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Ionic conduction at high fields in anodic oxide films on tantalum Dell'Oca, Conrad Joseph 1969

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IONIC CONDUCTION AT HIGH FIELDS IN ANODIC OXIDE FILMS ON TANTALUM by . CONRAD JOSEPH DELL'OCA B.A.Sc., Uni v e r s i t y of B r i t i s h Columbia, 1964 M.A.Sc., University of B r i t i s h Columbia, 1966 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS OF 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 Research Supervisor Members of the Committee Acting Head of the Department Members of the Department of E l e c t r i c a l Engineering THE UNIVERSITY OF BRITISH COLUMBIA December, 1969 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced degree at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y . I f u r t h e r agree tha p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Department o r by h i s r e p r e s e n t a t i v e s . It i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f 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 w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada ABSTRACT The technique anodic oxide f i l m s r e s u l growth. E l l i p s o m e t r y re Ta i n phosphoric a c i d ar which the oxide c o n s i s t s and oxygen i o n transport m c r o p o r a t i o n i n t o the o respect to the inner l a y w i t h a s i n g l e homogeneou r e f r a c t i o n changing l i n e n o n destructive method o The index of r by curve f i t t i n g e l l i p s o m e t r y r e s u l t s obtained as a f u n c t i o n of i n c r e a s i n g oxide t h i c k n e s s . Computer methods f o r s o l v i n g the e l l i p s o m e t r y equation and curve f i t t i n g are given. Computed r e s u l t s are given and discussed f o r cases of one and two l a y e r f i l m s growing on a metal. F i n a l l y , an e r r o r a n a l y s i s of e l l i p s o m e t r y i s made. E l l i p s o m e t r y r e s u l t s were obtained and c u r v e - f i t t e d f o r oxides grown i n v a r i o u s s o l u t i o n s , at d i f f e r e n t r a t e s and f o r a n o d i z a t i o n i n a sequence of e l e c t r o l y t e s . The major f i n d i n g s of t h i s part of the study are as f o l l o w s : E l e c t r o l y t e i n c o r p o r a t i o n decreases i o n i c c o n d u c t i v i t y , d i e l e c t r i c constant and index.of r e f r a c t i o n . At constant current formation, the f r a c t i o n of oxide made up by the outer l a y e r increases with current d e n s i t y , and e l e c t r o l y t e con-c e n t r a t i o n , and depends on previous formation of the oxide. The l o g J-E charac t e r i s t i c s at constant voltage i n d i l u t e phosphoric a c i d are curved and occur at higher f i e l d s than those f o r d i l u t e s u l p h u r i c a c i d . of e l l i p s o m e t r y was a p p l i e d to the study of nonuniform t i n g from e l e c t r o l y t e i n c o r p o r a t i o n i n t o the oxide on s u i t s obtained i n a i r and i n s i t u on oxides formed on e c o n s i s t e n t w i t h the r e s u l t s of t r a c e r s t u d i e s i n of two l a y e r s which grow simultaneously due to metal during a n o d i z a t i o n , and f u r t h e r that e l e c t r o l y t e uter l a y e r on growth modifies i t s p r o p e r t i e s w i t h er. The e l l i p s o m e t r y r e s u l t s were not c o n s i s t e n t s l a y e r f i l m or w i t h a f i l m possessing an index of a r l y w i t h t h i c k n e s s . Thus e l l i p s o m e t r y provides a new, f determining i o n transport numbers, e f r a c t i o n and thickness of each l a y e r were obtained Analysis of the above r e s u l t s indicates that: a) the conduction process i s bulk c o n t r o l l e d b) i o n i c conduction and d i e l e c t r i c properties a r i s e from the same process and c) that e l e c t r o l y t e incorporation i s responsible for part i f not a l l the curvature i n the logJ-E c h a r a c t e r i s t i c s of i o n i c conduction. Photo-stimulated growth at low e l e c t r i c f i e l d s was investigated by ellipsometry. The e f f e c t of r a d i a t i o n i s to f i r s t modify the properties of the e x i s t i n g oxide a f t e r which photo-stimulated growth occurs accompanied by a b u i l d up of secondary current. The secondary photocurrent i s i o n i c i n nature and the r a d i a t i o n rather than the applied f i e l d i s responsible, for the generation of ions to sustain t h i s current. The photo-grown oxide consists of two layers with the outer layer having a much lower index of r e f r a c t i o n than normally grown oxide. The thermal r e c r y s t a l l i z a t i o n of stripped anodic oxide films was studied using transmission electron microscopy. Various d i f f r a c t i o n patterns were obtained and analyzed. The major r e s u l t i n terms of i o n i c conduction i s that e l e c t r o l y t e incorporation i n h i b i t s r e c r y s t a l l i z a t i o n , again, consistent with a decreased i o n i c mobility with incroporation. A c r i t i c a l test has been devised and applied to a recently proposed theory of i o n i c conduction, the d i e l e c t r i c p o l a r i z a t i o n theory. This theory postulates that the a u t o c a t a l y t i c b u i l d up of i o n i c current on applying a constant high f i e l d to the oxide i s due to an i n t e r n a l f i e l d c o n t r o l l e d process and that the rate of b u i l d up of p o l a r i z a t i o n (P) towards i t s equilibrium value (P ) i s enhanced by the passage of current, J , given by dp/dt = AJ(P Q-P). It i s shown that t h i s theory predicts an increase i n small s i g n a l capacitance during the passage of the tr a n s i e n t . However, measurements in d i c a t e that the capacitance decreases. i i i TABLE OF CONTENTS Page INTRODUCTION 1 1. IONIC CONDUCTION PROPERTIES AND THEORY. 1. INTRODUCTION 3 2. IONIC CONDUCTION PROPERTIES 3 1. General P r o p e r t i e s of Anodic Oxide Films 3 2. E l e c t r o l y t e I n c o r p o r a t i o n 4 3. Oxide Formation 5 4. Average F i e l d i n the Oxide 6 5. E Dependence of J 7 6. Transient I o n i c Response 7 7. Evidence f o r both Metal and Oxygen Ion Motion 8 8. U.V. E f f e c t s on Oxide Growth 13 3. THEORIES OF IONIC CONDUCTION 14 1. C l a s s i c a l Theory of I o n i c Conduction - High F i e l d Approximation 14 2. High F i e l d F r e n k e l Defect Theory 16 a) F r e n k e l Defect Theory and E l e c t r o s t r i c t i o n Model 17 b) F r e n k e l Defect Theory and Morse P o t e n t i a l Model 17 c) Fr e n k e l Defect Theory and F i e l d Dependent A c t i v a t i o n Distance 18 3. Models of I o n i c Conduction Based on E f f e c t i v e F i e l d 19 a) The D i e l e c t r i c P o l a r i z a t i o n Model 19 b) T r a n s i t i o n S t a t e - P o l a r i z a t i o n Energy Model 20 4. The Channel Model 21 5. Normal Mode Model 22 4. SUMMARY 24 2. OPTICAL PROPERTIES OF ANODIC OXIDE FILMS DETERMINED BY ELLIPSOMETRY 1. INTRODUCTION 25 2. ELLIPSOMETRY 25 1. P r i n c i p l e s of E l l i p s o m e t r y 26 a) N o t a t i o n and F r e s n e l C o e f f i c i e n t s 26 b) The E l l i p s o m e t r y Equation 28 2. The E l l i p s o m e t e r 29 a) Apparatus and P r i n c i p l e s of Operation 29 3. Experimental Methods 32 i v Page a) Alinement • ••• 32 b) Specimen P r e p a r a t i o n 35 c) An o d i z a t i o n 37 d) E l l i p s o m e t r y Measurements 38 e) Computational Methods 40 3. COMPUTED RESULTS 42 1. S i n g l e Layer D i e l e c t r i c F i l m Growing on Tantalum 42 2. Two Layers Growing Simultaneously on Tantalum 44 4. EXPERIMENTAL RESULTS AND DISCUSSION 47 1. O p t i c a l P r o p e r t i e s of Anodic Oxides Formed i n E^PO^ or H 2S0^ e l e c t r o l y t e s 47 a) Oxides Grown i n Phosphoric A c i d E l e c t r o l y t e s 51 b) Oxides Grown i n 0.2N K^SO^ 53 2. A n o d i z a t i o n i n a Sequence of E l e c t r o l y t e s 55 3. O p t i c a l P r o p e r t i e s of Tantalum..... 60 5. ACCURACY IN DETERMINING OPTICAL PROPERTIES AND THICKNESS OF FILMS 61 1. E l l i p s o m e t e r Accuracy 61 a) Analyzer and P o l a r i z e r 62 b) Compensator 62 c) V a r i a t i o n i n Angle of Incidence 64 d) Accuracy of One E x t i n c t i o n S e t t i n g 67 e) Accuracy of Measurements From Two Zones 68 f ) Other E r r o r s 72 g) Summary of E r r o r s i n Measurements Made i n A i r 72 h) E r r o r s i n In S i t u Measurements 73 2. Accuracy of Curve F i t t i n g Technique 75 a) Accuracy of C r i t e r i a 75 b) Accuracy of Parameters 77 6. ON THE APPROPRIATENESS OF THE TWO LAYER MODEL.. 79 3. IONIC CONDUCTION PROPERTIES 1. INTRODUCTION 86 2. RESULTS 87 v Page 1. Constant Current of Steady State Formation 87 2. Formation i n a Sequence of E l e c t r o l y t e s 89 3. K i n e t i c s of Oxide Growth: LogJ-E C h a r a c t e r i s t i c s 92 3. DISCUSSION 97 1. E f f e c t of E l e c t r o l y t e Incorporation 98 a) Metal Ion Transport Number 99 b) Bulk Controlled Ionic Conduction? 100 c) Ionic Conduction and P e r m i t t i v i t y 100 d) E l e c t r o l y t e Incorporation: Explanation f o r LogJ-E Curvature? 101 e) Comparison of K i n e t i c s of Growth 104 4. PH0T0STIMULATED GROWTH 1. INTRODUCTION 105 2. EXPERIMENTAL 105 3. RESULTS AND DISCUSSION 106 4. SUMMARY I l l 5. THE CURRENT TRANSIENT AT CONSTANT FIELD: SMALL SIGNAL A-C CAPACITANCE 1. INTRODUCTION '.. 113 2. THEORETICAL FOUNDATION 114 3. EXPERIMENTAL METHODS 117 1. Specimen Preparation 117 2. Measurements .117 3. Reduction and Accuracy of Results 120 4. RESULTS 124 5. DISCUSSION 129 6. THERMAL RE CRY S TALLIZATION 1. INTRODUCTION 131 2. EXPERIMENTAL PROCEDURE 131 3. RESULTS 133 1. General Features 133 v i Page 2. E f f e c t of Growth Conditions 135 3. D i f f r a c t i o n Patterns.... 139 4. DISCUSSION 141 7. CONCLUSIONS 143 BIBLIOGRAPHY 146 APPENDIX A: Relation Between E x t i n c t i o n Positions and Ellipsometry Angles 150 APPENDIX B: Tot a l R e f l e c t i o n C o e f f i c i e n t f o r Many Layers on a Metal 153 v i i Table 1- 1 2- 1 2-2 2-3 2-4 2-5 2-6 2-7 2-8 2-9 2-10 LIST OF TABLES Page Oxygen ion transport number from i n e r t gas studies of anodic oxides formed on Ta i n 0.2N H.S0.31 10 I 4 Relation of P and A readings to p, a, and a (after McCrackin et a l . 6 2 ) . . . ? 31 Example of reduction of ellipsometry measurement i n two or four zones. Primed and double primed q u a n t i t i e s i n d i c a t e settings on either side of e x t i n c t i o n minimum 39 Upper: Shows method used i n curve f i t t i n g ellipsometry r e s u l t s by f i n d i n g minima i n EH 2 i n t h i s case for the 69 experimental A , 1 points i n figure 2-8 48 Lower: Shows how minimum i n upper part of table i s obtained for each value of n - 48 Summarizes the o p t i c a l properties (parameters of best f i t ) of oxides grown i n d i l u t e (0.2N) R^SO^ and i n d i l u t e (0.23N) or concentrated (85%) H3PO4 and other data obtained by curve f i t t i n g ellipsometry r e s u l t s using a one or two layer o p t i c a l model for the oxide. For oxides grown i n H0PO4 (^4 to 10) both the double and si n g l e layer f i t i s given "(Single layer i s denoted by no values for n 2 and G) 50 Date for f i t t i n g ellipsometry r e s u l t s from oxides formed i n a sequence of e l e c t r o l y t e s , n-^ , n 2 , n., and N n are from table 2-4 and are used to f i n d G of l s ^ and 2nd anodiza-t i o n 57 Properties of mechanical and electrochemically polished tantalum surfaces determined by the curve f i t t e d r e s u l t s of table 2-4 and 2-5. Subscripts c and e denote computed and experimental r e s u l t s and d i s the thickness of i n i t i a l f i l m on the unanodized surface 61 65 65 65 F i t to experimental r e s u l t s of f i g u r e 2-8 using an inhomo-geneous f i l m approximated by a stack of homogeneous layers (Index of i t h layer i s given by the index of the f i r s t layer plus i times the increment i n index. Index of the metal i s 3.3 - 2.24J) 83 v i i i Table Page 3-1 Average f i e l d , E, i n the oxide and f i e l d , E.. , i n outer layer for constant current formation i n H^SO^ and H^PO^ at 25° C as i n table 2-4. Where E ] = (E-E 2)/G + E 2 and'E ? i s the f i e l d i n the inner layer which i s taken to be 6.15 x 10 6.15 x 10^ V/cm as for oxides grown i n d i l u t e P^SO^ 87 -3 3- 2 Comparison of two formation sequences ending at 9.5 Acm and 115.85 V on Ta i n 0.23N at 25°C. „ n — £ Formation (1). lOmAcm to 136 v o l t s followed by 9.5 pAcm (for about seven v o l t s ) to V (A=300.16°, ¥=41.60°). Formation (2). Constant 9.5 yAcm~2 to V p(A=280.28°, ¥=32.75°) 88 4- 1 E f f i c i e n c y of secondary photocurrent f o r the production of oxide under u.v. r a d i a t i o n at 20 v o l t s 110 5- 1 Comparison of change i n thickness predicted by Faraday's law and Ellipsometry of an oxide formed at 95 V for 20 hr., annealed f o r 5 minutes at 100° C and subjected to 118 v o l t at 0° C 127 ix LIST OF ILLUSTRATIONS Figure Page 1-1 P o s s i b l e modes of oxide, growth depending on the mobile i o n species 9 1-2 P o t e n t i a l energy $ seen by i o n i n i n t e r s t i t i a l p o s i t i o n . H o a f i r s t approximation i s s i n u s o i d a l i n d i s t a n c e x. On l e f t : zero f i e l d . On r i g h t : f i e l d a p p l i e d 15 1-3 E f f e c t of e l e c t r i c f i e l d on p o t e n t i a l b a r r i e r of p a r a b o l i c extremes ( C h r i s t o v and Tkonopisov^l) 18 1- 4 Poole-Frenkel e f f e c t . P o t e n t i a l energy of the va r i o u s i n t e r -a c t i o n s as a f u n c t i o n of di s t a n c e i n the v i c i n i t y of a trap 21 2- 1 R e f l e c t i o n and r e f r a c t i o n at an i n t e r f a c e 27 2-2 Schematic Diagram of E l l i p s o m e t e r and attachments 29 2-3 Excursion of s l i t image on plane of X wires 32 2-4 L a t e r a l motion of s l i t image, cf>, i n minutes of arc as a f u n c t i o n of p o l a r i z e r , P, f o r two s e t t i n g s of the quarter wave p l a t e , QWP. Arrows i n d i c a t e s t r a i g h t through s e t t i n g of the e l l i p s o m e t e r f o r 2 or 4 zones 34 2-5 C a l i b r a t i o n of p o l a r i z e r and analyzer s c a l e s using an A l m i r r o r at <j> = 70° and X = 5461 A° 34 o 2-6 Computed e l l i p s o m e t r y curve f o r s i n g l e l a y e r f i l m . (nn=2.22) growing on tantalum (N2=3.3-2. 3j) at (j>0 = 67.5° and X = 5461 A° (Dell'Oca and Young63) 41 (' 2-7 Computed e l l i p s o m e t r y curve f o r two l a y e r s growing s i m u l -taneously (n-^2.13, n2=2.26) on tantalum (N 3=3. 3-2 . 3j ) . Departure of short dashed l i n e ( 3 r d c y c l e ) from f u l l curve i s exagerated (<}>0 = 67.5, X = 5461 A°. Dell'Oca and Young 6 3) 43 2-8 Curve f i t t e d e l l i p s o m e t r y r e s u l t s from Ta anodized i n d i l u t e H 3P0^ (#4, t a b l e 2-4). +, x, o and denote successive c y c l e s of experimental p o i n t s . ni=2.145, n 2=2.22, G=0.51 and N =3.3-2.25jused to compute curve and numbers on curve which represents t h i c k -ness i n A° 46 2-9 Curve f i t t e d i n s i t u e l l i p s o m e t r y r e s u l t s from Ta ano-diz e d i n d i l u t e H 3P0 4 (#7, t a b l e 2-4). +, x and o denote successive c y c l e s and ni=2.14, n2=2.20, G=0.51 and N =3. 3-2. 24j used to compute curve 52 x Figure Page 2-10 Experimental ellipsometry r e s u l t s on Ta anodized i n d i l u t e H2SO4. o and x: 1 s t and 2nc^ cycles, e l e c t r o -chemically polished Ta. +: 1 s t c y c l e , mechanically polished Ta. Curve computed using ni=2.22 and Nm=3.3-2.3j 54 2-11 Experimental ellipsometry r e s u l t s on tantalum anodized i n concentrated phosphoric acid followed by anodization i n d i l u t e sulphuric a c i d (cycles are denoted i n succes-sion by +, o and x, Dell'Oca and Young63) 56 2-12 As i n fi g u r e 2-11, except followed by anodization.in d i l u t e phosphoric acid and with f i t t e d curve computed from the values given i n table 2-5 f o r sequence 2 58 2-13 Change i n P and ¥ caused by small v a r i a t i o n i n angle of incidence, 4>, from 67.5°. : change i n p o l a r i z e r , AP, - - - -: change i n analyzer or AT. Both as a function of A. Computed from two layer model (n^=2.14, n2=2.21, G=0.51, Nm=3.3-2.4j and A=5461A°. Single layer f i l m (n2=2.22) shows s i m i l a r behaviour. Thickness increases from o to the l e f t as shown by arrow) 66 2-14 Difference i n a and p between zones two and four as a function of P 4 (from r e s u l t s of f i g . 2-8). o: 10-1 [Aa-A 2-(180°-A 4)], x: Ap=P 2~(P 4+90°) and A : same as x but P 2 and P^ are each average of two readings 180° apart 69 2-15 y = tan a / tan a s as a function of P 4. -ro-o- from r e s u l t s o? f i g . 2-8, -x-x- from r e s u l t s of #5 table 2-4 71 2-16 Difference i n p or Ap between zones as a function of P4 (for i n s i t u ellipsometry measurements shown i n f i g . 2-9). -x-x- denotes P 2-(P 4+90°) and - 0 - 0 - i s P 2-(P 4+90°) - [P]_-(P3+90°)] which i s the average Ap for a l l four zones.. 74 2-17 Calculated v a r i a t i o n i n delta,AA, as a function of A at a given oxide thickness for i n d i v i d u a l incremental changes of the o p t i c a l parameters of two layers on a metal, where the i n i t i a l values are: ni=2.14 and k-^0.0, n2=2.21 and k2=0.0, G=0.50 and the metal, Nm=3. 3-2. 24j 76 2-18 As i n f i g . 2-17, but giving AT as a function of A.... 78 2-19 E f f e c t of changing substrate parameters from nm=3.3 and k =2.24 on f and A as i n f i g s . 2-17 and 2-18 80 x i Figure Page 2-20 Computed ellipsometry curve for three layers growing simultaneously on tantalum (n-,=2.12, n2=2.18, n-^2.24). Curve s t a r t s at 0.0A° and cycles are numbered at top 82 2- 2.1 As i n F i g . 2-20 but for four l a y e r s , ni=2.12, n2=2.16, n =2.20 and n.=2.24... 84 3 4 3- 1 G dependence on i o n i c current density for constant currert formation i n d i l u t e E3PO4 a t 25°C,x from Randall et a l , l 2 o t h i s study 88 3-2 Dependence of average f i e l d on oxide thickness during second anodization of sequence 1 and 2, x x: experimental, •—•— model, and o: f i e l d at the end of 1 s t anodization... 90 3-3 LogJ-E c h a r a c t e r i s t i c s . Centre (-x-x-): r e s u l t s and f i t t e d curve for formation i n 0.23N H3PO4 at 25°. Inner curve (on l e f t ) : computed for d i l u t e H^SO^ and also for inner layer of oxides grown i n H^PO^. Outer curve: for outer layer 93 3-4 LogJ versus e l e c t r i c displacement (D/e Q i s plotted) f o r inner and outer layers shown i n f i g u r e 3.3 96 3- 5 Dependence of LogJ on El/2 for the H3PO4 and H2S04 charac-t e r i s t i c s of figure 3-3 103 4- 1 F i t t e d ellipsometry r e s u l t s on photogrown anodic oxide on tantalum at constant voltage. Points obtained as numbered. Dashed l i n e : ellipsometry curve f o r normal oxide growth... 107 4- 2 T o t a l (——) and secondary (-x-x-) phococurrents recon-structed from maxima i n these currents from i n d i v i d u a l sequential formations as shown i n exploded view 109 5- 1 C i r c u i t employing l o c k - i n a m p l i f i e r to measure small s i g n a l c e l l response 118 5-2 Capacitance bridge.... 118 5-3 120 5-4 Determination of e l e c t r o l y t e r esistance, R e(R s=R e+r s i s the t o t a l s e r i e s r e s i s t a n c e ) . 5-5a T y p i c a l constant f i e l d current tr a n s i e n t : current density as a function of time (Dell'Oca and Young^l) 123 5-5b Percentage change i n s e r i e s equivalent capacitance at 1 kHz during and a f t e r transient. Measured by capacitance bridge, x x, and by l o c k - i n amplifier, - - - - 123 x i i Figure Page 5-5c Change i n s e r i e s , r g , and p a r a l l e l , r , equivalent r e s i s -tance at 1 kHz given as the r a t i o of the r e s i s t a n c e at time t to the i n i t i a l r e s i s t a n c e at t=0. (Same time span as i n f i g u r e 5-5b) 124 5-6a Shows constant f i e l d current t r a n s i e n t f o l lowed by growth at constant voltage at 0° C a f t e r a p p lying a 120 v o l t step to an oxide grown i n 0.23N phosphoric a c i d e l e c t r o -l y t e 126 5-6b Small s i g n a l response during t r a n s i e n t and growth of f i g . 5-5a and on same time s c a l e 126 5-7 Change i n capacitance %ACg as a f u n c t i o n of voltage,V^j a p p l i e d to annealed f i l m s grown to 100 v o l t s i n d i l u t e H 2S0 4 (o) and H 3P0 4 (x,A) ( D e l l ' O c a 7 3 ) 128 5- 8 Ra t i o of s e r i e s r e s i s t a n c e to i n i t i a l s e r i e s r e s i s t a n c e as a f u n c t i o n of v o l t a g e , , f o r two of the specimens of f i g . 5-7 ( D e l l ' O c a 7 3 ) 128 6- 1 Very h i g h c o n c e n t r a t i o n of s m a l l c y r s t a l l i t e s (10,000X) accompanied by d i f f r a c t i o n p a t t e r n from square c y r s t a l l i t e (Oxide grown i n d i l u t e H2SO4, heated 1 hr. i n a i r at 700° C) 132 6-2 Extensive area of c y r s t a l l i z a t i o n and sm a l l c r y s t a l l i t e s (0.1 mA/cm2 i n 0.2N H 2S04; heated i n a i r 1 hr. at 700° C; 20,000X) 132 6-3 Twinned c r y s t a l l i t e (50,OOOX) and i t s d i f f r a c t i o n p a t t e r n 134 6-4 One of the few r e g u l a r l y shaped c r y s t a l l i t e s from oxides formed i n d i l u t e H^PO^ (20,000X) and i t s d i f f r a c t i o n p a t t e r n 134 6-5 Intermediate s i z e d g r a i n s of c r y s t a l l i z a t i o n . Top and bottom l e f t from HJ?0, grown oxides and heated respec-t i v e l y i n a i r (20,000X) and i n oxygen (25,000X). Top r i g h t from ^SO^ grown oxide and bottom r i g h t from HNO^ grown oxide, both heated i n a i r . ( A l l IN s o l u t i o n s and a l l grown at 1 mA/cm2) 136 6-6 to Show t y p i c a l r e c r y s t a l l i z e d area a f t e r heating at 750° C 6-10 i n oxygen of oxides formed r e s p e c t i v e l y at 1 mA/cm2 i n N HJPO,, and 1 mA/cm2, 10 mA/cm^ and 21 v o l t s overnight i n IN H 2S0 4 (25,000X) 138 6-11 Hexagonal d i f f r a c t i o n p a t t e r n of s u p e r l a t t i c e and main spots 140 6-12 Rectangular d i f f r a c t i o n p a t t e r n of s u p e r l a t t i c e and main spots 140 x i i i F i g u r e Page 6-13 D i f f e r e n t r e c i p r o c a l u n i t c e l l s found f o r r e c r y s t a l l i z e d anodic oxide f i l m s of tantalum. Lehovec^^, - - - -- - - - Harvey et al.^ -*» S p y r i d e l i s et al . 7 9 . (Taken from S p y r i d e l i s et a l . ^ ) 140 B - l L i g h t r e f l e c t e d from & l a y e r s on a metal (m) s u b s t r a t e . Z=0 chosen a r b i t r a r i l y at second i n t e r f a c e 154 x i v ACKNOWLEDGEMENT The author wishes to express h i s s i n c e r e a p p r e c i a t i o n to Dr. L. Young f o r i n v a l u a b l e support and guidance throughout t h i s i n v e s t i g a t i o n . The author x^ishes to thank the Sprague E l e c t r i c Company f o r the grant which supported t h i s work. The author i s indebted to Mrs. J . Larcher f o r her help i i i o p erating the e l e c t r o n microscope. The author thanks Dr. D.L. P u l f r e y f o r h e l p f u l d i s c u s s i o n and Mr. T.W. Tucker f o r proof-reading the manuscript. G r a t e f u l acknowledgement i s given to Messrs. H. Black, A. MacKenzie, J . Stuber and E. Voth f o r t h e i r t e c h n i c a l a s s i s t a n c e and to Miss B. Harasymchuk f o r t y p i n g t h i s t h e s i s . xv INTRODUCTION Although the growth process of anodic oxide f i l m s has been e x t e n s i v e l y •k i n v e s t i g a t e d many aspects of i o n i c conduction are not yet w e l l understood. Par t i c u l a r l y i n t r i g u i n g are the f o l l o w i n g p r o p e r t i e s some of which were chosen f o r study i n t h i s t h e s i s : a) both metal and oxygen i o n may be comparably mobile and c o n t r i b u t e to growth and i n c o n j u n c t i o n w i t h t h i s ; b) i n c o r p o r a t i o n of e l e c t r o l y t e species i n t o the oxide on growth produces non-uniform oxides and a f f e c t s i o n i c conduction; c) second order e f f e c t s of e l e c t r i c f i e l d on i o n i c current occur; d) the i o n i c current under c e r t a i n c o n d i t i o n s can e x h i b i t a n o n - d e s t r u c t i v e a v a l a n c h e - l i k e behaviour r e f e r r e d to as the constant f i e l d c urrent t r a n s i e n t and e) photo-stimulated growth of d i f f e r e n t p r o p e r t i e s occurs on i r r a d i a t i n g the oxide w i t h u.v. Anodic oxide f i l m s may be formed on a number of metals and semi-conductors f o r example Ta, T i , A l , Nb, Zr, S i , Ge InSb, more r e c e n t l y GaAs and others. However, anodic oxide f i l m s formed on Ta i n a c i d s o l u t i o n s were chosen f o r i n v e s t i g a t i o n f o r a number of reasons. F i r s t , a l l the phenomena discussed above have been observed i n t h i s oxide when grown i n e l e c t r o l y t e s . Secondly, oxide growth on tantalum can be very e f f i c i e n t so that l o s s e s due to e l e c t r o n i c leakage or s i d e reactions;may o f t e n be neglected. F i n a l l y , the oxide i s extremely r e p r o d u c i b l e both i n p r o p e r t i e s and t h i c k n e s s , and t h i s allows second order e f f e c t s i n a p p l i e d f i e l d to be r e s o l v e d , which i s not the case f o r most other anodic oxides, nor i s i t the case w i t h plasma a n o d i z a t i o n . Quite apart from the s u i t a b i l i t y of t h i s oxide f o r the i n v e s t i g a t i o n of i o n i c processes, the oxide i s of p a r t i c u l a r t e c h n i c a l importance. For example, - . • — * This f i e l d has been the t o p i c of a recent book , numerous reviews and of s e v e r a l symposia 6>^>8. ** Dell'Oca and Yan have r e c e n t l y anodized GaAs i n an ammonium pentaborate s o l u t i o n and b r i e f l y examined the p r o p e r t i e s of the oxide using e l l i p s o m e t r y (unpublished). tantalum e l e c t r o l y t i c capacitors have been widely used for years. More recently a new technology i s being developed based on sputtered tantalum t h i n f i l m c i r c u i t r y where capacitors are made using sputtered tantalum, tantalum anodic oxide and evaporated counterelectrode. Another p o t e n t i a l a p p l i c a t i o n of t h i s f i l m i s i n u l t r a - v i o l e t detectors. The p o t e n t i a l a p p l i c a t i o n of t h i s and other anodic oxides has increased with the recent discovery that anodization can also be c a r r i e d out i n an oxygen plasma. This method, x^hich i s s t i l l i n the development stage, i s more compatible x^ith present day methods of device f a b r i c a t i o n than i s conventional anodic oxide formation i n e l e c t r o l y t e s (see reference 5). This thesis i s mainly concerned with the development and a p p l i c a t i o n of ellipsometry (chapter 2) to the study of non-uniform anodic oxide films i n order to c l a r i f y some of the e f f e c t s of e l e c t r o l y t e incorporation on anodic oxide groxtfth (chapter 3). This technique i s also applied i n an i n i t i a l exploration of the properties of photoinduced oxide grox^th at loxv e l e c t r i c f i e l d s (chapter 4). In chapter 5 r e s u l t s of capacitance measurements made during the constant f i e l d current transient are used to d i s t i n g u i s h betx^een models for the mechanism of i o n i c conduction at high f i e l d s . Germane to i o n i c conduction are the r e c r y s t a l l i z a t i o n properties of the oxide and i n chapter 6 the e f f e c t of grow conditions and e l e c t r o l y t e incorporation on the r e c r y s t a l l i z a t i o n properties determined using electron microscopy are presented. A b r i e f review of the present understanding of i o n i c conduction properties and theory i s given at the beginning and conclusions are draxm at the end of t h i s work. It i s hoped that a better understanding of the grox^th process of anodic oxide films on Ta w i l l eventually lead to better a p p l i c a t i o n of t h i s and other anodic oxide f i l m s . I. IONIC CONDUCTION PROPERTIES AND THEORY 1. INTRODUCTION By anodic oxide f i l m i s meant a f i l m which grows at high e l e c t r i c f i e l d s on a metal when the metal acts as an anode i n a c e l l c o n s i s t i n g of metal/oxide/ e l e c t r o l y t e (or oxygen plasma)/cathode. In p r a c t i c e a voltage applied between metal and cathode r a i s e s the f i e l d across the e x i s t i n g oxide on the metal to a value between 10^ to lo'' V/cm where ion motion occurs. The e x i s t i n g oxide can be either a t h i n layer of thermally grown oxide or a previously formed anodic oxide. Thus the growth process of anodic oxides poses a problem i n i o n i c conduction at high f i e l d s not normally sustained by bulk materials. In the f i r s t part of t h i s chapter the general properties of anodic oxides formed on tantalum are b r i e f l y presented and the s a l i e n t features of i o n i c conduc-t i o n i n p a r t i c u l a r the features .studied i n t h i s thesis are reviewed. In the second part, the present models of i o n i c conduction are reviewed only to the extent to which they are relevant to i o n i c conduction properties. 2. IONIC CONDUCTION PROPERTIES 1. General Properties of Anodic Oxide Films Anodic oxides formed on tantalum under normal conditions are amorphous or have a glassy l i k e structure. The oxide i s transparent and on the metal, the index of r e f r a c t i o n of the oxide and the metal are such that interference e f f e c t s give r i s e to colours which change with oxide thickness. A uniform interference colour over the oxide area i s a f i r s t i n d i c a t i o n of uniform thickness. The oxide 9 i s very d u c t i l e , chemically r e s i s t a n t to acids, being attacked appreciably only by HF, and adheres well to the metal, except under c e r t a i n metal preparations where the oxide can be detached by d r i v i n g the metal cathodic i n solution''" . The oxide may be r e c r y s t a l l i z e d thermally or by prolonged p o l a r i z a t i o n i n the e l e c t r o ^ l y t e ^ . The properties of thermally r e c r y s t a l l i z e d anodic oxide films are reviewed i n the introduction to chapter 6 of this t h e s i s . 2. E l e c t r o l y t e I n c o r p o r a t i o n U n t i l r e c e n t l y i t was b e l i e v e d that oxide p r o p e r t i e s were unaffected by the s o l u t i o n when grown i n d i l u t e aqueous e l e c t r o l y t e s . This was because the capacitance of f i l m s formed to the same vo l t a g e at a given current d e n s i t y and temperature was observed to be h i g h l y independent of the e l e c t r o l y t e f o r d i l u t e s o l u t i o n s . Organic or concentrated e l e c t r o l y t e s were known, from the work of Vermilyea^"'" to produce a duplex (two layered) oxide i n which oxide d i s s o l u t i o n r a t e s showed that the outer l a y e r was a f f e c t e d by the e l e c t r o l y t e w h i l e the inner l a y e r was s t o i c h i o m e t r i c or normal oxide as produced i n d i l u t e s o l u t i o n s . R a n d a l l , 12 Bernard and W i l k i n s o n found us i n g r a d i o a c t i v e l y l a b e l l e d e l e c t r o l y t e s that the e l e c t r o l y t e e f f e c t was caused by species from the e l e c t r o l y t e incorporated i n t o the outer p o r t i o n of the oxide on growth, and that t h i s occurs even i n d i l u t e e l e c t r o l y t e s . Very l i t t l e i n c o r p o r a t i o n occurs i n d i l u t e E^SO^ and the two l a y e r s of oxides produced i n t h i s s o l u t i o n are not d i s t i n g u i s h a b l e (so f a r ) i n p r o p e r t i e s . However, i n H^PO^ the i n c o r p o r a t i o n ranges from 4 to 18% mole P to mole Ta on 2 going from growth i n d i l u t e (0.001 M) to concentrated a c i d (1 ma/cm , 25°C). The c o n c e n t r a t i o n of incorporated m a t e r i a l and the p r o p o r t i o n a l t h i c k n e s s of oxide a f f e c t e d by i t i n c r e a s e s w i t h r a t e of oxide growth, w i t h decreasing temperature of growth and w i t h e l e c t r o l y t e s t r e n g t h . The mechanism of i n c o r p o r a t i o n seems to be one of polyatomic ( i . e . phosphate not phosphorous) anions bonding w i t h the atoms of 12,13 the oxide ' r a t h e r than being mechanically trapped i n the oxide. The r e s u l t of e l e c t r o l y t e i n c o r p o r a t i o n i s a decrease i n d i e l e c t r i c constant (a s i m i l a r e f f e c t 14 was noted by Cheseldine f o r oxides grown on Ta i n formic a c i d ) and a decrease 12 i n i o n i c c o n d u c t i v i t y . P a r t i c u l a r l y ^ i n c o r p o r a t i o n seems to i n h i b i t oxygen motion as i s seen w i t h a decreased r a t e of oxide reformation a f t e r annealing"^ ( t h i s proceeds by oxygen moving inward i n the oxide) and by the increased p r o t e c t i o n of the metal to high temperature o x i d a t i o n " ^ . F i n a l l y , a decreased r a t e of 17 18 h y d r a t i o n occurs i n f i l m s formed on A l i n phosphate e l e c t r o l y t e s ' 3. Oxide. Formation The b u i l d up of oxide due to the a p p l i e d voltage causing an amount of charge Q to be passed through the c e l l i s given by Faraday's law as v = QJLjl_ p 2yF U - 1 ; Where: V i s the volume of oxide grown which when d i v i d e d by the area gives the oxide thickness f o r an oxide of d e n s i t y p , 2y represents the number of Faradays,F. which must be passed to produce one mole of oxide w i t h formula M 0 J J _ x y and molecular weight M, ry :denotes the e f f i c i e n c y of the growth process, that i s , the f r a c t i o n of the charge which goes towards producing M 0 , r a t h e r than s i d e x y r e a c t i o n s , e l e c t r o n i c leakage c u r r e n t s or metal l o s s to the e l e c t r o l y t e . The e f f i c i e n c y as estimated from equating weight gain and oxygen uptake may become greater than u n i t y i n cases where e l e c t r o l y t e i n c o r p o r a t i o n i n t o the oxide cannot be neglected. For the formation of Ta 20^ on ch e m i c a l l y or e l e c t r o c h e m i c a l l y pre-pared tantalum, where i n c o r p o r a t i o n i s n e g l i g i b l e (eg. w i t h d i l u t e H^SO^) 13 the e f f i c i e n c y approaches u n i t y w i t h l i t t l e l o s s of current to s i d e r e a c t i o n s or 19 metal l o s s to s o l u t i o n . Qn mechanically prepared tantalum the e f f i c i e n c y i s u s u a l l y lower and non-reproducible, t h i s i s p r i m a r i l y due to oxygen e v o l u t i o n at scratches i n the metal surface. The formation of anodic oxide f i l m s can be c a r r i e d out w i t h constant current or constant v o l t a g e a p p l i e d to the c e l l . The former represents a steady s t a t e i o n i c process i n the oxide i n which according to (1) the oxide t h i c k n e s s increases l i n e a r l y w i t h time. This mode of growth, at l e a s t f o r a given e l e c t r o l y t e seems to be bulk r a t h e r than i n t e r f a c e c o n t r o l l e d s i n c e no dependence of f i e l d ° 20 21 on i n c r e a s i n g oxide thickness i s observed, f o r oxides above 200A . ' Thus the voltage across the oxide a l s o increases l i n e a r l y w i t h time and i t s incremental r a t e of change (AV/At) should be constant w i t h t h i c k n e s s and can be used as a check that the a n o d i z a t i o n i s proceeding normally. Another advantage, i s that the process i s e a s i l y c o n t r o l l e d and can be used to a c c u r a t e l y give a predetermined thi c k n e s s of oxide. Formation at constant v o l t a g e i s not a steady s t a t e process f o r as the oxide grows the f i e l d across the oxide decreases causing the i o n i c c urrent (or oxide growth rate) to decrease. E v e n t u a l l y the current decreases to a point where e l e c t r o n i c leakage current predominates and the oxide ceases to grow. In component f a b r i c a t i o n anodic oxides are formed using a combination of these two methods i n an e m p i r i c a l l y determined sequence which u s u a l l y ends i n a constant v o l t a g e formation. I t i s b e l i e v e d that the low current d e n s i t i e s i n the f i n a l formation causes flaws i n the oxide to be r e p a i r e d . 4. Average F i e l d i n the Oxide The accepted method (see r e f . 1) and the one used i n the present work i s to determine the average e l e c t r i c f i e l d across the oxide from the c e l l over-p o t e n t i a l d i v i d e d by the oxide t h i c k n e s s . The o v e r p o t e n t i a l i s defined as the change i n p o t e n t i a l d i f f e r e n c e of the oxide-covered e l e c t r o d e w i t h respect to a r e v e r s i b l e e l e c t r o d e on going from e q u i l i b r i u m to n o n - e q u i l i b r i u m c o n d i t i o n s . This must be c o r r e c t e d f o r any ohmic p o t e n t i a l drop caused by current f l o w i n g through the e l e c t r o l y t e . The h y p o t h e t i c a l e q u i l i b r i u m p o t e n t i a l of the oxide-covered e l e c t r o d e w i t h respect to a hydrogen e l e c t r o d e i s c a l c u l a t e d from thermo-dynamic data to be about -0.85 V. The hydrogen e l e c t r o d e i s best approximated by a p l a t i n i z e d platinum e l e c t r o d e i n a s o l u t i o n saturated w i t h hydrogen. Thus the overvoltage of the c e l l Ta/Ta20,_/solution/H2/Pt i s the a p p l i e d v o l t a g e l e s s e l e c t r o l y t e ohmic drop plus 0.85 V. In p r a c t i c e f o r overvoltages above 100 v o l t s the 0.85 V represents l e s s than 1% c o r r e c t i o n . I f the s o l u t i o n ohmic p o t e n t i a l drop i s small so that the geometrical c o n s i d e r a t i o n s f o r producing an oxide of uniform t h i c k n e s s are not s t r i n g e n t then a small p l a t i n i z e d platinum e l e c t r o d e can be used and i f the current passed i s s u f f i c i e n t l y high the s o l u t i o n need not be saturated w i t h H_. 5. E Dependence of J The observed dependence of i o n i c current d e n s i t y (J) on f i x e d or changing e l e c t r i c f i e l d (E) has the form J = J Q exp-W(E)/k.T 21 22 where f o r the range of f i e l d i n v o l v e d the exponential f a c t o r can have the form ' W(E) = W - cxE + BE 2 (1.2) 23 or W(E) = W - y E 1 / 2 (1.3) These r e l a t i o n s represent a thermally a c t i v a t e d (T) e l e c t r i c f i e l d a s s i s t e d process. These r e l a t i o n s are at v a r i a n c e w i t h the l i n e a r k i n e t i c s of growth or l o g J versus E which i s expected f o r an e l e c t r o d e process or which i s p r e d i c t e d by the high f i e l d F r e n k e l defect theory of i o n i c conduction (to be d i s c u s s e d ) . The range of v a l i d i t y of (1.2) and (1.3) has r e c e n t l y been extended to 250°C by 24 Dreiner . The above r e s u l t s were obtained i n e l e c t r o l y t e s which give l i t t l e i n c o r p o r a t i o n . The e f f e c t of i n c o r p o r a t i o n i s to increase the f i e l d r e q u i r e d to 21 pass a given c u r r e n t , and e x p l a i n s the previous observation that at constant current formation the l o g J versus E curve becomes more curved and moves to higher f i e l d w i t h i n c r e a s i n g s u l p h u r i c a c i d s t r e n g t h of the s o l u t i o n (or i n c r e a s i n g i n c o r -poration) . Because of the increased curvature i t might be expected that (1.3) w i l l no longer be a good approximation of (1.2) 6. Transient I o n i c Response Time dependent i o n i c t r a n s i e n t response i s observed when the a p p l i e d c o n d i t i o n s to the c e l l are r a p i d l y changed. In t h i s case the measured response of the c e l l c o n s i s t s of the e l e c t r o l y t i c c a p a c i t o r response of the c e l l and the i o n i c response of the oxide. F o r t u n a t e l y the c a p a c i t o r response can i n most cases be made so r a p i d that i t i s e s s e n t i a l l y complete i n time to observe most of the i o n i c response. Although, e x t r a p o l a t i o n i s u s u a l l y required to determine the i o n i c response at the i n s t a n t the c o n d i t i o n s were changed. Thus changing from formation at one constant current to a second causes the e l e c t r i c 8 f i e l d to go through a maximum or minimum depending r e s p e c t i v e l y on whether the second current i s l a r g e r or smaller than the f i r s t . Another observation, i s that the i o n i c current at the i n s t a n t the formation f i e l d i s r e - a p p l i e d decreases from i t s value j u s t p r i o r to removing the f i e l d . This decrease increases w i t h the 25 time the f i e l d i s removed. A p a r a l l e l behaviour i s seen i n the measured capacitance and l o s s e s of the oxide, they a l s o decrease w i t h t h i s p e r i o d at 2 6 zero f i e l d . Under c e r t a i n c o n d i t i o n s i f a f i e l d much greater than the formation f i e l d i s a p p l i e d to the oxide the i o n i c current increases w i t h time at f i r s t s l o w l y and then more r a p i d l y i n an a c c e l e r a t i n g , a v a l a n c h e - l i k e f a s h i o n to a maximum. This i s c a l l e d the constant f i e l d current t r a n s i e n t and i t i s p a r t i c u l a r l y s i g -n i f i c a n t i n that the i o n i c conduction process must depend on the i o n i c c u r r e n t , i n a d d i t i o n to e l e c t r i c f i e l d and temperature, to accommodate the avalanche-22 l i k e c urrent behaviour. Several t h e o r i e s have been advanced f o r t h i s phen-22 27 omenon. ' In chapter 5 of t h i s t h e s i s the p r o p e r t i e s of t h i s t r a n s i e n t are reviewed and the r e s u l t s of small s i g n a l capacitance measurements are used to d i s t i n g u i s h between the two t h e o r i e s . 7. Evidence f o r Both Metal and Oxygen Ion Motion U n t i l r e c e n t l y i t was believed that only the metal i o n was mobile and that i t c o n t r i b u t e d s o l e l y to the i o n i c c u r r e n t . The evidence, though i n c o n c l u s i v e , was strengthened by t h e o r e t i c a l arguments showing that comparable metal and oxygen io n m o b i l i t y was u n l i k e l y . Now, marker l a y e r experiments have advanced seemingly i n d i s p u t a b l e evidence that both ions are indeed comparably mobile. This i s true 19 at l e a s t f o r oxides grown on Ta, A l , Nb and W, but only the oxygen i o n i s mobile f o r Zr. The consequence of both ions being mobile i s that new growth can now take place not at only one i n t e r f a c e but at both i n t e r f a c e s or i o n f o r ion' i n the oxide (see F i g . 1-1). Marker l a y e r s t u d i e s r e l y on the c r e a t i o n of a marked l a y e r of oxide at /. GROWTH BY SINGLE ION MOTION METAL EXISTING SOLUTION OXIDE NEW OXIDE (a) METAL ION (M+) MOTION ONLY METAL EXISTING SOLUTION OXIDE NEW OXIDE (b) OXYGEN ION(0~) MOTION ONLY GROWTH BY METAL AND OXYGEN ION MOTION METAL EXISTING OXIDE SOLUTION METAL EXISTING OXIDE SOLUTION NEW OXIDE NEW OXIDE (a) GROWTH AT BOTH INTERFACES (b) GROWTH ION FOR ION IN THE OXIDE 1-1: Possible modes of oxide growth depending on the mobile ion spec 10 a known p o s i t i o n w i t h i n the e x i s t i n g oxide. On f u r t h e r growth the increase i n thickness between t h i s marker and one of the i n t e r f a c e s represents the c o n t r i -b u t i o n to growth made by that p a r t i c u l a r i o n which causes growth at that i n t e r -face. An ion's transport number i s defined as the. r a t i o of current c a r r i e d by the ion to the t o t a l i o n i c c u r r e n t , or at constant current formation, t h i s i s the f r a c t i o n of new oxide grox\'th due to the i o n . The l a t t e r assumes the oxide i s uniform and that the marker l a y e r i s immobile. Presumably i f the oxide i s a f i x e d network, then atoms making up the marker l a y e r , i f they are immobile, remain i n t h e i r r e s p e c t i v e p o s i t i o n i n t h i s newtork, even though the growth process may d i s p l a c e the normal oxide atoms. Two types of marker l a y e r s have been used. The f i r s t , developed 19 28—31 and used by Davies, P r i n g l e and co-workers ' . at Chalk R i v e r , employs an a c c e l e r a t o r to implant a radiostope of an i n e r t gas i n t o the oxide, thus c r e a t i n g a marker l a y e r . (In the o r i g i n a l work, i m p l a n t a t i o n was i n t o the metal surface followed by a b r i e f a n o d i z a t i o n to produce a t h i n oxide l a y e r w i t h the i n e r t 28 29 gas i n i t ) ' . The p o s i t i o n of the marker was determined before and a f t e r growth, w i t h respect to the e l e c t r o l y t e - o x i d e i n t e r f a c e , at f i r s t by a or 3 ray spectroscopy and l a t e r by mechanical or chemical s t r i p p i n g of the oxide. 31 Thus, i n the l a t e s t work, P r i n g l e , has been able by chemical s t r i p p i n g com-bined w i t h o p t i c a l thickness measurements to determine w i t h high p r e c i s i o n the mean p o s i t i o n of the i n e r t gas d i s t r i b u t i o n i n the oxide before and a f t e r growth, and from these p o s i t i o n s he has determined the tra n s p o r t numbers given i n Table 1.1. Table 1.1 - Oxygen i o n tr a n s p o r t number from i n e r t gas « 1 • 1 • r 1 • • 1 *" 1 m • 0.2N H.SO. . 2 4 stu d i e s of anodic oxides formed on Ta 0°C 25°C 50°C 75°C 95°C 10 , 2 ma/cm 0.712 0.726 0.741 0.756 0.770 1 , 2 ma/cm 0.729 0.744 0.763 0.784 0.803 0.1 , 2 ma/cm 0.750 0.767 0.793 0.817 0.841 The net r e s u l t of the. i n e r t gas work i s that growth occurs on both sides of the marker i n d i c a t i n g that both ions are mobile with the metal i o n c o n t r i b u t i n g about a quarter of the growth. Furthermore,growth occurs at the i n t e r f a c e s and not i n the oxide, s i n c e almost no broadening of the marker 222 l a y e r was seen i n the o r i g i n a l work using a spectroscopy and Rn i n i t i a l l y 29 i n j e c t e d i n t o the metal surface The second type of marker l a y e r employs the e f f e c t s of e l e c t r o l y t e on • 11,12,14,17 . t , . ' oxide p r o p e r t i e s . A d i f f e r e n t or more concentrated e l e c t r o l y t e can be used to make a marker l a y e r which i s d e t e c t a b l e from the new oxide grown, 12 however, t h i s i s not r e a l l y necessary, as Randall et a l . point out, s i n c e i f the inco r p o r a t e d m a t e r i a l i s immobile then i n c o r p o r a t i o n can only occur i n t o that oxide produced at the oxide s o l u t i o n i n t e r f a c e as a r e s u l t of metal i o n motion. Thus the f r a c t i o n of oxide i n which i n c o r p o r a t i o n has occurred during growth at constant current i s equal to the metal i o n t r a n s p o r t number. Thus Randall et a l . found that the metal i o n t r a n s p o r t number was 0.51 f o r growth at 2 1 ma/cm i n d i l u t e H„P0, at 25°C and that t h i s number increased w i t h current 3 4 d e n s i t y , e l e c t r o l y t e i n c o r p o r a t i o n and decreasing temperature. They a l s o found 2 that the metal i o n t r a n s p o r t number f o r growth at 1 ma/cm i n 0.2N H^ SO^  at 25°C was 0.48 or about twice the value determined from t r a c e r work ( t a b l e 1-1). The values of the i o n t r a n s p o r t number determined by the two methods may be i n c o n f l i c t but that they are a measure of the same process seems evident from the s i m i l a r dependence of the metal i o n t r a n s p o r t number on current d e n s i t y and temperature found by these methods. The discrepancy probably a r i s e s from the " r e l a t i v e " i m m o b i l i t y of the two markers. 31 P r i n g l e found that the i n e r t marker atoms were i n f a c t not s t a t i o n a r y i n that t h e i r d i s t r i b u t i o n broadened s l i g h t l y w i t h oxide growth. The broadening 222 was found to increase w i t h decreasing atomic mass of i n e r t gas used (Rn to 12 4] Ar ), however the mean p o s i t i o n of the atoms, or the transport number was inde-pendent of atom mass. This l ed P r i n g l e to p o s t u l a t e , contrary to present ideiis of i o n i c t r a n s p o r t , that tantalum and oxygen atoms acted simultaneously i n such a way as to symmetrically b u f f e t the marker atoms. Thus the marker atoms are subjected to a form of Brownian motion which spreads them but maintains t h e i r mean p o s i t i o n independent of t h e i r mass, which would not be the case i f the atoms were b u f f e t e d by separate tantalum and oxygen i o n t r a n s p o r t . On the other hand i n the e l e c t r o l y t e marker experiments, sharp boundaries are found between l a y e r s of low and high i n c o r p o r a t i o n i n d i c a t i n g l i t t l e d i f f u s i o n of the i n c o r -12 15 porated species. ' These r e s u l t s seem to i n d i c a t e that both marker l a y e r s are immobile although there i s s t i l l the p o s s i b i l i t y that the i n e r t marker atoms are pushed outward by the metal ion motion or the n e g a t i v e l y charged species i n -corporated can move inward at a r a t e independent of c o n c e n t r a t i o n under the a c t i o n of the a p p l i e d f i e l d . Of p o s s i b l e importance to the r e l a t i v e m o b i l i t y of the two marker l a y e r s are the r e s u l t s obtained from anodic oxides formed on Zr. An io n implanted i n to t h i s oxide, Br, remains at the oxide surface during subsequent j 19 an o d i z a t i o n (which i s a l s o the case f o r i n p l a n t e d i n e r t gas atoms ), whereas, i f the Br i s put i n t o the e l e c t r o l y t e the i o n i s incorporated throughout the 30 oxide on growth. On the other hand, phosphate (from H^PO^) i s only incorporated 32 part way i n t o t h i s oxide on growth. At the moment i t seems reasonable to expect an incorporated anion which bonds w i t h atoms of the oxide to be l e s s mobile than a f o r e i g n implanted atom. The foregoing might seem to i n d i c a t e that i n d i v i d u a l metal and oxygen ions move r i g h t across the oxide before becoming f i x e d i n the oxide. At l e a s t f o r the oxygen i o n , t h i s i s not so, sin c e the atom order i n the oxide i s pre-16 18 31 served on successive a n o d i z a t i o n i n 0' followed by 0 r i c h e l e c t r o l y t e s . Thus the oxygen ion must move by a method s i m i l a r to vacancy m i g r a t i o n , not by 13 moving completely across the oxide which would reverse the atom order. 8. U.V. E f f e c t s on Oxide Growth The e f f e c t of u l t r a - v i o l e t r a d i a t i o n on anodic oxide growth on Ta was 33 39 studied by Bray, Jacobs and Young and by Vermilyea . (The paper by Bray et a l ma}' be consulted f o r references to previous work.) These s t u d i e s i n d i c a t e that anomalous oxide growth occurs when an anodic oxide f i l m under an a p p l i e d f i e l d i s subjected to u l t r a - v i o l e t r a d i a t i o n . At high f i e l d s , or normal growth c o n d i t i o n s (constant current) the u.v. enhances growth w h i l e at low f i e l d s (con-stant v o l t a g e ) growth occurs at f i e l d s where growth normally i s very small and undetectable f o r the l e n g t h of time i n v o l v e d . At high f i e l d s the oxide resembles more the normal oxide produced without u.v. w h i l e at low f i e l d s the oxide becomes l e s s normal and at times does not c o n t r i b u t e to c a p a c i t y measurements, although there i s a weight i n c r e a s e . Change of oxide d i s s o l u t i o n r a t e i n HF i n d i c a t e s that the oxide i s two l a y e r e d . The observed current c o n s i s t s of two p a r t s -the e l e c t r o n i c current which appears i n s t a n t l y on a p p l y i n g the u.v. and the secondary current which appears a f t e r an i n c u b a t i o n p e r i o d of minutes to hours. The secondary c u r r e n t , which i s observed by i n t e r r u p t i n g the .light i n t e r m i t t e n t l y i s b e l i e v e d to be i o n i c , because the oxide weight increase can be roughly c o r r e l a t e d to the charge passed by t h i s current and because of i t s slow decay on removing the l i g h t . T e n t a t i v e explanations given f o r the u.v. e f f e c t s were a photo-induced and maintained space charge which promotes i o n motion or a photo-induced change of s t r u c t u r a l p r o p e r t i e s of the outer p r o t i o n of the oxide which makes i t more con-d u c t i n g , however, the long i n c u b a t i o n p e r i o d to produce the secondary current remains to be explained. The u.v. e f f e c t s ' suggest a d e f i n i t e i n t e r p l a y of e l e c t r o n i c and i o n i c processes, however, present models of i o n i c conduction are based on the assump-t i o n that e l e c t r o n i c and i o n i c c u r r e n t s are independent. 14 3. THEORIES OF IONIC CONDUCTION 1. C l a s s i c a l Theory of Ionic Conduction - High F i e l d Approximation The c l a s s i c a l theory of i o n i c conduction describes the motion of a low f concentration of non-interacting defects i n a c r y s t a l l i n e s o l i d . Two types of defects are normally considered, the i n t e r s t i t i a l ion and the vacant l a t t i c e s i t e . These move by a s i m i l a r mechanism so that only the motion of one type of defect need be considered to obtain a r e l a t i o n for the i o n i c current density which holds for both. Consider the motion of i n t e r s t i t i a l ions. An ion i n an i n t e r -s t i t i a l p o s i t i o n i s pictured as a simple harmonic o s c i l l a t o r of frequency v. To move to the next p o s i t i o n the ion must overcome a b a r r i e r of a c t i v a t i o n energy W and a c t i v a t i o n distance a (figure 1-2). The p r o b a b i l i t y that the ion w i l l have t h i s energy i s given by exp -W/kT. Since the ion i s a v a i l a b l e for a jump v times per second and assuming that an applied e l e c t r i c f i e l d serves only to lower the b a r r i e r by qaE, the p r o b a b i l i t y of ion transfer i s P(E) = v exp-(W-qaE)/kT (1.4) Knowing the p r o b a b i l i t y of t r a n s f e r , the current density through a plane at a point x < x <x + 2a can be found and i s given by o— — o J = J - J = 2aq vn(x) P(E) - va[.n(x) + 2a^-] P(-E) Where i s the forward current due to an ion density n(x) t r a v e l l i n g the distance 2a and J i s the reverse current which includes a c o n t r i b u t i o n from ion d i f f u s i o n . At very high e l e c t r i c f i e l d s ion movement against the f i e l d and ion d i f f u s i o n are considered n e g l i g i b l e when compared to ion motion with the f i e l d . Assuming the ion density to be constant, the fundamental equation of i o n i c current t See for example Mott and Gurney (1948) Chapter II - for a discussion of defects and t h e i r motion.35 15 d e n s i t y at high f i e l d s i s J = 2avnq exp - (W-qaE)/kT = JQ exp - W(E)/kT (1.5) This r e l a t i o n holds i n general f o r the motion of ions over any b a r r i e r . F i g . 1-2: P o t e n t i a l energy $ seen by i o n i n i n t e r s t i t i a l p o s i t i o n . $ to a f i r s t approximation i s s i n u s o i d a l i n d i s t a n c e x. On left-, zero f i e l d . On r i g h t : f i e l d a p p l i e d . Equation (1.5) was f i r s t a p p l i e d to anodic oxide f i l m s by Verwey L a t e r , models of i o n i c conduction i n amorphous anodic oxides were developed based on t h i s equation and assumptions cn the r a t e l i m i t i n g step f o r i o n motion, charge n e u t r a l i t y or nature of space charge, type of mobile i o n species and mechanism f o r c r e a t i o n and a n n i h i l a t i o n of i o n s . A d i s c u s s i o n of some cases 1 37 which can a r i s e was given by Young ' , here only the most important model using (1.5), the high f i e l d F r e n k e l defect model i n i t i a l l y developed by Bean, F i s h e r and 38 Vermilyea w i l l be reviewed. Theories based on (1.5) were and s t i l l are the major t h e o r e t i c a l argument against comparable m o b i l i t y of metal and oxygen ions i n anodic oxides. This i s because the current due to each i o n i s given by an equation l i k e (1.5). Thus, unless the exponential f a c t o r s i n the current r e l a t i o n f o r the two ions are very s i m i l a r , one i o n w i l l dominate the process. F i n a l l y , a major c o m p l i c a t i o n i n applying the c l a s s i c a l theory to anodic oxides i s the amorphous nature of the oxide where a range of a c t i v a t i o n energies and di s t a n c e s would be expected. A s t a t i s t i c a l treatment has been made but does not r e s u l t i n increased agreement between observation and theory. "*" 38 2. High F i e l d F r e n k e l Defect Theory The b a s i c assumption i n t h i s theory i s that the oxide i s a r e g u l a r network and that ions can be created by the moving atoms from l a t t i c e p o s i t i o n s to i n t e r s t i t i a l s i t e s . Removal of an atom creates an i n t e r s t i t i a l i o n and a v vacancy or a Fre n k e l d e f e c t . The i o n i s assumed mobile w h i l e the vacancy i s f i x e d and serves as a trapping center f o r i n t e r s t i t i a l i o n s . The r a t e of pro-d u c t i o n of F r e n k e l d e f e c t s i s given by the generation r a t e of ions from l a t t i c e p o s i t i o n s l e s s the recombination r a t e of ions w i t h vacancies as dm/dt = (N -m) V exp-(W'-qa'E)/kT - Jam (1.6) where the primed parameters are c h a r a c t e r i s t i c of the process whereby an atom i s removed by the f i e l d as i n (1.4). i s the d e n s i t y of atoms and a i s the capture cross s e c t i o n of the vacancy. Assuming that the l a t t i c e p o s i t i o n s are the s o l e source of ions (m = n) and that m<<N the steady s t a t e current i s o J = J q exp-(W-qaE)/kT (1.7) where 2W = W + W and 2a = a' + a. W and a are the average of the process of removing an atom from a l a t t i c e p o s i t i o n and then moving the ion along i n t e r s t i t i a l p o s i t i o n s as i n (1.4). The model was developed i n p a r t i c u l a r to de s c r i b e t r a n s i e n t c o n d i t i o n s (the constant f i e l d current t r a n s i e n t had not been observed at t h i s time) and the r a t e determining step f o r t r a n s i e n t s was the production of F r e n k e l d e f e c t s (1.6). In p a r t i c u l a r on changing from one constant f i e l d E^ to a second the current i s given by " _ J = J ' exp-(W'-qa'E„)/kT (1 . 8 ) o 2 during the t r a n s i e n t . The above r e l a t i o n s (1.7), (1.3) do not agree w i t h the observed 2 W(E) = W-aE + BE , p r e d i c t the wrong dependence of T a f e l slope on temperature and do not d e s c r i b e the constant f i e l d c urrent t r a n s i e n t . Several models have been proposed to overcome the f i r s t and second o b j e c t i o n made and these are given below. a. F r e n k e l Defect Theory and E l e c t r o s t r i c t i o n Model 21 22 Young ' suggested that the a p p l i e d f i e l d a f f e c t e d the a c t i v a t i o n energy i n a more complex manner then given by a l i n e a r term. In p a r t i c u l a r f o r the high f i e l d s i n v o l v e d higher order terms i n f i e l d would be expected to occur n a t u r a l l y so that W(E) = W-aE + BE 2 + should be expanded i n powers of E. Such an e f f e c t could be accounted f o r by the p o t e n t i a l energy dependence on d i s t a n c e r e l a t i o n or by a n o n - l i n e a r e f f e c t of the f i e l d on the b a r r i e r and i t s a c t i v a t i o n d i s t a n c e . L a t e r i t was pointed out 39 by Young that compression of the l a t t i c e from e l e c t r o s t r i c t i o n , a process which 2 i s p r o p o r t i o n a l to E occurs. This could account i n part f o r the e f f e c t observed i n a model combining F r e n k e l defect theory and e l e c t r o s t r i c t i o n . b. F r e n k e l Defect Theory and Morse P o t e n t i a l Model 40 Dignam i n v e s t i g a t e d the p o t e n t i a l energy verses d i s t a n c e r e l a t i o n of the b a r r i e r to a r r i v e at the c o r r e c t W(E). A c l i p p e d p a r a b o l i c p o t e n t i a l , a cosine p o t e n t i a l and a Morse p o t e n t i a l f u n c t i o n were i n v e s t i g a t e d . The Morse f u n c t i o n p o t e n t i a l i s given i n the presence of an a p p l i e d f i e l d by y(u) = <(. (l-exp-u/oj*)-uE (1.9) where i n the n o t a t i o n used here <J) = W and u/w* = x/x ,where x i s a constant and o o u = qx. W(E) i s then given by the d i f f e r e n c e between maximum and minimum value of t h i s f u n c t i o n and when t h i s i s expanded i n powers of E the r e q u i r e d r e s u l t i s 18 obtained. Dignara shows that the experimental r e s u l t s of Ta, A l and Nb can be accounted by f i t t i n g the constants and concludes that the model i s appropriate. However, such a function for p o t e n t i a l energy, as already pointed out 23 by Young and Zobel bears l i t t l e resemblence to a model where an ion jumps from an i n t e r s t i t i a l p o s i t i o n to another over a p o t e n t i a l b a r r i e r which should be peaked even at zero f i e l d . In the Morse function the zero f i e l d p o t e n t i a l maximum i s at i n f i n i t y , such a p o t e n t i a l function i s more applicable to the channel model of i o n i c conduction ( t h i s chapter section 2.3). c. Frenkel Defect Theory and F i e l d Dependent A c t i v a t i o n Distance 41 Christov and Ikonopisov were not s a t i s f i e d with the Morse p o t e n t i a l approach and showed that the a c t i v a t i o n distance i s decreased i n a manner propor-t i o n a l to the applied f i e l d i f a p o t e n t i a l qEx i s superimposed on the p o t e n t i a l energy seen by the ion (figure 1-3). No assumption i s required about the actual nature of the b a r r i e r , except that i n the region of i t s maximum i t can be approx-imated by a parabolic function of distance which i s not n e c e s s a r i l y the same before and a f t e r the f i e l d i s applied. Consideration of the decrease e i t h e r i n ts* x Figure 1-3: E f f e c t of e l e c t r i c f i e l d on p o t e n t i a l b a r r i e r of parabolic extremes (Christov and Ikonopisov 4 ). 19 the maximum or minimum leads to an a c t i v a t i o n expression W(E) = W - aE + BE 2 and agreement w i t h experimental r e s u l t s . 3. Models of I o n i c Conduction Based on E f f e c t i v e F i e l d a. The D i e l e c t r i c P o l a r i z a t i o n Model This model i s proposed mainly to d e s c r i b e the constant f i e l d current t r a n s i e n t not p r e d i c t e d by the models p r e v i o u s l y discussed. The p i c t u r e has 42-44 changed a number of times (Dignam ) s i n c e the o r i g i n a l mathematical d e r i v a t i o n 27 of the model by Dignam . E s s e n t i a l l y , t h e model i s based on the idea that the e f f e c t i v e f i e l d r a t h e r than the a p p l i e d f i e l d i s r e s p o n s i b l e f o r mass t r a n s f e r . The oxide i s considered as a random network of atoms i n which bonds are broken and remade i n a f a s h i o n which allows net mass t r a n s f e r . The breaking of a bond and the subsequent se p a r a t i o n of atoms gives r i s e to p o s i t i v e and n e g a t i v e l y charged defects.; This allows f o r both metal and oxygen i o n motion. The movement of defects causes l o c a l rearrangement of s t r u c t u r e and changes the d i e l e c t r i c p o l a r i z a t i o n i n that l o c a l i t y . The d i e l e c t r i c p o l a r i z a t i o n c o n s i s t s of the c o n t r i -b u t i o n from the normal p o l a r i z a t i o n process due to e l a s t i c displacement of charge and the p o l a r i z a t i o n due to the t r a n s p o r t of charge. The e f f e c t i v e f i e l d i n the oxide i s dependent through geometrical c o n s i d e r a t i o n on the p o l a r i z a t i o n P and i s w r i t t e n as 6'-P E = E + 2-?-e e. o where 61 i s a term which depends on geometrical c o n s i d e r a t i o n of i o n p o s i t i o n s and i s 1/3 f o r a Lorentz F i e l d , and i s the e l e c t r i c p e r m i t t i v i t y of f r e e space. At steady s t a t e i t i s assumed that the formation and propagation of defects i s s i m i l a r to i o n motion over a Morse p o t e n t i a l f u n c t i o n (discussed e a r l i e r ) 20 and the current i s J = J exp-(W-aE +3E 2)/kT o e e where the e f f e c t i v e e l e c t r i c f i e l d i s s u b s t i t u t e d f o r the a p p l i e d f i e l d . To account f o r t r a n s i e n t behaviour i t i s p o s t u l a t e d that the r a t e of change of p o l a r i z a t i o n i s p r o p o r t i o n a l to the current passed as 4^- = e x,v^ + AJ (e x E-P) + Thermal (1.10) dt o l d t o s n . . . C o n t r i b u t i o n where Xj^  and X g are the dynamic and s t a t i c e l e c t r i c s u s c e p t i b i l i t i e s r e s -p e c t i v e l y . The f i r s t term on the r i g h t of (1.10) corresponds to the normal p o l a r -i z a t i o n response of the d i e l e c t r i c due to e l a s t i c displacements. The second term describes the constant f i e l d current t r a n s i e n t , during which, the t h i r d term, the thermal c o n t r i b u t i o n i s considered n e g l i g i b l e . Dignam has shown that (1.10) w i l l d e s c ribe the complete constant f i e l d c urrent t r a n s i e n t i n c l u d i n g the i n i t i a l anomalous charging current at zero time i f a v o l t a g e a p p l i e d i s not a step but r a t h e r a r a p i d l y i n c r e a s i n g voltage ramp up to the value of the step. b. T r a n s i t i o n State - P o l a r i z a t i o n Energy Model The t r a n s i t i o n s t a t e theory has been used to study a model w i t h allowance f o r the energy stored i n a d i e l e c t r i c c o n t a i n i n g a charged s p e c i e s . The f r e e 2 energy stored by such a system i s p r o p o r t i o n a l to eE . The form 2 45 W(E) = W - aE + BE was obtained by I b l 4. . The Channel Model 23 The o b s e r v a t i o n by Young and Zobel that the i o n i c conduction r e s u l t s , 1/2 W(E) = W - yE , could be a c c u r a t e l y described by a Schottky or Poole-Frenkel law of charged p a r t i c l e f i e l d enhanced emission from surface or traps respec-t i v e l y , l e d them to p o s t u l a t e a model which p i c t u r e s ions as moving along channels i n an oxide i n t e r s p e r s e d w i t h coulombic t r a p s . For a Poole-Frenkel e f f e c t the form of W(E) may be derived as f o l l o w s ( F i g . 1-4). Consider an i o n of charge q 21 trapped i n a trap centre of charge when empty. D e f i n i n g the p o t e n t i a l of q^ to be zero f a r away from the t r a p , i n the presence of an e l e c t r i c f i e l d the p o t e n t i a l seen by the i o n i s V = -q q /ATTEX - q xE 6 F i g . 1-4: Poole-Frenkel e f f e c t . P o t e n t i a l energy of the v a r i o u s i n t e r a c t i o n s as a f u n c t i o n of d i s t a n c e i n the v i c i n i t y of a t r a p . I f the p o t e n t i a l energy r e q u i r e d by q^ to escape i s W at zero f i e l d , the a p p l i c a t i o n of a f i e l d w i l l lower t h i s energy by q.x E. Where x i s the d i s t a n c e ° 2 m m to the maximum of the p o t e n t i a l b a r r i e r (dV/dx = 0) and i s . , .1/2 K / w - l / 2 x = (q n /4TTEE) = b/E m 1 The p r o b a b i l i t y of an i o n to overcome the b a r r i e r i s then given by 1/2 exp-CW-q^bE )/kT and the r e s u l t i n g current d e n s i t y i s 1/2 J = J q exp-(W-q 2bE ' )/kT 22 The model was not f o r m a l l y extended to cover t r a n s i e n t behaviour. A p o s s i b l e way of extending t h i s model to cover t r a n s i e n t s i s to consider that the p r o b a b i l i t y of trapping an i o n i s decreased by the presence of the f i e l d 1/2 and i s exp -(W + q^bF, )/kT. The time r a t e of i o n production i s then given by the r a t e of generation l e s s the r a t e of capture of ions as —- = (N-n) exp-(W-q 2bE 1 / 2)/kT - Joexp-(W+q 2bE 1 / 2)/kT when w r i t t e n analogously to equation (1.6). This leads to a steady s t a t e current d e n s i t y of the form 1/2 J = JQ exp - (W-yE ' )/kT 1/2 where y = 2q 2b = q2 C4!-^/fre) . However t h i s has the same drawback as the high f i e l d F r e n k e l defect theory i n that i t does not describe the constant f i e l d current t r a n s i e n t . In t h i s d e r i v a t i o n i t i s assumed that the high f i e l d s e l i m i n a t e any backward c u r r e n t . 5. Normal. Mode Model Young + i n a more fundamental approach to i o n motion has now considered the normal v i b r a t i o n a l modes of the oxide s l a b . This treatment considers the r e s -ponse of the oxide as a whole, that i s , the v i b r a t i o n a l modes of the oxide are governed by a l l the processes o c c u r r i n g i n the oxide. On the other hand, the c l a s s i c a l model considers the i o n as a s o l e e n t i t y and thus does not account f o r other e f f e c t s which occur. The argument i s based on S z i g e t i s ' work on i n f r a r e d 45 p o l a r i z a t i o n waves , which a r i s e mainly from the c r e a t i o n of d i p o l e moments due to atomic displacements. According to Young, the simplest case i s where a c r i t i c a l amplitude e x i s t s i n one of the normal modes to produce a displacement l a r g e enough to consider an i o n jump as having taken p l a c e . To i n t e r a c t w i t h a d-c e x t e r n a l f i e l d the normal modes are considered to have i n f i n i t e wavelength. + Put f o r t h i n a recent review by Dell'Oca, P u l f r e y , Young. ~* Since these modes are independent harmonic o s c i l l a t o r s t h e i r energy i s given b y 1 2 - 2 W(E) = | (/(q -q T t i l where f o r the j mode q i s the. thermal displacement and q. i s the mean displacement j 3 caused by the e x t e r n a l f i e l d . The l a t t e r turns out to be p r o p o r t i o n a l to _ , 2 . 1 / 2 , 2 V / 2 , 2 E. • . (e -n ) /n = e E . „ ( E - n ) /n i n t r r ext r where e i s the r e l a t i v e p e r m i t t i v i t y , n i s the r e f r a c t i v e index and E. i s the r r J ' i n t i n t e r n a l f i e l d being equal to e E _ f o r a slab p o l a r i z e d across. • r ext K The p r o b a b i l i t y that a normal mode has the c r i t i c a l energy i s given by exp -W(E)kT. This then leads to a current d e n s i t y of the form J = 2a vqexp - W(E)/kT. Where the i o n moves a di s t a n c e 2a , and v represents the frequency of the process across the s l a b . Thus, the r e q u i r e d W(E) i s found and a l s o a d i r e c t dependence of i o n i c conduction on d i e l e c t r i c constant and index of r e f r a c t i o n of the oxide i s obtained. 4. SUMMARY In summary the present understanding of oxide growth i s as f o l l o w s . The oxide c o n s i s t s of two l a y e r s which grow simultaneously at the i n t e r f a c e s due to metal and oxygen i o n transport across the oxide during a n o d i z a t i o n . Furthermore, e l e c t r o l y t e i n c o r p o r a t i o n occurs i n t o the outer l a y e r on growth making i t s p r o p e r t i e s d i f f e r e n t from an inner l a y e r which i s considered to be s t o i c h i o m e t r i c Ta^O^. Quite apart from the e f f e c t s of incorp o r a t e d s p e c i e s , the two l a y e r s might be expected to d i f f e r because of the d i f f e r e n t environments of growth at the metal oxide and oxide s o l u t i o n i n t e r f a c e . I o n i c conduction i s 2 a f i e l d a s s i s t e d t h e rmally a c t i v a t e d process where l o g J « ('aE - BE )/kT and which f u r t h e r depends on the current during the constant f i e l d c urrent t r a n -s i e n t and f i n a l l y , t h e i o n i c process a l s o i n t e r a c t s i n an unknown manner w i t h 24 e l e c t r o n i c processes under photostimulated growth. At the moment no theory exists which can account for more than one of these phenomena. I I . OPTICAL PROPERTIES OF ANODIC OXIDE FILMS DETERMINED BY ELLIPSOMETRY 1. INTRODUCTION In the previous o p t i c a l s t u d i e s of anodic oxide f i l m s formed on tantalum a homogeneous f i l m was assumed i n the determination of the o p t i c a l p r o p e r t i e s of the oxide. The agreement between computed and experimental data was found on 23 47-49 t h i s assumption to be s a t i s f a c t o r y f o r oxides formed i n d i l u t e s u l p h u r i c ' and a c e t i c a c i d e l e c t r o l y t e s . One exception was that a s l i g h t anomaly occurred i n the r e f l e c t i v i t y of p l i g h t at the Brewster angle which was taken to i n d i c a t e 47 the presence of a very t h i n absorbing l a y e r o v e r l y i n g the oxide. Oxides formed i n concentrated s u l p h u r i c a c i d were found to be homogeneous only up to 47 a c e r t a i n t h i c k n e s s . In t h i s s e c t i o n c a l c u l a t e d and experimental e l l i p s o m e t r y evidence i s presented which i n d i c a t e s that anodic oxide f i l m s formed i n phosphoric a c i d e l e c t r o l y t e s are non-uniform and c o n s i s t of two l a y e r s . 2. ELLIPSOMETRY* Several o p t i c a l techniques are a v a i l a b l e f o r the study of t h i n films'^ In the study of anodic f i l m s the major techniques used are: a) i n t e r f e r e n c e measurement of t h i c k n e s s ; ^ b) measurement of the r e f l e c t i v i t y of p l i g h t as a f u n c t i o n of angle of i n c i d e n c e to determine index of r e f r a c t i o n of the oxide and the m e t a l ^ and c) e l l i p s o m e t r y 2 " ^ ' ^  . Although e l l i p s o m e t r y might not 48 be as s e n s i t i v e as method (b) i s to index of r e f r a c t i o n of the f i l m , e l l i p s o m e t r y i s chosen f o r t h i s study because w i t h i t both the index of r e f r a c t i o n and t h i c k n e s s of the f i l m may be determined simultaneously. E l l i p s o m e t r y i s based on the measurement of two q u a n t i t i e s A and ¥ See references 51-54, f o r a c o l l e c t i o n of papers and reviews on the s u b j e c t . 26 c a l l e d the. e l l i p s o m e t r y angles. These angles c h a r a c t e r i z e the change i n p o l a r i z a t i o n s t a t e which occurs when 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 f l e c t e d from a su r f a c e . These q u a n t i t i e s are r e l a t e d to the p r o p e r t i e s of the surface through the e l l i p s o m e t r y equation. Before s t a t i n g t h i s equation the b a s i c p r i n c i p l e s and n o t a t i o n used i n e l l i p s o m e t r y are b r i e f l y presented. 1. P r i n c i p l e s of E l l i p s o m e t r y a) Notation Consider b r i e f l y the problem"*" 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 r e f l e c t e d and r e f r a c t e d at an i n t e r f a c e separating two media which are homogeneous ( F i g . 2-1) and each medium i s c h a r a c t e r i z e d w i t h a complex index of r e f r a c t i o n w r i t t e n i n the form N = n - jk In any medium 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 i s represented by a transverse e l e c t r i c wave E which i s the r e s u l t a n t of two mutually orthogonal plane e l e c t r i c waves, one i n the plane of inc i d e n c e E , and the other normal to t h i s plane E . The s o l u t i o n to Maxwell's equation f o r the case of V-E equal s zero i s taken to have the form E = A exp j( o i t - K-r + A) = E + E (2.1) s p where the dependence of l i g h t on the medium i s given by K = 2 T T N / A , X i s the wavelength. The p h y s i c a l r e p r e s e n t a t i o n of l i g h t i s given by the r e a l part of (2.1) and y i e l d s E = A cos (wt-K* r+6 ) and E = A cos (tdt-K-r+6 ) .„ ~ N p p p s s s (2.2) Where A = 6 -6 i s the phase d i f f e r e n c e between the two plane waves. I f p s A = imr, where m i s zero or any i n t e g e r , the l i g h t i s l i n e a r l y p o l a r i z e d . I f A = mir/2, where m i s a non zero odd i n t e g e r and A = A , the l i g h t i s c i r c u l a r l y P s + This problem i s discussed i n any t e x t on electromagnetic theory. For d e f i n i -t i o n s and conventions i n e l l i p s o m e t r y see the paper by M u l l e r and the d i s c u s s i o n to t h i s paper by Bennett.-* 7 27 p o l a r i z e d . F i n a l l y equation (2.2) may be w r i t t e n i n p o l a r complex form i n terms of A and azimuth angle ¥ ( F i g . 2-1) as E /E = tan¥ e j A P s Incident l i g h t R e f l e c t e d l i g h t F i g . 2-1: R e f l e c t i o n and r e f r a c t i o n at an i n t e r f a c e A n a l y s i s of r e f l e c t i o n and r e f r a c t i o n at the i n t e r f a c e using the boundary c o n d i t i o n s on phase and amplitude of the e l e c t r i c f i e l d components y i e l d s : a) law of r e f l e c t i o n , <f> = 6' o o b) S n e l l ' s law of r e f r a c t i o n , N cos<}> = N..cos<j>, 28 c ) the F r e s n e l c o e f f i c i e n t of r e f l e c t i o n and t r a n s m i s s i o n . The r e f l e c t i o n c o e f f i c i e n t f o r the p and s components are r = E ' / E = tan(<|> -< j ) n)/tan (A = (N^costj) -N cos*., ) / (N, coscj) +N cos*,) p op op o l o l 1 o o l l o o l r s E' /E = -sin(6 -A,) /sin(6 ) = (N cos* -N., cos*, ) / (N cosd)., +N. coscfc, ) OS OS o 1 o 1 o o 1 1 o 1 1 1 The F r e s n e l t r a n s m i s s i o n c o e f f i c i e n t s are r e l a t e d to the r e f l e c t i o n c o e f f i c i e n t s 2 through the law of conservation of energy which gives t ^ t ^ + r ^ = 1 and r-^ Q = - rQ2* Where sequence of s u b s c r i p t s denotes d i r e c t i o n of wave t r a v e l from medium to medium. b) The E l l i p s o m e t r y Equation In the preceding d i s c u s s i o n , the r e f l e c t e d and i n c i d e n t planes wave were r e l a t e d to each other by 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 . In an analogous manner the t o t a l r e f l e c t e d wave i s r e l a t e d to the t o t a l i n c i d e n t wave by a c o e f f i c i e n t p as f o l l o w s -i A ' tan¥'eJ o E' /E' E /E' R _ o _ op os _ op op _ p P ~ - «, J A ~ E / E ~ E /E " R~ tanT e o op os os os s and d e f i n i n g p = tan¥e j A = R /R (2.4) P s y i e l d s the e l l i p s o m e t r y equation. Where A i s the r e l a t i v e phase change on r e f l e c t i o n g i ven by A = A '-A = (<5 -6 )' - (6 -6 ) o o p s p s and tan¥ i s the r e l a t i v e amplitude a t t e n u a t i o n on r e f l e c t i o n given by tan f = tanY' /tanT o o R and R are 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 of p and s l i g h t and these p s r o c o e f f i c i e n t s g i ve the dependence of A and ? on the p r o p e r t i e s of the t h i n f i l m and the s u b s t r a t e . For the case of sub s t r a t e only, R and R reduce to r and r . 29 Thus from (2.4), one e l l i p s o m e t r y measurement which give s a A and a T r e s u l t s i n two equations which can be solved f o r two o p t i c a l unknown q u a n t i t i e s of the f i l m and s u b s t r a t e . I f more than two unknowns are to be determined i t i s necessary to curve f i t a number of d i f f e r e n t e l l i p s o m e t r y measurements. These measurements are most e a s i l y obtained as a f u n c t i o n of changing f i l m t h i c k -23,48-50,56 r 1 , .' 58 . . , . ness, as a f u n c t i o n of angle of incidence or as a f u n c t i o n or immer-s i o n m e d i u m " ^ A s such the study of anodic oxide f i l m s i s an almost i d e a l a p p l i c a t i o n of e l l i p s o m e t r y i n that measurements may be made on the oxide i n s i t u i n the forming e l e c t r o l y t e and the f i l m s i n most cases are of uniform t h i c k n e s s and may be grown over a wide range of t h i c k n e s s . 2. The E l l i p s o m e t e r a) Apparatus and P r i n c i p l e of Operation The Gaertner S c i e n t i f i c Corporation model L119 e l l i p s o m e t e r used i s shown s c h e m a t i c a l l y w i t h attachments i n F i g . 2-2. source chopper ... i . compensator p o l a r i z e r r A v-u | c o l l i m a t o r f i l t e r . O - Fixed Arm photodetector F i g . 2-2: Schematic Diagram of E l l i p s o m e t e r and attachments * A complete d e s c r i p t i o n of t h i s model i s given by Archer 61 The ellipsometer consists of a fixed arm which contains a c o l l i m a t o r , p o l a r i z e r and competisator and a movable arm which contains analyzer, telescope and eyepiece. The analyzer and p o l a r i z e r are Glan Thompson prisms while the compensator used was a cleaved mica quarter wave plate between glass coverings with a n t i r e f l e c t i o n coating. A S o l e i l Babinet compensator i s a v a i l a b l e but was not used. The analyzer, p o l a r i z e r and compensator are set i n divided c i r c l e s which can be rotated about the beam. The movable arm rotates about the centre of the specimen table and i s used to set angle of incidence using a divided c i r c l e . The specimen table also rotates about i t s centre and can be t i l t e d f o r correct specimen s e t t i n g . The ellipsometer i s f i t t e d with a D.C. powered mercury arc l i g h t source, followed by a l i g h t f i l t e r (Corning Glass) i n the green to pick out the mercury l i n e at 5461A 0. The l i g h t entering the collimator i s chopped at 1470 Hz to f a c i l i t a t e a m p l i f i c a t i o n of the s i g n a l from the photodetector (RCA - 931A photo-m u l t i p l i e r ) by a tuned a m p l i f i e r n u l l detector (General Radio Model 1231A). The p r i n c i p l e of operation of the ellipsometer i s as follows. The p o l a r i z e r produces l i n e a r l y p olarized l i g h t at a set angle to the plane of incidence. The quarter'wave plate changes the l i n e a r l y polarized l i g h t to some form of e l l i p t i c a l l y p o larized l i g h t by causing a r e l a t i v e phase change of 90° between components of l i n e a r l y p olarized l i g h t f a l l i n g along the slow and fast d i r e c t i o n s . R e f l e c t i o n from the specimen changes the p o l a r i z a t i o n of the l i g h t , the l i g h t then proceeds to the analyzer which i s j u s t another p o l a r i z e r . Now, i f the p o l a r i z e r and compensator can be set such that l i n e a r l y p olarized l i g h t occurs on r e f l e c t i o n from the specimen t h i s l i g h t may be exting-uished by the analyzer and thus i t s o r i e n t a t i o n may be deduced. Knowing the p o l a r i z e r , P, compensator, C, and analyzer, A, s e t t i n g s the change i n polar-i z a t i o n on r e f l e c t i o n , i . e . , A and f'can he determined. The equations 31 r e l a t i n g the e x t i n c t i o n s s e t t i n g s to the e l l i p s o m e t r y angles are derived i n Appendix A. TABLE 2-1. R e l a t i o n of P and A readings to p, a , and a ( a f t e r 62 V s McCrackin et a l . ) Zone Compensator P A P 4 + TT/4 TT — p TT " - a TT - P P 2TT - p TT -  a 2TT - P P TT - p 2TT - a P 2TT - p 2TT - a P 2 + TT/4 TT/2 - p a s TT/2 - P 3TT/2 - p a s 3TT/2 - P TT/2 - p a s + TT 3TT/2 - p a + TT s • 1 - TT/4 P a p P p + TT a P — TT P P a + TT P p + IT a + TT P 3 - TT/4 p + TT/2 TT- - a s P - TT/2 p + 3TT/2 TT a s P - 3TT/2 p + TT/2 2TT - a s. p + 3TT/2 2TT - a s TT — A TT - A The independent quarter wave p l a t e s e t t i n g s are chosen as +45° and f o r each of these s e t t i n g s two independent P and A e x t i n c t i o n s e t t i n g s occur where the P s e t t i n g s d i f f e r by TT/2 and the A s e t t i n g s add to TT or 2ir. E x t i n c -t i o n a l s o occurs at s e t t i n g s d i f f e r i n g , from these values by TT . ( A l l angles are measured p o s i t i v e counterclockwise when l o o k i n g i n t o the beam.) To d i s -62 t i n g u i s h between readings, McCrackin et a l d i v i d e d the readings i n t o four zones, each c o n t a i n i n g an independent set. They de f i n e q u a n t i t i e s a , a and p which p s f o r a quarter wave p l a t e at + 45° give the e l l i p s o m e t r y angles as A = 2p + 90° and ¥ = a = a p s 32 with - T T / 4 <_ p <_ , 0 <_ ¥ <_ 90° and 0 <_ A <_ 360° The r e l a t i o n s h i p between the defined q u a n t i t i e s and the e x t i n c t i o n s e t t i n g s are given i n Table 2-1, where the analyzer has been r e s t r i c t e d to a range 0 to T T ° . 3. Experimental Methods a) Alinement The procedure used to a l i n e the e l l i p s o m e t e r c o n s i s t e d of three p a r t s : (a) The telescope and c o l l i m a t o r were focused so the l i g h t f a l l i n g on the specimen was c l o s e to p a r a l l e l as p o s s i b l e . This was done by f o c u s i n g the eyepiece on the cross wires which are over the e x i t s l i t of the te l e s c o p e , the telescope was i n focus when the image of a small d i s t a n t object was focused on the plane of the cross w i r e s . S i m i l a r l y , the c o l l i m a t o r was i n focus when the image of the c o l l i m a t o r s l i t was focused i n the plane of the cross w i r e s . (b) The l e v e l and s t r a i g h t through p o s i t i o n of the o p t i c a l system was found so that angles of incidence could be a c c u r a t e l y s e t . I t was found that the s t r a i g h t through p o s i t i o n i s a f f e c t e d by r o t a t i n g the p o l a r i z e r and compen-sator s i n c e these r o t a t i o n s r e s p e c t i v e l y cause an e l l i p t i c a l e x c ursion of the s l i t image i n the plane of the x wires which extends over four and ten minutes of arc i n the plane of in c i d e n c e ( F i g . 2-3). X wires Caused by compensator. F i g . 2-3; Excursion of s l i t image on plane of X w i r e s . The l e v e l and s t r a i g h t through p o s i t i o n s were set by b r i n g i n g the cross wires to the centre of the s l i t image exc u r s i o n . This s e t t i n g depends on whether two or four zones were read, since the l a t t e r case r e q u i r e s that the quarter wave p l a t e take two p o s i t i o n s ( F i g . 2-6). Once the s t r a i g h t through p o s i t i o n was s e t , a p o l a r i z e r p o s i t i o n was found f o r a s e t t i n g of the quarter wave p l a t e which brought the s l i t image to a p o s i t i o n w i t h respect to the cross wires which was e a s i l y r e c o g n i z a b l e . These p o s i t i o n s were then used to c o r r e c t l y set the angle of i n c i d e n c e , (c) The p o l a r i z e r , analyzer and compensator s c a l e zeroes were c a l i b r a t e d . C a l i b r a t i o n of the p o l a r i z e r and analyzer s c a l e was b r i e f l y as f o l l o w s . + The compensator was removed from the e l l i p s o m e t e r and a r e f l e c t i n g metal surface was used w i t h the angle of i n c i d e n c e set c l o s e to the p r i n c i p a l angle of the metal. P and A were set to 0° and 90° r e s p e c t i v e l y . P was then changed i n small increments and the minimum at each P was determined by measuring A at equal i n t e n s i t i e s on each s i d e of the minimum. The d i r e c t i o n of the increments i n P were chosen so that the i n t e n s i t y of the minima a l s o scanned a minimum. The procedure was repeated w i t h A changed i n increments and P determining the minima. This l e d to two curves i n a P versus A p l o t which i n t e r s e c t e d at the lowest i n t e n s i t y minimum. (A t y p i c a l c a l i b r a t i o n f o r our e l l i p s o m e t e r i s shown i n F i g . 2-5). At the p o i n t of i n t e r s e c t i o n the l i g h t coming from the p o l a r i z e r i s i n the plane of i n c i d e n c e . Thus t h i s p o i n t gives the c o r r e c t i o n to be made to the p o l a r i z e r and analyzer readings which was -0.78° ( F i g . 2-5). The cross p o s i t i o n of analyzer and p o l a r i z e r found above were used to c a l i b r a t e the compensator s c a l e . That i s , t h e p o s i t i o n on the s c a l e where A complete d i s c u s s i o n of p r i n c i p l e s i n v o l v e d , and stepwise procedure i n t h i s c a l i b r a t i o n i s given by McCrackin et a l . 6 2 34 QWP at 315 180 270 P/deg F i g . 2-4: L a t e r a l motion of s l i t image, A, i n minutes of arc as a function of p o l a r i z e r , P, for two settings of the quarter wave p l a t e , QWP. Arrows in d i c a t e s t r a i g h t through s e t t i n g of the ellipsometer f o r 2 or 4 zones. A/deg F i g . 2-5: C a l i b r a t i o n of p o l a r i z e r and analyzer scales using an A l mirror at A Q = 7 0 ° and A = 5 4 6 1 A ° . 35 the fast axis of the compensator coincides with the p axis. This s e t t i n g was found by taking measurements with the compensator at equal i n t e n s i t i e s on each side of the minimum. b) Specimen Preparation 2 F71 Tantalum specimen about 4 cm on one side and with a tab (shown on r i g h t ) were cut from capa-c i t o r grade tantalum sheet 0.25 cm thick supplied by y j Fansteel Corporation. One side of the specimen was prepared for o p t i c a l studies by one of the I l-J following three methods: (a) In the f i r s t part of t h i s procedure the tanta-lum specimen was chemically polished i n a f r e s h l y prepared s o l u t i o n of acids i n the r a t i o s 5(98%' H^SO^):2(70% HNO^):2(48% HF) by volume, t h i s i s followed by a 10 second HF dip and a d i s t i l l e d water r i n s e . Chemical p o l i s h i s a standard method of producing a tantalum surface which has a high e f f i c i e n c y f or the growth of the anodic oxide. This was used i n the prepare t i o n of a l l specimens for non o p t i c a l studies. The chemical p o l i s h leaves a wavy surface. In the second part of t h i s procedure the specimen was mechanically polished by abrading on f i n e r m e t a l l u r g i c a l papers and t h i s was followed by p o l i s h i n g on a r o t a t i n g wheel using successively f i n e r powder abrasives f i n i s h i n g with 50 nm alumina powder. The speciman was then degreased and rinsed. A surface was accepted a) i f i t was free of surface contamination and scratches. b) If i t was f l a t as judged from the r e f l e c t i o n of s t r a i g h t l i n e s such as window blinds etc., and i n conjunction with t h i s i f i n the ellipsometer, the beam r e f l e c t e d by the specimen was round and well defined, and f i n a l l y c) If a f t e r a f i v e second 48% HF dip and r i n s e A was close to values measured for electropolished specimens which were close to 124° for an angle of incidence of 36 O 67.5° and A = 5461.A . (b) As i n the second part of ( a ) , except the m e t a l l u r g i c a l paper was followed by e l e c t r o p o l i s h i n g i n a t e f l o n c e l l c o n t a i n i n g a bath of 10% by volume 49% HF 2 i n concentrated ^SO^ and a current of about 0.1 amp/cm was passed. (The c e l l and the procedure has been used p r e v i o u s l y and i s described i n reference 2 3 . ) This was followed by a 10 second HF dip and r i n s e . (c) As i n the second part of (a) follox^ed by e l e c t r o p o l i s h i n g as i n (b). E l e c t r o p o l i s h i n g removes the work hardened or damaged surface l a y e r produced by mechanical p o l i s h i n g and presumably leaves a surface w i t h p r o p e r t i e s as c l o s e as p o s s i b l e to those of bulk m a t e r i a l . In ( c ) , the damaged l a y e r should be l e s s and the surface much smoother than that of the mechanical p o l i s h i n g p r e p a r a t i o n i n b. The r e s u l t i s that a f t e r e l e c t r o p o l i s h i n g (c) produces a b e t t e r surface (not as rough and u s u a l l y f l a t t e r ) than (b) but never as good as can be obtained by ( a ) . This r e s u l t i s due to d i f f e r e n t r a t e s of a t t a c k i n e l e c t r o p o l i s h i n on d i f f e r e n t c r y s t a l surface and on g r a i n boundaries of the Ta. S i n g l e c r y s t a l Ta specimens are much b e t t e r i n t h i s respect (Lee, P u l f r e y , Young, unpublished) but were not used i n t h i s study. (d) The damaged l a y e r can a l s o be removed i n (a) by s u c c e s s i v e l y anodizing a t h i c k oxide and removing i t i n HF and then using the sample f o r experiments. This removes the damaged l a y e r but does not remove scratches on the backside and edges of the specimen which occur i n the process from handling. Oxygen e v o l u t i o n occurs at scratches and reduces the anodizing e f f i c i e n c y , and t h i s can only be c o r r e c t e d by chemical or e l e c t r o c h e m i c a l p o l i s h i n g . In d i l u t e (about .2N) s u l p h u r i c or phosphoric a c i d s o l u t i o n s the e f f i c i e n c y of anodic oxide growth on specimens prepared as i n (a) and (d) was about 1 to 2% lower than obtained from methods (b) and ( c ) . However, i n concen-t r a t e d phosphoric a c i d the e f f i c i e n c y was lowered by as much as 50% and oxygen bubbles could be seen on the tantalum surface. F i n a l l y , a specimen which had been p r e v i o u s l y anodized was prepared f o r another e l l i p s o m e t r y experiment by removing the oxide w i t h 49% HF. Ta WIRE BRASS ROD TEFLON Ta WIRE STUBS (c) A n o d i z a t i o n The specimen was clamped at the tab between jaws made of t e f l o n which had small pieces of tantalum wire p r o t r u d i n g from them. The wires held the tab and two of the wires ex-tended up the t e f l o n jaws and provided e l e c -t r i c a l contact to the specimen. During a n o d i z a t i o n the tantalum specimen was completely immersed i n the e l e c t r o l y t e . A t h i c k l a y e r of oxide on the Ta wire coming out of the e l e c t r o l y t e prevented sparking at the e l e c t r o l y t e -meniscus and the w i r e . A small p l a t i n i z e d platinum w i r e served as cathode (0.04 cm diameter by about 1.5 cm. l o n g ) . A n o d i z a t i o n was c a r r i e d out at constant v o l t a g e or at constant current i n e l e c t r o l y t e s held at 25 +0.2° C by a thermostatted bath. In most cases the e l e c t r o l y t e was s t i r r e d . A hydrogen satura t e d e l e c t r o l y t e was used f o r anodiza-t i o n i n the case where e l l i p s o m e t r y measurements were made i n s i t u . A n o d i z a t i o n was i n t e r r u p t e d f o r e l l i p s o m e t r y measurements. Capacitance measurements i f r e q u i r e d were made about one minute a f t e r t h i s i n t e r r u p t i o n . These were made w i t h the specimen i n s o l u t i o n using the capacitance bridge described i n chapter V s e c t i o n 3.2 without the v o l t a g e b i a s c i r c u i t . A l a r g e 2 area 20 cm ) p l a t i n i z e d platinum sheet served as second e l e c t r o d e f o r c a p a c i -tance measurements. Some specimens were examined w i t h a m e t a l l u r g i c a l microscope at up to 600X to check f o r the presence of flaws i n the oxide. 38 ANODE SPHERICAL JOINT Scm l.D. SPECIMEN LIGHT BEAM OPTICAL FLAT d) Ellipsometry Measurements Ellipsometry measurements were made f i r s t on the unanodized surface and then at i n t e r v a l s during growth of the oxide. P r i o r to each ellipsometry measurement made i n a i r on the oxide covered specimen, the specimen was rinsed, dipped i n a dichromate s o l u t i o n c o n s i s t i n g of concentrated sulphuric a c i d saturated with potassium dichromate. This was followed by a thorough r i n s e and drying. For ellipsometry measurements made i n a i r the t e f l o n holder was attached to a mount which f i t t e d v i a two a l i n i n g screws to the specimen table. The t e f l o n holder could be adjusted with respect to the mount to f a c i l i -tate alinement of the Ta specimen i n the e l l i p -someter. Once alinement was completed the holder was f i x e d to the mount so that the mount specimen and holder were removed from the ellipsometer as one u n i t . This ensured that alinement of the specimen was maintained be-tween ellipsometry measurements during anodi-zation. For ellipsometry measurements made i n s i t u , the t e f l o n holder was held i n the e l e c t r o l y t e i n a water jacketed c e l l equipped with o p t i c a l l y f l a t glass windows which allowed ellipsometry measurements to be made at an angle of i n c i -dence of 67.5° (figure on r i g h t above). Measurements made on the oxide i n a i r were usually made i n two zones (compensator fixed at 45°) with periodic check readings of a l l four zones. In i n s i t u measurements a l l four zones were read. E x t i n c t i o n settings of the ellipsometer A and P were obtained o o using Archer's"^ method which i s 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 v a r i e s symmetrically about e x t i n c t i o n p o s i t i o n s of analyzer and p o l a r i z e r . The procedure used was as follows. The approximate e x t i n c t i o n p o s i t i o n was found by inspection from r o t a t i n g p o l a r i z e r and analyzer; then the exact P q was found WATER h- Scm 39 by averaging P values obtained at equal i n t e n s i t i e s on each side of the minimum. The p o l a r i z e r was set to t h i s v a l u e , P , and the same procedure was c a r r i e d out to f i n d A . The analyzer was set at A and P was checked at TT degrees o o o away from the previous P . This procedure was repeated f o r each zone" measured. A given zone was measured by r e q u i r i n g A^ to be i n the quadrant as given by Table 2-1, The measurements were reduced by the scheme i n Table 2-1 to values of A and An example i s given below, (Table 2-2) which shows measurements made i n a i r at. o an angle of incidence of 67..5° and X = 5461 A of an unanodized mechanically p o l i s h e d tantalum specimen. Compen-sator Zone P* P" P p A' A" A a o o 4 345.93 344.75 345.34 14.66 154.20 153.32 153.76 26.24 165.85 164.71 165.28 14.72 2 75.69 74.65 75.17 14.83 22.63 21.71 22.17 22.17 255.74 254.52 255.13 14.87 Average of two zones p = 14.77 + 0.78 =15.57 , a = 24.20 and A = 90 + 2(15.57) = 121.14 , V = 24.20 1 195.58 196.76 196.17 16.16 22.96 23.96 23.46 23.46 16.73 15.45 16.09 16.09 3 285.61 286.93 286.27 16.27 154.35 155.37 154.86 25.14 106.96 105.60 106.28 16.28 Average of two zones p = 16.20 - 0.78 =15.40 , a = 24.30 and A = 90 + 2(15.40) = 20.80 , ¥ = 24.30 Average of four zones p = 15.49 a = 24.25 and A = 120.98 f = 24.25 Scale c o r r e c t i o n to P readings, 45.36 315.36 Table 2-2: Example of red u c t i o n of e l l i p s o m e t r y measurement i n two or four zones. Primed and double primed q u a n t i t i e s i n d i c a t e s e t t i n g s on e i t h e r s i d e of e x t i n c t i o n minimum. 40 e) Computational Methods In appendix B the problem of r e f l e c t i o n and r e f r a c t i o n from Z homo-geneous l a y e r s on a metal i s considered. A r e l a t i o n i s derived, f o r the p or the s component between i n c i d e n t E , r e f l e c t e d E' and r e f r a c t e d wave i n the metal o o E as a product of m a t r i c e s . Each matr i x A. c h a r a c t e r i z e s an i n t e r f a c e and the m i next l a y e r . Thus \E'/ i = l t i t m \ r 1 /\0 j tl t2 Sn \ Z . . Z 0 0 o m x 21 22 where A.= l 2 1 r . e J i r.e 1 e ! I where 6^  = 2TTN c o s t f i ^ d^ / X i s the phase change s u f f e r e d by the l i g h t on c r o s s i n g a l a y e r of t h i c k n e s s d_^ . The s u b s c r i p t i r e f e r s to the i t b i n t e r f a c e or the i t b l a y e r . The r e f l e c t i o n c o e f f i c i e n t f o r the p and s l i g h t component has the form R = E'/E = Z . . / Z . . o o 21 11 Programs were w r i t t e n f o r the IBM 7044 ( l a t e r converted f o r the IBM 360/67) at the Computing Centre of the U n i v e r s i t y of B r i t i s h Columbia to c a l c u l a t e A and ¥ at f i r s t f o r the case of 2 or 1 l a y e r on a metal and l a t e r a general program f o r any number of l a y e r s on a metal was w r i t t e n . In the general case the computer i s given the f o l l o w i n g data: the number of l a y e r s , the index and i n i t i a l t h i c k n e s s of each l a y e r , the increment i n thickness of each l a y e r and the index of the ambient and of the metal s u b s t r a t e . The computer then computes a l l r ., r . and 6. and assigns the matrix elements to A. f o r the p and s compo-p i sx i b 1 ^ ^ nents. The matrices are m u l t i p l i e d together to o b t a i n R and R and f i n a l l y , p s J ¥ = t a n " 1 IR /R I 1 p s 1 and A = tan 1 {Imaginary (R /R ) / Real (R /R )} p s p s 41 are computed. This program i s the b a s i c sub-program of programs which, f o r exampl give t a b l e s of A and ¥ or computer p l o t s of A verses H' as f u n c t i o n of thic k n e s s or f i n d s a f i t to experimental A, 4* values and gives thickness and index of r e f r a c t i o n of each l a y e r . The b a s i c sub-program was checked against s i m i l a r c a l c u l a t i o n s made 23 on tantalum by Young and Zobel . The sub-program was a l s o checked f o r blunders by showing: that A and ¥ remained the same f o r a given t o t a l f i l m t h i c k n e s s when a one l a y e r f i l m was replaced by f i l m s c o n s i s t i n g of 2, 3, 4, 5, 10 and 20 l a y e r s a l l of the same index as the one l a y e r f i l m and that the r e s u l t s were unaffected when a h i g h l y absorbing l a y e r w i t h zero thickness was introduced i n t o the f i l m or when l a y e r s of non-zero thi c k n e s s were introduced next to the metal or ambient and r e s p e c t i v e l y given the same index of r e f r a c t i o n as these media. 3. COMPUTED RESULTS 1. S i n g l e Layer D i e l e c t r i c F i l m Growing on Tantalum Fi g u r e 2-6 shows a computed A verses Y curve as a f u n c t i o n of th i c k n e s s of an anodic oxide f i l m on tantalum r e s p e c t i v e l y w i t h i n d i c e s of r e f r a c t i o n of 23 2.22 and 3.3 - 2.3j as determined by Young and Zobel . The e l l i p s o m e t r y curve o s t a r t s at the poin t marked 0.0A which represents zero f i l m t h i c k n e s s or bare metal. As the thic k n e s s of the l a y e r increases a A-T curve i s traced out as shown by the arrow. When the curve reaches the f a x i s i t s t a r t s over at A equal 360° and e v e n t u a l l y w i t h i n c r e a s i n g t h i c k n e s s the curve r e t u r n s to the s t a r t i n g p o s i t i o n or r e c y c l e s . R e c y c l i n g occurs because the r e f l e c t i o n c o e f f i c i e n t R which f o r the case of one l a y e r on a metal i s R = ( r x + r 2 e ~ 2 j 5 l ) / ( l + r ^ e " 2 ^ 1 ) r e t u r n s to i t s o r i g i n a l value when 6^  reaches 180°. The same e l l i p s o m e t r y curve i s traced out again and again w i t h i n c r e a s i n g t h i c k n e s s . A3 20 30 40 SO PSI /deg F i g . 2-7: Computed e l l i p s o m e t r y curve f o r two l a y e r s growing simultaneously (nr=2.13, n 2=2.26) on tantalum (M 3=3.3-2.3j). Departure of short dashed l i n e (3 r c^ c y c l e ) from f u l l curve i s exagerated (tf> = 67.5, X = 5461A°. Dell'Oca and Young 63) 44 I f the l a y e r i s made absorbing (k^O) then r e c y c l i n g no longer occurs and each succeeding c y c l e of the curve tends to lower values of f, 2. Two Layers Growing Simultaneously on Tantalum With two l a y e r s growing on a metal the number of p o s s i b i l i t i e s i ncreases r a p i d l y . Perhaps the simplest case, and the one expected from t r a c e r s t u d i e s , i s the case of two non-absorbing l a y e r s w i t h only s l i g h t l y d i f f e r e n t i n d i c e s of r e f r a c t i o n which grow simultaneously at equal r a t e s on the metal. Figure 2-7 shows the case of two l a y e r s w i t h n^<n^. In t h i s case the e l l i p s o m e t r y curve again begins at the zero t h i c k n e s s p o i n t , however, two c y c l e s denoted by a f u l l curve followed by the dashed curve are now r e q u i r e d before r e c y c l i n g occurs. This r e c y c l i n g i s only approximate. That t h i s should occur every two c y c l e s can be shown by l o o k i n g at the equation f o r 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 f o r two l a y e r s on a metal which i s - 2 j 6 1 ^ j U ^ ) - 2 j 6 2 R = r l + r 2 £ + r 3 e + r l r 2 r 3 6 - 2 j 6 1 -2j ( 6 ^ 6 3 ) - 2 j 6 2 1 + r i r 2 e + r i r 3 e + r ^ e R does not r e t u r n to i t s o r i g i n a l value when the t o t a l phase change i n c r o s s i n g the f i l m reaches 180° as i n the case of a s i n g l e l a y e r . This i s because the terms i n 5^ and 8^ (which are approximately 90° i f the i n d i c e s d i f f e r only s l i g h t l y ) have changed s i g n . However, when S^+S^ - 360°, R re t u r n s to i t s o r i -g i n a l value and i n t h i s way there i s a tendency to r e c y c l e every twice around 63 the curve. Furthermore, s i n c e n^ = and n^< n^ < n^ then | | << or I r e l a n d s i n c e a l l ! r^| < x> the e l l i p s o m e t r y curve f o r the two l a y e r s remains i n the v i c i n i t y of the e l l i p s o m e t r y curve of a s i n g l e l a y e r of the same average index because R i s approximately, - 2 ^ ( 6 ^ 2 ) -IjiSj+S^ R = (r± + r 3 e ) / (1 + r ^ r e ) 45 the same as for a single f i l m case. The ellipsometry curve c h a r a c t e r i s t i c of two layers with n^ > n^ i s sketched on the ri g h t . This curve d i f f e r s from the curve i n the case n^ < n^ (Fig. 2-7) i n that the f i r s t cycle ( f u l l curve) i s traced out mostly to the r i g h t rather than to the l e f t of the second cycle (dashed l i n e ) . That t h i s should occur at le a s t at points on the curve where 6^ +62 = 0 or - 180° can be shown as follows. The r e f l e c t i o n c o e f f i c i e n t at <5^ +62 - 180° i s given approximately by R(180) - ( r i ~ r 2 + r 3 ~ r l r 2 r 3 ^ ^ ^ 1 _ r l r 2 + r l r 3 ~ r 2 r 3 ' ) Then the r a t i o of r e f l e c t i o n c o e f f i c i e n t s at 0° and 180° t o t a l phase Is given by x as where x = R(0)/R(180) = (a+br 2) / (a-br 2) J. J. 2 J - 2 2 2 / ^ 2 t \2 a = r 1 + r 3 + r 1 r 3 + r 1 r 3 - r 1 r 2 - r 2 r 3 - ( r 1 r 2 ) ^ - ( r ^ ) r± and b = l - r i 2 _ ^  + ( r i r 3 ) The r a t i o of the r e l a t i v e amplitude attenuation between 0° and 180° i s tanr(0) |R ( O ) | / | R ( O ) _E s  R (0) / R (180) P P  tan¥(180) |R (180)|/|R (180)| | R (0)|/|R (180)| [X | p s s s s This equation shows whether ¥(180) i s smaller or larger than ¥(0). For the values of the indic e s considered, i . e . , n, - n„ = 2.22 and n^ =3.3 - 2.3i , 1 2 3 the quantity b i s greater than zero. Then the case of n^ < n 2 gives r 2 > 0, r„ < 0, I x | > 1.- I x I < 1 and I x l/|x I <1 which shows f(180) < v ( 0 ) as expected 2s — 1 p 1 — 1 s 1 — 1 p' s' — — 360 300 240 QJ 780 WOO / / 712400 ft u 60 3600 900 +o + o F i g . 2-8: o \ I2700 \\0.0A„ ; K 0 0 \ g / BARE SURFACE 1201 > V 4200 & y>j6oo 4 4 0 0 Curve f i t t e d ellipsometry r e s u l t s from Ta anodized i n d i l u t e H3PO4 (//4, table 2-4). +, x, o and A denote successive cycles of experimental points-. n-[_-=2.145, n2=2.22, G=0.51 and Nm=3.3-2.25j used to compute curve and numbers on curve which represent thickness i n A°. 200 3000 3 ^ END 1900 ip/deg 47 ( f i g u r e 2-7). The other case, — n 2 reverses a l l the e q u a l i t y c o n d i t i o n s i n previous sentence, thus ¥(180)>_ ¥ ( 0 ) , again as expected. Other cases can occur f o r two l a y e r s on a metal. The l a y e r s may grow at unequal r a t e s i n which case, d i f f e r e n t e l l i p s o m e t r y curves are traced out. One or both l a y e r s may be made absorbing. In t h i s case the e l l i p s o m e t r y curve no longer r e c y c l e s and the two c y c l e s tend to lower 4! values as the thi c k n e s s i n c r e a s e s . F i n a l l y , the case where one l a y e r has a f i x e d t h i c k n e s s w i t h the other l a y e r growing gives e l l i s o m e t r y curves w i t h the same c h a r a c t e r i s t i c s as f o r one l a y e r groxving on a metal (previous s e c t i o n ) . In summary, c a l c u l a t i o n s i n d i c a t e that only a s l i g h t d i f f e r e n c e i n index i s needed f o r e l l i p s o m e t r y to detect the two l a y e r s t r u c t u r e of oxides growing on tantalum. computed p o i n t s . i - 1 4. EXPERIMENTAL RESULTS AND DISCUSSION 1. O p t i c a l P r o p e r t i e s of Anodic Oxides Formed i n H^PO^ or ^2*^4 E l e c t r o l y t e s E l l i p s o m e t r y r e s u l t s were obtained i n a i r and i n s i t u on oxides grown i n v a r i o u s e l e c t r o l y t e s at 25° C and at d i f f e r e n t current d e n s i t i e s on tantalum p o l i s h e d by d i f f e r e n t methods. T y p i c a l r e s u l t s and f i t t e d curves are presented i n ^ Figures 2-8 to 2-10. A l l e l l i p s o m e t r y measure-ments x^ere made w i t h an angle of incidence of 67.5° o and l i g h t of 5461 A. The experimental r e s u l t s were f i r s t curve f i t t e d by matching computed and experimental A-V p l o t s . L a t e r the computer was programmed to f i n d the best f i t t i n g curve to experimental p o i n t s . experimental p o i n t 4lf 48 O p t i c a l Parameters • De v i a t i o n s F i n a l o Th ickness n l n 2 N = n m m J m G E H < ° A > <a > o A 2 . 1 7 5 * 3 . 3 — 2 . 2 5 J 2 5 5 2 . 6 0 . 7 1 4 5 1 5 2 . 1 6 0 2 . 2 3 0 3 . 3 _ 2 . 2 8 j . 5 1 0 4 5 . 7 0 0 . 3 4 6 0 . 1 7 9 4 4 3 8 2 . 1 5 5 2 . 2 3 0 - 2 . 2 7 J . 5 1 0 2 9 . 8 0 0 . 3 3 0 0 . 1 3 0 4 4 4 4 2 . 1 5 0 2 . 2 2 0 - 2 . 2 6 J . 5 1 0 2 2 . 5 3 0 . 3 2 2 0 . 1 1 4 4 4 6 3 2 . 1 4 5 2 . 2 2 0 - ' 2 . 2 5 J . 5 1 0 1 5 . 1 8 0 . 2 9 5 0 . 0 8 9 4 4 6 8 2 . 1 4 0 2 . 2 1 5 - 2 . 2 4 j . 5 1 0 1 5 . 4 3 0 . 2 9 5 0 . 0 9 5 4 4 8 1 2 . 1 3 5 2 . 2 1 0 - 2 . 2 3 J . 5 1 0 2 1 . 6 0 0 . 3 1 8 0 . 1 2 2 4 4 9 3 2 . 1 3 0 2 . 2 0 5 - 2 . 2 2 J . 5 1 0 3 2 . 3 6 0 . 3 6 9 0 . 1 5 8 4 5 0 6 2 . 1 2 5 2 . 2 0 0 2 . 2 1 J . 5 0 5 4 8 . 5 0 0 . 4 0 9 0 . 2 0 0 4 5 1 8 O p t i c a l Parameters E H 2 n l n 2 N = n m m - j k ' m G = . 5 0 0 . 5 0 5 . 5 1 0 . 5 1 5 . 5 2 0 3 . 3 - 2 . 2 6 J 2 . 2 5 J • 3 0 . 8 2 1 . 5 2 8 . 9 1 6 . 6 3 0 . 5 1 7 . 2 2 . 2 2 2 -2 . 2 4 j 2 . 2 3 J 2 1 . 9 4 3 . 4 2 1 . 4 4 5 . 0 2 6 . 5 4 7 . 5 3 . 3 — 2 . 2 5 J 2 2 . 9 2 0 . 8 2 3 . 7 2 . 1 4 2 . 2 1 5 -2 . 2 4 J 2 . 2 3 J 1 8 . 3 3 1 . 2 1 5 . 4 3 2 7 . 6 1 7 . 5 2 8 . 8 3 . 3 _ 2 . 2 5 J 3 4 . 9 3 1 . 9 3 3 . 3 4 3 9 . 6 2 . 2 1 0 -2 . 2 4 J 2 . 2 3 J 2 1 . 2 2 0 . 2 1 7 . 6 1 9 . 9 1 7 . 9 2 4 . 2 Table 2 - 3 Upper: Shows method used i n curve f i t t i n g e l l i p s o m e t r y r e s u l t s by f i n d i n g minima i n E H 2 i n t h i s case f o r the 6 9 experimental A , ¥ p o i n t s i n f i g u r e 2 - 8 . Lower: Shows how minimum i n upper p a r t of t a b l e i s obtained f o r each value of . * Best s i n g l e f i l m f i t to p o i n t s r e s t r a i n i n g k to 2 . 2 5 . 49 In t h i s method the computer computes a A-1!' curve as a f u n c t i o n of f i l m t h i c k n e s s which i s increased i n increments. As the computed curve goes past an experimental 2 point i n the A-'F plane II i s found. H i s the perpendicular d i s t a n c e between 2 the curve and the p o i n t as shown on previous page. H i s computed f o r 2 a l l p o i n t s to give DI . The program then v a r i e s the o p t i c a l p r o p e r t i e s (input data) 2 so that EH i s minimized. This gives the best f i t on the c r i t e r i a that the com-puted and experimental ¥ values compared were weighted by a f a c t o r of four i n 2 determining each H . The f i l m t h i c k n e s s represented by an experimental p o i n t , t i l e.g., the t h i c k n e s s of the j p o i n t i s given i n terms of the f i l m t h i c k n e s s at the i * " ^ and i t b + l computed p o i n t s by d. = d. + (x/o)(d -d.) 3 i i + l i A b e t t e r estimate of the d e v i a t i o n and a check of the weighting c r i t e r i a was obtained by determining the mean standard d e v i a t i o n <o"^ > and <o^> f o r a l l p o i n t s by comparing p o i n t s computed using d 's and experimental p o i n t s . The ¥ values were not weighted i n t h i s case. Curve f i t t i n g was c a r r i e d out ...using an o p t i c a l model f o r the oxide f i l m which c o n s i s t e d of one c r two non-absorbing homogeneous l a y e r s . In the two l a y e r case G was defined as the r a t i o of i n c r e a s e i n outer l a y e r to the i n c r e a s e i n 2 f i l m t h i c k n e s s during an a n o d i z a t i o n . The minimum i n EH or the best f i t t i n g curve was found by v a r y i n g n^ f o r one l a y e r or n^,n^ and G f o r two layers, a l l i n steps of 0.005. The a b s o r p t i o n c o e f f i c i e n t of the metal, k , was a l s o v a r i e d m but i n steps of 0.01 w h i l e the index of the metal was f i x e d at 3.3 ( t h i s i s discussed l a t e r ) . Table 2-3 shows the method employed i n a t y p i c a l determination 2 2 of the minimum i n EH . In t h i s t a b l e i t i s seen that <a >,<a > and EH go through a minimum about the same time. This was found to be the case f o r a l l other r e s u l t s f i t t e d which are summarized i n Table 2-4. Thus the c r i t e r i a of weighting f by a f a c t o r of four i s v a l i d i n determining the best f i t and the o p t i c a l prop-e r t i e s of the f i l m and l a t e r i t w i l l be shown that i t i s a l s o v a l i d because^ i s „ „ ,, O p t i c a l Parameters Deviations „. ., Forma- Growth . # of F i n a l W : :ion Conditions E l l i p s o m e t r y Cycles - P t s . n l n 2 N = m. = n m m G <°A > Thickne A° 1 1 aDSA 1 - 13 2.210 3. 3 - 2.25J 0.270 0.140 1410 2 1 bDSA <2 - 29 2.215 3. 3 - 2.29J 0.488 0.155 2143 3 1 aDSW >1 - 19 2.20 3. 3 - 2.23J 1.790 0.170 1889 4 1 aDPA >3 - 69 2.145 2.22 3. .3 - 2.25J 0.510 0.295 0.089 4468 2.150 - 2.18J 1.08 0.386 4569 5 1 bDPA >2 - 41 2.145 2.215 - 2.29J 0.525 0.494 0.138 3278 2.155 - 2.23J 0.834 0.342 3316 6 1 cDPA >2 - 18 2.145 2.225 - 2.30J 0.520 0.319 0.122 3259 2.155 - 2.22J 1.630 0.147 3306 7 . 1 aDPW >2 - 52 2.14 2.20 - 2.24J 0.50 1.600 0.288 3683 2.165 - 2.24j 1.980 0.374 3689 8 10 cDPA >2 - 33 2.140 2.225 - 2.30J 0.565 0.537 0.155 3124 2.155 - 2.23J 0.950 0.367 3166 9 10 cDPW >2 - 29 2.145 2.20 - 2.31J 0.56 2.'500 0.330 2930 2.155 - 2.25J 3.360 0.408 2949 10 1 aCPA <1 - 21 1.980 2.22 - 2.24 0.65 0.390 0.105 1246 2. 000-0.028-i - 2.18 0.990 0.250 1305 Code used i n d i c a t e s : current d e n s i t y (1 or 10 mA/cm ); Ta specimen p r e p a r a t i o n (a,b or c ) ; growth i n d i l u t e s o l u t i o n (D), or concentrated s o l u t i o n (C); H SO,(S) or H PO. (P); measured i n a i r (A) or i n s i t u (W). Table 2-4 Summarizes the o p t i c a l p r o p e r t i e s (parameters of best f i t ) of oxides grown i n d i l u t e (0.2 N) H^SO^ and i n d i l u t e (0.23 N) or concentrated (85%) H^PO^ and other,data obtained by curve f i t t i n g e l l i p s o m e t r y r e s u l t s u s i n g a one or two l a y e r o p t i c a l model f o r the oxide. For oxides grown i n H^PO^ (#4 to 10) both the double and s i n g l e l a y e r f i t i s given. ( S i n g l e l a y e r i s denoted by no values f o r and G\ U l o 51 measured more a c c u r a t e l y than A. a) Oxides grown i n phosphoric a c i d e l e c t r o l y t e s The experimental e l l i p s o m e t r y curves obtained from oxides formed i n H„P0. e l e c t r o l y t e s i n d i c a t e that the oxide i s non-uniform and c o n s i s t s of 3 4 two l a y e r s . Table 2-4 (#4 to 10) summarizes the o p t i c a l parameters obtained from f i t t i n g these r e s u l t s on a two l a y e r model. This t a b l e a l s o gives the best f i t obtained using a one l a y e r model. Consider f i g u r e 2-8 which shows a t y p i c a l e l l i p s o m e t r y r e s u l t s and 2 f i t t e d curve f o r a mechanically p o l i s h e d specimen anodized at 1 mA/cm i n 0.23 N H^PO^ and measured i n a i r . The experimental p o i n t s obtained cover more than 63 three " c y c l e s " i n the A-V p l o t . The experimental curve begins at the bare surface p o i n t which represents unanodized Ta. As oxide growth proceeds or as v o l t a g e increases during a n o d i z a t i o n at constant c u r r e n t , the f i r s t c y c l e of experimental p o i n t s denoted by crosses i s traced out i n the d i r e c t i o n of the arrow. This i s f o l l o w e d by the second c y c l e denoted by c i r c l e s . Next i s the t h i r d c y c l e denoted by x's which l i e s e s s e n t i a l l y on the same curve as the f i r s t c y c l e . A n o d i z a t i o n ended part way i n t o the f o u r t h c y c l e on the t r i a n g u l a r p o i n t s which s t a r t out along the curve of the second c y c l e . Oxide breakdown occurred a f t e r the l a s t t r i a n g u l a r p o i n t . The best f i t to these r e s u l t s i n d i c a t e s that the oxide f i l m c o n s i s t s of two l a y e r s which grow simultaneously during a n o d i z a t i o n w i t h G = 0.51, n = 2.145 and = 2.22 and w i t h a standard d e v i a t i o n between computed and experimental p o i n t s of < 0 ^ > = u > 0 8 9 and <o"^ > = 0.295 ( t a b l e 2-3 and #4 t a b l e 2-4). R e s u l t s from i n s i t u e l l i p s o m e t r y measurements of oxides grown i n 0.23N H^PO^ were f i t t e d using 1.334 7 as the index of r e f r a c t i o n of the e l e c t r o -l y t e which was obtained from the r e l a t i o n given by Edwards, Dunn and H a t f i e l d ^ The f i t to these r e s u l t s i s not as good as f o r the dry measurements because of 52 360r 300 2401 180^ 7400 END 650 / L2150 V P 2300 1200 120 60 0 2500 F i g . 2-9: Curve f i t t e d i n s i t u e l l i p s o m e t r y r e s u l t s from Ta anodized i n d i l u t e H3PO^ (#7, t a b l e 2-4). +, x and o denote successive c y c l e s and n-^=2.14, n 2=2.20, G=0.51 and N m=3.3-2.24j used to comDute curve. AO A "BARE" SURFACE 3300/ 30^--450 zjoor J+x^^zD 3600 C X 2400 3675. 12 24 35 48 , /rJ so y/deg 72 84 53 systematic e r r o r s introduced by the windows (see t h i s chapter, s e c t i o n 5 . I f ) . However, these r e s u l t s a l s o i n d i c a t e that the oxide c o n s i s t s of two l a y e r s (e.g. F i g . 2-9) and that a two l a y e r model f i t s these r e s u l t s b e t t e r than a one la y e r model re g a r d l e s s of systematic e r r o r s ( t a b l e 2-4). E l l i p s o m e t r y r e s u l t s obtained from measurements made i n a i r on an oxide formed i n concentrated (85%) H_PO. a l s o i n d i c a t e that the oxide i s two . . 3 4 lay e r e d , even though, i n t h i s case only about three quarters of an e l l i p s o m e t r y c y c l e i s obtained before oxide breakdown occurs at about 95 v o l t s . In t h i s case using the index of the inner l a y e r (2.22) as found above the f i t to the r e s u l t s i s b e t t e r than that obtained using a s i n g l e l a y e r , even i f the s i n g l e l a y e r was absorbing ( t a b l e 2-4, //10). Curve f i t t i n g of r e s u l t s obtained from anodiza-t i o n i n a sequence of e l e c t r o l y t e s a l s o i n d i c a t e s that the two l a y e r model i s d e f i n i t l y more appropriate than the s i n g l e l a y e r f o r oxides grown i n 85% E^PO^ (see next section,-#2) . Thus, the r e s u l t s presented i n t a b l e 2-4 are c o n s i s t e n t w i t h the non-12 o p t i c a l r e s u l t s of Rand a l l et a l . i n that oxides grown i n E^PO^ e l e c t r o l y t e s c o n s i s t of two l a y e r s which grow simultaneously during a n o d i z a t i o n , that the p r o p e r t i e s of the outer l a y e r are modified due to e l e c t r o l y t e i n c o r p o r a t i o n i n t o t h i s l a y e r on growth;and that G incr e a s e s w i t h current d e n s i t y and e l e c t r o l y t e c o n c e n t r a t i o n . Furthermore, e l e c t r o l y t e i n c o r p o r a t i o n decreases the index of r e f r a c t i o n of the outer l a y e r from that of the inner l a y e r which has approximately the same index as obtained from oxides formed i n d i l u t e H„SO,. I 4 b) Oxides formed i n 0.2N H oS0, 2 4 The e l l i p s o m e t r y r e s u l t s f o r growth i n d i l u t e H^SO^ are c o n s i s t e n t 1 23 w i t h e a r l i e r r e s u l t s ' i n that the curve has c h a r a c t e r i s t i c s e x h i b i t e d by a one l a y e r f i l m on tantalum ( F i g . 2-10). 2 Curve f i t t i n g these r e s u l t s on a one l a y e r model produced £H which could not be s i g n i f i c a n t l y improved upon by curve f i t t i n g using a two l a y e r model. 360 300 240-CL) X *3 180 54 anodized i n d i l u t e K^SO^. and 2 nd cycles Experimental e l l i p s o m e t r y r e s u l t s on Ta o and x: 1 s t e l e c t r o c h e m i c a l l y p o l i s h e d Ta. +: 1 s t c y c l e , mechanically p o l i s h e d Ta. Curve computed using n-^=2.22 and N r a=3.3-2.3j. 120 \ 0.0A H 100 B A R E SURFACE \ 200 60 300 CX 400 0 20 SOO^x J • Q 30 yj/deg 40 50 Thus the non-uniformity of anodic oxides produced i n d i l u t e I ^ ^ 0 ^ ^ , a s n o t been detected so f a r . The index of r e f r a c t i o n of the f i l m was determined to be 23 2.21 ( t a b l e 2-4 #1 to 3) c o n s i s t e n t w i t h 2.22 found by Young and Zobel and i s s i m i l a r to the index of the inner l a y e r of oxides produced i n d i l u t e H^PO 2. A n o d i z a t i o n i n a Sequence of E l e c t r o l y t e s E l l i p s o m e t r y result's were a l s o obtained from oxides grown i n a 2 sequence of e l e c t r o l y t e s at 25° C on tantalum at 1 ma/cm and measured w i t h the el l i p s o m e t e r i n a i r . Figure 2-11 presents the r e s u l t s of an oxide grown on mechanically p o l i s h e d Ta to about 40 v o l t s i n concentrated (85%) H P0^ and then followed by a formation i n d i l u t e (0.2N) H^SO^. I f growth was c a r r i e d out only i n the concentrated a c i d , the curve would commence at the po i n t marked "bare" surface f o l l o w the plus signs and end on the dashed l i n e , a f t e r t h i s p o i n t , or approximately 95 v o l t s , the oxide would breakdown. However by changing from formation i n the concentrated to the d i l u t e e l e c t r o l y t e , the oxide may be grown t h i c k e r and more than one c y c l e of the e l l i p s o m e t r y curve i s obtained and these are denoted i n succession by l i n e s w i t h +, x, 0 signs r e s p e c t i v e l y . On sw i t c h i n g from the concentrated to the d i l u t e e l e c t r o l y t e the e l l i p s o m e t r y curve at f i r s t remains i n the p r o x i m i t y of the e l l i p s o m e t r y curve t y p i c a l of formation i n the concentrated a c i d and only s l o w l y d e v i a t e s from i t as a n o d i z a t i o n continues. Figure 2-12 shows s i m i l a r r e s u l t s but w i t h f i t t e d e l l i p s o m e t r y curve of an oxide formed on e l e c t r o p o l i s h e d Ta i n 85% H„P0. to about 45 v o l t s and then f o l l o w e d by formation i n d i l u t e (0.23 N) 3 4 H 3P0 4. Curve f i t t i n g of these r e s u l t s was c a r r i e d out using the model that the i n i t i a l oxide produced i n the f i r s t a n o d i z a t i o n was unaffe c t e d by the second a n o d i z a t i o n and that the oxide produced during the second a n o d i z a t i o n had the i n d i c e s of r e f r a c t i o n of oxides produced i n the second e l e c t r o l y t e alone ( t a b l e 2-4). Using t h i s model i t was found: a) that a f i t to the experimental 56 p / d e g 2-11:- Experimental e l l i p s o m e t r y r e s u l t s on tantalum anodized i n concentrated phosphoric a c i d f o l lowed by a n o d i z a t i o n i n d i l u t e s u l p h u r i c a c i d ( c v c l e s are denoted i n succession by +, o and x, Dell'Oca and Y o u n g 6 3 ) . 57 r e s u l t s could only be obtained i f the i n i t i a l oxide was sandwiched between two l a y e r s of oxide which grow simultaneously during the second a n o d i z a t i o n . 2 b) In t h i s f i t the minima i n EH was t e n f o l d lower i f the i n i t i a l oxide grown i n concentrated H PO^ co n s i s t e d of two non-absorbing l a y e r s rather than a s i n g l e absorbing l a y e r (as i n t a b l e 2-4). c) That G f o r the second a n o d i z a t i o n i n d i l u t e H_PO. has about the same value as f o r formation i n t h i s e l e c t r o l y t e 3 4 23 alone, and d) These r e s u l t s o p t i c a l l y v e r i f y the r e s u l t s of Rand a l l et a l . that the oxide produced i n successive e l e c t r o l y t e s c o n s i s t s of three d i s t i n c t l a y e r s ; - an outer l a y e r t y p i c a l of the new e l e c t r o l y t e - a middle l a y e r which i s the outer l a y e r from the f i r s t a n o d i z a t i o n - and - an inner l a y e r which c o n s i s t s of the two inner l a y e r s which would occur from separate a n o d i z a t i o n i n the two e l e c t r o l y t e s , these two l a y e r s have the same p r o p e r t i e s . The r e s u l t s presented here are tabulated (Table 2-5). SEQUENCE 1 SEQUENCE 2 1st A n o d i z a t i o n 2nd An o d i z a t i o n 1st A n o d i z a t i o n 2nd Ano d i z a t i o n Specimen Mech a n i c a l l y P o l i s h e d Ta E l e c t r o c h e m i c a l l y P o l i s h e d Ta E l e c t r o l y t e 85% H 3P0 4 0.2N H 2S0 4 85% H 3P0 4 0.23N F- 3P0 4 1.98 2.22 1.98 2.14 n 2 2.22 1.98 2.22 1.98 n 3 2.22 ' 2.22 G 0.63 0.44 0.70 .50 ' N m 3.3 - 2.25j 3.3 - 2.28j // of exp. p t s . 5 39 5 32 <cf> 0.13 0.35 0.06 0.375 <a> 0.42 0.71 0.08 0.63 A T o t a l Thickness (A) 527 3395 552 '3322 Table 2-5: Data f o r f i t t i n g e l l i p s o m e t r y r e s u l t s from oxides formed i n a sequence of e l e c t r o l y t e s , n , n_, n 3 and N^ are from t a b l e 2-4 and are used to f i n d G of 1 s t and 2 n° a n o d i z a t i o n . 2-12: As in figure 2-11, except followed by anodization i n d i l u t e phos-phoric acid and with f i t t e d curve computed from the values given i n table 2-5 for sequence 2. 59 The standard d e v i a t i o n s <o > and <a> i n the second a n o d i z a t i o n A H' ( t a b l e 2-5) are l a r g e r than those observed from a n o d i z a t i o n i n a s i n g l e e l e c t r o l y t e and measured i n a i r ( t a b l e 2-4). I t would be reasonable to expect that the presence of the i n i t i a l oxide would a f f e c t the p r o p e r t i e s of the second oxide and v i c e versa. To check t h i s , G of the i n i t i a l o xide, and n^ and n^ of the new oxide were v a r i e d from the values set by the f i t to experimental r e s u l t s , i . e . i s procedure d i d not n o t i c e a b l y improve the f i t to experimental r e s u l t s , i . e . the 2 q u a n t i t y EH decreased by l e s s than 5%. The p o s s i b i l i t y that during the second a n o d i z a t i o n G changes only slowly towards a value t y p i c a l of t h i s a n o d i z a t i o n was examined as f o l l o w s . The model was assumed as i n the i n i t i a l curve f i t t i n g procedure, however t h i s time the experimental p o i n t s were f i t t e d i n succession f i v e p o i n t s at a time 2 and overlapping two p o i n t s of the previous f i v e each time. That i s , EH was minimized f o r the f i r s t set of f i v e p o i n t s to f i n d the best G which was used to compute the f i l m t hickness at the t h i r d p o i n t i n t h i s set and t h i s f i l m t h i c k n e s s served as the i n i t i a l c o n d i t i o n f o r f i t t i n g of the next f i v e p o i n t s which included the l a s t two p o i n t s i n the f i r s t s e t . This method was not e n t i r e l y s u c c e s s f u l i n showing that G d i d change. Although, f o r the second a n o d i z a t i o n s t i n 0.2N ^SO^, G d i d decrease sl o w l y from a value t y p i c a l of the 1 e l e c t r o -o l y t e to about 0.35 i n the f i r s t 2000 A growth i n the second e l e c t r o l y t e . However, a f t e r t h i s point G f l u c t u a t e d e r r a t i c a l l y as was the case f o r the e n t i r e r e s u l t s where the second e l e c t r o l y t e was 0.2N H^ PO^ -. Such an a n a l y s i s i s not r e a l l y f e a s i b l e since an e r r o r i n one experimental point can have a l a r g e a f f e c t on G and t h i s i n turn w i l l a f f e c t the f i t of a l l subsequent set s of p o i n t s . 60 3. O p t i c a l Properties of Tantalum 47 Previous work i n t h i s laboratory using r e f l e c t i v i t y of p l i g h t and 4 8 ellipsometry measurements showed that the "apparent" o p t i c a l properties determined from unanodized tantalum specimen were i n error because of a t h i n f i l m overlying the metal. The true o p t i c a l properties of tantalum were then ob-tained by extrapolation to zero f i l m thickness of by curve f i t t i n g . In p a r t i c u l a r 23 Young and Zobel compared calculated and computed ellipsometry curves obtained for the same growth and measurement conditions of #2 (table 2-4) and assuming a homogeneous f i l m they determined that the metal film.had an index, N = (3.3 + 0.02) - J(2.3 + 0.05). m In t h i s i n v e s t i g a t i o n i t was found that by varying k along with n^, and G the f i t to the r e s u l t s from mechanically polished specimens improved considerably (table 2-3). It was not checked whether the same improvement could 2 have been obtained by varying n instead of k . However, once the best EH J m m was determined, i t was not improved by changing keeping a l l the other para-meters f i x e d . Using t h i s type of analysis the mechanically polished specimens were found to have a k = 2.24 + 0.02 and the ele c t r o p o l i s h e d specimens had m a k =2.29+0.02 (table 2-4). The l a t t e r value of k agrees with the value of m - - m Young and Zobel. The e f f e c t of surface preparation on o p t i c a l properties of the oxide i s not noticeable as can be seen from the s i m i l a r values of n^ and from the d i f f e r e n t preparation methods (table 2-4). Thus the two layer nature of the H^PO^ grown oxide i s not a r e s u l t of surface preparation. The thickness of o the i n i t i a l oxide on the unanodized tantalum was between 40 and 85 A, being greater for mechanically prepared specimens (table 2-6). Table 2-6 also shows that the A and lF for the unanodized metal except for one case, are as good as the best obtained i n curve f i t t i n g (table 2-4). This does not imply that the i n i t i a l f i l m has the same properties as the grown oxide since the p o s i t i o n 61 of the e l l i p s o m e t r y curve i s f a i r l y i n s e n s i t i v e to the i n d e x of r e f r a c t i o n of the f i l m f o r f i l m s of t h i s t h i c k n e s s . Formation A e e a) Mecha n i c a l l y p o l i s h e d Ta A¥ = ¥ - ¥ c e AA = A - A c e b) E l e c t r o p o l i s h e d Ta <v ,19 <a> = .22 d(A) 1 24.25 120, .98 .38 .42 67.0 4 24.13 118, .28 .04 .05 79.0 7 22.85 99, .52 -.02 -.08 81.8 10 23.71 123, ,68 -.09 -.11 55.4 sequence 1 23.95 119, .80 -.16 -.21 73.2 2 23. ,87 126.72 .14 .12 40.3 5 23. .87 123.32 .08 .08 42.4 6 24. .04 124.80 .09 .10 49.2 8 24. ,06 124.96 .11 .12 48.7 sequence 2 23. ,86 124.84 --.-12 <a > =0.11 -.14 <a > = .115 A 50.4 Table 2-6: P r o p e r t i e s of mechanical and e l e c t r o c h e m i c a l l y p o l i s h e d tantalum surfaces determined by the curve f i t t e d r e s u l t s of t a b l e 2-4 and 2-5. Sub-s c r i p t s c and e denote computed and experimental r e s u l t s and d i s the thick n e s s of i n i t i a l f i l m on the unanodized surface. 5. ACCURACY IN DETERMINING OPTICAL PROPERTIES AND THICKNESS OF FILMS 1. E l l i p s o m e t e r Accuracy The accuracy i n determining P q and A q and i n turn A and ¥ depends on a) the inherent accuracy of the instrument which i s a f f e c t e d by o p t i c a l components, alinement e t c . , b) the method of t a k i n g and reducing measurements i using t a b l e 2-1 and c) the presence of a r e a l specimen whose surface i s n e i t h e r i d e a l l y smooth nor f l a t . For the e r r o r d i s c u s s i o n i t w i l l be necessary to know the r e l a t i o n s h i p between A and ¥ and the e x t i n c t i o n p o s i t i o n s . For a quarter wave p l a t e set at w i t h i n one or two degrees of C = 45° these equations are given w i t h high accuracy by the two equations from appendix A as tanA = sinS tan2(P-C) A-7' w i t h cos 2lF = -cos6 cos 2P A - 8 ' o and w i t h cot 'V = tan ¥ „ A-9' ol o2 and f o r Y, tanV = cot 4' .tan a = cot 4' „tan a A - 1 0 ' o l p o2 s The d i s c u s s i o n w i l l . b e f i r s t concerned w i t h e r r o r s i n e l l i p s o m e t r y measurements made i n a i r . a. Analyzer and P o l a r i z e r The analyzer and p o l a r i z e r prism are taken as i d e a l components w i t h i n the accuracy of t h e i r s c a l e s . This i s because the minima observed w i t h analyzer and p o l a r i z e r crossed were sharper and lower than the minima incountered i n the measurement made on the specimen. A l s o , the analyzer and p o l a r i z e r s c a l e s i n cross p o s i t i o n followed each other w i t h i n a standard d e v i a t i o n of l e s s than the u n c e r t a i n t y i n reading the s c a l e s which i s + 0 . 0 1 ° . The random e r r o r i n the c a l i b r a t i o n of the zero p o s i t i o n of the p o l a r i z e r and analyzer s c a l e w i t h respect to the plane of inc i d e n c e was s m a l l . Of s i x c a l i b r a t i o n s performed i n the past year using an A l m i r r o r at 70° i n c i -dence and a l s o checked w i t h a s t a i n l e s s s t e e l m i r r o r the c o r r e c t i o n to the s c a l e was found to be - 0 . 7 8 ° w i t h a standard d e v i a t i o n of 0 . 0 2 ° and maximum d e v i a t i o n of + 0 . 0 3 ° . This c o r r e c t i o n , - 0 . 7 8 ° , to the readings A and P need not be made - o o i f readings are averaged over four zones and f o r readings made i n two zones, only P need be c o r r e c t e d . These c o n d i t i o n s a r i s e from t a b l e 2 - 1 . • o b. Compensator Improper s e t t i n g of quarter wave p l a t e introduces a systematic e r r o r i n A and P when two zones are read as expe r i m e n t a l l y shown i n the t a b l e on the o o next page ' ( c = 4 4 . 8 0 ° i s the c a l i b r a t e d p o s i t o n to give the 45° s e t t i n g of the compensator). 63 Compensator P A S e t t i n g (C) ° 0 46.00° -30.64° 47.52° 44.80 -29.26 47.36 45.60 -27.88 47.20 AP - -1.1AC AA = 0.13AC o o •That AP a AC f o r a AC of one or two degrees i s a l s o p r e d i c t e d from o equation A-7', which f o r these v a r i a t i o n s i s s t i l l a good approximation of A-7. The compensator s c a l e i s set w i t h respect to the P s c a l e when P and A are crossed, by f i n d i n g the average of compensator readings at equal i n t e n -s i t i e s on e i t h e r s i d e of the minimum. The minimum may be obtained w i t h i n a stand-ard d e v i a t i o n of l e s s than 0.005°. However, the compensator can only be set to the s c a l e accuracy of the p o l a r i z e r and to i t s own s c a l e accuracy. With t h i s method the systematic e r r o r i n P^ or p can be kept to l e s s than 0.04°. The e r r o r i n A i s smaller and cancels out when a i s determined from the average of o A and 180° - A ( t a b l e 2-1). I f measurements are made i n four zones the e r r o r o o i n p . and a cancel out provided the same e r r o r i s made i n s e t t i n g C at 45° and at -45° ( t a b l e 2-1). A quarter wave p l a t e w i t h a phase r e t a r d a t i o n not equal to 90° a l s o introduces a systematic e r r o r i n P . This can be shown from equation o A-7' where f o r a given A, dP o | = s i n 4P /4 tan5 d6 1A o' The quarter wave p l a t e s u p p l i e d has a 6 >_86°. Thus the maximum e r r o r i n P^ can be 0.07°. E f f e c t of compensator on analyzer i s discussed i n s e c t i o n e. c. V a r i a t i o n i n Angle of Incidence V a r i a t i o n i n angle of i n c i d e n c e a r i s e s from r o t a t i o n of p o l a r i z e r and compensator and from the f i n i t e s i z e of entrance and e x i t s l i t r e s p e c t i v e l y of c o l l i m a t o r and telescope. The v a r i a t i o n i n angle of incidence due to r o t a t i o n of p o l a r i z e r and compensator s c a l e shown i n f i g u r e 2-4 f o r the case of alinement f o r t a k i n g readings i n four zones i s approximately Acj> = (1/60) (-2 cos (P-20°) - 2 s i n 2C) 2.16 where Acj) i s the change i n angle of i n c i d e n c e . For alinement and readings taken i n two zones 2.16 reduces to A<f> - -.033 cos (P-20°) 2.16' From t h i s equation i t i s seen that f o r any one zone i f = P ^ i s read and P Q = P ^ + 180° i s checked, as was done, the average d e v i a t i o n i n angle of i n c i -dence, <Aa>, f o r the p o l a r i z e r i s zero. This then f o l l o w s f o r a l l zones. However fo r A , A + 180° i s not read. In t h i s case the maximum average d e v i a t i o n i n o o ° measuring two zones i s one h a l f that p r e d i c t e d by 2.16' and t h i s i s +0.016°. The f i n i t e s i z e of entrance and e x i t s l i t s of e l l i p s o m e t e r allows l i g h t w i t h a range i n angle of incidence to pass through the e l l i p s o m e t e r . In theory t h i s range i s l i m i t e d by the smallest s l i t , i n p r a c t i c e surface roughness of the specimen, n o n - i d e a l o p t i c a l components and m u l t i p l e r e f l e c t i o n of l i g h t i n the e l l i p s o m e t e r tend to make the e x i t s l i t most important to these e f f e c t s . This i s more so w i t h our e l l i p s o m e t e r where the entrance s l i t i s s maller than the e x i t s l i t which i s 2 mm i n diameter and can c o l l e c t l i g h t over a A<f> of up to 0.4°. Aside from v a r i a t i o n i n angle of i n c i d e n c e , the s l i g h t l y divergent beam which f a l l s on the p o l a r i z e r due to the f i n i t e s i z e of the entrance s l i t may give a s l i g h t degree of e l l i p t i c i t y to the l i g h t emerging from the p o l a r i z e r . This e f f e c t i s dismissed as a p o s s i b l e source of e r r o r f o r the same reasons that the p o l a r i z e r and analyzer were considered i d e a l components. The e x t i n c t i o n c h a r a c t e r i s t i c s of l i g h t r e f l e c t e d from the specimen at various angles of incidence were determined by making measurements on a specimen a l i n e d at cf> = 67.5° w i t h the r e g u l a r telescope s l i t replaced by a smaller s l i t as shown i n the f i g u r e accompanying t a b l e 2-7 and 2-8. Table 2-7 shows the c h a r a c t e r i s t i c s obtained by s e t t i n g the telescope at d i f f e r e n t angles of incidence and using s l i t / / l . Table 2-8 shows the c h a r a c t e r i s t i c as a func-t i o n of s l i t p o s i t i o n w i t h respect to the r e g u l a r s l i t i n t h i s case <j> was 67.5°. o The r e s u l t s i n these two tab l e s were obtained on an oxide grown to about 1820 A on e l e c t r o p o l i s h e d Ta i n 0.2N H„S0, and measured i n a i r . Table 2-9 shows the 2 4 Table 2-7: S l i t // cb ^ R e l a t i v e o I n t e n s i t y v£ ( r e g u l a r s l i t ) 2 QL A3 1 67.66 -29.90 47.14 6 1 67.50 -30.02 49.97 100 1 67.33 -29.75 47.28 6 Table 2-8: S l i t // P ^ R e l a t i v e o I n t e n s i t y Table 2-9: Beam P o s i t i o n P A o o Regular Beam -28.31 51.83 1 -30 .02 46 .97 100 and 2 -30 .05 47 .02 110 -2 -29 .80 47 .20 -15 and 3 -29 .86 47 .29 ~25 3 -29 .86 47 .29 ~6 4 -30 .04 47 .04 »100 #1 2 3 4 5 6 -28.32 51.83 -28.40 51.98 -28.36 51.96 -28.19 51.76 -28.60 52.16 -28.06 51.72 re g u l a r beam v a r i a t i o n i n A and P across the specimen area covered by the beam which were o o obtained using a reduced beam s i z e at p o s i t i o n s on the specimen shown i n the f i g u r e accompanying the t a b l e . The beam s i z e was reduced from about 6 to 1.2 mm i n diameter at the compensator. These measurements were made on the same Ta (j) =67.4 F i g . 2-13: Change i n P and ¥ caused by small v a r i a t i o n i n angle of i n c i d e n c e , <j>, from 67.5°. : change i n p o l a r i z e r , AP, - - - -: change i n analyzer or AY. Both as a f u n c t i o n of A. Computed from two l a y e r model (ni=2.14, n 2=2.21, G=0.51, N m=3.3-2.4j and A=5461A°. S i n g l e l a y e r f i l m (ni=2.22) shows s i m i l a r behaviour. Thickness increases from o to the l e f t as shown by arrow). 0 \ ON specimen as f o r t a b l e s 2-8 and 2-9, however the oxide was 3320 A t h i c k and was from sequence 2, t a b l e 2-5. These t a b l e s i n d i c a t e that the l i g h t c o l l e c t e d at angles other than the set angle of incidence does not c o n t r i b u t e s i g n i f i c a n t l y to A and P s i n c e the o o e x t i n c t i o n i n t e n s i t y of t h i s l i g h t f a l l s o f f r a p i d l y w i t h angle on e i t h e r side of the set angle of i n c i d e n c e . The d e v i a t i o n of A and P measured w i t h the o o small s l i t which gives a Acj) of 0.04° and the r e g u l a r s l i t which gives a Atj) of 0.4° can be c o n t r i b u t e d to the v a r i a t i o n i n A and P over the specimen. This o o v a r i a t i o n i s s u r p r i s i n g l y small c o n s i d e r i n g that A and P at the oxide thickness o o measured here are h i g h l y s e n s i t i v e to changes i n t h i c k n e s s , i . e . , AA^ - 0.16 Ad o and AP = 0.3 Ad, where the thickness d i s i n A. o F i n a l l y , c a l c u l a t i o n s using the o p t i c a l model which represents t h i s o xid i n d i c a t e that f o r small changes i n angle of incidence P^ and A q vary s y m e t r i c a l l y w i t h angle of incidence and that these v a r i a t i o n s which are shown i n f i g u r e 2-13 can be represented by: AP = 2.2 Ad) cos 2P o o 2.17 AA < 1.2 Atj) o — These r e s u l t s e l i m i n a t e at l e a s t i n theory the e f f e c t of f i n i t e s l i t s i z e but emphasize the importance of s e t t i n g the angle of incidence c o r r e c t l y . To summarize, the angle of i n c i d e n c e can be set to +0.006°, r o t a t i o n of the p o l a r i z e r can cause a Ad) of 0.033, then using 2.17 the e r r o r which can occur i n P or A i s r e s p e c t i v e l y .08 or .04. The v a r i a t i o n s i n A and P due to o o o o s l i t s i z e are r e l a t e d to the measurement of oxide t h i c k n e s s and are not con-sidered as e r r o r s . d. Accuracy of One E x t i n c t i o n S e t t i n g The procedure used i n determining A and P ( s e c t i o n 3d) assumes that • " o o l i g h t v a r i e s symmetrically about the e x t i n c t i o n minima. This assumption was checked at oxide thicknesses which produced the f l a t t e s t minima by determining the 68 minimum as a function of increasing i n t e n s i t y up to ten times the e x t i n c t i o n i n t e n s i t y . The minimum was found to be symmetrical since and P^ could be determined over t h i s i n t e n s t i y range within a standard deviation of 0.01°. For the e x t i n c t i o n i n t e n s i t i e s to be symmetrical i t i s also required that i n determining e x t i n c t i o n at one scale, the other scale i s close to i t s e x t i n c t i o n s e t t i n g . I t was found that the scales could be placed by inspection close enough to e x t i n c t i o n to introduce l i t t l e error i n A and P measured. Table 2-10 o o shows the a f f e c t of one scale set one degree from e x t i n c t i o n on the e x t i n c t i o n p o s i t i o n of the other scale, where i n t h i s minimum the e x t i n c t i o n p o s i t i o n s could be set by inspection to better than 0.5° on the scales. Table 2-10: Analyzer Set Off E x t i n c t i o n P o s i t i o n P o l a r i z e r Set Off E x t i n c t i o n P o s i t i o n A P P A o o 47.79 300.99 301.96 46.80 46.79 300.96 300.96 46.79 45.79 300.94 299.96 46.79 E x t i n c t i o n i s at A = 46.79 , P = 300.96 o o e. Accuracy of Measurements From Two Zones F i g . 2-14 shows the di f f e r e n c e between p and a determined i n zones 4 and 2. In theory t h i s d i f f e r e n c e should be zero, i n p r a c t i c e two or more zones are measured to improve accuracy by averaging. The cause of these d i f -ferences and the r e s u l t i n g error i n A and V are discussed below. Consider f i r s t the differ e n c e i n p values, that i s , Ap = P 2 ~ (P^+90°) (Fig. 2-14). This d i f f e r e n c e can be caused by multiple r e f l e c t i o n s and i n t e r -65 ference e f f e c t s i n the compensator . In our case these e f f e c t s are reduced by the a n t i r e f l e c t i o n coating of the compensator. Differences i n p may also a r i s e from diffe r e n c e i n the transmittance of l i g h t along slow and fast axis of the compensator.^ ^ According to Archer and Shank^, t h i s e f f e c t for the case of a quarter wave plate set at 45°, leads to an approximate r e l a t i o n Ap = -0.5 (1-cT2) cos 2P 4 (radians) 2.18 0.4^ p4/deg F i g . 2-14: D i f f e r e n c e i n a 0: 1 0 _ 1 [Aa=A2' two readings 180 and p between zones two and four as a f u n c t i o n of P^.(from r e s u l t s of f i g . 2-8) (I8O-A4)], x: Ap=P2-(P4+90°J and A: same as x but P 2 and P^ are each average o! apart. 70 Where the notation has been changed s l i g h t l y from the o r i g i n a l and where ais a measure of the r a t i o of the transmittances. These authors further show that for .90 < a < 1.1 the average value of p obtained by the method of McCrackin 6 2 et a l i s accurate to a scale d i v i s i o n (+.01). The experimental points (Fig. 2-14) obey an approximate r e l a t i o n Ap ~ (-2.4/57.3) cos2P 4 (radians) 2.18' This equation has the same form as 2.18 and y i e l d s an a of 1.01, so that the imperfection i n transmittances i s present but not to a degree which e f f e c t s accuracy. F i n a l l y , deviation i n angle of incidence due to r o t a t i o n of the p o l a r i z e r does not give r i s e to appreciable d i f f e r e n c e i n p from zone to zone as e v i -denced by the proximity of the points x and A i n F i g . 2-14. Consider now, the d i f f e r e n c e i n the a values between zones four and two (Fig. 2-14). The displacement of the iAa curve from the P^ axis i s caused by twice the scale c o r r e c t i o n which i s made to the analyzer readings. This cor-r e c t i o n cancels out i n averaging a and a but not i n Aa = a - a . It i s p s s p known that Aa i s caused mainly by quarter wave plate whose retardation d i f f e r s from 90°. However, i t remains to be shown that the dependence of Aa on P^ i s also caused by t h i s e f f e c t . From equation A-10 we have tan ¥ ./tan ¥ „ = tan a /tan a = y o4 o2 p s where for zone 4, P = P, and a = <y' o 4 p o4 and for zone 2, P = P = P + 90° + Ap and a = f ' o 2 4 s d2 where y i s one for a = a . From A-8' y becomes: p s y = (1 + k cos6 + Hcos28)^^2/(1 - k cos6 + Jc.cos^}''2 where and k = cos2P, + cos2:(P .+Ap) 4 4 £ = cos2P. cos2(P.+Ap) 4 4 • 71 Equation 2.19 can be s i m p l i f i e d i n two ways. F i r s t , Ap i s assumed to be zero and t h i s gives (1 + cos5 cos2P.) y = -j- — \ =1 + 2 cos5 cos2P. 2.19' J (1 - cos5 coszP.) 4 4 where i n the approximation 5 i s assumed to be close to 90°. Secondly, Ap i s . not zero and the following approximations are made i n equation 2.19. F i r s t , the 2 £ cos <5 terms are neglected, secondly, each square root i s expanded r e t a i n i n g only terms i n cos6, and t h i r d l y , the denominator i s expanded i n a geometric s e r i e s . These approximations give, y - (1 + 1/2 kcos6)(l + 1/2 kcos6) - 1 + kcos6 Ap i s small and y becomes y = 1 + 2 cos6 (cos2P 4 - 2Ap sin2P^) This equation takes into account the e f f e c t of Ap. Assuming that Ap a r i s e s only because of the transmittance e f f e c t then y - 1 + 2(1 + 2bsin2P 4)cos6 cos2P 4 where Ap = -b cos2P 4 as i n equation (2.18). F i g . 2-15: y = tana /tana g as a function of P^. -o-o- from r e s u l t s of f i g . 2-8, -x-x- from r e s u l t s of i'5 table 2-4. 72 . The observed y (Fig.- 2-14) has an approximate dependence on given by y = 1 + 0.14 cos(2P+60°) 2-20 which i s a curve s h i f t e d by about 60° from the dependence of y on P^ found i n theory. There seems to be no apparent reason why th i s s h i f t occurs except that i t occurs to about the same extent i n measurements made on d i f f e r e n t Ta spe-cimens with d i f f e r e n t anodic oxide f i l m s . Assuming that' the 60° s h i f t does not exist..in 2-20, then from 2-19' a 6 .>_ 86 i s obtained for our quarter ..wave plate The error which occurs i n f due to A a i s not large as long as the approximation (from A-10') , v l / 2 (a +a ) tan¥ = (tan a tan a ) = tan s p p s 2 The maximum error i n ¥ for the deviations i n F i g . 2-14 i s ~ +0.05°. f. Other Errors 54 Winterbottom describes the e f f e c t of m u l t i r e f l e c t i o n s i n the ellipsometer He concludes that 15 or more r e f l e c t i o n s are possi b l e . With our instrument the quarter wave plate has a no n - r e f l e c t i n g coating, furthermore, the p o l a r i z e r and quarter wave plate are not perpendicular to the beam, and f i n a l l y , determination of the c h a r a c t e r i s t i c s of l i g h t coming o f f the s p e c i -men at other than the angle of incidence indicates that the e f f e c t of multiple r e f l e c t i o n s may be neglected. g. Summary of Errors In Measurements Made i n A i r To r e c a p i t u l a t e , f o r the method used i n a l i n i n g the ellipsometer and reducing ellipsometry measurements, the maximum error i n one set of p and a values obtained from ellipsometry measurements made i n two zones i s approxi-mately: p 1. P o l a r i z e r and Analyzer Scale -1-0.03 2. Compensator Scale C a l i b r a t i o n + .04 and 6 >_ 86° - 0 7 3. Changes i n Angle of Incidence + .08 The t o t a l absolute maximum error i n p i s 0.22 and i n a i s 0.1 r e s u l t i n g i n 0.44 and 0.1 maximum error r e s p e c t i v e l y i n A and m . A maximum error i n delta i s not usually accompanied by a maximum error i n p s i . The average error should be much l e s s than the maximum error since the random errors tend to cancel out i n the curve f i t t i n g of many experimental points. Systematic errors do occur i n ellipsometer measurements p a r t i c u l a r l y from 6 4 90° and from compensator and angle of incidence not set c o r r e c t l y . The l a s t two can be kept to a minimum by proper alinement. What can be said a f t e r t h i s error discussion could have been said at the beginning and that i s , the double ellipsometry curve for oxides formed i n H^PO^ cannot be a r e s u l t of a systematic error since each cycle xrould have the same systematic error, unless a) the error depended on oxide thickness and not on A or' ¥;b) a f t e r each cycle or any span of 360° i n A, the ellipsometer i s misalined so that a systematic error occurs i n the opposite d i r e c t i o n to that o the previous cycle. h. Errors i n In Si t u Measurements A l l the errors j u s t discussed occur i n i n s i t u measurements and addi-t i o n a l errors occur because of the s l i g h t birefringence of the c e l l windows and increase i n multiple r e f l e c t i o n s because of the windows. A sin g l e i n s i t u e x t i n c t i o n measurement can only be obtained with a standard deviation of 0.04 i n P and 0.03 i n A . Also, the dif f e r e n c e i n p o o between zones 2 and 4 or between zones 1 and 3 can be as high as 3° ( f i g . 2-16) a +0.01 +0.05 +0.04 74 Such a l a r g e d i f f e r e n c e i n p leads to e r r o r s i n A which can be reduced by tak i n g measurements i n four zones. For four zones the average Ap as defined i n f i g u r e 2-16 reduces to l e s s than 0.8° and has the same dependence as Ap on i n the measurements made i n a i r ( F i g . 2-14). However, the average p values from zones 2 and 4 are approximately the same as the average values from zones 1 and 3. From t a b l e 2-1, these two averages should d i f f e r by twice the s c a l e c o r r e c t i o n or about -1.58°. The a c t u a l d i f f e r e n c e observed 31 F i g . 2-16: D i f f e r e n c e i n p c r Ap between zones as a f u n c t i o n of FA ( f o r i n s i t u e l l i p s o m e t r y measurements shown i n F i g . 2-9).-x—x—denotes P 2-(P^+90). and -o-o-is.P 2-(P 4+90) - [Pi-(?3+90)] which i s the average Ap f o r a l l : four zcnes. i s l e s s than 0.25°. Thus the b i r e f r i n g e n c e of the windows introduces a sys-tematic e r r o r of about a s c a l e c o r r e c t i o n i n P which r e s u l t s i n a A reduced o by twice t h i s e r r o r or about 1.6°. A systematic d i f f e r e n c e between f i t t e d curve and experimental r e s u l t s was i n f a c t observed f o r a l l i n s i t u r e s u l t s . Figure 2-9 shows a t y p i c a l example, i n t h i s case the average systematic d e v i a -t i o n <A computed - A experimental > i s 1.2°. Because of t h i s e r r o r the bulk of the e l l i p s o m e t r y measurements were made i n a i r , although, the i n s i t u r e s u l t s gave approximately the same values as r e s u l t s obtained i n a i r f o r n^, n^, G and k . m 2. Accuracy of Curve F i t t i n g Technique a) Accuracy of C r i t e r i a Curve f i t t i n g was accomplished by v a r y i n g the o p t i c a l parameters used 2 2 i n computing e l l i p s o m e t r y curves u n t i l EH was minimized, where i n computing H the d e v i a t i o n i n Y were weighted by a f a c t o r of four w i t h respect to the d e v i a t i o n i n A. This c r i t e r i a i s v a l i d on two counts; f i r s t , <o > and <a > which i s ' A V 2 unweighted p r e d i c t s the same f i t as EH and secondly the maximum e r r o r i n A i s about four times that i n f . In determining when the computed curve had gone past 2 an experimental p o i n t i n the plane, so that H could be found, only A or only by of experimental and computed p o i n t s were compared r e s p e c t i v e l y depending on whether the d i f f e r e n t i a l r a t e of change w i t h thickness 1-^ 41 or |4T I^ of the 1 Ad 1 Ad computed curve was g r e a t e s t . Where Ad i s the increment i n thi c k n e s s between s u c c e s s i v e l y computed p o i n t s . Thus the f i l m t hickness at the experimental p o i n t was determined by the parameter, AA or A(A<F), which changed most r a p i d l y w i t h t h i c k n e s s . This a n a l y s i s assumes that the curve i s piece-wise l i n e a r w i t h o thickness over Ad which was 20 A. I f the n o n - l i n e a r i t y w i t h t h i c k n e s s i s represented by A , AA AAY n ^d ( Ad ° r ~Ad } A / \ / '\-n? = 2.20 1 i • : i i i i ^5 f 20 \ 15 10 5 0 THICKNESS x 10 / A C a l c u l a t e d v a r i a t i o n i n d e l t a , AA, as a f u n c t i o n of A at a given oxide t h i c k n e s s f o r i n d i v i d u a l incremental changes of the o p t i c a l parameters of two l a y e r s on a metal, where the i n i t i a l values are: n 1=2.14 and k^O.O, n 2=2.21 and k 2=0.0, G=0.5"0; and the metal, N m=3.3-2.24j . 77 then the maximum no n - l i n e a r i t y which i s about the same for A and Ay, i s c a l -°2 culated to be less than 0.0005 deg/A . This may be neglected as a source of error. J b. Accuracy of Parameters In theory an i n d i c a t i o n of the required accuracy i n measuring A and f.can be found by computing the d i f f e r e n t i a l changes AA and AY, for a small increment v a r i a t i o n i n o t p i c a l parameters for a given oxide thickness. A s p e c i f i c example of two layers shown i n the next three graphs (Figs. 2-17 - 2-19). In these figures AT or AA i s given as a function of A for txro c y c l e s , s t a r t i n g at A = 136° representing a zero layer thickness with f i l m thickness increasing to the l e f t as shown i n the lower scale. Only the effect, of an increment i n one d i r e c t i o n i s shown. An increment i n the opposite d i r e c t i o n produced almost symmetrically opposite ¥ and A v a r i a t i o n s . A number of points which can be made from these graphs. Consider for example changed from 2.21 to 2.20. The e f f e c t on A and Y i s quite marked with AA being p o s i t i v e for both c y c l e s , however AY goes negative as well- as 2 p o s i t i v e . In the f i t t i n g technique such a deviation contributes more to EH i f i t occurs i n one d i r e c t i o n . Thus the contribution to EH^ by AY depends mostly on the imaginary part of the indices of r e f r a c t i o n of the layers and the metal while the co n t r i b u t i o n from AA, depends on the r e a l part of the indices and on G.. In t h i s way the s e n s i t i v i t y i s greatest for a l l parameters at A close to zero or 360°. In p a r t i c u l a r an experimental point at t h i s p o s i t i o n c a r r i e s more weight i n determining the parameters giving the best f i t . The s e n s i t i v i t y of AA and AY on . o p t i c a l parameters increases with f i l m thickness being le a s t s e n s i t i v e for very t h i n f i l m s . Consider the r e s u l t s shown i n fi g u r e 2-8. In curve f i t t i n g , the layer were assumed non-absorbing. This i s v a l i d because a) the ellipsometry curve 2 recycles, b) giving k or k„ a value of 0.005 increased EH from the best f i t value and c) assuming that the deviations i n Y between computed and experi-rd mental points at A close to 360° for the 3 cycle are contributed by or k 2 non-zero then k^ or k i s less than 0.001 i f A'F varies l i n e a r l y for small deviations i n these c o e f f i c i e n t s (Fig. 2-13). The accuracy i n determining n^ and n^ i s better than +0.01 and i n G the accuracy better than +0.02. These are obtained assuming that AA i s s o l e l y responsible for small deviations i n these quantities (Fig. 2-17) and the maximum error i n A i s 0.4°. F i n a l l y , n^, n^ and G determined by curve f i t t i n g the r e s u l t s i n a i r (table 2-4) l i e within the accuracy s p e c i f i e d above. The accuracy i n obtaining f i l m thickness within the accuracy set for n^, and G i s better than +1%. Table 2-3 which showed the approach to 2 minimum for EH also gives an i n d i c a t i o n of the v a r i a t i o n s n., n and k which 1 2 m maintain the t o t a l thickness measured to within +1% of thickness determined by the best f i t t i n g curve. This r e l a t i v e i n s e n s i t i v i t y of thickness to o p t i c a l properties a r i s e s from the method used i n determining f i l m thickness, that i s , by the i n t e r s e c t i o n point on the computed curve of the perpendicular from the experimental point to the curve. However, the r e l a t i v e thickness i s s e n s i t i v e to A and Y measured and c a l c u l a t i o n s show that for oxides grown i n d i l u t e H^PO^ the o l i m i t i n s e n s i t i v i t y computed using 20A i n t e r v a l s i s A 4 Y AA 0 < < 0.6 and 0.2 < < 0.7 — Ad — — Ad — o Thus for a maximum error of 0.4° i n A the error i n d i s +2 A. The non-uniformity i n oxide thickness over the area measured found to be smaller than th i s (table 2-9). 6. ON THE APPROPRIATNESS OF THE TWO LAYER MODEL So far i t has been shown, that the o p t i c a l properties can be determined with s u f f i c i e n t accuracy and that an o p t i c a l model c o n s i s t i n g of two homogeneous non-absorbing layers which grow simultaneously during anodization d e f i n i t i v e l y represents the ellipsometry r e s u l t s obtained under two d i f f e r e n t conditions, i n a i r and i n s i t u . This model seems to be the simplest way of representing the non-uniformity of these oxides. Furthermore, i t i s a model which i s expected from the previous non-optical evidence: a) that both metal and oxygen ions move so that the f i l m grows at the outer and inner i n t e r f a c e , b) that r e l a t i v e l y large amounts of phosphate are incorporated into the outer portion of the f i l m even i n d i l u t e s o l u t i o n and c) that t h i s has a marked e f f e c t on the index of r e f r a c t i o n , d i e l e c t r i c p e r m i t t i v i t y and i o n i c conduction. As f a r as the ellipsometry data alone i s concerned a number of questions can be r a i s e d : F i r s t i s a given two layer model d i s t i n c t from a l l other two layer models? Calculations show that for v a r i a t i o n s i n n^, n and G of up to 30% from the values considered here given d i s t i n c t curves. Also i n curve f i t t i n g of the r e s u l t s i n F i g . 2-8 the same o p t i c a l properties were found for d i f f e r e n t i n i t i a l conditions of n^, n^ and G i n curve f i t t i n g . Secondly, i s a two layer model d i s t i n c t form other models? I t i s d e f i n i t e l y d i s t i n c t from a one layer model both i n theory (compare F i g . 2-7 and 2-8) and i n p r a c t i c e (table 2-4). Whether i t i s d i s t i n c t from a l l other models i s impossible to show. F i n a l l y , can the r e s u l t s obtained here be f i t t e d as well by some other p h y s i c a l l y rea-l i z a b l e model other than the two layer model? One such model i s a l i n e a r gra-dient i n n through the thickness of the oxide. Two possible cases can a r i s e . F i r s t , the end points, i . e . , the index of the oxide at the i n t e r f a c e s remains fixed with increasing f i l m thickness which i s d e f i n i t e l y p ossible i f impurities d i f f u s e from metal and e l e c t r o l y t e into the oxide and these could be an excess of metal and oxygen ions r e s p e c t i v e l y . Secondly,, but le s s l i k e l y to occur, the gradient remains fixed furing f i l m growth. The inhomogeneous f i l m was approximated with a stack of homogeneous layers growing simultaneously at the same rate. Since the o p t i c a l measurements 82 F i g . 2-20: Computed e l l i p s o m e t r y curve f o r three l a y e r s growing simultaneously on tantalum (n-^2.12, n 2=2.18, n 3=2.24). Curve s t a r t s at 0.0A° and cy c l e s are numbered at top. 83 determine the product of an average index of the f i l m and t h i c k n e s s , then the case expected to give the best f i t i s 1 d l 1 d2 n, = —— f n(z)dz and n„ = - 7 — /, n(z)dz 1 d i 0 d ? - d l that i s , t h e average index of the outer and inner p o r t i o n of the inhomogeneous f i l m i s the same as that determined i n the two l a y e r s . In which case the gradient and i t s end p o i n t s are a u t o m a t i c a l l y f i x e d f o r the number of l a y e r s used. Thus f o r a one l a y e r approximation the best f i t would occur w i t h an average index ° f n d + n d <n> = - - 2.18 a which i s approximately the case ( t a b l e 2-3). For three or more l a y e r s the f i t obtained to the experimental r e s u l t s of F i g . 2-8 using the above assumptions and up to a 56 l a y e r approximation i s shown i n t a b l e 2-10. The f i t improves w i t h i n c r e a s i n g number of l a y e r s , however, the r a t e of improvement decreases w i t h number of l a y e r s . At the same time the t o t a l t h i c k n e s s which v a r i e s l e s s than 1% i s approaching the value determined by the two l a y e r model. Table 2-10: F i t to experimental r e s u l t s of f i g u r e 2-8 using an inhomogeneous f i l m approximated by a stack of homogeneous l a y e r s . (Index of i t h l a y e r i s given by the index of the f i r s t l a y e r plus i times i n index. Index of the metal i s 3. .3 - 2.24j) • // of Index of Increment F i n a l Layers 1st Layer i n Index < V Thickness 3 2.12 0.06 1.6 0.69 4521 4 2.12 0.04 1.2 0.45 4468 5 2.11 0.02 1.27 0.44 4499 6 2.12 0.02 1.2 0.40 4503 7 2.11 0.02 1.18 0.42 4502 8 2.11 0.02 1.1 0.45 4475 14 2.11 0.01 1.04 0.41 4490 28 2.11 0.005 1.0 0.41 4484 56 2.11 0.0025 0.95 0.44 4488 1* 2.175 2.6 0.71 4515 2* 2.145 0.075 0.295 0.089 4468 * best s i n g l e and double l a y e r f i t ( t a b l e 2-3) . 85 Figures 2-20 and 2-2.1 present the computed e l l i p s o m e t r y curve p l o t t e d by the computer f o r the case of the three and four l a y e r approximation. The small wiggles i n the curve are due to the q u a n t i z a t i o n of the p l o t t i n g pen. From these f i g u r e s i t i s seen that f o r small d i f f e r e n c e s i n i n d i c e s between the l a y e r s : a) that approximate r e c y c l i n g occurs when the number of c y c l e s equals the number of l a y e r s and b) the c h a r a c t e r i s t i c separation at A ~180° between f i r s t and second c y c l e which occurs i n the two l a y e r model does not occur i n these curves. The case t r e a t e d thus f a r was where the end p o i n t s of the index are f i x e d w i t h i n c r e a s i n g t h i c k n e s s . The second case where the index gradient remains f i x e d w i t h t h i c k n e s s i s discounted as f o l l o w s . The f i l m s may be anodized from o about 40 to over 4000 A, thus any gradient chosen must be small or w i t h i n c r e a s i n g thickness a l a r g e d i f f e r e n c e w i l l occur between the index at the end p o i n t s . Since the e l l i p s o m e t r y curve r e c y c l e s every two c y c l e s , t h i s means that the part of the f i l m grown a f t e r r e c y c l i n g must have approximately the same p r o p e r t i e s as the part grown i n the f i r s t two c y c l e s . This i s not the case w i t h a f i x e d gradient,nor f o r that matter, w i t h f i x e d end p o i n t s ( F i g . 2-20, and 2-21). Thus a l i n e a r v a r i a t i o n of n w i t h thickness can f i t the experimental r e s u l t s b e t t e r than a s i n g l e f i l m but d e f i n i t e l y not as w e l l as the txro f i l m model. 86 I I I . IONIC CONDUCTION PROPERTIES" 1. INTRODUCTION In the previous chapter i t was v e r i f i e d using e l l i p s o m e t r y that anodic oxide f i l m s formed i n phosphoric a c i d s o l u t i o n s c o n s i s t of two l a y e r s : an outer l a y e r whose p r o p e r t i e s , because of incorpo r a t e d e l e c t r o l y t e s p e c i e s , are changed from an inner l a y e r which i s f r e e from i n c o r p o r a t i o n and i s considered s t o i -c h iometric Ta 20^ and which i s s i m i l a r to oxides formed i n d i l u t e s u l p h u r i c a c i d e l e c t r o l y t e s where the degree of i n c o r p o r a t i o n i s much l e s s . In t h i s chapter the f i l m t hickness and G determined from e l l i p s o m e t r y are used to deter-mine the i o n i c conduction and d i e l e c t r i c p r o p e r t i e s of the f i l m and of each l a y e r . The p r o p e r t i e s of each l a y e r are obtained by assuming the model that the i o n i c conduction and d i e l e c t r i c behaviour of the inner l a y e r can be approximated by the behaviour of anodic oxide f i l m s formed i n d i l u t e H^SO^. This assump-t i o n n e g l e c t s the e f f e c t of the s l i g h t degree of e l e c t r o l y t e i n c o r p o r a t i o n which occurs i n the outer l a y e r of s u l p h u r i c a c i d grown f i l m s . F i n a l l y , to d i s c u s s i o n t r a n s p o r t , g i s defined analogous to G as the instantaneous r a t i o of growth at the e l e c t r o l y t e i n t e r f a c e to the t o t a l oxide growth, that i s , g = dx^/dx. I f the oxide grown at each i n t e r f a c e has the same d e n s i t y then g i s the metal i o n • tra n s p o r t number which i s the f r a c t i o n of t o t a l i o n current c a r r i e d by the metal i o n . I f the inc o r p o r a t e d m a t e r i a l remains i n the oxide grown at the outer i n t e r -face during growth then at constant current g = G. 68 5 Some of t h i s work has been presented and reviewed . 87 2. RESULTS 1. Constant Current or Steady State Formations Table 3-1 summarizes the average e l e c t r i c f i e l d and the f i e l d i n the outer l a y e r observed i n oxides grown at constant current at 25° C and used i n the o p t i c a l s t u d i e s . Oxides grown i n d i l u t e e l e c t r o l y t e s on mechanically or e l e c t r o -p o l i s h e d specimens give approximately the same f i e l d , however i n concentrated H^PO^ the d i f f e r e n c e between f i e l d s obtained i n the two preparations i s n o t i c e a b l e . The f i e l d s found f o r oxide grown i n 0.2 N H^SO^ are i n agreement w i t h pre-23 vious r e s u l t s and are lower than that found f o r oxides grown under the same c o n d i t i o n s but i n 0.23 N H.PO,. For H„P0. grown oxides the f i e l d i ncreases w i t h 3 4 3 4 e l e c t r o l y t e c o n c e n t r a t i o n i.e., w i t h i n c r e a s i n g i n c o r p o r a t i o n of e l e c t r o l y t e . These r e s u l t s v e r i f y that e l e c t r o l y t e i n c o r p o r a t i o n increases f i e l d under constant current formation. Table 3-1: Average f i e l d , E, i n the oxide and f i e l d , E , i n outer l a y e r f o r constant current formation i n h^SO^ a n d ^'34 a t ^ a s ^ n t a ^ i e 2-4, Where E^ = (E-E«)/G + E 2 and E 2 i s the f i e l d i n the inner l a y e r which i s taken to be 5.15 x 10 6 V/cm as f o r oxides grown i n d i l u t e H„S0,. 2 4 Growth Conditions G E/106 V/cm E^ I O V/cm 1 aDSA 6.08 1 bDSA 6.15 1 aDSW 6.10 1 aDPA .51 6.46 6.78 1 bDPA .525 6.50 6.82 1 cDPA .52 6.48 6.78 1 aDPW .50 6.48 6.83 lOcDPA .565 7.15 7.92 lOcDPW .565 7.21 8.02 1 aCPA i; .65 ~7.8 ~8.7 sequence 2 .70 8.15 9.0 * F i r s t a n o dization, t a b l e 2-5. 88 Table3-2 : Comparison of two formation sequences ending at 9.5 Acm and 115.85 V on Ta i n 0.23N H3PO4 at 25°C. -2 -2 Formation (1). lOmAcm to 136 v o l t s followed by 9.5 uAcm ( f o r about seven v o l t s ) to V (A=300.16°, ¥=41.60°). Formation (2). Constant 9.5 uAcm~2 to (A=280.28°, Y=32.75°). r Assumed R e f r a c t i v e Indices Apparent T o t a l Thickness O (A) Outer Inner Metal G Formation (1) Formation (2) F i l m F i l m 2.22 2.22 3.3 - 2.30j Sin gle f i l m (a) 1989 2077 2.14 2.21' 3.3 - 2.26j 0.56 (b) 2040 2135 2.14 2.21 3.3 - 2.26j 0.51 (c) 2038 2133 (a) As i n the case of oxide grown i n d i l u t e H„S0.. 2 4 (b) and (c) as i n the case of growth at 10 and 1 mA/ 2 cm d i l u t e H„P0, 3 4 F i g . 3-1: G dependence on i o n i c current d e n s i t y f o r constant current formation i n d i l u t e H PO at 25°C. X from Randall et a l , 1 2 O t h i s study. 89 12 Combining the r e s u l t s of tracer studies by Randall et a l and those of table 3-1, G i s found to depend l i n e a r l y on log J for formation at 25° C i n 2 d i l u t e H^PO^ (fig> 3-1). At 1 mA/cm the tracer r e s u l t s and the r e s u l t s of t h i s study are i n agreement. Evidence that G also depends on previous h i s t o r y of the oxide i s shown i n table 3-2. In t h i s table formation 1 would give an oxide thickness between (b) and (c) and for formation 2 the thickness should be 2 between (a) and (b). Thus the average f i e l d at 9.15 pA/cm i s between 5.58 2 and 5.33. Using the average of these two values as the f i e l d at 10 uA/cm then G, as expected, i s approximately l i n e a r l y dependent on f i e l d over the range of currents shown i n f i g . 3-1. Capacitance measurements at 1 kHz v e r i f y the r e s u l t s of Randall et a l that e l e c t r o l y t e incorporation reduced the d i e l e c t r i c - c o n s t a n t of the oxide. From capacitance measurements taken i n the e l e c t r o l y t e about one minute a f t e r 2 formation of the oxide at 1 and 10 mA/cm i n 0.23 N H„P0, at 25° C the d i e l e c t r i c 3 4 constant of the outer layer was determined to.be 25. This i s 'assuming that the inner layer has a d i e l e c t r i c constant of oxides formed i n d i l u t e H2S0^ which • 07 A 6 9 i s 27.6 2. Formation i n a Sequence of E l e c t r o l y t e s F i g . 3-2 shoxtfs the dependence of e l e c t r i c f i e l d on oxide thickness during the second anodization of oxide formation i n a sequence of e l e c t r o l y t e s where the i n i t i a l e l e c t r o l y t e was 85% H.P0, and the second e l e c t r o l y t e was 0.2N H oS0. J 3 4 2 4 in sequence / / l or 0.23 N H PO^ for sequence #2 (as i n table 2-5). A l l formations 2 were at 1 mA/cm at 25° C. The oxide thickness during the second anodization was determined from ellipsometry assuming that the oxides layers produced i n the l S t and 2 n^ e l e c t r o l y t e were independent and each oxide has properties as determined for formation i n that e l e c t r o l y t e alone. On th i s model, the average f i e l d across the oxide during the 2 n^ anodization would be expected to obey the X SEQUENCE 7 s 10 75 20 25 30 FILM THICKNESS x W~2/A F i g . 3-2: Dependence of average f i e l d on oxide thickness during second a n o d i z a t i o n of sequence 1 and 2 X X: experimental, : model, and o: f i e l d at the end of ] s t a n o d i z a t i o n . r e l a t i o n E = E + ( E ^ - E ^ x ^ x C 3 - 1 ) where i n t h i s case the s u b s c r i p t s 1 and 2 r e f e r to l S t and 2 n d a n o d i z a t i o n and st x^ i s the oxide thickness produced i n the 1 a n o d i z a t i o n and x i s the t o t a l oxide t h i c k n e s s . The curves computed on t h i s mode], are a l s o shown i n F i g . 3-2 and the values used i n the computation are taken from t a b l e 3-1 and 2-4 and these were , 6 ° E /10 V/cm E 2/10 V/cm x±/A Sequence #1 7.74 6.07 527 Sequence #2 8.15 6.46 552 The agreement between computed and observed f i e l d s i s w i t h i n exper-imental e r r o r f o r most pa r t of the second a n o d i z a t i o n . However, the computed curve i s expected to l i e below r a t h e r than above the observed f i e l d . This i s because i f G depends on f i e l d , which seems to be the case, then G during the 2°^ a n o d i z a t i o n would be expected to change not a b r u p t l y as i n the model but slowly from the value i n the l S t e l e c t r o l y t e towards a value t y p i c a l of the 2°^ e l e c t r o l y t e Thus the f i e l d should be higher than c a l c u l a t e d s i n c e the outer l a y e r which has a higher f i e l d e x i s t f o r a time i n l a r g e r p r o p o r t i o n s than i n the model. The mechanically p o l i s h e d specimen used i n sequence 1 had a lower e f f i c i e n c y than the e l e c t r o p o l i s h e d specimen used i n sequence 2 and r e s u l t s i n a lower E^. Furthermore, during the second a n o d i z a t i o n of sequence 1, the o e f f i c i e n c y remained low up to about 1000 A and then increased w i t h t h i c k n e s s o l e v e l l i n g out at 1500 A w i t h about the same e f f i c i e n c y as specimen 1 aDSA ( t a b l e 3-1). This r e s u l t e d i n an i n c r e a s e i n i o n i c current passed and i n turn an increased f i e l d which i s one reason why the experimental r e s u l t s come c l o s e r to o the computed curve about 2000 A. In sequence 2, the e f f i c i e n c y d i d not change nd during the 2 a n o d i z a t i o n and the e f f i c i e n c y had a value t y p i c a l of formation on e l e c t r o n o l i s h e d specimens i n 0.23N H„P0. alone. 3 4 Although the average f i e l d changed slowly during the second anodiza-t i o n the d i f f e r e n t i a l f i e l d ( ™ ) changed r a p i d l y from the value i n the f i r s t anodization to a value t y p i c a l of the second anodization. In sequence 2, the capacitance was measured and a plot of r e c i p r o c a l capacitance versus thickness i s l i n e a r during the second anodization. Further-more, the product of capacitance and voltage, CV, i s constant to within 1% during the formation sequence. The expected behaviour of r e c i p r o c a l capacitance ± S I = X " X l 1_ C e 0 z A C. 2r o 1 again using the model that the oxide layers from the two anodization act indepen-dently and i n se r i e s where A i s the area and the notation i s the same as i n equation (3-1), Thus 1/C i s linear, with x as found. However, the slope of 1/C verses x gives an z which i s about 2% higher than expected from the model 2 where the new oxide i s the same as that produced at 1 mA/cm i n 0.23N H^PO^. 3. K i n e t i c s of Oxide Growth: Log J - E C h a r a c t e r i s t i c s The log J - E c h a r a c t e r i s t i c s or the k i n e t i c s of oxide growth at 25° C i n 0.23 N H^PO^ are shown by the experimental points i n F i g . 3-3. These points 23 were obtained using the method of Young and Zobel . In t h i s method the oxide 2 i s i n i t i a l l y grown at a high current density (10 mA/cm ) to about 100 v o l t s and then i t i s held at th i s voltage and allowed to grow, the current decaying as the oxide grows. The i o n i c current passed during growth i s obtained using Faraday's law and graphical d i f f e r e n t i a t i o n of a graph of t o t a l thickness versus logarithm of time. The thickness was obtained by i n s i t u ellipsometry measure-ments assuming the quantities G and index of r e f r a c t i o n of the i n i t i a l formation 2 at 10 mA/cm . The average f i e l d across the oxide i s determined from the applied voltage plus the reaction voltage (0.85 V) less the voltage drop across the sol u t i o n which has an e l e c t r o l y t e resistance of 15 Q (see chapter 5, section 3.2 for method used to determine e l e c t r o l y t e r e s i s t a n c e ) . 93 F i g . 3-3: LogJ-E c h a r a c t e r i s t i c s . Centre (—;;—x—): r e s u l t s and f i t t e d curve f o r formation i n 0.23N H^l'O^ at 25°. Inner curve (on l e f t ) : computed f o r d i l u t e H.-.SO, ana a l s o f o r inner l.-iyer of oxides grown i n H PO . Outer curve: f o r outer l a y e r . ~2Qr E*10 cm /volt 94 During the constant voltage formation two e f f e c t s are expected to occur because the current and f i e l d are decreasing. F i r s t , g of the new oxide i s decreasing so that G at any thickness w i l l be d i f f e r e n t and secondly, the amount of e l e c t r o l y t e incorporation w i l l also be decreasing so that the index of the new oxide i n the outer layer w i l l be increasing s l i g h t l y . Because of these e f f e c t s i t i s necessary to show that the f i l m thickness determined during the constant voltage formation by assuming the G, n^ and n^ of the i n i t i a l formation at constant current i s v a l i d . An estimate of the v a r i a t i o n i n G may be made i f i t i s assumed that g depends on current density at constant voltage as G depends on steady state or constant current formation. That i s g ( J ) | v = G(J)| . From f i g . 3-1, the experimentally determined dependence of G on J i s approximately given by G = 0.05 l o g 1 Q J +0.66 The magnitude of g can then be calculated f or each increment i n thickness of each experimental point of f i g . 3-3. In t h i s approximation g i s found to vary from 0.56 to 0.35 during the constant voltage formation. G i s then found at each thickness i n verms of the preceeding one using x x +Ax x +gAx G = — = \ = (3-2) x x +A X x +A X o o where x i s the t o t a l oxide thickness at the point considered, x. , thickness of outer layer at the previous point, gAx and Ax are the increase i n outer layer thickness and i n t o t a l thickness r e s p e c t i v e l y from the previous point. In t h i s way G was determined to vary from 0.56 to 0.53 over the constant voltage formation. This v a r i a t i o n introduces very l i t t l e error i n the thickness as determined by ellipsometry, assuming G constant. Compare for example the di f f e r e n c e i n t o t a l thickness of case (b) and (c) i n table 2. Furthermore, the o oxide only grew from 1437 to 1974 A during the constant voltage formation. 95 The e f f e c t of decreasing e l e c t r o l y t e i n c o r p o r a t i o n i n t o the outer l a y e r of the new growth on i t s index of r e f r a c t i o n and hence thickness cannot be estimated from t h i s work. The e f f e c t i s again probably very small s i n c e no 2 s i g n i f i c a n t change i n o p t i c a l p r o p e r t i e s was found on going from 1 to 10 mA/cm growth. Thus determination of f i l m t h i c k n e s s using i n i t i a l values i s v a l i d . Having a s c e r t a i n e d the v a l i d i t y of the thic k n e s s measurements the con-stant v o ltage r e s u l t s show that the k i n e t i c s f o r formation i n d i l u t e H^PO^ occur at higher f i e l d s f o r a given current d e n s i t y than f o r formation i n H^SO^ 23 ( f i g . 3-2). Young and Zobel found that e x c e l l e n t agreement e x i s t e d i n the k i n e t i c s of growth determined from the constant voltage formation and those obtained from d i f f e r e n t constant current formations. However, i n H^PO^ i o n i c conduction depends on oxide h i s t o r y (eg., t a b l e 3-2) and agreement would not be 2 expected. At 10 and 1 mA/cm the agreement i s e x c e l l e n t but at 9.5 yA (forma-t i o n 2 t a b l e 3-2) the agreement i s poor. In the l a t t e r formation the f i e l d s determined at thicknesses (a) and (c) are 1 to 2.5% lower than the corresponding value at constant v o l t a g e . The l o g J - E c h a r a c t e r i s t i c s of oxide produced i n d i l u t e H PO, are . 3 4 non- l i n e a r and curve i n the same d i r e c t i o n a the c h a r a c t e r i s t i c s f o r d i l u t e ^SO^ ( F i g . 3-3). F i t t i n g the H^PO^ c h a r a c t e r i s t i c s by an expression of the form J = J q exp q(a+bE)E/kT where q = 5e gives l o g ( J / ( A cm" 2)) = -38.42 , a = 10.693 A and b = -6.514'A/(10 ? V/cm) 21 These values may be compared w i t h those • obtained by Young from anodic oxides grown i n d i l u t e ^SO^ . These values are l o g ( J / ( A cm" 2)) = -28.71 , a = 6.995 A and b = -3.34 A/(10 ? V/cm) These values were used to compute the inner curve i n F i g . 3-3. The k i n e t i c s of growth f o r the outer l a v e r are a l s o shown i n F i g . 3-3. 96 F i g . 3-4: LogJ versus e l e c t r i c displacement (D/e- i s plotted) for inner and outer layers shov<n i n fi g u r e 3.3. - 2 . Or -7.01 — « " — 1 1 • 13.0 14.0 15.0 16.0 17.0 18.0 19.0 ( D / e ) x 1 0 c m / v o l t these are obtained by assuming the model that the inner layer has the same properties of oxides fromed i n H^SO^. That i s , the f i e l d required to pass a given current i n the inner layer i s assumed to be given by the k i n e t i c s of grov/th for ll^SO^ i n th i s f i g u r e . It i s further assumed that G va r i e s as calculated i n equation (3.2). Thus the k i n e t i c s of growth of the inner layer are represented by the inner curve and those of the outer layer by the outer curve ( f i g . 3-2). The f i e l d s i n each layer could have been obtained by assuming that the e l e c t r i c displacement i s continuous across the oxide. Figure 3-4 shows that t h i s might be the case. This f i g u r e presents log J versus e l e c t r i c d i s -placement divided by the p e r m i t t i v i t y of free space or D/e^. The curves are computed by multipl y i n g the f i e l d i n the inner and outer layer of fi g u r e 3-3 r e s p e c t i v e l y by the d i e l e c t r i c constant of the layer. The outer layer having an e, of 25 and the inner and e„ of 27.6. The two curves E.. ° l r 2r l r 1 and £2r^2 s u P e r P o s e within experimental error ( f i g . 3-4). This r e s u l t i n d i -cates that the e f f e c t of e l e c t r o l y t e incorporation can be accounted for at le a s t i n part i f the current density i s made on exponential function of e l e c t r i c displacement rather than applied f i e l d . 3. DISCUSSION Besides ch a r a c t e r i z i n g the e f f e c t of e l e c t r o l y t e incorporation the r e s u l t s presented give insight into the general c h a r a c t e r i s t i c of i o n i c conduction i n p a r t i c u l a r on the metal ion transport number, on bulk rather than i n t e r f a c e c o n t r o l l e d i o n i c current, on the c o r r e l a t i o n between i o n i c conduction and p e r m i t t i v i t y and f i n a l l y on the curvature of the log J - E c h a r a c t e r i s t i c s . -Before discussing these topics the e f f e c t s of e l e c t r o l y t e incorporation are given. 1. Ef f e c t of E l e c t r o l y t e Incorporation E l e c t r o l y t e incoporation into the f i l m has the following e f f e c t s : a) It decreases index of r e f r a c t i o n and p e r m i t t i v i t y of the outer layer. Various authors have used a "step gauge" of oxides formed i n d i l u t e H SO^ to esimtate the thickness of oxides formed i n d i l u t e H PO, by v i s u a l 3 4 > comparison of co l o r s . This leads to an underestimate of thickness due to the lower index of the outer layer (see di f f e r e n c e between one layer and two layer model i n table 3-2) and an overestimate i n e^ _, E, etc. b) It makes i o n i c conduction properties dependent on the past h i s t o r y of the oxide. c) It may be responsible for the decreasing breakdown voltage of oxide f o r -mation observed with increasing e l e c t r o l y t e concentration. For example, 2 at 25° C, and 1 mA/cm oxide breakdown occurs at about 290 v o l t s i n 0.23N H oP0. verses 95 v o l t s f o r 85% H_P0.. 3 4 3 4 d) It decreases i o n i c conductivity by increasing the f i e l d required to pass a given current density or moves the log J - E c h a r a c t e r i s t i c s of growth to higher f i e l d s . The f i r s t observation of the e f f e c t of incorporated e l e c t r o l y t e on f i e l d , although not a t t r i b u t e d to t h i s cause at the time, was shown i n that the voltage required to reach a given interference color ( i . e . , thickness) increased with concentration of H„S0, e l e c t r o l y t e used for constant current 2 4 21 formation. Also, a s i m i l a r displacement of the k i n e t i c s of higher f i e l d s has been noted f o r oxides grown on sputtered tantalum th i n films i n d i l u t e H„S0,. This e f f e c t was i n i t i a l l y a t t r i b u t e d to metal-oxide i n t e r f a c e c o n t r o l 2 4 49 of current. The present r e s u l t s suggests that i t i s more l i k e l y due to incorporation into the oxide of impurities from the sputtered tantalum. It i s well known that i n sputtering, material from the sputtering atmosphere, i s incorporated into the sputtered metal. In fact the incorporation of the 99 species i n t o the metal i s used i n p r a c t i c e as one of the c o n t r o l s a f f e c t i n g the thermal p r o p e r t i e s of the sputtered m a t e r i a l or the subsequent oxide. a. Metal Ion Transport Number I f G i s taken to represent the metal ion t r a n s p o r t number at constant c u r r e n t , then t h i s number v a r i e s l i n e a r l y w i t h l o g j or e l e c t r i c f i e l d and depends on the previous h i s t o r y of the oxide. The value of the tr a n s p o r t 2 number determined f o r growth at 1 mA/cm' and 25° C i n 0.23N R ^ P O ^ or f o r growth i n 85% H„PO, followed by 0.23N K„PO, are i n agreement w i t h the value found by 3 4 3 4 12 Ran d a l l et a l from t r a c e r and from marker l a y e r s t u d i e s . These r e s u l t s i n d i c a t e 2 that the metal i o n c o n t r i b u t e s about 0.51 to 0.52 to oxide.growth at 1 mA/cm i n d i l u t e H^PO^ at 25° C. For growth i n H^SO^, the a n o d i z a t i o n i n a sequence of e l e c t r o l y t e s where the l a y e r produced i n concentrated H^PO^ provided the marker l a y e r , the metal ion t r a n s p o r t number found, 0.44, ( t a b l e 2-5) i s c l o s e r to 12 that determined by Randall et a l , 0.48, than that found by i n e r t gas marker 2 31 l a y e r which i s 0.26 f o r growth at 1 mA/cm i n 0.2N R^SO at 25° C ( t a b l e 1-1) . The discrepancy between the f i r s t two and the l a s t value i n d i c a t e s that one of the markers i s l e s s immobile than the other. However, i t i s evident from the s i m i l a r dependence of the tra n s p o r t number on l o g J of the e l e c t r o l y t e and i n e r t gas marker that these two markers measure the same e f f e c t to d i f f e r e n t extents. A method of checking the m o b i l i t y of the e l e c t r o l y t e i n c o r p o r a t i o n marker l a y e r would be by using sputtered tantalum f i l m and determining the tran s p o r t number from i m p u r i t i e s incorporated i n t o the oxide from the sputtered m a t e r i a l on growth. 100 b. Bulk Controlled Ionic Conduction? Dignam recently proposed a model i n which the e l e c t r o l y t e i n t e r f a c e controls the i o n i c conduction process rather than the bulk of the oxide. 44 Except for an extended abstract the d e t a i l s of t h i s model are not a v a i l a b l e . The previous evidence for bulk control was that the average f i e l d i n the oxide o i s within experimental accuracy independent of thickness above about 200 A 20 21 for growth at constant current i n a given e l e c t r o l y t e . ' The r e s u l t s obtained here further i n d i c a t e that the oxide bulk has a d e f i n i t e influence on the i o n i c conduction process i n that: a) the i o n i c conduction process depends on the previous oxide h i s t o r y for a given e l e c t r o l y t e i n t e r f a c e and b) on changing from one e l e c t r o l y t e to another the average f i e l d across the oxide changes only gradually from the value t y p i c a l for the f i r s t e l e c t r o l y t e towards a value t y p i c a l of the second e l e c t r o l y t e . Thus the oxide bulk con-t r o l s conduction even on changing; the nature of the e l e c t r o l y t e i n t e r f a c e . Furthermore, the d i f f e r e n t i a l f i e l d changed r a p i d l y to a value t y p i c a l of the new e l e c t r o l y t e . From these r e s u l t s i t seems u n l i k e l y that the e l e c t r o l y t e i n t e r f a c e exerts the major influence on i o n i c conduction as claimed by Dignam. c. Ionic Conduction and P e r m i t t i v i t y . Young^ noted that at a given current the product of average f i e l d and d i e l e c t r i c constant was about the same for oxides produced on Ta, Nb and A l and that t h i s suggests a correlation'between d i e l e c t r i c properties and i o n i c conduction. Furthermore, for oxides on Ta, CV at a given current density i s independent of e l e c t r o l y t e for d i l u t e s o l u t i o n s . (This i s the reason why incorporation e f f e c t s i n d i l u t e solutions went unnoticed for so long). Also, the decay of capacitance with time at zero f i e l d a f t e r removing the f i e l d which i s p a r a l l e l e d by a s i m i l a r decay i n instantaneous i o n i c current seen reapplying 25 26 the f i e l d . ' The r e s u l t s of t h i s study strengthens t h i s c o r r e l a t i o n further i n that; a) the e f f e c t of e l e c t r o l y t e incorporation may be accounted for by 101 making the current an exponential f u n c t i o n . o f e l e c t r i c displacement r a t h e r than average f i e l d and b) that the CV product i s a l s o constant during successive formation i n two e l e c t r o l y t e s , i . e . , compensating completely f o r the observed change i n f i e l d during a n o d i z a t i o n i n the second e l e c t r o l y t e . P o s s i b l e explanations of t h i s phenomena are as f o l l o w s . The i o n i c process i s c o n t r o l l e d by an e f f e c t i v e f i e l d eg., Lorentz f i e l d , roughly pro-p o r t i o n a l to e l e c t r i c displacement. Or, the process which gives r i s e to 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 i n the oxide are very s i m i l a r as p r e d i c t e d by the normal mode model of i o n i c conduction. And f i n a l l y , the e l e c t r i c d i s -69 placement i s constant across the oxide. Dignam r e c e n t l y p o s t u l a t e d that t h i s a r i s e s from e l e c t r o s t a t i c a l l y imposed boundary c o n d i t i o n s . However, unless l o g J °= D t h i s w i l l not be the case. A l a y e r of charge w i l l develop at the boundary between the two l a y e r s u n t i l the f i e l d i n the two p a r t s of the oxide are such as to give equal current d e n s i t i e s . The bulk of the oxide w i l l be n e u t r a l . d. E l e c t r o l y t e I n c o r p o r a t i o n : E x p l a n a t i o n f o r Log J-E Curvature-As discussed e a r l i e r the c l a s s i c a l theory of high f i e l d i o n i c conduc-t i o n and the high f i e l d Frenkel defect theory p r e d i c t a l o g J - E c h a r a c t e r i s t i c which i s l i n e a r , i . e . , J = Jo expaE. In p r a c t i c e , these c h a r a c t e r i s t i c s are n o n - l i n e a r and curve toward higher f i e l d values w i t h i n c r e a s i n g i o n i c c u r r e n t . A number o f . e x p l a n a t i o n s have been put f o r t h to account f o r t h i s curvature (see Chapter 1, s e c t i o n 3-2). A simpler e x p l a n a t i o n seems to a r i s e from the observed e f f e c t s of e l e c t r o l y t e i n c o r p o r a t i o n . At constant current formation two e f f e c t s occur w i t h i n c r e a s i n g J : a) G i n c r e a s e s , that i s the o u t e r l a y e r increases i t s p r o p o r t i o n of the oxide and b) the c o n c e n t r a t i o n of i n c o r -p o r a t i o n species i n t o the outer l a y e r i n c r e a s e s . F i r s t , s i n c e the f i e l d i n the outer l a y e r i n c r e a s e s w i t h c o n c e n t r a t i o n of i n c o r p o r a t e d s p e c i e s , then w i t h i n c r e a s i n g J , the increase f i e l d i n the outer l a y e r has an added c o n t r i b u t i o n because of the i n c r e a s i n g c o n c e n t r a t i o n . Thus the l o g J - E c h a r a c t e r i s t i c s of the outer l a y e r are more curved than they normally would be i f the concentra-t i o n d i d not i n c r e a s e . Secondly, s i n c e e l e c t r o l y t e i n c o r p o r a t i o n causes the f i e l d to be higher i n the outer l a y e r than i n the inner l a y e r , then the f i e l d across the oxide \ v T i l l have an added increase due to an i n c r e a s e i n G w i t h J . Thus the. l o g J - E c h a r a c t e r i s t i c f o r the oxide w i l l be curved. This curvature i s f u r t h e r increased because of e f f e c t (b). At the moment i t i s not known whether the curvature i s i n f a c t i n t r i n s i c to the i o n i c process i . e . i n t r i n s i c to the inner l a y e r or i n general to oxides where no i n c o r p o r a t i o n occurs. The general f e e l i n g f o r the present i s that the curvature of the l o g J - E p l o t i s i n t r i n s i c to the i o n i c process i n that i t occurs f o r a number of e l e c t r o l y t e s where i n c o r p o r a t i o n i s very s m a l l . The r e a l q u e s t i o n , however, i s what l e v e l of i m p u r i t i e s can be t o l e r a t e d before the i o n i c conduction process i s i n f l u e n c e d . C e r t a i n l y i n semi-conductors the i m p u r i t y c o n c e n t r a t i o n can be small but the e f f e c t on e l e c t r o n i c conduction l a r g e . The present s i t u a t i o n i n v o l v e i o n i c processes which are probably l e s s s e n s i t i v e than e l e c t r o n i c processes to i m p u r i t i e s , however, only second order e f f e c t s are i n v o l v e d i n t h i s case. I t can e a s i l y be shown that i f the e l e c t r i c displacement i s constant across the oxide, i f the i n n e r , non-incorporated l a y e r has a l i n e a r l o g J - E c h a r a c t e r i s t i c i . e . , l o g J = aE^ and that i f G * l o g J as e m p i r i c a l l y found ( f i g . 3-1) then l o g J versus the average f i e l d across the oxide i s non-l i n e a r . C a l c u l a t i o n s using the value f o r a as determined i n d i l u t e H^SO^ growth y i e l d s the constants which c h a r a c t e r i z e f a i r l y w e l l the n o n - l i n e a r i t y i n the H^PO^ k i n e t i c s found here. The agreement does not c o n s t i t u t e proof of the model, but i t i s presented as a d e f i n i t e p o s s i b i l i t y . 104 e. Comparison of K i n e t i c s of Growth 2 I f the l o g J-E curve i s described by l o g J = q(aE+bE )/kT + l o g i t i s found that the values of a and b of oxides grown i n d i l u t e P-^ PO^  a r e almost twice as l a r g e as the values of oxides grown i n d i l u t e H^SO^. I f 2a i s the average jump distance of an i o n as i n the c l a s s i c a l theory i f i o n i c conduction or i n the high f i e l d F r enkel defect model then e l e c t r o l y t e i n c o r -p o r a t i o n increases the jump di s t a n c e of i o n s . I f b a r i s e s as a r e s u l t of e l e c t r o s t r i c t i o n of as a r e s u l t of a decrease of the jump d i s t a n c e w i t h f i e l d (chapter I , s e c t i o n 3.2a and 3.2c) i t i s d i f f i c u l t to see how a 5 or 6% increase i n f i e l d of the l o g J-E p l o t from H^SO^ to P j P 0 ^ can account f o r a two f o l d i n c r e a s e i n b. 23 Young and Zobel found that the k i n e t i c s of growth i n d i l u t e F^SO^ could a l s o be represented by a Poole-Frenkel or Schottky type law i n which 1/2 log J « E . They then proposed that ions moved along channels i n the oxide i n t e r s p e r s e d w i t h o c c a s i o n a l coulombic t r a p s . In f i g u r e 3-5 the l o g J 1/2 verses E c h a r a c t e r i s t i c s f o r the P^PO^ k i n e t i c s of f i g u r e 3-3 are compared to the computed c h a r a c t e r i s t i c s f o r H.SO,. The H„P0. c h a r a c t e r i s t i c s do not 2 4 3 4 1 '2 obey l o g J <= E ' very w e l l and show a d e f i n i t e curvature. F i n a l l y , the d i f f e r e n c e s discussed above are probably somewhat exagerated because of the constant v o l t a g e method used i n o b t a i n i n g the k i n e t i c s of growth i n H^PO^. This i s because the oxide grown at high current p r i o r to the constant v o l t a g e formation w i l l i n f l u e n c e the f i e l d s at the lower currents i n the constant v o l t a g e formation. Thus at the lower c u r r e n t s the constant v o l t a g e method w i l l measure a higher f i e l d than would be obtained at constant c u r r e n t . This leads to absolute value of a and b which are some-what l a r g e r than those which would be obtained i n the constant current k i n e t i c s . 105 IV. PHOTOSTIMULATED GROWTH 1. INTRODUCTION Study of photostimulated anodic oxide growth on Ta.is of theore t i c a l and p r a c t i c a l importance. In theory u.v. e f f e c t s i n d i c a t e an interdepen-dence of i o n i c and e l e c t r o n i c processes i n the oxide which i s not yet under-stood. In p r a c t i c e u.v. e f f e c t s are important because of the p o t e n t i a l a p p l i -c a t i o n of t h i s oxide as an u l t r a v i o l e t photodetector , and because of the u.v. r a d i a t i o n present i n plasma a n o d i z a t i o n of Ta which i s more compatible w i t h device f a b r i c a t i o n than i n conventional a n o d i z a t i o n . In view of t h i s prac-t i c a l and t h e o r e t i c a l importance e l l i p s o m e t r y measurements were made p r i m a r i l y to i n v e s t i g a t e the anomalous oxide growth. 2. EXPERIMENTAL The tantalum specimen was held h o r i z o n t a l l y i n a 0.2N H„S0, e l e c t r o -2 4 l y t e at 25° C. The specimen was i l l u m i n a t e d using a mercury arc lamp w i t h a quartz envelope and w i t h about 95% of i t s i n t e n s i t y at 2537° A. The lamp was held a few cm. above the s o l u t i o n . The r e s u l t i n g photocurrent was very s e n s i t i v e to the specimen-lamp d i s t a n c e but not to the depth of s o l u t i o n above the specimen (2 to 10 cm), i n d i c a t i n g that l i t t l e a b sorption of u.v. takes place i n the e l e c t r o l y t e . E l l i p s o m e t r y measurements were made i n a i r f i r s t on the oxide present p r i o r to i r r a d i a t i o n and then at i n t e r v a l s during oxide growth under i r r a d i a t i o n . On the average, about one-half hour was r e q u i r e d to complete the procedure. The specimen was then returned to the e l e c t r o l y t e and the u.v. and v o l t a g e r e a p p l i e d . The photocurrent was monitored across a small r e s i s t o r i n s e r i e s w i t h 2 the c e l l . Only one side of the Ta specimen, aproximately 3.8 cm , was i r r a d i a t e d . 106 3. RESULTS AND DISCUSSION Fig s . 4-1 and 4-2 r e s p e c t i v e l y preseiit the ellipsometry r e s u l t s and the photocurrents of an oxide held at constant voltage and subjected to u l t r a -v i o l e t r a d i a t i o n . I n i t i a l l y the oxide had been formed at 20 v o l t s overnight to o a thickness of 457 A and a leakage current of 2.7 uA, i . e . , to a n e g l i g i b l e growth rate. The primary and secondary photocurrent are reconstructed from a sequence of constant voltage formations under i r r a d i a t i o n ( f i g . 4-2) - part of the sequence i s shown i n Figure 4-2a. The numbers on each figure correspond to the end of a formation of the sequence where an ellipsometry measurement i s made. The f i r s t part of the u.v. formation was with 20 v o l t s applied to the specimen and i s represented by points 1 through 22. Aside from point 1 ( f i g . 4-1) which i s taken before the onset of secondary photocurrent ( f i g . 4-2) and indicates almost no growth, the ellipsometry curve of points 2 to 22 i n d i c a t e the following: F i r s t , that the r a d i a t i o n enhances growth as expected. Secondly, points 2 to 22 are f i t t e d best with a f i l m c o n s i s t i n g of two layers which grow simultaneously with a G of 0.68 and with index of r e f r a c t i o n 1.82 and 2.24 r e s p e c t i v e l y f or the outer and inner layer. A si n g l e layer does not f i t these r e s u l t s nor does a two or three layer f i l m where one of the layers i s the o r i g i n a l oxide. In f a c t , i f the o r i g i n a l oxide did remain unchanged, the u.v. ellipsometry curve should at f i r s t follow i n proximity of the curve t y p i c a l of the o r i g i n a l oxide ( dashed l i n e of f i g . 4-1). Such i s the case, for example, for growth i n concentrated followed by d i l u t e e l e c t r o l y t e ( f i g . 2-1). Thus the incubation period i s associated with some s t r u c t u r a l change of the e x i s t i n g oxide. The ellipsometry points #23 and 24, 25 and 26, 27 and 28, and 29 to 32 were obtained by r e s p e c t i v e l y increasing the voltage from 20 to 25, 30, 40 and 50 v o l t s , with the f i r s t formation following each increase i n 107 360 270 180 CD 90 NORMAL OXIDE • 0.0 A \ NORMAL OXIDE 7 7 ^ INITIAL O X / D E ^ ^ ) ^ 1 -0 10-0 WATER EFFECT 20.0 30.0 40.0 50.0 60.0 70-0 Fig. 4 - 1 : F i t t e d ellipsometry results on photogrown anodic oxide on tantalum at constant voltage. Points obtained as numbered. Dashed l i n e : ellipsometry curve for normal oxide growth. 108 voltage c a r r i e d out without r a d i a t i o n . This extends the ellipsometry curve almost another c i r c l e (Fig. 4-1). It i s expected that as the f i e l d across the oxide changes because of oxide growth, the properties of the oxide also change, and i t might not be too d i f f i c u l t to accept the deviation of the f i t t e d curve from the experimental points 20 onward. However, i f the oxide properties are not affected by the f i e l d then the experimental points ,2-32 i n d i c a t e that the outer layer should be of higher index than the inner i f a two layer model i s used. No s a t i s f a c t o r y f i t was found using t h i s requirement. Furthermore, ellipsometry r e s u l t s obtained during stepwise d i s s o l u t i o n of t h i s oxide i n 10% HF gives an e l l i p -sometry curve which indicates that the outer layer has the lower index. How-o ever, the l a s t 5 or 600 A of the ellipsometry curve which should be e n t i r e l y from the inner layer indicates that the index of the inner layer i s somewhat higher (about 2.28) than that determined i n the f i r s t 22 points ( f i g . 4-1). F i n a l l y , at large thicknesses the oxide takes up water. This was noted at point 32 ( i t was not looked for i n the f i r s t 22 p o i n t s ) . Here the ellipsometry measurements could be recycled between values of A and ¥ of about 0 31.3 and 59.8 to 46.0 and 54.5 when the oxide was measured immediately a f t e r dipping i n water and drying to a f t e r standing i n the atmosphere for a few hours. This r e c y c l i n g i s shown by the double ended arrow ( f i g . 4-1). The secondary photocurrent i s observed by i n t e r r u p t i n g the r a d i a t i o n for a few seconds at which time the photocurrent decays at f i r s t very r a p i d l y , then there i s a break i n i t s speed where the current begins to decay very slowly. The break point i s taken as the value of the secondary current. If the secondary current i s s o l e l y responsible for growth, then i t s e f f i c i e n c y i s greater than 100% (Table 4-1). An e f f i c i e n c y greater than 100% probably ar i s e s because the normal oxide density was used i n c a l c u l a t i n g the change i n thickness from Faraday's law. The photgrown oxide i s expected to have 100 200 300 600 700 TIME/min F i g . 4.2: T o t a l ( ) and secondary (-x-x-) photocurrents reconstructed from maxima i n these c u r r e n t s from i n d i v i d u a l s e q u e n t i a l formations as shown i n exploded view. • 110 'able 4--1: E f f i c i e n c y of s econdary photocurrent f o r the. production of oxide under u.v. r a d i a t i o n and 20 v o l t s 'oint# Exposure Apparent E/10 5 Vcm 1 Change i n o thickness A E f f i c i e n c y to u.v. (min) Thickness o A E l l i p -sometry Faraday's law* % 0 0 457 44 1 2.5 459 44 2 2 20.0 792 25 343 136 + 5% 252 3 7.6 919 22 127 96 132 4 6.7 1028 19 109 80 136 5 8.8 1163 17 135 97 139 6 11.0 - 1287 15.5 124 90 138 7 14.9 1426 14 139 98 142 8 21.6 1566 13 140 112 125 9 21.9 1680 12 114 100 114 10** (25.1) 1737 11.5 57 45 126 11 29.5 1774 11 37 32 115 12 42.0 1946 10 172 146 118 13 32.4 2045 9.8 99 80 123 14 20.0 2104 9.5 59 50 118 15 18.7 2147 9.3 43 37 119 22 319 2743 7.3 594 500 119 : area 3.8 cm 2, den s i t y of 3 oxide 8 g/cm no u.v. a lower d e n s i t y corresponding to a lower index of r e f r a c t i o n of t h i s oxide to the normal oxide. A second p o s s i b i l i t y could be that that h i g h e f f i c i e n c y i s caused by photoenhanced e l e c t r o l y t e i n c o r p o r a t i o n i n t o the oxide. Although, the extremely high e f f i c i e n c y between p o i n t s 1 and 2 of t a b l e 4-1 i s probably a s s o c i a t e d w i t h a change i n p r o p e r t i e s of the i n i t i a l oxide. The secondary current goes through a maximum with time on r e a p p l y i n g the v o l t a g e and the u.v. a f t e r removing them to f a c i l i t a t e e l l i p s o m e t r y mea-surements ( F i g . 4-2a) The time r e q u i r e d to reach the maximum incre a s e s w i t h decreasing c u r r e n t . This type of behaviour of current w i t h time i s a l s o observed under normal oxide growth at constant v o l t a g e when the vo l t a g e i s r e a p p l i e d a f t e r a pe r i o d w i t h the vo l t a g e removed. This i s f u r t h e r i n d i c a t i o n that the I l l secondary current i s i o n i c i n nature. However, i n t h i s case the u.v. r a t h e r than the a p p l i e d f i e l d i s p r i m a r i l y r e s p o n s i b l e f o r the generation of ions since i f only the voltage i s r e a p p l i e d the current -decays slowly and no maximum i s observed (#10 F i g . 4-2). Furthermore, on rea p p l y i n g the u.v. a f t e r t h i s formation the current b u i l d s up slo w l y again towards a maximum. F i n a l l y , i n c r e a s i n g the a p p l i e d voltage from 20 to 25 v o l t s , a f t e r a p p l i c a b l e photogrowth has taken p l a c e , does not immediately increase the secondary c u r r e n t . In t h i s case both sides of the specimen c o n t r i b u t e to the c u r r e n t , however, the current decreases f a i r l y r a p i d l y towards the value of the secondary current p r i o r to changing the v o l t a g e and even a f t e r 65 minutes exposure to u.v. an increase i n secondary current i s not observed (// 23 and 24 F i g . 4-2). 4. SUMMARY 33-3 The e l l i p s o m e t r y r e s u l t s v e r i f y the r e s u l t s obtained by other methods. That i s , the e f f e c t of u.v. r a d i a t i o n i s to f i r s t modify the p r o p e r t i e s of the e x i s t i n g oxide a f t e r which photostimulated growth occurs accompanied by a b u i l d up i n secondary c u r r e n t . Photostimulated growth occurs at f i e l d s which are too low to support n o t i c e a b l e oxide growth, i n t h i s case at f i e l d s lower than 0.7 x 10^ V/cm. The oxide produced i s two layer e d w i t h a G of 0.68, but may have graded p r o p e r t i e s as a f u n c t i o n of f i e l d or i n c r e a s i n g t h i c k n e s s and greater a b s o r p t i o n of r a d i a t i o n . The r a d i a t i o n has a pro-nounced a f f e d t on the o p t i c a l p r o p e r t i e s of the oxide. In p a r t i c u l a r , the index of the outer l a y e r i s 1.82 (compared to 2.22 f o r normal oxide) which i s s i m i l a r to the value determined f o r anodic oxide f i l m s produce on Ta i n an oxygen plasma"*. I t seems from the long i n c u b a t i o n p e r i o d , slow decay and b u i l d up of secondary c u r r e n t , the observed maximum i n the secondary current w i t h time on rea p p l y i n g the u.v. and the v o l t a g e , that the secondary current i s d e f i n i t e l y i o n i c i n nature. The photogrown oxide probably has a lower-density giving r i s e to a computed e f f i c i e n c y of better' than 100% for the formation of oxide by the secondary current. F i n a l l y , the cr e a t i o n of ions to support the secondary current i s p r i m a r i l y due to the r a d i a t i o n and not t the e l e c t r i c f i e l d . 113 V. THE CURRENT TRANSIENT AT CONSTANT FIELD: SMALL'SIGNAL A - C CAPACITANCE 1. INTRODUCTION 22 The constant f i e l d current t r a n s i e n t was discovered by Young who was at that time studying the r a t e of c r e a t i o n of F r e n k e l ^ d e f e c t s i n r e l a t i o n to the p r e d i c t i o n s of the high f i e l d F r e n k e l defect theory. To observe the production of defects without i n t e r f e r e n c e , the c o n c e n t r a t i o n of defects were reduced by growing the oxide at constant v o l t a g e (v^) u n t i l the i o n i c current was small and then annealing the specimen at 100° C. The annealing i n terms of the theory causes i n t e r s t i t i a l ions to recombine w i t h vacancy s i t e s and thus reduce the c o n c e n t r a t i o n of Frenkel d e f e c t s . On a p p l i c a t i o n of a voltage step V > the i o n i c current observed would g i v e an i n d i c a t i o n of the r a t e of production of F r e n k e l d e f e c t s . Equation 1-6 p r e d i c t s that on applying V the current should b u i l d up w i t h time at f i r s t r a p i d l y and then more slo w l y towards a maximum as the r a t e of recombination of ions w i t h vacancies i n c r e a s e s . The observed behaviour i s that the current b u i l d s up at f i r s t s l o w l y and then more r a p i d l y i n an a c c e l e r a t i n g f a s h i o n to a maximum. A f t e r the maximum i s reached the current f a l l s o f f as the oxide grows at constant v o l t a g e . The t r a n s i e n t i s f u r t h e r c h a r a c t e r i z e d by 2 dJ/dt = KJ during the i n i t i a l p art of the t r a n s i e n t , w i t h constant of pro-p o r t i o n a l i t y , K, h i g h l y f i e l d and temperature dependent. To e x p l a i n t h i s behaviour a p a r t l y current c o n t r o l l e d process i s needed r a t h e r than a s o l e l y e l e c t r i c f i e l d c o n t r o l l e d process. I n i t i a l l y a model of i o n avalanche process i n which two ions are r e q u i r e d and act to make another i o n a v a i l a b l e f o r conduction was proposed by Young. More r e c e n t l y the d i e l e c t r i c p o l a r i z a t i o n model i n which the. time development of p o l a r i z a t i o n 27 depends on the i o n i c current was advanced by Dignam . A method has now been devised to t e s t t h i s m o d e l . ^ 114 This section deals with the t h e o r e t i c a l foundation, experimental method and r e s u l t s of t h i s t e s t . Some general properties of the transient are also given. 2. THEORETICAL FOUNDATION Equation 1.10 which describes the constant f i e l d current transient i n the d i e l e c t r i c p o l a r i z a t i o n theory may be derived phenomelogically as follows. Experimentally and t h e o r e t i c a l l y the steady state i o n i c conduction currents are described by an expression J = J q exp F(E) F(E) can have forms: I - 3E 2)/kT, (5.1) (a) F(E) = (aE  g(b) F(E) = qaE/kT, as an approximation to (a) and (c) F(E) = Y E 1 / 2 / k T . If i t i s assumed that the e f f e c t i v e f i e l d i s responsible f o r ion motion then the e f f e c t i v e f i e l d may be substituted f o r the applied f i e l d i n F(E) which becomes F ( E £ ) . The time rate of change of current during constant applied f i e l d can then be ascribed to adjustment of i n t e r n a l f i e l d with time or , dF(E ) dJ/dt = (dJ/dE )(dE /dt) = AV e e e at dt o e since E = E + 6'P/c , where P i s the e l e c t r i c p o l a r i z a t i o n and 6'is e o .5 for a Lorentz f i e l d . This gives dJ/dt = JC dP/dt where C i s almost independent of J and i s given f o r the d i f f e r e n t forms i n 5-1 as: (a) C = 6'[a 2-48kTln (J/J ) ] / e kT o o (b) C = 6' qa/c kT o (c) C = 6 ' Y 2 / [ 2 e o ( k T ) 2 l n ( J / J Q ) ] 115 r e s p e c t i v e l y . C i s constant only i n case (b) Experimentally during the i n i t i a l a c c e l e r a t i n g part of the t r a n s i e n t dJ 72 — — cc J dt Therefore at t h i s stage dP/dt a J . I f a s i n g l e Debye type process i s r e q u i r e d to give the time dependence of P then the normal Debye equation dP/dt = (1/x )'( e x E-P ) O O S i s modified f o r non zero i o n i c current to dP/dt = J / T ( e x E-P ) o o s which i s the equation d e s c r i b i n g the t r a n s i e n t i n the d i e l e c t r i c p o l a r i z a t i o n model. This equation reduces to dP/dt J when the p o l a r i z a t i o n i s f a r from e q u i l i b r i u m or P << x E. o s ' -The normal d i e l e c t r i c behaviour under an a.c. f i e l d at low frequencies i s that the l o s s e s or the imaginary part of the d i e l e c t r i c constant, £ i s n e a r l y independent of frequency. For t h i s to occur a s u p e r p o s i t i o n of Debye terms w i t h a range of r e l a x a t i o n times i s required."'" Thus the r a t e of change of p o l a r i z a t i o n should be of the form dP • j r = E J / T . ( G x E-P) dt ^ 1 o s where i t seems reasonable to assume, i f the d i e l e c t r i c p o l a r i z a t i o n theory i s c o r r e c t , that a l l the c o n t r i b u t i n g s i t e s or a l l the r e l a x a t i o n processes are a f f e c t e d by the passage of current i n an analogous manner. I f a small a-c s i g n a l i s superimposed on a d-c v o l t a g e which i s causing some i o n i c current to flow, the a-c response should c o n s i s t of the normal d i e l e c t r i c response of the oxide which i s a f f e c t e d by the passage of i o n i c current and the i o n i c current response due to the a-c s i g n a l , where the equivalent c i r c u i t of the oxide i s supposed to be a l o s s y d i e l e c t r i c i n p a r a l l e l 72 w i t h a frequency-dependent impedance a s s o c i a t e d w i t h the i o n i c c u r r e n t . 1 1 6 The frequency dependence of the i o n i c impedance i s not known, however, i t i s expected to decrease f a i r l y r a p i d l y with frequency at low f r e -quencies- At high frequencies or neglecting the i o n i c current response and for a process with a single relaxation time, the r e l a t i v e p e r m i t t i v i t y E (to) =• e]_(to) ~ Je^ Cw), as given by the well known Debye equations as e..-= (e +ej ( 1 + U 2 T 2 ) - 1 1 s 0 0 2 2-1 ?2 = 10T (c - E ^ ) (1+10 T ) with f or the case of i o n i c current flowing the re l a x a t i o n time i s T = T /J, and o where from equation 1.10, rewritten below | f = E x,77- + A J ( E X - E - P ) , dt o l d t o s E = £ (0) = 1 + X s r s £=o = E r ( ° ° ) = 1 + X 1 A N D T = (AT)" 1 The small s i g n a l capacitance i s r e l a t e d to while the d i e l e c t r i c losses are r e l a t e d to E . At a given frequency i f J increases as i s the case i n the constant f i e l d current transient then £., or the capacitance w i l l also show some increase since £ > For a range of re l a x a t i o n times each affected by the current i n the same manner t h i s increase i n capacitance w i l l be enhanced. F i n a l l y , i n p r a c t i c e there i s ample evidence that the process giving r i s e to capacitance i s d e f i n i t l y correlated to the i o n i c conduction process as was discussed i n chapter 3 section 3.1c. Thus measurement of c a p a c i t a t i v e current during the constant f i e l d current transient should provide a test to the d i e l e c t r i c p o l a r i z a t i o n theory of i o n i c conduction. 4. EXPERIMENTAL METHODS 1. Specimen P r e p a r a t i o n The tantalum specimens were cut from F a n s t e e l c a p a c i t o r grade metal 3 sheet and were about 2 x 1 x 0.12 cm w i t h a tab. The specimens were chemi c a l l y p o l i s h e d . This was fol l o w e d by a 10 second 48%' HF dip and d i s t i l l e d water r i n s e . A t h i c k anodic oxide was formed on the tab. The specimen were then anodized i n batches at constant voltage f o r 24 hours i n an e l e c t r o l y t e of 5cc (98% H.SO.) or (85% H„P0.) i n one l i t r e of water. The anodizing v o l t a g e , V , 2 4 3 4 r was approximately 100 v o l t s . The leakage current a f t e r formation at V f o r 24 hour r 2 was l e s s than 0.3 uamp/cm . The specimens were annealed f o r f i v e minutes i n b o i l i n g d i s t i l l e d water and stored t i l l r e q u i r e d . P r i o r to use, a specimen was immersed f o r 10 seconds i n a dichromate solution"*" and then thoroughly r i n s e d i n d i s t i l l e d water. The -specimen was clamped i n a holder which f i t t e d i n t o a c e l l . In the c e l l a l a r g e p l a t i n i z e d platinum e l e c t r o d e served f o r capacitance measurements and cathode. The c e l l was immersed i n a thermostatted bath of water and g l y c e r o l (temperature c o n t r o l b e t t e r than + 0.1° C). The e l e c t r o l y t e i n the c e l l was s t i r r e d c ontinuously to minimize temperature gradients at the specimen. The d i l u t e U SO^ e l e c t r o l y t e mentioned above was used f o r a l l t r a n s i e n t experiments. 2. Measurements The change i n small s i g n a l capacitance of the Ta / T a 2 0 ^ / e l e c t r o l y t e / Pt c e l l was monitored during the t r a n s i e n t using two d i f f e r e n t methods. The f i r s t method employed a l o c k i n a m p l i f i e r to monitor the change i n small s i g n a l current i n the c e l l c i r c u i t ( F i g . 5-1). A regulated power supply gave the vo l t a g e step, connection being made to the c i r c u i t v i a toggle + S o l u t i o n of concentrated s u l f u r i c a c i d saturated w i t h potassium dichromate. 118 CELL s 1 1 S> n t S 2 R3 -AA / : 7 7tta l2 PREFERENCE SIGNAL METER OUT LOCK IN AMPLIFIER 0 CHANNEL 7 W O CHANNEL CHART RECORDER CHANNEL 2 F i g . 5-1: C i r c u i t employing l o c k - i n a m p l i f i e r to measure s m a l l s i g n a l c e l l response. V9 RECORDER 6h CELL INDUCTIVE LOAD F i g . 5-2: Capacitance bridge. switch which a l s o opened r e l a y S2. The a-c s i g n a l to .the c e l l was provided across R (v = 7.2 m i l l i v o l t s ) by an o s c i l l a t o r (Wavetek //111) v i a an i s o l a t i o n transformer and voltage d i v i d e r . A l o c k i n a m p l i f i e r monitored the d e s i r e d component VQ(d) of the small s i g n a l v o l t a g e v^ across R q due to the a-c current f l o w i n g i n the c i r c u i t . The phase angle 6 i s s e l e c t a b l e and i s w i t h respect to the o s c i l l a t o r s i g n a l . Using the zero suppress to reduce v (6.) to zero on the s c a l e of the l o c k i n a m p l i f i e r meter, then the change i n V Q ( 6 ) o r Av ( 8 ) appeared d i r e c t l y on the meter. The two channels of the recorder o (Mosely 7100 BM) r e s p e c t i v e l y monitored the meter d e f l e c t i o n and d-c v o l t a g e drop V across R due to i o n i c c u r r e n t . Thus the c a p a c i t i v e current change and 0 o i o n i c current were recorded simultaneously. The c e l l i s made the unknown arm of an R-C Wien b r i d g e , i n the second method used to measure change i n capacitance ( F i g . 5-2). C o - a x i a l cables were used f o r go and r e t u r n leads to the arms of the b r i d g e . These are made of equal l e n g t h on each side of the bridge to reduce e r r o r s . ^ The c e l l was balanced against a s e r i e s R-C combination DY v a r y i n g R^ and R^ or R^ keeping C^ f i x e d , and n u l l was detected using a n u l l d e tector a m p l i f i e r whose output i s connected to an o s c i l l o s c o p e . N u l l occurred when only harmonics of the small s i g n a l were observed on the o s c i l l o s c o p e . The t r a n s i e n t was again monitored by- a recorder. The time length of the t r a n s i e n t allowed a number of n u l l s to be determined during i t s course. The t h i c k n e s s of oxides formed i n d i l u t e H„S0. was determined from 2 4 the minima i n the specular r e f l e c t i v i t y as a f u n c t i o n of wavelength using a Carey double beam rec o r d i n g spectrophotometer"*". To o b t a i n the t h i c k n e s s , the minima observed are compared w i t h a chart of t h i c k n e s s versus wavelength of + Courtesy of B.C. Research C o u n c i l 120 minima f o r these oxides. 3. Reduction and Accuracy of Results The a-c impedance of the e l e c t r o l y t i c c e l l can be represented by a p a r a l l e l r , C combination of the oxide i n s e r i e s w i t h the e l e c t r o l y t e P P r e s i s t a n c e R . This r e p r e s e n t a t i o n and i t s equivalent s e r i e s r e p r e s e n t a t i o n e i s shown below i n f i g u r e 5-3. e l e c t r o l y t e R oxide r - V \ A A e l e c t r o l y t e f - < = > -VNAA R oxide Figure 5-3 w i t h the conversion: and r = r (1-a )- r a p s s C = C /(1+a ) = C p s s (5.2) • r l Where a - co C r = (uC r ) equals tan 6, the l o s s tangent, which i n p r a c t i c e s s p p i s l e s s than 0.02, so the approximation i n 5-2 i s accurate (.1%). The e l e c t r o l y t e r e s i s t a n c e i s determined from the zero i n t e r c e p t of t o t a l s e r i e s r e s i s t a n c e verses 1/f as 1/f goes to zero.''" At t h i s p o i n t only the e l e c t r o l y t e r e s i s t a n c e c o n t r i b u t e s to the d i s s i p a t i o n f a c t o r (D) sin c e the oxide r e s i s t a n c e i s e f f e c t i v e l y shorted by the oxide reactance. A t y p i c a l r e s u l t i s shown i n F i g . 5-4 f o r d i l u t e H 2 S°4 el e c t r°lyte at 0° C. 121 10 sec/f F i g . 5.4: Determination of e l e c t r o l y t e r e s i s t a n c e , R g (R g = R o + r g i s the t o t a l s e r i e s r e s i s t a n c e ) The a-c v o l t a g e sampled by the l o c k i n a m p l i f i e r ( F i g . 5-1) using the sm a l l s i g n a l model of the c e l l i s v (e) = o R (Z+r -ho 2C 2r 2Z)v + iwC R r 2 v o p p p s J p o p s (Z + r ) 2 + (ioC r Z ) 2 P P P where v =v R n/(R 0 + R.+jcoL) w i t h toL << R„ and Z = R +R„+R +Z , where Z s g 2 • 2 3 3 o / e s , s i s the power supply impedance which i s approximately 4Q. The c a p a c i t i v e v o l t a g e w i l l be toC r R v v (go*) = _P P o s R to C v o s s (z+r ) 2 + (wC Zr ) 2 1 + 2Z/r + (toC Z ) 2 P P P P s 5.3 where Z « r . By prooer choice of R , 5.3 reduces to p o> v (90°) a uc R v or Av (90°) = k'AC O S O S o s 5.4 122 However, the best choice of R i s a compromise between the above, the s i g n a l to noise r a t i o of the a m p l i f i e r and the s t a b i l i t y of v . For the values i n v o l v e d r s (C ~ 0.67 uf, f = IKH and r ~ 30 Kfi) a range 100ft < R < 50ft s a t i s f i e s s z p o these requirements. The a c t u a l method i s to set R so that v (90°) i s 2 M o o m i l l i v o l t s and then suppress t h i s to zero on the 200 Pvolt s c a l e of the lo c k i n a m p l i f i e r meter f o r maximum s e n s i t i v i t y . Avo(90°) i s then monitored during the t r n a s i e n t . The change i n capacitance i s a r r i v e d at as f o l l o w s . The c e l l i s replaced w i t h R , r and C as measured by a capacitance bridge"*" p r i o r to e p p the t r a n s i e n t . Assuming 5.4 ho l d s , i s v a r i e d to o b t a i n the p r o p o r t i o n a l i t y constant K'. The change i n C can be c a l c u l a t e d from the recorded Av (90°). P o The accuracy of t h i s method depends on the value of R and the amount that r o p changes during the t r a n s i e n t . I f R i s w i t h i n the s p e c i f i e d range and r o p decreases by l e s s than f i f t y percent the accuracy i n measuring AC^ i s l e s s than 5% too l a r g e . In the second method the n u l l c o n d i t i o n of the bridge assuming the Z, i s a s e r i e s combination of C, and R. y i e l d s : 4 4 4 C s = C 4 = C 3 R ] L / R 2 and R 4 = r g + R e = R 3 R ^ The bridge accuracy (.1%) was checked by r e p l a c i n g the c e l l by a p a r a l l e l combination of standard R-C components. The two methods o u t l i n e d complemented one another. The f i r s t gave a c o n t i n u o u s ' i n d i c a t i o n of the capacitance change while the second checked t h i s change q u a n t i t a t i v e l y . + General Radio Model 1615A, 6 place accuracy. 123 300 TIME /SEC F i g . 5~5a: T y p i c a l constant f i e l d current t r a n s i e n t : current density as a function of time (Dell'Oca. and Young?!). TIME / S E C F i g . 5 -5h: Percentage change i n and a f t e r transient, lock-in amplifier, -5. RESULTS Figure 5-5a i s t y p i c a l of the constant f i e l d current t r a n s i e n t s observed at 0° C a f t e r a p plying a 125 v o l t step or 6.2 x 10^ V/cm f i e l d to oxides i n i t i a l l y formed to a f i n a l f i e l d of 4.9 x 10^ V/cm i n 0.2N ll^SO^ and then annealed f o r 5 min. at 100° C. The t r a n s i e n t d u r a t i o n i s about 3 minutes and time development of current i s as f o l l o w s . The i n i t i a l charging 2 current decays at f i r s t r a p i d l y and then more slowly to about 0.5 pA/cm i n the f i r s t 15 to 20 seconds, then the current gegins to b u i l d up slow l y but w i t h i n c r e a s i n g speed. (This minimum i s not re s o l v e d i n F i g . 5-5a but was observed at other times by changing to more s e n s i t i v e ranges on the r e c o r d e r ) . The b u i l d up i n current continues w i t h r a p i d l y a c c e l e r a t i n g speed to a maximum 2 of 42 yA/cm or about a 100 f o l d i n c r e a s e . The f i e l d i s removed when the peak i n the current occurs. 6-0 4.0 2-0 10 [ r J t ) / r p ( t = 0 ) l - O •O' .O' o . 0 ft)/rs(t=0) o o o— 0 F i g . 5-5c: 100 200 300 TIME/'sec Change i n s e r i e s , r g , and p a r a l l e l , r p , equivalent r e s i s t a n c e at 1 kHz given as the r a t i o of the r e s i s t a n c e at time t to the i n i t i a l r e s i s t a n c e at t- -0. (Same time span as i n f i g u r e 5-5b). The corresponding change i n the measured a-c response during the t r a n s i e n t i s presented i n f i g u r e s 5-5b and c. Although the % change i n s c r i e s capacitance from the i n i t i a l capacitance i s p l o t t e d ( f i g . 5-5b), the p a r a l l e l capacitance has approximately the same change (and value) s i n c e tan 6 i s small (< .02) during the t r a n s i e n t . This i s the case even though the measured s e r i e s r e s i s t a n c e increases almost by f i v e f o l d ( f i g . 5-5c) by the end of the t r a n s i e n t . The l o c k i n a m p l i f i e r measurements gave e s s e n t i a l l y the same r e s u l t s (dashed l i n e F i g . 5-5a) and show that most of the capacitance change occurs i n the i n i t i a l part of the t r a n s i e n t . The agreement between l o c k i n a m p l i f i e r and b r i d g e measurements becomes poorer near the end of the t r a n s i e n t , the a m p l i f i e r p r e d i c t i n g a l a r g e r change because r ^ has decreased by a f a c t o r of f o u r . Oxides t r e a t e d i n the same manner (same voltages but not n e c e s s a r i l y same f i e l d s ) but grown i n 0.23N H^PO^ give s i m i l a r r e s u l t s . The lower i o n i c oxides gives r i s e to a lower current maxima of s l i g h t l y greater t r a n s i e n t time span which i s about capacitance change i s s l i g h t l y g reater than f o r oxides The s e r i e s r e s i s t a n c e increased by about the same r a t i o as r o r a^i>u^ grown oxides. I n c r e a s i n g a p p l i e d f i e l d (voltage) or oxide temperature g e n e r a l l y shortens the t r a n s i e n t s time span and i n c r e a s e s the maximum current observed. For example, i n the above experiments the t r a n s i e n t span i s shortened to about 6 seconds i f the temperature i s r a i s e d to 25° C or the f i e l d i ncreased by about 7%. (Figure 5-5a shows a t r a n s i e n t f o r decreased f i e l d . ) I f the v o l t a g e i s maintained a f t e r the peak i n the t r a n s i e n t i s reached, then the i o n current decreases as the oxide thickness i n c r e a s e s . Figure 5-6 shows t h i s case along w i t h the capacitance and s e r i e s r e s i s t a n c e c o n d u c t i v i t y i n these 2 about 32 uA/cm and a 200 sec. long. The % grown i n d i l u t e H SO. F i g . 5-6a(above): Shows constant f i e l d c urrent t r a n s i e n t followed by growth at constant v o l t a g e at 0° C a f t e r a p p l y i n g a 120 v o l t step to an oxide, grown in/'0.23N phosphoric a c i d _ e l e c t r o l y t e . F i g . 5-6b(below): Small s i g n a l response during t r a n s i e n t and growth of f i g . 5-6a and on same time s c a l e . ^ change measured. The change in capacitance i s at f i r s t rapid and then i t s speed decreases and becomes almost l i n e a r with time as transient proceeds. A smooth t r a n s i t i o n occurs into the region oxide growth. On the other hand the end of the transient i s accompanied by a peak i n the ser i e s resistance or a minimum i n p a r a l l e l resistance as i s expected (Fig. 5-5b). A check was made using ellipsometry to v e r i f y i f the current during the transient was i o n i c as assumed i n previous i n v e s t i g a t i o n s on the grounds that normal growth behaviour was observed i f the voltage was maintained a f t e r the transient was complete. Table 5-1 v e r i f i e s that the current during the transient i s within experimental error, i o n i c . This table further shows that the annealing process i s not r e f l e c t e d by the o p t i c a l measurements, as expected. Table 5-1 Comparison of change i n thickness predicted by Faraday's law and Ellipsometry of an oxide formed at 95 V for 20 hr.,annealed for 5 minutes at 100°C and subjected to 118 v o l t at 0°C. A ¥ Thickness O After Formation 309.46 43.23 ~ 1968 A o A f t e r Anneal 309.48 A3-II ~ 1968 A Af t e r Transient 305.80 42.16 ~ 1978 A Change i n thickness - Ellipsometry 10 A o - Faraday's Law 10.6 A The change i n thickness during the transient i n F i g . 5.5a i s calculated to be about 0.4%. Thus the. f i e l d i s e s s e n t i a l l y constant during t h i s type of transient behaviour. The s l i g h t increase i n thickness accounts for a s l i g h t l y increasing rate of decrease of capacitance during the f i n a l portion of the transient and this i s also why on removing the f i e l d the capacitance does not return completely to i t s i n i t i a l value p r i o r to the t r a n s i e n t . Thus 128 0-4 L i i i . 0 20 40 60 80 WO vb/volt F i g . 5 - 7 (above): Change i n capacitance %A'Cg as a function of voltage ,y^.,anplied to annealed films grown to 1 0 0 v o l t s in. d i l u t e H 9 S 0 , (o) and H , P 0 . ( x,A$. ( D a l l ' O c a 7 3 ) . ^ J 4 F i g . 5 - 8 (below): Ratio of serie s resistance to i n i t i a l s e r i e s resistance as a function of voltage jV^y. for two of the specimens of f i g . 5 - 7 ( D e l l ' Oca 7 3) . 129 the observed behaviour of capacitance during the t r a n s i e n t i s that the c a p a c i -tance decreases at f i r s t r a p i d l y by about 4 % and then decreases l i n e a r l y . On r e -moving the f i e l d the capacitance returns c l o s e to i t s i n i t i a l v alue. Figure 5-7, shows the percent change i n C g as a f u n c t i o n of v o l t a g e , V, < V , a p p l i e d to the oxide i n s o l u t i o n at 0 ° C. The p o i n t s were obtained b r by manually changing the voltage and measuring C g and d i s s i p a t i o n f a c t o r w i t h a G . E . capacitance b r i d g e . The r e s u l t s depend on time a f t e r i s changed, how-ever, a l l r e s u l t s i n d i c a t e a decrease i n C as V approaches V . Thus part of the s b h i n i t i a l r a p i d decrease i n capacitance during the t r a n s i e n t i s probably c o n t r i b u t e d by the processes o c c u r r i n g at V < V . I t might be expected that s i n c e the b r f i l m s had been p r e v i o u s l y annealed the a p p l i c a t i o n of i n steps would cause some t r a n s i e n t i o n i c response even w i t h V < V . This i s u n l i k e l y D r because a) the time i n v o l v e d i n t a k i n g the measurements was r e l a t i v e l y s h o r t , a few minutes; b) normal d-c and a-c t r a n s i e n t behaviour was observed w i t h specimens f i r s t subjected to these measurements; and c) the s e r i e s r e s i s t a n c e decreased w i t h ( f i g . 5-8) whereas during the current t r a n s i e n t i t i n c r e a s e s ( f i g s . 5-5a, 5-6a) and remains l a r g e r than the i n i t i a l s e r i e s r e s i s t a n c e showing a p a r a l l e l behaviour to the current when the t r a n s i e n t i s complete and normal growth occurs ( f i g . 5-6a). This behaviour i n d i c a t e s that the t r a n s i e n t current i s i o n i c s i n c e the current during normal growth i s i o n i c , and that a d i f f e r e n t process i s o c c u r r i n g at voltages below the formation voltage of the oxide. 6. DISCUSSION The r e s u l t s i n d i c a t e that the capacitance decreases during the constant f i e l d current t r a n s i e n t contrary to the p r e d i c t i o n of the d i e l e c t r i c p o l a r i z a -t i o n model. However, t h i s a n a l y s i s considers only the i o n i c current a f f e c t e d d i e l e c t r i c response of the oxide. I t i s expected that a c o n t r i b u t i o n to the measured c a p a c i t a t i v e current would be made by the component of i o n i c current 130 responding to the a-c s i g n a l but not i n phase with i t . Since the frequency i s f i x e d , i f an out of phase i o n i c component does exist .its contribution to the capacitance should p a r a l l e l the behaviour of the t o t a l i o n i c current, that i s , i t should change with time at f i r s t slowly and then more r a p i d l y i n an acce-l e r a t i n g fashion. The observed behaviour i s that the- capacitance changes at f i r s t r a p i d l y and then more slowly becoming l i n e a r with time so that the out of phase i o n i c current component i s not present to an extent which a f f e c t s the above conclusion. The high f i e l d Frenkel defect model predicts that on a p p l i c a t i o n of the f i e l d step the number of i n t e r s t i t i a l ions should r a p i d l y increase. If these ions are a v a i l a b l e for p o l a r i z a t i o n e f f e c t s than an increase i n capaci-tance should occur. On the other hand, the high f i e l d step would promote ions from t h e i r s i t e s and put them i n t r a n s i t and these ions might not be a v a i l a b l e for to- and - fro motion i n response to an a-c s i g n a l . An e f f e c t which occurs i s e l e c t r o s t r i c t i o n which would serve to decrease the response by compressing the l a t t i c e . Another explanation i s that on a p p l i c a t i o n of the f i e l d step impuri-t i e s i n the oxide begin to migrate to the i n t e r f a c e s e f f e c t i v e l y increasing the distance between charges c a r r i e d by the impurities and thus decreasing the measured capacitance. This would also explain the behaviour of capacitance with voltage below V . 131 VI. THERMAL RECRYSTALLIZATION 1. INTRODUCTION Anodic oxide f i l m s on tantalum are normally amorphous. This amorphous oxide may be r e c r y s t a l l i z e d on the metal, however, i t i s more u s e f u l to remove the oxide from the metal which can be done by cathodic l i b e r a t i o n of hydro-gen or (with damage) by s t r e t c h i n g the metal."'" The s t r i p p e d oxide i s c r y s t a l l i z e d by heating i n a furnace or by heating w i t h the e l e c t r o n beam i n an e l e c t r o n microscope. I n v e s t i g a t i o n of the c r y s t a l l i z a t i o n p r o p e r t i e s has been l i m i t e d to a temperature range which i n bulk Ta^O^ produces the 3 or low temperature phase. 74. (This occurs below 1300°C according to Kofstad ). The present understanding 75-81 from these i n v e s t i g a t i o n s i s that the s t r u c t u r e of the c r y s t a l l i z e d oxide i s b u i l t around a s u p e r l a t t i c e . That i s , the oxide c o n s i s t s of a b a s i c s t r u c -77 78 ture which i s b e l i e v e d to be orthrohombic "' which i s b u i l t i n t o r e g u l a r l y o c c u r r i n g s u p e r l a t t i c e planes which are d i s t i n c t from and spaced much f u r t h e r apart than the planes of the b a s i c s t r u c t u r e . Recently both b a s i c l a t t i c e planes and the s u p e r l a t t i c e planes have been r e s o l v e d d i r e c t l y . ^ ' ^ 75 76 81 R e c r y s t a l l i z a t i o n of the oxide occurs between 500 to 800° C. ' ' However, there i s l i t t l e i n f o r m a t i o n on the e f f e c t of oxide growth c o n d i t i o n s on r e c r y s t a l l i z a t i o n p r o p e r t i e s . R e c r y s t a l l i z a t i o n processes are germane to understanding oxide p r o p e r t i e s and i o n i c motion and the object of t h i s study was to determine the a f f e c t of growth c o n d i t i o n s p a r t i c u l a r l y that of e l e c t r o l y t e i n c o r p o r a t i o n on the r e c r y s t a l l i z a t i o n p r o p e r t i e s . 2. EXPERIMENTAL PROCEDURE Anodic oxide f i l m s were grown on tantalum f o i l (0.003") at d i f f e r e n t 2 current d e n s i t i e s (0.1, 0.5, 1.0 and 10 mA/cm ) to 30 v o l t s or at 21 v o l t s 132 Fig. 6-1 (above): Very high concentration of small c r y s t a l l i t e s (10,000X) accompanied by d i f f r a c t i o n pattern from square c r y s t a l l i t e (Oxide grown i n d i l u t e H-SO^, heated 1 hr. i n a i r at 700° C). Fig. 6-2 (below): Extensive area of c r y s t a l l i z a t i o n and small c r y s t a l l i t e s (0.1 mA/cm2 in 0.2N H SO : heated i n a i r 1 hr. at 700°C: 20,000X). overnight (corresponding to a low f i n a l current d e n s t i y ) i n va r i o u s d i l u t e H^SO^, 1LP0. and HNC" s o l u t i o n s at 25°C. P r i o r to a n o d i z a t i o n the f o i l was chemically 3 4 3 p o l i s h e d and r i n s e d . The f i l m s were removed from the metal by making the metal cathodic i n the forming e l e c t r o l y t e . Some f i l m s were removed w i t h a s o l u b l e adhesive. The b i t s of oxide were f l o a t e d onto platinum g r i d s (200 mesh) and r i n s e d . R e c r y s t a l l i z a t i o n of the oxide on the g r i d was c a r r i e d out i n a s i l i c a tube furnace w i t h f l o w i n g oxygen or a i r atmosphere. Heating was u s u a l l y f o r one hour at one of three temperatures 650°C, 700°C and 750°C. Specimens grown under d i f f e r e n t c o n d i t i o n s were heated simultaneously f o r comparison of extent of r e c r y s t a l l i z a t i o n . The r e c r y s t a l l i z e d specimen were analyzed by tra n s m i s s i o n e l e c t r o n microscopy using an HU 11A e l e c t r o n microscope at 100 KV. Some specimens were a l s o r e c r y s t a l l i z e d using the e l e c t r o n beam. The percentage of r e c r y s t a l l i z e d area of a speciman was c a l c u l a t e d from the area of r e c r y s t a l l i z a -t i o n o c c u r r i n g i n at l e a s t seven g r i d squares of an area which was judged r e p r e s e n t a t i v e of the specimen. 3. RESULTS 1. General Features The general features of r e c r y s t a l l i z a t i o n a f t e r heating s t r i p p e d oxide specimens f o r one hour at 650, 700 or 750°C are as f o l l o w s . Less than 0.001% of the area has c r y s t a l l i z e d at 650°C. While at 750°C, c r y s t a l l i z a t i o n of the oxide i s e s s e n t i a l l y completed w i t h more than 95% of the area r e c r y s -t a l l i z e d . However, at 700°C the amount of c r y s t a l l i z a t i o n depends on the growth c o n d i t i o n s . C r y s t a l l i z a t i o n occurs e i t h e r as small i s o l a t e d c r y s t a l l i t e s ( f i g . 6-1) or as extensive areas of r e c r y s t a l l i z a t i o n w i t h jagged contours. The small c r y s t a l l i t e s are the dominant form at 650°C but p e r s i s t at 700°C where the 134 F i g . 6 - 4 : One of the few regularly shaped c r y s t a l l i t e s from oxides formed i n d i l u t e H_P0^ (20,000X) and i t s d i f f r a c t i o n pattern. 135 extensive areas give r i s e to most of the c r y s t a l l i z a t i o n (Fig. 6-2). The c r y s t a l l i t e s are more prevalent i n oxides formed i n d i l u t e H~SO, than i n d i l u t e H„PO.. In 2 4 3 4 R^SO^ grown oxides, the c r y s t a l l i t e s are more prevalent when the oxide i s heated i n an a i r rather than i n an oxygen atmosphere. The c r y s t a l l i t e s seem to occur independent of rate of oxide growth or concentration of e l e c t r o l y t e . Figure 6-1 i s taken from an area with much greater than normal concentration of these c r y s t a l l i t e s . This f i g u r e shows that the c r y s t a l l i t e s , which are at the most a couple of micrometers across, can be square, rectangular and can have a twin structure. The twin structure shows up i n l i g h t and dark con-t r a s t (Fig- 6-3). Figure 6-4 shows one of the few r e g u l a r l y shaped c r y s t a l s found i n oxides i n H„PO,. 3 4 It i s not apparent whether the small c r y s t a l l i t e s give r i s e , or act as nucleation centres f o r the extensive areas of r e c r y s t a l l i z a t i o n , because some of the small c r y s t a l l i t e s observed at 650° show l i t t l e change 0 n reheating at 700°. Some of the intermediate sized grains of c r y s t a l l i z a t i o n which do give r i s e to the extensive areas are shown i n F i g . 6-5. The grains of oxides grown i n H^PO^ or HNO^ tended to be of a slender l e a f l i k e shape whereas those of H^PO^ grown oxides were broad i n d i c a t i n g a more uniform outward growth. 2. E f f e c t of Growth Conditions D e f i n i t e e f f e c t of growth conditions were observed on heating at 700°C for one hour. At t h i s temperature oxide specimens formed under d i f f e r e n t conditions showed d i f f e r e n t extents of c r y s t a l l i z a t i o n when they were heated simultaneously as a set. The extent of r e c r y s t a l l i z a t i o n varied between s i m i l a r specimens from d i f f e r e n t sets and t h i s was probably because the furnace could only be set to within about 10° of the desired temperature. However, the r e c r y s t a l l i z a t i o n trend between specimens i n a set was reproducible from set to set. An i n d i c a t i o n of the v a r i a t i o n i n extent of r e c r y s t a l l i z a t i o n encountered 136 Fig. 6-5: Intermediate sized grains of c r y s t a l l i z a t i o n . Top and bottom l e f t from H 3 P 0 4 grown oxides and heated respectively i n a i r (20,000X) and i n oxygen (25,OOOX). Top right from H^SO^ grown oxide and bottom righ t from HNO3 grown oxide, both heated i n a i r . ( A l l IN solutions and a l l grown at 1 mA/cm^). between sets i s shown below, i n t h i s case from heating i n oxygen. E l e c t r o l y t e Formation Extent of r e c r y s t a l l i z a t i o n % Set 1 Set 4 0. IN H 2S0 4 1 mA/cm 2 3.8 0.09 p. IN H 3 P ° 4 1 mA/cm 2 2.4 0.01 1. ON H 2S0 4 1 mA/cm 2 50 0.26 1. ON H 3 P ° 4 1 mA/cm 2 4.4 0.04 1. ON H 2S0 4 10 mA/cm 70 0.4 1. ON V ° 4 21 V overnight 66 0.2 The most pronounced e f f e c t was caused by the e l e c t r o l y t e , i n that oxides formed i n d i l u t e H 3P0 4 always showed l e s s r e c r y s t a l l i z a t i o n than those formed i n the same normality H 2S0 4 (0.1 and IN were compared). Less pronounce but i n most cases evident was that the amount of c r y s t a l l i z a t i o n increased 2 with current density (1 to 10 mA/cm ) and with normality (0.1 to IN) i n each e l e c t r o l y t e . However, films grown at 21 v o l t overnight had s i m i l a r charac-2 t e r i s t i c s to oxides grown at 10 mA/cm although, the f i n a l current i n the 2 former case was less than 0.4 uA/cm . The e f f e c t of growth conditions can -ulzo be seen i n most cases i n the electron micrographs from oxides heated for one hour at 750°C ( f i g . 6-6 to 6-10). Films formed i n E^PO^ always show a l i g h t e r contrast than those of H_S0, and can be distinguished when viewed i n the electron microscope 2 4 This i s perhaps because the E^PO^ films are somewhat thinner, although other features such as a less pronounced grain structure distinguished them from r e c r y s t a l l i z e d H 2S0 4 grown oxides. The e f f e c t of growth rate i n r e c r y s t a l l i z e H 2S0 4 films i s shown i n f i g s . 6-7 to 6-10. A more pronounced grain structure 2 i s usually obtained from r e c r y s t a l l i z e d oxides grown at 1 mA/cm than those 2 grown at 10 mA/cm or 21 v o l t overnight. The l a s t two again show s i m i l a r features. 138 i g . 6-6 to 6-10(as numbered): Show t y p i c a l r e c r y s t a l l i z e d area a f t e r heating at 750° C i n oxygen of oxides formed r e s p e c t i v e l y at 1 mA/cm2 i n N H3PO4, and 1 mA/cm2, 10 mA/cm2 and 21 v o l t s overnight i n IN H 2S0 4 (25,000X). 139 The r e c r y s t a l l i z a t i o n behaviour of oxides heated i n a i r was s i m i l a r to that i n oxygen, presented above. 3. D i f f r a c t i o n P a t t e r n s A l a r g e v a r i e t y of d i f f r a c t i o n p a t t e r n s were observed, most of these were complicated by the presence of s u p e r l a t t i c e spots between main spots a r i s i n g from the b a s i c l a t t i c e . The extensive areas of c r y s t a l l i z a t i o n always gave r i s e to complex arrangement of the two d i f f e r e n t spots and some of the simpler arrangements are shown i n f i g s . 6-11 and 6-12. The most pr e v a l e n t of the simpler arrangements was the hexagonal arrangement of main s u p e r l a t t i c e spots f i r s t d i s -75 covered by Harvey and Willman upon which they proposed a hexagonal c e l l f o r the oxide (see f i g . 6-14). In t h i s case each main spot i s surrounded by s i x s u p e r l a t t i c e spots which are e q u a l l y spaced or form a hexagon. The main and s u p e r l a t t i c e spots a l s o form a hexagonal g r i d . Also observed were d i f f r a c t i o n p a t t e r n s x>7ith main spots on rox-7S of s u p e r l a t t i c e spots as reported by 79 S p y r i d e l i s et a l . . A d i f f r a c t i o n p a t t e r n not p r e v i o u s l y reported i s shoxm i n f i g . 6-12. This c o n s i s t s of a r e c t a n g u l a r p a t t e r n of main spots, each main spot i s surrounded by a group of s u p e r l a t t i c e spots ( f i g . 6-12). The groups s u p e r l a t t i c e spots a l s o have a r e c t a n g u l a r arrangement. Further a n a l y s i s i n d i c a t e s that the main spots may be indexed on the orthorombic u n i t c e l l 77 ° proposed by Lehovec x^ith the dimensions, a = 6.20, b = 3.66 and c = 3.88A. Taking the s m a l l e s t r e c t a n g l e of main spots ( f i g . 6-12) i t s dimensions corresponds to the f o l l o w i n g lengths i n the r e a l l a t t i c e ( a l l i n A); length 1.83; width 3.88, diagonal 1.65, and represent d i r e c t i o n s d Q 2 Q ; d 0 0 1 ; d 0 2 i o r d 3 l 0 ' d001 and ^311 ' r e s p e c t i v e l y xvithin a maximum d e v i a t i o n of 2.5% betxveen c a l c u l a t e d and measured q u a n t i t i e s . Thus the txro dimensional r e c i p r o c a l l a t t i c e of f i g . 6-12 i s at r i g h t angles to and s u p p l i e s the t h i r d dimension along a plane c o n t a i n i n g 010 and 001 or 310 and 001 to the txro dimensional r e c i p r o c a l l a t t i c e of f i g . 6-13. 140 • 9 • 9 it F i g . 6-11: Hexagonal d i f f r a c t i o n p a t t e r n of s u p e r l a t t i c e and main spots. F i g . 6-12: Rectangular d i f f r a c t i o n p a t t e r n of s u p e r l a t t i c e and main spots. " f t * ! •*»' •/"• 1-020 .4. F i g . 6-13: D i f f e r e n t r e c i p r o c a l u n i t c e l l s found f o r r e c r y s t a l l i z e d anodic oxide f i l m s of tantalum. Lehovec??, - - - - Harvey et al.''-'' S p y r i d e l i s et a l . ^ . (Taken from S p v r i d e l i s et a l . 7 9 ) . 141 The small c r y s t a l l i t e s give r i s e to various patterns i n which no s u p e r l a t t i c e spots are seen. The. d i f f r a c t i o n pattern from the twinned c r y s t a l ( f i g . 6-3) a c t u a l l y consists of two i n t e r s e c t i n g patterns of d i f f r a c t i o n spots. The l i g h t contrast section gives r i s e to a squashed hexagonal or diamond l i k e pattern which i s t y p i c a l of a l l rectangular c r y s t a l l i t e s . The dark contrast region gives r i s e to a s i m i l a r array with every other l i n e missing as a r e s u l t of interference e f f e c t s . These patterns could not be s a t i s f a c t o r i l y indexed on the orthorombic c e l l , nor, on the hexagonal c e l l of Harvey and Willman. The simplest pattern obtained comes from the square c r y s t a l l i t e s l i k e those.of f i g . 6-1 and give r i s e to simple rectangular patterns which can be indexed on the orthorombic c e l l . For the case shown i n f i g . 6-1 indexing gives d i r e c t i o n s 010, 001 and O i l along the short, long and diagonal rows of spots d i r e c t l y with the maximum deviation between calculated and measured of less than 4%. 4. DISCUSSION Evidence was obtained that oxides grown i n d i l u t e H^PO^ c r y s t a l l i z e less r a p i d l y than oxides formed i n d i l u t e U^SO^. Jt i s suggested that t h i s e f f e c t i s due to the greater incorporation of e l e c t r o l y t e species which occur i n the former. This i s consistent with other evidence which indicates that e l e c t r o l y t e incorporation decreases i o n i c motion. The e f f e c t s of growth rate and'concentration of e l e c t r o l y t e on r e c r y s t a l l i z a t i o n were les s w ell established. Presumably e f f e c t s such as s t r a i n s the oxide, defects etc. due to growth rates anneal out at lower temperatures. Annealing occurs even at room temperature as shown xtfith the observed decrease in' instantaneous current on reapplying a f i e l d to the oxide with the time 25 the oxide i s held at zero f i e l d . R e c r y s t a l l i z a t i o n occurs i n two modes, small c r y s t a l l i t e s and extensive areas of c r y s t a l l i z a t i o n . Whether the l a t t e r evolves from the former has not been determined, but there i s some evidence that the small c r y s t a l l i t e s are at least not due. to impurities, i n that some of the d i f f r a c t i o n patterns can be indexed on the same unit c e l l as the main spots of the extensive areas. Apparently there i s not enough material i n the small c r y s t a l l i t e s to give r i s e to the s u p e r l a t t i c e spots. 143 V I I . CONCLUSIONS A number of anodic oxide p r o p e r t i e s were s t u d i e d to o b t a i n i n f o r m a t i o n on the i o n i c conduction mechanism i n these f i l m s . This i n c l u d e d ; a j an e l l i p s o m e t r i c study of non uniform anodic oxide p r o p e r t i e s produced by e l e c t r o l y t e i n c o r p o r a t i o n ; b) an i n i t i a l study of anomalous oxide growth caused by u l t r a - v i o l e t r a d i a t i o n using e l l i p s o m e t r y ; c) the e f f e c t of growth c o n d i t i o n s on r e c y r s t a l l i z a t i o n and: d) measurement of capacitance during the constant f i e l d current t r a n s i e n t to d i s t i n g u i s h between models of i o n i c conduction. The r e s u l t s obtained i n these s t u d i e s i n d i c a t e : • (1) E l l i p s o m e t r y can be used to re s o l v e the two l a y e r s of oxides formed i n phosphoric a c i d , the three l a y e r s of oxide formed i n m u l t i p l e a n o d i z a t i o n and the oxide growth under u l t r a - v i o l e t r a d i a t i o n . By curve f i t t i n g the e l l i p s o m e t r y measurements obtained as a f u n c t i o n of i n c r e a s i n g oxide t h i c k n e s s i t i s p o s s i b l e to determine not only the thickness of the oxide but a l s o the t h i c k n e s s of each l a y e r , and f u r t h e r , the o p t i c a l p r o p e r t i e s of two l a y e r f i l m s may als o be determined. This allows the e f f e c t of e l e c t r o l y t e i n c o r p o r a t i o n and u l t r a v i o l e t r a d i a t i o n on i o n i c conduction to be s t u d i e d . Under c e r t a i n assumptions, e l l i p -sometry a l s o provides a non-destructive o p t i c a l method of determining i o n t r a n s p o r t numbers i n phosphoric a c i d grown oxides. (2) There i s now o p t i c a l evidence i n support of an oxide model which i n d i c a t e s t h a t : a) both metal and oxygen ions are mobile so that part of the f i l m grows at the metal oxide i n t e r f a c e and part at 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 . b) e l e c t r o l y t e species are incorporated i n t o the part which grows at the e l e c t r o l y t e i n t e r f a c e . c) phosphate i s inc o r p o r a t e d more stongly than i s sulphate. d) the inner l a y e r of oxides produced i n phosphoric a c i d a l s o have s i m i l a r o p t i c a l p r o p e r t i e s to oxides formed i n d i l u t e s u l f u r i c a c i d and e) e l e c t r o l y t e i n c o r p o r a t i o n decreases not only i o n i c c o n d u c t i v i t y and d i e l e t r i c p e r m i t t i v i t y but a l s o decreases index of r e f r a c t i o n and r a t e of r e c r y s t a l i z a t i o n of anodic oxides. (3) I f i t i s c o r r e c t to assume that the i n c o r p o r a t e d e l e c t r o l y t e remains w i t h i n that part of the oxide produced by metal i o n motion t h i s study o p t i c a l l y confirms that the metal ion transport number increases w i t h current d e n s i t y of growth and w i t h e l e c t r o l y t e i n c o r p o r a t i o n and that i t depends on previous h i s t o r y of the oxide has been determined. In e f f e c t a l l these, p r o p e r t i e s i n d i c a t e that the metal i o n transport number depends on the e l e c t r i c f i e l d . ( 4 ) That the e l e c t r i c f i e l d changes only s l o w l y towards a value t y p i c a l of the new e l e c t r o l y t e on going from formation i n one e l e c t r o l y t e to another and f u r t h e r that the i o n i c conduction process depends on oxide h i s t o r y i n d i c a t e s o at l e a s t f o r t h i c k f i l m s (above 200 A) that the oxide r a t h e r than the i n t e r f a c e exert the dominant i n f l u e n c e on the i o n i c conduction process. (5) E l e c t r o l y t e i n c o r p o r a t i o n i s r e s p o n s i b l e f o r some i f not a l l the observed curvature i n the k i n e t i c s of growth or Log J - E c h a r a c t e r i s t i c s . This i s because of two e f f e c t s which occur w i t h i n c r e a s i n g current d e n s i t y . F i r s t , the outer l a y e r increases i t s p r o p o r t i o n of the oxide and secondly, the concentra-t i o n of incorporated species i n the outer l a y e r i n c r e a s e s . Since the f i e l d i ncreases w i t h c o n c e n t r a t i o n , the second e f f e c t , i n d i c a t e s that the l o g J - E r e l a t i o n f o r the outer l a y e r must be n o n - l i n e a r . Since the f i e l d i n the outer l a y e r i s higher than i n the i n n e r , the average f i e l d across the oxide increases f a s t e r due to the f i r s t e f f e c t than i f there were no i n c o r p o r a t i o n and thus the l o g J - E p l o t f o r the t o t a l oxide would be n o n - l i n e a r . The curvature would be f u r t h e r increased by the second e f f e c t . I t i s not known whether the curvature i s i n t r i n s i c to non-incorporated oxides. A question which w i l l be answered by forming oxides i n e l e c t r o l y t e s g i v i n g no i n c o r p o r a t i o n . A l k a l i n e e l e c t r o l y t e s might f u l f i l t h i s requirement. 145 ( 6 ) The u l t r a - v i o l e t r a d i a t i o n e f f e c t on an oxide held at the formation voltage i s to f i r s t modify the properties of the e x i s t i n g oxide a f t e r which oxide growth occurs. Oxide growth i s accompanied by a secondary current which i s i o n i c i n nature since i t hehaves i n a s i m i l a r manner to normal growth currents when the voltage and the u.v. i s taken o f f or applied and further the charge passed by the secondary current accounts for most of the oxide increase i n thickness. The oxide grown i s at l e a s t two layered with an outer layer whose index of r e f r a c t i o n i s 2 0 % lower then that of normal oxide. Ionic conduction i n the presence of u.v. occurs at f i e l d s almost a magnitude lower than normal oxide growth. And f i n a l l y , the production of ions for conduction i s stimulated by r a d i a t i o n rather than the e l e c t r i c f i e l d . (7) There appears to be a c o r r e l a t i o n between i o n i c conduction and d i e l e c t r i c properties of the oxide. This i s shown i n that the e f f e c t of e l e c t r o l y t e incorporation can be accounted for by making the current density an exponential function of the e l e c t r i c displacement rather than the applied f i e l d and that the CV product i s constant for anodization i n a sequence of e l e c t r o l y t e s and constant for formation i n d i f f e r e n t d i l u t e e l e c t r o l y t e s . This might be accounted for by an e f f e c t i v e f i e l d dependent ion motion. However, the capa-citance decrease during the transient at constant f i e l d cannot be explained by an increase i n e f f e c t i v e f i e l d as proposed by Dignam. 146 BIBLIOGRAPHY 1. L. Young,"Anodic Oxide Films".Academic Press, London and New York (1961). 2. D.A. Vermilyea, Chapter in"Non-Crystalline S o l i d s " Edtr. V.D. Freschette, J. Wiley & Sons, New York and London (1960). 3. D.A. Vermilyea, Chapter in"Advances i n Electrochemistry" _3, Edtr. P. Delahay, Interscience Publishers, Inc., New York (1963), 4. W.S. Goruk, L. Young and F.G.R. Zobel, Chapter i n Modern Aspects of E l e c t r o -chemistry, 4_, Edtr. J.O'M. Bockris, Plenum Press, New York (1966). 5. C.J. Dell'Oca, D.L. Pulfrey and L. Young, review a r t i c l e i n "Physics of Thin Films", i n press. 6. Extended abstract booklet, Electrochemical Society Meeting, Dallas (1967). 7. P.F. Schmidt and D.M. Smyth , Edtr., " E l e c t r o l y t i c R e c t i f i c a t i o n " , S o c , New York (1967) . 8. Extended abstract booklet, Electrochemical Society Meeting, New York (1969). 9. S.F. Bubar and D.A. Vermilyea, J . Electrochem. S o c , 882 (1967); i b i d . , 113, 892 (1966). 10. 'D.A. Vermilyea, J . 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Stromberg and H.L. Steinberg, J . Res. Natl. Bur. Std. 67A, 373 (1963). 63. C.J. Dell'Oca and L. Young, pp. 331-339 reference 52. 64. O.W. Edwards, R.L. Dunn and J.D. H a t f i e l d , J. Chem. Eng. Tech. 1, 688 (1964). 65. H.T. Yolken, R.M. Waxier and J . Kruger, J. Opt. Soc. Am. 57_, 283 (1967). 66. D. A. Holmes and D.L. Feucht, J . Opt. Soc. Am. _5J7, 466 (1967). 67. R.J-. Archer and C.V. Shank, J. Opt. Soc. Am., _57, 191 (1967). 68. C.J. Dell'Oca and L. Young, Paper presented by C.J.D. at the Electrochem. Soc. Spring Meeting, New York 1969. Abstract. # 14,. reference //8. 69. L. Young, Proc. Roy. Soc. (London) A244, 41 (1958). 149 70. L. Young, Can. J. Chem., 38, 1141, (1958). 71. C.J. Dell'Oca and L. Young, App. Phys. Let., JL3, 228 (1968). 72. P. Winkel, CA. P i s t o r i u s and W. Ch. van Geel, P h i l i p s Res. Rept. 13, 277 (1958). 73. C J . Dell'Oca, Interim Report to Sprague E l e c t r i c Company, January 1968. 74. P.F. Kofstad, J. Less-Common Metals 5, 158 (1963). 75. J . Harvey and H. Willman, Acta Cryst., 14, 278 (1967). 76. D.A. Vermilyea, Acta. Met. JL, 282 (1953). 77. K. Lehovec, J. of the Less-Common Metals, J7, 397 (1964). 78. L.D. Calvert and P.H.G. Draper, Canad. J . Chem., 40, 1943 (1962). 79. J . S p y r i d e l i s , P. Delvaignette and S. Amelinckx, Phys. Stat. Sol.. 19, 683 (1967). 80. J . S p y r i d e l i s , P. Delavignette and S. Amelinckx, Mat. Res. B u l l . J3, 31 (1968); 2, 113 (1967). 81. R. E. Pawel and J . J . Campbell, J. Electrochem. S o c , 111, 1230 (1964). 150 APPENDIX A: RELATION BETWEEN EXTINCTION POSITIONS AND ELLIPSOMETRY ANGLES The r e l a t i o n between e x t i n c t i o n settings of p o l a r i z e r analyzer and quarter wave plate and the ellipsometry angles i s found by determining the condition on the incident l i g h t required for the r e f l e c t e d l i g h t to be l i n e a r l y p o l arized. The l i g h t incident on the specimen i s found by considering the two figures to the r i g h t , x^ith the convention that angles are measured counter-clockwise from the plane of incidence when looking into the beam. The l i n e a r l y p o a l i r z e d l i g h t which leaves the polar-i z e r set at an angle P (top r i g h t ) i s resolved along the slow, s l , and f a s t , f, d i r e c t i o n s of the compensator (loxver l e f t ) as E =Ecos(C-P) and E =Esin(C-P) r s l A - l On traversing the compensator, E s u f f e r s a S J -phase retardation 6 of the compensator with respect to E .. Thus the components of the incident l i g h t along the o r i g i n a l p and s axis are E = E^ cosC + E . sinC e op f s l -J6 E = E r sinC - E . sinC e os f s i -j<5 A-2 i n Polar form t h i s becomes E E os jA 1 + tan(C-P) tanC e tan 7 e J o = 11 '-tanC - tan (C-P) e A-3 NoX'7, the e l l i p s o m e t r y e q u a t i o n p r o v i d e s a r e l a t i o n s h i p between 151 incident and r e f l e c t e d l i g h t given by tan Y' e^ A° = tan H'e^A tanY e^ Ao A-4 o o The requirement that the r e f l e c t e d l i g h t i s l i n e a r l y polarized imposes the condition that A ' = 0 or IT o and thus tan A = -tanA . i . e . , A = -A or ~A + TT A - 5 o o and tanY = cot Y tanY' A - 6 o o must occur from equation A-4. Equations for A and Y are obtained from equations A - 2 and A - 3 i n o terms of the p o l a r i z e r e x t i n c t i o n s e t t i n g as tanA = - s i n 2(C-P) s i n 5 [ s i n 2C cos 2(C-P) - s i n 2(C-P) cos 2C c o s f i ] " 1 A-7 and cos 2Y = -cos2(C-P) cos 2C - s i n 2(C-P) s i n 2C cos6 A - 8 o These r e l a t i o n s may be s i m p l i f i e d i f the compensator i s f i x e d at +45°. For the compenstor at 45° the l a s t two equations become tanA = sincS tan (2P-90°) A - 7 ' cos 2m = -cos6 cos 2P A - 8 ' o o For a given A, there are two independent p o l a r i z e r settings P = P ' and P = P = D o 1 o z P.,+90° which s a t i s f y A-7'. This requires from A-8' that the 4' , and Y 0 1 J ^ o l o2 corresponding to P^ and P^ obey the i d e n t i t y cot f . = t a n Y n o o l 02 thus the r e l a t i o n betx^een Y and the e x t i n c t i o n settings of the p o l a r i z e r cor-responding to P^ and P^ from A - 9 and A - 6 i s 2 tan 1' = tanM"- tanY' o l o2 152 Since A has a range from 0 to 2IT there i s a range of p o l a r i z e r 67 settings depending on the choice of A^ that i s -45° < P, < 135° for A = -A + 180° — 1 — o and -135° < P . < 45° for A =' -A. — 2 — o A l l the d i s t i n c t settings of the analyzer can be obtained from any range of the scale extending over TT° . R e s t r i c t i n g o <_ A <_ TT then e x t i n c t i o n by the analyzer occurs at A = 180 - ¥ ' and A. = ¥ I or 1 o l 2 o2 tan¥ = tan(180°-Aj cotY , = tan(A ) Cot¥ „ A-10' 1 o l ^ oZ where i n the notation of McCrackin et a l . who organized the e x t i n c t i o n settings into four zones, a i s ¥ ' and a is f ' (see chapter 2, section 1.2a). p o l s o2 153 APPENDIX B: TOTAL REFLECTION COEFFICIENT FOR MANY LAYERS ON A METAL 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 for a system of many layers on a metal ( f i g . 6-1) may be computed using matrix methods. Consider mono-chromatic l i g h t of wavelength A incident on plane p a r a l l e l homogenous i s o t r o p i c layers. The media, are characterized by a complex index of r e f r a c t i o n , N = n-jk, the films by a thickness d and the i n t e r f a c e s by the Fresnel c o e f f i c i e n t s . The l i n e a r i t y of the wave equation governing the motion of l i g h t allows the p and s components of l i g h t to be treated separately and to obtain the resultant l i g h t by vector addition. Thus only one component i s considered which i s written as E without subscript p or s. o In general each medium w i l l have a forward and reverse (primed) t r a v e l l i n g wave. Consider one i n t e r f a c e , say #2, the relationbetween the f i e l d vector on e i t h e r side of the i n t e r f a c e i s given i n terms of the Fresnel c o e f f i c i e n t s , thus E^ and Ej^ can be expressed i n terms of E^ and E^ a l l at z = o as follows: E l E 2 / t : l 2 ( r21 / t :12 ) E2 E i = r 1 2 E i + hJ2 = 1 / t 1 2 [ E 2 ( t 2 1 t 1 2 - r i 2 r 2 1 ) + r l 2 E 2 ] = . l / t 1 2 [ E 2 + r 1 2 E 2 ] using t^2 t21 + r l 2 = a n d r i 2 = r21 ^ c ^ a P t e r ^» s e c t : L o n 2-2) where sequence of subscripts denotes d i r e c t i o n of wave t r a v e l . The above written i n matrix form i s : A wave t r a v e l l i n g a distance z = 0 + to z = d 2 s u f f e r s a phase and * See for example, O.S. Heavens,"Optics of Than S o l i d Films" Butterworths, London (1955). 154 F i g . B - l : L i g h t r e f l e c t e d from £ l a y e r s on a metal (m) s u b s t r a t e . Z=0 chosen a r b i t r a r i l y at second i n t e r f a c e . 155 amplitude change given i n terms of the wave at z=o as: + " j k 2 d 2 E 2 ( d 2 ) •= E 2(0^) e + j k 2 d 2 E^(d 2) = E£(CT) e or again i n matrix form E : le 0 2 'z=o + \0 ^ k 2 d 2 F' V 2 / z=d 2 th In general then the r e l a t i o n s h i p between the i-1 and i region i s given i n terms of a matrix as: J i - 1 ^ i E ! . , , 1-1 /z = z + o where r. ant t. correspond to those of i-1 to i * " ^ medium. The f i l m i s characterized by an o p t i c a l length 6. = k.d. = 2TT N. cos i>. d./x i l l i i i Then for m-1 films on a metal substrate the incident and r e f l e c t e d l i g h t i s given by 'E E' o' m-1 A m 1_ n t. i = l 3 ' l l Z12 Z21 Z22 / E where the metal i s considered absorbing and thick enough to produce no returning wave (E = 0) . m The r e f l e c t i o n c o e f f i c i e n t for the p and s component i s then given by re s p e c t i v e l y s u b s t i t u t i n g the p and s r e f l e c t i o n c o e f f i c i e n t s i n the equation R = E'/E - z /z . o o 21 11 Thus f o r : a) Metal only R = ri b) Single, f i l m on a metal . - 2 j 6 . - 2 j 6 . R = ( r i + r 2 e 1 ) / ( 1 + r ^ e 1 ) c) Two f i l m s on a metal su b s t r a t e r + r e " 2 j 6 l + r e " ^ ( 6 1 + 6 V + r r r e " 2 ^ r l 2 3 r l 2 r3 - 2 j 6 1 - 2 j ( 6 1 + 5 2 ) - 2 j 6 2 1 + r i r 2 e + r i r 3 e + r 2 r 3 e where i n each case the l a r g e s t s u b s c r i p t r e f e r s to the metal s u b s t r a t e . 

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