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Field-induced optical anisotropy in thin niobium oxide films Yee, Kai Kwan 1974

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FIELD-INDUCED OPTICAL ANISOTROPY IN THIN NIOBIUM OXIDE FILMS  by  KAI KWAN YEE B.A.Sc, University  of B r i t i s h  Columbia, 1972  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n t h e Department  of Electrical  We a c c e p t t h i s required  Engineering  t h e s i s as conforming  t o the  standard  THE UNIVERSITY OF BRITISH COLUMBIA November,  1974  In p r e s e n t i n g t h i s  thesis  in p a r t i a l  f u l f i l m e n t o f the requirements f o r  an advanced degree at the U n i v e r s i t y of B r i t i s h the L i b r a r y s h a l l I  make i t  freely available  f u r t h e r agree t h a t p e r m i s s i o n  for  Columbia,  I agree  r e f e r e n c e and  f o r e x t e n s i v e copying o f t h i s  that  study. thesis  f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s of  this  representatives. thesis  It  is understood that copying or p u b l i c a t i o n  f o r f i n a n c i a l gain s h a l l  written permission.  Depa rtment The U n i v e r s i t y o f B r i t i s h Vancouver 8, Canada  Date  > c .  Columbia  2 , I JILL ,  not be allowed without my  ABSTRACT An automated ellipsometer was used to study field-induced o p t i c a l anisotropy i n anodic niobium oxide f i l m s .  The oxide films were  found to change from the o p t i c a l l y i s o t r o p i c state to the o p t i c a l l y a n i sotropic state when an e l e c t r i c f i e l d was applied normal to the f i l m surface.  The anisotropic r e f r a c t i v e indices of the oxide films decreased  quadratically while the thickness of the films increased with the applied f i e l d . determined.  quadratically  The quadratic e l e c t r o - o p t i c c o e f f i c i e n t s were  The changes i n r e f r a c t i v e indices and i n thickness of the  oxide films were found to be independent of time. F i e l d r e c r y s t a l l i z a t i o n of the anodic -niobium oxide films was investigated using a scanning electron microscope. ccirps^sd. V —till t  The r e s u l t s are  oss ^r°po*"t — — for ~ si? od.ic ~ t BJV "t 51 ^JT" • oy^ Hp. f 7. T TT»C v  lished l i t e r a t u r e .  i  -1 rt  t~.r» mi re-  TABLE OF CONTENTS Page ABSTRACT TABLE OF LIST OF  ,  . . . . . . . . . . . . .  i  CONTENTS  i i  ILLUSTRATIONS  iv  ACKNOWLEDGEMENT  vi  1.  INTRODUCTION .  1  2.  THEORY OF ELECTRO-OPTIC EFFECT IN THIN OXIDE FILMS  3  3.  PREVIOUS WORK  9  4.  PRINCIPLES OF ELLIPSOMETRY 4.1 4.2  5.  E l l i p s o m e t r y f o r a Homogeneous I s o t r o p i c S u b s t r a t e Covered by a S i n g l e - l a y e r Homogeneous I s o t r o p i c F i l m .  10  E l l i p s o m e t r y f o r Homogeneous U n i a x i a l A n i s o t r o p i c Non-absorbing F i l m s on I s o t r o p i c S u b s t r a t e s  12  EXPERIMENTAL ARRANGEMENTS 5.1  The  16  5.1.1 5.1.2  System Components The B a l a n c i n g Routine  5.1.3  E l l i p s o m e t e r Alignment  5.2  Anodization  5.3  Window E r r o r  5.4  16  Ellipsometer  5.3.1 5.3.2  6.  10  16 16 .  Cell  22 24  E r r o r of Windows Before Mounting on the C e l l E r r o r of Windows A f t e r Mounting on the C e l l .  . .  Sample P r e p a r a t i o n  30 O p t i c a l Anisotropy 6.1.1 6.1.2 6.1.3  6.2  of Anodic Niobium Oxide F i l m s .  . .  E x p e r i m e n t a l Procedure Results Discussion  F i e l d and Time Dependence of E l e c t r o - o p t i c and trostrictive Effects 6.2.1 6.2.2 6.2.3  6.3  24 28 28  RESULTS 6.1  19  30 31 36 Elec-  E x p e r i m e n t a l Procedure Results Discussion  R e p r o d u c i b i l i t y of E l l i p s o m e t e r Measurements. . . . .  ii  30  37 37 38 42 43  Page 7.  FIELD  RECRYSTALLIZATION  8.  CONCLUSIONS  OF  ANODIC  NIOBIUM  OXIDE  FILMS  .  .  .  .  47 -53>  BIBLIOGRAPHY.  54  APPENDIX.  56  iii  LIST OF  ILLUSTRATIONS Page  Fig.  2.1  I n d i c a t r i x before  and a f t e r an e l e c t r i c f i e l d i s  applied  7  Fig.  4.1  R e f l e c t i o n from a f i l m - c o v e r e d  Fig.  5.1  Schematic of the automated e l l i p s o m e t e r system  17  Fig.  5.2  Zero e r r o r i n p o l a r i z e r and a n a l y z e r  21  Fig.  5.3  S t r u c t u r e of the c e l l  surface  for in situ  10  scales  ellipsometer  measurements Fig.  5.4  Poincare  23  sphere r e p r e s e n t a t i o n o f the e f f e c t of window  e r r o r on the p o l a r i z a t i o n s t a t e of l i g h t  24 27  Fig.  5.5  Window e r r o r i n A a g a i n s t r o t a t i o n of the window  Fig.  6.1  Lower p o r t i o n o f the of a niobium oxide  A-iJi  plot for increasing  thickness  f i l m up to two c y c l e s  32  Fig.  6.2  Upper p o r t i o n o f the A — p l o t  33  Fig.  6.3  (a) T h e o r e t i c a l v a l u e s of minimum A as f u n c t i o n s of 3 and n (b) T h e o r e t i c a l v a l u e s of maximum A as f u n c t i o n s of 0  34  Q  35  8 and n  Fig.  6.4  The change i n r e f r a c t i v e i n d i c e s n  Fig.  6.5  The change i n f i l m t h i c k n e s s  Fig.  6.6  The change i n o r d i n a r y r e f r a c t i v e index and i n t h i c k n e s s with  Q  and n  against E  time when the f i e l d was switched  1.78 x 1 0  6  g  against E  6.7  I n t e r p o l a t i n g a s e t of  Fig.  6.8  Error  39 40  2  from zero to  v/cm  Fig.  . .  41 A-iJ>  data  44  ( d i s t a n c e ) between two e x p e r i m e n t a l  versus  t h i c k n e s s o f the oxide  field,  (b) With a p p l i e d f i e l d  iv  film:  A - i p curves  (a) No a p p l i e d 45  Page F i g .  7.1  R e c r y s t a l l i z e d  areas  of  anodic  niobium  oxide  f i l m  2 formed  at  constant  0.2  mA/cm  to  150  v o l t s ,  at  23°C  i n 0 . 2 N H2SO4 F i g .  7.2  Same  sample  amorphous F i g .  7.3  23°C,  v o l t s , A . l  f i l m  R e c r y s t a l l i z e d at  F i g .  as  i n  49 F i g . was  at  Locus  of  the  l i g h t  i n  a  of  H^SO^,  constant  e l e c t r i c  plane  R e c r y s t a l l i z e d  etched  areas  0.2N  then  7.1.  off  w i t h  niobium at  vector  normal  to  F i g .  A.2  Representation  of  p o l a r i z e d  F i g .  A . 3  Representation  of  phase  for  the  f i l m  0.2  for  10  e l l i p t i c a l l y  on  retardation  149 51  p o l a r i z e d  propagation  Poincare on  to  2  hours  of  50  anodized  mA/cm  d i r e c t i o n  l i g h t  v  .  oxide  v o l t s  the  HF  constant  120  a f t e r  .  56  .  .  58  sphere.  .  58  sphere.  Poincare  ACKNOWLEDGEMENT I from  my  wish  to  supervisor I  also  express Dr.  thank  L.  my  sincere  Young  Dr.  M.  g r a t i t u d e  throughout  Hopper  and  the  Mr.  for  course  W.  the of  Cornish  guidance t h i s for  received  work.  many  h e l p f u l  d i s c u s s i o n s .  I A.  L a c i f  patience  for in  am  indebted  t h e i r typing  F i n a l l y , of  Canada  i s  to  Messrs.  t e c h n i c a l t h i s the  g r a t e f u l l y  J .  Stuber,  a s s i s t a n c e ,  and  A. to  MacKenzie, Miss  Shelagh  H.  Black,  Lund  for  and her  t h e s i s . f i n a n c i a l  support  acknowledged.  v i  of  the  N a t i o n a l  Research  C o u n c i l  1 1.  INTRODUCTION  I t has been suggested"*" t h a t f i l m s o f Ta^O^ used  as l i g h t modulators  and Nb^O^- c o u l d be  because of the dependence of t h e i r  optical  2 c o n s t a n t s on e l e c t r i c  field.  F i l m s o f la^O^  and ^ 2 ^ 5  n  a  v  e  been found  to  be a p r o m i s i n g m a t e r i a l f o r use as o p t i c a l waveguides because they are to p r e p a r e , are c h e m i c a l l y s t a b l e , and have h i g h r e f r a c t i v e i n d i c e s l a r g e bandgaps.  The e l e c t r o - o p t i c p r o p e r t i e s o f Ta^O^  i n v e s t i g a t e d i n some d e t a i l " * " ' ^ ' ^ ' " ^ ^ . • The was  to extend  easy  and  f i l m s have been  o b j e c t i v e of the p r e s e n t work  the knowledge i n the e l e c t r o - o p t i c p r o p e r t i e s o f niobium  oxide  f i l m s which have not. been f u l l y . i n v e s t i g a t e d ' . In  the p u b l i s h e d l i t e r a t u r e , t h i n Ta^O^  f i l m s have been taken  o p t i c a l l y i s o t r o p i c except by C o r n i s h and Young^ who became o p t i c a l l y films.  showed t h a t such  a n i s o t r o p i c when an e l e c t r i c f i e l d was  The work d e s c r i b e d i n t h i s t h e s i s was  in  this  oxide f i l m s would show.  films  a p p l i e d a c r o s s the  to study t h e o r e t i c a l l y  e x p e r i m e n t a l l y the f i e l d - i n d u c e d o p t i c a l a n i s o t r o p y which i t was t h a t anodic niobium  as  and  expected  In s i t u e l l i p s o m e t r y was  used  study. P r e s e n t e d i n chapter 2 o f t h i s t h e s i s i s the theory o f e l e c t r o -  o p t i c e f f e c t i n t h i n oxide Chapter in  films of T a ^  films.  3 d e s c r i b e s the p r e v i o u s work on e l e c t r o - o p t i c  effect  and Nb 0 . 2  The e l l i p s o m e t r y p r i n c i p l e s which have been a p p l i e d i n t h i s work are p r e s e n t e d i n chapter  4.  Chapter 5 d e s c r i b e s the g e n e r a l e x p e r i m e n t a l arrangements: the automated e l l i p s o m e t e r , the c e l l , the windows, and the p r e p a r a t i o n of samples.  D e s c r i b e d a l s o i n t h i s c h a p t e r i s a method which was  d e v i s e d to  i n v e s t i g a t e the b i r e f r i n g e n c e of the c e l l windows, which i s a p o s s i b l e  2 source of e r r o r w i t h i n s i t u e l l i p s o m e t r y . P r e s e n t e d i n chapter 6 are the e x p e r i m e n t a l r e s u l t s on: (a) the field-induced  o p t i c a l a n i s o t r o p y i n anodic niobium oxide f i l m s ,  (b) q u a d r a t i c  electro-optic  and e l e c t r o s t r i c t i v e e f f e c t s , and (c) the r e p r o d u c i b i l i t y o f  e l l i p s o m e t e r measurements. F i e l d r e c r y s t a l l i z a t i o n of the niobium oxide f i l m s was be a s e r i o u s problem encountered  i n a n o d i z a t i o n d u r i n g t h i s work.  r e c r y s t a l l i z e d oxides were examined by u s i n g a s c a n n i n g microscope.  The r e s u l t s are d i s c u s s e d i n c h a p t e r 7. C o n c l u s i o n s are p r e s e n t e d i n chapter  8.  electron  found to The  3  2.  THEORY OF ELECTRO-OPTIC EFFECT IN THIN OXIDE FILMS  The e f f e c t o f changing a p p l y i n g an e l e c t r i c f i e l d tro-optic effect.  the r e f r a c t i v e index o f a m a t e r i a l by  ( i n our case a dc f i e l d ) i s c a l l e d the e l e c -  The r e f r a c t i v e index o f a m a t e r i a l as a f u n c t i o n o f  the d i r e c t i o n of the l i g h t - w a v e normal i s s p e c i f i e d by the " o p t i c a l i n d i c a t r i x " which i s the e l l i p s o i d d e f i n e d by B  ± j  x  ±  X  j  = 1  ( i , j = 1,2,3)  (2.1)  where x^, X£ and x^ a r e the p r i n c i p a l axes o f  the r e l a t i v e d i e l e c t r i c  i m p e r m e a b i l i t y t e n s o r a t o p t i c a l f r e q u e n c i e s , where  3E° B  and K  ij  =  K  o 9D°  i s the p e r m i t t i v i t y  o f a vacuum, and the s u p e r s c r i p t o s i g n i f i e s  o p t i c a l frequency f i e l d s .  The change i n r e f r a c t i v e index o f a m a t e r i a l  Q  due t o an a p p l i e d f i e l d  o r o t h e r cause i s i n g e n e r a l r e p r e s e n t e d by a  change i n the shape, s i z e and o r i e n t a t i o n  o f the i n d i c a t r i x .  The oxide f i l m s under study a r e b e l i e v e d t o be amorphous and hence s h o u l d be i s o t r o p i c w i t h no e l e c t r i c f i e l d  applied.  Its refractive  index, n^, can be r e p r e s e n t e d by an i n d i c a t r i x which i s a sphere o f the form B (x, + x + x ) = o Jz J 2  where B  2  2  1  = 1/n , x,. i s d e f i n e d a l o n g the d i r e c t i o n normal t o t h e f i l m n' 3 2  o  b  s u r f a c e , x^ and X2 a r e p a r a l l e l t o t h e f i l m s u r f a c e . When an e l e c t r i c f i e l d  i s a p p l i e d normal t o the f i l m s u r f a c e ,  the oxide f i l m has a r o t a t i o n a l symmetry about the a x i s i n x^ d i r e c t i o n . The  i n d i c a t r i x s h o u l d t h e r e f o r e become an e l l i p s o i d o f r o t a t i o n  about  4  the f i l m  normal. I f we had  optical,  f i e l d s of one  frequency, say dc, i n s t e a d o f dc p l u s  the e l e c t r i c displacement D c o u l d be expressed i n terms of the  electric field  as  D. = a. . E. + 6. ., E .E  + ) . , . „E,E,E, +  ...  ( i , j , k , £ = 1,2,3) where a^_., B ^ j ^  d  a n  Y^jj^  a  r  t e n s o r components.  e  the d i r e c t i o n o f the e l e c t r i c f i e l d E  become -E., -E,  orphous,  and -E  = - a . .E. + 6.  i] ]  l  S i n c e the o x i d e f i l m i s  " s e e s " an i d e n t i c a l o x i d e f i l m as  i s expected t o become -D^. -D.  L e t us suppose t h a t  r e v e r s e d so t h a t E., E, and J k  , respectively.  the r e v e r s e d f i e l d  so that  i s now  (2.2)  ljk  E q u a t i o n 2.2  -y. .. .E.E, E„ + 'ljkJl j K H  E.E.  j k  originally  becomes ...  ( i , j , k , J l = 1,2,3) E q u a t i o n s 2.2 for  and 2.3  am-  can h o l d s i m u l t a n e o u s l y o n l y i f the  (2.3) coefficients  the even power terms e q u a l z e r o . The  s t a t i c p e r m i t t i v i t y o f the amorphous o x i d e f i l m i s d e f i n e d  3D. K  ij  =  air  =  a  i j  +  Y  ijkA  *  E  +  ••• ( i , j , k , £ = 1,2,3)  In our c a s e , we  are concerned w i t h the p e r m i t t i v i t y a t o p t i c a l  quencies f o r r e l a t i v e l y l a r g e dc e l e c t r i c mittivity  low i n t e n s i t y l i g h t as a f u n c t i o n o f a  field.  By analogy w i t h the above dc c a s e ^  (2.4) frerelatively the p e r -  a t o p t i c a l f r e q u e n c i e s can be expressed as a power s e r i e s i n  the dc e l e c t r i c  field: K  lj  =  3iy  =  a  i j  +  b  ijkA £ E  +  •• •  (l,j,k,£ = 1,2,3)  (2.5)  5  where the s u p e r s c r i p t and  o (as b e f o r e ) stands f o r o p t i c a l f r e q u e n c i e s , E  E ^ a r e the components o f the dc e l e c t r i c f i e l d .  power two a r e n e g l e c t e d .  By c o n t r a s t  there i s no l i n e a r e l e c t r o - o p t i c  Terms h i g h e r than  w i t h non-centrosymmetric  effect.  o p t i c a l p e r m i t t i v i t y when the dc f i e l d  k  crystals  The c o e f f i c i e n t a ^ i s the  i s zero.  8 9 Since i t i s considered mental p h y s i c a l v a r i a b l e electric field,  '  t h a t p o l a r i z a t i o n i s t h e more funda-  i n e l e c t r o - o p t i c e f f e c t as compared t o t h e  the r e l a t i o n f o r the q u a d r a t i c e l e c t r o - o p t i c  effect i s  c o n v e n t i o n a l l y expressed as B  °  r  ij  A B  =  B  ij  o  "  +  8  ijkA i> P  (2.6) (i,j,k,£ = 1,2,3)  8ijk£ k £ P  P  where P i s the p o l a r i z a t i o n , and A B „ i s t h e change i n r e l a t i v e o p t i c a l i m p e r m e a b i l i t y when a f i e l d It a l l P P^.  i s known t h a t  i s applied. f o r thermodynamic reasons  10  AB.. = AB.. f o r  Hence  k  8  ijk£  8  jik£  S i n c e P^P^ = P P » we have £  8  The  ijki,  k  8  ij£k  tensor r e l a t i o n 2.6' can therefore be reduced to the matrix form AB = g A m mn n  where  AB = m  AB 11 AB 22 AB 33 AB 23 AB 13 AB 12  (m,n  = 1,2,...6)  (2.7)  6  A = n  P P r  P  2 3  r  P  3 p P 12 when n = 1,2,3  mn —  and  g  mn  In tion.  "  0 S  when n = 4,5,6  ijk£  the case c o n s i d e r e d h e r e , the p o l a r i z a t i o n  U s i n g the form o f g °  is in  direc-  f o r i s o t r o p i c m a t e r i a l " ^ , e q u a t i o n 2.7 i s mn  w r i t t e n out i n f u l l AB^ AB AB  "  2  S  g  3  g  AB, 4 AB  l l  S  12  g  12  12  g  l l  8  12  12 0  5  AB, 6  8  12 0  l l 0  g  0  0  0  0  0  0  0  0  0  0  0  0  ' 0  0  0  •o  0  0  0  0  0  0  0  44 0  0  0  0  0  g  g  44 0  8  P  44_  where g ^ may be shown t o depend on g ^ and g-j^' 44 3  3  3  12  P  3  8  11  P  3  2  2  (2.8)  indices  as (2.9)  =j= B^, because o f the symmetry.  AB. = -(-^-r) An.  8  P  By d e f i n i t i o n B^,  ( i = 1,2,3)  For o u r case.B^ =  12  2  and B^ correspond t o t h e t h r e e p r i n c i p a l r e f r a c t i v e B. = — 2 l n.  g  From e q u a t i o n 2.9  ( i = 1,2,3)  I  Because the change i n r e f r a c t i v e  index a f t e r a f i e l d  compared t o the z e r o - f i e l d r e f r a c t i v e to a s u f f i c i e n t a p p r o x i m a t i o n . therefore A  n  l  =  A n  2  =  n  A n  3  =  " 2  n~ n g  i s applied i s small  index n^, we may r e p l a c e n^ by n  The changes i n r e f r a c t i v e  n  indices are  12 3 " P  (2.10) v  n " f "  g  l l  P  3  2  Because An^ = A i ^ =f= An^, when a dc e l e c t r i c  field  normal t o the f i l m s u r f a c e , the o x i d e f i l m i s expected  i s applied  t o be u n i a x i a l  a n i s o t r o p i c w i t h i t s o p t i c a x i s i n the d i r e c t i o n o f t h e s u r f a c e normal. The i n d i c a t r i x f o r the a n i s o t r o p i c f i l m i s an e l l i p s o i d o f r o t a t i o n about the s u r f a c e normal, t h e s i g n o f the e f f e c t s b e i n g , as i t t u r n s o u t , as shown i n exaggerated  Fig.  2.1  i n the x ^ x  2  manner i n F i g . 2.1.  The o r d i n a r y r e f r a c t i v e i n d e x n  I n d i c a t r i x b e f o r e and a f t e r an e l e c t r i c  field  p l a n e , and the e x t r a o r d i n a r y r e f r a c t i v e i n d e x n  £  i s applied.  i n x^ d i r e c -  t i o n a r e expressed as n An  = n o  An  e  =n  - n o n  e  Since A n field  - n  Q  n  = -  and A n  2  P °12 3  n  g,, P_  x— g ,  =  g  —TJ— 11  e  (2.11)  3  b o t h have q u a d r a t i c dependence on t h e a p p l i e d  they s h o u l d be r e l a t e d through An  2  0  0  the r e l a t i o n  (2.12)  = B An • o  where B i s a c o n s t a n t independent o f t h e a p p l i e d f i e l d . a l s o c h a r a c t e r i z e s the changing  The v a l u e o f 6  o f t h e f i l m from the i s o t r o p i c s t a t e t o  8  the a n i s o t r o p i c s t a t e when a f i e l d f i l m remains  isotropic.  i s applied.  I f 3 e q u a l s one,  the  9 3.  The anodic was  oxide  PREVIOUS WORK  e l e c t r i c f i e l d - i n d u c e d m o d u l a t i o n of i n t e n s i t y r e f l e x i o n i n  f i l m s was  d i s c o v e r e d by Holden and  a t t r i b u t e d to the e l e c t r o s t r i c t i v e  Ullman^'^.  The  modulation  compression o f the oxide  films.  1 3 Frova  and M i g l i o r a t o ' , a n a l y z i n g the e l e c t r o m o d u l a t i o n  the i n t e r f e r e n c e spectrum of anodic dominant e f f e c t was of the  T a  2°5  f i l m s , suggested t h a t  the  the e l e c t r o - o p t i c m o d u l a t i o n o'ffethe r e f r a c t i v e  f i l m s , r a t h e r than e l e c t r o s t r i c t i o n .  The  experimental  the q u a d r a t i c e l e c t r o - o p t i c c o e f f i c i e n t s of Ta^O those of oxygen-octahedra f e r r o e l e c t r i c Ord,  crystals.  Hopper and Wang , a p p l y i n g e l l i p s o m e t r y to the problem,  suggested t h a t the o n l y c o n t r i b u t i o n to the  thickness  ).  of  f i l m s were compared to  index decreased l i n e a r l y on i n c r e a s i n g the a p p l i e d f i e l d .  f i e l d was  index  values  reportedhthattitheifdilmhthltcknessriinereasediMnea.rly'iwhereas' the  with  of  the  change i n the b u l k  refractive  They a l s o  change i n r e f r a c t i v e  d e n s i t y of the  Only a narrow range of e l e c t r i c  film  f i e l d was  index  ( i . e . the  film  used i n t h e i r  studies. All isotropic.  the above authors took the oxide  Cornish  were o p t i c a l l y  f i l m s as  and Young^ showed t h a t anodic  tantalum oxide  films  i s o t r o p i c i n . t h e absence of an e l e c t r i c f i e l d , but became  a n i s o t r o p i c when an e l e c t r i c f i e l d was A l s o v a r y i n g the  applied f i e l d  they showed t h a t the  a p p l i e d normal to the  from zero to j u s t below the  film  slow components i n the  time-dependence of the  surface.  formation  changes i n a n i s o t r o p i c r e f r a c t i v e i n d i c e s  t h i c k n e s s were both q u a d r a t i c a l l y f i e l d - d e p e n d e n t .  thickness.  optically  field,  and  They observed f a s t  changes i n i n d i c e s  and  and  10  4. PRINCIPLES OF  4.1  Ellipsometry  ELLIPSOMETRY  f o r a Homogeneous I s o t r o p i c S u b s t r a t e  Covered by  a  S i n g l e - l a y e r Homogeneous I s o t r o p i c F i l m Ellipsometry  i s a convenient method f o r the  i n v e s t i g a t i o n o f t h i n f i l m s on r e f l e c t i n g s u r f a c e s provided different  t h a t the  immersed i n l i q u i d s ,  r e f r a c t i v e index of the sample i s s u f f i c i e n t l y  from t h a t of the  measure the  optical  liquid.  The  p r i n c i p l e of e l l i p s o m e t r y i s to  changes of s t a t e of p o l a r i z a t i o n when an  elliptically  p o l a r i z e d monochromatic l i g h t beam i s r e f l e c t e d by a s u r f a c e , covered w i t h a t r a n s p a r e n t of the system can be  so t h a t only  From these changes, the  optical  surface constants  calculated.  Ellipsometry shown i n F i g . 4.1,  film.  or a  has  f o r systems of homogeneous i o s t r o p i c l a y e r s , as been d e s c r i b e d  a b r i e f o u t l i n e need be  i n d e t a i l by many authors given  11,12,13  here.  LIGHT A  M  B  I  E  N  C  E  n, F  ->  I  L  M  7  »"  SUBSTRATE  Fig.  The resolved  4.1  R e f l e c t i o n from a f i l m - c o v e r e d  e l e c t r i c f i e l d vector  i n t o component E  component E  surface  of an i n c i d e n t p l a n e wave can  , p a r a l l e l to the p l a n e of i n c i d e n c e ,  , normal to the plane of i n c i d e n c e .  be  and  A system o f an i s o t r o p i c  s u b s t r a t e covered by i n t o p-  and  an  isotropic  f i l m r e f l e c t s p-  s-polarized light respectively.  coefficients  for p-light, R  , and  The  s-light, R  P  R =  =  4  +  a n < 2  f i l m and  i  r 2  ^  a r e  , have the  reflection form  1 6  e  2  2  e  3  -216  ( 4  Fresnel r e f l e c t i o n coefficients  t n e  film/substrate interface . <S =  where  "2  r  1  where r ^  total  s-polarized l i g h t  s  l2 23 " 1 + r r  r  and  2ft d , 2 — ( n  d=*= t h i c k n e s s of  respectively,  2  - n  and  f o r the  6 i s the  -  1 }  ambience/  quantity  2.2. . l/2 s i n <)>].))  . (4.2)  N  0  film  A = wavelength of l i g h t i n vacuum n^=  refractive  index of  ambience  n=  refractive  i n d e x of  film  $1=  angle of  2  The  incidence.  Fresnel coefficients  ,P "12  f o r p-  _  and  s - l i g h t are  n  2  cos  $i  n  2  cos  <\>i + n^  cos  4* j  of the  form  <t>2  c o s  cos <t> 2  (4.3) n^  s "12  The  changes of s t a t e  c h a r a c t e r i z e d by  the  $i  n^cos  relative  phase change, A , which are  n _ c o s <J>2  -  2  +  n  2  of p o l a r i z a t i o n  related  are  reflection  to R  and  R  and  through the  are relative  "fundamental  s  ellipsometry"  tan ^ e An  on  amplitude r e d u c t i o n , t a n ' i j i ,  P e q u a t i o n of  <j>2  cos  e l l i p s o m e t e r measures the  R  .(4.4)  = --f— K  S  q u a n t i ' t i e s ^ d a n d A.  taken, or enough i n f o r m a t i o n about the  I f enough measurements  substrate i s available,  the  12  o p t i c a l constants  of the f i l m can be c a l c u l a t e d u t i l i z i n g e q u a t i o n s 4.1,  4.2 and 4.3.  4.2  Ellipsometry  f o r Homogeneous U n i a x i a l A n i s o t r o p i c Nonabsorbing  on I s o t r o p i c The  Substrates.  r e f l e c t i o n , r e f r a c t i o n and a b s o r p t i o n  m a t e r i a l s were f i r s t s t u d i e d by Drude  14  .  by M o s t e l l e r and Wooten  15  of b i r e f r i n g e n t f i l m s .  .  Schopper  16  formulated  Azzam and Bashara  o f l i g h t by a n i s o t r o p i c  The complex F r e s n e l e q u a t i o n s  f o r r e f l e c t a n c e f o r u n i a x i a l a n i s o t r o p i c absorbing  ellipsometry  Films  17  c r y s t a l s were d e r i v e d the o p t i c a l  and De Smet  18  properties  studied  f o r a n i s o t r o p i c m a t e r i a l s withe t h e i r o p t i c axes p a r a l l e l t o 19 20 Both Den Engelsen, and Tomar and S r i v a s t a v a  the m a t e r i a l surface.. studied ellipsometry media i n a three  f o r a u n i a x i a l a n i s o t r o p i c f i l m between two i s o t r o p i c  l a y e r system, w i t h the o p t i c a x i s o f the a n i s o t r o p i c  normal t o the f i l m s u r f a c e .  Here we w i l l r e s t r i c t o u r s e l v e s  film  to the case  s t u d i e d by Den E n g e l s e n and by Tomar e t a l . s i n c e i t a p p l i e s to the system s t u d i e d i n t h i s work. As shown i n chapter 2, f o r a system o f a u n i a x i a l l y a n i s o t r o p i c f i l m on an i s o t r o p i c s u b s t r a t e , w i t h the o p t i c a x i s normal to the f i l m s u r f a c e , the r e f r a c t i v e index i s r e p r e s e n t e d which i s an e l l i p s o i d and  by an o p t i c a l  of r o t a t i o n about the s u r f a c e normal.  indicatrix The s - l i g h t  the p - l i g h t i n the f i l m respond t o two d i f f e r e n t r e f r a c t i v e i n d i c e s ,  namely n  s  and n  p  respectively.  These two r e f r a c t i v e i n d i c e s obey the  equat ions <: ua t i ons n  •  2  n „  '  2  A  2  sxn <f>  P  P 2  n  e  - +  2  n P  2  2 2 = n o s  (4.5)  ,  cos d> P = 1 n o  (4.6)  13 where  and n  indices,  and < j >  Q  are r e s p e c t i v e l y  the e x t r a o r d i n a r y and o r d i n a r y  i s the r e f r a c t i o n angle f o r p - l i g h t .  refractive  The d i r e c t i o n s  of the  wave normals obey S n e l l ' s law n,  1  where  s i n <()i = n x  s i n cf) = n  p  n^ = r e f r a c t i v e  p  s i n <j>  o  = n„  o  3  s i n <j>„  (4.7)  3  index o f ambience  n^ = r e f r a c t i v e index o f s u b s t r a t e <(>]_ = angle of i n c i d e n c e tf>  = refraction  o  angle f o r s - l i g h t  cj> = r e f r a c t i o n  angle i n s u b s t r a t e .  3  The r e f l e c t i o n c o e f f i c i e n t s R and R are c a l c u l a t e d i n the same s P wayf as fo.rtisotropic,:'fiilmseexcepttthatand andanc a r e d u s e d t i n s t e a d of,, the • ;s,p O p p i s o t r o p i c r e f r a c t i v e index. F o r the s - l i g h t r = —  R S  1  + r|!  s  exp (-2iB ) =  — <2  +  r  23  e  X  P  (  " §o>  s s where r and r „ . are the F r e s n e l c o e f f i c i e n t s 12 23 a m b i e n c e / f i l m and f i l m / s u b s t r a t e r  l2  a  n  d  r  23  a  r  (4.8)  2 i  interface  f o r the s - l i g h t a t the  respectively.  The c o e f f i c i e n t s  e  s c  12  =  n. cos d) - n 1 o n cos <h + n n  1  n  cos d> o cos <b (4.9)  n  cos <j> - n_ cos <b„ o ^o 3 3 n cos <b + n„ cos <f>„ o o 3 3  s 23  o  is  Y  the phase d i f f e r e n c e 2ir  6  = o  f o r the o r d i n a r y wave  d n  cos  ? A  <f) = 2ir d(  °  =  n^  - n!?  :  sin^tfii) :  ( 4  .  1 0 )  A  where A i s the wavelength o f the l i g h t i n vacuum, and d i s the t h i c k n e s s o f theaanisotropic  film.  For  the p - l i g h t 1? —  r P  R  = P  1  +  r  exp (-218 ) - —  +  —  !2 2 3 *** r  (  where r?„ r ^ are the F r e s n e l 12 and ^23 p r  r  The  =  12  p 23  phase d i f f e r e n c e  n e  n o  cos  n  n  cos  e o  2 i e  (4.11)  e>  coefficients  AT  1  2 2 2 1/2 - n, ( n - n, s i h <h ) 1 e 1  A < f>-i + 1  1  '  /  n,  ( n  1  2  e  2  - n,  1  s •i n Ad>i ^) 2  /  2  1  (4.12)  2 2 2 1/2 n . ( n - n, s i n <f>i ) - n n cos <|>Q _ 3 e 1 e o _ 2 2 2 1/2 n „ ( nz - n, s i n <j>i ) + n n cos <j>q 3 e 1 e o 1  8 is e 2iTd n  •FT  e  p A  cos  r  i>  p =  2i\d n  o  (n  2  2  - n,  e Xn  1  2  s i n 1<j>i)  1/2  ^  (4.13) O  N  e The  ellipsometric  angles  and A are found from the  usual  expression R  tan  e  lA  Rp s  I t i s seen from e q u a t i o n 4.5 t h a t n the  circular p r i n c i p a l section  incident  angle.  interfaces  g  i s e q u a l to the r a d i u s o f  o f the i n d i c a t r i x , and i s independent o f the  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  a r e t h e r e f o r e analp.gous t o the i s o t r o p i c  Fresnel coefficients  for p-light  from those f o r i s o t r o p i c media.  differences  o  But the 8g  In the case o f i s o t r o p i c  non-absorbing  However, f o r a n i s o t r o p i c 8  case.  and the phase d i f f e r e n c e  f i l m , the l o c u s i n the A-ij; p l a n e f o r i n c r e a s i n g closed loop.  f o r s - l i g h t at both  f i l m thickness follows a  non-absorbing f i l m s ,  and 8 a r e not the same. e  Since 8  are d i f f e r e n t  o  the phase  and 8 vary w i t h e  film  t h i c k n e s s d i f f e r e n t l y , the r e l a t i v e phase change A depends on t h i c k n e s s  15 through the A  f i l m  values  two  different  thickness or  lower  elements,  i n c r e a s e s , A  v a l u e s ,  exp  the  (-2i8  Q  )  A-iJj=curve  depending  on  the  and  e x p ( - 2 i 8  s p i r a l s s i g n  of  e  ) .  towards  Therefore,as e i t h e r  b i r e f r i n g e n c e .  higher  16  5. 5.1  The  EXPERIMENTAL ARRANGEMENTS  Ellipsometer  5.1.1  System components The  automated e l l i p s o m e t e r system used was  43603-200B) i n t e r f a c e d to a DEC The  light  PDP-8/E computer  source was  a Rudolph  (Fig.  (type  5.1).  a He-Ne l a s e r ( S p e c t r a P h y s i c s model  133)  o producing  light  of wavelength 6328 A.  each d r i v e n by a s t e p p i n g motor (IMC which produced a 0.01° p o l a r i z e r and CW/D).  The  was  p o l a r i z e r and  r o t a t i o n per s t e p .  The  source) was  azimuthal  by D e c i t r a k  encoder u n i t outputs the angles photomultiplier  (RCA  #PIN 008-008) p o s i t i o n s of  s h a f t encoders  as BCD  to the  8645 )tube w i t h Kepco  used as a d e t e c t o r .  then monitored as one  I t s output v o l t a g e  the i n t e r f a c e to a s i n g l e A/D the e r r o r s i g n a l was i n p u t of the A/D  of the f o u r analog  converter.  regulated (error signal)  was  in  connected to  a l s o i n t e r f a c e d to the  measured by a c l o c k i n c o r p o r a t e d  s i g n a l , g i v i n g a b a s i c u n i t o f 0.1  The  con-  For convenience of alignment the  balancing  The  t r i g g e r e d by a 60  Hz  seconds.  routine  p r i n c i p l e of o p e r a t i o n  l i g h t passing  computer.  i n the i n t e r f a c e .  c l o c k c o n s i s t e d of a d i v i d e - b y - s i x counter which was  The  zero  converter.  time was  5.1.2  511-  inputs multiplexed  a l s o d i s p l a y e d on a meter which was  A Tyco d i g i t a l v o l t m e t e r Elapsed  (TR  the  computer.  a m p l i f i e d by a v a r i a b l e g a i n a m p l i f i e r w i t h an a d j u s t a b l e  t r o l , and  The  a n a l y z e r were  Magnetic C o r p o r a t i o n  a n a l y z e r were d e t e c t e d  A RCA voltage  The  of the e l l i p s o m e t e r i s as  through the p b l a r i z e r becomes l i n e a r l y  angle to the p l a n e of i n c i d e n c e .  The  follows.  polarized at  q u a r t e r wave p l a t e changes  the  an  ENCODER OUTPUT UNIT  MOTOR DRIVE CIRCUITS  DVM OUTPUT. ANALOG INPUTS  INTERFACE  -  PDP8E  VARIA DL E GAIN AMPLIFIER  COMPUTER  111 III TELETYPE  F i g . 5.1  Schematic o f the automated  ellipsometer  system.  18  l i n e a r l y polarized l i g h t to e l l i p t i c a l l y polarized l i g h t .  The p o l a r i z a -  t i o n of t h e l i g h t i s f u r t h e r changed by r e f l e c t i o n from the sample.  If  the p o l a r i z e r and the q u a r t e r wave p l a t e a r e s e t such t h a t the l i g h t r e f l e c t e d from the sample becomes l i n e a r l y p o l a r i z e d , the l i g h t can be e x t i n g u i s h e d by the a n a l y z e r . s a i d t o be  Under t h i s c o n d i t i o n the e l l i p s o m e t e r i s  "balanced". B a l a n c i n g the e l l i p s o m e t e r i s automated by u s i n g t h e PDP-8/E  computer. and  The computer program begins by i n i t i a l i n g v a r i o u s p o i n t e r s ,  a s k i n g f o r date and s p e c i f i c a t i o n o f time i n t e r v a l between s u c c e s s i v e  balancings.  A heading i s then p r i n t e d out and the b a l a n c i n g r o u t i n e i s  started. The b a l a n c i n g r o u t i n e i s based on the p r i n c i p l e t h a t t h e l i g h t i n t e n s i t y d e t e c t e d by the p h o t o m u l t i p l i e r v a r i e s s y m m e t r i c a l l y  about the  e x t i n c t i o n p o s i t i o n o f t h e p o l a r i z e r o r the a n a l y z e r f o r s m a l l e x c u r s i o n 21'. from the e x t i n c t i o n p o s i t i o n  .  The p o l a r i z e r i s b a l a n c e d  first  since  i t s e x t i n c t i o n s e t t i n g i s independent o f t h e exact s e t t i n g o f the a n a l y z e r f o r s m a l l d e v i a t i o n s o f the l a t t e r .  The computer program f i r s t  mines which way the motor should be stepped It  t o minimize the e r r o r s i g n a l .  s t e p s the motor i n t h a t d i r e c t i o n and takes e r r o r s i g n a l  a f t e r each step u n t i l a s e t o f 16 r e a d i n g s  deter-  readings  a r e taken and summed.  The  s t e p p i n g o f the motor i s c o n t i n u e d u n t i l t h e e r r o r s i g n a l goes through the minimum and b e g i n s minimum i s s t o r e d .  to increase again.  The t h i r d sum back from the  The program then c a l c u l a t e s a second sum o f 16  error s i g n a l readings.  As t h e s t e p p i n g c o n t i n u e s  t h i s sum i s updated  a f t e r each s t e p so t h a t i t c o n t a i n s o n l y the 16 most r e c e n t When the second sum equals  the f i r s t  readings.  sum on the o t h e r s i d e o f the minimum,  19  the b a l a n c e p o s i t i o n which correspond t o the m i d - p o i n t between these equal sums can be l o c a t e d , and the p o l a r i z e r i s stepped t o t h a t The a n a l y z e r i s then a d j u s t e d by the same r o u t i n e , f o l l o w e d by  two  position. another  b a l a n c i n g o f the p o l a r i z e r . A f t e r the p o l a r i z e r and the a n a l y z e r have been b a l a n c e d , the n e t number o f s t e p s each motor takes i s compared w i t h the change i n pos i t i o n of the r e s p e c t i v e s h a f t encoder.  T h i s checks f o r any e r r o r  due  to gear b a c k l a s h or t o the motor m i s s i n g s t e p s . The program then reads the encoder s e t t i n g s o f the p o l a r i z e r and a n a l y z e r , the step e r r o r s , the c l o c k time, and the d i g i t a l v o l t m e t e r . The r e a d i n g s are s t o r e d i n a b u f f e r a r e a i n the computer memory to w a i t f o r output on the t e l e t y p e which i s operated on an i n t e r r u p t b a s i s . b u f f e r a r e a c o n s i s t s of 1664 manner.  The  The  l o c a t i o n s and i s arranged i n a c i r c u l a r  time r e q u i r e d f o r each b a l a n c i n g c y c l e i s about  2  seconds,  but p r i n t i n g out the d a t a r e q u i r e s 5 t o 6 seconds. 5.1.3  Ellipsometer Alignment  alignment  of the e l l i p s o m e t e r f o l l o w e d the method d e v i s e d by  22 Aspnes and Studna e l l i p s o m e t e r was alignment.  .  In t h i s alignment procedure the symmetry o f the  used t o p r o y i d e the i n f o r m a t i o n needed f o r i t s own  The a c c u r a c y o f the alignment was  of the e l l i p s o m e t e r i t s e l f . (a)  l i m i t e d p r i m a r i l y by  that  The alignment method i s o u t l i n e d below,  D e t e r m i n a t i o n of zero e r r o r i n angle o f i n c i d e n c e s c a l e With'.the compensator removed, and the p o l a r i z e r and a n a l y z e r  arms i n s t r a i g h t - t h r o u g h p o s i t i o n , the azimuth angles o f b o t h and a n a l y z e r were s e t a t 90°.  The a n a l y z e r arm was  s t r a i g h t - t h r o u g h p o s i t i o n i n 0.01°  polarizer  r o t a t e d about  the  s t e p s u n t i l the peak e r r o r s i g n a l  was  20  found.  From the s c a l e r e a d i n g f o r the peak s i g n a l p o s i t i o n , t h e angle  of i n c i d e n c e (b)  s c a l e e r r o r was determined t o be -0.04°.  D e t e r m i n a t i o n o f zero e r r o r i n p o l a r i z e r and a n a l y z e r  azimuthal angles  With the compensator removed, the angle o f i n c i d e n c e 62.77°, and both the p o l a r i z e r and t h e a n a l y z e r  set at  s e t a t 90° a z i m u t h a l  a n g l e s , an o p t i c a l l y f l a t q u a r t z p l a t e was mounted as a beam r e f l e c t o r . The  p o s i t i o n o f the q u a r t z p l a t e was a d j u s t e d u n t i l a maximum s i g n a l was  •detected by the d e t e c t o r .  T h e n - t h e ' a n a l y z e r was b a l a n c e d near A = 0° f o r  d i f f e r e n t s e t values, of P-about 90° t o o b t a i n A.  a s t r a i g h t l i n e p l o t of P versus  In the same procedure the p o l a r i z e r was b a l a n c e d near P = 0 f o r d i f f e r e n t  s e t v a l u e s o f A about 90°. - The r e s u l t s a r e shown i n F i g . 5.2. The  i n t e r s e c t i o n o f the two s t r a i g h t l i n e s i n F i g . 5.2 gave  the e r r o r o f the P and A s c a l e s .  T h i s e r r o r was c o r r e c t e d  s e t t i n g the P and A to the i n t e r s e c t i o n v a l u e s , s h a f t encoders so t h a t  f o r by f i r s t  and then a d j u s t i n g the  the output o f one encoder r e a d 0.00° w h i l e the  other read 90.00°. (c)  S e t t i n g the q u a r t e r wave p l a t e azimuth angle a t 315° In t r a c k i n g  the growth o f f i l m s the e l l i p s o m e t e r  taken w i t h the q u a r t e r wave p l a t e s e t a t 315°. was as f o l l o w s .  r e a d i n g s were  The s e t t i n g o f t h e QWP  With the p o l a r i z e r and t h e a n a l y z e r  in  straight-through  p o s i t i o n and s e t a t 315° and 45° r e s p e c t i v e l y i n azimuth a n g l e , the QWP was i n s t a l l e d .  The azimuth a n g l e o f the QWP was s e t around 315°, and  then f i n e adjustment was made u n t i l a minimum e r r o r s i g n a l was o b t a i n e d . In t h i s c o n d i t i o n transmission  the f a s t a x i s o f the QWP was p a r a l l e l t o the p o l a r i z e r  a x i s , which was a t 315° t o the p l a n e o f i n c i d e n c e .  '  I  .4  .5  F i g . 5.2  I  I  .6  .7  i  L  .8  .9  I  0 90 P/deg.  I  .7  _l  .2  I  —I  1  i-  .3  .4  .5  .6  Zero e r r o r i n p o l a r i z e r and a n a l y z e r s c a l e s . x - x - x balancing p o l a r i z e r with analyzer s t a t i o n a r y near 90°. o - o - o balancing analyzer with p o l a r i z e r s t a t i o n a r y near 90°.  22  (d)  D e t e r m i n a t i o n o f the t r a n s m i s s i o n r a t i o , T , and the phase r e t a r d a t i o n , A , of the q u a r t e r wave p l a t e . An i n c o n e l s l i d e w i t h a m i r r o r s u r f a c e was  was  carefully aligned.  The angle of i n c i d e n c e was  zone r e a d i n g s were then taken.  used as a sample and  s e t a t 62.77°.  Two-  For p e r f e c t alignment o f the sample and  w i t h an i d e a l q u a r t e r wave p l a t e , t h e r e would be no d i f f e r e n c e between r e a d i n g s of two d i f f e r e n t  zones*  To minimize  s h i f t produced by the compensator was on the compensator.  The  the zone d i f f e r e n c e the phase  a l t e r e d by a d j u s t i n g the  f i n a l two-zone r e a d i n g s were taken.  micrometer Using  23 McCrackin's  program  the t r a n s m i s s i o n r a t i o , T , c  and the phase r e t a r d a -  t i o n , A(i, were c a l c u l a t e d to be 0.997 and 90.00° r e s p e c t i v e l y . 5.2  Anodization C e l l The a n o d i z a t i o n c e l l used i n our s t u d i e s had to be  w i t h i n s i t u e l l i p s o m e t e r measurements.  I t had  to meet the  compatible requirements  t h a t i t be r e s i s t a n t to c h e m i c a l s , have s m a l l window e r r o r , and be to  a d j u s t i n the alignment p r o c e d u r e .  c e l l was  With these f a c t o r s i n mind, the  designed as shown i n F i g . 5.3. The  threaded i n .  c e l l was  made o f a t e f l o n c y l i n d e r w i t h a bottom p i e c e  The angle between the two windows was  the angle o f i n c i d e n c e 62.77°.  b r a s s base which was  the t i l t  fitted  There were two  125.54°, which made  A more d e t a i l e d d e s c r i p t i o n o f the win-  dows w i l l be g i v e n i n the next s e c t i o n .  someter.  easy  The c e l l was  supported by a  to the s t a n d a r d sample h o l d e r f o r the  ellip-  s e t s of screws on the base, one f o r a d j u s t i n g  o f the c e l l and the o t h e r one f o r l o c k i n g the p o s i t i o n once the  d e s i r e d t i l t i n g had been made.  The c e l l  c o u l d be t i l t e d  w i t h o u t d i s t u r b i n g the alignment o f the sample.  and  rotated  23  TEFLON CYLINDER  WINDOW  •A  SCREWS  •1_ f- H  BASE  L_  SHAFT NOT TO SCALE  F i g . 5.3  S t r u c t u r e o f the c e l l f o r i n s i t u e l l i p s o m e t e r measurements.  24  5.3  Window  E r r o r  The i  n  in  s i t u  %-inch on  were  used.  the  e l l i p s o m e t e r  t h i c k ,  ness  on  b i r e f r i n g e n c e  both  fused s i d e s ,  The  the  windows  measurements.  s i l i c a and  1  windows  windows sec.  To  i s  a  p o s s i b l e  minimize  (1-inch  i n  p a r a l l e l i s m )  the  were  tested  before  windows  before  mounting  window  diameter,  s u p p l i e d and  1/20  by  a f t e r  source  e r r o r  e r r o r wave  O r i e l  they  of  two  i n  f l a t -  C o r p o r a t i o n  were  mounted  c e l l .  5.3.1  E r r o r The  analyzer, through  of  of  windows,  were  tested  arrangement.  the  p o l a r i z a t i o n  the  Poincare  F i g .  between  i n d i v i d u a l l y The  state  sphere  5.4  placed  of  (see  the  of  sphere  error  on  c e l l  quarter  the  e l l i p s o m e t e r  beam shown  wave  b i r e f r i n g e n c e can i n  be  best  F i g .  r e p r e s e n t a t i o n the  the  the  the  l i g h t  appendix)  Poincare window  e f f e c t  by  on  p l a t e  and  i n  s t r a i g h t -  of  a the  the  windows  v i s u a l i z e d  u s i n g  5.4.  of  the  p o l a r i z a t i o n . s t a t e  e f f e c t of  of  l i g h t .  on  25  The window i s c o n s i d e r e d t o be a wave p l a t e w i t h a s m a l l  rela-  t i v e phase r e t a r d a t i o n 6, and i t s f a s t and slow axes p a r a l l e l t o the s u r face.  Consider  first  the case when t h e r e i s no window and a l l t h e com-  ponents o f the e l l i p s o m e t e r a r e i d e a l .  When the l i g h t i s e x t i n g u i s h e d by  the a n a l y z e r , the p o l a r i z e r s h o u l d be a t the same azimuth angle as the q u a r t e r wave p l a t e , • r e p r e s e n t e d by Q on the P o i n c a r e  sphere.  When the  window i s p l a c e d between the q u a r t e r wave p l a t e and the a n a l y z e r , and a t an azimuth angle a balanced  <|>, i t i s r e p r e s e n t e d by W on the P o i n c a r e w  c o n d i t i o n the p o l a r i z e r i s s e t t o P.  sphere.  When the l i g h t  Under  goes  through the q u a r t e r wave p l a t e the p o i n t on the sphere r e p r e s e n t i n g the p o l a r i z a t i o n o f the l i g h t beam i s r o t a t e d about the OQ a x i s by 90° from P t o P^.  The phase r e t a r d a t i o n o f t h e window r o t a t e s P^ about the 0W  a x i s by an angle  6 t o T?2> which l i e s on'the equator,  so t h a t the l i g h t  i s a g a i n l i n e a r l y p o l a r i z e d and i s e x t i n g u i s h e d by the a n a l y z e r . the r o t a t i o n about 0W i s f i x e d by the angle P2»  Since  6, the d i s t a n c e P-^ t r a v e l s t o  o r i n o t h e r words the d i f f e r e n c e between P and Q, depends on the po-  s i t i o n o f W.  When W c o i n c i d e s w i t h o r i s 180° away from Q, P s h o u l d be  the same as Q, as i n the case o f no^window.  As W i s r o t a t e d away from Q,  the d i f f e r e n c e between P and Q which r e p r e s e n t s window e r r o r i n c r e a s e s . The maximum d i f f e r e n c e o c c u r s when W i s 90° away from Q, i . e . the f a s t a x i s o f the window i s 45° away from t h a t o f the q u a r t e r wave p l a t e . W i s on the o t h e r s i d e o f t h e sphere,  When  t h i s d i f f e r e n c e should be o f oppo-  site sign. T h e r e f o r e when the window i s r o t a t e d about i t s s u r f a c e normal, it  i s expected  equals  t h a t the d i f f e r e n c e between t h e e l l i p s o m e t e r angle A (which  the sum o f r e a d i n g s  (P, + P,) f o r zones 1 and 3 when Q = -45°) f o r  26  the case w i t h window and t h a t f o r the case w i t h o u t window w i l l v a r y i n a s i n u s o i d a l form.  Two c y c l e s o f such v a r i a t i o n a r e expected  f o r one com-  p l e t e r o t a t i o n o f the window because W makes two r o t a t i o n s on the P o i n care  sphere. U s i n g the p r i n c i p l e e x p l a i n e d above, t h e v a r i a t i o n o f window  e r r o r w i t h the r o t a t i o n o f the window was examined.  The window was  mounted on a h o l d e r which a l l o w e d r o t a t i o n o f the window.  The angle o f  r o t a t i o n , r e l a t i v e t o some a r b i t r a r y d i r e c t i o n , c o u l d be read on an a t t a c h e d c i r c u l a r d i a l w i t h degrees marked. the s u r f a c e normal and f o r every 15 degrees someter r e a d i n g s were taken.  The window was r o t a t e d about o f r o t a t i o n two-zone  ellip-  Care had t o be taken t h a t f o r every mea-  surement the window s u r f a c e was normal t o the beam.  The e l l i p s o m e t e r  r e a d i n g s were compared t o those' o b t a i n e d when no Window was p l a c e d i n the e l l i p s o m e t e r arrangement, and t h e d i f f e r e n c e s were the e r r o r s due t o the window.  No d i f f e r e n c e was observed  i n Tp.  The e r r o r s i n A f o r d i f -  f e r e n t r o t a t i o n s were as shown i n F i g . 5.5. Fig.  5.5 agrees v e r y w e l l w i t h the p r i n c i p l e d i s c u s s e d above.  The e r r o r i n A v a r i e s s i n u s o i d a l l y w i t h the r o t a t i o n a n g l e . two Fig.  There a r e  c y c l e s o f v a r i a t i o n f o r one complete r o t a t i o n o f the window. 5.5 one can determine  From  the d i r e c t i o n o f the f a s t and slow axes o f  the window. The  important  c o n c l u s i o n from these window e r r o r measurements  i s t h a t the q u a l i t y of the window was c o n s i d e r e d v e r y good. e r r o r i n A was ±0.04°.  No e r r o r i n I|J was observed,  The maximum  i m p l y i n g the absorp-  t i o n s a l o n g the f a s t and slow axes o f the window were e i t h e r the same or the d i f f e r e n c e c o u l d cause a change o f l e s s than 0.01° i n  F i g . 5.5  Window e r r o r i n A a g a i n s t r o t a t i o n o f the window. A i s t h e A v a l u e w i t h window. A i s the A v a l u e w i t h no window. R o t a t i o n a n g l e i s r e l a t i v e to an a r b i t r a r y d i r e c t i o n . w  Q  28  5.3.2  E r r o r o f windows a f t e r mounting  on the  cell  When the windows were mounted on the c e l l , more e r r o r s be i n t r o d u c e d by the s t r e s s e x e r t e d on them.  could  To determine the window  24 e r r o r a method d e v i s e d by McCrackin  was  used.  An i n c o n e l s l i d e w i t h a m i r r o r s u r f a c e was sample i n the e l l i p s o m e t e r measurements. set  at 62.77°.  The angle of i n c i d e n c e  r e a d i n g s f o r two cases gave the window e r r o r .  The d i f f e r e n c e between the For a l l experiments done  t h i s work, the e r r o r i n A ranged from 0.02° t o 0.06°. was  always w i t h i n ±0.01° which was  a n a l y z e r and 5.4  The e r r o r i n  a l s o the adjustment s t e p o f the  polarizer.  Sample P r e p a r a t i o n The samples  used i n t h i s work were c u t from a s i n g l e  niobium rod s u p p l i e d by M a t e r i a l Research C o r p o r a t i o n . cut  was.  Two-zone e l l i p s o m e t e r r e a d i n g s were taken w i t h the i n -  c o n e l s l i d e i n the c e l l and out of the c e l l .  in  a g a i n used as a  The samples were  i n the shape of a c i r c u l a r d i s k , % " i n diameter, 0.1"  w i t h the s u r f a c e s o r i e n t e d i n the (110) d i r e c t i o n .  crystal  thick,  A heavy  and  tantalum  w i r e spot-welded a t the back of the sample a c t e d as an e l e c t r i c a l  con-  n e c t i o n as w e l l as the support t o the sample by f i t t i n g  i n t o a sample  holder.  to be  in  The lower h a l f of the tantalum w i r e , which was  immersed  the e l e c t r o l y t e d u r i n g the a n o d i z a t i o n of the niobium sample,  i n s u l a t e d b e f o r e h a n d by a n o d i z i n g a t h i c k o x i d e f i l m on i t .  This  was was  done w i t h the sample masked by non-conductive A p i e z o n grease. Since the samples were used i n o p t i c a l s t u d i e s , a f l a t s u r f a c e on each sample was  required.  a n i c a l f o l l o w e d by c h e m i c a l p o l i s h i n g  The s u r f a c e was 25  reflecting  prepared by mech-  29  One s i d e o f the sample was abraded on 0/0, 2/0, 3/0 and 4/0 emery papers i n t h a t sequence.  The sample was then immersed i n a chem-  i c a l p o l i s h i n g s o l u t i o n which c o n s i s t e d o f 1:1:1 by volume o f 85%  phos-  p h o r i c a c i d , 48% HF and 70% HNO^,  gentle  f r e s h l y mixed  i n that order.  A  a g i t a t i o n by moving the sample about i n the s o l u t i o n was r e q u i r e d . time o f immersion r e q u i r e d  to o b t a i n a good s u r f a c e  The  ranged from 5 t o 20  minutes, depending on the m e c h a n i c a l c o n d i t i o n o f the s u r f a c e .  Upon  removal from the s o l u t i o n , the sample was r i n s e d immediately i n d i s t i l l e d water t o a v o i d uneven  a t t a c k on the s u r f a c e .  The sample was then dipped  i n HF f o r 5 seconds, f o l l o w e d by a d i s t i l l e d water r i n s e .  30  6.  6.1  RESULTS  O p t i c a l A n i s o t r o p y of Anodic Niobium Oxide 6.1.1  Experimental  Films  procedure  The e l l i p s o m e t r y p r i n c i p l e s d e s c r i b e d i n chapter 4 were a p p l i e d to study the o p t i c a l a n i s o t r o p h y of the niobium oxide f i l m s . growing I t was  under c o n s t a n t f i e l d was t h e r e f o r e expected  growing The  expected  film  to be i n the a n i s o t r o p i c  state.  t h a t the e l l i p s o m e t e r angles measured d u r i n g the  process would s p i r a l e i t h e r upwards o r downwards i n the A-^  e x p e r i m e n t a l procedure was The p o l i s h e d niobium  as  The  a l i g n e d on the e l l i p s o m e t e r a t  c e l l was  p o s i t i o n e d and a l i g n e d so  that both windows were normal to the l a s e r beam. checked beforehand by 0.2N  a temperature  H2SO4.  The window e r r o r  the method d e s c r i b e d i n s e c t i o n 5.3.2. I t :  w  controller.  a  s t i r r e d and m a i n t a i n e d  s  plane.  follows.  sample was  an angle of i n c i d e n c e of 62.77°.  l y t e was  A  at 25.0  The  was electro-  ± 0.1°C  A p l a t i n i z e d p l a t i n u m e l e c t r o d e was  using  used  as the  cathode. The sample was volts two in  anodized at constant c u r r e n t of 0.11  (2240 A i n t h i c k n e s s ) .  reasons.  (a)  The  t h i c k n e s s o f the f i l m was  The e l l i p s o m e t e r angles A and  f i l m was  to be used  i n second  i n s t u d i e s d e s c r i b e d i n s e c t i o n 6.2.  c y c l e of the A - ijj curve w h i l e 92 v o l t s was  7.  to 92  so chosen f o r  T h i s was  v o l t a g e which would cause the oxide f i l m t o r e c r y s t a l l i z e , cussed i n chapter  2  i> at t h i s t h i c k n e s s were  the r e g i o n most s e n s i t i v e to the f i l m t h i c k n e s s .  the sample was  mA/cm  required i f (b)  The  below the  as w i l l be  dis-  31  The off  the f i e l d  a n o d i z a t i o n p r o c e s s was (i.e. short-circuiting  p e r i o d i c a l l y i n t e r r u p t e d by s w i t c h i n g the constant c u r r e n t s u p p l y ) .  Contin-  uous one-zone e l l i p s o m e t e r r e a d i n g s were taken d u r i n g the growth p r o c e s s and d u r i n g the p e r i o d s w i t h the f i e l d  removed.  Before and a f t e r the o v e r a l l a n o d i z a t i o n e l l i p s o m e t e r r e a d i n g s were taken.  Based on these two-zone r e a d i n g s ,  c o r r e c t i o n s to the one-zone r e a d i n g s were made. and  process,two-zone  E r r o r s due  to the windows  the q u a r t e r wave p l a t e were c o r r e c t e d f o r . The  e x p e r i m e n t a l meansurements were a n a l y z e d by p l o t t i n g  a l a r g e graph paper programmes  6.1.2  and  fitting  them to t h e o r e t i c a l curves computed by  360/67.  f o r IBM  Results The  e x p e r i m e n t a l measurements o f A and $ w i t h the f i e l d  are shown i n F i g s . 6 . 1 and 6 . 2 .  off  the A - i> p l o t up to two  s p i r a l s upwards.  i s on, the A - ty. curve  But once the f i e l d i s switched o f f , the A - # p o i n t s on  c y c l e s f a l l on the same c u r v e , and these e x p e r i m e n t a l p o i n t s f i t a  index, n , n  equal to  e q u a l to  3.01  - i  2.329,  and the index o f the niobium  substrate, n3,  the f i e l d  on were  t h e o r e t i c a l curve f o r a homogeneous a n i s o t r o p i c f i l m i n the The  spiralling  refractive  3.555.  The e x p e r i m e n t a l p o i n t s o b t a i n e d w i t h  way.  and  c y c l e s , w h i l e F i g . 6 . 2 shows the upper p o r t i o n .  t h e o r e t i c a l curve f o r a s i n g l e - l a y e r i s o t r o p i c f i l m w i t h the f i l m  to  on  F i g . 6 . 1 shows the lower p o r t i o n o f  These f i g u r e s show t h a t when the f i e l d  the two  them on  fitted  following  c h a r a c t e r i s t i c s of a i - I curve f o r an a n i s o t r o p i c f i l m i s the a l o n g the A - a x i s .  maximum A between each  The  d i f f e r e n c e i n the v a l u e s o f minimum A o r  c y c l e depends on the c o n s t a n t (3, which i s d e f i n e d  35  40  45  V/ Fig.  6.1  50  55  deg  Lower portion of the A-f plot f o r increasing thickness of a niobium oxide f i l m up to two cycles. S o l i d points are experimental measurements f o r zero f i e l d : • , f i r s t cycle; X , second cycle. Blank points are measurements with f i e l d on: o, f i r s t cycle; A, second cycle. ( ) i s a theoretical curve for i s o t r o p i c f i l m . ( ) i s a theoretical curve f o r anisotropic f i l m *  w  *°  246  y /deg Fig. 6.2  Upper portion of the A - f p l o t .  Key as for Fig.  6.1.  34  2.31  2.30.  F i g . 6.3(a)  2.32  T h e o r e t i c a l v a l u e s o f minimum A as f u n c t i o n s o f 3 and n . ( ) i s f o r the f i r s t c y c l e . ( ) i s f o r the second c y c l e . Shaded areas a r e e x p e r i m e n t a l v a l u e s . D  35  F i g . 6.3(b)  T h e o r e t i c a l v a l u e s o f maximum A as f u n c t i o n s Key as f o r F i g . 6.3(a).  o f B and n . Q  36  by e q u a t i o n 2.12,  and the o r d i n a r y r e f r a c t i v e index n .  The  Q  v a l u e s of minimum A and maximum A as f u n c t i o n s of 3 and n computed and shown i n F i g . 6.3. that found  from  fitting  The v a l u e s of  the i s o t r o p i c c u r v e .  Q  theoretical  have been  and n^ were based  on  The e x p e r i m e n t a l v a l u e s o f  the minimum A's and maximum A are shown w i t h i n a shaded area which r e p r e s e n t s the e s t i m a t e d e x p e r i m e n t a l e r r o r of ±0.05°.  From F i g . 6.3,3  were e s t i m a t e d at such v a l u e s t h a t the f i t t i n g s o f the three v a l u e s were compromised.  By v a r y i n g 3 and n  a curve which b e s t f i t t e d  the e x p e r i m e n t a l p o i n t s was  shown i n F i g s . 6.1 w i t h i n the l i m i t  and 6.2.  g i v e s some i n d i c a t i o n on how  The  o b t a i n e d and i s which a l l l i e  F i g . 6.3  the chosen  therefore also  c l o s e the e x p e r i m e n t a l p o i n t s were f i t t e d  curve.  a n i s o t r o p i c o p t i c a l c o n s t a n t s of the f i l m determined  from  curve f i t t i n g were as f o l l o w s :  3 = 1.6 n  D  = n  n  e  = 2.2978  n  p  = 2.3064  n  n  = 2.329  n  3  = 3.01  s  = 2.3095  - i 3.555  A l l symbols above are as d e f i n e d i n s e c t i o n 6.1.3  4.2.  Discussion The e x p e r i m e n t a l  the niobium  r e s u l t s show t h a t a p p l y i n g a f i e l d normal to  oxide f i l m caused  Q  experimental  of e x p e r i m e n t a l e r r o r , are v a l u e s o b t a i n e d from and 6.2.  n  about the e s t i m a t e d v a l u e s ,  P o i n t s A, B and C i n F i g . 6.3,  t h e o r e t i c a l curve shown i n F i g s . 6.1  the t h e o r e t i c a l  Q  and  the f i l m to change from the  optically  to  37  i s o t r o p i c s t a t e to the o p t i c a l l y  anisotropic state.  This e f f e c t i s  s i m i l a r to t h a t r e p o r t e d f o r anodic Ta2C>5 f i l m s by C o r n i s h and Young^. Fig.  shows t h a t i f n  i s varied a l i t t l e  Q  i n curve  fitting,  good f i t can s t i l l be o b t a i n e d by v a r y i n g 3 from 1.55  a reasonably The  4.3  v a l u e 3 = 1.6  ± 0.05  f o r niobium  oxide f i l m s happens to be  to  1.65.  the same  as r e p o r t e d f o r Ta20s f i l m s ^ . T h i s presumably r e f l e c t s the s i m i l a r i t y of these two  oxides. The  o p t i c a l a n i s o t r o p y of the oxide  c o u l d have been demonstrated b e t t e r by curve.  U n f o r t u n a t e l y the oxide f i l m tended  6.2  grown t o cover o n l y one  and  f i e l d applied  three or more c y c l e s of the A - \p  v o l t a g e , as w i l l be d i s c u s s e d i n c h a p t e r f i l m was  f i l m with  to r e c r y s t a l l i z e  7.  Due  at h i g h  to t h i s problem the  a h a l f c y c l e s o f the A - ip  F i e l d and Time Dependence o f E l e c t r o - o p t i c and  oxide  curve.  Electrostrictive  Effects 6.2.1  Experimental  procedure  T h i s experiment was  designed  to examine the f i e l d  dependence of the a n i s o t r o p i c r e f r a c t i v e f i l m s of anodic niobium  oxide.  ment d e s c r i b e d i n s e c t i o n 6.1 left  The was  i n d i c e s and  recorded by the computer. digital  The  time  the t h i c k n e s s of  same oxide f i l m grown i n the e x p e r i -  used i n t h i s study.  i n the c e l l i n the same e l l i p s o m e t e r s e t up.  a p p l i e d a c r o s s the f i l m and was  and  monitored conduction  The sample  was  A d-c v o l t a g e  was  by a d i g i t a l v o l t m e t e r  and  c u r r e n t was  monitored  by a  ammeter. The v o l t a g e was  (2/3 o f the f o r m a t i o n  v a r i e d i n 5 - v o l t s t e p s from zero to 60  field).  d u r i n g the time the f i e l d was  The  e l l i p s o m e t e r was  on, and  balanced  volts  continuously  the time i n t e r v a l between  two  38  s u c c e s s i v e b a l a n c i n g s was approximately dependences o f A n examined.  two seconds.  In t h i s way the time  and Ad f o r e v e r y a p p l i e d f i e l d were s i m u l t a n e o u s l y  Q  Between every  two v o l t a g e s t e p s , the f i e l d was switched o f f to  check i f t h e r e had been any growth o f the f i l m , i Corrections in  the same way as d i s c u s s e d i n s e c t i o n 6.1.1.  was based The  f o r e l l i p s o m e t e r e r r o r s were made to the measurements The a n a l y s i s o f the d a t a  on the v a l u e s of B, n^ and n3 o b t a i n e d i n the experiment  6.1.  changes i n o r d i n a r y r e f r a c t i v e index, A n , and i n t h i c k n e s s , Ad, were Q  determined  i n d e p e n d e n t l y by f i t t i n g  the e x p e r i m e n t a l A -  v a l u e s to the  contours of c o n s t a n t no and the contours o f c o n s t a n t d i n the A - ^ domain. 6.2.2  Results With no f i e l d  a p p l i e d , the oxide f i l m had been found i n s e c t i o n  6.1 to have an i s o t r o p i c r e f r a c t i v e i n d e x , n , e q u a l t o 2.329, and t h i c k o  ness equal to 2239.1 A. Fig.  6.4 shows A n  and A n  Q  as a f u n c t i o n of E . 2  g  p o i n t s shown a r e f o r A i ^ o n l y s i n c e A n 2.12.  The q u a d r a t i c f i e l d  was determined  from  the e q u a t i o n  dependence o f Ad i s shown i n F i g . 6.5.  e x p e r i m e n t a l e r r o r s were e s t i m a t e d for  g  The e x p e r i m e n t a l  to be ±0.15 x 10~  5  The  f o r A n a n d ±0.2 A c  Ad. From the r e s u l t s shown i n F i g . 6.4 the q u a d r a t i c e l e c t r o - o p t i c  c o e f f i c i e n t s gn  and g j  were computed u s i n g e q u a t i o n s 2.11 and the  2  relation P = e ( K - 1)E 0  where the r e l a t i v e d i e l e c t r i c c o n s t a n t , K, of anodic Nb 05 f i l m s was 2  26 as 41.4 m^/coul  . 2  The v a l u e s o f g i  and 0.105 m ^ / c o u l  2  2  and 8l 1  were determined  respectively.  t o be 0.065  taken  39  F i g . 6.5  The change i n f i l m thickness against  E.  2.01  yl  }  I I l,l  i i i I  * tI { I  f  I jI I  o  i  0  7.5  2 "73  10  20 SECONDS (a)  30  40  70  20  30  40  l-,4  10 0.51  0  SECONDS (b) F i g . 6.6  The change i n o r d i n a r y r e f r a c t i v e index and i n t h i c k n e s s w i t h time when t h e f i e l d was switched from z e r o t o 1.78 x 1 0 V/cm. 6  42  No The  time dependence of An  changes i n n  Fig.  6.6  v a l u e s from  Q  detected i n t h i s  experiment.  the change i n a p p l i e d f i e l d .  and Ad as a f u n c t i o n of time when the a p p l i e d f i e l d  zero to 1.78.  the average  x 10  6  V/cm.  The d e v i a t i o n s of the  was  experimental  v a l u e s were w i t h i n the e s t i m a t e d e l l i p s o m e t e r e r r o r  which i s r e p r e s e n t e d by 6.2.3  and Ad was  and d f o l l o w e d immediately  Q  shows A n  switched from  Q  the e r r o r b a r s .  Discussion The  r e s u l t s o f t h i s experiment  show t h a t the changes i n the  o r d i n a r y and the e x t r a o r d i n a r y r e f r a c t i v e i n d e x , and the change i n t h i c k ness o f the niobium oxide f i l m s v a r y q u a d r a t i c a l l y w i t h tric field.  the a p p l i e d e l e c -  These r e s u l t s are s i m i l a r t o those r e p o r t e d f o r f i l m s o f  tantalum o x i d e by C o r n i s h and Young^. The observed  q u a d r a t i c e l e c t r o - o p t i c c o e f f i c i e n t s gi\  found i n t h i s experiment  are i n the same o r d e r of magnitude as  r e p o r t e d f o r oxygen-octahedra 28, and f o r KTN for  to •  c r y s t a l s by Chen e t a l .  From the e x p e r i m e n t a l  2  2  and 0.088 m V c o u l  2  a n 1 2  respectively.  the r e s u l t s o b t a i n e d i n t h i s experiment.  ^  §11  2  those  f e r r o e l e c t r i c c r y s t a l s i n r e f e r e n c e s 27  T a 0 5 f i l m s r e p o r t e d by C o r n i s h et a l . ^ , g  as 0.055 m V c o u l  and g i  and  results  were e s t i m a t e d  These v a l u e s are c l o s e  However, the q u a d r a t i c e l e c t r o -  o p t i c c o e f f i c i e n t s f o r T a 0 s f i l m s . r e p o r t e d by F r o v a e t al.'*' were about 2  five  times s m a l l e r than our r e s u l t s .  follows. in  Frova e t a l . , who  used  a field-modulated reflectance  the study, assumed t h a t the change i n t h i c k n e s s of the f i l m  negligible.  The  r e f l e c t a n c e technique a c t u a l l y measures the  t h i c k n e s s which i s the product nd. +Ad  T h i s d i f f e r e n c e can be e x p l a i n e d as  when a f i e l d  S i n c e -An  technique was  optical,  i s i n f a c t accompanied by  i s a p p l i e d , and Ad i s not n e g l i g i b l e , the v a l u e of  An,  43  and hence the q u a d r a t i c e l e c t r o - o p t i c c o e f f i c i e n t , o b t a i n e d by F r o v a e t a l . i s expected  t o be  underestimated.  Slow e x p o n e n t i a l time-dependences o f the changes i n r e f r a c t i v e i n d i c e s and  the change i n t h i c k n e s s were r e p o r t e d f o r tantalum o x i d e  f i l m s by C o r n i s h and Young?. These slow time-dependences were not i n niobium oxide f i l m s i n our experiment.  The  tantalum o x i d e f i l m s  by C o r n i s h e t a l . were f a b r i c a t e d i n a d i f f e r e n t way first  observed  from ours by  growing  a t c o n s t a n t c u r r e n t to a d e s i g n a t e d v o l t a g e , and then growing  that constant v o l t a g e f o r a few hours. caused  used  at  T h i s d i f f e r e n t p r o c e s s might have  t h e i r f i l m t o behave d i f f e r e n t l y , although the mechanism i s not  understood. 6.3  R e p r o d u c i b i l i t y o f E l l i p s o m e t e r Measurements T h i s experiment  was  designed to check whether o p t i c a l  a n i s t r o p y o f the oxide f i l m was  observed under c o n t r o l l e d c o n d i t i o n s ,  and  whether the e x p e r i m e n t a l r e s u l t s were r e p r o d u c i b l e . A p o l i s h e d niobium e l l i p s o m e t e r i n the same way  sample was  as d e s c r i b e d i n s e c t i o n 6.1.1.  a n o d i z a t i o n c u r r e n t d e n s i t y was thermostated the The  A -  at 23°C.  The  0.087 mA/cm  2  f i l m was  e l l i p s o m e t e r , the same experiment was A -  and the e l e c t r o l y t e  ip curves f o r two  was  c y c l e of  no r e c r y s t a l l i z a t i o n o f the o x i d e .  then taken out and the oxide f i l m was  s o l u t i o n of HF s a t u r a t e d w i t h NH^F.  the  The  anodized to cover only one  jjj curve to make sure t h e r e was  sample was  Hence two  anodized and measured by  etched o f f using a  With t h i s sample mounted back on run under i d e n t i c a l  conditions.  oxide f i l m s grown under as near  p o s s i b l e i d e n t i c a l c o n d i t i o n s were o b t a i n e d .  as  the  44  A computer program was w r i t t e n t o check f o r t h e c l o s e n e s s o f t h e two A - ip- c u r v e s .  The a l g o r i t h m o f t h e program was as f o l l o w s ;  p o i n t P-^ i n one s e t o f the A - if; d a t a , t h e program s e a r c h e s Q2 i n the second  For a  f o r a point  s e t o f d a t a which i s c l o s e s t t o P^, as shown i n F i g . 6.7.  A  Fig.  6.7  Interpolating a s e t of  The d a t a p o i n t Q^, immediately  data  p r e c e d i n g Q , and p o i n t Q3, i m m e d i a t e l y 2  lowing Q2, a r e taken i n the same s e t . through  A—Tp  A second  order polynomial which  folpasses  these three p o i n t s i s constructed by Lagrangian polynomial i n t e r p o -  l a t i o n and p o i n t s A j and A3 a r e found. i s then computed.  The m i d - p o i n t  A2 between A^ and A3  Among the p o i n t s A±, A , A3 and Q2 t h e one a t t h e s h o r t e s t 2  d i s t a n c e from P-^ i s chosen and t h a t d i s t a n c e i s c o n s i d e r e d as t h e t r u e d i s t a n c e between the p o i n t P^ and t h e second  A - if; c u r v e .  A l l points i n  the f i r s t d a t a s e t a r e examined i n t h i s way and the d i s t a n c e between the two A - ijj curves a r e thus  (error)  computed.  F i g . .6.8 shows the e r r o r between two e x p e r i m e n t a l A - if; c u r v e s as a f u n c t i o n o f f i l m t h i c k n e s s .  F o r b o t h t h e cases when t h e f i e l d was  on and when the f i e l d was o f f , t h e mean v a l u e o f e r r o r was 0.075°.  This  .20  Q:  .751  o  ft:  Ui  .05 400  800  1200  THICKNESS  ±  1600  /A  (a)  .20]  .75 • • • .05}  0  400  800  1200  THICKNESS  1600  / A  (b) Fig.  6.8  Error (distance) between two experimental A-f curves versus thickness of the oxide film (a) No applied field [ (b) With applied f i e l d  46  e r r o r can be  r e s o l v e d i n t o an e r r o r of 0.05° i n b o t h A and ip.  The readings  s e n s i t i v i t y of the e l l i p s o m e t e r i s ±0.01° i n P and  ( i . e . ±0.02° i n A and  alignment, windows and not  l i m i t e d by  ±0.01° i n  ty).  However, due  to e r r o r s i n  component i m p e r f e c t i o n , the e x p e r i m e n t a l  the s e n s i t i v i t y .  A  error i s  A l s o i n t h i s experiment removing  re-mounting the sample might have i n t r o d u c e d windows, and e t c h i n g o f f the oxide  and  more e r r o r i n alignment  and  f i l m c o u l d have caused s l i g h t damages  to the s u r f a c e of the niobium s u b s t r a t e which i n t u r n c o u l d cause a s l i g h t d i f f e r e n c e i n experimental estimate  the e x p e r i m e n t a l  results.  Therefore  i t i s reasonable  e r r o r as 0.05° i n both A and  mean d i f f e r e n c e between the two i s w i t h i n the l i m i t o f e s t i m a t e d  readings.  A - IJJ curves determined i n t h i s experimental  error.  to The  experiment  T h i s experiment  e s t a b l i s h e s the r e p r o d u c i b i l i t y o f the e l l i p s o m e t e r measurements.  47  7.  FIELD RE CRY S TALLIZ AT ION As  oxide f i l m s films the  a l r e a d y s t a t e d , the c o u l d be  i n the  •T  Vermilyea  limited The  by  anodic n i o b i u m  r e c r y s t a l l i z a t i o n of  recrystallized  the  I t was  anodic niobium o x i d e f i l m s was  to t h a t of anodic T a 0 2  5  films  oxide  areas a p p e a r i n g  a s c a n n i n g e l e c t r o n microscope.  r e c r y s t a l l i z a t i o n " of  ways s i m i l a r  ANODIC NIOBIUM OXIDE FILMS  t h i c k n e s s to which the  anodization process.  f i l m were examined by  that " f i e l d  r e p o r t e d by  Jackson  on  found i n many  29  and  30,31 In " f i e l d  in  grown was  OF  recrystallization"  the  o r i g i n a l amorphous f i l m i s  f a c t , r e c r y s t a l l i z e d , except p o s s i b l y where a n u c l e u s of  oxide i s produced, but anodization.  i s d i s p l a c e d by  not,  crystalline  a c r y s t a l l i n e phase which grows  Two  mechanisms have been suggested on how  the  f i r s t one  by  recrystallization  31 starts is  .  In  transformed i n t o  suggested t h a t  the  which happen to be  a s m a l l p o r t i o n of  crystalline  the  existing  amorphous phase  oxide at a n u c l e a t i o n s i t e .  n u c l e a t i o n s i t e s may at  the  be  small inclusions  metal/oxide i n t e r f a c e .  d i f f e r e n c e i n d e n s i t y between the  I t has of  impurity  S t r e s s e s produced by  c r y s t a l l i n e oxide and  the  amorphous f i l m .  Once a crack i s produced  crystalline  c o n t a c t w i t h the  electrolyte  anodization. The amorphous f i l m i s pushed up and the c r y s t a l l i n e area grows r a d i a l l y . In the underneath the pore i n the  off  and the  amorphous f i l m .  New  the  thickens rapidly metal at  second suggested mechanism a n u c l e a t i o n s i t e  amorphous f i l m has  a  amorphous oxide  produce c r a c k s i n the oxide has  been  access of e l e c t r o l y t e  the  by  cracks  created  through a narrow  c r y s t a l l i n e oxide grows at  the  base  of  29 the  pore by  anodization.  r e c e n t l y confirmed the  T h i s mechanism i s supported by  e x i s t e n c e of s m a l l pores at  the  Jackson  who  recrystallized  has areas.  48  In F i g . 7.1 t h e scanning e l e c t r o n micrographs tallized  areas o f a niobium  to 150 v o l t s . cracked.  show the r e c r y s -  oxide f i l m anodized a t c o n s t a n t OJ'2 mA/cm  The amorphous f i l m a t these areas was pushed up and  I n F i g . 7.1(b) a d i s t i n c t i v e growth of c r y s t a l l i n e oxide w i t h i n  the c r a c k can be seen.  The c r a c k e d amorphous f i l m was p e e l e d back by t h e  c r y s t a l l i n e growth, and s p l i t The  recrystallized  sample s u r f a c e .  into  s t r i p s which c u r l e d  areas d i d not d i s t r i b u t e  On the s u r f a c e o f the niobium  of p i t s which had been produced  outwards. e v e n l y over t h e  sample t h e r e were a number  from the c h e m i c a l p o l i s h i n g  However, these p i t s seemed t o have no apparent  effect  process.  on r e c r y s t a l l i z a t i o n  of t h e f i l m . The amorphous f i l m on t h e sample shown i n F i g . 7.1 was etched o f f w i t h HF. The  F i g . 7.2 shows the s u r f a c e o f t h e sample a f t e r  c r y s t a l l i n e oxide had remained on t h e s u r f a c e .  Ta205 f i l m s  E v i d e n t l y , as w i t h  t h e c r y s t a l l i n e oxide d i s s o l v e s v e r y s l o w l y i n HF as compared  to t h e amorphous o x i d e . of  the etching.  However, i t was i n t e r e s t i n g  to f i n d that part  the p e e l e d back f i l m had n o t d i s s o l v e d i n HF ( F i g . 7 . 2 ( b ) ) .  The same  29 r e s u l t has been observed I t was suggested crystals,  on a n o d i c tantalum oxide f i l m s by Jackson  t h a t as t h e amorphous f i l m was p e e l e d back by t h e growing  a t h i n l a y e r o f c r y s t a l l i n e oxide a t the i n t e r f a c e  became de-  tached and remained i n i n t i m a t e c o n t a c t w i t h the amorphous f i l m ,  thus  p e e l i n g back w i t h the amorphous f i l m . Fig.  7.3 shows the r e c r y s t a l l i z e d  areas o f a f i l m anodized a t  c o n s t a n t 0.2 mA/cm2 t o 149 v o l t s , and then a t c o n s t a n t 120 V f o r 10 h o u r s . The  recrystallized  areas had grown r a d i a l l y from the i n i t i a l  shown i n F i g . 7.1 i n t o  large polygonal areas.  stage as  The amorphous f i l m was  49  (b) Fig.  7.1  Recrystallized  areas o f anodic niobium  oxide  2 film  formed a t constant 0.2mA/cm  v o l t s , at 23 C i n 0.2N H S 0 . 2  (a) 8000x  (b) 9200x  4  to 150  (a)  Fig.  7.2  Same sample as F i g . 7.1.  Recrystallized  areas  a f t e r the amorphous f i l m was etched o f f w i t h  HF.  (a) 2000x  (b) 14000x  52  p e e l e d back f u r t h e r as the c r y s t a l s grew.  The c r a t e r - l i k e c e n t r e of each  p o l y g o n a l a r e a was presumably t h e s i t e where r e c r y s t a l l i z a t i o n  started.  Why i t was shaped d i f f e r e n t l y from the r e s t o f t h e a r e a , o r whether i t r e p r e s e n t e d a pore i n t h e amorphous f i l m , as found  i n tantalum  oxide  film  29 by Jackson  , i s n o t known. I t may be seen i n F i g . 7.3(b) t h a t t h e s u r f a c e o f t h e r e c r y s -  t a l l i z e d area  (and t h e u n d e r s i d e o f t h e peeled-back f i l m , which was : .  a c t u a l l y a t h i n l a y e r o f c r y s t a l s ) has a f i b r o u s n a t u r e . oriented r a d i a l l y .  The f i b r e s a r e  I t can a l s o be seen from F i g . 7.2(b) t h a t s m a l l  f i b r e - o r rod-shaped c r y s t a l s had a t t a c h e d themselves t o t h e edge o f t h e r e c r y s t a l l i z e d oxides. has  surface  a l s o been observed  The f i b r o u s n a t u r e o f t h e r e c r y s t a l l i z e d 29 30 31 on tantalum o x i d e f i l m s ' '  I t was found  t h a t i n constant c u r r e n t ( c o n s t a n t f i e l d )  anodiza-  t i o n , r e c r y s t a l l i z a t i o n o f oxide f i l m s seemed t o depend on the v o l t a g e . Although  a c r i t i c a l v o l t a g e has n o t beenddetermined i n t h i s 2  i t was found  t h a t a f i l m anodized  a t 0.2 mA/cm  investigation,  d i d n o t show r e c r y s t a l -  l i z a t i o n below 100 v o l t s . I t was found  t h a t t h e constant c u r r e n t / v o l t a g e a n o d i z a t i o n  technique produced r e c r y s t a l l i z e d o x i d e even when t h e c o n s t a n t  voltage  was below the v a l u e a t which r e c r y s t a l l i z a t i o n would n o t have o c c u r r e d i n constant c u r r e n t a n o d i z a t i o n . 2  R e c r y s t a l l i z a t i o n was found on an o x i d e  f i l m anodized  a t 0.2 mA/cm  t o 80 v o l t s , and then a t constant  80 v o l t s  f o r A hours.  T h i s suggests  t h a t the p e r i o d a v o l t a g e i s a p p l i e d a c r o s s  the f i l m may be one o f the main f a c t o r s which cause r e c r y s t a l l i z a t i o n .  53  8. The  CONCLUSIONS  f i e l d - i n d u c e d o p t i c a l a n i s o t r o p y i n niobium  studied using i n s i t u ellipsometry. f i l m s was  F i e l d r e c r y s t a l l i z a t i o n of the  i n v e s t i g a t e d u s i n g a scanning e l e c t r o n I t was  oxide f i l m s  found t h a t a n o d i c niobium  was  oxide  microscope.  o x i d e f i l m s were o p t i c a l l y  iso-  t r o p i c i n the absence of an e l e c t r i c f i e l d , b u t became a n i s o t r o p i c when an e l e c t r i c f i e l d was  a p p l i e d normal t o the f i l m s u r f a c e .  r e f r a c t i v e i n d i c e s of the oxide f i l m decreased  The  anisotropic  quadratically with  the  a p p l i e d f i e l d , w h i l e the f i l m t h i c k n e s s i n c r e a s e d q u a d r a t i c a l l y w i t h applied  field. The  r a t i o g of the change i n e x t r a o r d i n a r y r e f r a c t i v e  Atile,. to the change i n o r d i n a r y r e f r a c t i v e index, A n , Q  1.6  the  ± 0.05.  was  index,  found  t o be  T h i s v a l u e i s the same as t h a t r e p o r t e d f o r tantalum  oxide  q u a d r a t i c e l e c t r o - o p t i c c o e f f i c i e n t s of the niobium  oxide  films^. The  f i l m s were found for  to be i n the same o r d e r of magnitude as those r e p o r t e d  oxygen-octahedra No  f e c t s were  f e r r o e l e c t r i c c r y s t a l s and KTN  time dependences of e l e c t r o - o p t i c and  crystals  28  observed.  t h a t the c r y s t a l l i n e o x i d e was 29 30 tantalum o x i d e f i l m s  '  o x i d e f i l m s showed  i n many ways s i l i m a r t o t h a t r e p o r t e d on  31 '  .  The  c r y s t a l l i n e oxide was  found  to c o n s i s t  a number of s m a l l f i b r e - o r rod-shape c r y s t a l s w i t h t h e i r l o n g axes  oriented i n r a d i a l direction.  The  c r y s t a l l i n e oxide d i s s o l v e d very slowly  i n HF as compared t o the amorphous o x i d e . was  '  electrostrictive ef-  S t u d i e s on f i e l d r e c r y s t a l l i z a t i o n of niobium  of  8  found  The  o c c u r r e n c e of r e c r y s t a l l i z a t i o n  t o depend on v o l t a g e i n the c o n s t a n t c u r r e n t a n o d i z a t i o n , and  depend on time i n the c o n s t a n t c u r r e n t / v o l t a g e a n o d i z a t i o n .  54  BIBLIOGRAPHY 1.  A. F r o v a and P. M i g l i o r a t o , A p p l . Phys. L e t t e r s 13, 328  2.  Y.C.  3.  A. F r o v a and P. M i g l i o r a t o , A p p l . Phys. L e t t e r s 15, 406  4.  B.J. Holden and F.G.  5.  F.G.  6.  J . L . Ord, M.A. (1972).  7.  W.D.  39  (1973).  8.  F.S. Chen, J . E . G e u s i c , S.K. K u r t z , J.G. S k i n n e r and S.H. J . A p p l . Phys. 37, 388 (1966).  Wemple,  9.  W. K a n z i g i n " S o l i d S t a t e P h y s i c s " , e d i t e d by F. S e i t z and D. b u l l (Academic P r e s s I n c . , New York, 1957), V o l . 4, p. 89.  Cheng and W.D.  Westvood, J . E l e c t r o n i c Mat.  (1968).  3_, 37  (1974). (1969).  Ullman, J . E l e c t r o c h e m . Soc. 116,  Ullman and B.J. Holden, B u l l . Am. Hopper and W.P.  280  (1969).  Phys. Soc. 12, 1132  (1967).  Wang, J . E l e c t r o c h e m . Soc. 119,  C o r n i s h and L. Young, P r o c . R. Soc. Lond. A. 335,  Turn-  10.  J . F . Nye,  11.  F.L. M c C r a c k i n , E. P a s s a g l i a , R.R. Stromberg Res. Nat. Bur. Stand. A. 67, 363 (1963).  12.  K.H.-Zaininger and A.G.  13.  R.J. A r c h e r , "Manual on E l l i p s o m e t r y " , G a e r t n e r S c i e n t i f i c Corp.  14.  P. Drude, Wied. Ann.  15.  L.P. M o s t e l l e r , J r . and F. Wooten, J . Opt. Soc. Am.  16.  O.S.  17.  R.M.A. Azzam and N.M.  18.  De Smet, J . Opt. Soc. Am.  19.  D. Den E n g e l s e n , J . Opt. Soc. Am.  20.  M. Tomar and V.K.  21.  R.J. A r c h e r , J . Opt. Soc. Am.  22.  D.E.  Ra  " P h y s i c a l P r o p e r t i e s of C r y s t a l s " , Oxford P r e s s  439  (1957).  and H. S t e i n b e r g , J .  c  Revesz, RCA  Phys. 32, 623  Review 25  ( 1 ) , 85  (1964).  (1887). 58, 511  Heavens, " T h i n F i l m P h y s i c s " , Methuen, London, 1970, Bashara, J . Opt. 6_4, 631  Soc. Am.  64, 128  p.  (1968). 88.  (1974).  (1974) 61, 1460  (1971).  S r i v a s t a v a , T h i n S o l i d F i l m s 15, 207 52, 970  Aspnes and A.A.. Studna, App.  (1968)  (1962).  Opt. 10, 1024  (1971).  (1973).  55  23.  F.L. M c C r a c k i n , "A F o r t r a n Program f o r A n a l y s i s of E l l i p s o m e t e r measurements", N.B.S. T e c h n i c a l Note 479 (1969).  24.  F.L. McCrackin, J . Opt. Soc. Am. 60, 57 (1970).  25.  M.L. K i n t e r , I . Weissman and W.W. (1970).  26.  L . Young, "Anodic Oxide F i l m s " , Academic P r e s s , New York, 1961.  27.  S.H. Wemple, M. D i Domenico, J r . , and I . Cambibel, A p p l . Phys. L e t t e r s 12, 209 (1968).  28.  M. D i Domenico, J r . and S.H. Wemple, J . A p p l . Phys. 40, 720 (1969).  29.  N.F. J a c k s o n , J . A p p l . E l e c t r o c h e m . 3_» 91 (1973).  30.  D.A. V e r m i l y e a , J . E l e c t r o c h e m . Soc. 102, 207 (1955).  31.  D.A. V e r m i l y e a , J . E l e c t r o c h e m . Soc. 104, 542 (1957).  32.  W.A.  S t e i n , J . A p p l . Phys.  41^, 828  S h u r c l i f f , " P o l a r i z e d L i g h t " , H a r v a r d c U n i v e r s i t y P r e s s , 1962.  56  APPENDIX Poincare  Sphere R e p r e s e n t a t i o n  of P o l a r i z a t i o n  For a l i g h t wave t r a v e l l i n g  of Light  i n the z d i r e c t i o n o f an a r b i t r a r y  c o o r d i n a t e system, the e l e c t r i c v e c t o r i s g i v e n by E  x  = a j cos (x  Ey = a  2  cos (x  &i)  +  + <5 ) 2  where T = w(t - / v ) , and u and v are the a n g u l a r z  v e l o c i t y o f the l i g h t ,  respectively.  can be d e s c r i b e d by the amplitudes 6 = S  2  - 6j.  This e l e c t r i c  The p o l a r i z a t i o n 2  v e c t o r has an e l l i p t i c a l  and l i n e a r  o f the l i g h t wave  aj and a , and t h e phase  normal t o the d i r e c t i o n o f p r o p a g a t i o n , elliptical  frequency  difference  l o c u s i n the p l a n e  as shown i n F i g . A . l .  The  l o c u s i s c h a r a c t e r i z e d by t h e azimuth, cf>, and the e l l i p t i c i t y  tan  x = ±~ a  where a and b a r e the semi-axes o f the e l l i p s e .  Fig.  A . l Locus o f the e l e c t r i c v e c t o r f o r e l l i p t i c a l l y p o l a r i z e d l i g h t i n a p l a n e normal to t h e d i r e c t i o n of p r o p a g a t i o n .  x»  57  Another r e p r e s e n t a t i o n o f the s t a t e of p o l a r i z a t i o n o f the l i g h t i s by the Stokes 5  0  parameters = a\ + a  51 -  5  2  -  = 2a}a  2  af  2  cos 6  53 = 2&i&2 s i n 6 where SQ i s p r o p o r t i o n a l to the i n t e n s i t y o f the l i g h t wave. ellipsometry because  the Stokes parameters  can be n o r m a l i z e d so that SQ = 1  one i s n o t concerned w i t h the i n t e n s i t y o f l i g h t .  shown-'--'-»32 t h a t the n o r m a l i z e d Stokes parameters 5  0  For  I t can be ;  are g i v e n by  =1  51 = cos 2a = cos  2x  cos 2(j> (A.l)  5  2  = s i n 2a cos6 = cos 2x s i n 2cf>  53 = s i n 2a sin6 = s i n 2x where a i s an a u x i l i a r y angle d e f i n e d by A  tan It  a =  a  2  —  l  can be seen from e q u a t i o n s A . l that SQ = 1, 2<j>, 2x are the  s p h e r i c a l c o o r d i n a t e s e q u i v a l e n t t o the c a r t e s i a n c o o r d i n a t e s S j , S  2  and S .  Thus the s t a t e of p o l a r i z a t i o n o f a l i g h t wave can be r e p r e s e n t e d by a p o i n t P on a sphere of u n i t r a d i u s , as shown i n F i g . A.2. c a l l e d the P o i n c a r e s p h e r e .  T h i s sphere i s  3  58  Fig.  A.2  Representation of p o l a r i z e d l i g h t on Poincare sphere.  The Poincare sphere provides a convenient method f o r representing p o l a r i z e d l i g h t and f o r p r e d i c t i n g how o p t i c a l elements w i l l change the polarization.  From equations A.1 and F i g . A.2 i t can be seen that the  equator of the Poincare sphere represents l i n e a r l y p o l a r i z e d l i g h t .  The  upper and lower p o l e s , c^ and c , represent c i r c u l a r l y p o l a r i z e d l i g h t . 2  Other points on the sphere i n d i c a t e e l l i p t i c a l p o l a r i z a t i o n . The Poincare sphere i s used to p r e d i c t the e f f e c t of a retarder  59  ( a l s o c a l l e d wave p l a t e ) on a beam of l i g h t  i n the f o l l o w i n g method.  p o l a r i z a t i o n o f a l i g h t beam i n c i d e n t on a r e t a r d e r F i g . A.3.  R represents  azimuth i s < j > .  The  i s r e p r e s e n t e d by P i n  a r e t a r d e r whose phase r e t a r d a t i o n i s 6 and whose  A f t e r the l i g h t beam has passed through the r e t a r d e r , i t s  p o l a r i z a t i o n i s o b t a i n e d by r o t a t i n g P about the a x i s OR through an angle 6.  The f i l i a l l o c a t i o n P' r e p r e s e n t s  from the r e t a r d e r .  the p o l a r i z a t i o n o f l i g h t  emerging  

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