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MEASUREMENTS OF THE DISLOCATIONVELOCITIES IN SILICON

A. George

To cite this version:A. George. MEASUREMENTS OF THE DISLOCATION VELOCITIES IN SILICON. Journal dePhysique Colloques, 1979, 40 (C6), pp.C6-133-C6-137. �10.1051/jphyscol:1979627�. �jpa-00219043�

https://hal.archives-ouvertes.fr/jpa-00219043https://hal.archives-ouvertes.fr

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 app l iquee 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 pour l e s deux d i s l o c a t i o n s a 60' d 'une demi bou- c l e sont presentees p l u s en d e t a i l .

Abs t rac 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 concen t ra t i on 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 ow s t resses 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 reso l ved

shear s t r e s s T, t h e concen t ra t i ons 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 sub jec ted t o repeated 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 recorded a f t e r each

l oad a p p l i c a t i o n by X-ray topographs taken a t room

temperature 11-31. Spec ia l c a r e was necessary t o en-

sure t he s t r e s s homogeneity.

T h e o r e t i c a l aspects o f t he d i s l o c a t i o n ve lo -

c i t y i n semiconductors have been d iscussed 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

exper imenta 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 ven f i r s t

and then more d e t a i l s a r e presented 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 ow s t resses 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 igu re 1

shows t h e temperature 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 va r i ous s t resses . The

behav iour i s w e l l descr ibed by t he l aw :

v(T,T) - C(T) exp(-Q/kT) ( 1 Relevant va lues 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 va r i ous

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-'. Fo r sma l l e r s t resses 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 spec ia l e f f e c t s appear a t ve ry

" t a b o r a t o i r e assoc ie au CNRS no 155

low s t resses as i t w i l l be seen l a t e r

F ig . 1 : v e l o c i t y s t resses 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 energ ies o r s t r e s s exponents, t he v e l o c i t i e s

measured f o r g i ven 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 exper imenta 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 the k i n k f o rma t i on

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 ex i s tence o f weak and s t rong obs tac les (spac ings

0.1 and 1 urn r e s p e c t i v e l y ) a l ong t h e d i s l o c a t i o n l i n e ; 2) when assuming on the 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

http://www.edpsciences.orghttp://dx.doi.org/10.1051/jphyscol:1979627

C 6 - 1 3 4 .JOURNAL DE PHYSIQUE

t h e doub le k i n k f o rma t i on 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 mot ion .

Table I

Doping I T I c s I Qs , I a t . c r 3 M N . ~ - ~ cm.s-' I C50.1 960' ey eV : cm.s ,

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 lO l8P : 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 : 1.41 : 1 . 6 3 x 1 0 4 : 1.50 , I I I I 2.7 x 1Ol7BI 30 : 9.3 x l o 7 ! 2.34 7 . 1 x l o 7 : 2.31

I I I I I 1

6.8 x 1Oi78: 30 1 1.5 x l o 7 1 2.20 5.2 x l o 7 : 2.29 , I , I I

V energ ies and p reexponen t i a l f a c t o r s (see t a b l e I ) . (cm .s-l) D e t a i l e d measurements n o t shown here prove t h a t t h e

dop ing e f f e c t vanishes a t temperatures g r e a t e r than

t h e (dop ing dependent) temperature 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 50 520 710680650 610 580 550 520 'f (2)

F i g . 3 : The e f f e c t o f dop ing 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 . cm- 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 ress dependence o f t h e d i s l o c a t i o n ve lo - 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 sma l l e r e f f e c t . Fo r screw d i s -

l o c a t i o n s , t h e smal l 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 the 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 exper imenta l u n c e r t a i n t y . For 60" d i s l o c a -

dence o f the 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 concen t ra t i ons o f phosphorous o r boron. measured f o r Nca = 2.7 x 1017 a t . ~ m - ~ B , a r e lower

n-dop ing i s seen t o i nc rease t h e v e l o c i t y o f bo th than 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 . Equat ion (I) can s t i l l t u r n lower t han 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 lower a c t i v a t i o n l o c i t y shou ld e x i s t f o r some Nca < 6.8 x 10" a t . ~ m - ~ .

A. George C6-135

There fore 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 nc rease o f t h e d i s l o c a t i o n v e l o c i t y repo 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 behav iour 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 exp la ined by a model o f

Haasen /9/ based on t h e i d e a t h a t t he doub le k i n k

f o rma t i on 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 he 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 van 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 he 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 nc rease o f t he 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 the same model shou ld

app l y b u t cannot be used a t t h e p resen t t ime 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 these 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 he 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 ig . 2 ) t o be h i g h e r than

f o r T > 6 MN.m-2. Accord ing t o p rev ious 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 found f o r screw d i s l o c a t i o n s f rom ' ~ 2 t o

4 MN.m-' /I/. It was suggested t h e r e t h a t t h i s unex-

pected behav iour cou ld depend on r e s i d u a l i m p u r i t i e s ,

as the c r y s t a l s conta ined up t o 1016 a t . ~ m - ~ phospho-

rous. New measurements f o r s t resses rang ing f rom 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 concen t ra t i on . As f i g u r e 4

shows, no e f f e c t cou ld be found f o r con ten ts rang ing

f rom 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 (wh ich was enough t o a v o i d any dop ing

e f f e c t ) . Consequently, t h e l ow 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 rom

another i m p u r i t y b u t m igh 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 behav iour i n pu re 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 cou ld account f o r

it. S i m i l a r measurements i n t h e low 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 add i -

t i o n a l d i f f i c u l t i e s t o be descr ibed 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 hav ing

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 he same

behaviour. One o f them i s sub jec ted t o " g l i d e unsta-

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 ig -zag" 1 i n e c o n s i s t i n g o f smal l e r components, These

changes o f shape seem t o r e s u l t f rom 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 taken 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, wh ich

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-

quent a p p l i c a t i o n o f 19 MN.~ - ' a t 580°C d u r i n g 60 min.

( topograph c) a l s o moved r e g u l a r l y a l l t h e l oops w i t h

t h e excep t i on o f t h a t marked by 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 ighe r by 50% than t h a t o f t h e r e -

main ing 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 con ten t a t 710°C. Concent ra t ions 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 ressed t h a t t h e s lower 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 . It means t h a t t h e

observed change was n o t t he 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 ve lo -

c i t y .

Even i f o n l y r e g u l a r l y shaped l oops a r e con-

s idered, 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 separa te-

l y s i n c e they a r e n o t we11 r e p r o d u c i b l e : I n a g i ven

t e s t a g i ven 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 neve r the less have i t s v e l o c i t y

increased by 40% i n a f u r t h e r t e s t conducted a t t h e

same temperature 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 igh t be

i n f l u e n c e d by t he thermal c y c l i n g s t o which t h e spe-

cimen i s sub jec ted 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 presen ts t h r e e s teps o f t h e expansion

o f h a l f - l o o p s be long ing 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 annea l ing a t t h e t e s t tempe-

r a t u r e , produced a d i s tu rbance 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 ( topograph 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 han the p a r t CD and t h e

o t h e r 60" segment. It may be n o t i c e d t h a t t h e p a r t

CD was c rea ted b y t he g l i d e o f t he screw segment

and d i d n o t e x i s t d u r i n g t h e annea l ing . I n t h i s

case, i t i s l i k e l y t h a t annea l ing 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 exc luded i n t h e general

case.

These obse rva t i ons r a i s e t he ques t i on 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 he two 60" segments o f r e g u l a r h a l f - l o o p s was g iven. I t

would be b e t t e r t o measure the 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

cons tan t . A p r e l i m i n a r y exper iment 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 oops k e p t a t cons tan t temperature. Th i s i m p l i e s

t h a t X-ray topographs a r e taken a t the t e s t tempera-

t u r e . A h i g h temperature de fo rma t i on s tage was then

adapted t o a Lang camera. The specimen was kep 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 seve ra l t imes 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 taken i n a 10 min. exposure t ime.

$2 The expanding loops were observed t o r e t a i n a regu- d-" A

a b c 250rn l a r shape and each segment moved w i t h a remarkab ly

F ig . 6 : E f f e c t o f thermal c y c l i n g and annea l i ng on the 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 .

On ly t h e l a r g e s t loops w i l l be cons idered here,

which have a Burgers 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

su r face . They were c rea ted a t 650°C by 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 annea l i ng 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

mot ion o f t h e loops ( topograph 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-

cons tan 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, 60°0i7 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 exper iments a t d i f f e r e n t

s t resses and temperature w i l l be conducted i n t he

f u t u r e u s i n g t h e synch ro t ron r a d i a t i o n o f LURE

(Orsay) which w i l l reduce t h e exposure t ime t o a few

seconds.

Two reasons were found t o e x p l a i n t h e d i f f e -

r e n t behav iour o f t h e two 60' segments o f a g i ven

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 he s l i p p lane ( 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 occu r i ng on one g i ven 60" segment. These

changes c o u l d be due t o some changes i n t he core

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.

References

/1/ George, A . , Escaravage, C . , Champier, G . , S c h r o t e r N., Phys. S t a t u s S o l i d i ( b ) 2 (1972) 483.

/2/ George, A . , Escaravage, C . , S c h r o t e r , W . , Champier, G . , C rys t . L a t t i c e Defects - 4 (19731 29.

/3/ George, A . , ThPse d l E t a t (1977) Nancy. /4/ Rybin, V . V . , Orlov, A . N . , Sov. Phys .So l id S t a t e , 11

(1970) 2635.

/5/ George, A . , Champier, G . , Phys. S t a t u s S o l i d i ( a ) ( t o be pub l i shed ) .

/6/ Erofeev, V . N . , Niki tenko, V.I . , Osvenski i , V . B . , Phys. S t a t u s S o l i d i 2 (1969) 79.

/7/ P a t e l , J .R., T e s t a r d i , L.R., Free land, P.E. , Phys. Rev. B - 13 (1976) 3548.

/8/ Kul k a r n i , S.B., ! l i l l i ams , W.S., J . Appl. Phys. 47 (1976) 4318.

/9/ Haasen, P . , Phys. S t a t u s S o l i d i ( a ) (1975) 145.

/ l o / MBller, H.J., Acta Metal 1 . - 26 (1978) 963. /11/ Wessel, K . , Alexander, ti., P h i l o s Mag. 35 (1978)

1523.