PLASTIC DEFORMATION AND ELECTRONIC MECHANISMS IN SEMICONDUCTORS AND INSULATORS

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PLASTIC DEFORMATION AND ELECTRONIC MECHANISMS IN SEMICONDUCTORS AND

INSULATORS

P. Hirsch

To cite this version:

P. Hirsch. PLASTIC DEFORMATION AND ELECTRONIC MECHANISMS IN SEMICONDUC- TORS AND INSULATORS. Journal de Physique Colloques, 1981, 42 (C3), pp.C3-149-C3-160.

�10.1051/jphyscol:1981313�. �jpa-00220704�

JOURNAL DE PHYSIQUE

Colloque CZ, supplément au n°6, Tome 42, juin 1981 page C3-149

PLASTIC DEFORMATION AND ELECTRONIC MECHANISMS IN SEMICONDUCTORS AND INSULATORS

P . B . H i r s c h

Department of Metallurgy and Science of Materials, University of Oxford, Parks Road, Oxford, England

Résumé.- On propose ici que les décrochements sur les dislocations soient associés à des états chargés dans la bande interdite des semi-conducteurs et des isolants, et que la vitesse des dislocations et donc les propriétés plastiques soient fonction de la position du niveau de Fermi. La théorie est appliquée à l'effet du dopage sur la vitesse des dislocations dans Si et Ge, et l'on discute la mise en cause de ce mécanisme lors de l'effet "hydrolytic weakening" dans le quartz.

A b s t r a c t . - I t i s proposed t h a t d i s l o c a t i o n kinks are associated with charged s t a t e s in the energy gap of semiconductors and i n s u l a t o r s , and t h a t the d i s - location v e l o c i t y and therefore the p l a s t i c p r o p e r t i e s are a function of the p o s i t i o n of the Fermi l e v e l . The theory i s applied to the doping effect on d i s l o c a t i o n v e l o c i t y in Si and Ge, and the possible relevance of the mecha- nism to the "hydrolytic weakening" effect in quartz i s discussed.

I n t r o d u c t i o n . - I t i s w e l l known t h a t p o i n t d e f e c t s i n i o n i c a n d c o - v a l e n t l y b o n d e d s o l i d s c a n o c c u r i n c h a r g e d c o n f i g u r a t i o n s , t h e e l e c - t r o n / h o l e s t a t e s o c c u r i n g a s d e e p l e v e l s i n t h e b a n d g a p . The c o n c e n - t r a t i o n o f c h a r g e d p o i n t d e f e c t s , a n d t h e r e f o r e t h e d i f f u s i o n c o e f f i - c i e n t s , d e p e n d on t h e p o s i t i o n o f t h e F e r m i l e v e l , w h i c h i n t u r n i s c o n t r o l l e d by d o p i n g w i t h s u i t a b l e i m p u r i t i e s ( K o f s t a d / l / , K r o g e r / 2 / , S w a l i n / 3 / ) . S t e a d y s t a t e a n d d i f f u s i o n c r e e p c a n t h e n b e a f f e c t e d by t h e p o s i t i o n o f t h e F e r m i l e v e l ( e . g . B r e t h e a u , C a s t a i n g , R a b i e r a n d V e y s s i e r e / 4 / ) .

T h e r e i s h o w e v e r a n o t h e r m e c h a n i s m of p l a s t i c d e f o r m a t i o n w h i c h s h o u l d b e a f f e c t e d by t h e F e r m i l e v e l . When t h e m o t i o n o f t h e d i s l o c a - t i o n s i s c o n t r o l l e d by t h e P e i e r l s s t r e s s , t h e d i s l o c a t i o n l i n e s a d - v a n c e a n d l e n g t h e n by t h e g e n e r a t i o n and m o t i o n of d o u b l e k i n k s . A t t h e c o r e o f t h e d i s l o c a t i o n t h e e l e c t r o n e n e r g y l e v e l s w i l l b e s h i f t e d r e l a t i v e t o t h o s e i n t h e p e r f e c t c r y s t a l , by a m o u n t s d e p e n d i n g on t h e d e g r e e o f r e c o n s t r u c t i o n o f t h e b o n d s . F o r d a n g l i n g b o n d s i n a c o v a l e n t - l y b o n d e d s o l i d one m i g h t e x p e c t e n e r g y l e v e l s t o o c c u r n e a r t h e m i d d l e o f t h e g a p , i . e . a b o u t midway b e t w e e n b o n d i n g a n d a n t i b o n d i n g s t a t e s . I f r e c o n s t r u c t i o n o c c u r s a c c e p t o r a n d d o n o r l e v e l s w o u l d b e e x p e c t e d t o o c c u r n e a r e r t o t h e c o n d u c t i o n a n d v a l e n c e b a n d s , t h e i r p o s i t i o n s d e - p e n d i n g on t h e d i s t o r t i o n of t h e b o n d s . K i n k s m i g h t b e a s s o c i a t e d w i t h

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981313

c3- 150 JOURNAL DE PHYSIQUE

d e e p e r l e v e l s i f t h e d i s t o r t i o n s a r e g r e a t e r t h a n a t t h e d i s l o c a t i o n c o - r e s . Charged a s w e l l a s n e u t r a l k i n k s c a n t h e n e x i s t , t h e c o n c e n t r a t i o n of c h a r g e d k i n k s d e p e n d i n g on t h e p o s i t i o n o f t h e F e r m i l e v e l . S i n c e t h e d i s l o c a t i o n v e l o c i t y d e p e n d s o n t h e c o n c e n t r a t i o n oE k i n k s a n d t h e i r m o b i l i t y , t h e v e l o c i t y w i l l depend o n t h e p o s i t i o n o f t h e F e r m i l e v e l p a r t l y b e c a u s e o f t h e e f f e c t o n t h e c o n c e n t r a t i o n o f c h a r g e d k i n k s , a n d p a r t l y b e c a u s e t h e v e l o c i t y o f t h e k i n k may b e c h a r g e d e p e n d e n t .

I n t h i s p a p e r we s h a l l a p p l y t h i s model t o t h e e f f e c t o f d o p i n g on t h e d i s l o c a t i o n v e l o c i t y i n S i a n d G e , and s p e c u l a t e a b o u t i t s app- l i c a t i o n t o q u a r t z .

2 . B a s i c t h e o r y a n d a p p l i c a t i o n t o s e m i c o n d u c t o r s . - F i g u r e 1 shows t h e model a d o p t e d , w i t h k i n k a c c e p t o r a n d d o n o r l e v e l s (EKa, EKd) between t h e d i s l o c a t i o n l e v e l s (EDa, E D d ) . From F e r m i - D i r a c s t a t i s t i c s i t f o l l o w s t h a t t h e c o n c e n t r a t i o n s o f n e g a t i v e l y a n d p o s i t i v e l y c h a r g e d k i n k s i n thermodynamic e q u i l i b r i u m a r e g i v e n by

w h e r e o ~ k i s t h e c o n c e n t r a t i o n o f n e u t r a l k i n k s , E7 t h e Fermi l e v e l , e V t h e e l e c t r o s t a t i c e n e r g y o f t h e c h a r g e d d i s l o c a t i o n l i n e ( i n c l u d i n g t h e c h a r g e on k i n k s ) , k t h e Boltzmann c o n s t a n t and T t h e t e m p e r a t u r e .

Fig. 1.- E l e c t r o n i c energy l e v e l scheme. C , V a r e conduction

-~d

-

and valence b a n d s ; 12 a r c d i s l o c a t i o n nccel,tor/donor V l e v c l s ; EKa, EKd arcD$ink a c c e p t o r / d o n o r l e v e l s .

The e q u i l i b r i u m c o n c e n t r a t i o n o f n e u t r a l k i n k s ( o ~ k ) i s assumed t o b e i n d e p e n d e n t o f t h e c o n c e n t r a t i o n o f c h a r g e d k i n k s ; t h i s a s s u m p t i o n i s j u s t i f i e d p r o v i d e d t h e c o n c e n t r a t i o n s o f c h a r g e d a n d u n c h a r g e d k i n k s a r e s m a l l , s o t h a t t h e number o f a v a i l a b l e s i t e s i s e f f e c t i v e l y con- s t a n t , i n d e p e n d e n t o f o c k , i c k , and t h e d i f f e r e n c e i n f r e e e n e r g y b e t - ween t h e u n c h a r g e d a n d c h a r g e d c o n f i g u r a t i o n s i s e q u a l t o t h e d i f f e r e n c e i n e l e c t r o n f r e e e n e r g y (EF - EKa - eV f o r n e g a t i v e l y c h a r g e d k i n k s ) , i . e . t h e r e i s no c h a n g e i n t h e s t r a i n e n e r g y o f t h e d e f e c t .

A t low s t r e s s e s and h i g h t e m p e r a t u r e s t h e " d r i f t " model c a n be used t o d e s c r i b e t h e motion o f d i s l o c a t i o n s by t h e k i n k mechanism ( s e e H i r t h and Lothe / 5 / ) . Under t h e s e c o n d i t i o n s , and assuming t h a t t h e mean f r e e p a t h o f k i n k s i s d e t e r m i n e d by a n n i h i l a t i o n by o t h e r s moving i n t h e o p p o s i t e d i r e c t i o n , t h e v e l o c i t y o f t h e d i s l o c a t i o n s i s propor- t i o n a l t o t h e c o n c e n t r a t i o n o f s i n g l e k i n k s , and t o t h e r a t e o f migra- t i o n o f k i n k s a l o n g t h e d i s l o c a t i o n . Thus, i f t h e v e l o c i t y v- i s con- t r o l l e d by n e g a t i v e l y c h a r g e d k i n k s ,

- -

⁼ exp (EF

-

^EKa

-

eV

-

AWm)/kT

T 7

where vo i s t h e v e l o c i t y o f n e u t r a l k i n k s , and AVJm t h e d i f f e r e n c e i n a c t i v a t i o n e n e r g y o f m i g r a t i o n f o r n e g a t i v e l y c h a r g e d and n e u t r a l k i n k s . There i s a s i m i l a r e x p r e s s i o n , u s i n g ( 2 ) , i f t h e v e l o c i t y i s c o n t r o l l e d by p o s i t i v e l y c h a r g e d k i n k s .

where AWm i s t h e d i f f e r e n c e i n a c t i v a t i o n e n e r g y o f m i g r a t i o n f o r p o s i - 1 t i v e l y c h a r g e d and n e u t r a l k i n k s .

S i n c e t h e c o n c e n t r a t i o n o f n e u t r a l k i n k s i s c o n s t a n t , t h e d i s l o - c a t i o n v e l o c i t y w i l l i n c r e a s e w i t h i n c r e a s i n g c o n c e n t r a t i o n s o f c h a r g e d k i n k s . R e f e r r i n g t o f i g u r e 1, it f o l l o w s from ( 3 ) and ( 4 ) t h a t i f t h e k i n k l e v e l s a r e n e a r t h e middle o f t h e gap t h e v e l o c i t i e s of d i s l o c a - t i o n s of n and p t y p e m a t e r i a l s h o u l d b e g r e a t e r t h a n t h a t o f i n t r i n s i c m a t e r i a l ; i . e . t h e " s t r e n g t h " o f t h e c r y s t a l s h o u l d be a maximum f o r i n t r i n s i c m a t e r i a l ; d o p i n g by e l e c t r i c a l l y a c t i v e i m p u r i t i e s c a u s e s s o f t e n i n g . On t h e o t h e r hand, i f t h e k i n k l e v e l s a r e c l o s e t o t h e va- l e n c e band t h e v e l o c i t y s h o u l d d e c r e a s e from n t o p t y p e m a t e r i a l , i . e . n t y p e m a t e r i a l i s w e a k e r , and p t y p e s t r o n g e r t h a n i n t r i n s i c m a t e r i a l . I n t h i s c a s e d o p i n g o f t h e p u r e m a t e r i a l c a n c a u s e h a r d e n i n g o r s o f t e - n i n g depending on t h e i m p u r i t y .

The a p p l i c a t i o n o f t h i s model t o s i l i c o n and germanium h a s b e e n d e s c r i b e d i n d e t a i l e l s e w h e r e ( H i r s c h / 6 / , / ' 7 / ) . I n t h e s e m a t e r i a l s t h e P e i e r l s v a l l e y s a r e a l o n g [110] d i r e c t i o n s , and v e l o c i t i e s o f b o t h 60' and s c r e w d i s l o c a t i o n s h a v e b e e n measured by s e v e r a l workers. I t t u r n s o u t t h a t s i l i c o n behaves l i k e a c r y s t a l w i t h k i n k l e v e l s n e a r t h e middle o f t h e gap, w h i l e germanium seems t o have k i n k l e v e l s n e a r t h e v a l e n c e

c3- 152 JOURNAL DE PHYSIQUE

band. S c h r G t e r h a s r e c e n t l y f i t t e d t h e t h e o r y t o r e s u l t s due t o George /8/ f o r 60' d i s l o c a t i o n s i n S i , assuming t h a t eV and AW m c a n be n e g l e c - t e d . I n t h a t c a s e t h e v e l o c i t y i s p r o p o r t i o n a l t o ( o ~ k

+

-ck + + c k ) . F i g u r e 2 shows t h e e x p e r i m e n t a l p o i n t s and t h e o r e t i c a l c u r v e s . B e s t

f i t s a r e produced f o r

( e n e r g i e s measured r e l a t i v e t o v a l e n c e b a n d ) . These l e v e l s a r e v e r y c l o s e t o t h e v a l u e s o b t a i n e d from c a p a c i t y t r a n s i e n t s p e c t r o s c o p y o f deformed and s u b s e q u e n t l y a n n e a l e d ( a t 900°C) S i ( P a t e l and Kimerling / 9 / ) , and a r e a t t r i b u t e d t o d i s l o c a t i o n s . I t i s however n o t a t a l l c e r - t a i n whether t h e l e v e l s d e t e c t e d by t h i s t e c h n i q u e a r e t o b e i d e n t i f i e d w i t h t h o s e d e r i v e d from v e l o c i t y measurements. F i r s t l y , t h e k i n k l e v e l s may b e a f u n c t i o n o f t h e c h a r a c t e r o f t h e d i s l o c a t i o n , and t h e s p e c i - mens t o which t h e s p e c t r o s c o p i c t e c h n i q u e h a s been a p p l i e d a r e l i k e l y t o c o n t a i n d i s l o c a t i o n s o f v a r i o u s c h a r a c t e r s . Secondly, i n i n t e r p r e t i n g

Fig. 2.- R a t i o o f v e l o c i t i e s v of 60" d i s l o c a t i o n s i n S i t o t h a t of i n t r i n s i c mate- r i a l , vi, a s a f u n c t i o n of ( t e m p e r a t u r e ) - I f o r v a r i o u s doping c o n c e n t r a t i o n s , donors:

A= 14 x 1018 c k 3 , B = 6 x 1018 ~ m - ~ , C = 1 . 2 x 1018 C,~, a c c e p t o r s : - D = 80 x 10 17

-

³

cm

,

E = 6.8 x 10 l 7 c m 3 , F = 2 . 7 x l 0 I 7 Measurements of George/8/; f i t t i n g c a r r i e d o u t by ~ c h r 6 t e r .

t h e d i s l o c a t i o n v e l o c i t y d a t a , t h e eV and AW t e r m s s h o u l d b e t a k e n i n - m

t o a c c o u n t . The former depend a l s o on t h e (unknown) d i s l o c a t i o n a s w e l l a s on t h e k i n k l e v e l s . With r e g a r d t o AWm, i f t h e a d i a b a t i c p r i n c i p l e a p p l i e s t h e e l e c t r o n s w i l l f o l l o w t h e motion o f ' t h e i o n s d u r i n g t h e a c t i v a t i o n , and t h e e l e c t r o n l o c a l i s e d a t t h e k i n k w i l l move from l e v e l s EKa, EKd t o c o r r e s p o n d i n g l e v e l s a t t h e s a d d l e p o i n t , ESa, ESd. Under t h e s e c o n d i t i o n s AWm = ESa

-

EKa; AWm 1 - - EKd

-

ESd. The l e v e l s i n f e r r e d from t h e v e l o c i t y measuremehts w i l l t h e n c o r r e s p o n d t o ESa, ESd. A s J o n e s /lo/ h a s p o i n t e d o u t t h e s e l e v e l s a t t h e s a d d l e p o i n t c o n f i g u r a - t i o n a r e l i k e l y t o be d e e p e r t h a n t h e ground s t a t e k i n k l e v e l s , s i n c e bonds a r e e f f e c t i v e l y broken a t t h e s a d d l e p o i n t s . I t s h o u l d b e n o t e d h e r e t h a t J o n e s has developed an a l t e r n a t i v e t h e o r y which a s c r i b e s t h e doping e f f e c t on d i s l o c a t i o n v e l o c i t y t o c h a r g e d s a d d l e p o i n t c o n f i g u - r a t i o n s ; t h e t h e o r y assumes t h a t t h e k i n k s a r e n e u t r a l i n t h e ground s t a t e l a n d t h a t thermodynamic e q u i l i b r i u m i s e s t a b l i s h e d between t h e l a t t i c e and t h e e l e c t r o n gas a t t h e s a d d l e p o i n t . The d i f f e r e n c e between t h e two t h e o r i e s h a s been d i s c u s s e d e l s e w h e r e ( H i r s c h / 7 / ) . The p r e s e n t a u t h o r b e l i e v e s t h a t t h e c r o s s - s e c t i o n s f o r e l e c t r o n / h o l e c a p t u r e a r e n o t s u f f i c i e n t t o a l l o w thermodynamic e q u i l i b r i u m t o b e e s t a b l i s h e d d u r i n g t h e l i f e t i m e o f t h e s a d d l e p o i n t f o r k i n k m i g r a t i o n . On t h e o t h e r hand, p r o v i d e d thermodynamic e q u i l i b r i u m i s e s t a b l i s h e d i n t h e ground s t a t e , a s assumed i n t h e p r e s e n t t h e o r y , and i f t h e a d i a b a t i c p r i n c i p l e a p p l i e s , w i t h t h e above v a l u e s o f AWm t h e p r e d i c t i o n s o f t h e two theo- r i e s become v i r t u a l l y i d e n t i c a l .

The t h e o r y o u t l i n e d h e r e (and d e s c r i b e d i n more d e t a i l i n H i r s c h / 6 / ) a p p l i e s s t r i c t l y t o t h e low s t r e s s and h i g h t e m p e r a t u r e regime.

Many o f t h e measurements a r e however made a t h i g h s t r e s s e s and low

t e m p e r a t u r e , when t h e v e l o c i t y i s c o n t r o l l e d by t h e n u c l e a t i o n o f d o u b l e k i n k s . F o r n e u t r a l k i n k s , a c c o r d i n g t o H i r t h and Lothe / 5 / , t h e same e x p r e s s i o n s f o r d i s l o c a t i o n v e l o c i t y a r e o b t a i n e d , assuming t h a t t h e mean f r e e p a t h of t h e k i n k s i s d e t e r m i n e d by mutual a n n i h i l a t i o n , i . e . t h e d i s l o c a t i o n v e l o c i t y i s d e t e r m i n e d by t h e f o r m a t i o n e n e r g y o f h a l f a d o u b l e k i n k . P r o v i d e d t h e c o n c e n t r a t i o n o f c h a r g e d double k i n k s can b e assumed t o b e t h a t i n thermodynamic e q u i l i b r i u m w i t h t h e e l e c t r o n g a s , t h e t h e o r y under n u c l e a t i o n c o n t r o l l e d c o n d i t i o n s becomes s i m i l a r t o t h a t under d r i f t c o n d i t i o n s . F i g u r e 3 shows s c h e m a t i c a l l y t h e e n e r g y o f a double k i n k a s a f u n c t i o n o f s e p a r a t i o n o f t h e two k i n k s . E q u i l i - brium can be e s t a b l i s h e d a t A , p r o v i d e d t h e l i f e t i m e i s l o n g enough;

a l t e r n a t i v e l y however n u c l e a t i o n may o c c u r a t c h a r g e d p o i n t s o f t h e d i s - l o c a t i o n ( i n thermodynamic e q u i l i b r i u m w i t h t h e e l e c t r o n g a s ) ; a p p l y i n g t h e a d i a b a t i c p r i n c i p l e t h e e l e c t r o n s / h o l e s w i l l move t o t h e k i n k e n e r - gy l e v e l s A, and t o t h e s a d d l e p o i n t l e v e l s B d u r i n g t h e n u c l e a t i o n ,

c3- 154 JOURNAL DE PHYSIQUE

and t h e t h e o r y becomes v i r t u a l l y i d e n t i c a l t o t h e d r i f t t r e a t m e n t .

F i g . 3 . - Energy a s a f u n c t i o n o f d i s t a n c e between two k i n k s c o n s t i t u t i n g a n u c l e a t e d double k i n k . A p a r t i a l l y formed double k i n k X may w a i t i n t h e s u b s i d i a r y v a l l e y s ( e . g . A)

and e q u i l i b r a t e w i t h t h e e l e c t c o n gas.

3. P o s s i b l e a p p l i c a t i o n s t o q u a r t z . - The t h e o r y o u t l i n e d above s h o u l d a p p l y a l s o t o i o n i c s o l i d s . I f t h e r e i s some c o n v a l e n t b i n d i n g , t h e c h a r g e t r a n s f e r t o t h e i o n s i s n o t c o m p l e t e , and some c h a r g e s h o u l d r e s i d e i n t h e bonds. Then a t t h e c o r e o f t h e d i s l o c a t i o n , o r a t a p o i n t d e f e c t o r k i n k , t h e s t r a i n e d o r d a n g l i n g bonds would be a s s o c i a t e d w i t h a c c e p t o r / donor s t a t e s i n t h e gap. Thus, i n t h e "low" t e m p e r a t u r e r e - gime o f t h e d e f o r m a t i o n o f o x i d e s , o r c e r a m i c s i n g e n e r a l , when t h e P e i e r l s s t r e s s i s c o n t r o l l i n g , doping i n d u c e d h a r d e n i n g and s o f t e n i n g e f f e c t s s h o u l d o c c u r , depending on t h e r e l a t i v e p o s i t i o n s of t h e Permi and k i n k l e v e l s . F u r t h e r m o r e , t h e w i d e r t h e e n e r g y gap o f t h e s o l i d , t h e g r e a t e r t h e s e n s i t i v i t y o f t h e Fermi l e v e l (and t h e r e f o r e o f t h e d i s l o c a t i o n v e l o c i t y ) t o s m a l l amounts o f e l e c t r i c a l l y a c t i v e d o p a n t s .

I n t h e c a s e o f q u a r t z t h e r e i s a w e l l known s o f t e n i n g e f f e c t due t o t h e p r e s e n c e o f s m a l l amounts o f w a t e r ( h y d r o l y t i c weakening) o f con- s i d e r a b l e i m p o r t a n c e i n geology ( G r i g g s and B l a c i c /11/). Following a s u g g e s t i o n o f F r a n k , Griggs / 1 2 / proposed t h a t t h e e f f e c t i s due t o t h e weakening o f t h e Si-0-Si bonds by h y d r o l y s i s t o Si-OH-HO-Si, and t h a t

i f t h i s o c c u r s a t t h e d i s l o c a t i o n c o r e t h e n u c l e a t i o n o f d o u b l e k i n k s i s f a c i l i t a t e d . The model r e q u i r e s t h e d i f f u s i o n o f OH t o t h e d i s l o c a - t i o n , and p i p e d i f f u s i o n a l o n g t h e d i s l o c a t i o n w i t h t h e m i g r a t i n g k i n k . ivlcLaren and R e t c h f o r d /13/ however showed t h a t t h e r a t e o f r e c o v e r y i s

a l s o dependent on t h e c o n c e n t r a t i o n o f OH ( o r H ) . They s u g g e s t e d t h a t t h e r a t e o f r e c o v e r y by c l i m b , i s c o n t r o l l e d by t h e t r a p p i n g of H20 a t t h e d i s l o c a t i o n , presumably f a c i l i t a t i n g n u c l e a t i o n o f j o g s . By e q u a t i n g t h e r a t e o f r e c o v e r y t o t h e workhardening r a t e , W , t h e y o b t a i n t h e e x p r e s s i o n

where N i s t h e c o n c e n t r a t i o n of hydrogen atoms, Tc t h e c r i t i c a l weake- ning temperature, a t which t h e flow s t r e s s drops s h a r p l y , E an a c t i v a - t i o n energy made up of s e v e r a l terms, and A a c o n s t a n t . A r e l a t i o n of t h e form of e q u a t i o n ( 5 ) seems t o f i t t h e a v a i l a b l e experimental d a t a adequately / 1 3 / . I t i s c l e a r however from t h e work of Morrison-Smith, P a t e r s o n and Hobbs /14/ t h a t i n t h e low temperature regime t h e d i s l o - c a t i o n motion i s c o n t r o l l e d by t h e double kink mechanism, s i n c e t h e d i s l o c a t i o n s a r e found t o l i e a l o n g c r y s t a l l o g r a p h i c d i r e c t i o n s , t h e P e i e r l s v a l l e y s . The s t r u c t u r e s a t high temperature s u g g e s t a recovery p r o c e s s . The r e s u l t s of Hobbs, McLaren and P a t e r s o n /15/ i n d i c a t e two e f f e c t s : - a ) t h e y i e l d s t r e s s appears t o d e c r e a s e w i t h i n c r e a s i n g temperature, approximately a s exp U/kT, w i t h an a c t i v a t i o n energy U which d e c r e a s e s with i n c r e a s i n g H/Si ( s e e F i g . 4 1 , b ) t h e flow s t r e s s

F i g . 4.- Temperature dependence o f y i e l d s t r e s s ( u p p e r y i e l d s t r e s s Ouy; i n i t i a l y i e l d s t r e s s O when y i e l d p o i n t a b s e n t ) from 1151.

Y

c3- 156 JOURNAL DE PHYSIQUE

a t 2% s t r a i n d r o p s s h a r p l y a t a p a r t i c u l a r t e m p e r a t u r e Tc, which v a r i e s w i t h H/Si a c c o r d i n g t o l o g H/Si = l/Tc ( s e e F i g s . 5 , 6 ) .

0 4 i

3 0 0 500 7 0 0 900 1000

TEMPERATURE 'C

F i g . 5.- Flow s t r e s s a t 2% s t r a i n a s a func- t i o n o f t e m p e r a t u r e f o r q u a r t z c r y s t a l s (S1: H / S i 6100 ppm; W1: H/Si 1850 ppm; H / S i 1600 ppm; W 4 : H/Si 730 ppm) from 1151.

Both e f f e c t s , i . e . r e l a t i n g t o t h e y i e l d s t r e s s and t o t h e r e - c o v e r y r a t e , can i n p r i n c i p l e be e x 2 l a i n e d by an e l e c t r o n i c mechanism, w i t h o u t n e e d i n g t o p o s t u l a t e t h e p r e s e n c e o f H20 o r OH a t t h e d i s l o c a - t i o n . The b a s i c i d e a i s t h a t H20 goes i n t o s o l u t i o n i n a form i n which i t a c t s e i t h e r a s a donor o r a c c e p t o r c e n t r e . Kekulawala, P a t e r s o n and Boland /16/ have p u t forward e v i d e n c e t h a t t h e weakening e f f e c t c o r r e - l a t e s w i t h a b r o a d hydroxyl a b s o r p t i o n " g e l - t y p e " band i n t h e r e g i o n 340 mm-I wavenumber ( Q 0.4 e V ) . I t seems p l a u s i b l e t h a t t h i s i s a s s o - c i a t e d w i t h OH s t r e t c h i n g modes which o c c u r i n t h i s p a r t o f t h e spec- t r u m . I t i s n o t c l e a r whether t h e r e i s any e v i d e n c e f o r an e l e c t r o n i c t r a n s i t i o n l e v e l a t h i g h e r e n e r g i e s . Suppose however t h a t t h e r e i s an a c c e p t o r l e v e l EHa a t , s a y 2 eV, from t h e v a l e n c e band. I f t h e Fermi l e v e l i n t h e w a t e r f r e e c r y s t a l i s n e a r t h e middle o f t h e gap ( t h e gap energy i s a b o u t 9 eV f o r q u a r t z ) , i t s p o s i t i o n b e i n g d e t e r m i n e d by some

o t h e r e l e c t r i c a l l y a c t i v e i m p u r i t y (e.9. A 1 o r N a ) , a s t h e c o n c e n t r a - t i o n of H 2 0 i n c r e a s e s , t h e Fermi l e v e l moves towards t h e H 2 0 a c c e p t o r l e v e l . Assuming t h a t t h e c h a r g e d k i n k l e v e l s o r ( p r o b a b l y doubly) c h a r - ged a n i o n vacancy l e v e l s a r e somewhere n e a r t h e middle o f t h e gap ( s e e F i g . 7 1 , t h e c o n c e n t r a t i o n s of p o s i t i v e l y c h a r g e d k i n k s and a n i o n vacan- c i e s i n c r e a s e s u b s t a n t i a l l y r e s u l t i n g i n i n c r e a s e s i n t h e d i s l o c a t i o n v e l o c i t y and i n t h e d i f f u s i o n o f oxygen i o n s ; t h e l a t t e r may a c c e l e r a t e t h e r a t e o f c l i m b and r e c o v e r y i f t h e d i f f u s i o n o f oxygen i o n s i s r a t e c o n t r o l l i n g .

L

^{Fig. 6.-} R e l a t i o n between OH c o n t e n t and c r i -

2.0 t i c a l temperature, T

,

corresponding t o most

12 1.3 I 4

lOOO/., ^l.5 r a p i d d e c r e a s e of flgw s t r e s s with temperature

i n f i g u r e 5 , from 1151.

Fig. 7.- P o s t u l a t e d energy l e v e l diagram f o r q u a r t z (schematic). E EKd a r e kink a c c e p t o r / d o n o r l e v e l s , P i s doubly charged anion vacancy l e v e l ,

!ha'

i s H20 accep- t o r l e v e l , E .

,

EFH a r e P g r m i l e v e l s i n i n t r i n s i c and H 0 doped m a t s i a l .

F1 2

c3- 158 JOURNAZ. DE PHYSIQUE

I n t h e regime where t h e y i e l d s t r e s s T i s c o n t r o l l e d by t h e double k i n k mechanism, i n w a t e r f r e e c r y s t a l s t h e y i e l d s t r e s s may be Y determined by n e u t r a l k i n k s , t h e s t r a i n r a t e

E n

b e i n g g i v e n approxima- t e l y by

E~ = B T m exp

-

(FK

+

^{Wm) /kT}

Y

where FK, Wm a r e t h e f o r m a t i o n and m i g r a t i o n e n e r g i e s of n e u t r a l k i n k s , B i s p r o p o r t i o n a l t o t h e mobile d i s l o c a t i o n d e n s i t y a t t h e y i e l d s t r e s s , m i s a c o n s t a n t . I n wet c r y s t a l s , a s E, moves down towards t h e H20 a c c e p t o r l e v e l p o s i t i v e l y charged kink; may c o n t r o l t h e s t r a i n r a t e

and ^{P I}

where EKd i s t h e k i n k donor l e v e l ( s e e F i g . 7) and AWm 1 t h e d i f f e r e n c e i n m i g r a t i o n e n e r g i e s between charged and n e u t r a l k i n k s . E q u a t i o n s

( 6 ) , ( 7 ) a r e c o n s i s t e n t w i t h t h e o b s e r v a t i o n s t h a t a t c 6 n s t a n t s t r a i n r a t e T a exp U/kT, and t h a t U i s a f u n c t i o n of w a t e r c o n t e n t .

Y With r e g a r d t o t h e r e c o v e r y r a t e R , i f we assume t h a t a ) R i s c o n t r o l l e d by climb, b ) t h a t oxygen d i f f u s i o n i s r a t e d e t e r m i n i n g , c ) d i f f u s i o n by p o s i t i v e l y charged a n i o n v a c a n c i e s i s predominant o v e r t t h e r a n g e of B / S i c o n s i d e r e d ,

R a exp

-

(VF

+

Vm)/kT exp (Em

-

EF

-

AVm)/kT

where VF, Vm a r e f o r m a t i o n e n e r g y , and a c t i v a t i o n energy o f m i g r a t i o n o f n e u t r a l a n i o n vacancy, EVd t h e donor l e v e l o f t h e a n i o n vacancy, AVm t h e change i n m i g r a t i o n energy between p o s i t i v e l y charged and neu- t r a l vacancy. A t low t e m p e r a t u r e s r e l a t i v e t o t h e a c c e p t o r l e v e l and l a r g e c o n c e n t r a t i o n s of H20, N H r t h e Fermi l e v e l v a r i e s a s

where EHa i s t h e H 2 0 a c c e p t o r l e v e l , Nv t h e e f f e c t i v e d e n s i t y o f s t a t e s i n t h e v a l e n c e band, i . e . Nv = 2 ( 2 n rnh k ~ / h ~ ) ~ " , where mh i s t h e e f f e c - t i v e mass of a h o l e i n t h e v a l e n c e band, and h P l a n c k ' s c o n s t a n t ( f o r e x p r e s s i o n s f o r EF, N s e e e . g . /17/. From ( 8 ) and ( 9 )

v

N~

*

R cc (-1 exp

-

^(VF

+

Vm

-

EVd + E:

+

Avm)/kT

Ha ⁽¹⁰⁾

Nv

D e f i n i n g a c r i t i c a l t e m p e r a t u r e T s u c h t h a t R = W (workharde-

C

-

1

n i n g r a t e , assumed t e m p e r a t u r e i n d e p e n d e n t ) , g i v e s l o g NH CC TC

,

a s o b s e r v e d a p p r o x i m a t e l y i n t h e e x p e r i m e n t s .

Three f u r t h e r p o i n t s s h o u l d b e n o t e d . ~ i r s t l y , a t 600°C, Nv %

10 l 9

- l o 2 '

~ m - ~ , and f o r H/Si ?. EF ^%

i~~~

^% 1 eV ( s a y ) . The

c o n c e n t r a t i o n o f h o l e s ( s e e /17/) p % (2NH) ''2~:bexp

-

^{EHa/2kT %} 1 0 l ~ c m - ~ . T h i s would c o r r e s p o n d t o i n t r i n s i c germanium a t room t e m p e r a t u r e , i . e . even a t 600°C wet q u a r t z would s t i l l be a r e a s o n a b l y good i n s u l a t o r . Secondly, d e f o r m a t i o n i t s e l f w i l l i n t r o d u c e k i n k l e v e l s , and t h i s w i l l t e n d t o r a i s e t h e Fermi l e v e l and t h e r e f o r e l e a d t o h a r d e n i n g , i . e . t h e w a t e r s o f t e n i n g e f f e c t may be reduced w i t h i n c r e a s i n g s t r a i n . Third- l y , t h e d e f o r m a t i o n i t s e l f may c a u s e a n i o n v a c a n c i e s t o b e produced, and t h i s c a n c a u s e a c c e l e r a t i o n o f t h e r e c o v e r y r a t e .

F i n a l l y , i t s h o u l d b e emphasised t h a t t h i s s e c t i o n i s h i g h l y s p e c u l a t i v e , and o v e r s i m p l i f i e d . The purpose o f i t i s t o show t h a t e l e c t r o n i c e f f e c t s c o u l d i n p r i n c i p l e a c c o u n t f o r t h e o b s e r v e d hydro- l y t i c weakening e f f e c t . T h i s s u g g e s t i o n h a s a l s o been made r e c e n t l y i n d e p e n d e n t l y by F r i e d e l /18/ and by Hobbs /19/; t h e l a t t e r h a s a t - t r i b u t e d t h e e f f e c t t o a c c e l e r a t e d d i f f u s i o n o f oxygen and of (OH) t o

d i s l o c a t i o n s , c a u s i n g the c l i m b r a t e t o i n c r e a s e . Experiments a r e now needed t o e s t a b l i s h t h e e f f e c t o f w a t e r on d i s l o c a t i o n v e l o c i t y and c l i m b r a t e s e p a r a t e l y , t o measure e l e c t r i c a l c o n d u c t i v i t y a s a func- t i o n of H 2 0 c o n t e n t , and t o produce e v i d e n c e on e l e c t r o n i c l e v e l s a s s o c i a t e d w i t h w a t e r i n q u a r t z .

Acknowledgements.- I am g r a t e f u l f o r h e l p f u l d i s c u s s i o n s w i t h and i n - f o r m a t i o n from v a r i o u s c o l l e a g u e s , i n c l u d i n g H. Alexander, J . F r i e d e l , A. George, P. Haasen, B.E. Hobbs, R . J o n e s , R. Labusch, A.C. McLaren, A. Ourmazd, J . R . P a t e l , P. P i r o u z , W . S c h r b t e r .

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( 1 9 7 2 ) , p. 29

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