MOTION OF PARTIAL DISLOCATIONS

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MOTION OF PARTIAL DISLOCATIONS

H. Gottschalk

To cite this version:

H. Gottschalk. MOTION OF PARTIAL DISLOCATIONS. Journal de Physique Colloques, 1979, 40

(C6), pp.C6-127-C6-131. �10.1051/jphyscol:1979626�. �jpa-00219042�

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JOURNAL DE PHYSIQUE CoZZoque C6, suppZ&ent au n06, tome 40, j u i n 1979, page C6-127

MOTION OF P A R T I A L DISLOCATIONS H. G o t t s c h a l k

AbteiZung fur MetaZZphysik im I I . PhysikaZischen I n s t i t u t der U n i v e r s i t a t zu KBZn, ZiiZpicher Str.77, 0-5000 KBZn 41, F. R.G.

Resume.- On P t u d i e 1

'

i n f l u e n c e des c o n t r a i n t e s e l e v e e s s u r l a l a r g e u r de d i s s o c i a t i o n des d i s l o c a - i o n s dans l e s i l i c i u m dope e t dans l e germanium p u r . Tandis que pour un dopage au b o r e ( 6 )

(8.3 x 1018cm-3) aucune i n f l u e n c e n ' a

e t @

observee, on remarque, p a r c o n t r e , que l e s d i s l o c a t i o n s v i s se s o n t r e s s e r r g e s pour un dopage au phosphore ( 7 x 1 0 ' ~ c m - ~ ) ; c e c i s i g n i f i e que l e s deux p a r - t i e l l e s "30"" o n t approximativement l a meme m o b i l i t e . Pour l e s d i s l o c a t i o n s "60°", c e l l e s d o n t l a p a r t i e l l e "90°" e s t en t 6 t e e s t l a p l u s r a p i d e . Dans l e Ge, on t r o u v e ggalement une d i f f e r e n c e e n t r e l a m o b i l i t e des p a r t i e l l e s , mais, l a v a r i a t i o n des v a l e u r s mesurees e s t prononcee. On a, en o u t r e , r e d e t e r m i n e l ' e n e r g i e des f a u t e s d'empilement pour l e S i p u r ( y = 58

+

6 m J / m 2 ) e t l e Ge ( y = 75

+

1 0 d / m 2 ) .

A b s t r a c t . - The i n f l u e n c e o f h i g h s t r e s s on t h e d i s s o c i a t i o n w i d t h o f d i s l o c a t i o n s i n doped S i and p u r e Ge was i n v e s t i g a t e d . Whereas h i g h B-doping (8.3 x 1 0 " ~ m - ~ ) has no i n f l u e n c e , i n p-doped ( 7 x 1018cm-3) c r y s t a l s we f i n d a l l screw d i s l o c a t i o n s narrowed; i .e. b o t h 30" p a r t i a l s have about t h e same m o b i l i t y . 60' d i s l o c a t i o n s having t h e i r 90" p a r t i a l i n f r o n t a r e f a s t e r i n t h i s m a t e r i a l and i n Ge t h a n a r e 60" d i s l o c a t i o n s w i t h t h e r e v e r s e d o r d e r o f p a r t i a l s . I n Ge a d i f f e r e n c e i n 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 s found t o o ; b u t t h e v a r i a t i o n o f t h e measured values i s p r o - nounced. The s t a c k i n g f a u l t e n e r g i e s o f p u r e S i ( y = 58

+

6 m ~ / m ~ ) and Ge ( y = 75

+

10 mJ/m2) a r e redetermined

.

1. I n t r o d u c t i o n . - The e f f e c t o f h i g h e x t e r n a l s t r e s s a p p l i e d t o s l i g h t l y B-doped S i - c r y s t a l s on t h e d i s - s o c i a t i o n w i d t h o f d i s l o c a t i o n s was f i r s t r e p o r t e d by Wessel and Alexander /I/. W i t h t h e concept o f d i f f e r e n t m o b i l i t i e s o f t h e l e a d i n g and t h e t r a i l i n g p a r t i a l ( ~ 3 0 1 f

v 3 ~ t ;

U901 f p 9 ~ t ) t h e a u t h o r s i n - t e r p r e t e d t h e i r experimental r e s u l t s . The r a t i o s o f m o b i l i t i e s o f t h e p a r t i a l s a can be e v a l u a t e d f o r t h e t h r e e types o f d i s l o c a t i o n s l y i n g s t r a i g h t a l o n g t h e <110> - d i r e c t i o n s (PQ p a r a l l e l t o t h e p r i m a r y Burgers v e c t o r , PU, PK). The d i f f e r e n t a ( a

w

= U 3 0 t / u 3 ~ 1 , aPU = u 9 0 t / ~ 3 0 1 , apK = U30t / ~ 9 0 1 ) a r e

connected w i t h t h e measured s e p a r a t i o n s o f t h e d i s - l o c a t i o n s d by

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 w i t h o u t e x t e r n a l s t r e s s , f a g e o m e t r i c a l f a c t o r ( f = 1/6 f o r compres- s i o n a l o n g <213>), b t h e Burgers v e c t o r , T t h e shear s t r e s s and y t h e s t a c k i n g f a u l t energy (SFE). From (1) i t f o l l o w s t h a t a d e f i n i t e change i n d i s expected i f b ~ / 2 y > O . 5.

I n t h i s paper experiments on h e a v i l y P- and B- doped S i and undoped Ge a r e r e p o r t e d , and i t i s t r i e d t o proceed n o t from measurements o f i n d i v i d u a l d i s l o c a t i o n loops, b u t f r o m histograms o f t h e d i s s o - c i a t i o n w i d t h s . F o r t h e e v a l u a t i o n a c c o r d i n g t o ( 1 ) i t i s necessary t o know y and do o f doped S i and o f

Se, r e s p e c t i v e l y . As y = 5 1

+

5 m ~ / m ~ /2/ f o r S i and y = 60

+

8 mJ/m2/3/ f o r Ge i n some cases l e d t o nega- t i v e a, t h e SFEs o f t h e m a t e r i a l s i n q u e s t i o n and a d d i t i o n a l l y o f undoped S i were measured.

2. Experimental.-The f o l l o w i n g m a t e r i a l s were used : S i undoped (B, n = 5 x 1012cm-3), S i B-doped

( n = 8.3 x 1018cm-3), S i P-doped (n = 7 x 1018cm-3) and Ge undoped.

S i n g l e c r y s t a l s were deformed i n u n i a x i a l com- p r e s s i o n a l o n g <213>. I n c r y s t a l s o f S i c o o l e d down w i t h s t r e s s e s r e l e a s e d t h e r e was a p a r t i c u l a r l y h i g h f r a c t i o n o f d i s l o c a t i o n s f o r m i n g d i p o l e s (about 75%

o f t h e t o t a l d i s l o c a t i o n l e n g t h ) /4/which sometimes c o u l d n o t be c l e a r l y d i s t i n g u i s h e d f r o m d i s s o c i a t e d d i s l o c a t i o n s . To g e t a g r e a t e r D a r t o f s i n g l e d i s l o - c a t i o n s t h e deformed c r y s t a l s were c o o l e d down under a small load.

I n a l l specimens c o n s t r i c t i o n s a l o n g t h e d i s - l o c a t i o n s were found, b u t f o r an undoped S i - c r y s t a l c o o l e d down under l o a d (12 ~ / m m ~ ) , t h e number o f c o n s t r i c t i o n s was c o n s i d e r a b l y s m a l l e r than f o r an annealed S i - c r y s t a l . 25 c o n s t r i c t i o n s were concen- t r a t e d on a d i s l o c a t i o n l e n g t h o f 2 pm whereas a l e n g t h o f 17 pm was f r e e o f c o n s t r i c t i o n s .

F o r t h e doped c r y s t a l s an i n f l u e n c e o f doping on t h e e l a s t i c c o n s t a n t s s h o u l d be taken i n t o account, b u t a rough e s t i m a t e u s i n g measurements o f H a l l /5/ bhows t h a t i t can be h e g l e c t e d

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979626

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C 6 - 128 JOURNAL DE PHYSIQUE

F i g u r e 1 shows t h e measured s e p a r a t i o n s and t h e i r severe s c a t t e r i n g i n undoped S i . The r e s u l t s a r e l i s t e d i n t a b l e I . W i t h i n t h e m a r g i h o f e r r o r t h e r e was no d i f f e r e n c e i n y f o r an undoped S i c r y s t a l c o o l e d down under l o a d and an annealed one(700°C, 15 min). For doped S i t h e SFE was found s l i g h t l y h i g h e r b u t independent o f t h e d o t a t i o n element.

These values, however, a r e p r e l i m i n a r y r e s u l t s ; a d d i - t i o n a l measurements must be performed.

r a t i o n s , t h e s o - c a l l e d noses /1/ (N i n f i g u r e 2a), were found i n a l l specimens. A l l s t a c k i n g f a u l t s ana- l y s e d were o f i n t r i n s i c c h a r a c t e r .

3.1. :-i-;:dgegd

1 : - : - 2 9 4 - ~ ! ~ ~ 1 - 1 9 - m j ! 1 ) . -

T h i s spe- cimen g i v e s q u i t e s i m i l a r r e s u l t s as known f r o m t h e undoped c r y s t a l s /1/ c o n c e r n i n g t h e arrangement o f d i s l o c a t i o n s , t h e i r r a t i o s o f d e n s i t i e s (NpQ" NPU ² PIpK), t h e i r s e p a r a t i o n s and t h e m o b i l i t y r a t i o s a . T h i s was expected because d i s l o c a t i o n v e l o c i t i e s o f undoped S i and o f B-doped S i ( n = 8 . 3 x 10'8cm-3) d i f f e r o n l y by a f a c t o r o f about 3 as an e x t r a p o l a - t i o n u s i n g r e s u l t s o f /6/ shows.

3.2. 5-PIdg@ed

[~-r-E9~-~!mm'2-~5-mjnl) .-

The d i s l o - c a t i o n arrangement i s shown i n f i g u r e 2b. 50% o f t h e d i s l o c a t i o n s a r e screws (PQ-type), 43% a r e d i s l o c a - t i o n s o f t h e PU-type and o n l y 7% a r e P K - d i s l o c a t i o n s . T h a t means t h a t PK- d i s l o c a t i o n s must have moved w i t h t h e h i g h e s t v e l o c i t y . T h i s i s a remarkable d i f f e r e n c e between P-doped S i and undoped o r B-doped S i r e s p e c t i -

,

v e l y . F i g u r e 3a shows t h e histograms o f t h e w i d t h d f o r t h e t h r e e d i s l o c a t i o n types. C o n t r a r y t o t h e r e - s u l t s o f undoped S i a l l P Q - d i s l o c a t i o n s a r e narrowed.

S i m i l a r t o t h e undoped S i t h e P U - d i s l o c a t i o n s a r e narrowed and t h e P K - d i s l o c a t i o n s a r e widened. Using F i g . 1 : D i s l o c a t i o n w i d t h vs. d i s l o c a t i o n c h a r a c t e r , e q u a t i o n ( 1 ) one can o a l c u l a t e a f o r each d i s l o c a - S i (undoped); ( I ) , ( 2 ) , ( 3 ) c a l c u l a t e d u s i n g y = 50,

58, and 66 mJ/m2. t i o n s e p a r a t i o n and t h e t h r e e d i s l o c a t i o n c h a r a c t e r s . The r e s u l t i s shown i n f i g u r e 3b. The a a r e w i d e l y For t h e d e f o r m a t i o n experiments under h i g h spread b u t t h e r e a r e accumulations a t a p Q = l , a p u z l , s t r e s s s i n g l e c r y s t a l specimens were p r e p a r e d as ~ ~ ~ 2 0 . 4 . From t h i s i t f o l l o w s under t h e assumption d e s c r i b e d i n /I/. The p r e d e f o r m a t i o n was done a t o f o n l y f o u r d i f f e r e n t p a r t i a l m o b i l i t i e s : vpU/vpK=

750°C f o r S i and a t 520-550°C f o r Ge. To a v o i d f a t a l 0.7, ~ p ~ / ~ p ~ = l . 4 , and v p K > ~ p ~ " ~ p U , what i s c o n f i r m e d d i s l o c a t i o n mu1 t i p 1 ic a t i o n i n t h e h i g h l y s t r e s s e d by t h e r a t i o s o f d i s l o c a t i o n d e n s i t i e s . F o r t h e se- c r y s t a l s t h e f o l l o w i n g d e f o r m a t i o n temperatures were quence o f m o b i l i t i e s we g e t u 9 0 1 > p ~ o t : p 3 0 1 = u 3 0 t .

chosen : Because o f t h e l a c k o f v e r y wide s e p a r a t i o n s we f i n d

S i ( B ) TD = 420°C, S i ( P ) TD = 360°C, Ge TD = 220°C. apq, apU>0.7, apK>0.2. I n r e s p e c t t o screws we see h e r e an i m p o r t a n t d i f f e r e n c e t o undoped and B-doped S i Table I : S t a c k i n g f a u l t e n e r g i e s and e x p e r i m e n t a l d e t a i l s

Deformation Resolved Y do(B = 0') d0(8 = 60')

temperature shear s t r e s s

("C) ( N/mm2 ) (mJ/m2) (nm) (nm) .

Ge 550 10 75 c 10 2.4 3.9

I

S i (undoped) 750 12 5 8 c 6 3.6 5.8

1

3 . R e s u l t s . - As observed i n undoped S i t h e d i s l o c a - I t s h o u l d be n o t e d h e r e t h a t t h e s c a t t e r and t h e t i o n s have m a i n l y t h e p r i m a r y Burgers v e c t o r and l i e e r r o r s i n t h e d e t e r m i n a t i o n o f d cause a s e r i o u s un- n e a r l y p e r f e c t l y s t r a i g h t a l o n g t h e < l l O > - d i r e c t i o n s c e r t a i n t y i n a , p a r t i c u l a r l y i f a i s n e a r t o 1 o r (PQ, PU, PK) ( F i g . 2a). A l l d i s l o c a t i o n s a r e d i s s o - g r e a t e r t h a n 1, t h a t means i f t h e s e p a r a t i o n s a r e c i a t e d w i t h o u t any c o n s t r i c t i o n s . L o c a l l y wide sepa- s m a l l . T h i s f o l l o w s f r o m t h e f o r m o f t h e c u r v e d/do(a)

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H . Gottschalk C6-129

which l e a d s a s y m p t o t i c a l l y t o dm /do f o r a + m.

The b a r s o f u n c e r t a i n t y f o r d i f f e r e n t a a r e shown i n t n e diagrams.

F i g . 2a F i g . 2b

F i g . 2 : D i s l o c a t i o n arrangement i n h i g h l y s t r e s s e d c r y s t a l s (TEM)

a ) Ge2 (undoped)- see

5

3.3.2. f o r d e f i n i t i o n b ) S i (P-doped)

3.3. (;e-und~peE.- When Ge c r y s t a l s a r e h i g h l y s t r e s s e d f o r more than 2 hours no more d i s l o c a t i o n s o f t h e PK-type a r e t o be found. T h i s o b s e r v a t i o n means t h a t t h e P K - d i s l o c a t i o n s i n Ge move much f a s - t e r t h a n t h e o t h e r t y p e s o f d i s l o c a t i o n s .

As t h e t r a n s p a r e n t r e g i o n s i n Ge a r e s m a l l e r t h a n i n S i , t h e number o f measurements i s decreased.

T h e r e f o r e n o averages o f t h e measured d-values c o u l d be formed as i n t h e case o f S i . The e r r o r i n d was t h e r e f o r e assumed t o be g r e a t e r (*I nm). T h a t means

t h a t t h e v a l u e s o f a a r e u n r e l i a b l e f o r ~ 0 0 . 5 . 3.3.1.

Ge-i

( ~ - : - ' ~ $ - N / t y l z _ 30 mi!).- I n f i g u r e 4a d i s t r i b u t i o n s o f t h e d i s s o c i a t i o n w i d t h s a r e shown.

Some screw d i s l o c a t i o n s a r e widened; most o f them, however, have n o t changed t h e i r s e p a r a t i o n s . The 6 O 0 - d i s l o c a t i o n s o f t h e PU-type a r e m a i n l y narrowed, whereas t h e P K - d i s l o c a t i o n s a r e widened. These r e - s u l t s a r e t o some e x t e n t s i m i l a r t o t h o s e on undoped S i . The c o r r e s p o n d i n g a - d i s t r i b u t i o n s a r e shown i n f i g u r e 4c. As i n P-doped S i t h e a a r e w i d e l y spread

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JOURNAL DE PHYSIQUE

but f o r screws and PK-dislocations even t h e region unreasonable t o g i v e d e f i n i t e values f o r a (Fig.4d).

a t a = 0 i s covered. Especially f o r the PU-dislocations t h e s c a t t e r i n g i s pronounced. Nevertheless, assuming frequent values

SI

n p ~

of a ( a p Q = 0.5, apu = 0 . 9 , apK = 0.2, e . g . ) leads t o

PQ

+-I---+

^PQ⁰

- - - t - -

^{- - - -} ^vpu/vpK^>1 i n c o n t r a s t t o the experience. This i n d i -

4- c a t e s t h a t t h e assumption of only f o u r d i f f e r e n t mo- m , A

,

2 b i l i t i e s

.i-. ( m ~ / ~ ~ ~ ~

⁼

!ms)

8 -

+-i---+

^{u 3 0 l} U S 0 l P U

PU

of t h e p a r t i a l s in t h i s case a t l e a s t i s not f u l f i l -

W a .

i a,, 3 1 ed.

&. -b PK 4. Discussion.- Wessel and Alexander /1/ have shown

t h a t i t must be assumed t h a t the d i f f e r e n t p a r t i a l 2 ~ P K 3

b d i s l o c a t i o n s forming t h e screw and t h e 60' d i s l o c a - t i o n s have d i f f e r e n t m o b i l i t i e s . The screw d i s l o c a - Fig. 3 : a ) Histograms of d , Si ( P ) ; d = d ( ~ = o)

b) Histograms of

a,

Si ( P ) ; d%shed b a r s t i o n i s t h e only one made up of two p a r t i a l s of t h e i n d i c a t e u n c e r t a i n t i e s : same c h a r a c t e r . Therefore i t gives t h e s t r o n g e s t a r -

guments f o r t h e e x i s t e n c e of d i f f e r e n t m o b i l i t i e s of t h e leading and t h e t r a i l i n g p a r t i a l . For a l l mate- r i a l s except P-doped Si t h e t r a i l i n g 30'-dislocation i s l e s s mobile than t h e leading one. For Ge addi- t i o n a l l y a time-and stress-dependent i n c r e a s e of t h e d i f f e r e n c e between t h e m o b i l i t i e s was found. There- f o r e a change of t h e core s t r u c t u r e of t h e leading and/or t r a i l i n g p a r t i a l s , r e s p e c t i v e l y , may be suppo sed.

In / I / t h e authors have pointed out t h a t t h e a s s o c i a t e d 30"-di s l o c a t i o n ( / 7 , 8/ a p a r t i a l accompa- nied by a row of point defects)should lead t o a decreased mobi 1 i t y . As t h e actual d i s l o c a t i o n v e l o c i t y i s not known i t cannot be decided from t h e mobility r a t i o a which of t h e p a r t i a l d i s l o c a t i o n s i s respon-

&&- s i b l e f o r t h e p a r t i c u l a r value of a .

Nevertheless, assuming a v a r i a b l e core s t r u c - t u r e of t h e d i s l o c a t i o n s t h e severe s c a t t e r i n g of t h e s e p a r a t i o n s observed in highly s t r e s s e d c r y s t a l s could be explained. Another c o n t r i b u t i o n t o t h e s c a t t e r i n g which must be taken i n t o account may be t h e f i n i t e d i s l o c a t i o n core /9/, which must be assumed t o be v a r i a b l e now.

PK

Acknowledgments.- The author wishes t o thank Prof.

Dr. H. Alexander f o r many s t i m u l a t i n g d i s c u s s i o n s ,

d )

H . Eppenstein and S. Wendler f o r t h e i r experimental

Fig. 4 : D i s t r i b u t i o n s of d f o r Gel ( a ) and Ge2 ( b ) c o n t r i b u t i o n s , B . Roehl f o r help i n t h e computations, D i s t r i b u t i o n s of a f o r Gel ( c ) and Ge2 ( d ) and I . Simons f o r c a r e f u l photographic work.

3.3.2.

se2

~ ~ - : - 3 j 3 - ~ l q m ~ ~ - 6 ~ - m j n ~ ) . - The e f f e c t of higher s t r e s s and longer deformation time i s shown by t h i s sample. Compared t o Gel t h e widening of t h e PQ-and-PK-dislocations i s s t r o n g l y increased ( F i g . 4 b ) . Since t h e ranges of a a r e so l a r g e i t i s

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H. Gottschalk

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K. and Alexander, H . , Philos. Mag. - 3 5 , (1977) 1523.

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/9/ Cockayne, D.J.H. and Vitek, V . , Phys. S t a t u s S o l i d i ( b ) _-65 (1974) 751.