RECENT RESULTS ON THE STRUCTURE OF DISLOCATIONS IN TETRAHEDRALLY COORDINATED SEMICONDUCTORS

HAL Id: jpa-00219022

https://hal.archives-ouvertes.fr/jpa-00219022

Submitted on 1 Jan 1979

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

RECENT RESULTS ON THE STRUCTURE OF DISLOCATIONS IN TETRAHEDRALLY

COORDINATED SEMICONDUCTORS

P. Hirsch

To cite this version:

P. Hirsch. RECENT RESULTS ON THE STRUCTURE OF DISLOCATIONS IN TETRAHE-

DRALLY COORDINATED SEMICONDUCTORS. Journal de Physique Colloques, 1979, 40 (C6),

pp.C6-27-C6-32. �10.1051/jphyscol:1979606�. �jpa-00219022�

JOURNAL DE PHYSIQUE Colloque C6, suppZ6ment au n06, tome 40, j u i n 1979, page C6-27

RECENT RESULTS ON THE STRUCTURE OF DISLOCATIONS IN TETRAHEDRALLY COORDINATED SEMICONDUCTORS

P.B. H i r s c h

Department of ~ 4 e t a l l u r g y and Science of Materials, U n i v e r s i t y of Oxford, Parks Road, Oxford, U.K.

Resume.- Cet a r t i c l e d e c r i t : a ) des modeles s t r u c t u r a u x de d i s l o c a t i o n s d i s s o c i 6 e s dans l e u r p l a n de g l i s s e m e n t dans l e s semiconducteurs 5 c o o r d i n a t i o n t e t r a h e d r i q u e , e t c o r r e l e ces s t r u c t u r e s avec l e s p r o p r i @ t @ s e l e c t r i q u e s

-

b ) un mecanisme de montee p o u r l a t r a n s f o r m a t i o n d ' u n d e f a u t d'empilement i n t r i n s e q u e dans une d i s l o c a t i o n d i s s o c i e e , en un d e f a u t d'empilement e x t r i n s e q u e

-

c ) l e s s i t u a t i o n s 00 l e s i n t e r a c t i o n s coulombiennes e n t r e p a r t i e l l e s d e v i e n n e n t i m p o r t a n t e s

-

d ) des r e s u l t a t s r e c e n t s s u r l a d i s s o c i a t i o n des d i s l o c a t i o n s dans GaAs.

A b s t r a c t . - T h i s paper d e s c r i b e s : a ) s t r u c t u r a l models o f d i s l o c a t i o n s d i s s o c i a t e d on g l i d e p l a n e s i n t e t r a h e d r a l l y c o o r d i n a t e d semiconductors, and c o r r e l a t e s t h e s e s t r u c t u r e s w i t h e l e c t r i c a l p r o p e r - t i e s - b) a c l i m b mechanism f o r t h e t r a n s f o r m a t i o n o f t h e i n t r i n s i c s t a c k i n g f a u l t bounded by p a r t i a l d i s l o c a t i o n s i n a d i s s o c i a t e d d i s l o c a t i o n , i n t o an e x t r i n s i c s t a c k i n g f a u l t

-

c ) t h e c o n d i t i o n s under which Coulomb f o r c e s between p a r t i a l s may be i m p o r t a n t

-

d) r e c e n t r e s u l t s on t h e d i s s o c i a t i o n o f d i s l o c a t i o n s i n GaAs.

1. I n t r o d u c t i o n . - S i n c e t h e development o f t h e weak beam t e c h n i q u e o f e l e c t r o n m i c r o s c o p y /I/, i t has been e s t a b l i s h e d w i t h o u t a m b i g u i t y t h a t t h e d i s l o c a - t i o n s i n S i and Ge, deformed under normal c o n d i 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 o v e r most o f t h e i r l e n g t h s /2-5/, a l t h o u g h some c o n s t r i c t e d segments have a l s o been observed. S i m i l a r l y , d i s l o c a t i o n s i n 111-V compounds have been shown t o be d i s s o c i a t e d /6-9/. Furthermore, " i n s i t u " experiments i n t h e e l e c t r o n microscope have shown g l i d e o f p a r t i a l d i s - l o c a t i o n s i n Ge

/ l o / ,

and o f d i s s o c i a t e d d i s l o c a - t i o n s i n Ge and S i w i t h o u t p r i o r c o n s t r i c t i o n /11/.

I t appears t h e r e f o r e t h a t e x p e r i m e n t a l d a t a on p h y s i c a l p r o p e r t i e s o f d i s l o c a t e d semiconductor c r y s t a l s s h o u l d be i n t e r p r e t e d i n terms o f d i s s o c i a - t e d d i s l o c a t i o n s and t h a t band s t r u c t u r e c a l c u l a - t i o n s s h o u l d be performed on models o f such c o n f i g u - r a t i o n s .

I n t h i s paper we a ) d e s c r i b e some s t r u c t u r a l models o f d i s l o c a t i o n s d i s s o c i a t e d on t h e g l i d e p l a n e s ( t h e s i m p l e s t t y p e o f d i s s o c i a t e d d i s l o c a - t i o n s

-

t h e d i s s o c i a t e d s h u f f l e d i s l o c a t i o n s i n t r o - duced by H o r n s t r a /12/ and Haasen and Seeger /13/

w i l l n o t be discussed)

-

b) a t t e m p t t o c o r r e l a t e s t r u c t u r e w i t h e l e c t r i c a l p r o p e r t i e s

-

c ) d i s c u s s t h e n a t u r e and o r i g i n o f e x t r i n s i c a l l y d i s s o c i a t e d and anomalously wide d i s l o c a t i o n s w i t h screw compo- n e n t s

-

d ) examine t h e c o n d i t i o n s under which Cou- lomb f o r c e s between p a r t i a l s may become i m p o r t a n t

-

e ) r e p o r t on r e c e n t r e s u l t s on t h e d i s s o c i a t i o n o f d i s l o c a t i o n s i n GaAs.

2. S t r u c t u r e o f d i s l o c a t i o n s . - 2.1. @"_dslolaI t & m s . - B a l l and spokes models have been c o n s t r u c t e d o f d i s l o c a t i o n s o f v a r i o u s o r i e n t a t i o n s . F i g u r e 1 shows t h e Thompson t e t r a h e d r o n used f o r t h e d i s l o c a - t i o n on 6 examined; D i s below t h e p l a n e o f t h e paper.

F i g . 1 : Thompson t e t r a h e d r o n and e s s e n t i a l f e a t u r e s o f t h e c o r e s t r u c t u r e s o f t h e 90' (C6) and 30' ( 6 6 ) p a r t i a l s o f a d i s s o c i a t e d 60' d i s l o c a t i o n (CB). E l 1 and open c i r c l e s r e f e r t o atoms on d i f f e r e n t , n e i g h - b o u r i n g (111) p l a n e s . D i s below t h e p l a n e o f t h e paper.

The s t r u c t u r e s o f t h e c o r e s o f t h e 30'

( E )

^{and 90'}

( C 8 ) a r e a l s o shown. The d o t s a ~ d open c i r c l e s r e - p r e s e n t atoms on t h e two n e i g h b o u r i n g c l o s e l y spaced (111) p l a n e s between which g l i d e t a k e s p l a c e and s t a c k i n g f a u l t s a r e formed. The approximate d i r e c - t i o n s o f t h e d a n g l i n g bonds, which f o r p a r t i a l s a r e a p p r o x i m a t e l y para1 l e l t o t h e g l i d e planes ( u n l i k e t h e d a n g l i n g bonds f o r u n d i s s o c i a t e d d i s l o c a t i o n s /14/), a r e i n d i c a t e d by s h o r t l i n e s . F i g u r e 2 shows

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979606

C6-28 JoURNAL DE PHYSIQUE

thesame d i s l o c a t i o n s i n t h e model, i n which t h e t o p h a l f o f t h e c r y s t a l has been removed, and t h e b o t t o m h a l f r e t a i n e d b u t n o t shown below t h e p l a n e s c o n t a i - n i n g t h e d i s l o c a t i o n cores. There i s a n i n t r i n s i c f a u l t between t h e two p a r t i a l s . Each o f t h e p a r t i a l s i n f i g u r e 2 i s shown w i t h a k i n k i n i t .

F i g . 2 : D i s s o c i a t e d 60' d i s l o c a t i o n . Core s t r u c t u r e o f 90" p a r t i a l on t h e r i g h t , and o f t h e 30" p a r t i a l on t h e l e f t , viewed normal t o t h e s l i p p l a n e . The t o p h a l f o f t h e c r y s t a l has been removed, and t h e b o t t o m h a l f r e t a i n e d , b u t o n l y t h e p l a n e s c o n t a i n i n g t h e d i s l o c a t i o n c o r e s a r e shown. There i s an i n t r i n - s i c f a u l t between t h e two p a r t i a l s . K i n k s a r e shown on b o t h p a r t i a l s .

The arrangement o f t h e atoms a l o n g t h e 30' p a r t i a l i n f i g u r e 2 ( o r t h e r i g h t hand one i n f i g u r e 3) suggests sp2d r a t h e r t h a n sp3 h y b r i d i s a t i o n . The d i s t a n c e between atoms a l o n g t h e c o r e i s b ~ , t h e second n e a r e s t n e i g h b o u r d i s t a n c e , and equal t o t h e magnitude o f t h e t o t a l Burgers v e c t o r . An a l t e r n a t i - ve s t r u c t u r e i s shown on t h e l e f t hand s i d e o f f i g u r e 3, i n which n e i g h b o u r i n g atoms a l o n g t h e c o r e have been j o i n e d by s i n g l e bonds; t h e r e a r e no dang- l i n g bonds i n t h i s s t r u c t u r e .

F i g . 3 : D i s s o c i a t e d screw d i s l o c a t i o n , viewed n o r - mal t o t h e s l i p p l a n e . Only t h e p l a n e s c o n t a i n i n g t h e c o r e s t r u c t u r e s o f t h e two 30" p a r t i a l s a r e shown. Two a l t e r n a t i v e c o r e s t r u c t u r e s o f t h e 30"

p a r t i a l a r e shown. The r i g h t hand p a r t i a l i s shown w i t h a k i n k i n i t .

The d i s t a n c e between atoms across t h e c o r e o f t h e 90" p a r t i a l i s o n l y 25% g r e a t e r t h a n t h e normal n e a r e s t n e i g h b o u r d i s t a n c e . Bonding across t h e c o r e i s t h e r e f o r e l i k e l y . I t i s p o s s i b l e i n p r i n c i p l e t o j o i n t h e atoms across t h e c o r e o f t h e 90' p a r t i a l i n p a i r s f o r m i n g s i n g l e bonds, b u t r e s u l t i n g i n c o n s i - d e r a b l e d i s t o r t i o n , and t h e s y m e t r i c a l s t r u c t u r e shown i n f i g u r e 2 seems q u i t e l i k e l y , w i t h h y b r i d o r b i t z l s b e i n g formed between b o t h n e i ghbours a c r o s s t h e core.

2.2. ~crwy-ljslgcatjgn.- The screw c o n s i s t s o f two 30" p a r t i a l s , a1 t e r n a t i v e s t r u c t u r e s o f which a r e shown i n f i g u r e 3, and which have a l r e a d y been d i s - cussed above. The 30" p a r t i a l on t h e r i g h t o f f i g u r e 3 shows a k i n k .

2.3. ,Eclge-dizloczxtjop.- The edge d i s l o c a t i o n con- s i s t s o f two 60" p a r t i a l s , a l t e r n a t i v e s t r u c t u r e s o f which a r e shown i n f i g u r e 4 f o r t h e two p a r t i a l s bounding t h e f a u l t . The 60" p a r t i a l can be c o n s i d e r e d as made up o f k i n k s i n t h e 90' p a r t i a l ( s e e F i g . 2), o r i n t h e 30" p a r t i a l (see F i g . 3 ) . The p o s i t i o n o f one o f t h e t h r e e atoms making up t h e r e p e a t u n i t a l o n g t h e c o r e o f t h e 60° p a r t i a l i s u n c e r t a i n ; a l - t e r n a t i v e c o n f i g u r a t i o n s a r e shown on t h e l e f t and r i g h t hand p a r t i a l s . S i m i l a r a l t e r n a t i v e p o s i t i o n s a p p l y t o t h e c o r r e s p o n d i n g atoms i n t h e k i n k o f t h e 90' p a r t i a l ( F i g . 2) and o f t h e 30" p a r t i a l ( F i g . 3);

i n b o t h t h e s e cases t h e a l t e r n a t i v e shown f o r t h e r . h . 60" p a r t i a l i n f i g u r e 4 has been shown.

F i g . 4 : D i s s o c i a t e d edge d i s l o c a t i o n s c o n s i s t i n g o f two 60' p a r t i a l s , viewed normal t o t h e s l i p p l a n e . Two a l t e r n a t i v e c o r e s t r u c t u r e s a r e shown.

3. C o r r e l a t i o n o f s t r u c t u r e w i t h e l e c t r o n i c p r o p e r - t i e s . - E l e c t r i c a l measurements a t l o w temperatures -

i n n and p t y p e Ge, deformed i n compression o r t o r - s i o n , have been i n t e r p r e t e d s u c c e s s f u l l y Labusch and S c h e t t l e r /15/, by Labusch and S c h r o t e r /16/ and Haasen and Wagner /17/ i n terms o f : 1 ) f o r screws a f u l l donor band a t 0.035 eV, and an empty a c c e p t o r band a t 0.59 eV above t h e v a l e n c e band

-

2 ) f o r edge

P . B . H i r s c h C6-29

d i s l o c a t i o n s a h a l f f u l l band i n t h e n e u t r a l s t a t e a t 0.09 eV above t h e valence band. F o r S i t h e band f o r edge d i s l o c a t i o n s l i e s a t 0.34 eV above t h e valence band.

Since t h e screw c o n s i s t s o f two 30" p a r t i a l s we s u g g e s t t h a t t h e 30" p a r t i a l i s a s s o c i a t e d ( i n t h e n e u t r a l s t a t e ) w i t h t h e f u l l donor band c l o s e t o t h e v a l e n c e band and t h e empty a c c e p t o r band c l o s e t o t h e c o n d u c t i o n band. T h i s b e h a v i o u r would be c o n s i s t e n t e i t h e r w i t h t h e s t r u c t u r e shown on t h e 1.h.s. o f f i g u r e 3, i n which t h e r e a r e no d a n g l i n g bonds, t h e s t a t e s near t h e c o n d u c t i o n and v a l e n c e bands b e i n g presumably a s s o c i a t e d w i t h shear and d i l a t i o n a l s t r a i n f i e l d s 1181, o r w i t h t h e r. h.s.

s t r u c t u r e o f f i g u r e 3, and t h a t o f t h e 1.h. p a r t i a l i n f i g u r e 2, assuming t h e r e t o be a l a r g e M o t t - Hubbard gap between t h e donor and a c c e p t o r s t a t e s / 19,23/.

The h a l f f u l l band a t 0.09 eV f o r Ge and 0.34 eV f o r S i i s presumably a s s o c i a t e d w i t h t h e 60" p a r - t i a l s c o n s t i t u t i n g t h e edge d i s l o c a t i o n , s i n c e edge d i s l o c a t i o n s a r e t h e m a j o r t y p e o f d i s l o c a t i o n s found i n compressed specimens /21/. T h i s i s c o n s i s - t e n t w i t h t h e s t r u c t u r e f o r t h e 60" p a r t i a l shown i n f i g u r e 4; t h e r e a r e t h r e e e l e c t r o n s p e r r e p e a t u n i t c o n s i s t e n t w i t h a f u l l and h a l f f u l l band.

T h i s l e a v e s open t h e problem o f t h e e l e c t r i c a l p r o p e r t i e s o f t h e 90" p a r t i a l , one o f t h e p a r t i a l s making up t h e 60' d i s l o c a t i o n . The p e r i o d i c i t y o f t h e s t r u c t u r e i n f i g u r e 2 i s bT, b u t t h e r e a r e two e l e c t r o n s p e r c e l l , s u g g e s t i n g a f u l l band. But e l e c t r o n s w i t h k v e c t o r s a l o n g t h e d i s l o c a t i o n T i n e a r e n o t r e f l e c t e d by p l a n e s spaced a t bT because o f c o n t r i b u t i o n s f r o m atoms a t bT/2. T h i s suggests t h a t f o r t h e u n d i s t o r t e d s t r u c t u r e t h e r e i s no energy gap a t t h e f i r s t B r i l l o u i n zone boundary o f t h e one d i - mensional band, and t h e band c o u l d appear e f f e c t i v e - l y h a l f f u l l . However, t h e shear s t r a i n due t o t h e 30" p a r t i a l d e s t r o y s t h e a d d i t i o n a l symmetry, r e s u l - t i n g i n a gap. I n any case, a Hott-Hubbard gap c o u l d occur, o r t h e atoms may be j o i n e d i n p a i r s by s i n g l e bonds; i n e i t h e r case a gap would e x i s t between any donor and a c c e p t o r s t a t e s .

It s h o u l d be n o t e d t h a t t h e a t o m i c s t r u c t u r e a t a k i n k i n a 90" p a r t i a l ( s e e F i g . 2 ) , and a t one o f t h e two t y p e s o f k i n k s i n t h e 30" p a r t i a l (see F i g . 3 ) i s s i m i l a r t o t h a t o f a r e p e a t p e r i o d i n an edge d i s l o c a t i o n . T h i s suggests t h a t l o c a l i s e d s t a - t e s a t such k i n k s may have energy l e v e l s s i m i l a r t o t h o s e i n t h e band a s s o c i a t e d w i t h edge d i s l o c a t i o n s .

The s t r u c t u r e o f t h e second t y p e o f k i n k i n a 30"

p a r t i a l ( s e e F i g . 2) seems however t o be d i f f e r e n t . 4. S t r u c t u r e o f e x t r i n s i c a l l y d i s s o c i a t e d d i s l o c a - t i o n s

.-

Gomez, Cockayne, H i r s c h and V i t e k /5/ have

-

r e p o r t e d t h a t i n b o t h Ge and S i , d i s l o c a t i o n s w i t h screw c h a r a c t e r , generated by d e f o r m a t i o n a t h i g h temperature, a r e o f t e n d i s s o c i a t e d i n t o e x t r i n s i c f a u l t s , and t h a t these d i s l o c a t i o n s have anomalously l a r g e w i d t h s . I t has been assumed i n t h e p a s t t h a t e x t r i n s i c a l l y d i s s o c i a t e d d i s l o c a t i o n s a r e generated f r o m i n t r i n s i c a l l y d i s s o c i a t e d d i s l o c a t i o n s by a r e a c t i o n o f t h e t y p e :

on a g l i d e p l a n e =

+

&3 (1

on a n e i g h b o u r i n g 0 = - A6

+ 3

p l a n e ( 2 )

combined

-

CB =

(E +

s )

+

(6B

+ -

6A) ( 3 )

= - 6B

+ -

C6 ( 4 )

i .e. t h e e f f e c t i v e p o s i t i o n o f t h e two p a r t i a l s

E,

68 i s r e v e r s e d by n u c l e a t i n g

A6 + A

on t h e n e i g h -

-

b o u r i n g p l a n e . An a1 t e r n a t i v e c o n f i g u r a t i o n i s f o r - med as f o l l o w s . Suppose vacancies ( o r i n t e r s t i t i a l s ) n u c l e a t e a d i s l o c a t i o n loop, Burgers v e c t o r on

B

o f t h e screw d i s l o c a t i o n i n f i g u r e 5a, b. On t h e p l a n e o f t h e i n t r i n s i c f a u l t @

+

⁼

3

and on a p a r a l l e l p l a n e c o n t a i n i n g t h e t o p of t h e loop, d i s s o c i a t e s i n t o p l u s

3

( F i g . 5 c ) ; t h e l a t t e r sweeps across t h e p l a n e t o l i e above t h e o t h e r p a r - t i a l @ ( F i g . 5d). I f t h i s process occurs on a d j a - c e n t g l i d e p l a n e s an e x t r i n s i c f a u l t w i l l be formed.

F i g . 5 : Mechanism of c l i m b o f d i s s o c i a t e d screw

g,

forming an e x t r i n s i c a l l y d i s s o c i a t e d d i s l o c a t i o n . See t e x t f o r d e t a i l s .

The mechanism can s t i l l o c c u r on a more d i s t a n t pa- r a l l e l p l a n e , b u t t h e t o t a l energy o f t h e two f a u l t s w i l l i n c r e a s e f r o m t h a t f o r t h e e x t r i n s i c f a u l t ( y E ) t o t h a t o f two o v e r l a p p i n g i n t r i n s i c f a u l t s (2Yi) w i t h a consequent n a r r o w i n g o f t h e d i s l o c a t i o n r i b b o n . The d i f f e r e n c e between t h i s c o n f i g u r a t i o n o f an e x t r i n s i c a l l y d i s s o c i a t e d d i s l o c a t i o n (produced by c l i m b ) and t h a t produced by t h e g l i d e mechanism

C6-30 JOURNAL DE PHYSIQUE

i s t h a t two o f t h e p a r t i a l s making up a p a i r boun- t h e donor/acceptor bands f o r t h e two o a r t i a l s , i . e . d i n g one s i d e o f t h e f a u l t i n t e r c h a n g e p l a n e s ( i . e .

EF = El t

2 %

( l o g

- -

^{-) t} -

E Z e Q 2 ( l o g * - $ ) +

6B and i n eq. 2, 3 and F i g . 5 d ) . The d i s l o c a t i o n

- R 2 E

fll

can a l s o be c o n s i d e r e d as c o n s i s t i n g o f two 60' d i s - kT l o g --

1-fll ( 9 )

l o c a t i o n s @ and

&

o v e r l a p p i n g on n e i g h b o u r i n g p l a - and a s i m i l a r e x p r e s s i o n f o r E2, w i t h ?,and Q 2 i n t e r - nes. I n p r a c t i c e t h e l o o p - BA i s p r o b a b l y n u c l e a t e d changed, and fll r e p l a c e d by f 2 1

.

^{f l l = f,,}

a t a node where @ has pronounced edge c h a r a c t e r . T h i s mechanism o f f o r m a t i o n o f e x t r i n s i c f a u l t s appears more p l a u s i b l e t h a n t h a t suggested t e n t a t i v e l y i n ( 5 ) ; t h e d r i v i n g f o r c e f o r t h e c l i m b mechanism of t h e i n t r i n s i c -t e x t r i n s i c t r a n s f o r m a - t i o n i s t h e n a s u p e r s a t u r a t i o n o f vacancies o r i n - t e r s t i t i a l ~ on c o o l i n g from t h e h i g h t e m p e r a t u r e o f d e f o r m a t i o n . Recent experiments by Gomez have shown t h a t when S i i s c o o l e d v e r y s l o w l y f r o m a b o u t 820°C n o e x t r i n s i c f a u l t s a r e formed, c o n s i s t e n t w i t h t h e c l i m b mechanism.

5. Coulomb f o r c e s between p a r t i a l d i s l o c a t i o n s . - U s i n g a model i n which t h e charge on t h e p a r t i a l d i s l o c a t i o n i s d i s t r i b u t e d u n i f o r m l y o v e r a c y l i n - d e r , o f r a d i u s R, and i s screened b y f r e e c a r r i e r s ( e l e c t r o n s and h o l e s ) , and a s s u m i n g ' t h a t t h e poten- t i a l energy eV a t t h e d i s l o c a t i o n s < kT, i t can be shown t h a t t h e e l e c t r o s t a t i c energy p e r u n i t l e n g t h o f t h e d i s s o c i a t e d d i s l o c a t i o n i s

where QIQ, a r e t h e charges p e r u n i t l e n g t h a l o n g t h e d i s l o c a t i o n , E t h e d i e l e c t r i c c o n s t a n t and

X

(assumed > R) t h e Debye s c r e e n i n g l e n g t h , i .e.

X~ = kT€/4ve2(n t p ) ( 6 )

where e i s t h e e l e c t r o n i c charge, n, p t h e d e n s i t i e s o f e l e c t r o n s and h o l e s away f r o m t h e charged d i s l o - c a t i o n ,

D

i s t h e s e p a r a t i o n o f t h e two p a r t i a l s . The t e r m i n Ee i n v o l v i n g Q1Q2 o c c u r s o n l y i f

X

> D, i . e . below c r i t i c a l t e m p e r a t u r e Tc a 500°C, 800°C f o r Ge, S i r e s p e c t i v e l y , and l e a d s t o a Coulomb f o r c e ( p e r u n i t l e n g t h ) between p a r t i a l s

The s e p a r a t i o n o f t h e p a r t i a l s i n then g i v e n by 29102

D = D o + -

EY ( 8 )

where Do i s t h e e q u i l i b r i u m s e p a r a t i o n i n t h e absen- ce o f a-coulomb f o r c e . E x t e n d i n g t h e t r e a t m e n t o f Read /22/ and Labusch and S c h r o t e a /16/ f o r non- i n t e r a c t i n g e l e c t r o n s t o d i s s o c i a t e d d i s l o c a t i o n s ,

Q1, Q2 a r e c o n t r o l l e d by t h e p o s i t i o n o f t h e Fermi Energy

EF

r e l a t i v e t o t h e energy l e v e l s El, E2 f o r

1

+

1fl

,

1

+

fl f o r empty, h a l f f u l l and f u l l bands r e s p e c t i v e l y , where fl i s t h e f r a c t i o n o f t h e s t a t e s i n t h e band occupied by e l e c t r o n s ; f 1 i s nega- t i v e f o r h o l e s i n a f u l l band. Expressions s i m i l a r t o (9) a p p l y t o a l l bands a s s o c i a t e d w i t h t h e d i s l o c a - t i o n s ; t h e parameters fi

,

and c o r r e s p o n d i n g Ei

,

a p p l y t o t h e o c c u p a t i o n o f t h e p a r t i c u l a r band considered;

however Q1, Q2 a r e t h e n e t l i n e charges summing o v e r a1 1 t h e p o s s i b l e s t a t e s ( e l e c t r o n s and h o l e s ) asso- c i a t e d w i t h t h e d i s l o c a t i o n .

Q1, Q2 i n c r e a s e w i t h i n c r e a s i n g t e m o e r a t u r e , as

X

decreases; t h e maximum Coulomb f o r c e i s expec- t e d t o o c c u r f o r temperatures j u s t below Tc; f o r i n - t r i n s i c a l l y d i s s o c i a t e d d i s l o c a t i o n s , and f o r i n t r i n - s i c m a t e r i a l s we expect t h e Coulomb f o r c e t o be a maximum f o r edge d i s l o c a t i o n s . I f R = bT, we f i n d f o r Ge a t 700 K, f, = f 2 a 0.12, and w i t h ^{Q 1} = Q 2 =

%,

t h e Coulomb f o r c e i s found t o be n e g l i g i b l e . However, i f t h e d i s l o c a t i o n s a r e surrounded b y c l o u d s o f charged p o i n t d e f e c t s o r i m p u r i t i e s , p o s s i b l y bound a l s o t o t h e f a u l t , t h e t o t a l charge on t h e d i s - l o c a t i o n and i t s a s s o c i a t e d c l o u d can be c o n s i d e r a - b l y g r e a t e r , and t h e Coulomb f o r c e can become impor- t a n t . Thus, i f t h e p o i n t d e f e c t s have donor l e v e l s v e r y c l o s e t o t h e valence band, t h e y w i l l t e n d t o be p o s i t i v e l y charged n e a r t h e d i s l o c a t i o n core, where t h e Fermi l e v e l w i l l be c l o s e t o t h e valence band ( b e n t by t h e screened charge a s s o c i a t e d w i t h t h e d i s l o c a t i o n ) . F u r t h e r away f r o m t h e d i s l o c a t i o n t h e p o i n t d e f e c t s a r e expected t o be n e g a t i v e l y charged, i f t h e y have an a c c e p t o r l e v e l below t h e m i d d l e o f t h e gap. The t o t a l l i n e charge around t h e d i s l o c a t i o n w i t h i n a r a d i u s ^% D, which w i l l c o n t r o l t h e Coulomb i n t e r a c t i o n between t h e p a r t i a l s , may now be c o n s i d e r a b l y l a r g e r s i n c e R i n e q u a t i o n ( 9 ) f o r t h e c l o u d s u r r o u n d i n g t h e d i s l o c a t i o n can be much g r e a t e r t h a n by. Thus t h e anomalously l a r g e w i d t h s o f e x t r i n s i c a l l y d i s s o c i a t e d screw d i s l o c a - t i o n s i n Ge and S i ( 5 ) m i g h t be due t o Coulomb forces;

if t h e e x t r i n s i c and i n t r i n s i c s t a c k i n g f a u l t ener- g i e s a r e t h e same, u s i n g (8) t h e l a r g e w i d t h s can be e x p l a i n e d i f t h e p a r t i a l s had a n e t e f f e c t i v e 1 in e charge of % e/bT, of e i t h e r s i g n , w i t h i n a r a - d i u s ^% D.

P . B . H i r s c h C6-31

A t t h i s s t a g e t h e importance o f Coulomb f o r c e s on w h i c h t h e e x t r a h a l f - p l a n e s t e r m i n a t e , and i n i s u n c e r t a i n , b u t i n view o f t h e i n t e r a c t i o n between t h e i r m o b i l i t i e s ( E r o f e e v a and Osipyan / 2 5 / ) . Weak d i s l o c a t i o n and p o i n t d e f e c t s , and t h e charged s t a - beam i n v e s t i g a t i o n s have been c a r r i e d o u t on n t y p e t e s o f t h e l a t t e r , t h e p o s s i b i l i t y o f Coulomb f o r c e s GaAs (Nd

-

Na b 2 x 1016 ~ m - . ~ ) w i t h a view t o exten- and t h e i r e f f e c t on p a r t i a l d i s l o c a t i o n s e p a r a t i o n d i n g t h e r e s u l t s o f ( 8 ) t o d i s l o c a t i o n s w i t h a w i d e r must be borne i n mind. The Coulomb f o r c e e f f e c t seems range o f o r i e n t a t i o n s and t o l o o k f o r p o s s i b l e e f f e c t s t o o f f e r a more p l a u s i b l e e x p l a n a t i o n f o r t h e anoma- from t h e p o l a r i t y on edge d i s l o c a t i o n s o f o p p o s i t e l o u s l y wide screw d i s l o c a t i o n s i n Ge and S i t h a n s i g n ( a and

B

t y p e d i s l o c a t i o n s ) . F i g u r e 6 summarises t h e a1 t e r n a t i v e assumption o f

?.$

^yi

^,

s i n c e t h e t h e r e s u l t s o f p a r t i a l d i s l o c a t i o n s e p a r a t i o n as a s t a c k i n g sequence f o r b o t h types o f f a u l t a r e i n t e r - f u n c t i o n o f o r i e n t a t i o n (Gomez and H i r s c h /9/). Only r u p t e d o n l y a t t h e f o u r t h n e a r e s t p l a n e s /23/. d i s l o c a t i o n s w i t h i n t r i n s i c f a u l t s were found. The 6. D i s s o c i a t e d d i s l o c a t i o n s i n GaAs.- Gai and Howie i n t r i n s i c s t a c k i n g f a u l t energy was determined t o be /6/ and G o t t s c h a l k , P a t z e r and Alexander /8/ have y = 48

*

6 e r g ~ , r n - ~ , i n r e a s o n a b l e agreement w i t h demonstrated t h e e x i s t e n c e of d i s s o c i . a t e d d i s l o c a t i o n s t h e v a l u e o b t a i n e d i n ( 8 ) (55 k 5 e r g ~ m - ~ ) f r o m d i s - i n 111-V compounds, t h e f o r m e r i n Gap, t h e l a t t e r l o c a t i o n s w i t h p r e d o m i n a n t l y edge c h a r a c t e r . Data f o r i n a number o f t h e s e compounds. I n b o t h cases no a and 6 d i s l o c a t i o n s a r e i n c l u d e d ( i n d i c a t e d b y f u l l account was t a k e n of p o s s i b l e d i f f e r e n c e s between and open c i r c l e s i n f i g u r e 6 ) . B o t h t y p e s o f d i s l o c a - t h e two t y p e s of d i s l o c a t i o n s (a and 8 ) w i t h edge t i o n s have t h e same w i d t h s t o w i t h i n t h e e x p e r i m e n t a l components w h i c h can be d i s t i n g u i s h e d i n t h e s e p o l a r e r r o r . These o b s e r v a t i o n s suggest t h a t t h e d i f f e r e n t s t r u c t u r e s (Haasen / 2 4 / ) . These have Burgers v e c t o r s c o r e s t r u c t u r e s o f t h e two t y p e s o f d i s l o c a t i o n s which o f o p p o s i t e s i g n and d i f f e r i n t h e s p e c i e s o f atOms may be r e s p o n s i b l e f o r t h e i r d i f f e r e n t m o b i l i t i e s have

no e f f e c t on t h e p a r t i a l d i s l o c a t i o n s e p a r a t i o n s . GaAs 650'~

oc-type

o p-type

erg. c m - 2

erg.cm - 2

F i g . 6 : S e p a r a t i o n o f p a r t i a l d i s l o c a t i o n s ( a f t e r c o r r e c t i n g image p o s i t i o n s ) i n GaAs as a f u n c t i o n o f d i s l o c a t i o n o r i e n t a t i o n 0 , t o g e t h e r w i t h t h e o r e t i c a l curves u s i n g a n i s o t r o p i c e l a s t i c i t y t h e o r y , f o r values o f y = 41 and 54 e r g ~ m - ~ . F u l l and open c i r c l e s r e p r e s e n t v a l u e s f o r ci and

B

t y p e d i s l o c a t i o n s r e s p e c t i - v e l y (9); crosses f o r d i s l o c a t i o n s t h e s i g n o f which was n o t determined.

JOLTRNAL DE PHYSIQUE

References

/1/ Cockayne, D.J .H., Ray, I .L.R. and Whelan, M.J., P h i l . Mag. 20 (1969) 1265. -

/2/ Ray, I.L.R. and Cockayne, D.J.H., Proc. R. Soc.

A325' (1971) 534.

-

/3/ Ray, 1 .L.R. and Cockayne, D.J.H., J . Microsc.

98

(1973) 170.

/4/ Haussermann, F. and Schaumburg, H., P h i l . Mag.

27

(1973) 745.

/5/ ~ 6 m e z , A., Cockayne, D.J .H., H i r s c h , P.B. and V i t e k , V., P h i l . Mag.

31

(1975) 105.

/6/ Gai, P.L. and Howie, A., P h i l . Mag. - 30 (1974) 939.

/ 7 / Alexander, H., Proc. 6 t h Europ. Congr. E l e c t r o n Vicroscopy, Jerusalem, 1976, p. 208.

/8/ G o t t s c h a l k , H., Patzer, G. and Alexander, H., Phys. S t a t u s S o l i d i ( a )

5

(1978) 207.

/9/ ~ 6 m e z , A. and H i r s c h , P.B., P h i l . Mag. 38

(1978) 733. -

/ l o /

Meingast, R. and Alexander, H., Phys. S t a t u s So- l i d i ( a ) - 17 (1973) 229.

J

/11/ Gomez, A. and H i r s c h , P.B., P h i l . Mag. - 36 (1977) 169.

/12/ H o r n s t r a , J., J. Phys. Chem. S o l i d s - 5 (1958) 129.

/13/ Haasen, P. and Seeger, A., H a l b l e i t e r p r o b l e m e I V (Braunschweig)

,

1958, p.68.

/14/ Shockley, W . , Phys. Rev. - 9 1 (1953) 228.

/15/ Labusch, R. and S c h e t t l e r , R., Phys. S t a t u s So- l i d i ( a ) - 9 (1972) 455.

/16/ Labusch, R. and S c h r o t e r , W., L a t t i c e D e f e c t s i n Semiconductors, I n s t . Phys. Conf. Ser. No.%

(1975) p.56.

/17/ Wagner, R. and Haasen, P., L a t t i c e D e f e c t s i n Semiconductors, I n s t . Phys. Conf. Ser. No.23 (1975),

-

p.387.

/18/ C e l l i

,

V., Gold, A. and Thomson, R., Phys. Rev.

L e t t .

-

⁸ (1962) 96.

/19/ Mott, N.F. and Davis, E.A., E l e c t r o n i c Processes i n N o n - c r y s t a l 1 i n e Sol i d s ( O x f o r d : Cl arendon Press)

1971, p. 123.

/20/ Jones, R., P h i l . Mag. - 35 (1977) 57.

/21/ S p r i n g e r , E., Diploma Thesis, Gottingen, 1967.

/22/ Read, W.T., P h i J . Mag.

-

45 (1954) 775, 1119.

/23/ H i r t h , J.P. and Lothe, J., Theory o f d i s l o c a t i o n s (New York : McGraw-Hill) 1968, p.355.

/24/ Haasen, P., Acta M e t a l l o g r .

5

(1957) 598.

/25/ Erofeeva, S.A. and Osipyan, Yu.A., Sov. Phys. So- l i d S t a t e

15

(1973) 538.