PLASTIC DEFORMATION OF SILICON AT LOW TEMPERATURE AND THE INFLUENCE OF DOPING

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TEMPERATURE AND THE INFLUENCE OF DOPING

J. Rabier, P. Veyssière, J. Demenet

To cite this version:

J. Rabier, P. Veyssière, J. Demenet. PLASTIC DEFORMATION OF SILICON AT LOW TEM-

PERATURE AND THE INFLUENCE OF DOPING. Journal de Physique Colloques, 1983, 44 (C4),

pp.C4-243-C4-253. �10.1051/jphyscol:1983429�. �jpa-00223048�

JOURNAL DE PHYSIQUE

Colloque C4, supplément au n°9, Tome 44, septembre 1983 page C4-243

PLASTIC DEFORMATION OF SILICON AT LOW TEMPERATURE AND THE INFLUENCE OF DOPING

J. Rabier, P. Veyssiere and J.L. Demenet

Labovatoire de Metalluvgie Physique, L.A, 131 au C.N.R.S., Faaulte des Soienees, 86022 Poitiers, France

Résumé ; Des essais de déformation plastique ont été effectués à basse tem- pérature (T<450°C) sous pression de confinement pour obtenir un glissement

des dislocations à des températures où le silicium est habituellement fragile.

Un mécanisme de déformation plastique par dislocations partielles a été mis en évidence ainsi que l'influence du dopage sur la déformation plastique ma- croscopique. Le désaccord entre le comportement plastique sous pression de confinement et des essais conventionnels réalisés dans le domaine des tempé- ratures moyennes (400°C < T < 650°C) est discuté.

Abstract : Plastic deformation tests have been performed at low temperature (T<450 C) under a confining pressure in order to promote dislocation motion at temperature where samples are usually brittle. A mechanism for plastic deformation by partial dislocations has been evidenced as well as the in- fluence of dopants on the macroscopic plastic deformation. Discrepancies between low temperature plastic deformation under confining pressure and con- ventional compressive tests conducted in the range of medium temperatures

(400°C < T < 650°C) are discussed.

INTRODUCTION

Macroscopic plastic deformation of silicon has been investigated at low tempera- ture with the view of studying*.

i) High stresses deformation mechanisms

ii) The effect of dopants on the macroscopic plasticity : this effect is expec- ted to increase when the temperature decreases (1).

iii) The effects of the decrease of point defects mobilities on the plastic pro- perties .'Point defects are expected to control the glide mechanism through the glide of dislocation associated with point defects rows (2). Furthermore a tran- sition has been evidenced from EPR measurements in the structure of dislocation at 750°C (see ref. 2 ) .

Plastic deformation of silicon at temperature below 700°C is difficult to achieve using standart compression apparatus. Only microhardness testshave been performed at temperatures as low as room temperature (3), but it is difficult to derive quantitative data from this kind of test. In order to obtain data on lower yield stress and activation parameters in the temperature range 300-700°C ,.two techniques of deformation have been used in the present study :

- compression under a confining pressure which prevents samples from failing in a temperature range where silicon is usually brittle.

- compression, after a pre-straining at higher temperature, in a standart machine with strong alumina jigs.

I - PLASTIC DEFORMATION OF SILICON UNDER A CONFINING PRESSURE (T < 450"C).

In a previous paper (.4) it has been shown that it is possible to achieve macrosco- pic plastic deformation of silicon single crystals in the temperature range 3OO°C-450°C provided an hydrostatic pressure is superimposed on the sample. This

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983429

t e c h n i q u e (Grigg device) used f o r g e o l o g i c a l a p p l i c a t i o n s p r e v e n t s c r a c k s from c r e a - t i n g and propagating a t temperatures where t h e samples a r e u s u a l l y b r i t t l e .

S i n g l e c r y s t a l s w i t h <loo> o r i e n t a t i o n a x i s were deformed down t o 300°C a t 2.10-6s-1 under a c o n f i n i n g p r e s s u r e of 1.5 GPa. C o n s i s t e n t with t h e o r d e r of magnitude of t h e flow s t r e s s (U > 600 MPa) a new mechanism of deformation was s u g g e s t e d t o c o n t r o l t h e p l a s t i c p r o p e r t i e s of s i l i c o n i n t h i s temperature r a n g e , i . e . : p l a s t i c deformation by i n d i v i d u a l p a r t i a l d i s l o c a t i o n s .

I n o r d e r t o a s c e r t a i n t h i s mechanism s i n g l e c r y s t a l s o r i e n t e d f o r s i n g l e s l i p ( <123> o r i e n t a t i o n ) were deformed i n t h e p r e s e n t s t u d y . The e f f e c t of o r i e n t a - t i o n on p l a s t i c i t y ( < l o o > , < l l O > 0 r i e n t a t i o n s ) a s w e l l a s t h e deformation s u b s t r u c - t u r e were examined. The e f f e c t o f dopants on t h e p l a s t i c p r o p e r t i e s was a l s o i n v e s t i g a t e d .

I . a

-

-5 -1 S i n g l g s f y s t a l s of s i l i c o n were deformed a t c o n s t a n t s t r a i n r a t e s (2.10 s and 2.10 s ) between 275OC and 450°C i n a Griggs anparatus.The s o l i d c o n f i n i n g me- dium used a s p r e s s u r e t r a n s m i t t e r was NaC1, t h e p a r a l l e l i p i p e d i c samples were ja-

cketed i n s i l v e r . I n t h e t e m p e r a t u r e range where t h e s a m p l e s were s t r a i n e d d i f f u - s i o n of s i l v e r i n t o s i l i c o n d u r i n g an experiment i s n e g l i g i b l e . F u r t h e r e x p e r i - mental d e t a i l s a r e given i n r e f . ( 4 ) .

-

G o types of samples were used i n t h i s s t u d y : i n t r i n s i c (n = 1013 and P doped S i (n = 10'' ~ m - ~ ) . The two s e t s of c r y s t a l s were grown by t h e FZ method.

These k i n d s of sample were choosen s i n c e t h e y e x h i b i t t h e extreme r a t i o of d i s l o - c a t i o n v e l o c i t i e s a s p r e v i o u s l y shown by measurement of i n d i v i d u a l d i s l o c a t i o n v e l o c i t i e s a s a f u n c t i o n of doping ( 1 ) . These samples remain i n t r i n s i c and e x t r i m - s i c r e s p e c t i v e l y i n t h e whole r a n g e of i n v e s t i g a t e d t e m p e r a t u r e s .

P a r a l l e l i p i p e d s w i t h <123>, < l o o > and <110> compression a x i s were cutfrorn t h e s e boules

.

The samples were p r e - s t r a i n e d a t a t e m p e r a t u r e of 400-450°C. This procedure e l i - minates y i e l d i n g and e n a b l e s us t o measure flow s t r e s s a t t e m p e r a t u r e s where t h e samples would have u n d e r g o n e f r a c t u r e a t s t r e s s l e v e l s between t h e lower and t h e upper y i e l d p o i n t s .

1.b - R e s u l t s .

Lower y i e l d s t r e s s a s a f u n c t i o n of t h e o r i e n t a t i o n .

The o r i e n t a t i o n dependence on t h e m a c r o s c o p ~ c ~ l a s t i c i t y was checked f o r t h e o r i e n t a t i o n s ' < l 2 3 >

,

,

The engineering s t r e s s e s o b t a i n e d a t t h e lower y i e l d p o i n t (LYP) a r e r e p o r t e d i n f i g . 1 .

F o r t h e two s t r a i n - r a t e s t h e LY s t r e s s e s a r e n e a r l y e q u a l f o r t h e t h r e e d i f f e r e n t o r i e n t a t i o n s i n t h e whole range of t e m p e r a t u r e . These r e s u l t s have t o be compared w i t h t h o s e o b t a i n e d by O m r i (5) a t h i g h e r t e m p e r a t u r e where p l a s t i c deformation i s induced by t h e g l i d e of p e r f e c t d i s l o c a t i o n s with-a/2 <110> Burgers v e s t o r . Indeed t h e Schmid f a c t o r s f o r t h e g l i d e systems a / 2 <110> ( 1 11) and a16 < I 12>{-1?1}

have d i f f e r e n t v a l u e s a s a f u n c t i o n of t h e o r i e n t a t i o n . The t a b l e 1 shows t h e ob- t a i n e d e n g i n e e r i n g s t r e s s e s a t t h e lower y i e l d p o i n t f o r h i g h temperature t e s t s and t e s t s r e p o r t e d h e r e .

Comparison of t h e s e d a t a shows a d i f f e r e n t behaviour a s a f u n c t i o n of t h e o r i e n t a - t i o n f o r low t e m p e r a t u r e and high t e m p e r a t u r e deformation. This i s c o n s i s t e n t w i t h a d i f f e r e n t deformation mechanism below 600°C. Schmid f a c t o r s on t h e p a r t i a l s d i s - l o c a t i o n a s a f u n c t i o n of t h e s t r e s s a x i s were c a l c u l a t e d . I t appears t h a t i n t h e t h r e e o r i e n t a t i o n s one of t h e p a r t i a l undergoes t h e same r e s o l v e d s h e a r s t r e s s i n t h e g l i d e p l a n e which i s c o n s i s t e n t w i t h t h e f a c t t h a t t h e e n g i n e e r i n g s t r e s s a t 400°C i s n e a r l y c o n s t a n t f o r <123>

,

F i g . 1 :

Lower yield s t r e s s uvs T f o r i n t r i n s i c S i depending on t h e o r i e n t a t i o n

-6 - 1

( a ) ;= 2 - 1 0 s

b -5 - I

(b) E= 2.10 s

3 00 4 00

500

compression a x i s

j 1

: ULY MFs

19. 6 36. 6 29.3

.

: oLY MPa

691 : 646 713 ^' 121'

TABLE I 0.47

.

-.

. C h a r a c t e r of t h e :

.

.

.

1

~ n t i - i n s i c 0.336 a

.

.

f a u l t

-6 - 1 -6 - 1

117 LY s t r e s s a t 750°C, ;= 6.10 s ( 5 ) ; / 2 / LY s t r e s s a t 400°C, ;= 2.10 s ( t h i s work).

SFT:Sehmid f a c t o r on t h e t r a i l i n g p a r t i a l ; SFL : Schmid f a c t o r on t h e i e a d i n g p a r t i a l .

/3/ : S t a c k i n g f a u l t c h a r a c t e r when t h e more s t r e s s e d p r o p a g a t s independently from t h e o t h e r ; / 4 / : S t r e s s a p p l i e d on t h e p a r t i a l d i s l o c a t i o n t h a t c r e a t e s i n t r i n s i c s t a c k i n g f a u l t by p r o p a g a t i n g .

s h e a r s t r e s s e s a c t i n g on t h e i n d i v i d u a l p a r t i a l d i s l o c a t i o n s of a d i s s o c i a t e d Schockley p a i r a r e s i g n i f i c a n t l y d i f f e r e n t . S t a r t i n g w i t h a d i s s o c i a t e d configura- t i o n with an i n t r i n s i c s t a c k i n g f a u l t (which i s u s u a l l y observed i n S i ) t h e s h e a r s t r e s s a c t i n g on t h e t r a i L i n g p a r t i a l i s g r e a t e r t h a n f o r t h e l e a d i n g one i n t h e

< 123> and <110> o r i e n t a t i o n . I f t h e d e f o r m a t i o n proceeded through t h e p a r t i a l d i s - l o c a t i o n which undergoes t h e h i g h e r s t r e s s , t h e n a t u r e of t h e s t a c k i n g f a u l t s h o u l d be d i f f e r e n t , i . e . : e x t r i n s i c f o r <123> and <110>,and i n t r i n s i c f o r < l o o > . F u r t h e r - more t o b e c o n s i s t e n t w i t h t h e e n g i n e e r i n g s t r e s s e s , t h e s e p a r t i a l s o f diPEerent na- t u r e have t o overcome f r i c t i o n s t r e s s ^T from t h e l a t t i c e of t h e same o r d e r of ma- g n i t u d e OLY = Ta

-

0 ' a

with t h e r e s u l t s of Wessel and Alexander ( 6 ) and h a s t o b e checked a t a microsco- p i c s c a l e .

Analysis of a c t i v a t i o n p a r a m e t e r s .

I n t h i s l i m i t e d range of t e m p e r a t u r e b o t h t h e u s u a l Arrhenius law :

as w e l l as t h e phenomenological e q u a t i o n :

n

Q

y = T exp

-

kT

f i t t h e d a t a o b t a i n e d f o r t h e t h r e e o r i e n t a t i o n s . Law / 1 / a p p l i e s w i t h an a c t i - v a t i o n volume vicrl/-r ( s e e f i g . 1 and r e f . ( 4 ) ) a s w e l l a s law /2/ with Q/n = 0.4eV deduced from t h e s l o p e of h~ v e r s u s 1/T ( F i g . 2 ) .

Fig.

-- 2

-

D i s l o c a t i o n v e l o c i t i e s have been measured r e c e n t l y i n a range of t e m p e r a t u r e and s t r e s s c l o s e t o o u r experiments(325'c < T < 420°c, T 'L 300 MPa) ( 7 ) ( 8 ) . These d i s l o c a t i o n - v e l o c i t i e s were determined by t h e double e t c h i n g hechnique o n i n t r i n s i c s i l i c o n compressed a l o n g <123> a f t e r i n t r o d u c i n g d i s l o c a t i o n s a t 650'6. These experiments expressed as :

= exp - Q / ~ T / 3/

y i e l d an a p p a r e n t a c t i v a t i o n energy Q = 1.82 eV (7) and a s t r e s s exponent m 2 2 (8)

.

A v a l u e n - 4 can b e deduced from o u r a c t i v a t i o n volumes ( s t r e s s r e l a x a t i o n and s t r a i n - r a t e jumps) t h i s g i v e s an a c t i v a t i o n energy Q = 1.6 eV deduceti from f i g u r e 2. Our a p p a r e n t a c t i v a t i o n energy a s w e l l as t h e s t r e s s exponent (n = m + 2) a g r e e w i t h t h o s e of d i s l o c a t i o n v e l o c i t y a t high s t r e s s e s and low t e m p e r a t u r e s .

I n a high t e m p e r a t u r e and low s t r e s s (10-30 )Pa) ranpe, Yonenaga el: Sumino ( 9 ) using a same a n a l y s i s found a l s o a good f i t with d i s l o c a t i o n v e l o c i t y measure- ments i n t h e same t e m p e r a t u r e range i . e . n = 3 (m = 1 ) and Q = 2.4 eV, which i s q u i t e d i f f e r e n t from t h e low temperature a c t i v a t i o n p a r a m e t e r s .

Comparison of ; d i s l o c a t i o n v e l o c i t y measurements as w e l l a s t h e a c t i v a t i o n para- meters f o r p l a s t i c d e f o r m a t i o n s u g g e s t t h a t a d i f f e r e n t d i s l o c a t i o n mechanism con- t r o l the low t e m p e r a t u r e p l a s t i c deformation i n s i l i c o n .

Microscopic o b s e r v a t i o n s :

A t a m i c r o s c o p i c s c a l e , t h e deformation i s c h a r a c t e r i z e d by t h e u s u a l C 11 1 ) g l i d e planes.iIowever, a f t e r h i g h s t r a i n s e t c h i n g of t h e l a t e r a l s u r f a c e s r e v e a l s twinning which s u p p o r t s t h e i d e a t h a t g l i d e o p e r a t e s by p a r t i a l d i s l o c a t i o n s (Fig. 3).

F i g . 3 :

E t c h i n g of ( 1 11) f a c e (sample w i t h < 123> compres- s i o n a x i s T = 550°C,

-5 -1

€ = 2.10 s ) .

A t t h e TEM s c a l e , t h e deformation s u b s t r u c t u r e shows extended s t a c k i n g f a u l t s and microtwins ( 4 ) . A sample deformed i n s i n g l e s l i p up t o t h e UY p o i n t has been c u t p a r a l l e l t o t h e primary g l i d e plane. The deformation s u b s t r u c t u r e i s heteroge- neous and i s c h a r a c t e r i z e d by .abundant s t a c k i n g f a u l t s . However, t h e nuclea- t i o n of t h e s e s t a c k i n g f a u l k can b e s e e n from p e r f e c t d i s l o c a t i o n s (Fig. 4 ) . The observed d i s s o c i a t i o n w i d t h s a r e s c a t t e r e d . Even f o r t h e same d i s l o c a t i o n segment t h e d i s s o c i a t i o n w i d t h is n o t c o n s t a n t a l l a l o n g t h e d i s l o c a t i o n l i n e

( s e e f i g . 4a). When t h e d i s l o c a t i o n i s widely d i s s o c i a t e d , t h e p a r t i a l d i s l o c a - t i o n s a r e confined t o <110> d i r e c t i o n s i n t h e i r g l i d e p l a n e l i k e t h e p e r f e c t d i s l o c a t i o n s . Rather t h a n e x c e p t i o n " t h e noses" found by Wessel and Alexander ( 6 ) a r e t h e r u l e ( s e e f i g . 4b) : one of t h e p a r t i a l d i s l o c a t i o n seems t o b e pinned s t r o n g l y by sbme l o c a l o b s t a c l e s . I n t h e s e experiment, t h e n a t u r e of t h e s t a c k i n g f a u l t h a s n o t been determined y e t .

( a ) F o i l p l a n e ( 1 10) (2) F o i l ? l a n e ( 1 11)

a ) V a r i a t i o n of t h e d i s s o c i a t i o n width o n t h e same d i s l o c a t i o n segments : one of t h e p a r t i a l d i s l o c a t i o n i s o u t of c o n t r a s t .

b) Important d e n s i t y of "noses".

c ) Extended s t a c k i n g f a u l t s .

( c ) F o i l p l a n e (! 10)

F i g u r e s 4 : I n t r i n s i c S i a e f o r m e d i n s i n g l e s l i p up t o t h e UY p o i n t a t 425OC,

,

.

A l l t h e s e observations a r e c o n s i s t e n t w i t h a mechanism of deformation c o n t r o l l e d by g l i d e of u n c o r r e l a t e d p a r t i a l d i s l o c a t i o n s . Indeed t h e t h e o r 6 t i c a l s t r e s s

= I

Tie e f f e c t of doping on mechanical p r o p e r t i e s .

The i n f l u e n c e of doping on 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 i s w e l l e s t a b l i s h e d . I n d i v i d u a l d i s l o c a t i o n v e l o c i t i e s were measured by d i f f e r e n t methods ( e t c h i n g , Lang

topography). It h a s been shown t h a t t h e d i s l o c a t i o n v e l o c i t y i s enhanced f o r n type s i l i c o n ( 5 2 0 ' ~ < T < 750°C) ( 1 ) . T h i s e f f e c t i s a s c r i b e d t o t h e i n f l u e n c e of l i n e charge on t h e g e n e r a t i o n of double k i n k $ o r t o t h e k i n k s m o b i l i t i e s (13).

The e f f e c t of dopkng on t h e d i s l o c a t i o n v e l o c i t i e s i s g r e a t e r a t lower temperz- t u r e s ( 1 ) . This e f f e c t should b e observed a t a macroscopic s c a l e by comaression t e s t s inasmuch a s t h e t e m p e r a t u r e of t h e t e s t i s lower. A t h i g h e r temperature where s i l i c o n can b e deformed i n s t a n d a r t c o n d i t i o n s , t h e mechanical p r o p e r t i e s of S i has been proved t o be c o n t r o l l e d by s o l i d s o l u t i o n h a r d e n i n g due t o do- p a n t s (11).

Onthese basis it i s of i n t e r e s t t o Study t h e e f f e c t of doping on t h e macroscopic p l a s t i c i t y a t t e m p e r a t u r e a s low a s p o s s i b l e . The same experimental procedure was used f o r e x t r i n s i c and i n t r i n s i c c r y s t a l s , i . e . a pre-deformation a t 400-

450°C i n o r d e r t o g e t a p l a s t i c i t y a t t e m p e r a t u r e a s low a s p o s s i b l e . F i g u r e 5 shows t h e e n g i n e e r i n g curves o b t a i n e d on t h e two t y p e s of c r y s t a l s a t L % O O O C w i - t h o u t any p r e - s t r a i n i n g , f o r a s t r a i n - r a t e of E = 2.10-6s-1. The e x t r i n s i c c r y s - t a l s proved t o b e s o f t e r t h a n i n t r i n s i c one ( i n agreement w i t h t h e measurement of d i s l o c a t i o n v e l o c i t i e s ) .

I ' \

SIP

~ o ~ ~ ~ m - ~

---_-

19 -3

\ . - - . - S ~ : P 10 c r n

F i g . 5 : E f f e c t of dopants on t h e macroscopic p l a s t i c i t y .

The r a t i o between t h e LY s t r e s s e s of t h e e x t r i n s i c c r y s t a l and t h e i n t r i n s i c one i s about two. This r a t i o i s c o n s t a n t i n t h e t e m p e r a t u r e range i n v e s t i g a t e d (300- 450°C) (Fig. 6 ) . The homologous t e m p e r a t u r e f o r doped c r y s t a l i s 50°C lower t h a n f o r i n t r i n s i c one which y i e l d s t h e same s h i f t i n t h e b r i t t l e - d u c t i l e t r a n s i t i o n from i n t r i n s i c t o p doped c r y s t a l s . This was expected from d i s l o c a t i o n v e l o c i t i e s measurements (10).

The observed p l a s t i c b e h a v i o u r as a f u n c t i o n of doping cannot b e simply r e l a t e d t o t h e v e l o c i t y measurementsin a n o t h e r range of temperature. I n t h e u s u a l t h e o r i e s t h e r a t i o of d i s l o c a t i o n v e l o c i t i e s as a f u n c t i o n of doping i s temperature d e ~ e n - d a n t which i s n o t t h e c a s e i n o u r e x p e r i m e n t s . This could be r e l a t e d : i ) t o t h e deformation mechanism which proceeds by p a r t i a l d i s l o c a t i o n s : t h e v e l o c i t y of t h e p a r t i a l r e s p o n s i b l e of t h e deformation h a s t o be taken i n t o account, ( i i ) t h e inaccuracy of t h e s t r e s s measurements a t "low s t r e s s " ( i n t h e Griggs d e v i c e ) could h i d e a d i f f e r e n t temperature dependence f o r doped and undoped c r y s t a l s . However an a n a l y s i s of o u r d a t a u s i n g an e x t r a p o l a t i o n of t h e measurements of George e t a 1 (1) (which d e s c r i b e s a t i s f a c t o r i l y t h e p l a s t i c y i e l d i n g a t tempera- t u r e h i g h e r t h a n 50o0C ( s e e ^§ I b ) ) g i v e s a good o r d e r of magnitude between t h e r a t i o of t h e LY s t r e s s e s f o r t h e two samples. This s u g g e s t s t h a t t h e v e l o c i t y of p a r t i a l & s l o c a t i o n s i s d i r e c t l y r e l a t e d t o t h e v e l o c i t y of t h e ~ e r f e c t d i s l o c a - t i o r s (deformation c o n t r o l l e d by t h e s l o w e s t ~ a r t i a l ) .

F i g . 6 : Lower y i e l d s t r e s s u v s T f o r e x t r i n s i c and i n t r i n s i c S i .

a ) e x t r i n s i c P , n = 10 19 cm-3 ) -6 -1 -3 ) E = 2.10 s b) i n t r i n s i c P , n = 1013 cm 1

I1

-

1 I . a

-

Conventional compression t e s t s were performed i n an equipement a t t a c h e d t o an I n s t r o n machine designed t o deform ceramics ( I ? ) . The j i g s were b u i l t of alumina rods. Using t h i s a p p a r a t u s it was ~ o s s i b l e t o deform s i l i c o n s i n g l e c r y s t a l s a t temperature a s low a s 385'C provided a pre-deformation a t h i g h temperature has been performed.

The same types of c r y s t a l as i n s e c t i o n I were used. The compression a x i s was a l o n g

<123>. P r e - s t r a i n i n g was c a r r i e d o u t a t T = 1050°C and

i

permanent s t r a i n was o b t a i n e d (E = 1.5 %)

.

1 I . b

-

The s t r e s s - s t r a i n curves e x h i b i t t h e u s u a l pronounced y i e l d p o i n t . Each sample was deformed u n t i l t h e lower y i e l d p o i n t , t h i s f o r d i f f e r e n t t e m p e r a t u r e s provi- ded t h e t o t a l s t r a i n ^E does n o t exceed 5 t o 6 %. The S t a t e of deformation does n o t a f f e c t t h e subsequent p l a s t i c p r o ~ e r t i e s : i . e . t h e LY s t r e s s i s n e a r l y t h e same whether t h e l a s t t e s t i s performed immediatly a f t e r t h e p r e - s t r a i n a t 1050°C o r f o l l o w i n g p r e v i o u s o t h e r deformations a t h i g h e r temperatures. A deformation sequence y i e l d s a d e c r e a s e of t h e UY s t r e s s a t a given t e m p e r a t u r e . No meaning- f u l l i n f l u e n c e of t e m p e r a t u r e o r of t h e s t r a i n - r a t e pke-deformation c o n d i t i o n s can be d e t e c t e d .

A s o f t e n i n g i s observed on P doped S i . The r a t i o between t h e LY s t r e s s e s measu- r e d on two d i f f e r e n t l y doped samples deformed a t t h e same t e m p e r a t u r e i s tempera- t u r e dependent. The r e s u l t s a r e p l o t t e d i n t h e form of Lnr v e r s u s T-' i n o r d e r t o be compared w i t h t h e d a t a of George e t a 1 ( I ) * A law ofleype / 2 / ( s e e I I b ) s a t i s f a c t o r i l y d e s c r i b e s t h e d a t a i n t h e i n v e s t i g a t e d temperature range ( s e e f i g . 7 ) .

1000t

I

F i g . 7 : Ln a v e r s u s - 1

IY T

upper p a r t of t h e f i g u r e : r e s u l t s w i t h a c o n f i n i n g p r e s s u r e

lower p a r t of t h e f i g u r e : s t a n d a r t t e s t s a f t e r p r e - s t r a i n i n g a t h i g h t e m 9 e r a t u r e . Following George e t a 1 (1) t h e v e l o c i t y of a d i s l o c a t i o n submitted t o a r e s o l v e d s h e a r s t r e s s can be e x p r e s s e d by / 3 / . Then t h e r e s o l v e d flow s t r e s s a t LY p o i n t w r i t e s (Alexander and Haasen (14)) :

The r a t i o Q/m+2 can b e d i r e c t l y d e r i v e d from t h e s l o p e s of t h e curves o f f i g u r e 7 , i . e . 0.51 eV and 0.81 eV f o r e x t r i n s i c and i n t r i n s i c S i r e s p e c t i v e l y :

+

Qd Qi _{) which} i s i n good agreement w i t h t h e r a t i o c a l t u l a t e d from ~ e o r g e ' s

- -

d a t a : Q. = 2 . 2 eV, Q = 1.4 eV, m. c md = 1 . 2 d

Using e q u a t i o n /4/ and assuming m. = md, t h e r a t i o o f t h e r e s o l v e d flow s t r e s s a t LY p o i n t f o r doped arid i n t r i n s ? c s a m p l e s i s :

Table I1 r e p o r t s t h e v a l u e s of t h i s r a t i o c a l c u l a t e d f o r s e v e r a l t e m p e r a t u r e s from e q u a t i o n / 5 / w i t h Bi/Bd % 103, m = 1.2, Qd = 1.5 eV, Qi = 2.2 eV (1) and

- -

t h e v a l u e s deduced from o u r p l a s t i c d e f o r m a t i o n d a t a . These r e s u l t s a r e i n c l o s e agreement.

*

TABLE I1

--

a) C a l c u l a t e d r a t i o s o f t h e Ly s t r e s s e s f o r doped and i n t r i n s i c c r y s t a l s .

b) Experimental v a l u e s .

However, a subsequent a n a l y s i s u s i n g d i f f e r e n t s t r a i n - r a t e s confirms t h e agree- ment w i t h t h e s t r e s s exponant m f o r doped c r y s t a l s : m = 1.15 c 0 . 3 5 whereas a d i s - crepancy h a s been found f o r i n t r i n s i c c r y s t a l s : t h e m v a l u e s a;e very s c a t t e r e d m = 2.8 f 1.6 and s t r o n g e r t h a n t h o s e deduced from v e l o c i t y measurement. T h i s e f - f e c t i s n o t understood.

CONCLUSION.

F i n a l l y a comparison s h o u l d b e made between t h e two s e t s of d a t a r e s u l t i n g from deformation under a c o n f i n i n g p r e s s u r e o r from d e f o r m a t i o n a f t e r p r e - s t r a i n i n g a t h i g h e r t e m p e r a t u r e s ( F i g . 7 ) . A t t h e t e m p e r a t u r e s where t h e two s e t s of expe- riments o v e r l a p , t h e d i s c r e p a n c y between t h e measurements i s o u t of t h e domain of u n c e r t a i n i t y . No s i g n i f i c a n t p r e s s u r e e f f e c t has been found by v a r y i n g t h e c o n f i n i n g p r e s s u r e i n low t e m p e r a t u r e t e s t s . S e v e r a l e x p l a n a t i o n s f o r t h i s d i s - crepancy can be p u t forward :

-

*

'Yd' TIYi

Aif f e r e n t from t h e r a t i o n 0 . 5 o b t a i n e d e x ~ e r i m e n t a l l y .

( i ) The c h a r a c t e r o f t h e d i s l o c a t i o n s d i f f e r s between t h e two s e t s o f t e s t s : p r e - s t r a i n i n g a t h i g h t e m p e r a t u r e (1050°C) c r e a t e s d i s l o c a t i o n s o f h i g h t e m p e r a t u r e t y p e whereas t h e d e f o r m a t i o n s made u n d e r a c o n f i n i n g p r e s s u r e h a v e b e e n performed w i t h a n o t h e r t y p e o f d i s l o c a t i o n s .

( i i ) T h i s e f f e c t c o u l d b e a s c r i b e d t o a y i e l d p o i n t e f f e c t : t h e h i g h s t r e s s e s r e q u i - r e d t o m u l t i p l y d i s l o c a t i o n s i n v i r g i n c r y s t a l s a t 450°C y i e l d t h e c r e a t i o n o f a d i s l o c a t i o n s u b s t r u c t u r e b u i l t up w i t h e x t e n d e d s t a c k i n g f a u l t s s i n c e t h e t h e o r e - t i c a l s t r e s s T r e q u i r e d t o move a p a r t i a l d i s l o c a t i o n a p a r t i s o v e r s h o o t e d d u r i n g t h e m u l t i p l i c a f i o n o f d i s l o c a t i o n s . C r y s t a l s c o n t a i n i n g a s u f f i c i e n t p r e - e x i s t i n g d i s l o c a t i o n d e n s i t y s h o u l d n o t e x h i b i t a y i e l d p o i n t . T h e r e f o r e t h e f l o w s t r e s s s h o u l d remain s m a l l e r t h a n T which g i v e s r i s e t o d i f f e r e n t d i s l o c a t i o n s u b s t r u c - t u r e and d e f o r m a t i o n mechanigm. T h i s h a s t o b e c o n f i r m e d by t e s t s on sample w i t h d i f f e r e n t p r e - e x i s t i n g d i s l o c a t i o n d e n s i t y .

ACKNOWLEDGMENTS :

The a u t h o r s t h a n k S.H. K i r b y (U.S. G e o l o g i c a l S u r v e y , Menlo P a r k , CA) f o r p r o v i d i n g t h e f a c i l i t i e s f o r m e c h a n i c a l t e s t i n g . J. R a b i e r acknowledges t h e f i n a n c i a l s u p p o r t o f NATO.

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( 3 ) HILL M . J . , ROWCLIFFE D.J., J. M a t e r . S c i . , 9 (1974) 1569.

(4) CASTAING J., VEYSSIERE P . , KUBIN L.P., RABIER J . , ~ h i l . Mag. A,

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(5) OMRI M., ThPse 3Sme c y c l e Nancy (1981).

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(11) SIETHOFF H . , A c t a Met.,

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(12) RABIER J . , ThPse P o i t i e r s ( 1 9 7 9 ) .

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2