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MODELS OF THE DISLOCATION STRUCTURE
H. Alexander
To cite this version:
H. Alexander. MODELS OF THE DISLOCATION STRUCTURE. Journal de Physique Colloques,
1979, 40 (C6), pp.C6-1-C6-6. �10.1051/jphyscol:1979601�. �jpa-00219017�
JOURNAL DE PHYSIQUE CoZZoque C6, suppZ6ment au n06, tane 40, j u i n 1979, page C6-1
MODELS 3 F THE DISLOCATION STRUCTURE
H. Alexander
Abt. f. MetalZphysik i r n 11. Phys. I n s t . Univ. KijZn, W-Germany
Resume.- Dn montre que l e s d i s l o c a t i o n s s o n t d i s s o c i e e s non seulement au repos mais a u s s i en mouvement.
En u t i l i s a n t l e s r k s u l t a t s obtenus p a r microscopic G l e c t r o n i q u e , mesures g l e c t r i q u e s e t s p e c t r o s c o ~ i e EPR, il e s t montre que pendant l a d e f o r m a t i o n ~ l a s t i q u e de nombreux d e f a u t s o o n c t u e l s s o n t r e l a c h e s p a r l e s d i s l o c a t i o n s en dessous d ' u n e temoerature c r i t i q u e . Ceci montre q u ' a u moins une o a r t i e des d i s l o c a t i o n s e x i s t e sous forme d ' u n e a s s o c i a t i o n de d i s l o c a t i o n d i s s o c i e e avec une rangee de d e f a u t s p o n c t u e l s . Les e n e r g i e s de f o n t e d'emoilement dans l e germanium (75
+
10 mJ/m2) e t l e s i l i c i u m ( 5 8+
6 mJ/m2) o n t 6 t ea
nouveau determinees.A b s t r a c t . - I t i s demonstrated t h a t d i s l o c a t i o n s n o t m e r e l y a t r e s t b u t d u r i n g t h e i r m o t i o n a r e d i s s o - c i a t e d . Combining r e s u l t s o f e l e c t r o n microscopy, e l e c t r i c measurements and EPR spectroscopy i t i s concluded t h a t d u r i n g p l a s t i c d e f o r m a t i o n below a c r i t i c a l temperature numerous p o i n t d e f e c t s a r e r e l e a s e d by t h e d i s l o c a t i o n s . T h i s i n d i c a t e s t h a t a t l e a s t p a r t o f t h e d i s l o c a t i o n s e x i s t s i n f o r m o f a n . a s s o c i a t i o n o f a s p l i t d i s l o c a t i o n w i t h a l i n e a r row o f p o i n t d e f e c t s . The s t a c k i n g f a u l t e n e r g i e s o f germanium (75 2 10 mJ/m2) and s i l i c o n (58 2 6 mJ/m2) a r e redetermined.
1. I n t r o d u c t i o n . - I n t h e i n i t i a l work on t h e d i s l o c a - t i o n s i n diamond l i k e c r y s t a l s Shockley /1/ and Read / 2 / o u t l i n e d t h e core s t r u c t u r e o f t h e d i s l o c a t i o n s
i n such a way t h a t t h e number o f s e v e r l e y d i s t o r t e d c o v a l e n t ( s p 3 ) bonds became as s m a l l as p o s s i b l e . From t h i s p r i n c i p l e f o l l o w e d t h e e x i s t e n c e of w e l l 1 o c a l i zed u n p a i r e d e l e c t r o n s , so c a l l ed d a n g l i n g bonds i n t h e c o r e o f most d i s l o c a t i o n types, o n l y t h e d i s t a n c e between two d a n g l i n g bonds depending on t h e d i s l o c a t i o n c h a r a c t e r . A second assumption made i n t h e p i o n e e r i n g papers concerned t h e c h o i c e o f t h e g l i d e plane: whereas t h e r e was n e v e r any doubt t h a t t h e g l i d e systems o f those c r y s t a l s a r e o f t h e t y p e (111)
[Oil],
t h e r e remained two p o s s i b i l i t i e s o f s h e a r i n g p a r a l l e l t o (111) planes. F i g u r e 1 shows a p r o j e c t i o n o f t h e s t r u c t u r e on a (110) olane.The s t a c k i n g o r d e r p a r a l l e l t o
[ Z l i l I
i s deduced f r o m t h a t o f t h e face c e n t r e d c u b i c ( f c c ) l a t t i c e A-B-C by d o u b l i n g t h e atoms i n t h e u n i t c e l l : A-a3- bC-cA-.. .
We may t h e r e f o r e shear one art o f t h e c r y s - t a l a g a i n s t t h e o t h e r e i t h e r between w i d e l y spaced planes (e.g. A and a ) o r between n a r r o w l y spaced ones (a and B ) . F o r a l o n g t i m e p e o p l e f o l l o w e d Shockley assuming t h a t t h e a c t u a l g l i d e p l a n e s s h o u l d be p l a - ced between w i d e l y spaced p l a n e s f o r two reasons : f i r s t l y t h e number o f c o v a l e n t bonds t o be broken i s t h r e e t i m e s s m a l l e r i n t h i s case and secondly t h e g l i d e p l a n e s a r e commonly t h e most d i s t a n t planes i n a s t r u c t u r e . These arguments l e a d t o an i d e a o f t h e d i s l o c a t i o n s i n t h e diamond s t r u c t u r e which was used i n t h e f o l l o w i n g y e a r s i n d i s c u s s i o n o f e l e c t r i c a l and magnetic p r o p e r t i e s o f d i s l o c a t i o n s i n semicon- d u c t o r s . The i n t e r p r e t a t i o n o f t h e r e s u l t s o f many c a r e f u l e x p e r i m e n t s i n these f i e l d s t u r n e d o u t t o be- - A
n o t c l e a r - c u t . I t s h o u l d be n o t e d t h a t H o r n s t r a / 3 / C i n 1958 i n an i m p o r t a n t paoer d i s c u s s e d a w i d e r va-c
r i e t y o f d i s l o c a t i o n s t r u c t u r e s which a p ~ e a r e d t o beb
c o n c e i v a b l e i n t h e diamond s t r u c t u r e . B u t w h i l e anI B
experime'ntal d e c i s i o n between t h e v a r i o u s p o s s i b i l i -5" a
t i e s was l a c k i n g t h e s i m p l e d a n g l i n g bond model pre-v a i l e d . I t was t h e i n t r o d u c t i o n o f weak beam e l e c t r o n microscopy /4/ w h i c h p u t t h e t r e a t m e n t o f t h e s i n g l e d i s l o c a t i o n i n c o v a l e n t semiconductors on a more r e - l i a b l e base o f knowledge. S i n c e t h a t t i m e t h e number F i g . 1 : P r o j e c t i o n o f t h e diamond StrLJCture on a of researchers w o r k i n g i n t h i s f i e l d markedly i n - (110) plane.
creased and now t h e t i m e m i g h t be a p p r o p r i a t e t o com- p a r e and t o d i s c u s s t h e v a r i o u s approaches.The s i t u a -
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979601
C6-2 JOURNAL DE PHYSIQUE
t i o n seems t o be more c o m p l i c a t e d t h a n even H o r n s t r a ' s a s u b s t i t u t i n g bond n o r m a l l y a r e s p i n p a i r e d and occu- model suggested. I f e e l one p o s s i b l e reason f o r t h i s py energy l e v e l s above t h e v a l e n c e band.
c o u l d be an i n t i m a t e i n t e r c o r r e l a t i o n between d i s l o - c a t i o n s and p o i n t d e f e c t s which i s j u s t coming i n t o c o n s i d e r a t i o n .
2. D i s l o c a t i o n s a r e d i s s o c i a t e d i n t o p a r t i a l s . - From e l e c t r o n microscopy u s i n g veak bean c o n t r a s t s i n c e 1970 came t h e d e f i n i t e v e r i f i c a t i o n o f f o r m e r f i n - d i n g s /5-7/ t h a t by f a r most o f t h e d i s l o c a t i o n s i n s i l i c o n /8/, germanium /9/ and 1 1 1 - V compounds
/ l o /
a r e s p l i t i n t o two Shockley p a r t i a l s :
The n a t u r e o f t h e s t a c k i n g f a u l t r i b b o n i n most d i s -
F i g . 2 : B a l l and w i r e model o f a s p l i t ( a 8 ) 60' l o c a t i o n s produced b y g l i d e p r o v e d t o be i n t r i n s i c . ( ') d i s l o c a t i o n .
The d o u b l i n g o f { I l l ) p l a n e s w h i c h c o n v e r t s t h e f c c s t r u c t u r e i n t o t h e diamond s t r u c t u r e (A -+A-a) must be p r e s e r v e d i f t h e t e t r a h e d r a l c o o r d i n a t i o n s h o u l d b e r e t a i n e d i n t h e s t a c k i n g f a u l t s . T h a t means : a s t a c k i n g f a u l t o f a reasonable energy i s p o s s i b l e o n l y between narrow (111) p l a n e s (aB). F o r t h a t rea- son t h o s e d i s l o c a t i o n s which were t h o u g h t t o be more m o b i l e cannot d i s s o c i a t e i n a t r u e sense.
F i g u r e 2 shows a " b a l l and w i r e " model o f a 60"
d i s l o c a t i o n o f a0 t y o e . The ,30°- and t h e e d g e - o a r t i a l a r e t o b e seen a t t h e l e f t and a t t h e r i g h t s i d e o f t h e s t a c k i n g f a u l t r i b b o n , r e s p e c t i b e l y . Such a model p r e s e n t s n o t more t h a n t h e t o p o l o g i c a l s i t u a t i o n a f t e r t h e shear displacement. I n t h e c o r e s o f t h e p a r t i a l d i s l o c a t i o n s one f i n d s ~ e r i o d i c rows o f atoms t h e neighbourhood o f which i s no more t e t r a h e d r a l . T h i s f a c t r e s u l t s a t f i r s t i n a number o f d a n g l i n g bonds. I t i s one o f t h e most i m p o r t a n t aims of theo- r y and experiment t o c l a r i f y how t h o s e t o p o l o g i c a l d a n g l i n g bonds m i n i m i z e t h e i r energy. From t h e
E P R
s p e c t r a o f deformed s i l i c o n c r y s t a l s we conclude t h a t i n many cases where two atoms w i t h d a n g l i n g bonds s t a y o p p o s i t e each o t h e r a c o v a l e n t bond can be f o r - med, t h e l e n g t h and o r i e n t a t i o n o f which d i f f e r f r o m t h e t e t r a h e d r a l s t r u c t u r e . Those s t r e t c h e d and miso- r i e n t e d bonds w i l l be c a l l e d s u b s t i t u t i n g bonds i n t h e f o l l o w i n g . They a r e known t o e x i s t i n r a d i a t i o n d e f e c t s i n s i l i c o n and were i n s e r t e d by H o r n s t r a /3/
i n many o f h i s drawings. The two e l e c t r o n s f o r m i n g
Tl Some e x c e p t i - o K w e r e f o u n d /11-13/. l h e r e a r e i n - d i i a t i o n s t h a t t h e t r a n s i t i o n f r o m t h e i n t r i n s i c d i s -
I n t h e c o r e o f t h e 90" o a r t i a l d i s l o c a t i o n two rows o f broken bonds s t a n d o o p o s i t e t o each o t h e r l i k e two combs; t h e y p r o b a b l y g i v e r i s e t o a l i n e a r c h a i n o f s u b s t i t u t i n g bonds which a r e d i r e c t e d p a r a l - l e l t o a <110> d i r e c t i o n . I n t h e c o r e o f t h e 30" p a r - t i a l d i s l o c a t i o n t h e s h e a r displacement o f atom @ produces a p l a n a r arrangement around t h e atom y w h i c h has some s i m i l a r i t y w i t h a " m o l e c u l e " bound by sp2 h y b r i d bonds. As t h e f o u r atoms 13-6 b r i n g i n 7 valen- ce e l e c t r o n s one o f t h e s e s h o u l d occupy t h e p Z o r b i - t a l o r t h o g o n a l t o t h e spZ p l a n e ( i . e . p a r a l l e l t o t h e d i s l o c a t i o n l i n e ) . The d i s t a n c e between two h a l f f i l - l e d p Z o r b i t a l s b e i n g o f t h e o r d e r o f 0.4nrn s e v e r a l p o s s i b i l i t i e s o f e l e c t r o n i c rearrangement e x i s t : 1 ) t h e y atoms may be p a i r w i s e l i n k e d b y a s u b s t i t u -
t i n g c o v a l e n t bond;
2) t h e u n p a i r e d e l e c t r o n s may be more o r l e s s deloca- l i z e d , i . e . form a one dimensional h a l f f i l l e d band o f a c e r t a i n w i d t h ,
3) t h o s e e l e c t r o n s f i n a l l y may f o r m t r u e l o c a l i z e d d a n g l i n g bonds t h e s p i n s o f which e v e n t u a l l y may be coupled b y d i r e c t o r i n d i r e c t exchange and d i p o l e - d i p o l e i n t e r a c t i o n .
The screw d i s l o c a t i o n d i s s o c i a t e s i n t o two 30°
p a r t i a l d i s l o c a t i o n s ( F i g . 3 ) . There a r e s t r o n g i n d i - c a t i o n s t h a t
EPR
s o e c t r o s c o p y g i v e s i n f o r m a t i o n j u s t about e l e c t r o n s i n t h e c o r e of t h e s e d i s l o c a t i o n s : Very r e c e n t l y E. Weber i n o u r g r o u p succeded by accu- m u l a t i o n o f s p e c t r a t o f i n d t h e h y p e r f i n e s t r u c t u r e o f t h e S =-
1 l i n e s i n t h e c e n t r a l p a r t o f t h eEPR-
s o c i a t i o n t o t h e e x t r i n s i c one i s h i n d e r e d b y a f r e e spectrum o f d i s l o c a t i o n s in s i l i c o n /14/. ~t turned energy b a r r i e r which needs t h e r m a l a c t i v a t i o n t o be
overcome. So t h e predominance o f i n t r i n s i c s p l i t t i n g o u t , t h a t t h e two l i n e s b e l o n g i n g t o each a c t i v e i s n o t n e c e s s e r a l y due t o a d i f f e r e n c e of t h e ener- g l i d e system /15/ a r e due t o electrons of m a i n l y p- g i e s o f i n t r i n s i c and e x t r i n s i c s t a c k i n g f a u l t s , r e s -
p e c t i v e l y . I w i l l r e s t r i c t myself h e r e t~ i n t r i n s i c c h a r a c t e r w i t h t h e i r o r b i t a l s o r t h o g o n a l t o t h e p r i - d i s s o c i a t i o n s . mary ( P ) and t o t h e c r o s s g l i d e ( Q ) p l a n e , r e s p e c t i -
C6-3 H. Alexander
v e l y , of t h e d i s l o c a t i o n s . T h i s symmetry shows, i n t i o n s b e i n g n o t p a r a l l e l t o a <110> d i r e c t i o n gene- o u r view, t h a t t h e u n p a i r e d e l e c t r o n s causing t h i s r a l l y shows t h e occurence o f t h e same t o p o l o g i c a l p a r t o f t h e spectrum a r e l o c a l i z e d i n t h e screw d i s - elements as found i n t h e 30" and 90" p a r t i a l s , r e s - l o c a t i o n s , i . e . i n t h e core o f 30" p a r t i a l s . p e c t i v e l y . So we may r e s t r i c t o u r d i s c u s s i o n t o t h e
screw and 60' d i s l o c a t i o n .
3. D i s l o c a t i o n s a r e s p l i t d u r i n g t h e i r motion.- As t h e m o t i o n o f a aB d i s l o c a t i o n ( d i s s o c i a t e d o r n o t ) needs b r e a k i n g o f t h r e e t i m e s as much c o v a l e n t bonds t h a n does a A-a d i s l o c a t i o n i t was d i s c u s s e d f o r some t i m e t h e c a r r i e r s o f p l a s t i c d e f o r m a t i o n c o u l d be A-a d i s l o c a t i o n s which produce a s t a c k i n g f a u l t r i b b o n on t h e n e i g h b o u r i n g aB o l a n e as soon and as l o n g as t h e y come t o r e s t /18/. T h i s r i b b o n s h o u l d be bounded by two p a r t i a l d i s l o c a t i o n s w i t h o p p o s i t e Burgers
~ 3 i : B a l l and ~ . model of a s p l i t ( a ~ ) screw Vectors. The conceot o f such an a s s o c i a t i o n o f a p e r - d i i l o c a t i o n
P : normal on t h e p r i m a r y g l i d e p l a n e Q : normal on t h e c r o s s g l i d e p l a n e
The r e m a i n i n g l i n e s o f t h e spectrum f o r m a f i n e s t r u c - t u r e w i t h i t s symmetry a x i s p a r a l l e l t o t h e B u r g e r s v e c t o r /16,17/. T h i s p o i n t s t o c h a i n s o f u n p a i r e d b u t i n t e r a c t i n g s p i n s p a r a l l e l t o $, i . e . a g a i n t h e screw d i s l o c a t i o n s . Both s p e c t r a i n c r e a s e when t h e d e f o r m a t i o n i n made under a h i g h s t r e s s , e n l a r g i n g t h e f r a c t i o n o f screw d i s l o c a t i o n s f r o m a few p e r c e n t t o about one t h i r d . From t h e s e f i n d i n g s we t e n t a t i v e - l y conclude t h a t t r u e d a n g l i n g bonds e x i s t o n l y i n t h e screw d i s l o c a t i o n which h i t h e r t o was b e l i e v e d t o be t h e o n l y d i s l o c a t i o n t y p e w i t h o u t d a n g l i n g bonds
f e c t A-a d i s l o c a t i o n
D
w i t h a s t a c k i n g f a u l t was con- s i d e r e d a l r e a d y by H o r n s t r a /3/ and c a l l e d by him" d i s s o c i a t i o n o f t h e (A-a) d i s l o c a t i o n " l o n g b e f o r e any e x p e r i m e n t a l evidence o f s t a c k i n g f a u l t s connec- t e d w i t h d i s l o c a t i o n s . As t h e d r i v i n g f o r c e f o r t h e f o r m a t i o n o f t h e s t a c k i n g f a u l t r i b b o n s h o u l d b e t h e r e l a x a t i o n o f t h e s t r e s s f i e l d n e a r t h e c o r e o f t h e d i s l o c a t i o n D t h e sum o f t h e Burgers v e c t o r s o f D and o f t h e p a r t i a l bounding t h e s t a c k i n g f a u l t on t h e s i d e o f D must equal t h e Burgers v e c t o r o f t h e Shockley p a r t i a l l o c a t e d a t t h e same s i d e i n t h e case o f s p l i t t i n g o f a aB d i s l o c a t i o n :
t Cli7-J
s t a c k i n g f a u l t; Ci121
( 2 )/3/. The number o f u n p a i r e d s p i n s may be determined
D: + Loll1
f r o m o u r s p e c t r a n o t v e r y e x a c t l y . I t amounts t o c i r - ca 10 % o f t h e y s i t e s ( F i g . 3) i n screw d i s l o c a t i o n s . From t h i s we conclude t h a t p i e c e s o f 30" p a r t i a l s o u t o f screw d i s l o c a t i o n s e x i s t i n a t l e a s t t h r e e d i f f e r e n t s t a t e s : a) t h o s e c o n t a i n i n q s i n q l e s p i n s , b ) segments w i t h two t o f i v e coupled s p i n s , and f i - n a l l y c ) p i e c e s which have no d a n g l i n g bonds. Tran- s i t i o n may be induced f r o m a ) and b ) t o c ) b y annea- l i n g above 750" C ( i r r e v e r s i b l y ) (R.Erdmann unpubl.) There remain s e v e r a l problems t o be solved. Two o f them I w i l l m e n t i o n : 1 ) S p l i t 60" d i s l o c a t i o n s c o n t a i n 30" p a r t i a l s t o o ( F i g . 2 ) . They seem t o be f r e e o f d a n g l i n g bonds. 2) The o r i e n t a t i o n o f t h e pz- o r b i t a l s i n t h e c o r e o f t h e screw d i s l o c a t i o n marks two o u t o f t h r e e bond d i r e c t i o n s i n t h e "sp2 molecu- le'. A f u t u r e LCAO
NO
t r e a t m e n t s h o u l d show i f t h i s i s due t o t h e a s s y m e t r i e s u r r o u n d i n g of t h e "molecu- l e " o r i f h a l f o f t h e EPR a c t i v e screw segments a r e s p l i t on t h e c r o s s g l i d e p l a n e , which i s d i f f i c u l t t o be1 i e v e .C o n s t r u c t i n g b a l l and w i r e models o f d i s l o c a -
sum :
%
[ I 1 2 1 1The r e s u l t i n g s t r a i n f i e l d o f t h e two d i s l o c a - t i o n s on t h e one s i d e o f t h e s t a c k i n g f a u l t i s t h e r e - f o r e always p r a c t i c a l l y t h e same as t h a t o f t h e cor- r e s p o n d i n g o a r t i a l o f a s p l i t (aB) d i s l o c a t i o n . T h i s i s why i t i s i m p o s s i b l e a t p r e s e n t t o decide between t h e two s t r u c t u r e s b y means o f t h e e l e c t r o n microsco- pe.
D u r i n g t h e l a s t y e a r s s e v e r a l s t u d i e s were made, however, which i n d i c a t e t h a t t h e s t a c k i n g f a u l t connected w i t h t h e d i s l o c a t i o n does n o t c o l l a p s e when t h e d i s l o c a t i o n i s moving /19-21/. V e i n g a s t /19/ s h o t a f i l m o f p a r t i a l d i s l o c a t i o n s i n a t h i n f o i l o f g e r - manium moving f o r w a r d s and backwards. Roehl ( t o be p u b l . ) by c o n t r a s t computation v e r i f i e d t h a t Shockley s p l i t t i n g was under c o n s i d e r a t i o n . S i m i l a r observa- t i o n s a r e r e p o r t e d b y Sato and Sumino /21/. The s t a - tement t h a t d i s l o c a t i o n s move i n t h e d i s s o c i a t e d f o r m does n o t mean, o f course, t h a t t h e d i s s o c i a t i o n w i d t h d s h o u l d b e independent o f t h e s t a t e o f motion.
C6-4 JOURNAL DE PHYSIQUE
Wessel and Alexander /13/ i n v e s t i g a t e d d i s l o c a t i o n s i n s i l i c o n which were f r o z e n i n under r a t h e r h i g h s t r e s s e s (150-350 *), N i.e. i n t h e s t a t e o f (slow) motion. They f o u n d a1 1 d i s l o c a t i o n s para1 l e l t o
<110> d i r e c t i o n s ( P e i e r l s v a l l e y s ) and w i t h o u t any c o n s t r i c t e d p o i n t s o r segments. The measured v a l u e s o f d were n o t i n agreement w i t h t h o s e c a l c u l a t e d me- r e l y from t h e forces w o r k i n g on t h e i n d i v i d u a l p a r - t i a l s . The r e s u l t s l e d t o t h e c o n c l u s i o n t h a t t h e l a t t i c e f r i c t i o n depends on t h e c h a r a c t e r o f t h e p a r t i a l s and on i t s p o s i t i o n b e f o r e o r b e h i n d t h e s t a c k i n g f a u l t . G o t t s c h a l k w i l l r e p o r t on new r e s u l t s l a t e r on i n t h i s conference. A s p e c i a l f e a t u r e obser- ved a t h i g h s t r e s s i s t h e f o r m a t i o n o f so c a l l e d
"noses" ; these a r e s i t e s where t h e two p a r t i a l s are c o l n p l e t e l y separated. I n o u r c o n t e x t i t seems worth- w h i l e t o n o t e t h a t always t h e t r a i l i n q p a r t i a l (which f o l l o w s t h e s t a c k i n g f a u l t ) i s r i g o r o u s l y bound t o
<110> d i r e c t i o n s whereas t h e l e a d i n g one i s n o t /13/
( F i g . 4 ) .
F i g . 4 : S i l i c o n . Two noses i n a d i s l o c a t i o n f r o z e n i n under h i g h s t r e s s
(T = 3 5 0 - , mmz N Tdef = 420" C)
1.2 : l e a d i n g and t r a i l i n g p a r t i a l d i s l o c a t i o n , res- p e c t i v e l y .
So t h e r e must be a p r i n c i p a l d i f f e r e n c e between t h e t r a i l i n g and t h e l e a d i n g p a r t i a l even i n t h e case o f two 30" p a r t i a l s f o r m i n g a screw d i s l o c a t i o n .
Knowing t h a t t h e m o t i o n o f a d i s l o c a t i o n i n S i and Ge does n o t need a c o l l a p s e o f t h e s t a c k i n g f a u l t , t h e o r i g i n a l reason f o r t h i n k i n g about t h e associa- t i o n ceased. B u t t h e r e a r e s e v e r a l o t h e r experimen- t a l r e s u l t s which seem t o be e a s i e r t o understand i f one assumes t h a t p a r t o f t h e d i s l o c a t i o n s m i g h t e x i s t n o t siimply as d i s s o c i a t e d aB d i s l o c a t i o n b u t as an a s s o c i a t i o n . B e f o r e d i s c u s s i n g t h e s e o b s e r v a t i o n s I
s h o u l d l i k e t o extend somewhat t h e concept o f t h e a s s o c i a t i o n , H i r t h and L o t h e /22/ p r o b a b l y were t h e f i r s t t o ~ o i n t o u t t h a t t h e a s s o c i a t i o n of a 60' (A-a) d i s l o c a t i o n w i t h a s t a c k i n g f a u l t r i b b o n ( c a l l e d
" s h u f f l e s e t " d i s l o c a t i o n by t h e a u t h o r s ) can be i n - t e r p r e t e d as a normal d i s s o c i a t e d (aB) d i s l o c a t i o n
( " g l i d e s e t " d i s l o c a t i o n i n /22/)which has absorbed a l i n e a r c h a i n o f p o i n t d e f e c t s i n t h e c o r e o f one o f i t s p a r t i a l s . T h i s row of vacancies ( o r i n t e r s t i - t i a l s) may f o r m a l l y be r e p r e s e n t e d b y a v e r t i c a l d i p o l e
('1
o f 60' d i s l o c a t i o n s i$
c O l l > :The r e s u l t s i s t h e same as i n process ( 2 ) b u t t h e i n t e r p r e t a t i o n i s d i f f e r e n t : the c a r r i e r s o f g l i d e now a r e s p l i t (aB) d i s l o c a t i o n s which may o r may n o t i n t r o d u c e i n t o one of t h e i r p a r t i a l s p o i n t d e f e c t s i n a c o r r e l a t e d manner ( 3 )
Depending on t h e Burgers v e c t o r o f t h e v e r t i - c a l d i p o l e t h e d e n s i t y o f p o i n t d e f e c t s may be varied i n c e r t a i n l i m i t s . E s p e c i a l l y t h e s p l i t screw d i s l o - c a t i o n may absorb p o i n t d e f e c t s too, which f o r m a 60" d i ~ o l e .
The t r a n s i t i o n f r o m a s p l i t (aB) d i s l o c a t i o n i n t o an a s s o c i a t i o n i s now r e c o g n i z e d as an elemen- t a r y s t e p o f c l i m b . I t may t a k e p l a c e (weakly c o r r e - l a t e d ) a l o n g l i m i t e d p i e c e s o f a d i s l o c a t i o n by t h e movement o f a h a l f j o g a l o n g t h e d i s l o c a t i o n p i e c e .
D u r i n g t h e l a s t few y e a r s many r e s u l t s were
~ u b l i s h e d which i n d i c a t e t h a t a remarkable d e n s i t y o f p o i n t d e f e c t s ( c l u s t e r s ) i s produced by p l a s t i c d e f o r m a t i o n i n s i l i c o n /24,25/ and germanium /26/.
The c o n c e n t r a t i o n o f EPR a c t i v e p o i n t d e f e c t c e n t r e s i s p r o p o r t i o n a l t o t h e shear s t r a i n a f t e r deforma- t i o n a t 650" C and e x h i b i t s a complex dependence on
-
t 2 1
I n v e r t i n g t h e d i p o l e+
a <011> r e s u l t s i n a row o f i n t e r s t i t i a l s i n s t e a 2 o f vacancies.( 3 ) The m o t i o n o f such an a s s o c i a t i o n o f a s p l i t (aB) d i s l o c a t i o n w i t h a row o f p o i n t d e f e c t s i s known as s h u f f l i n g / 2 2 / . O b v i o u s l y t h i s s p e c i a l k i n d o f a zonal d i s l o c a t i o n moves w i t h o u t d i f f i c u l t i e s from a g e o m e t r i c a l p o i n t o f view /23/, b u t t h e t r a n s p o r t o f t h e c o r e r e g i o n o f m o d i f i e d d e n s i - t y i s e q u i v a l e n t w i t h a component o f d i f f u s i o n .
H. Alexander C6-5
t h e d e f o r m a t i o n temperature and shear s t r a i n r a t e (Erdmann u n p u b l . ) . The number o f d i s l o c a t i o n c u t t i n g processes seems t o p l a y no r 8 1 e /24/. T a k i n g a l l t h e s e o b s e r v a t i o n s t o g e t h e r we conclude t h a t d i s l o c a - t i o n s may l o o s e p o i n t d e f e c t s d u r i n g t h e i r motion.
T h i s can be imaged more e a s i l y i f one assumes t h a t a t l e a s t p a r t o f t h e d i s l o c a t i o n s e x i s t i n t h e f o r m o f an a s s o c i a t i o n . The process o f t r a n s i t i o n o f d i s - l o c a t i o n segments between t h e s t a t e s ( s p l i t aB d i s - l o c a t i o n and a s s o c i a t i o n , r e s p e c t i v e 1 y ) may t h e n work as a source o f p o i n t d e f e c t s i n t h e f o l l o w i n g way : p o s s i b l y r e s t i n g aB d i s l o c a t i o n s t u r n i n t o associa- t i o n s p r o d u c i n g t h e c o r r e s p o n d i n g number o f p a i r s o f p o i n t d e f e c t s b y l o w e r i n g t h e i r s t r e s s energy. The assumption seems reasonable t h a t t h o s e a s s o c i a t i o n s have a l o w e r m o b i l i t y t h a n p u r e aB d i s l o c a t i o n s . So below a c r i t i c a l temperature a shear s t r e s s o f s u f f i - c i e n t magnitude may s e p a r a t e t h e d i s l o c a t i o n f r o m i t s p o i n t d e f e c t s , r e s t o r i n g i t s f u l l s t r e s s f i e l d . T h i s process may r e p e a t when t h e d i s l o c a t i o n comes t o r e s t again. A t h e o r y of t h e m o b i l i t y o f such d i s - l o c a t i o n s has t o t a k e i n t o account t h e t e m p e r a t u r e and s t r e s s dependence o f t h e b i n d i n g f o r c e between p o i n t d e f e c t s and d i s l o c a t i o n s . O b s e r v a t i o n s concer- n i n g t h e dependence o f t h e e l e c t r i c a l /26,27/ p r o p e r - t i e s o f d i s l o c a t i o n s on t h e d e f o r m a t i o n temperature p o i n t t o t h e f a c t t h a t t h e mentioned c r i t i c a l tempe- r a t u r e i s about 400' C i n Ge.
T a b l e I : Veasurements o f t h e energy
Another i n t e r e s t i n g argument f o r t h e p r e v a i l i n g o f a s s o c i a t i o n s i s p u t f o r w a r d by H o l t ( t o be o u b l . ) . He r e i n t e r p r e t s r e s u l t s ' o f B e l l and coworkers /28/.
These a u t h o r s i n v e s t i g a t e d t h e p o l a r i t y o f edge t y p e d i s l o c a t i o n s i n InSb c r y s t a l s b e n t i n o p p o s i t e d i r e c - t i o n s . They concluded (1965) t h a t t h e p o l a r i t y was i n agreement w i t h t h a t t o be expected when (A-a) d i s - l o c a t i o n s produced t h e bending. Now, as we know t h a t d i s l o c a t i o n s a r e s p l i t i n InSb t o o
/ l o /
t h i s argument p o i n t s t o a s s o c i a t i o n s , because t h e most d i s t o r t e d s i t e s i n t h e c o r e o f s p l i t aB d i s l o c a t i o n s a r e occu- p i e d by I n i o n s when t h e d a n g l i n g bond i o n s i n A-a d i s l o c a t i o n s a r e Sb and v i c e versa. (comp. F i g . 2 ) .I n c o n c l u s i o n I want t o r e p o r t on a new d e t e r - m i n a t i o n o f t h e s t a c k i n g f a u l t e n e r g i e s o f Ge and S i w h i c h t u r n e d o u t t o be necessary because t h e values accepted h i t h e r t o (yGe = 60
+
8 mJ/m2 and ySi = 5 1+
5 mJ/m2 / 8 / ) r e s u l t e d i n a b s u r d r a t i o s a o f mo- b i l i t i e s o f t h e p a r t i a l d i s l o c a t i o n s i n germanium( E p p e n s t e i n unpubl
.
) and doped s i l ic o n (Wendler un- pub1 . ) . Table I g i v e s t h e v a l u e s f o r y p u b l i s h e d so f a r . There i s a s t r i k i n g tendency t o i n c r e a s i n g values w i t h t i m e and a remarkable s c a t t e r i n each determina- t i o n i t s e l f . We e v a l u a t e y(Ge) = 75+
10 mJ/mZ, y ( S i ) = 58 i 6 mJ/m2 /29/). I f e e l t h e r e i s no d o u b t t h a t y(Ge) i s l a r g e r t h a n y ( S i ) . The e v a l u a t i o n o f a t u r n e d o u t t o be a s e n s i b l e t e s t f o r t h e s t a c k i n g f a u l t energy w h i c h was used.o f i n t r i n s i c s t a c k i n g f a u l t s
-
1) Germanium
Type o f D i s s o c i a t i o n S t a c k i n g f a u l t Ref. Remarks d i s l o c a t i o n w i d t h d(nm) energy y (F) mJ
Edge 5.4 k 1.1 (63
+
13)" /9/Edge-60" 60 t 8 / 30/
Screw
I
EdgeI
600 3.0 t 0.3 100 k 10 /32/ L a t t i c eimage
I
Screw
Edge-60'
/33/ p?;lec:;:s e r i m e n t s
75
+
10 t h i swork
2) S i l i c o n
Edge-60' 5 1
+
5 / 8/Edge-screw 58 + 6 t h i s
work x o u r e v a l u a t i o n
C6-6 JOURNAL DE PHYSIQUE
Acknowledgment. The a u t h o r wants t o thank h i s cowor- /29/ G o t t s c h a l k , H,.
,
J. Physique C o l l o q . 40 (1979) k e r s , e s p e c i a l 1 y Dr. H. G o t t s c h a l k and Dr. E. Weber t h i s i s s u e .f o r many f r u i t f u l d i s c u s s i o n s . D i p l . Phys. R. /30/ Ray, I.L.F. and Cockayne, D. J.H., J. Microsc.
98 (1973) 170.
Erdmann made u n p u b l i s h e d r e s u l t s a v a i l a b l e . -
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35
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