DISLOCATION MOTION NEAR A SURFACE

(1)

HAL Id: jpa-00219044

https://hal.archives-ouvertes.fr/jpa-00219044

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.

DISLOCATION MOTION NEAR A SURFACE

H. Möller, H. Ewaldt

To cite this version:

H. Möller, H. Ewaldt. DISLOCATION MOTION NEAR A SURFACE. Journal de Physique Colloques,

1979, 40 (C6), pp.C6-139-C6-141. �10.1051/jphyscol:1979628�. �jpa-00219044�

(2)

JOURNAL DE PHYSIQUE CoZZoque C6, suppZ6ment a u n 0 6 , t o m e 40, j u i n 1979, page C6-139

DISLOCATION MOTION NEAR A S U R F A C E

H.J-. M i j l l e r and H. Ewaldt

I n s t i t u t fiir M e t a Z Z p h y s i k , H o s p i t a Z s t r . 12, U n i v e r s i t i i t 3400 G&t{ngen, F.R.G.

Resume.- On a u t i l i s 6 l a methode du double e t c h i n g e t l a t o p o g r a p h i e aux rayons X pour e t u d i e r l e comportement de demi b o u c l e s de d i s l o c a t i o n i s o l e e s au v o i s i n a g e de l e u r s p o i n t s duemergence

a

l a s u r f a c e dans l e Ge e t l e S i , p o u r des temperatures comprises e n t r e 0,6 e t 0,7 Tfus.on. On observe une c o m p e t i t i o n e n t r e deux mecanismes : l a r 6 d u c t i o n de t a i l l e des b o u c l e s e t l e g l ~ s s e m e n t d e v i e des segments v i s emergeant d l a s u r f a c e . On a determine l a v i t e s s e de r 6 t r 6 c i s s e m e n t des b o u c l e s a i n s i que l a f r e q u e n c e du g l i s s e m e n t d e v i e . On compare l e s e n e r g i e s d ' a c t i v a t i o n mesurees pour l e s deux processus avec l e s c a l c u l s t h e o r i q u e s .

A b s t r a c t . - The b e h a v i o u r o f s i n g l e d i s l o c a t i o n h a l f l o o p s a t a s u r f a c e d u r i n g a n n e a l i n g i n t h e temperature range T : 0.6

-

0.7 T m e l t i n g was i n v e s t i g a t e d b o t h by t h e d o u b l e e t c h

-

p i t method and b y X-ray topography i n Ge and SI. Two competing processes were observed : t h e s h r i n k a g e o f t h e l o o p s and t h e c r o s s s l i p o f t h e screw segments i n t e r s e c t i n g t h e s u r f a c e . The v e l o c i t y o f s h r i n k a g e and t h e c r o s s s l i p r a t e were determined. The measured a c t i v a t i o n e n e r g i e s o f b o t h processes a r e compared w i t h t h e o r e t i c a l c a l c u l a t i o n s .

1. I n t r o d u c t i o n . - The i n v e s t i g a t i o n o f t h e m o t i o n o f s i n g l e d i s l o c a t i o n s i n semiconductors i s m o s t l y c a r - r i e d o u t on d i s l o c a t i o n h a l f l o o p s l y i n g near a s u r - f a c e . The movement o f t h e segments i n t e r s e c t i n g t h e s u r f a c e can be e a s i l y observed by t h e d o u b l e e t c h - p i t method o r by X-ray-topography. D u r i n g an annea- l i n g t r e a t m e n t i n t h e t e m p e r a t u r e range T : 0.6 Tm (Tm = m e l t i n g p o i n t ) (Ge) and 0.7 Tm ( S i ) two p r o - cesses a r e found i n germanium and s i l i c o n : d i s l o c a - t i o n h a l f l o o p s (up t o d i a m e t e r s a t t h e s u r f a c e o f 1000 pm) s h r i n k and t h e screw segments f r e q u e n t l y move i n t o t h e c r o s s s l i p p l a n e . The t o p o g r a p h i c i n - v e s t i g a t i o n shows t h a t i n b o t h cases t h e segment i n t e r s e c t i n g t h e s u r f a c e bends ( e i t h e r i n t h e o r i - g i n a l p l a n e o r i n t h e c r o s s s l i p p l a n e ) and s h o r t e n s t h e l i n e l e n g t h . O b v i o u s l y t h i s process i s induced by image and l i n e t e n s i o n f o r c e s n e a r t h e s u r f a c e . They have been measured t o be o f t h e o r d e r o f 1 N/rnm2.

kage has been i n v e s t i g a t e d m a i n l y by t h e double e t c h - p i t t e c h n i q u e i n two ways :

a ) The specimens were annealed a t c o n s t a n t tempera- t u r e and t h e d i s t a n c e s s t h e segments moved on t h e s u r f a c e were measured depending on t h e annea- l i n g t i m e . F i g u r e l shows t h a t 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 d s / d t decreases w i t h i n c r e a s i n g t i m e .

Silicon

I I I

I n m a t e r i a l s w i t h a h i g h P e i e r l s p o t e n t i a l 1 0 20 30

-

40 ^t^Cminl as expected f o r Ge and S i t h e t h e r m a l l y a c t i v a t e d

m o t i o n o f a d i s l o c a t i o n s h o u l d be o n l y p o s s i b l e F i g . 1 : D i s t a n c e s s a t a (111)

-

s u r f a c e moved by e i t h e r by d o u b l e k i n k o r b y s i n g l e k i n k n u c l e a t i o n (screw)

-

d i s l o c a t i o n segments d u r i n g annealing.

a t t h e s u r f a c e . Because o f t h e low d r i v i n g s t r e s s e s

b ) The maximal v e l o c i t y v a t t = 0 i s measured de- t h e second process should p l a y t h e dominant r o l e .

pending on temperature. F i g u r e 2 shows t h a t t h e S h r i n k a g e and c r o s s s l i p have been i n v e s t i g a t e d

t e m p e r a t u r e dependence f o l l o w s an A r r h e n i u s l a w . q u a n t i t a t i v e l y t o g e t i n f o r m a t i o n about s i n g l e

The a c t i v a t i o n energy o f t h e s h r i n k a g e process k i n k n u c l e a t i o n and m i g r a t i o n and a b o u t t h e a c t i v a -

(E,) i s determined f r o m t h e s l o p e and g i v e n i n t i o n energy o f t h e c r o s s s l i p process.

Table I f o r Ge and S i . To compare t h e s e a c t i v a - 2 . Shrinkage o f d i s l o c a t i o n h a l f l o o p s . - The s h r i n - t i o n e n e r g i e s w i t h t h e a c t i v a t i o n energy ( Q ) o f

d i s l o c a t i o n m o t i o n under an e x t e r n a l s t r e s s a

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979628

(3)

C6-140 JOURNAL DE PHYSIQUE

t h e o r e t i c a l model o f t h e s h r i n k a g e process i s We assume t h e k i n k m i g r a t i o n v e l o c i t y vK t o be

necessary. determined by o b s t a c l e s on t h e d i s l o c a t i o n l i n e . A t

l o w s t r e s s e s T as expected h e r e i t can be a p p r o x i -

F i g . 2 : S h r i n k a g e v e l o c i t y v o f 60' and screw segments i n t e r s e c t i n g a (111)

-

s u r f a c e versus annea- l i n g temperature.

T a b l e I : Es a c t i v a t i o n energy o f shrinkage, Q a c t i - v a t i o n e n e r g y o f d i s l o c a t i o n m o t i o n , E b i n d i n g ener-

gy o f t h e o b s t a c l e s t o d i s l o c a t i o n s , E d o u b l e k i n k n u c l e a t i o n energy ( a t l o w stressespf. Ed obsta- c l e p o t e n t i a l , EQ a c t i v a t i o n energy o f c r o s s s l i p , y s t a c k i n g f a u l t energy.

L e t us l o o k a t a s t r a i g h t d i s s o c i a t e d segment i n c l i n e d t o t h e s u r f a c e . The d i s l o c a t i o n bends by n u c l e a t i n g s i n g l e k i n k s a t t h e s u r f a c e and m i g r a t i o n o f t h e k i n k s a l o n g t h e segment. I f t h e k i n k m i g r a t i o n v e l o c i t y vK i s l o w t h e n u c l e a t i o n energy o f a s i n g l e k i n k a t t h e s u r f a c e i s i n c r e a s e d because o f t h e r e - p u l s i v e f o r c e o f s u c c e s s i v e k i n k s . The e f f e c t i v e nu- c l e a t i o n r a t e i s g i v e n by

- vo;(~C, + Eint )/KT

" e f f - ( 1 )

Ek k i n k n u c l e a t i o n energy a t t h e s u r f a c e , Eint i n t e - r a c t i o n energy o f s u c c e s s i v e k i n k s . F o l l o w i n g t h e model f o r t h e d i s l o c a t i o n m o t i o n i n an e x t e r n a l s t r e s s f i e l d /1/ i t i s p o s s i b l e t o d e r i v e t h e f o l l o w - i n g e q u a t i o n s f o r t h e s h r i n k a g e v e l o c i t y : ( s t r o n g k i n k - k i n k i n t e r a c t i o n )

t '

w i t h v = voe -':/KT,

u

s h e a r modulus, bp p a r t i a l B u r g e r s v e c t o r , B o r i e n t a t i o n f a c t o r . I f t h e k i n k - k i n k i n t e r a c t i o n i s weak one o b t a i n s

v = av ( vK/v)>>b ( 3 )

mated by /2/ ( T abpR/KT < 1)

V K = v o ;K TI!^ - ( E d + 2 ~ ) / K T

0 ( 4 )

where t h e mean d i s t a n c e o f o b s t a c l e s i s assumed t o be t e m p e r a t u r e dependent : I! = Lo e-E/KT, Ed obsta- c l e b a r r i e r . I n s e r t i n g e q u a t i o n ( 4 ) i n t o ( 2 ) ( t h e r e s u l t s w i l l show t h a t e q u a t i o n ( 2 ) i s v a l i d ) we o b t a i n

= A

=1/2

e - ( ~ i + Ed + 2€)/2KT

The a c t i v a t i o n energy o f s h r i n k a g e ES i s determined b y t h r e e terms now \.rhich can be compared w i t h t h e a c t i v a t i o n energy o f d i s l o c a t i o n m o t i o n i n an e x t e r - n a l s t r e s s f i e l d ( d o u b l e k i n k mechanisrn,~<-r~) /1/

Q = 7 1 ( E i K + Ed + ^{E )} ( 6 )

Together w i t h t h e d a t a p u b l i s h e d elsewhere /1/

i t was p o s s i b l e t o determine EiK: 2E; and Ed s e p a r a t - l y f r o m 2(Es-Q) = E-E: (see t a b l e I ) . I t i s b e l i e v e d t h a t t h e r a t h e r s t r o n g o b s t a c l e s a r e t h e observed c o n s t r i c t i o n s 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 segment /3/

-

The decrease o f t h e s h r i n k a g e v e l o c i t y d u r i n g m o t i o n c o u l d be e x p l a i n e d q u a n t i t a t i v e l y w i t h t h e decrease o f t h e l i n e t e n s i o n when t h e segments bends p e r p e n d i c u l a r t o t h e s u r f a c e .

3. Cross s l i p p i n g o f screw d i s l o c a t i o n s . - D u r i n g t h e a n n e a l i n g t r e a t m e n t t h e c r o s s s l i p o f t h e screw segments i s a c o m p e t i t i v e process t o t h e s h r i n k a g e because i t p r e v e n t s f u r t h e r m o t i o n o f t h i s segment.

T h e r e f o r e i f one i n v e s t i g a t e s a f i n i t e number o f s i n g l e screw segments t h e r e l a t i v e number o f c r o s s s l i p e v e n t s P f i r s t i n c r e a s e s w i t h a n n e a l i n g t i m e and t h e n s a t u r a t e s . The s a t u r a t i o n v a l u e Ps i s dependent on t h e v e l o c i t y o f s h r i n k a g e and on t h e cross s l i p r a t e / 4 / . The t e m p e r a t u r e dependence o+ each process s h o u l d f o l l o w an A r r h e n i u s law, t h e n t h e r a t i o o f t h e e x p o n e n t i a l f a c t o r s RQ/RS i s g i v e n b y

RQ/RS = e-(EQ-Es)/KT ( 7 )

I t has been shown t h a t RQ/Rs can be determined f r o m Ps. T h e r e f o r e one can determine t h e d i f f e r e n c e o f t h e a c t i v a t i o n e n e r g i e s o f c r o s s s l i p (EQ) and s h r i n k a g e (E,) f r o m t h e s l o p e o f t h e temperature dependence ( s e e f i g u r e 3 ) . S i n c e Es has been d e t e r - mined s e p a r a t l y EQ can be c a l c u l a t e d ( T a b l e I ) . I t

i s b e l i e v e d t h a t t h e u n d e r l y i n g process o f c r o s s s l i p i s t h e c o n s t r i c t i o n and r e d i s s o c i a t i o n on t h e c r o s s s l i p p l a n e of screw d i s l o c a t i o n s . T h i s process has been s t u d i e d t h e o r e t i c a l l y b y v a r i o u s a u t h o r s .

(4)

H.J. M6ller and H. E w a l d t

Silicon

Fig.3 : R a t i o o f cross s l i p and shrinkage r a t e o f screw d i s l o c a t i o n segments versus annealing tempera- t u r e .

The best agreement w i t h our r e s u l t s was given w i t h t h e theory o f Escaig /5/. The t h e o r e t i c a l l y develop- ed a c t i v a t i o n energy i s depending on t h e s t a c k i n g f a u l t energy y o f the m a t e r i a l . From our measured a c t i v a t i o n energies EQ both i n Ge and S i reasonable values o f y c o u l d be d e r i v e d (see t a b l e I).

E s c a i g ' s theory assumes t h a t cross s l i p s t a r t s a t p r e - e x i s t i n g c o n s t r i c t i o n s . I t i s known from weak-beam TEM i n v e s t i g a t i o n s 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 near a s u r f a c e t h a t t h e d i s s o c i a t i o n w i d t h may be widened o r narrowed depending on t h e d i r e c t i o n o f the B u r g e r ' s v e c t o r /6/. The a n a l y s i s o f our r e s u l t s showed t h a t cross s l i p occured i n a l l cases a t those surfaces where a narrowing i s expected.

References

/ I / M'oller, t i . J . , Acta Metal I.,

26

(1978) 963.

/2/ Rybin, V.V. and Orlov, A.N., Sov. Phys. S o l i d State, 11 (1970) 2635.

-

/3/ Packeiser, G. and Haasen, P., P h i l o s Mag.,

2

(1977) 821.

/4/ M d l l e r , H.J., P h i l o s . Mag.,

37

(1978) 41.

/5/ Escaig, B., D i s l o c a t i o n Dynamics (New York : Mc Graw H i l l ) 1968, 655.

/6/ Hazzledine, P.M., Karnthaler, H.P., Wintner, E., P h i l o s . Mag.,

32

(1975) 81.