c a t e glass tube. This tube was mounted i n a double 0-ring feedthrough 123 Fi g . 9.1 Electron f i l t e r , i n the anode end cap of system B, so that the f i l t e r could be positioned d i r e c t l y i n front of the sample holder. To obtain s u i t a b l e voltages across the g r i d , the l a t t e r was connected as the capacitor of a p a r a l l e l LC c i r c u i t , the inductance being a 9 turn 7 cm diameter secondary c o i l of an air-co r e d transformer con-structed with 1 mm diameter copper wire, and a 5V r f s i g n a l generator was connected across the two-turn primary c o i l as shown i n F i g . 9.2. The voltage gain of t h i s tuned a m p l i f i e r i s pr o p o r t i o n a l to w^ QM at r e --1/2 sonance, where co = (LC) , Q i s the figure of merit for the secondary c o i l and M i s the mutual inductance of the transformer. By tuning the generator with the LC c i r c u i t , s ignals as high as 50 V peak-to-peak at 12 4 ~HV m-AjSj CATHODE CRT —rasas* p\> 2\ 6/x7D F i g . 9.2 C i r c u i t used f o r e l e c t r o n f i l t e r e x p e r i m e n t s . 125 5 MHz could be applied between adjacent g r i d wires. A dc bias could be applied to the f i l t e r v i a a centre-tap on the transformer secondary c o i l To i n v e s t i g a t e the performance of the f i l t e r , the device was positioned about 3 mm i n front of a gold-plated sample i n the p o s i t i v e column of system B and the current-voltage ( I -V ) c h a r a c t e r i s t i c of ° s s the sample was measured as a function of the dc and r f voltages V , gdc and V f applied to the g r i d , a l l dc voltages measured with respect to o ground, f o r p = 70 mtorr and I = 40 mA. d The f o l l o w i n g i s a summary of the r e s u l t s , some of which are presented i n Figures 9.3 and 9.4. (a) Introduction of the g r i d ( e l e c t r i c a l l y i s o l a t e d ) i n front of the sample reduced the sample current I by a facto r of -5 i n the electron saturation region, and the g r i d f l o a t i n g poten t i a l V _ va r i e d i n the same d i r e c t i o n as V . gr s (b) The I g ~ v s curve was a strong and complicated function of the g r i d dc p o t e n t i a l . Raising V , above V £ caused I „ & v b gdc gf s'V gconst. to increase by up to a f a c t o r of .4, decrease through a saddle point and then pass through another maximum. (c) Increasing the amplitude V ^ of the r f s i g n a l superimposed on V , caused I to decrease, but the expected current gdc s minimum plateau was not observed - see F i g . 9.4. The maximum av a i l a b l e r f voltage of 50 V produced a maximum decrease of 17% i n I , i r r e s p e c t i v e of the value of V , . s S (d) As measured by tbe electrometer E i n F i g . 9.2, the maximum current flow from g r i d to ground caused by the superposition nf V = 50 V on V , = V r was about 2 x 10 ^A, which may grf gdc gf 126 4.0 3.0 i o 2.0 7.0 0.5 NO GRID gdc_max-vs~Vs f= 1 0 V -0.51 GRID FLOATING F i g . 9.3 Dependence of the c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s o f a g o l d - p l a t e d sample on the dc and r f v o l t a g e s V g d c and V g r f a p p l i e d to the g r i d (p = 70 mtor r , I . 40mA). 127 0 0 10 20 30 40 Vrf (PEAK V) 50 F i g . 9.4 V a r i a t i o n of sample c u r r e n t at f i x e d sample v o l t a g e w i t h g r i d r f v o l t a g e , f o r d i f f e r e n t g r i d dc v o l t a g e s . 128 be compared with the decrease of ~1 x 10 JA i n I I „ f o r s IV > V s p the same g r i d conditions. The geometrical transparency of the g r i d being about 90%, ob-servations (a) and (b) must be a consequence of the p o s i t i v e i o n sheath of each wire extending w e l l i n t o the i n t e r - w i r e space and p a r t i a l l y s h i e l -ding the sample against slox«:r negative p a r t i c l e s from the plasma (the sheath thickness may have been of the same order as the i n t e r - w i r e space -see Appendix B). This implies that the f i l t e r should be operated with Vgdc held near to plasma p o t e n t i a l so as to reduce the space charge sheath of the g r i d wires. However, the f r a c t i o n a l decrease i n I due to V _ s grf was quite i n s e n s i t i v e to V , , and together with the absence of a current gdc plateau t h i s suggests that the device was not functioning w e l l as an e l e c -tron f i l t e r . A closer wire spacing coupled with l a r g e r r f amplitudes may have improved the e f f i c i e n c y of el e c t r o n capture, but the simpler approach of superposition of an r f s i g n a l to a sample undergoing constant current anodization was pursued instead, as described i n the fo l l o w i n g s e c t i o n . 9.3 Modulation of the Negative Ion Flux to a Sample by the Simultaneous A p p l i c a t i o n of r f and dc Biases 9.3.1 Constant dc voltage approach The d i f f e r e n t responses of electrons and negative ions to a high frequency p o t e n t i a l as mentioned i n the previous s e c t i o n , together with the n o n - l i n e a r i t y of the current-voltage c h a r a c t e r i s t i c of a Lang-muir probe, can be u t i l i z e d to reduce the negative i o n f l u x component i n the anodic current to a sample. Consider f i r s t the c i r c u i t of F i g . 9.5(a), which permits the (a) -600 V, OSCILLOSCOPE ' 5Vr HI CATHODE ZL, SAMPLE (b) 8x10  4 A ELECT ROME CONSTANT CURRENT GENERATOR F i g . 9.5 (a) C i r c u i t f o r simultaneous a p p l i c a t i o n of dc and r f biases to a sample (b) I-V r e l a t i o n s f o r sample subject to dc and dc+rf bias conditions at a pressure of mtorr, 130 a p p l i c a t i o n of an r f voltage to a sample that i s biased e i t h e r at con-stant dc voltage or so as to draw a constant dc current from the plasma. The sample behaves l i k e a large plane probe and i n the absence of any r f i n j e c t i o n i t has the s t a t i c current-voltage c h a r a c t e r i s t i c shown i n F i g . 9.5(b). A metal sample i s o l a t e d from the dc b i a s i n g c i r c u i t w i l l assume a f l o a t i n g p o t e n t i a l V f which i s a few v o l t s negative to the plasma p o t e n t i a l V . The a p p l i c a t i o n of an r f voltage to t h i s dc i s o l a t e d sample w i l l cause the mean sample p o t e n t i a l to assume a new value VV r f r f which i s more negative than V^s since the current to the sample must average to zero over a cycle. I f a dc voltage i s now applied so as to bias the sample more p o s i t i v e l y , say to i t s o r i g i n a l p o t e n t i a l f o r instance, then the sample w i l l draw a net anodic current, since the cur-rent during the h a l f cycle p o s i t i v e to V^ . w i l l g r e a t l y exceed the nega-t i v e h a l f cycle current. However, the plasma negative ions w i l l not be able to reach the sample, since due to t h e i r low energy they are unable to surmount the dc p o t e n t i a l b a r r i e r - V^, and t h e i r large mass pre-vents them from reaching the sample during the p o r t i o n of the r f cycle when t h i s b a r r i e r may be s u f f i c i e n t l y reduced - the electrons and negative ions e f f e c t i v e l y experience d i f f e r e n t p o t e n t i a l b a r r i e r s . These conditions of an r f voltage superimposed on a dc voltage bias equal to V f were applied to an aluminum sample i n the negative glow of a dc oxygen discharge by O'Hanlon and Pennebaker 1971. From the behaviour of the sample current with time, curve (a) i n F i g . 9.6, they i n f e r r e d that the sample did not anodize, and concluded that t h i s was due to the e l i m i n a t i o n of plasma negative ions from the anodic current to the sample. However, an analysis of O'Hanlon and Pennebakers' experiment indicates that oxide growth would not be expected to occur even i f negative 131 F i g . 9.6 Current decay through aluminum sample: (a) dc bias = V • (b) dc bias = + 5.5V. In both cases V r£ = 10V peak-to-peak (from O'Hanlon and Pennebaker 1971). ions were a v a i l a b l e from other processes such as el e c t r o n attachment at the oxide surface, since t h e i r bias conditions rendered the f i e l d i n the oxide very small. This can be seen as follows. The p o t e n t i a l of the un-oxidized aluminum sample w i l l vary symmetrically at r f frequency about V^. This r f p o t e n t i a l across the space charge sheath w i l l give r i s e to a net anodic current to the sample as explained above. I f now a t h i n 'thermal' oxide layer i s formed on the sample, as O'Hanlon and Pennebaker suggested, then to a good approximation the r f p o t e n t i a l w i l l s t i l l ap-pear across the sheath region because the capacitance of the sheath C g^ w i l l be much lower than that of the oxide, C . The only e f f e c t of the oxide w i l l be to present an extra impedance to the dc current, which w i l l decrease s l i g h t l y , and the new steady state may include a small time 132 averaged e l e c t r i c f i e l d i n the oxide f i l m . The time-averaged s i t u a t i o n w i l l not be s i g n i f i c a n t l y d i f f e r e n t from that of a sample at f l o a t i n g p o t e n t i a l with an e q u i l i b r i u m growth of oxide, A rough estimate of the f i e l d developed i n the thermal oxide can be obtained by approximating the sample I-V c h a r a c t e r i s t i c to a s t r a i g h t l i n e above V f, and the r f sine wave to a t r i a n g u l a r form. Then the i n i t i a l 20% decrease i n sample current (see Tig. 9.6(a)) would have been caused by a negative s h i f t i n the dc p o t e n t i a l at the oxide edge of the sheath equal to 10% of the peak r f amplitude of 10 V. This 1 o v o l t p o t e n t i a l difference would be developed across the ~20A of 'thermal' A^O^, gi v i n g a f i e l d strength s i m i l a r to that i n A^O^ at the end of a constant voltage anodization when oxide growth has f o r p r a c t i -c a l purposes ceased. Thus under O'Hanlon and Pennebakers* stated conditions, no high dc f i e l d w i l l be developed i n the oxide to act as a d r i v i n g force for i o n i c motion and further o x i d a t i o n , and although exclusion of negative ions i s accomplished, t h e i r experiment does not j u s t i f y the conclusion that negative i o n e x t r a c t i o n from the plasma i s e s s e n t i a l to plasma anodization. However, by using a dc and-rf b i a s i n g arrangement and also constraining the dc current through the sample to a constant value, information can be obtained as to the importance of plasma negative ions (Olive et a l . 19 72). 9.3.2 Constant dc current approach When an r f bias i s applied to a sample being anodized at con-stant dc current (e.g. I , on F i g . 9.5(b)), the e f f e c t i v e dc bias point dc (V d on F i g . 9.5(b)) w i l l move to a more negative value, say V^, i n order that the new current has the same average value as before a p p l i c a t i o n 133 of the r f b i a s . Because of the r e l a t i v e magnitudes o f C and C , the ox sh r f v o l t a g e w i l l appear ac r o s s the sheath and s i n c e the dc c u r r e n t through the o x i d e i s c o n s t a n t the mean f i e l d i n the o x i d e s h o u l d be unchanged. Thus, f o r the case o f dc and r f b i a s the p o t e n t i a l b a r r i e r t o oxygen n e g a t i v e i o n f l o w a c r o s s the sheath to the sample s u r f a c e w i l l be i n c r e a s e d from t h a t f o r dc b i a s o n l y . A c c o r d i n g l y , the o x i d e growth r a t e s h o u l d decrease on the a p p l i c a t i o n of the r f b i a s i f oxygen n e g a t i v e i o n s from the plasma are i m p o r t a n t i n plasma a n o d i z a t i o n . To o b t a i n a q u a n t i t a t i v e measure of the expected change i n growth r a t e i t i s f i r s t n e c e s s a r y to o b t a i n an e x p r e s s i o n f o r the r a t e of a r r i v a l of plasma n e g a t i v e i o n s at the o x i d e s u r f a c e . I f i t i s a s -sumed t h a t the plasma n e g a t i v e i o n s have a M a x w e l l i a n d i s t r i b u t i o n i n v e l o c i t y then the oxygen n e g a t i v e i o n c u r r e n t d e n s i t y a c r o s s the sh e a t h can be w r i t t e n ( c f . Eqns. 4 . 2 and 4 . 5 ) j _ = J _ s ex P(-eAV/kT_) (9.1) where j _ g i s the n e g a t i v e i o n random c u r r e n t d e n s i t y , T_ the i o n tempera-t u r e , and -AV the sheath p o t e n t i a l drop (the minus s i g n s i g n i f i e s t he assumption o f a p o s i t i v e space charge i n the sheath and thus a r e t a r d i n g p o t e n t i a l b a r r i e r to n e g a t i v e p a r t i c l e f l o w from the plasma t o the sam-p l e ) . A f u r t h e r assumption i m p l i c i t i n Eqn. 9.1 i s t h a t the mean f r e e path o f the plasma n e g a t i v e i o n s i s comparable to or g r e a t e r than the sheath t h i c k n e s s . For the plasma used i n t h i s experiment t h i s assump-t i o n seemed j u s t i f i e d as the Debye s h i e l d i n g l e n g t h was 0.9 mm and the n e g a t i v e i o n mean f r e e path l e n g t h c a l c u l a t e d from Langevin's s i m p l e s o l i d e l a s t i c sphere e x p r e s s i o n f o r m o b i l i t y was 1 mm (see Appendix B ) . Once plasma n e g a t i v e i o n s reach the oxid e s u r f a c e then, i f they are to c o n t r i b u t e to oxide growth, presumably one of two mechanisms i s 134 o p e r a t i v e , namely (a) the n e g a t i v e Ions are embedded i n the o x i d e on f i r s t impact o r (b) the n e g a t i v e i o n s are f i r s t adsorbed, a f t e r which the a d i o n would have to move over the s u r f a c e to i t s f i n a l l o c a t i o n at some low energy s i t e . In case (a) the o x i d e growth r a t e and the i o n i c c u r r e n t d e n s i t y i n the o x i d e j , w i l l be l i n e a r l y dependent on the r a t e of a r r i v a l o f n e g a t i v e i o n s j _ . Thus, assuming t h a t the a p p l i c a t i o n of the r f b i a s to the sample does not a f f e c t the b u l k plasma n e g a t i v e i o n p r o p e r t i e s , i . e . j _ g and kT_/e, we have from e q u a t i o n 9.1 t h a t the r a t i o o f o x i d e i o n i c c u r r e n t w i t h o u t r f b i a s to t h a t w i t h r f b i a s i s g i v e n by j . (AV - A V ) lo8io(r7> = - 1 ^ 0 3 - • ( 9 - 2 ) J i r f where AV ^ i s the time-averaged p o t e n t i a l drop a c r o s s the sheath f o r the c o n d i t i o n o f dc p l u s r f b i a s . I n case (b) i t would be expected t h a t adions would compete w i t h each o t h e r f o r the f i n a l low energy s i t e s , which w i l l be taken t o be near excess m e t a l i o n s ( a l t h o u g h another p o s s i b i l i t y would be near oxygen n e g a t i v e i o n v a c a n c i e s i n the o x i d e ) . Thus some low power depen-dence of the c o n c e n t r a t i o n n of f i n a l l y - l o c a t e d oxygen i o n s on the cr a r r i v a l r a t e o f plasma n e g a t i v e i o n s , 0 o r 0^ , might be a n t i c i p a t e d , e.g. n 2-0 J 0 (9.3) where x i s l e s s than 1 and a and j Q are c o n s t a n t s . Hence i n t h i s case we have n , n „ (9.4) where n i s the c o n c e n t r a t i o n of the m e t a l i o n s near the s u r f a c e , and M 135 g i s some constant term r e l a t i n g to the f i e l d and d i e l e c t r i c properties at the oxide surface. P u t t i n g (9.1) and (9.3) i n t o (9.4) and assuming n^ i s constant we have that the r a t i o of i o n i c current without r f bias to that with r f bias i s given by j i e ( A V r f - A V ) l o g 1 0 ( — ) = x ~ " ^ 3 0 3 - (9.5) i r f Comparison of the calculated values of i o n i c current r a t i o given by equations 9.2 and 9.5 with actual experimental values w i l l thus demonstrate whether bulk plasma negative Ions are important to plasma anodization. 9.3.3 Experiment and r e s u l t s The estimation of the r a t i o of the oxide i o n i c currents and the d i f f e r e n c e i n sheath p o t e n t i a l drop AV ^ - AV f o r constant current plasma anodization with and without r f bias was c a r r i e d out i n the p o s i -t i v e column of system B with a 40 mA discharge current, using the two oxide masked Ta samples described i n s e c t i o n 8.3.4. The r a t i o of to j^r£ was c a l c u l a t e d from oxide growth rates which were obtained from s i n g l e zone ellipsometry measurements during anodization by the method outl i n e d i n section 8.3.6. To estimate the sheath p o t e n t i a l drop i t was assumed that f o r a given plasma, sample geometry, dc sample current and r f sample b i a s , AV and AV r are independent of the sample surface, whether m e t a l l i c or r f oxide coated. With t h i s assumption, AV r f - AV could be estimated from I-V measurements on the sample which was gold-plated, thereby avoiding oxide formation and consequent d i s t o r t i o n of the I-V c h a r a c t e r i s t i c s . For the d i r e c t current I i n F i g . 9.5(b), AV i s given by V p - V d (the voltage reference i s the anode). By using the c i r c u i t of F i g . 9.5(a) 136 the time-averaged p o t e n t i a l caused by the a p p l i c a t i o n of a 3.5 MHz voltage to the sample, constrained to draw a constant d i r e c t current, was determined f o r various dc currents and r f voltages. This enabled determination of AV^ f - AV as given by V d - V'd (see F i g . 9.5(b)). The gold-plated sample I-V data were also used to estimate the f i e l d strength E i n the anodic oxide during growth. Thus, at a given t o t a l current I and oxide thickness D, E was taken to be given ox ° by (V -V ) - (V -V ) ox D v9- b) where V m (or V A ) was the voltage difference between the tantalum (or Ta Au gold-plated tantalum) and the anode. Any changes i n f l o a t i n g p o t e n t i a l during anodization as detected by a small gold probe located 2 mm i n front of the oxide were allowed f o r (the j u s t i f i c a t i o n f o r Eqn. 9.6 and other methods of estimating the f i e l d i n the oxide are given i n the next chapter, s e c t i o n 10.2). The Ta sample was anodized at constant currents of 0.1 and 0.2 mA ( i . e . below V^ on the I-V c h a r a c t e r i s t i c of F i g . 9.5(b) so that Eqn. 9.1 applies) with a discharge current of 40 mA and pressures of 60 and 100 mtorr, and r f voltages between 10 and 30 v o l t s peak to peak were applied for portions of each formation. The e f f e c t of the r f bias v o l -tage on the oxide growth rate and oxide f i e l d , while constraining tbe average dc anodizing current to a constant value, i s shown i n Table 9.1. Whereas (V ) T changed s i g n i f i c a n t l y (up to 7 v o l t s ) , as a n t i c i p a t e d i n section 9.3.2 the a p p l i c a t i o n of the r f bias changed the estimated f i e l d i n the oxide only marginally. The e f f e c t of the r f bias on the oxide growth rate was also small. 137 Pressure I s r f bias AD/At O A E ox mtorr mA pk-pk-volts A/10 sec 10 V/cm 0 0.14 2.82 10 0.16 2.90 0.1 20 0.20 2.94 0 0.18 2.86 30 0.23 3.00 60 0 0.22 2.88 0 0.65 3.17 0.2 30 0.61 3.16 0 0.65 3.17 0 0.24 2.92 20 0.43 3.04 0 0.35 2.93 100 0.1 0 0.44 2.98 30 0.58 3.10 0 0.57 2.98 0 1.45 3.19 0.2 30: 0,75 3.20 0 1.22 3.21 Table 9.1 The e f f e c t of the r f bias on the oxide growth rate and f i e l d streng 138 '9.3.4 Discussion To compare the data i n Table 9.1 with the changes i n growth rate expected from the t h e o r e t i c a l considerations discussed i n sec t i o n 9.3.2, consider f i r s t equation 9.2. I t i s required to know the negative kT_ ion temperature T and f o r t h i s purpose i s taken as 0.1 v o l t as r e -- e ported by Thompson 1961a. From Table 9.2 i t i s seen that the large change i n growth ra t e that would be expected i f the plasma negative ions were embedded i n the oxide on f i r s t impact are not obtained i n p r a c t i c e . The other possible mechanism of plasma negative ion contribu-t i o n to oxide growth discussed i n section 9.3.2 leads to equation 9.5. I n s e r t i n g the measured changes i n i o n i c current from Table 9.1 i n t o equation 9.5 y i e l d s values for the parameter x. I t i s found that x i s -2 always l e s s than 10 , again showing, through equations 9.3 and 9.4, that the oxide i o n i c current docs not depend upon the rate of supply of negativ ions from the plasma. From these r e s u l t s i t - must be concluded that i f Thompson's mean ion energy and the dependence of rate of supply of negative ions on sheath p o t e n t i a l drop given by Eqn. 9.1 are v a l i d , then negative oxygen ions i n the plasma are not u t i l i z e d i n plasma anodization. This does not exclude the p o s s i b i l i t y of negative Ions produced by el e c t r o n attach-ment at or very close to the oxide surface. However, as was noted i n section 4.3 a further i o n i z a t i o n process would be required before these ions are incorporated i n the oxide f i l m , since gaseous negative ions are i n v a r i a b l y s i n g l y charged (McDaniel 1964). 139 Pressure mtorr I s mA r f bias pk-pk V AV -AV r f V V j i r f from Eqn.9.2 measured 60 0.1 10 20 30 1.3 3.9 7.25 5 10 i o 1 7 i o 3 1 0.9 0.9 1.0 0.2 30 5.3 i o 2 3 1.1 100 0.1 20 30 3.8 7.0 i o 1 6 i o 3 0 0.8 1.0 0.2 30 4.5 i o 2 0 1.2 Table 9.2 Comparison of expected change i n j on a p p l i c a t i o n of r f bias as c a l c u -l a t e d from equation 9.2, with that measured by ellipsometry. 140 10. THE RELATION BETWEEN OXIDE GROWTH RATE, ELECTRIC FIELD STRENGTH IN THE OXIDE AND OXIDE TEMPERATURE DURING PLASMA ANODIZATION 10.1 Introduction The formation of an oxide f i l m on a metal or semiconductor, whether by thermal oxidation, anodic oxidation i n l i q u i d e l e c t r o l y t e s , or plasma anodization, requires the transport of one or more reactant species (metal and/or oxygen) through the oxide. The simplest model of thermal oxidation involves the diffusion of neutral molecules under a con-centration gradient. The electrochemical model of thermal f i l m growth as-sumes the transport of ioni c species with counterflow of electrons and holes to maintain e l e c t r i c a l neutrality. In solution anodization at room temperature, i o n i c species are considered to migrate through the oxide by high f i e l d transport, and electronic transport usually accounts for less than 1% of the t o t a l charge passed. The ioni c conduction mechanism involved gives r i s e to an exponential dependence of oxide growth rate on mean e l e c t r o s t a t i c f i e l d i n the oxide, as discussed i n section 3.2. The growth mechanism i n plasma anodization might also be expected to involve high f i e l d i o n i c conduction. I t was reported above that conditions in the dc discharge could affect the growth rate, but that the results were not inconsistent with an ionic conduction-limited growth - see section 8.4. Also discussed i n that section were the high growth rates obtainable i n high frequency excited discharges. An additional factor which may be contributing i n such cases i s a higher sample temperature due to a high thermal energy input from the plasma. The aim of the work to be described below was to see whether the ionic current density i n the oxide could be i d e n t i f i e d as a function of the f i e l d strength in the oxide and i t s 141 temperature T. Data w i l l be presented on niobium, tantalum, aluminum and s i l i c o n . 10.2 The Estimation of F i e l d Strengths i n the Oxide In attempting to r e l a t e measurable q u a n t i t i e s to the f i e l d i n tbe oxide during plasma anodization, quite considerable problems a r i s e . These problems have been discussed i n the l i t e r a t u r e (O'Hanlon 1969, Olive et a l . 1970, Ramasubramanian 1970), but only p a r t i a l s o lutions have been suggested. The simplest approach, used by most of the e a r l y i n v e s t i g a t o r s , was to assume that the voltage across the growing oxide was equal to the voltage applied to the sample with respect to the grounded anode. While t h i s approximation may not be too s e r i o u s l y i n e r r o r i n c e r t a i n b e l l - j a r geometries s i m i l a r to F i g . 8.7, i t becomes meaningless f o r c y l i n d r i c a l discharges where due to the p o t e n t i a l gradient i n the plasma, a sample drawing a considerable anodic current may s t i l l be tens of v o l t s negative with respect to ground ( t h i s s i t u a t i o n also necessitated care i n the se-l e c t i o n of a constant current supply f o r t h i s study). The measurement of sample p o t e n t i a l with respect to a small e l e c t r i c a l l y i s o l a t e d metal probe located near to the anodizing sample i s a considerable improvement, both i n respect of r e g i s t e r i n g the l o c a l f l o a t i n g p o t e n t i a l and monitoring any v a r i a t i o n s i n the l a t t e r with time during anodization. However, even i f tbe probe i s s u f f i c i e n t l y close to the sample that random v a r i a t i o n s i n time i n the p o t e n t i a l gradient •through the plasma are n e g l i g i b l e , t h i s method s t i l l neglects (a) work-function differences and (b) changes i n the p o t e n t i a l drop across the sample sheath when a net current i s drawn, as pointed out i n section 4.2.2, An attempt was made to overcome these d i f f i c u l t i e s i n the present study by 1 4 2 e v a p o r a t i n g a g o l d e l e c t r o d e onto a p a t c h o f t h i c k o x i d e formed i n i t i a l l y on the sample by s o l u t i o n a n o d i z a t i o n . I t was i n t e n d e d to b i a s such an e l e c t r o d e u n t i l i t drew the same c u r r e n t d e n s i t y as the main a n o d i z i n g a r e a , but proneness of the o x i d e t o e l e c t r i c a l breakdown on exposure t o the plasma p r e v e n t e d t h e i r a p p l i c a t i o n . I f the phenomena i n the plasma sheath a d j a c e n t t o the o x i d e may be assumed to be the same f o r a g i v e n c u r r e n t d e n s i t y independent of o x i d e t h i c k n e s s , i t would appear t h a t w i t h c o n s t a n t c u r r e n t a n o d i z a t i o n an i n c r e m e n t a l f i e l d measurement, as by a d e t e r m i n a t i o n o f o x i d e t h i c k -nesses and sample p o t e n t i a l s ( w i t h r e s p e c t t o f l o a t i n g probe V ) at the sp b e g i n n i n g and end of a f o r m a t i o n , would e l i m i n a t e the problems of sheath p o t e n t i a l drops and work f u n c t i o n d i f f e r e n c e s . However, such measurements i n v a r i a b l y r e s u l t e d i n a l a r g e s c a t t e r i n f i e l d v a l u e s , and t h i s was p r e -sumed t o be caused by v a r i a t i o n s I n the oxide f i e l d d u r i n g a f o r m a t i o n . R e l a t i v e l y s m a l l v a r i a t i o n s (perhaps due t o a b u i l d - u p of space charge i n the o x i d e ) can have s i g n i f i c a n t e f f e c t s on i n c r e m e n t a l measurements, as may be seen from F i g . 1 0 . 1 . I f i n growing ( a t c o n s t a n t c u r r e n t ) from an o x i d e t h i c k n e s s to D„ the i n t e g r a l o x i d e f i e l d decreases from E to E-.-6, then the i n c r e -2 &V m e n t a l measurement becomes E 1 - _ D , and i f the increment D 2 - I ) 1 i s 2 1 6D s m a l l compared to the i n i t i a l t h i c k n e s s , 7—37- may be l a r g e even f o r S s m a l l . A procedure f o r e s t i m a t i n g the p o t e n t i a l d i f f e r e n c e V q due t o sources (a) and (b) above would be t o c a r r y out a s e r i e s of f o r m a t i o n s a t the same co n s t a n t c u r r e n t I , p l o t the p.d. between sample and probe v e r s u s o x i d e t h i c k n e s s D both e v a l u a t e d at the end of each f o r m a t i o n , and e x t r a p o l a t e back to D = 0 . The i n t e r c e p t on the v o l t a g e a x i s would be the s p v 2 - ^ 1 / / 0 D 1 D2 D F i g . 10,1 E s t i m a t i o n of ox i d e f i e l d from sample-prob p o t e n t i a l and ox i d e t h i c k n e s s d a t a . I n t e g r a l f i e l d s : \ = ( v ^ V ^ / D ^ ^ = ( V ^ ) / ^ . I n c r e m e n t a l f i e l d : AV/AD = (V2"V1)/(W* 144 unknown p o t e n t i a l difference V 0 I for t h i s p a r t i c u l a r current, providing the oxide f i e l d and V Q I did not vary much among the formation end points. A l e s s laborious approach i s to i n i t i a l l y obtain the current-voltage c h a r a c t e r i s t i c of the unanodized sample with respect to an i n v a r -i a n t probe over the range of anodizing currents to be used. This charac-t e r i s t i c y i e l d s c o r r e c t i o n factors for any formation current to be deduc-ted from subsequent sample - probe p o t e n t i a l measurements during anodiza-t i o n , assuming gas pressure and discharge current can be accurately r e -produced. The problems here are that the unanodized sample possesses a t h i n 'thermal'oxide, and although t h i s may be corrected for a f t e r analy-s i s of the t o t a l ellipsometry data, i t s e l e c t r i c a l properties may d i f f e r from those of the subsequent anodic oxide. Furthermore, the t h i n oxide may Increase i n thickness during the i n i t i a l I-V measurement. This method was modified s l i g h t l y to use the sample f l o a t i n g p o t e n t i a l between formations as a reference l e v e l rather than that of the probe, since the l a t t e r could not be positioned reproducibly with respect to the oxide surface. Thus, the oxide f i e l d strength at given oxide thickness D and anodizing current I was taken as (V -V )_ - (V -V ) s u I s u 1=0 ,ir. l N E = (10.1) ox D - D u where the subscript u denotes measurements on the unanodized sample, and V (or V ) was the voltage difference between the sample (or unanodized s u sample) and the anode. The sample-probe p o t e n t i a l difference was s t i l l monitored continuously on a chart recorder'as i n F i g . 8.3 to provide an i n d i c a t i o n of anodization progress. F i n a l l y , as a possible improvement on the above, a gold-plated sample was used f o r the i n i t i a l I-V measurements to avoid the complications 145 due to the oxide on the unanodized sample. In this case the f i e l d was taken as (V -V ) - (V -V ) ox D \i-v-*J where denotes the voltage of the gold-plated sample with respect to the anode. This method i s subject to the same assumptions mentioned in section 9.3.3 with respect to gold-plated sample measurements. 10.3 Variation of Voltage with Time at Constant Total Current Figure 10.2 shows a plot of the potential V of a niobium sp sample r e l a t i v e to a probe during anodization at constant current. The plot i s f a i r l y t y p i c a l of both tantalum and niobium specimens i n that the potential rises rapidly when the current i s f i r s t applied and then settles to a slower, more or less constant rate of r i s e . The explanation of the fast i n i t i a l r i s e Is probably as follows. Since the current i s mostly electronic the effect i s cl e a r l y an increase of resistance to elec-tronic current. Electron injection from the plasma appears to occur at comparatively low f i e l d s . With l i t t l e or no space charge i n the oxide, the f i e l d throughout the oxide i s also low. However, electronic space charge develops due to capture of electrons by the heavy concentration of traps present in the amorphous oxide. This would cause the f i e l d at the plasma interface to be reduced so that a higher mean f i e l d would be re-quired to maintain the given electronic current. F i n a l l y , a steady state would be reached in which the slow r i s e of voltage would be due more or less entirely to the slow rate of growth"of the oxide. An alternative explanation i s possible i n terms of patching of leaky spots in the oxide, but this seems unlikely i n view of the fact that the same behaviour was exhibited by films prepared by wet anodization and then tested i n the F i g . 10.2 T y p i c a l v a r i a t i o n of sample p o t e n t i a l with respect to a f l o a t i n g probe during a constant current formation (niobium sample i n negative glow of system A ) . 147 plasma. 10.4 Voltage vs. Thickness f or Steady-State Conditions Figure 10.3 (which i s for niobium) shows voltages with respect to a nearby probe recorded at the end of each of a s e r i e s of formations at the same t o t a l current i n the negative glow of system A, p l o t t e d against the corresponding thickness of oxide. The corresponding i o n i c current density, as deduced from the change of thickness during the anodization period, i s recorded beside each point. C l e a r l y the l i n e a r dependence of voltage on thickness i n d i c a t e s a constant mean f i e l d strength i n the f i l m i n the l a t t e r part of each formation. This constant f i e l d gave a more or less constant i o n i c current. This i s analogous with wet anodization, but does not mean n e c e s s a r i l y that the f i e l d was constant through the thickness of the f i l m . 10.5 Thickness and Oxide P o t e n t i a l Difference Versus Time During a Formation In contrast to F i g . 10.3, which shows data obtained at the end of several formations at a current of 0.5 mA, F i g . 10.4 shows estimated oxide p.d. and thickness versus time during a p a r t i c u l a r formation on niobium under s i m i l a r conditions but at a higher current l e v e l of 1 mA (see also F i g . 8.11). Such a large v a r i a t i o n i n growth rate was not t y p i c a l , but i s presented to i l l u s t r a t e a possible source of e r r o r i n i o n i c currents c a l c u l a t e d from mean growth rates. I t i s i n t e r e s t i n g to f i n d that the data of F i g . 10.4 i s consistent with an exponential de-pendence of growth rate on f i e l d , as w i l l be shown below. 10.6 V a r i a t i o n of Ionic Current with Estimated Oxide F i e l d In F i g . 10.5, i o n i c current d e n s i t i e s obtained from the anodiza-149 150 151 3 t i o n of an el e c t r o p o l i s h e d p o l y c r y s t a l l i n e niobium sample at 30°C i n the negative glow of system A are p l o t t e d against oxide f i e l d evaluated at the end of each formation. The current d e n s i t i e s j were ca l c u l a t e d from mean growth rates using Eqn. 3.1 and assuming the oxide density to be 4.74 gm/cm as found for wet anodic Nb2°5 (Sch r i j n e r and Middlehoek 1964), and the f i e l d s f o r the points (0) were estimated according to , ( V i - <Vi-o ox D Some of these f i e l d s were corrected using factors V obtained from p l o t s s i m i l a r to F i g . 10.3, and are shown as the points (A), The corrected values reduce the s c a t t e r , and suggest that the i o n i c current i s indeed determined by the f i e l d i n the oxide, with an exponential dependence. This view i s also supported by F i g . 10.6, which shows incremental growth rates (as i o n i c currents) and i n t e g r a l f i e l d estimates during a s i n g l e 2 formation, namely that associated with F i g . 10,4. This 1 mA/cm forma-t i o n followed one of about an hour at the r e l a t i v e l y low current density 2 of 0.2 mA/cm , and a space charge e f f e c t i s i n d i c a t e d . A l t e r n a t i v e l y i t i s possible that the new oxide grown at 1 mA/cm required a lower f i e l d to s ustain the e l e c t r o n i c current than the p r e - e x i s t i n g oxide l a y e r , which has received a low current 'forming' treatment (see secti o n 3.1). Ionic current - oxide f i e l d data f o r the anodization of a poly-c r y s t a l l i n e tantalum sample (Ta2) at 30°C using three d i f f e r e n t pressures i n the c o n s t r i c t e d p o s i t i v e column of system B are shown i n F i g . 10.7. The oxide f i e l d estimations were made with the a i d of data from a gold-plated sample according to equation 10.2. An exponential r e l a t i o n i s again evident, and i t i s e s s e n t i a l l y independent of pressure. Another remark-able aspect of th i s data i s the range of magnitudes of the f i e l d s . In the 152 15 3 70' 70 -6 W • 60 mtorr x WO ' A 150 " EXTRAPOLATION FROM THE DATA OF YOUNG AND ZOBEL 1966 I I I i 2.0 3.0 4.0 Eox no 6 V/cm) Fig. 10.7 Ionic current density versus oxide f i e l d for the anodization of sample Ta2 at 30°C i n the positive column of system B at different pressures (extrapolation from wet anodization data also shown) 154 anodization of tantalum i n dilute sulphuric acid, the same io n i c current density range of between 10 and 10 A/cm is observed to require f i e l d 6 6 strengths almost a factor of two higher, i . e . 4.6 x 10 to 5.0 x 10 VI cm. The broken l i n e i n Fig. 10.7 i s from an empirical r e l a t i o n for the solution anodization case (Young and Zobel 1966). The large discrepancy in f i e l d s was not observed for niobium or tantalum anodized i n the negative glow of system A (although there were deviations from the solution anodization r e l a t i o n - see Lee et a l . 1970) and i t may be a consequence of conditions i n the positive column of system B, p a r t i c u l a r l y the amount of u l t r a - v i o l e t radiation f a l l i n g on the sam-ple. The effect of uv. radiation on solution anodization has been studied by various investigators. In a recent ellipsometric study, Dell'Oca 1969 found that uv i r r a d i a t i o n of tantalum during anodization i n dilute sulphuric acid resulted i n appreciable oxide growth at f i e l d s down to ~1 x 10^ V/cm, i . e . at f i e l d strengths that alone would not sup-port any noticeable growth. He found the photo-grown oxide to consist of two layers growing simultaneously, the outer layer being thicker than the inner, and of a higher refractive index according to his o v e r a l l e l -lipsometry data. Similarly, the present ellipsometry results can be f i t t e d by a two layer model for the plasma oxide, with the outer layer approx-imately four times as thick and of a higher refractive index (1.88) than ft the inner layer (1.63). Furthermore, Dell'Oca found that the photo-groxra oxide took ft Both of these values are considerably lox^er than the refractive index o found at 6328A in section 8.3.1 for the oxide grown normally i n d i l u t e sulphuric acid. 155 up water, and lost i t on prolonged drying. Compared to this reversible process, a more drastic but perhaps related phenomenon was observed with the plasma-grown oxide. When the anodized sample was exposed to the at-mosphere for the f i r s t time (after i n i t i a l l y l e t t i n g the vacuum system up to atmospheric pressure with nitrogen gas from a cylinder), the uni-formly coloured oxide f i l m developed many lighter-coloured c i r c u l a r spots which over a period of 30 minutes expanded i n number and size to cover the whole surface. Under microscopic observation these l i g h t areas were found to be regions where the oxide f i l m had separated from the tantalum substrate. This phenomenon, which was only observed with tantalum and nio-o bium samples anodized to oxide thicknesses of 1000-2000A i n the positive column of system B, suggests a somewhat open oxide structure susceptible to the absorption of water i n common with the oxide photo-grown i n solution. It i s discussed further i n section 10.8. 10.7 Dependence of Ionic Current on Temperature Measurements on the anodization of tantalum at 31°C and 77°C i n the negative glow of system A (Lee et a l . 1970) indicated that the so-called Tafel plot of los i . versus E shifted to lower f i e l d strengths f & J X ox ° as the temperature was raised, i n agreement with a f i e l d - a s s i s t e d thermal activation process for the ionic conduction mechanism. However, the slopes d log i . / d E for plasma anodization were considerably lower than the & J i ox corresponding slopes for solution anodization at these temperatures, whereas i n the work to be described below on aluminum, reasonable agree-ment with solution anodization data was obtained. o The sample consisted of a 2400A layer of aluminum vacuum eva-porated from 99.999% Al wire on a tungsten filament onto the polished surface of a s i l i c o n substrate at a pressure of ~1 x 10 ~* torr. This 156 produced a highly r e f l e c t i n g Al f i l m while giving better thermal contact to the sample holder than would a glass s l i d e . The Si wafer was mounted on the sample holder with conducting s i l v e r paint, which was also brought over the front surface to contact the edge of the Al layer. In view of the moisture effects on films produced i n the posi-tive column reported i n the previous section, and also to obtain faster growth rates, an alternative annular geometry cathode was introduced into system B to permit anodization i n the negative glow region. This cathode consisted of a planar 3 turn c o i l of 1.5 mm diameter 99.999% A l wire mounted on a pyrex tube having a tungsten wire feedthrough, and could be located between the anode and the plane of the sample i n the position marked AC i n Fig. 7.1. The cathode regions of the discharge extended from both faces of this c o i l , i . e . towards the sample as well as towards the anode, although no portion of the discharge current flowed to the o r i g i n a l hollow cathode which was isol a t e d . The positive column was absent with this arrangement, so that although the sample was surrounded by the negative glow region, i t s f l o a t i n g potential was only about 7 volts negative with respect to the grounded anode. The aluminum sample was anodized at current densities of 0.1 2 to 1.5 mA/cm and temperatures of 40°C and 70°C with a reduced discharge current of 20 mA (to decrease the possible sputtering from the cathode) and pressure of 100 mtorr. The results of ellipsometry measurements made at the end of each formation are shown in Fig. 10.8. These measure-ments were made i n two zones with the calibrated S o l e i l Babinet compen-sator as quarter wave plate, and were corrected for window errors as indicated i n section 7.2.3(d). The s o l i d curve was f i t t e d to the points using the program by Dell 1Oca 1969 suitably modified to deal with sharply 15 7 260r 801 L _ _ _ _ _ _ j i L i u . 40 42 44 46 48 50 V (deg) F i g . 10.8 E l l i p s o m e t r y data f o r the a n o d i z a t i o n of evaporated aluminum (sample A l l ) i n the n e g a t i v e glow of system B. S o l i d curve i s f o r s i n g l e oxide f i l m , N]_ = 1.45, growing on s u b s t r a t e o f i n d e x N 2 = 1.22-6.17J, 0 O = 69.29°, X - 6328A. Markers on curve are 100A f i l m t h i c k n e s s i n c r e m e n t s . 158 turning closed loops, and the model arrived at was a single non-absorbing oxide f i l m of refractive index .1.45 on a substrate of index 1.22 - 6.17J. While other investigators (Waxman and Zaininger 1968, Locker and Skolnick 1968) have evaluated the refractive index of plasma-anodized alumina, o their results (1.68, 1.75 respectively) pertained to a wavelength of 5461A. The values quoted here may be compared with 1.65 for anodic Al^O^ grown i n ammonium pentaborate (Goldstein et a l . 1970), 1.58 for sputtered Al^O^ (Ruiz-Urbeita et a l . 1971) and 1.21 - 6.93j.for evaporated annealed alum-o inum (Hass and Waylonis 1961), a l l at 6328A. Mean growth rates obtained from the above f i t were converted, to 3 i o n i c current densities by assuming an oxide density of 3.1 gm/cm as for wet anodic Al^O^ (Young 1961) and are shown plotted against oxide f i e l d strength i n Fig. 10.9. Hie fi e l d s were estimated according to Eqn. 10.1, which was considered to be a reasonable approximation since the (possibly o erroneous) correction voltage across the ~10A of thermal oxide would be small compared with (V - V ) T . The s o l i d lines i n Fig. 10.9 were c a l -1 s u 1 ° culated from the relation given by Harkness and Young 1966 for the aqueous solution anodization of bulk aluminum, and i t can be seen that there i s goo agreement at both temperatures. The improved agreement over the data for tantalum or niobium may be a consequence of a number of possible factors, e.g. a greatly decreased uv effect i n the negative glow region, or more ac-curate f i e l d measurements resulting from (a) a smaller space charge effect i n A1„0 , as evidenced by linear V versus time plots, and/or (b) reduced 2 3 sp potential drops i n the plasma with the annular cathode arrangement. In order to investigate the effect of the different sample tem-peratures usually obtained i n different types of discharge, a s i l i c o n sample was anodized i n system B (positive column) at several temperatures 159 F i g . 10.9 Ionic current d e n s i t i e s and estimated oxide-f i e l d s for the anodization of sample A l l (negative glow, system B) at 40°C(x) and 70°C(o). The s o l i d l i n e s are calcula t e d for these temperatures from a r e l a t i o n given for s o l u t i o n anodization of bulk aluminum (Harkness and Young 1966). 160 for comparison with growth rate data for the anodization of s i l i c o n i n an r f excited plasma (Hathorn, Pulfrey and Young, unpublished). The 1.8 cm square sample was cut from one of several 1-1/4" diameter n-type (phosphorus dopant) wafers with r e s i s t i v i t i e s i n the range 3 to 6 ficm purchased from the Monsanto Company. These wafers had received a chemical-mechanical polish ('Syton') on one face. To make an ohmic contact to the wafer, the l a t t e r was f i r s t cleaned in a 20% by volume HP etch (1 volume 49% HF i n 5. vols, d i s t i l l e d H^O) for 1 minute, rinsed in d i s t i l l e d water o and blown dry with nitrogen gas. Then a -3000A layer of Au + 0.1% Sb alloy was deposited on the back surface by vacuum evaporation from a molybdenum boat, and the gold layer was alloyed to the s i l i c o n by heating the wafer to 425°C for 5 minutes i n a stream of dry nitrogen. The sample was mounted on the sample holder with the mica mask i n place, and was anodized i n the positive column at a pressure of 100 mtorr with sample temperatures of 30, 50, 70 and 80°C using values of sample current I s from 0.2 to 0.8 mA, and a discharge current 1^ of 40 mA. At constant I, and I the oxide growth rates increased with temperature as shown in d s ° Fig. 10.10. For various values of I , straight lines have been drawn through the points and extrapolated to higher temperatures, where three growth rates for the anodization of s i l i c o n i n the r f system are shown. Since I i s predominantly electronic the straight l i n e extrapolation, implying a temperature-independent oxide f i e l d term i n the i o n i c current activation energy, i s only j u s t i f i e d i f the electronic current-field re-l a t i o n i n the oxide has a very small temperature dependence. Furthermore, the oxide f i e l d required for a given t o t a l current to be drawn through the oxide from the plasma might be expected to depend on the energy d i s -tribution of the electrons reaching the oxide surface as discussed in 161 .01 18 p o s i t i v e , c o l u r m o f dc discharge, I d = 40 nA ~2 2 2.6 T " 1 (°K" 1x10 3) 3.0 Fig. 10.10 Rates of anodization of s i l i c o n (sample S i l ) a various temperatures in the dc and r f discharges. 162 s e c t i o n 8.4. N e v e r t h e l e s s , as can be seen from F i g . 10.10, oxi d e growth r a t e s o b t a i n e d i n the r f - i n d u c e d plasma w i t h h i g h e r sample temperatures are i n the g e n e r a l r e g i o n of e x t r a p o l a t i o n from the lower temperature dc plasma d a t a , which tends to s u p p o r t t h e r m a l l y a c t i v a t e d h i g h f i e l d i o n i c t r a n s p o r t as a g r o w t h - r a t e - d e t e r m i n i n g p r o c e s s w i t h b o t h plasmas, and p a r t i a l l y e x p l a i n s the h i g h e r growth r a t e s i n r f plasmas (see a l s o s e c -t i o n 8.4). M i k h a l k i n and Odynets 1971 and Makara e t a l . 1971 have r e -c e n t l y p u b l i s h e d X a f e l p l o t s f o r the a n o d i z a t i o n o f t a n t a l u m and n i o b i u m r e s p e c t i v e l y i n an r f i n d u c e d d i s c h a r g e which have good l i n e a r i t y at s e v e r a l temperatures as i n F i g . 10.9 and are r e p o r t e d to be independent of d i s c h a r g e c o n d i t i o n s , a l t h o u g h the parameters v a r i e d were n o t g i v e n . 10.8 D i s c u s s i o n The p o s s i b i l i t y t h a t a c r o s s - t h e - s h e a t h t r a n s p o r t of n e g a t i v e i o n s - c o u l d g i v e r i s e to the observed e x p o n e n t i a l dependence of growth r a t e on f i e l d through an e l e c t r o n i c c u r r e n t - f i e l d r e l a t i o n s h i p (as o u t l i n e d i n s e c t i o n 4.3) appears to have been e l i m i n a t e d by the r e s u l t s of s e c t i o n 9.3. Thus, the r e s u l t s p r e s e n t e d above suggest t h a t i n the case o f dc d i s c h a r g e a n o d i z a t i o n the growth mechanism i s b a s i c a l l y the same as i n s o l u t i o n a n o d i z a t i o n , but w i t h l i m i t a t i o n s on the o x i d e f i e l d s t r e n g t h s i n v o l v e d due t o the energy spread of plasma e l e c t r o n s , and w i t h more or l e s s pronounced m o d i f i c a t i o n s due to the d i f f e r e n t n a t u r e of the o x i d e -e l e c t r o l y t e i n t e r f a c e . These m o d i f i c a t i o n s may be produced by uv i r -r a d i a t i o n as a l r e a d y mentioned, or a l t e r n a t i v e l y by random bombardment of high-energy p a r t i c l e s . I t appears t h a t the t h e r m a l l y a c t i v a t e d h i g h f i e l d i o n i c c o n d u c t i o n mechanism i s o p e r a t i v e i n r f - d i s c h a r g e a n o d i z a t i o n a l s o , w i t h sample temperatures h a v i n g the a p p r o p r i a t e e f f e c t onvthe growth r a t e s , but the d a t a as p r e s e n t l y e x i s t do not p e r m i t a g e n e r a l i z a t i o n of 163 t h i s c o n c l u s i o n t o a l l types of d i s c h a r g e used i n plasma a n o d i z a t i o n . The o x i d e l i f t i n g phenomenon observed on niobium and t a n t a l u m samples a n o d i z e d i n the p o s i t i v e column of system B i s o f c o n s i d e r a b l e i n t e r e s t . I t c o n s t i t u t e s e vidence f o r both a p l a n e of weakness and a compressive s t r e s s i n the o x i d e f i l m . The former i s most p r o b a b l y a s s o c i a t e d w i t h the sample s u r f a c e p r e p a r a t i o n t r e a t m e n t , as i t i s known t h a t adhesion of anodic o x i d e s i s a f f e c t e d by the p r e e x i s t i n g f i l m produced by c h e m i c a l p o l i s h i n g . The cause of the compressive s t r e s s w h i c h produces the l i f t i n g of the o x i d e away from the s u b s t r a t e i s o f more g e n e r a l s i g n i f i c a n c e . I t i s sometimes s t a t e d t h a t i f an o x i d e f i l m o c c u p i e s more volume th a n the m e t a l used i n i t s growth, then i t w i l l be under compressive s t r e s s . T h i s statement s t r i c t l y o n l y h o l d s f o r growth on a convex s u r f a c e and where the new o x i d e i s produced at the o x i d e -m e t a l I n t e r f a c e . V e r m i l y e a 1963 found a t e n s i l e s t r e s s i n anodic o x i d e s formed on t a n t a l u m and n i o b i u m i n aqueous s o l u t i o n s . A l o c a l i z e d com-p r e s s i v e s t r e s s c o u l d a r i s e d u r i n g a n o d i z a t i o n from the smoothing out o f a s p e r i t i e s i n the metal s u r f a c e (Young 1961). However the compressive s t r e s s i n v o l v e d i n the p r e s e n t e f f e c t may not develop u n t i l the f i l m i s exposed t o water vapour, as i s the case w i t h e v a p o r a t e d SiO f i l m s . F o r i n s t a n c e , H o l l a n d e t a l . 1960 found t h a t SiO f i l m s d e p o s i t e d r a p i d l y a t -5 low p r e s s u r e (<5 x 10 t o r r ) tend t o be d e f i c i e n t i n oxygen and are i n i t i a l l y under t e n s i o n which changes to compression as they absorb gas when exposed to the atmosphere. P r i e s t e t a l . 1963 found t h i s e f f e c t to be a c c e n t u a t e d when the e v a p o r a t i o n was at o t h e r than normal i n c i -dence and they observed b u c k l i n g of the SiO f i l m from i t s s u b s t r a t e w i t h i n a few minutes of exposure t o a i r . As i n t h i s s tudy the e f f e c t was a t t r i b u t e d t o the a b s o r p t i o n of water vapour, s i n c e no s t r e s s change 164 was measured f o r exposure t o dry n i t r o g e n a t atmospheric p r e s s u r e . I t i s p o s s i b l e then t h a t the plasma-anodized o x i d e may be u n s t r e s s e d a f t e r f o r m a t i o n , but have a h i g h p o r o s i t y t o w a t e r s i m i l a r to photo-grown a n o d i c o x i d e s . On exposure to a i r t h i s h i g h p o r o s i t y p e r m i t s e x t e n s i v e h y d r a t i o n of the o x i d e w i t h a r e s u l t i n g compressive s t r e s s . T h i s mechanism i s the converse of one proposed by V e r m i l y e a 196 3 to e x p l a i n h i s o b s e r v a t i o n s on s t r e s s i n anodic o x i d e s . He sug-g e s t e d t h a t o x i d e s formed w i t h aqueous e l e c t r o l y t e s are i n i t i a l l y hy-d r a t e d , but t h a t d e h y d r a t i o n o c c u r s by p r o t o n m i g r a t i o n d u r i n g c o n t i n u e d a n o d i z a t i o n and produces the observed t e n s i l e s t r e s s . I t s h o u l d be mentioned t h a t marked m e c h a n i c a l i n s t a b i l i t y has a l s o been observed i n plasma-anodized s i l i c o n o x i d e f i l m s produced under c e r t a i n c o n d i t i o n s i n an r f plasma ( P u l f r e y and Reche, unpublished) and i n plasma-anodized alumina (Morgan 1971), a l t h o u g h water vapour was n o t i m p l i c a t e d i n these examples. 165 11. THE PRODUCTION OF DIELECTRIC FILMS FOR METAL-INSULATOR-SEMICONDUCTOR DEVICES 11.1 I n t r o d u c t i o n One of the most i m p o r t a n t p o t e n t i a l a p p l i c a t i o n s of plasma a n o d i z a t i o n i s the p r o d u c t i o n of t h i n d i e l e c t r i c f i l m s f o r the gate i n s u l a t o r i n a c t i v e s o l i d s t a t e d e v i c e s such as the m e t a l - o x i d e - s e m i c o n -d u c t o r f i e l d e f f e c t t r a n s i s t o r (MOSFET or MOST). Th e r m a l l y grown s i l i c o n d i o x i d e has been used almost e x c l u s i v e l y i n m o n o l i t h i c s i l i c o n t e c h n o l o g y , because o f i t s w e l l u n d e r s t o o d p r o -p e r t i e s and i t s g e n e r a l l y good c o m p a t i b i l i t y and s a t i s f a c t o r y i n t e r f a c e w i t h s i l i c o n , b u t i t does not meet a l l of the requirements f o r t h i s ap-p l i c a t i o n . These requirements are o u t l i n e d below w i t h a c o n s i d e r a t i o n of p o s s i b l e a l t e r n a t i v e m a t e r i a l s , f o l l o w e d by a r e v i e w o f c u r r e n t i n -v e s t i g a t i o n s i n t h i s a r e a . Plasma a n o d i z a t i o n appears to be p a r t i c u l a r l y w e l l s u i t e d t o the f a b r i c a t i o n of double i n s u l a t o r l a y e r f i e l d e f f e c t d e v i c e s f o r memory a p p l i c a t i o n s s i m i l a r to the m e t a l - n i t r i d e - o x i d e - s i l i c o n (MNOS) t r a n s i s t o r (Wallmark and S c o t t 1969). These d e v i c e s u t i l i z e the s t o r a g e of charge at the i n t e r f a c e between a t h i n S i 0 2 ^L3^&x ( a d j a c e n t to the s i l i c o n ) and a t h i c k e r o u t e r l a y e r of h i g h e r p e r m i t t i v i t y d i e l e c t r i c such as s i l i c o n n i t r i d e . The p r e s e n t d e v i c e s r e q u i r e r a t h e r l a r g e w r i t e / e r a s e v o l t a g e s on account of the o x i d e - n i t r i d e p e r m i t t i v i t y r a t i o and the minimum p i n - h o l e f r e e n i t r i d e t h i c k n e s s which can be employed, so t h a t the use of an o u t e r l a y e r i n s u l a t o r of h i g h e r p e r m i t t i v i t y than s i l i c o n n i t r i d e i s d e s i r a b l e , as i s c l o s e r c o n t r o l over the i n s u l a t o r f i l m t h i c k n e s s . Such double i n s u l a t o r s t r u c t u r e s may be produced by 166 f i r s t v a cuum-depositing an a p p r o p r i a t e l a y e r of the chosen m e t a l (e. g . A l ) on the s i l i c o n s u b s t r a t e and then plasma a n o d i z i n g such t h a t the m e t a l ft i s c o m p l e t e l y c o n v e r t e d t o o x i d e and the d e s i r e d i n t e r m e d i a t e l a y e r of S i C ^ i s produced. However, the s u c c e s s o f t h i s approach depends on the u n i f o r m i t y of and accuracy w i t h which the i n t e r m e d i a t e l a y e r t h i c k n e s s can be c o n t r o l l e d , and an e x p e r i m e n t a l i n v e s t i g a t i o n o f t h i s problem was undertaken. The p r o d u c t i o n of double i n s u l a t o r s t r u c t u r e s i n two s e p a r a t e stages ( t h e r m a l o x i d a t i o n and/or plasma a n o d i z a t i o n ) has been i n v e s t i g a t e d r e c e n t l y by Pappu 1972. 11.2 D i e l e c t r i c M a t e r i a l s f o r Gate I n s u l a t i o n The o p e r a t i o n and c h a r a c t e r i s t i c s o f m e t a l - i n s u l a t o r - s e m i c o n -d u c t o r d e v i c e s are v e r y s e n s i t i v e t o the p r o p e r t i e s o f the i n s u l a t o r f i l m . T h i s l e a d s to a s e t of b a s i c requirements f o r the f i l m m a t e r i a l '(Zain-i n g e r and Wang 1969), some of the most i m p o r t a n t of which a r e : (a) A c c e p t a b l e i n t e r f a c e w i t h the semiconductor - low s u r f a c e s t a t e d e n s i t y (b) High d i e l e c t r i c s t r e n g t h (c) High p e r m i t t i v i t y (d) Low d i e l e c t r i c l o s s e s (e) I m p e r m e a b i l i t y to i m p u r i t i e s ( f ) S p e c i a l requirements such as r a d i a t i o n r e s i s t a n c e f o r s a t e l l i t e c i r c u i t r y . ft " I t i s p o s s i b l e t h a t the SiO^ l a y e r might be produced at the o u t e r s u r f a c e of the Al^O^, by f i e l d - a s s i s t e d m i g r a t i o n of S i i o n s through the A l ^ O ^ r a t h e r than oxygen i o n s through the A l ^ O ^ to the s u b s t r a t e . E v i -dence of enhanced m o b i l i t y of s i l i c o n has been p r o v i d e d r e c e n t l y by he-l i u m i o n b a c k - s c a t t e r i n g measurements on h e a t - t r e a t e d l a y e r s of g o l d on s i l i c o n ( H i r a k i e t a l . 1972).' 167 Requirement (a) i s of paramount i m p o r t a n c e , as s u r f a c e s t c i t e s can s e r i o u s l y degrade the o p e r a t i o n and c h a r a c t e r i s t i c s o f MOS t r a n s i s t o r s i n the areas o f leakage c u r r e n t s , n o i s e , frequency response and c u r r e n t a m p l i f i c a t i o n . Needless t o say i t . does not ap p l y to an o u t e r o x i d e f i l m i n double i n s u l a t o r l a y e r FET's. The use of m a t e r i a l s w i t h s i m i l a r d i -e l e c t r i c s t r e n g t h b u t h i g h e r p e r m i t t i v i t y than SiO,-, would be advantageous i n p r o v i d i n g lower t h r e s h o l d v o l t a g e s and i n c r e a s e d t r a n s conductance f o r the same v o l t a g e r a t i n g s . T h i s can be seen from the way t h a t the gate i n s u l a t o r c a p a c i t a n c e p er u n i t a r e a C^ e n t e r s the f o l l o w i n g e x p r e s s i o n s f o r an i d e a l i z e d n-channel enhancement t r a n s i s t o r (Sze 1969): 1/2 t h r e s h o l d v o l t a g e V T = 2i|i + l ^ q N ^ ^ ) ] x and s a t t i r a t i o n t r a n s conductance A 8 I D =m 3V G = const where w and I are the w i d t h and l e n g t h o f the c h a n n e l , u i s the channel c a r r i e r ( e l e c t r o n ) m o b i l i t y , V_ i s the gate v o l t a g e , the p o t e n t i a l d i f f e r e n c e between the Fermi and i n t r i n s i c Fermi l e v e l s o f the semicon-d u c t o r , e g i t s p e r m i t t i v i t y , and N^ the a c c e p t o r dopant c o n c e n t r a t i o n . I n c h o o s i n g d i e l e c t r i c m a t e r i a l s , an e x a m i n a t i o n by Harrop and Campbell 1968 of the p e r i o d i c t a b l e and the d i e l e c t r i c p r o p e r t i e s of v a r i o u s m e t a l o x i d e s i n d i c a t e s o x i d e s o f the groups T i , Zr and Hf; V, Nb and Ta; Cr, Mo and W t o be of i n t e r e s t f o r h i g h p e r m i t t i v i t y . These authors suggest t h a t o x i d e s h a v i n g a h i g h e r mean atomic number per molecule g e n e r a l l y have, h i g h e r p e r m i t t i v i t i e s but a l s o h i g h e r l o s s e s and lower breakdown f i e l d s . However, t h e r e are some e x c e p t i o n s , f o r i n s t a n c e 168 wet a n o d i z e d T a 2 0 5 h a s a c c e p t a b l e l o s s e s (<1%) , and TiO,, can have a h i g h v a l u e of r e l a t i v e p e r m i t t i v i t y (up to 80 i n t h i n f i l m form - Feuer-sanger 1964). T i t a n i u m h a v i n g the same v a l e n c y as S i , TiO^ might be ex-p e c t e d t o g i v e an i n t e r f a c e w i t h the s i l i c o n l a t t i c e s i m i l a r to t h a t of S i 0 2 ' A f a c t o r i n f a v o u r of Ta among the v a l v e metals i s t h a t Ta-Ta^O^ t h i n f i l m t e c hnology i s w e l l e s t a b l i s h e d , and the use of plasma-anodized Ta^O^ as a gate i n s u l a t o r s h o u l d f a c i l i t a t e the f a b r i c a t i o n of i n t e g r a t e d c i r c u i t s c o m p r i s i n g t h i n f i l m p a s s i v e and a c t i v e d e v i c e s . 11.3 B r i e f Review of Recent Work on M e t a l Oxide T h i n F i l m s U s e f u l f o r Gate I n s u l a t i o n A p art from s i l i c o n n i t r i d e , a l umina has perhaps r e c e i v e d the most a t t e n t i o n as an a l t e r n a t i v e to SiO^. Salama 1970 found alumina f i l m s d e p o s i t e d on s i l i c o n by r f s p u t t e r i n g to g i v e a s u r f a c e charge den-11 2 s i t y l e s s than 10 charges/cm a f t e r a n n e a l i n g but t o have a charge t r a p p i n g i n s t a b i l i t y . Alumina produced by plasma a n o d i z a t i o n has e n a b l e d the f a b r i c a t i o n of MOS t r a n s i s t o r s w i t h improved performance i n the a r e a of r a d i a t i o n r e s i s t a n c e ( M i c h e l e t t i e t a l . 1970). MOS t r a n s i s t o r s f a b r i c a t e d w i t h r e a c t i v e l y s p u t t e r e d TiO^ have been r e p o r t e d ( W a k e f i e l d and Gamble 1970), and w h i l e the d e v i c e s showed i n c r e a s e d t r a n s conduc-t a n c e , the i n c r e a s e was not as g r e a t as e x p e c t e d , due perhaps to the i n -f l u e n c e of the T i 0 2 ~ S i i n t e r f a c e on the c a r r i e r m o b i l i t y i n the enhanced n-channel. ^±0^ f i l m s have been d e p o s i t e d on s i l i c o n by c h e m i c a l vapour d e p o s i t i o n (Wang e t a l . 1970), b u t they had e x c e s s i v e l y h i g h conductance, oxi d e charge and i n t e r f a c e s t a t e d e n s i t y . Z i r c o n i u m has been plasma-anodized (Ramasubramanian 1970), but the o x i d e p r o p e r t i e s were not g i v e n . Some work has a l s o been performed on plasma-anodized HfO^, and C(V) 169 measurements on MIS c a p a c i t o r s t r u c t u r e s demonstrated the m o d u l a t i o n of semiconductor s u r f a c e p o t e n t i a l ( N o r r i s and Z a i n i n g e r 1970). Nb 20^ and Ta^O^ f i l m s d e p o s i t e d on s i l i c o n by c h e m i c a l vapour d e p o s i t i o n (Wang e t a l . 1970) were found t o have a low i n t e r f a c e s t a t e d e n s i t y and ox i d e charge, and t h e i r r a d i a t i o n r e s i s t a n c e was b e t t e r than t h a t o f t h e r m a l S iO^, but they were not e f f e c t i v e b a r r i e r s a g a i n s t i o n i c i m p u r i t i e s . As mentioned e a r l i e r , Lee e t a l . 1970 found the p e r m i t t i v i -t i e s o f plasma-anodized Nb„0,_ and Ta^0 c f i l m s produced on the b u l k .. 2 5 2 5 metals t o be 34 and 17 r e s p e c t i v e l y , and the l o s s f a c t o r s were about 1%. S i m i l a r v a l u e s were r e p o r t e d by Jennings and M c N e i l l 1969 f o r Ta^O^ ob-t a i n e d u s i n g an i o n cathode. V r a t n y 1967 p r e p a r e d b o t h plasma-anodized and r e a c t i v e l y s p u t t e r e d f i l m s o f Ta 20,-. The d i e l e c t r i c s t r e n g t h s were lo w e r and l o s s e s h i g h e r than f o r wet anodic Ta 20,-, b u t i t i s p o s s i b l e t h a t h i s plasma-anodized f i l m s a l s o c o n t a i n e d r e a c t i v e l y s p u t t e r e d Ta„0^ as p o i n t e d out by O'Hanlon 1970. Of the group VIA m e t a l s , chromium was plasma-anodized i n the e a r l y work of M i l e s and Smith 1963, but no p r o p e r t i e s o f , t h e o x i d e were g i v e n , and molybdenum has a l s o been i n v e s t i g a t e d (O'Hanlon 1970) b u t no d e t a i l s are a v a i l a b l e . R e c e n t l y b u l k T i , Z r , V, Nb, Ta and W have been anodized by the i o n cathode method (Husted e t a l . 1971), and the r e s u l t i n g o x i d e s had l o s s f a c t o r s i n the range 1% to 6%. P e r m i t t i v i t i e s were g i v e n f o r Nb 20^ and T a 2 ° 5 o n l y (28 and 22 r e s p e c t i v e l y ) , and'breakdown f i e l d s were not e v a l u a t e d . 11.4 Plasma A n o d i z a t i o n of M e t a l F i l m s on S i l i c o n 11.4.1 I n t r o d u c t i o n The a n o d i z a t i o n of a m e t a l f i l m coated on a s i l i c o n s u b s t r a t e 170 may be used to f a b r i c a t e a gate i n s u l a t i o n l a y e r f o r FET's. However, as has been p o i n t e d out by N o r r i s and Z a i n i n g e r 1970, f o r the s i m p l e MOS t r a n s i s t o r s t r u c t u r e i t i s e s s e n t i a l t h a t the a n o d i z a t i o n be t e r m i n -ated as soon as the m e t a l l a y e r has been c o m p l e t e l y c o n v e r t e d t o o x i d e , s i n c e the growth of an a n o d i c S i 0 2 l a y e r on the s i l i c o n would i n t r o d u c e i n t o l e r a b l e h y s t e r e s i s e f f e c t s due t o charge t r a p p i n g . On the o t h e r hand, the p r o d u c t i o n of a c o n t r o l l e d t h i c k n e s s of SiO^ i s e s s e n t i a l to the f a b r i c a t i o n of the memory type d e v i c e . Thus, the m o n i t o r i n g of the ft o x i d e f i l m t h i c k n e s s i s o f c o n s i d e r a b l e importance , and i t was d e c i d e d to study the a n o d i z a t i o n of metal f i l m s on s i l i c o n s u b s t r a t e s w i t h the automated e l l i p s o m e t e r , i n combination w i t h i n s i t u measurement o f the s m a l l s i g n a l ac d i f f e r e n t i a l c a p a c i t a n c e of the anodized f i l m - s i l i c o n system as a f u n c t i o n of dc b i a s . This l a t t e r measurement i s s e n s i t i v e to the c o n d i t i o n s at the s i l i c o n s u r f a c e , as w i l l be shown below. The metals chosen f o r i n i t i a l e x a m i n a t i o n were A l and Ta - the f i r s t because i t can be d e p o s i t e d w i t h ease i n t h i n f i l m form by vacuum e v a p o r a t i o n , and the second because of i t s p r e s e n t a p p l i c a t i o n i n m i c r o e l e c t r o n i c s . 11.4.2 E l l i p s o m e t r i c c o n s i d e r a t i o n s Computations were undertaken to e v a l u a t e the e x p e c t e d form and t h i c k n e s s s e n s i t i v i t y o f the A - ij; e l l i p s o m e t r y curve t r a c e d out as a m e t a l l a y e r of a p p r o p r i a t e t h i c k n e s s i s c o n v e r t e d t o i t s o x i d e , and then as the s i l i c o n s u r f a c e anodizes t o g i v e an i n c r e a s i n g t h i c k n e s s o f SiO^ beneath the now c o n s t a n t t h i c k n e s s o f metal o x i d e . The s e n s i t i v i t y o f the e l l i p s o m e t r i c measurement to f i l m t h i c k n e s s v a r i e s c o n s i d e r a b l y w i t h t h i c k n e s s , b e i n g h i g h e s t i n the r e g i o n of the A - ijj curve where \p * The sample v o l t a g e v e r s u s time p l o t cannot be expected t o r e v e a l the m e t a l consumption p o i n t s i n c e the growth o f S i 0 2 r a t h e r than the m e t a l o x i d e , say A1 20 , would cause o n l y a g r a d u a l change of the s l o p e dV/dt from t h a t t y p i c a l of A1 20 3 towards t h a t t y p i c a l of S i O ^ 171 i s a maximum. R e f e r r i n g to F i g . 10.8, t h i s i s seen t o cor r e s p o n d to O about 1250A of A l o 0 o on aluminum. The r a t i o of al u m i n a t h i c k n e s s t „ 2 3 M 2 3 produced to aluminum t h i c k n e s s t ^ consumed i s g i v e n by A 1 2 0 3 A 1 2 0 3 p A 1 t A l 2 \ l P A 1 2 0 3 where W and p are m o l e c u l a r w e i g ht and f i l m d e n s i t y r e s p e c t i v e l y and the ox i d e i s assumed s t o i c h i o m e t r i c . U s i n g the d e n s i t y o f s o l u t i o n a n o d i c 3 3 A 1 2 0 3 (3.1 gm/cm , Young 1961) and a v a l u e o f 2.58 gm/cm. f o r the d e n s i t y o f t h i n f i l m aluminum (Hartman 1965) g i v e s t . - n / t = 1.57 so t h a t o o ^ ^ -800A o f aluminum s h o u l d produce -1250A o f A^O.^. The t h e o r e t i c a l e l l i p -O 0 sometry curve f o r the c o n v e r s i o n of 800A o f A l to 1250A o f A 1 2 0 3 on a s i l i c o n s u b s t r a t e and the .subsequent growth o f an S i 0 2 l a y e r i s shown o ' i n F i g . 11.1. The r e f r a c t i v e i n d i c e s at 6328A used f o r the v a r i o u s media were as f o l l o w s : 3.87 - 0.017J f o r s i l i c o n ( i m a g i n a r y p a r t from P h i l l i p and T a f t I960, r e a l p a r t from d a t a o b t a i n e d i n the s i l i c o n a n o d i z a t i o n r e p o r t e d i n s e c t i o n 10.7), 1.47 f o r S i 0 2 ( s e c t i o n 10.7), 1.21 - 6.93j f o r A l (Hass and Waylonis 1961) and 1.45 f o r A l ^ (from F i g . 10.8). On comparing t h i s f i g u r e w i t h F i g . 1 0 . 8 , the normal i n f i n i t e A l s u b s t r a t e curve i s seen t o be 'peeled open' as the o p t i c a l p r o p e r t i e s o f the s i l i c o n s u b s t r a t e become dominant v i a the i n c r e a s i n g t r a n s m i t t a n c e o f the d i m i n i s h i n g m e t a l f i l m . The p o i n t at which the l a s t of the m e t a l i s f i n a l l y consumed and a n o d i z a t i o n o f the s i l i c o n commences i s c l e a r l y i d e n t i f i a b l e as a ve r y sharp l o c a l minimum i n A and i>. T h i s t u r n i n g p o i n t , t o g e t h e r w i t h the h i g h s e n s i t i v i t y to f i l m t h i c k n e s s on each s i d e of the p o i n t , demonstrate t h a t e l l i p s o m e t r y i s p o t e n t i a l l y u s e f u l as a m o n i t o r o f t h i s c r i t i c a l s tage o f the p r o c e s s , d e s p i t e statements t o the c o n t r a r y ( N o r r i s and Z a i n i n g e r 1970). I n the case 172 160 r Si _| I \ < L_ 50 60 70 ip (cleg) F i g . 11.1 Computed e l l i p s o m e t r y curve f o r the a n o d i z a t i o n of an 800A evaporated aluminum f i l m (N = 1.21 - 6.93J) on s i l i c o n ( N 3 = 3.87 - 0.017]) to 1280A of A 1 2 0 3 CS± = 1.45) and the subsequent,, grox^th of an i n t e r m e d i a t e f i l m . o f S i 6 2 (N?_ = 1.47) , 0 O = 70°, X = 6328A. Markers on curve are 50A increments of A 1 2 0 3 or S i 0 2 . of t a n t a l u m , however, the s e n s i t i v i t y to the p o i n t of t o t a l m e t a l con-3 v e r s i o n I s v e r y much i n f e r i o r . U s i n g 15.6 and 8.0 gm/cm f o r the d e n s i t -i e s o f Ta and a n o d i c Ta„0 q r e s p e c t i v e l y g i v e s the r a t i o t / t = 2 .38, £ j i ^ l a and F i g . 11.2 shows a c a l c u l a t e d e l l i p s o m e t r y curve f o r the c o n v e r s i o n o o of 450A of s p u t t e r e d Ta to 1071A of T a 2 0 ^ and the subsequent growth o f o an SiO^ l a y e r . The v a l u e of 450A was the l o w e s t Ta f i l m t h i c k n e s s among some s p u t t e r e d Ta on S i samples made a v a i l a b l e by Microsystems I n t e r n a t i o n a l L t d . , and the r e f r a c t i v e i n d e x of 2.99-2.82j used f o r the t a n t a l u m was determined from a f i t to e x p e r i m e n t a l e l l i p s o m e t r y d a t a o b t a i n e d d u r i n g the s o l u t i o n a n o d i z a t i o n of a s i m i l a r s p u t t e r e d t a n t a l u m l a y e r (see s e c t i o n 8.3.1). The v a l u e of 1.85 f o r the r e f r a c t i v e i n d e x of plasma-grown T a 2 0 ^ was taken from s e c t i o n 10.6. The p o i n t at which a l l the t a n -talum i s j u s t consumed and s i l i c o n a n o d i z a t i o n commences i s o n l y a s l i g h t i n d e n t a t i o n on an o t h e r w i s e smooth curve. The l a c k of s e n s i t i v i t y r e -l a t i v e t o the aluminum case i s p r i n c i p a l l y a consequence of the l o w e r o p t i c a l a b s o r p t i o n of the t a n t a l u m ( a l t h o u g h the i n d e n t a t i o n i s somewhat more marked f o r a lower i n i t i a l t a n t a l u m t h i c k n e s s ) , and f o r t h i s reason the e x p e r i m e n t a l i n v e s t i g a t i o n was c o n c e n t r a t e d on the use of aluminum. 11.4.3 C(V) measurements The measurement of the c a p a c i t a n c e of MIS s t r u c t u r e s as a f u n c t i o n of b i a s i s p r e s e n t l y the p r i n c i p a l t o o l f o r the i n v e s t i g a t i o n of s i l i c o n s u r f a c e phenomena (Gray 1969), and such measurements at f r e -quencies of 100 kHz o r 1 MHz can be made c o n v e n i e n t l y by u s i n g a Boonton c a p a c i t a n c e meter. For i n s i t u measurements on samples i n the a n o d i z a -t i o n c e l l , a probe assembly was f a b r i c a t e d which enabled an e l e c t r o d e t o be brought i n t o i n t i m a t e c o n t a c t with- the o u t e r s u r f a c e of the anodic o x i d e . Three cases can be a n t i c i p a t e d as a n o d i z a t i o n of the aluminum-o n - s i l i c o n sample p r o g r e s s e s : (a) For the case where the A l l a y e r i s continuous over the s i l i c o n , the c a p a c i t a n c e measured w i l l be t h a t o f the probe through the A l o 0 o to t h i s l a y e r , s i n c e the s e r i e s c a p a c i t a n c e of the 174 756V 150 A Ta ON Si o F i g . 11.2 Computed e l l i p s o m e t r y curve f o r the a n o d i z a t i o n of a 450A s p u t t e r e d t a n t a l u m f i l m ( N 2 = 2.99 - 2.82j) on s i l i c o n (N3 = 3.87 0.017J) to 1071A of T a 2 0 5 (Ni_ = 1.85) and the subsequent growth of an i n t e r m e d i a t e f i l m of SiOo (N 7 = 1.47) " ' curve are 100A increments -of Ta 205 or S i 0 2 . 0O - 70' 6328A. Markers on 1 7 5 l a r g e a r e a A l - S i j u n c t i o n w i l l be much l a r g e r by comparison. T h i s Al^O c a p a c i t o r i s not expected to be v o l t a g e v a r i a b l e . For the case where the m e t a l l a y e r has j u s t been consumed, tbe s t r u c t u r e w i l l comprise a s i n g l e i n s u l a t o r l a y e r MIS c a p a c i t o r and the u s u a l h i g h frequency C ( V ) curve t y p i c a l of such s t r u c t u r e s s h o u l d be observed ( w i t h d e v i a t i o n s from the i d e a l curve due t o work f u n c t i o n d i f f e r e n c e s , o x i d e charge and s u r f a c e s t a t e s ) . The t h e o r e t i c a l b a s i s f o r the a n a l y s i s of such curves i s f u l l y d i s c u s s e d by Sze 1 9 6 9 . B r i e f l y the i d e a l form of the h i g h frequency C ( V ) c u r v e , shown i n F i g . 1 1 . 3 f o r an n-type s u b s t r a t e , can be u nderstood as f o l l o x ^ s : I f the m e t a l c o n t a c t i s b i a s e d p o s i t i v e l y w i t h r e s p e c t to the n-type s i l i c o n s u b s t r a t e then e l e c t r o n s w i l l be a t t r a c -t e d t o the s u r f a c e to form an a c c u m u l a t i o n l a y e r , and the measured c a p a c i t a n c e i s j u s t t h a t of the o x i d e CQ which i s i n -dependent of v o l t a g e . An a p p l i e d n e g a t i v e b i a s w i l l r e p e l s u r -f a c e e l e c t r o n s r e s u l t i n g i n a s u r f a c e d e p l e t i o n l a y e r h a v i n g a f i x e d volume charge d e n s i t y e q u a l t o the s i l i c o n donor im-p u r i t y c o n c e n t r a t i o n N . T h i s l a y e r d e v o i d of f r e e c a r r i e r s c o n s t i t u t e s a c a p a c i t a n c e i n s e r i e s w i t h CQ and reduces the t o t a l c a p a c i t a n c e C. B i a s i n g more n e g a t i v e l y widens the space charge l a y e r , r e d u c i n g C^ and C u n t i l f i n a l l y a t h i n l a y e r - o f m i n o r i t y c a r r i e r h o l e s forms at the s u r f a c e , which i s then s a i d t o be i n v e r t e d . F u r t h e r n e g a t i v e b i a s w i l l i n c r e a s e the number of h o l e s I n the i n v e r s i o n l a y e r b u t w i l l not widen the space charge l a y e r a p p r e c i a b l y , and s i n c e the h o l e concen-t r a t i o n i s not able, t o f o l l o w the h i g h frequency ac s i g n a l the t o t a l c a p a c i t a n c e C remains c o n s t a n t . 176 7. 0,-0.8. 0-6 c j i 0-4\ FLAT BANDS 0.21 0.01 INVERSION DEPLETION -6 •4 ACCUMULATION -2 0 2 BIAS (V) 4 6 F i g . 11.3 Form of h i g h frequency c a p a c i t a n c e - v o l t a g e curve f o r an i d e a l MIS c a p a c i t o r (n-type s e m i c o n d u c t o r ) . 177 (c) A f t e r a t h i n s i l i c o n d i o x i d e l a y e r has grown between the A l ^ O ^ and the s i l i c o n the C(V) curve i s e x p e c t e d t o show semiperma-nent s t o r a g e e f f e c t s (Wallmark and S c o t t 1969) o r at l e a s t v e r y s t r o n g h y s t e r e s i s v a r y i n g w i t h the b i a s v o l t a g e as charge t r a n s f e r o c c u r s between the the s i l i c o n and s t a t e s a t the S i C ^ - ^ 2 ^ 3 l n t e r r a c e " 11.4.4 E x p e r i m e n t a l A sample was p r e p a r e d by f i r s t p r o d u c i n g an ohmic c o n t a c t on the back o f a Monsanto 5 Qcm n-type s i l i c o n w a f e r and then vacuum evap-o r a t i n g 99.999% A l onto the p o l i s h e d f r o n t s u r f a c e as i n s e c t i o n 10.7. A s h u t t e r was used to c o n t r o l the d e p o s i t i o n I n c o n j u n c t i o n w i t h a q u a r t z c r y s t a l o s c i l l a t o r t h i c k n e s s d e p o s i t m o n i t o r and a s u i t a b l e f i l m t h i c k n e s o was o b t a i n e d (705A as e s t i m a t e d from the f i n a l f r equency o f the m o n i t o r a f t e r the c r y s t a l had c o o l e d down to room t e m p e r a t u r e ) . The sample was mounted w i t h the mica mask on the sample h o l d e r u s i n g a s m a l l q u a n t i t y o f c o n d u c t i v e s i l v e r p a i n t , and e l l i p s o m e t e r r e a d i n g s taken as u s u a l p r i o r to system assembly and pump down f o r d e t e r m i n a t i o n of the window c o r r e c t i o n f a c t o r . The probe f a b r i c a t e d f o r the i n s i t u c a p a c i t a n c e v o l t a g e mea-surements i s shown i n F i g . 11.4, and c o n s i s t e d of a -1.5 mm diameter g o l d b a l l , s e a l e d when molten onto a .05 mm diameter t u n g s t e n w i r e and h a v i n g a f l a t t e n e d f a c e . A c u s h i o n of indium was p r e s s e d onto the f a c e of the b a l l , which was supported i n a countersunk r e c e s s i n the end of a d r i l l e d t e f l o n i n s e r t (T) s l i d i n g i n an aluminum ho u s i n g . The h o u s i n g was p r e s s e d i n an aluminum arm mounted on a pyrex tube ( P ) , w i t h a tungsten f e e d t h r o u g h , t h a t passed through an '0' r i n g s e a l i n the anode end cap (A). A micrometer-type b a r r e l (B) threaded F i g . 11.4 Probe f o r i n s i t u c a p a c i t a n c e measurements. 179 on the s e a l h o u s i n g c o u l d be brought to bear on a r i n g (R) clamped on the tube so t h a t the probe c o u l d be brought i n t o c o n t a c t w i t h the sample s u r f a c e , and a s p r i n g between the t e f l o n i n s e r t and a d r i l l e d screw s e r v e d t o apply a r e p r o d u c i b l e l o a d to the i n d i u m c o n t a c t . U s i n g the a n n u l a r cathode w i t h a d i s c h a r g e c u r r e n t o f 20 mA and oxygen p r e s s u r e of 100 m t o r r , the sample was anodized i n the n e g a t i v e glow a t c u r r e n t l e v e l s from 0.1 to 1.5 mA, and the growth mo n i t o r e d c l o s e l y by b a l a n c i n g the e l l i p s o m e t e r a t one minute i n t e r v a l s . I n s i t u c a p a c i t a n c e measurements at 1 MHz were made w i t h a Boonton model 71A c a p a c i t a n c e meter a f t e r s w i t c h i n g the d i s c h a r g e o f f a t c e r t a i n p o i n t s . A f t e r c o n n e c t i n g the probe to the meter h i g h t e r m i n a l and the sample to the low t e r m i n a l , the probe was c o n t a c t e d t o the o x i d e and a dc b i a s o r slow ramp v o l t a g e was a p p l i e d a c r o s s these t e r m i n a l s v i a the meter c i r c u i t r y . The meter analog output and the dc b i a s v o l t a g e were a l s o f e d t o an x~y r e c o r d e r , and i n t h i s way tbe v a r i a t i o n of the probe-Al^O^ A l / S i 0 2 _ s i l i c o n s m a l l - s i g n a l ac d i f f e r e n t i a l c a p a c i t a n c e as a f u n c t i o n of dc b i a s c o u l d be o b t a i n e d . 11.4.5 R e s u l t s The two-zone-averaged A — v a l u e s o b t a i n e d from r e a d i n g s be-tween f o r m a t i o n s are shown i n F i g . 11.5. The s o l i d curve i n F i g . 11.5 i s the b e s t f i t to the e x p e r i m e n t a l A — d a t a which c o u l d be o b t a i n e d , o and i s f o r an i n i t i a l 670A of aluminum (of r e f r a c t i v e i n d e x 1.21-6.80J) o g i v i n g 1100A of A1 20 ( o f i n d e x 1.45 - 0 . 0 2 j ) . The t i g h t e r l oop i n t h i s curve compared to t h a t i n F i g . 41.1 i s a consequence of the s m a l l e r s t a r t i n g t h i c k n e s s of .• aluminum. I t i s e v i d e n t t h a t the o a n o d i z a t i o n of the l a s t 70A o r so of aluminum does n o t proceed a c c o r d i n g to the assumed model of a w e l l - d e f i n e d p l a n e o x i d e - m e t a l i n t e r f a c e moving u n i f o r m l y towards the s i l i c o n , s u r f a c e 180 ANODIZATION OF AI ANODIZATION OF Si o Y 50 V (deg) 60 70 F i g . 11.5 E l l i p s o m e t r y data f o r the a n o d i z a t i o n of an eva-p o r a t e d aluminum f i l m on a s i l i c o n s u b s t r a t e (sample A l - S i l ) i n the n e g a t i v e glow of system B. S o l i d curve i s ( N 2 = 1.21 - 6.80j) forming 1100A of A1 20 f o r i n i t i a l 6 70A of A l ( N - L = 1.45 - 0. 02j) , on S i (N3 = 3.87 - 0.017J) f o l l o w e d by growth o f i n t e r m e d i a t e f i l m of S i 0 2 ( N 2 = 1.47), 0 O = 69.29°, X = 6328A. Broken l i n e i s f o r S i 0 2 growth on top of A^Og l a y e r . 181 (and p a r a l l e l to the l a t t e r ) u n t i l the m e t a l l a y e r t h i c k n e s s decreases o to z e r o . I n s t e a d t h e r e appears to be a g r a d u a l t r a n s i t i o n of the 70A l a y e r between the Al^O^ and the s i l i c o n from a m e t a l l i c n a t u r e t o a d i e l e c t r i c n a t u r e . T h i s e f f e c t c o u l d r e s u l t from the A ^ O ^ - A l i n t e r f a c e o h a v i n g a roughness on the s c a l e of 100A, such t h a t the A l f i l m e v e n t u a l l y becomes d i s c o n t i n u o u s w i t h a topography s i m i l a r to a s l i c e o f Swiss cheese. The o x i d e h o l e s would then grow at the expense o f the m e t a l u n t i l the f i l m becomes i s l a n d s o f aluminum which e v e n t u a l l y d i s a p p e a r c o m p l e t e l y . The 1 mm diameter of the e l l i p s o m e t e r l i g h t beam would have an a v e r a g i n g e f f e c t on these p r o c e s s e s , g i v i n g the measured g r a d u a l t r a n s i t i o n . The e x p e r i m e n t a l d a t a between p o i n t s X and Y i n F i g . 11.5 are more c o n s i s t e n t w i t h oxygen i o n motion p r o d u c i n g SiO^ under the Al^O^ l a y e r than w i t h s i l i c o n I on motion p r o d u c i n g SiO^ on top of the Al^O^ - the broken l i n e shown i n the f i g u r e i s the c a l c u l a t e d curve f o r the l a t t e r p o s s i b i l i t y . Another p o s s i b l e source of the e f f e c t i s the t h i n n a t i v e o x i d e p r e s e n t on the s i l i c o n s u r f a c e , which has been i g n o r e d i n c a l c u l a t i n g the t h e o r e t i c a l curves i n F i g u r e s 11.1 and 11.5. However, t h i s o x i d e i s ex-p e c t e d t o be l a r g e l y 'absorbed' by the h i g h l y r e a c t i v e aluminum when i t f i r s t a r r i v e s from the e v a p o r a t i o n s o u r c e , and cause o n l y a minor change i n the o p t i c a l p r o p e r t i e s of the aluminum n e x t t o the s i l i c o n . Even i f the o x i d e p e r s i s t s as an i n t a c t l a y e r , i t would o n l y move the t u r n i n g p o i n t s l i g h t l y . I n s i t u c a p a c i t a n c e measurements made a t p o i n t X i n F i g . 11.5 v a r i e d o n l y v e r y s l i g h t l y x^ith dc b i a s , showing t h a t the A l f i l m x^as s t i l l e s s e n t i a l l y continuous at t h i s s t a g e , but measurements at p o i n t Y gave the c h a r a c t e r i s t i c h i g h frequency C(V) curve of an MIS c a p a c i t o r shox«7n i n F i g . 11.6 (curve A ) . The -40 V spread of the s l o p i n g p o r t i o n 183 of the curve i n d i c a t e s the presence of a l a r g e number of s u r f a c e s t a t e s and the h y s t e r e s i s i s i n the d i r e c t i o n of t r a p p i n g o f h o l e s from the s i l i c o n a t s i t e s w i t h i n the o x i d e . A more q u a n t i t a t i v e a n a l y s i s i s not f e a s i b l e because of the u n c e r t a i n t y i n the o x i d e t h i c k n e s s and i n d i u m probe c o n t a c t a r e a . Evidence of charge s t o r a g e i n t h e o x i d e at s i t e s more remote from the s i l i c o n s u r f a c e was suggested by the v o l t a g e d i s p l a c e m e n t to curve B which was o b t a i n e d a f t e r a p p l y i n g a b i a s of -50 V t o the probe f o r 10 seconds (the s m a l l e r h y s t e r e s i s i n B i s due t o the s m a l l e r b i a s sweep a m p l i t u d e ) . Curve B r e l a x e d a t z e r o b i a s towards curve A over a p e r i o d of s e v e r a l minutes, or i t c o u l d be r e t u r n e d by a p p l i c a t i o n of a p o s i t i v e b i a s . I n an attempt to a s c e r t a i n whether the e f f e c t i v e n o n u n i f o r m i t y i n the r e s i d u a l m e t a l l a y e r t h i c k n e s s was a consequence o f the a n o d i z a -t i o n p rocess i t s e l f , t h a t i s , a development o f i r r e g u l a r i t i e s i n the o x i d e -m e t a l i n t e r f a c e as a n o d i z a t i o n p r o g r e s s e s , a sample c o n s i s t i n g o f o n l y o 200A of A l on S i was p r e p a r e d i n the same manner and a n o d i z e d under the same c o n d i t i o n s as b e f o r e u s i n g c u r r e n t s from 0.1 t o 0.8 mA. The e l l i p -sometry r e s u l t s are shown i n F i g . 11.7, t o g e t h e r w i t h the c l o s e s t t h e o -r e t i c a l curve found, which was f o r 200A of A l ( o f r e f r a c t i v e i n d e x 1.2.-o 6.30j) g i v i n g 320A o f A l ^ ( o f i n d e x 1.52-0.02J). The e x p e r i m e n t a l p o i n t s a g a i n show a smoothing out r e l a t i v e to the c a l c u l a t e d c u r v e , b u t over a s m a l l e r range and w i t h l e s s d e v i a t i o n from the curve than i n F i g . 11.5 so t h a t the degree of n o n u n i f o r m i t y may have been l e s s f o r the s h o r t e r a n o d i z a t i o n . I n s i t u C(V) measurements taken a t p o i n t X a l r e a d y showed m o d u l a t i o n o f s u r f a c e charge i n the s i l i c o n , b u t the curves were u n s t a b l e and not r e p r o d u c i b l e . Measurements a t p o i n t Y were more s t a b l e , but w i t h some h y s t e r e s i s . The sample was s u bsequently removed from the 184 UOr 1301 1 ANODIZATION tllOF AI 120V 770 ANODIZATION OF Si 700 70 F i g . 11.7 E l l i p s o m e t r y data f o r the a n o d i z a t i o n of a 200A evaporated aluminum f i l m on s i l i c o n (sample A l - S i 2 , system B, n e g a t i v e glow). S o l i d curve i s f o r 200A of A l ( N 2 = 1.21 - 6.30j) forming 320A of A1 9CU (1-52 - 0.02J) f o l l o w e d by growth o o f i n t e r -mediate f i l m o f S i 0 2 ( N 2 = 1.47), 0 O = 69.29°, A = 6328A. 185 vacuum system and 0.76 mm d i a . gold counterelectrodes were deposited over the anodized area. C(V) measurements were made using these electrodes, and also a f t e r each of two thermal annealing treatments, namely a 30 minute anneal i n nitrogen at 300°C, and a one hour anneal i n hydrogen at 350°C. Such treatments are commonly used to reduce i n t e r f a c e state d e n s i t i e s i n MIS structures (Kooi 1966). Figures 11.8 and 11.9 show C(V) curves obtained f o r two adjacent electrodes before annealing. These curves are steep and have a high r a t i o of maximum to minimum capa-citance, as expected f o r a t h i n I n s u l a t o r l a y e r of higher p e r m i t t i v i t y than SiO^. Taking the t o t a l anodic oxide to consist of 320A of Al^O^ and 65A of Si02> i . e . the i d e a l i z e d model values close to point Y i n F i g . 11.7, and assuming the SiO^ l a y e r to have a r e l a t i v e p e r m i t t i v i t y of 3.8 (as f o r thermal oxide, Sze 1969), the maximum capacitance value (EQ) gives 6.8 f o r the r e l a t i v e p e r m i t t i v i t y of tbe Al^O^. This may be compared with a value of 8 found by N o r r i s and Zaininger 1970. For the MIS diode of F i g . 11.8, the amount of h y s t e r e s i s was small and r e l a t i v e l y independent of the amplitude of the t r i a n g u l a r b i a s sweep. However, by sweeping about a mean l e v e l of -3V (Au electrode r e l a t i v e to s i l i c o n ) the curve could be s h i f t e d b o d i l y 2V negative (curve A to curve B). The second diode showed l a r g e r h y s t e r e s i s , which was also dependent on the amplitude of the bias sweep (Fig. 11.9). The steepness of the curves suggests a low density of i n t e r f a c e states (a q u a n t i t a t i v e estimate of the density could be made by compari-son with the i d e a l curve, but c a l c u l a t i o n of the l a t t e r requires precise knowledge of the oxide thicknesses and p e r m i t t i v i t i e s ) . This i s suppor-ted by the observation that neither of the annealing procedures produced steeper curves, although the anneal i n nitrogen did cause a small (-0.5V) 600 r BIAS (V) F i g . 11.8 High frequency c a p a c i t a n c e - v o l t a g e curves f o r A120 - S i O ^ - S i sample (A1-S12) anodiz p o i n t Y i n F i g . 11.7 o b t a i n e d w i t h e v a p o r a t e d g o l d c o u n t e r e l e c t r o d e . Curve A: sweeping symmet-c a l l y about zero b i a s , curve B: sweeping about -3V. 187 F i g . 11.9 High frequency c a p a c i t a n c e - v o l t a g e curve f o r g o l d e l e c t r o d e on sample A l - S i 2 a d j a c e n t to M I S diode of F i g . 11. showing l a r g e r h y s t e r e s i s . 188 s h i f t of the curves i n the p o s i t i v e d i r e c t i o n . F i g . 11.10 p r e s e n t s C(V) curves taken a f t e r the a n n e a l i n hydrogen, which show the above s h i f t compared to F i g u r e s 11.8 and 11.9 and a l s o the e f f e c t of dc b i a s a m p l i -tude on the amount of h y s t e r e s i s . W h i l e the above measurements d i d n o t y i e l d a q u a n t a t i v e measure of the d e n s i t y o f i n t e r f a c e s t a t e s a t the A l ^ O ^ - S i o r S i O ^ - S i i n t e r f a c e , f o r the l a t t e r case an e s t i m a t e of s u r f a c e charge was o b t a i n e d from C(V) measurements on the plasma-anodized s i l i c o n sample r e f e r r e d to i n s e c t i o n 10.7. F i g . 11.11 shows a 1 MHz C(V) curve f o r an e v a p o r a t e d g o l d c o u n t e r -e l e c t r o d e on t h i s sample, which had a 700A t h i c k o x i d e . E v a l u a t i o n of the f l a t - b a n d v o l t a g e f o r t h i s curve and e q u a t i n g t h i s to Q /C where Q i s the s u r f a c e s t a t e charge ( n e g l e c t i n g any f i x e d o x i d e charge and 12 w o r k - f u n c t i o n d i f f e r e n c e s ) at f l a t - b a n d s g i v e s Q as 1.4 x 10 p o s i -s s 2 t i v e charges/cm < T h i s v a l u e i s s i m i l a r t o those o b t a i n e d f o r o t h e r 12 t h i n f i l m d i e l e c t r i c s on s i l i c o n ( Z a i n i n g e r and Wang 1969), e.g. 2 x 10 11 12 f o r Al o0„, 5 x 10 f o r N b o 0 c and 4 x 10 f o r Ta„0 c. 2 3 2 5 2 5 11.5 D i s c u s s i o n The e l l i p s o m e t r y and C(V) r e s u l t s above i n d i c a t e t h a t f o r the e v a p o r a t e d aluminum f i l m s s t u d i e d h e r e , the A l - A ^ O ^ i n t e r f a c e i s non-p l a n a r d u r i n g the f i n a l stages of plasma a n o d i z a t i o n of the m e t a l . T h i s i n t e r f a c e roughness, which must be e l i m i n a t e d b e f o r e s a t i s f a c t o r y double i n s u l a t o r l a y e r d e v i c e s can be f a b r i c a t e d , may o r i g i n a t e i n s e v e r a l ways. A n a t i v e S i O ^ l a y e r i s expected to have a s m a l l e f f e c t as mentioned above. The roughness appeared to be l a r g e r f o r the more p r o l o n g e d a n o d i z a t i o n of the t h i c k e r f i l m a l t h o u g h the a n o d i z a t i o n process more u s u a l l y has a smoothing e f f e c t on the m e t a l - o x i d e i n t e r f a c e . A more l i k e l y source 189 F i g . 11.10 High frequency c a p a c i t a n c e v o l t a g e curves sanmle A1-S12 a f t e r a n n e a l i n g f o r 30 minutes at 300 ° C i n n i t r and*then f o r one hour at 350°C i n hydrogen. 190 OL. 1 ' L -20 -10 0 10 BIAS (V) F i g . 11.11 High frequency capacitance-voltage curve f o r sample S i l anodized i n the p o s i t i v e column of systen B (sec s e c t i o n 10.7), w i t h evaporated gold c o u n t e r e i e c t r o d e . Oxide thickness = 700A, s u b s t r a t e donor concentration N = 1 x 1 0 1 5 cm""3. 191 of the i n t e r f a c e roughness could be roughness i n the o r i g i n a l outer sur-face of the aluminum f i l m . While the aluminum fi l m s vacuum evaporated on the polished s i l i c o n surface had a m i r r o r - l i k e appearance to the unaided eye, some samples were found to s c a t t e r the ellipsometer l a s e r l i g h t over a wide angular range, even approaching the 70° angle of the in c i d e n t beam d i r e c t i o n . A c e r t a i n surface roughness must be expected because of the randomness of the vacuum deposition process. For f i l m s deposited on room temperature substrates (as here) where l i t t l e surface d i f f u s i o n i s p o s s i b l e a f t e r impingement, porous f i l m structures can r e s u l t , and considerable roughness which increases with f i l m thickness may be observed (Neugebauer 1970). Thus the i n t e r f a c e roughness problem might be l a r g e l y a l l e v i a t e d by depositing the aluminum f i l m onto heated substrates, and removal of the native SiO^ f i l m p r i o r to metal deposition (e.g. by r f sputter etching) may y i e l d a d d i t i o n a l improvement. A porous aluminum f i l m s t r u c t u r e may also be the cause of the rather low p e r m i t t i v i t y and r e f r a c t i v e index of the A^O^ f i l m s . Because of the above problems with f i l m uniformity only a very rudimentary switching behaviour was observed, and i t could not be determined beyond doubt that t h i s behaviour was due to charge tra n s f e r to the oxide - oxide i n t e r f a c e as opposed to the f i l l i n g of hole traps as-sociated with oxide defects near the semiconductor-oxide i n t e r f a c e . However, the anodization approach o f f e r s promise, at l e a s t f o r c e r t a i n applications not req u i r i n g long storage retention times such as memory switches f o r matrix-addressed electroluminescent displays (Fischer 1971). 192 X I I . CONCLUSIONS The phenomenon of a n o d i z a t i o n i n the plasma of a low p r e s s u r e oxygen glow d i s c h a r g e has been s t u d i e d from b o t h the v i e w p o i n t o f the mechanisms i n v o l v e d and t h a t of p o t e n t i a l a p p l i c a t i o n s o f the p r o c e s s . U s i n g automated i n s i t u e l l i p s o m e t r y and e l e c t r i c a l probe t e c h n i q u e s , the f o l l o w i n g aspects were i n v e s t i g a t e d : (a) the dependence of the a n o d i z a t i o n r a t e on c o n d i t i o n s i n the d i s c h a r g e , (b) the s i g n i f i c a n c e of the s u p p l y o f n e g a t i v e oxygen i o n s from the n e u t r a l plasma, (c) the r e l a t i o n between i o n i c c u r r e n t , e l e c t r o s t a t i c f i e l d s t r e n g t h and tempera-t u r e i n the o x i d e , and (d) an i n i t i a l s tudy o f the a n o d i z a t i o n o f m e t a l f i l m s on s i l i c o n f o r MIS d e v i c e s . The f o l l o w i n g r e s u l t s were o b t a i n e d i n these s t u d i e s : (1) The a n o d i z a t i o n p r o c e s s does not u t i l i z e gaseous n e g a t i v e oxygen i o n s p r e s e n t i n the n e u t r a l plasma. T h i s was demon-s t r a t e d by the n e g l i g i b l e v a r i a t i o n i n a n o d i z a t i o n r a t e when the t r a n s p o r t of such i o n s to the sample s u r f a c e was v a r i e d by means of combined dc and r f b i a s i n g . (2) The mechanism of s p e c i e s t r a n s p o r t through the oxid e d u r i n g plasma a n o d i z a t i o n i s the same h i g h f i e l d i o n i c c o n d u c t i o n p rocess t h a t i s o p e r a t i v e i n s o l u t i o n a n o d i z a t i o n . Evidence f o r t h i s was t h a t the i o n i c c u r r e n t d e n s i t y d u r i n g plasma a n o d i z a t i o n w i s e x p o n e n t i a l l y dependent on the oxide f i e l d s t r e n g t h , and t h i s r e l a t i o n and i t s temperature dependence agreed w i t h the data f o r s o l u t i o n a n o d i z a t i o n of the r e s p e c t i v e m e t a l , the agreement b e i n g e x c e l l e n t i n the case of an aluminum sample anodized i n the n e g a t i v e glow r e g i o n . A d e v i a t i o n from 193 s o l u t i o n a n o d i z a t i o n f i e l d s t r e n g t h v a l u e s observed under c e r t a i n c o n d i t i o n s was thought to be the r e s u l t o f u l t r a -v i o l e t r a d i a t i o n from the d i s c h a r g e . With the above o b s e r v a t i o n s , the v a r i a t i o n of the a n o d i z a t i o n r a t e w i t h d i s c h a r g e c o n d i t i o n s such as p r e s s u r e , d i s c h a r g e c u r r e n t and d i s c h a r g e dimensions can be a t t r i b u t e d p r i n c i p a l l y to a dependence of the e l e c t r i c f i e l d s t r e n g t h i n the o x i d e on the energy d i s t r i b u t i o n and d e n s i t y o f e l e c t r o n s i n the plasma, w i t h these i m p l i c a t i o n s : (a) The a n o d i z a t i o n r a t e i s governed by the h i g h f i e l d i o n i c t r a n s p o r t mechanism i n the o x i d e , and i s l i m i t e d to about o 1 to 10A per minute by the magnitude of the random e l e c t r o n c u r r e n t d e n s i t y of the plasma, which determines the maximum c u r r e n t d e n s i t y t h a t can be drawn from the plasma w i t h o u t d i s t u r b i n g the e l e c t r o n energy d i s t r i b u t i o n , and t h e r e f o r e the maximum oxid e f i e l d s t r e n g t h . T h i s i s shown by the de-crease i n growth r a t e o b t a i n e d when the t o t a l c u r r e n t d e n s i t y drawn from the plasma i s i n c r e a s e d too f a r above the random f l u x l e v e l . (b) The low c u r r e n t e f f i c i e n c y o f the plasma p r o c e s s appears to be a consequence of the plasma e l e c t r o n s h a v i n g a wide d i s t r i b u t i o n o f e n e r g i e s , some o f which may be q u i t e h i g h compared w i t h those encountered i n the s o l u t i o n case. These h i g h e l e c t r o n e n e r g i e s r e s u l t ' i n h ot e l e c t r o n s i n j e c t e d i n the o x i d e , which g i v e v e r y l a r g e c u r r e n t s through the o x i d e at the f i e l d s t r e n g t h s n e c e s s a r y f o r i o n i c t r a n s p o r t . (c) The type of plasma b e s t s u i t e d to a n o d i z a t i o n would be 194 one I n which, the e l e c t r o n s a l l have r e l a t i v e l y low e n e r g i e s but are p r e s e n t i n a s u f f i c i e n t d e n s i t y t o m a i n t a i n the con-d u c t i v i t y o f the plasma. T h i s seems to be borne out by the i n c r e a s e d a n o d i z a t i o n r a t e s o b t a i n a b l e i n dc a r c and r f i n d u c e d d i s c h a r g e s . I n the f a b r i c a t i o n of t h i n d i e l e c t r i c f i l m s f o r MIS d e v i c e s by the plasma a n o d i z a t i o n o f d e p o s i t e d m e t a l f i l m s on s i l i c o n , the u t i l i t y o f e l l i p s o m e t r y f o r i d e n t i f y i n g the p o i n t when the m e t a l i s t o t a l l y c o n v e r t e d t o o x i d e depends s t r o n g l y on the o p t i c a l p r o p e r t i e s o f the m e t a l . By a n o d i z i n g t h i n l a y e r s o f aluminum on s i l i c o n s u b s t r a t e s , MIS s t r u c t u r e s were o b t a i n e d w i t h a s u r f a c e s t a t e d e n s i t y low enough to a l l o w s t r o n g m o d u l a t i o n of s u r f a c e charge i n the s i l i c o n , and s t o r a g e e f f e c t s were observed, a l t h o u g h these were o n l y s h o r t - l i v e d . The o p t i c a l measurements i n d i c a t e d c o n s i d e r a b l e s p a c i a l n o n u n i f o r -m i t y i n the c o n v e r s i o n of the r e s i d u a l m e t a l l a y e r t o o x i d e , w h i c h was a t t r i b u t e d t o inhomogeneties i n the s t a r t i n g l a y e r of aluminum. C a r e f u l c o n t r o l o f m e t a l d e p o s i t i o n c o n d i t i o n s s h o u l d p e r m i t d e v i c e s w i t h s t a b l e memory s t o r a g e p r o p e r t i e s to be f a b r i c a t e d . 195 REFERENCES 1. A l e x e f f , I . , and Jones, W.D., A p p l . Phys. 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Appendix C i s a b r i e f summary of a r e c e n t l y r e p o r t e d method o f d e t e r m i n -i n g the plasma p o t e n t i a l , w i t h some e x p e r i m e n t a l r e s u l t s r e l e v a n t t o t h i s method. Appendix A: V e l o c i t y and Energy D i s t r i b u t i o n s . The p a r t i c l e s of a gas i n * thermodynamic e q u i l i b r i u m at tempera-t u r e T have speeds d i s t r i b u t e d a c c o r d i n g t o Maxwell's d i s t r i b u t i o n , w h ich may be e x p r e s s e d i n the form 2 -, J / / m \ 3/2 2 r-mv T , /« i \ f ( v , d v = 4 T r n ( ^ ) v exp [ - ^ } dv ( A . l ) where f ( v ) d v i s the number of p a r t i c l e s w i t h speeds between v and v+dv, m i s the p a r t i c l e mass and n the number d e n s i t y o f p a r t i c l e s i n the gas. For an i s o t r o p i c d i s t r i b u t i o n the random p a r t i c l e f l u x c r o s s i n g a u n i t a r e a i n one d i r e c t i o n i s g i v e n by nv/4, where v i s the mean random speed and the f a c t o r (1/4) a r i s e s because o n l y h a l f the p o p u l a t i o n d e n s i t y have a component of v e l o c i t y towards the probe, and the average of the d i r e c t i o n c o s i n e over a hemisphere = 1/2. The d i s t r i b u t i o n f u n c t i o n of ( A . l ) g i v e s v as - 1 f c, \ A ,8kT.l/2 v = - j f (v)vdv = (-jj-) (A.2) o 2 1/2 Making the s u b s t i t u t i o n s e = mv 12 and dv = de/(2me) i n ( A . l ) g i v e s the energy d i s t r i b u t i o n : 202 f(e)de = C n e 1 / 2 exp ] de (A. 3) where f ( e ) de i s the number of p a r t i c l e s w i t h k i n e t i c energy i n the -1/2 -3/2 range e t o e + de and C = 2 (IT) ' (kT) . For p a r t i c l e s i n an e x t e r n a l force, f i e l d , the Boltzmann f a c t o r exp(-V/kT), where V i s the p o t e n t i a l energy p e r p a r t i c l e , must be i n c l u -ded i n (A.3) above t o g i v e the Maxwell-BoItzmann energy d i s t r i b u t i o n : f ( e ) de = C n o e 1 / 2 e x p - d e (A.4) where-n i s the p a r t i c l e number d e n s i t y at a p o i n t a t which V = 0. I n t h i s case the v a r i a t i o n of p a r t i c l e d e n s i t y w i t h p o s i t i o n i s g i v e n by Boltzmann's law: n = n Q expu~|] (A.5) Appendix B: Mean Free Path Lengths and Sheath T h i c k n e s s (a) Mean f r e e paths a c c o r d i n g t o a s o l i d e l a s t i c sphere model. 3 C o n s i d e r a gas c o n t a i n i n g N molecules/cm . I f the mo l e c u l e s are assumed t o be i m p e n e t r a b l e e l a s t i c spheres o f diameter d whose g v e l o c i t i e s are d i s t r i b u t e d a c c o r d i n g to the Maxwell!an law w i t h a mean v e l o c i t y v, i t can be shown (Jeans 1940) t h a t the number of c o l l i s i o n s 3 r~ 2 2— per cm per s e c . i s (ir//2)N d v. Each c o l l i s i o n marks the end of two g g f r e e paths (one f o r each o f the c o l l i s i o n p a r t n e r s ) , so t h a t the t o t a l 3 — 2 2 — number o f f r e e paths executed per cm - s e c . i s /2TTN d v. The t o t a l . g g l e n g t h o f a l l these f r e e paths i s N v, so- t h a t the mean f r e e p a t h l e n g t h x s x = ( B > 1 ) /2TTN d g & 203 I f the gas a l s o c o n t a i n s N charged c a r r i e r s of diameter d c c then the mean f r e e path of the c a r r i e r s i s X = [/2rrN d 2 + TTN d 2 (1 + m /m ) 3 " / 2 ] ~ 1 (B.2) c c c g gc e g ^ ' where m and m are the c a r r i e r and gas m o l e c u l e masses r e s p e c t i v e l y , c g and d = (d + d )/2. gc g c" For p o s i t i v e i o n s moving i n t h e i r own gas, m = m and (B.2) c g reduces to ( B . l ) . I n the case of e l e c t r o n s , m << m and d << d g i v i n g c g c g TTN d g g T h i s s i m p l i f i e d treatment assumes the r i g i d sphere p a r t i c l e s t o i n t e r a c t o n l y a t the i n s t a n t of i m p a c t , and may be s e r i o u s l y i n e r r o r f o r e l e c t r o n s , Hoxrever, i t can be used t o o b t a i n an e x p r e s s i o n f o r the m o b i l i t y u of i o n s i n a low e l e c t r i c f i e l d (Langevin's s i m p l e theory -see McDaniel 1 9 6 4 ) . On c o l l i s i o n w i t h a m o l e c u l e , each i o n was assumed t o l o s e a l l of the energy t h a t i t had a c q u i r e d from the f i e l d d u r i n g the p r e c e d i n g f r e e p a t h , and the e x p r e s s i o n a r r i v e d a t was u = ~ (B.4) mv ' • (b) E s t i m a t i o n of the sheath t h i c k n e s s (McDaniel 1964) The i n t e r f a c e between a plasma and a s o l i d s u r f a c e c o n s i s t s o f a sheath r e g i o n w i t h a net space charge which i n e f f e c t p r o t e c t s the plasma from the p h y s i c a l boundary. I n o r d e r to e s t i m a t e the t h i c k -ness of the sheath c o n s i d e r a t h i n s l a b - l i k e r e g i o n , o f h a l f - w i d t h L, p e r p e n d i c u l a r to the x a x i s and c e n t r e d about the o r i g i n of the l a t t e r , i n which the e l e c t r o n c o n c e n t r a t i o n n g r e a t l y exceeds the p o s i t i v e i o n e c o n c e n t r a t i o n n_j_. The r e s u l t i n g n e t charge g i v e s r i s e t o a p o t e n t i a l 204 d i f f e r e n c e AV between the c e n t r e o f the s l a b and the n e u t r a l plasma boun-d a r i e s governed by P o i s s o n ' s e q u a t i o n , which g i v e s d V _ e A 2 £ dx o (B.5) where e i s the f r e e space p e r m i t t i v i t y . I n t e g r a t i n g and p u t t i n g 4^ - = 0 and V = 0 a t x = 0 g i v e s dx 2 n ex V = ^ - (B.6) o i . e . n e l A Y - / ; - ( B ' 7 ) o The p o t e n t i a l appears as a " h i l l " t o e l e c t r o n s and a " t r o u g h " to i o n s . The w i d t h of the r e g i o n over which n g >> n + cannot be a r b i t r a r i l y l a r g e , s i n c e a p o i n t would be reached at which the e l e c t r i c a l p o t e n t i a l energy would exceed the mean thermal energy and charge f l o w would then o c c u r i n such a way as t o r e s t o r e n e u t r a l i t y . T a k i n g the mean k i n e t i c energy i n one d i r e c t i o n as kT^/2 l e a d s t o 2 2 kT n e^L - t - ^ f ^ (B .8) o x . e . e kT . ,0 L = [ ^ ] 1 / 2 (B.9) max I n e e Th i s e x p r e s s i o n f o r tbe d i s t a n c e over which a plasma can have an appre-c i a b l e d e p a r t u r e from charge e q u i l i b r i u m . i s e q u i v a l e n t to the Debye s h i e l d i n g l e n g t h f o r i o n s by e l e c t r o n s as d e r i v e d by a p p l y i n g P o i s s o n ' s e q u a t i o n t o the charge d i s t r i b u t i o n around a s i n g l e i o n i n the n e u t r a l plasma. Thus the t h i c k n e s s of the space charge sheath r e g i o n i n f r o n t 205 of a probe a t moderate p o t e n t i a l , i . e . $ kT^/e from plasma p o t e n t i a l , i s of the o r d e r o f the Debye l e n g t h . Appendix C: The 'Sounding Probe' Method of D e t e r m i n i n g Plasma P o t e n t i a l T h i s method, proposed by Dote e t a l . 1966, i s based on the dependence of the charged p a r t i c l e d e n s i t y w i t h i n the sheath r e g i o n of a probe on the probe p o t e n t i a l . As the probe i s b i a s e d n e g a t i v e l y w i t h r e s p e c t to plasma p o t e n t i a l , the e l e c t r o n d e n s i t y a t a p o s i t i o n i n the sheath decreases (some e l e c t r o n s are r e p e l l e d and a n e t p o s i t i v e space charge r e s u l t s ) . When the probe i s b i a s e d above plasma p o t e n t i a l , the e l e c t r o n d e n s i t y i n the now n e g a t i v e space charge sheath a g a i n d e c r e a s e s , s i n c e the e l e c t r o n c u r r e n t d e n s i t y to the sheath edge i s the c o n s t a n t random c u r r e n t from the plasma, whereas the e l e c t r o n v e l o c i t y i n c r e a s e s w i t h p o s i t i v e probe b i a s . The same arguments can be a p p l i e d to the p o s i t i v e i o n d e n s i t y , so t h a t the d e n s i t i e s o f b o t h p o s i t i v e l y and nega-t i v e l y charged p a r t i c l e s i n the sheath become a maximum when the probe i s at plasma p o t e n t i a l . The c u r r e n t t o a v e r y s m a l l probe ('sounding probe') p l a c e d c l o s e to a l a r g e r r e f e r e n c e probe and h e l d a t c o n s t a n t v o l t a g e ( w i t h r e s p e c t to the anode) i s used as a measure of charge c a r r i e r d e n s i t y . Assuming t h a t v a r i a t i o n s i n the sounding probe c u r r e n t when the r e f e r e n c e probe v o l t a g e i s v a r i e d are due o n l y to c a r r i e r den-s i t y v a r i a t i o n s i n the sheath r e g i o n o f the l a r g e r probe, then plasma p o t e n t i a l i s taken as the r e f e r e n c e probe v o l t a g e which maximizes the sounding probe c u r r e n t . For the above assumption to be v a l i d , the sounding probe s h o u l d be b i a s e d w e l l i n t o e i t h e r i t s p o s i t i v e i o n or e l e c t r o n s a t u r a t i o n c u r r e n t c o l l e c t i o n r e g i o n s , r a t h e r than between ( o r near) plasma p o t e n t i a l and f l o a t i n g p o t e n t i a l where the net c u r r e n t depends on the c o m p e t i t i o n between both c a r r i e r d e n s i t i e s . This can be seen i n F i g . C l , where 206 V p r r v f V s ~ V f (V) F i g . C l Sounding probe c u r r e n t v e r s u s r e f e r e n c e probe v o l -tage f o r v a r i o u s v a l u e s o f sounding probe b i a s . Reference probe: 8.5 mm d i a . g o l d - p l a t e d t antalum sample; sounding probe: 1 mm d i a . g o l d b a l l probe. Reference probe c u r r e n t - v o l t a g e c h a r a c t e r i s t i c a l s o shown. 207 sounding probe current (I ) versus reference probe voltage (V - V_) pr s f curves f o r a l l three regions are given. An oxide-masked, gold-plated 8.5 mm diameter area on a tantalum sample con s t i t u t e d the reference probe, and the 1 mm diameter gold b a l l sounding probe was s i t u a t e d 2 mm i n f r o n t . An order of magnitude estimate of the sheath thickness, as 2 1/2 furnished by the Debye s h i e l d i n g length = (e okT e/n ee ) , gives 8 —3 ~1 mm f o r the measured values kT = 2eV and n-, = 1 x 10 cm , but e e ' from the r e s u l t s In F i g . C l the sounding probe i s c l e a r l y w i t h i n the influ e n c e of the reference probe f i e l d . However, i t appears that the e l e c t r o n current maximum may be the more r e l i a b l e i n d i c a t o r of plasma p o t e n t i a l , since the reference probe voltage which maximized the p o s i -t i v e ion current was found to vary with sounding probe-reference probe distance i n the range 0.5 mm to 4 mm, whereas the e l e c t r o n peak was •"reTatively s t ab1e. Appendix D: Summary of i n s i t u Ellipsometry Results f o r the Plasma Anodization of Niobium and Tantalum The f o l l o w i n g sets of A, \p p a i r s were obtained from ellipsometry measurements at d i f f e r e n t stages of oxide growth, and the p a i r s i n each set are arranged i n order of measurement, i . e . , i n c r e a s i n g oxide t h i c k -ness. Tbe f i r s t three data s e t s , from system A, were determined using o l i g h t of wavelength 546IA and an angle of incidence of 65°. Sample Nbl: e l e c t r o p o l i s h e d p o l y c r y s t a l l i n e niobium. A ip 125.50 31.55 116.84 32.03 208 A * 109.86 32.49 99.88 33.29 91.14 34.50 80.58 37.70 64.58 49.66 60.42 54.18 58.48 55.78 1.70 73.04 344.50 73.11 280.32 49.02 268.82 39.57 247.68 32.50 232.96 30.56 This data was f i t t e d by a model c o n s i s t i n g of two non-absorbing f i l m s growing simultaneously but at d i f f e r e n t r a t e s . Assuming o p t i c a l constants of 3.60-3.60J f o r the niobium substrate (Young and Zobel 1966), the outer f i l m had a r e f r a c t i v e index of 2.15 and comprised 40% of the t o t a l oxide thickness, and the inner f i l m had an index of 2.37. Sample Nb2: e l e c t r o p o l i s h e d p o l y c r y s t a l l i n e niobium. A \p 131.20 31.30 118.52 32.18 97.62 33.88 73.25 43.37 54.58 60.25 47.98 64.79 209 A • ^ 41.44 67.98 10.36 73.85 307.50 68.45 298.70 65.13 286.08 57.46 274.70 46.07 258.38 34.19 This data was also f i t t e d with a two non-absorbing f i l m s model and with the same substrate o p t i c a l constants as above. The inner and outer f i l m i ndices were 2.38 and 2.12 r e s p e c t i v e l y , with the outer f i l m comprising 47.5% of the t o t a l thickness. Sample Nb5: e l e c t r o p o l i s h e d p o l y c r y s t a l l i n e niobium. 'A -ip 134.85 31.24 107.41 32.07 77.09 38.92 43.15 61.71 29.60 66.84 262.99 35.49 251.10 32.67 122.91 32.04 94.48 34.41 This data was analyzed using a two non-absorbing f i l m s model, the outer f i l m of r e f r a c t i v e index 2.17 comprising 20% of the t o t a l oxide thickness, the inner f i l m having an index of 2.36 on a substrate wit h o p t i c a l constants 3.60-3.60J. 210 The remaining r e s u l t s were a l l obtained at a wavelength of o 6328A w i t h an angle of incidence of 69.29°, i n system B. Sample Nb4: e l e c t r o p o l i s h e d s i n g l e c r y s t a l niobium, o r i e n t a -t i o n (110) . A 112.58 31.59 106.54 32.21 95.20 33.49 88.74 34.37 85.52 34.83 84.99 34.98 81.31 35.77 74.96 37.54 6-8.03 41.12 60.32 52.03 57.46 56.82 50.90 63.99 33.19 72.22 8.37 75.69 349.36 75.86 332.16 74.52 314.56 70.63 301.38 63.63 294.59 ' 56.24 292.56 52.94 289.02 46.68 286.29 42.70 284.54 40.88 211 A s i m p l e model of a s i n g l e n o n - a b s o r b i n g o x i d e f i l m w i t h a r e f r a c t i v e i n d e x of 2.36 growing on a s u b s t r a t e of i n d e x 3.90-4.49j was found to f i t t h i s d a t a w i t h o u t a s e p a r a t e s u b s t r a t e i n d e x d e t e r m i n a -t i o n , and growth r a t e s were e s t i m a t e d on t h i s b a s i s . Sample Nb3: e l e c t r o p o l i s h e d p o l y c r y s t a l l i n e n i o b i u m . A * 122.73 29.51 107.57 30.88 92.04 34.19 87.34 35.08 81.03 36.51 66.51 43.51 60.43 51.84 39.84 69.83 340.86 75.55 307.27 66.66 295.27 55.57 293.44 53.34 289.48 47.03 281.17 38.28 258.41 32.20 257.89 31.99 212.30 28.93 166.71 28.43 The model used to f i t t h i s d a t a c o n s i s t e d of two non-absorbing f i l m s growing s i m u l t a n e o u s l y on a s u b s t r a t e of r e f r a c t i v e i n d e x 3.55-3.75j, the o u t e r f i l m of i n d e x 1.80 c o m p r i s i n g 28% of the t o t a l oxide t h i c k n e s s , 212 the i n n e r f i l m h a v i n g an i n d e x o f 2.24. The s u b s t r a t e o p t i c a l c o n s t a n t s used here were determined w i t h d a t a from the s o l u t i o n a n o d i z a t i o n o f a s i m i l a r p o l y c r y s t a l l i n e sample. Sample Ta2: e l e c t r o p o l i s h e d p o l y c r y s t a l l i n e t a n t a l u m . A * . 100.27 27.62 81.62 31.71 68.95 38.12 63.09 51.67 62.28 56.94 61.64 59.90 59.49 65.11 50.03 74.20 33.03 •79.16 10.06 81.50 347.37 81.81 340.73 81.60 321.03 80.55 302.61 77.20 289.90 70.12 285.36 64.44 282.19 58.64 280.34 53.33 277.81 45.94 275.81 40.70 271.93 35.70 260.02 30.66 213 A 241.87 27.01 219.53 24.88 197.41 23.87 176.14 23.74 151.64 24.58 132.45 25.75 131.52 25.92 122.51 26.67 116.17 27.20 Using 2.46-2.56j f o r the o p t i c a l constants of the substrate as determined from s o l u t i o n anodization measurements, the best f i t obtained f o r the above data was given by an oxide model of two non-abso bing f i l m s growing simultaneously, the outer f i l m of index 1.88 compri-s i n g 80% of the t o t a l oxide thickness, the inner f i l m having an index of 1.63. 

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