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MEASUREMENTS OF THE DISLOCATION VELOCITIES IN SILICON
A. George
To cite this version:
A. George. MEASUREMENTS OF THE DISLOCATION VELOCITIES IN SILICON. Journal de Physique Colloques, 1979, 40 (C6), pp.C6-133-C6-137. �10.1051/jphyscol:1979627�. �jpa-00219043�
JOURNAL DE PHYSIQUE CoZZoque C6, suppl6ment au n06, tome 40, juin 1979, page C6-133
MEASUREMENTS OF THE D I S L O C A T I O N V E L O C I T I E S IN. S I L I C O N A. George
Laboratoire de Physique du ~ o ~ i d e ? ENSMIM, I n s t i t u t National PoZytechnique de Lorraine, Nancy, France.
Resume.- L ' i n f l u e n c e de l a temperature, de l a c o n t r a i n t e a p p l i q u e e e t du dopage s u r l e s v i t e s s e s des d i s l o c a t i o n s v i s e t 60' dans l e s i l i c i u m e s t resumee. La v i t e s s e des d i s l o c a t i o n s v i s f a i b l e c o n t r a i n t e e t l e s d i f f e r e n c e s de v i t e s s e s observees p o u r l e s deux d i s l o c a t i o n s a 60' d ' u n e demi bou- c l e s o n t presentees p l u s en d e t a i l .
A b s t r a c t . - The dependence o f t h e v e l o c i t i e s o f screw and 60" d i s l o c a t i o n s i n s i l i c o n upon temperatu- r e , s t r e s s and doping c o n c e n t r a t i o n i s reviewed. The v e l o c i t y o f screw d i s l o c a t i o n s a t l o w s t r e s s e s and t h e d i f f e r e n t v e l o c i t i e s observed f o r t h e two 60' d i s l o c a t i o n s o f a h a l f - l o o p a r e discussed i n some d e t a i 1.
1. I n t r o d u c t i o n . - The g l i d e v e l o c i t i e s o f screw and 60' d i s l o c a t i o n s i n s i l i c o n have been i n v e s t i g a t e d as a f u n c t i o n o f t h e temperature T, t h e r e s o l v e d s h e a r s t r e s s T, t h e c o n c e n t r a t i o n s o f i m p u r i t i e s o f group 111, Nca o r V, Rc3.
I s o l a t e d d i s l o c a t i o n h a l f - l o o p s were i n t r o d u - ced i n c r y s t a l s s u b j e c t e d t o r e p e a t e d t e n s i l e s t r e s - ses. D i s l o c a t i o n l o c a t i o n s were r e c o r d e d a f t e r each l o a d a p p l i c a t i o n by X-ray topographs t a k e n a t room t e m p e r a t u r e 11-31. S p e c i a l c a r e was necessary t o en- s u r e t h e s t r e s s homogeneity.
T h e o r e t i c a l aspects o f t h e d i s l o c a t i o n v e l o - c i t y i n semiconductors have been d i s c u s s e d i n o t h e r communications o f t h i s conference, t h e r e f o r e o n l y e x p e r i m e n t a l r e s u l t s and problems w i l l be erlphasized here. A b r i e f survey o f t h e r e s u l t s i s g i v e n f i r s t and t h e n more d e t a i l s a r e p r e s e n t e d on two " c r i t i c a l "
problems : i ) t h e v e l o c i t y o f screw d i s l o c a t i o n s a t v e r y l o w s t r e s s e s and i i ) t h e d i f f e r e n c e s i n t h e ve- l o c i t i e s o f t h e two 60' components o f a hexagonal h a l f - l o o p .
2. D i s l o c a t i o n v e l o c i t i e s i n i n t r i n s i c S i . - F i g u r e 1 shows t h e t e m p e r a t u r e dependence o f t h e v e l o c i t y o f screw and 60' d i s l o c a t i o n s f o r v a r i o u s s t r e s s e s . The b e h a v i o u r i s w e l l d e s c r i b e d by t h e l a w :
v(T,T) - C(T) exp(-Q/kT) ( 1
Relevant v a l u e s o f C and 0 a r e l i s t e d i n t a b l e I . F i g u r e 2 shows t h e s t r e s s dependence f o r v a r i o u s temperatures. It i s c l e a r t h a t a power l i k e depen- dence o f t h e v e l o c i t y on s t r e s s i s obeyed o n l y f o r
T > 6MN.m-'. F o r s m a l l e r s t r e s s e s t h e s t r e s s s e n s i t i - v i t y i s h i g h e r and s p e c i a l e f f e c t s appear a t v e r y
" t a b o r a t o i r e a s s o c i e au CNRS no 155
low s t r e s s e s as i t w i l l be seen l a t e r
F i g . 1 : v e l o c i t y s t r e s s e s 4. 6 l1N
Temperature dependence o f t h e d i s l o c a t i o n i n i n t r i n s i c S i , screw, o 60" d i s l o c a t i o n s . : 1.30 !lN.m-', 2. 19 1IN.m-', 3. 10 tl!J.m-Z .m-', 5. 4 ~ l N . m - ~ .
A comparison w i t h t h e r e s u l t s of o t h e r workers shows t h a t d e s p i t e t h e general agreement f o r t h e ac- t i v a t i o n e n e r g i e s o r s t r e s s exponents, t h e v e l o c i t i e s measured f o r g i v e n T and T can d i f f e r by a f a c t o r o f two i n d i f f e r e n t works.
When a f i t i s t r i e d of t h e e x p e r i m e n t a l p o i n t s t o t h e c u r r e n t t h e o r i e s o f d i s l o c a t i o n v e l o c i t y i n semi conductors, one encounters t h e we1 1 known d i f f i -
c u l t i e s /1,4/ : 1) when assuming t h e k i n k f o r m a t i o n r a t e t o be t h e c o n t r o l l i n g process, one must suppose t h e e x i s t e n c e o f weak and s t r o n g o b s t a c l e s ( s p a c i n g s 0.1 and 1 urn r e s p e c t i v e l y ) a l o n g t h e d i s l o c a t i o n l i n e ; 2) when assuming on t h e o t h e r hand t h a t t h e a n n i h i l a t i o n o f k i n k s c o n t r o l s t h e v e l o c i t y , w i d e l y spaced h i g h b a r r i e r s t o k i n k m i g r a t i o n have t o be supposed, as w e l l as a s t r o n g s t r e s s dependence o f
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979627
C 6 - 1 3 4 .JOURNAL DE PHYSIQUE
t h e d o u b l e k i n k f o r m a t i o n energy. Because o f t h e great number o f parameters e n t e r i n g t h e models such f i t s are n o t f e l t t o g r e a t l y c o n t r i b u t e t o a b e t t e r understan- d i n g o f t h e mechanism o f t h e d i s l o c a t i o n m o t i o n .
Table I
Doping I T I I c s I Qs ,
a t . c r 3 M N . ~ - ~ cm.s-' I eV : cm.s C50.1 , 960' ey
I 8 I
I
I 30 : 1.1 x l o 7 1 2.17 : 1.09 x l o 7 \ 2.16
I I I I I
0- I
I 19 1 8 . 2 x 1 0 6 : 2.19 1 1 . 8 3 x 1 0 7 : 2.22
I I I I
I - , I
I n t r i n s i c 1 10 : 6 . 2 x 1 0 6 1 2.22 : 1 . 6 5 x 1 0 7 : 2.28
I I 6 I I
I I -1
,
I 6 1 4 x l o 6 : 2.23 1 4.4 x l o 7 : 2.42
I I I I I
I I I I
I
I 4 : 7.3 x l o 5 : 2.17 1 2.17 x l o 7 : 2.43
I I I I I
I r
1.2 x l O l 8 P : 30 1 2.9 x l o 4 : 1.67 : 2.4 x l o 4 : 1.65
6 I I I
I I
1 . 4 ~ 1 0 ' ~ ~ : 30 , 1 5 . 3 x 1 0 3 : I I 1.41 : 1 . 6 3 x 1 0 4 : I I 1.50 2.7 x 1Ol7BI I 30 : I 9.3 x l o 7 I ! 2.34 I 7 . 1 x l o 7 : I 2.31
1
6.8 x 1Oi78: , 30 1 I 1.5 x l o 7 1 , 2.20 I 5.2 x l o 7 : I 2.29
V e n e r g i e s and p r e e x p o n e n t i a l f a c t o r s ( s e e t a b l e I ) .
(cm .s-l) D e t a i l e d measurements n o t shown h e r e p r o v e t h a t t h e d o p i n g e f f e c t vanishes a t temperatures g r e a t e r t h a n t h e ( d o p i n g dependent) t e m p e r a t u r e where t h e m a t e r i a l becomes i n t r i n s i c .
V(cm 5 . ' )
lo6-
710680650 610 580 5 0 520 710680650 610 580 550 520 'f ( 2 ) F i g . 3 : The e f f e c t o f d o p i n g on t h e temperature dependence o f 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 f o r T = 30 MN.m-'. F u l l symbols, screw, o en symbols, 60' d i s l o c a t i o n s . Doping : . 1.4 x 10" a t . c m - l phosphorous, A . 1.2 x 10" a t . ~ m - ~ phosphorous,
4 6 10 20 30 ( M N . ~ - ' ) V. 2.7 x 1017 a t . ~ m - ~ boron, m . 6.8 x 10'7at.cm-3
boron, d o t t e d l i n e , i n t r i n s i c S i . F i g . 2 : S t r e s s dependence o f t h e d i s l o c a t i o n v e l o -
c i t y i n i n t r i n s i c S i , screw, o 60' d i s l o c a t i o n .
Temperatures : 1. 710°C, 2. 550°C, 3. 580°C. p-doping has a s m a l l e r e f f e c t . F o r screw d i s - l o c a t i o n s , t h e small decrease o f t h e v e l o c i t y f o r 3. The e f f e c t o f n and p-doping on t h e d i s l o c a t i o n Nca = 2.7 x l o L 7 a t . ~ m - ~ B i s h a r d l y s i g n i f i c a n t due v e l o c i t i e s . - F i g u r e 3 shows t h e temperature depen- t o t h e e x p e r i m e n t a l u n c e r t a i n t y . F o r 60" d i s l o c a - dence o f t h e d i s l o c a t i o n v e l o c i t y f o r T = 30 MN.m-2 t i o n s , t h e e f f e c t i s more c l e a r . The v e l o c i t i e s f o r v a r i o u s c o n c e n t r a t i o n s o f phosphorous o r boron. measured f o r Nca = 2.7 x 1017 a t . ~ m - ~ B , a r e l o w e r n - d o p i n g i s seen t o i n c r e a s e t h e v e l o c i t y o f b o t h t h a n f o r Nca = 6.8 x 1017 at.cm-'0, which a r e i n screw and 60" d i s l o c a t i o n s . E q u a t i o n (I) can s t i l l t u r n l o w e r t h a n i n i n t r i n s i c S i . Thus a minimum ve- he t r + ~ r I t o f i t t h e r e s u l t s w i t h l o w e r a c t i v a t i o n l o c i t y s h o u l d e x i s t f o r some Nca < 6.8 x 10" a t . ~ m - ~ .
A . George C6-135
T h e r e f o r e these r e s u l t s appear t o be q u i t e compatible w i t h t h e i n c r e a s 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 r e p o r - t e d i n o t h e r works i n more h e a v i l y doped p-Si 16-8/.
The b e h a v i o u r o f 60" d i s l o c a t i o n s i n doped S i can be q u a n t i t a t i v e l y e x p l a i n e d by a model o f Haasen /9/ based on t h e i d e a t h a t t h e d o u b l e k i n k f o r m a t i o n energy i s lowered when t h e d i s l o c a t i o n i s charged, whatever t h e s i g n o f t h e charge. As t h e d i s l o c a t i o n charge depends on doping and o n l y v a n i s - hes i n p - S i /9/ t h e model can s u c c e s s f u l l y account f o r a minimum o f t h e d i s l o c a t i o n v e l o c i t y i n p-Si and an i n c r e a s e o f t h e v e l o c i t y w i t h t h e n-doping l e v e l . F o r screw d i s l o c a t i o n s t h e same model s h o u l d a p p l y b u t cannot be used a t t h e p r e s e n t t i m e as l o n g as 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 s e d i s l o c a t i o n s a r e n o t w e l l known.
4. C r i t i c a l problems.- 4.1. ~ e l g c f t j g ~ - g f - s c y e w - ~ ~ $ -
lgcatfgns-"-:smpll-s,tresse_s.- I n t h e s t r e s s range 4-6 M N . ~ - ~ , t h e s t r e s s s e n s i t i v i t y o f t h e d i s l o c a - t i o n v e l o c i t y i s observed ( F i g . 2 ) t o be h i g h e r t h a n f o r T > 6 MN.m-2. A c c o r d i n g t o p r e v i o u s measurements, a s t r e s s range w i t h a v e r y l o w s t r e s s s e n s i t i v i t y had been f o u n d f o r screw d i s l o c a t i o n s f r o m ' ~ 2 t o 4 MN.m-' /I/. I t was suggested t h e r e t h a t t h i s unex- p e c t e d b e h a v i o u r c o u l d depend on r e s i d u a l i m p u r i t i e s , as t h e c r y s t a l s c o n t a i n e d up t o 1016 a t . ~ m - ~ phospho- r o u s . New measurements f o r s t r e s s e s r a n g i n g f r o m 3 t o 6 MN.m" were performed t o l o o k f o r a p o s s i b l e e f f e c t o f t h e phosphorous c o n c e n t r a t i o n . As f i g u r e 4 shows, no e f f e c t c o u l d be found f o r c o n t e n t s r a n g i n g f r o m l o i 4 t o 1.2 x 10" at.cmw3 a t t h e t e s t tempera- t u r e o f 710°C ( w h i c h was enough t o a v o i d any d o p i n g e f f e c t ) . Consequently, t h e l o w s t r e s s behaviour can- n o t be a t t r i b u t e d t o phosphorous. I t may come f r o m a n o t h e r i m p u r i t y b u t m i g h t as w e l l be c h a r a c t e r i s t i c o f t h e b e h a v i o u r i n p u r e S i . M i l l e r / l o / argued t h a t 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 c o u l d account f o r i t . S i m i l a r measurements i n t h e l o w s t r e s s range f o r 60' d i s l o c a t i o n s were n o t r e t a i n e d because o f a d d i - t i o n a l d i f f i c u l t i e s t o be d e s c r i b e d now.
4.2. q n - $ h g _ y g l ~ c j t i e s _ p f f 6 _ g ~ - ~ i s l p c g t i p n s . - Vel o-
c i t y measurements were made w i t h h a l f - l o o p s h a v i n g one screw and two 60' segments. As r e p o r t e d previous- l y /1,3/ t h e two 60' d i s l o c a t i o n s have n o t t h e same behaviour. One o f them i s s u b j e c t e d t o " g l i d e u n s t a - b i l i t i e s 1 ' and p r o g r e s s i v e l y t u r n s t o a " z i g - z a g "
1 i n e c o n s i s t i n g o f smal l e r <110> components, These changes o f shape seem t o r e s u l t f r o m l o c a l i z e d changes o f t h e v e l o c i t y . A s t r i k i n g case i s shown i n f i g u r e 5. Topograph a was t a k e n a f t e r t h e nuelea- ti on o f ha1 f - l o o p s . yoPograph b a f t e r t h e appl i c a -
t i o n of r = 10 MN.m-2 a t 800°C d u r i n g 15s, w h i c h produced a r e g u l a r expansion of t h e loops, w i t h about equal v e l o c i t i e s f o r t h e two 60" segments. The subse- q u e n t a p p l i c a t i o n o f 19 M N . ~ - ' a t 580°C d u r i n g 60 min.
( t o p o g r a p h c ) a l s o moved r e g u l a r l y a l l t h e l o o p s w i t h t h e e x c e p t i o n o f t h a t marked b y an arrow. On t h i s h a l f - l o o p , a p a r t o f one o f t h e 60" segments moved w i t h a v e l o c i t y h i g h e r by 50% t h a n t h a t o f t h e r e - m a i n i n g p a r t s .
F i g . 4 : S t r e s s dependence o f t h e v e l o c i t y o f screw d i s l o c a t i o n s as a f u n c t i o n o f phosphorous c o n t e n t a t 710°C. C o n c e n t r a t i o n s i n a t . ~ r n - ~ : - loi4,
A - 1015, + - lo1=, v - 1017, a 1 . 2 x 1o18.
F i g . 5 : Change i n t h e v e l o c i t y . o f a 60' d i s l o c a t i o n (+) . See t e x t f o r d e t a i 1 s .
C6-136 JOURNAL I)E PHYSIQUE
I t must be s t r e s s e d t h a t t h e s l o w e r p a r t s o f t h i s segment moved w i t h t h e same v e l o c i t y as t h e second 60" segment o f t h e h a l f - l o o p . I t means t h a t t h e observed change was n o t t h e r e s u l t o f a p i n n i n g process b u t o f a l o c a l i z e d enhancement o f t h e v e l o - c i t y .
Even i f o n l y r e g u l a r l y shaped l o o p s a r e con- s i d e r e d , t h e v e l o c i t i e s o f t h e two 60" segments can d i f f e r and i t i s d i f f i c u l t t o measure them s e p a r a t e -
l y s i n c e t h e y a r e n o t we11 r e p r o d u c i b l e : I n a g i v e n t e s t a g i v e n 60" segment may have a v e l o c i t y equal w i t h i n 10% t o t h a t o f t h e o t h e r 60" segment o f t h e same h a l f - l o o p and n e v e r t h e l e s s have i t s v e l o c i t y i n c r e a s e d by 40% i n a f u r t h e r t e s t conducted a t t h e same t e m p e r a t u r e and s t r e s s .
The v e l o c i t y o f t h e 60" d i s l o c a t i o n s m i g h t be i n f l u e n c e d by t h e t h e r m a l c y c l i n g s t o which t h e spe- cimen i s s u b j e c t e d as shown i n t h e f o l l o w i n g exam- p l e : f i g u r e 6 p r e s e n t s t h r e e s t e p s o f t h e expansion o f h a l f - l o o p s b e l o n g i n g t o two s l i p systems.
r i m e n t a l u n c e r t a i n t y . A new t e s t i n v e r y s i m i l a r c o n d i t i o n s , T = 650°C, T = 10 MP4.m-2 a p p l i e d 20 min.
b u t a f t e r a two hours a n n e a l i n g a t t h e t e s t tempe- r a t u r e , produced a d i s t u r b a n c e on t h e 60' segment a t t h e r i g h t s i d e o f t h e h a l f - l o o p s ( t o p o g r a p h c ) . A k i n k BC appeared on t h a t segment ( F i g . 6d) and t h e p a r t AB moved 10% f a s t e r t h a n t h e p a r t CD and t h e o t h e r 60" segment. I t may be n o t i c e d t h a t t h e p a r t CD was c r e a t e d b y t h e g l i d e o f t h e screw segment and d i d n o t e x i s t d u r i n g t h e a n n e a l i n g . I n t h i s case, i t i s l i k e l y t h a t a n n e a l i n g was r e s p o n s i b l e f o r t h e observed change, b u t a p o s s i b l e e f f e c t o f coo- l i n g and h e a t i n g cannot be e x c l u d e d i n t h e general case.
These o b s e r v a t i o n s r a i s e t h e q u e s t i o n o f how t o measure r e p r o d u c i b l e v e l o c i t i e s o f 60" d i s l o c a - t i o n s . I n 5 1 and 2 , an average v e l o c i t y o f t h e two 60" segments o f r e g u l a r h a l f - l o o p s was g i v e n . I t would be b e t t e r t o measure t h e v e l o c i t y o f each 60"
segment i n c o n d i t i o n s such t h a t t h i s v e l o c i t y i s c o n s t a n t . A p r e l i m i n a r y e x p e r i m e n t was conducted t o see whether t h e v e l o c i t i e s would be more s t a b l e f o r l o o p s k e p t a t c o n s t a n t temperature. T h i s i m p l i e s t h a t X-ray topographs a r e t a k e n a t t h e t e s t tempera- t u r e . A h i g h temperature d e f o r m a t i o n s t a g e was t h e n adapted t o a Lang camera. The specimen was k e p t a t 710°C. D i s l o c a t i o n s were i n t r o d u c e d by a p p l y i n g
C
6P 19 HN.m-' d u r i n g 2 rniitn. and moved s e v e r a l t i m e s i n
9 t h e same c o n d i t i o n s . Between two l o a d a p p l i c a t i o n s ,
1;;;". a topograph was t a k e n i n a 10 min. exposure t i m e .
$2 The expanding l o o p s were observed t o r e t a i n a r e g u -
d -
" A
a b c 2 5 0 r n l a r shape and each segment moved w i t h a r e m a r k a b l y
F i g . 6 : E f f e c t o f thermal c y c l i n g and a n n e a l i n g on t h e v e l o c i t y o f 60" d i s l o c a t i o n s . See t e x t f o r d e t a i l s .
O n l y t h e l a r g e s t l o o p s w i l l be c o n s i d e r e d here, which have a B u r g e r s v e c t o r p a r a l l e l t o t h e c r y s t a l s u r f a c e . They were c r e a t e d a t 650°C b y t h e a p p l i c a - t i o n o f 25 MN.m-2 d u r i n g 3 min. (topograph a ) . A p p l y i n g 10 M?4.6i7-2 a t 650°C d u r i n g 30 min. w i t h a b r i e f a n n e a l i n g o f 15 min. a t t h e t e s t temnerature before s t r e s s a p p l i c a t i o n r e s u l t e d i n a r e g u l a r m o t i o n o f t h e l o o p s ( t o p o g r a p h b ) . The two 60" seg- ments moved w i t h equal v e l o c i t i e s w i t h i n t h e expe-
c o n s t a n t v e l o c i t y . The r e l a t i v e v e l o c i t i e s o f t h e t h r e e segments were : screw 1, 6Ool10 1.1, 6 0 ° 0 i 7 1 . 5 ( s l i p system (111) t e n s i l e a x i s [ _ I z ~ ) .
F u r t h e r s i m i l a r experiments a t d i f f e r e n t s t r e s s e s and t e m p e r a t u r e w i l l be conducted i n t h e f u t u r e u s i n g t h e s y n c h r o t r o n r a d i a t i o n o f LURE (Orsay) which w i l l reduce t h e exposure t i m e t o a few seconds.
Two reasons were f o u n d t o e x p l a i n t h e d i f f e - r e n t b e h a v i o u r o f t h e two 60' segments o f a g i v e n h a l f - l o o p : 1) t h e d i f f e r e n t o r d e r o f t h e p a r t i a l d i s l o c a t i o n s , 2) t h e d i f f e r e n c e i n t h e a p p l i e d f o r - ces normal t o t h e s l i p p l a n e ( c l i m b f o r c e s ) . The d i f f e r e n t o r d e r o f p a r t i a l d i s l o c a t i o n s can e x p l a i n d i f f e r e n t v e l o c i t i e s , as demonstrated by Wessel and Alexander /11/, b u t does n o t e x p l a i n t h e v e l o c i t y changes o c c u r i n g on one g i v e n 60" segment. These changes c o u l d be due t o some changes i n t h e c o r e s t r u c t u r e , which themselves c o u l d r e s u l t o f a c l i m b mechanism.
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