DYNAMICAL RECOVERY AND DIFFUSION

(1)

HAL Id: jpa-00219052

https://hal.archives-ouvertes.fr/jpa-00219052

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 published 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.

DYNAMICAL RECOVERY AND DIFFUSION

H. Siethoff

To cite this version:

H. Siethoff. DYNAMICAL RECOVERY AND DIFFUSION. Journal de Physique Colloques, 1979, 40 (C6), pp.C6-177-C6-179. �10.1051/jphyscol:1979636�. �jpa-00219052�

(2)

JOURNAL DE PHYSIQUE Colloque C6, suppldment au n06, tome 40, juin 1979, page C6-177

DYNAMICAL RECOVERY AND DIFFUSION H. S i e t h o f f

Physikalisches I n s ti t u t der Universitat Wiirzburg, Rontgenring 8, 0-8700 Krzburg, F. R. G.

Resume.- I 1 e s t p o s s i b l e d ' a p p l i q u e r l e s techniques de l a deformation p l a s t i q u e pour e t u d i e r l ' a u t o - d i f f u s i o n dans l e s i l i c i u m e t l e germanium. On a pu deduire de c e t t e facon des energies d ' a c t i v a t i o n de 2,8 eV e t de 3,6 eV pour l e Ge e t l e S i respectivement. Pour l e S i , l e f a c t e u r preexponentiel Do a @ t e estime ti 0,5 cm2/s. On d i s c u t e ces r e s u l t a t s en terme de d i f f u s i o n par monolacunes.

Abstract.- P l a s t i c deformation techniques can be a p p l i e d t o i n v e s t i g a t e s e l f - d i f f u s i o n i n S i and Ge.

By t h i s way, a c t i v a t i o n energies o f 2.8 eV and 3.6 eV f o r Ge and S i , r e s p e c t i v e l y , were deduced. For S i , t h e pre-exponential f a c t o r D was estimated t o be 0.5 cm2/s. These r e s u l t s are discussed i n terms of d i f f u s i o n by a monovacancy mephanism.

1. I n t r o d u c t i o n . - Dynamical recovery i n c r y s t a l s i s t h e r e d u c t i o n o f work hardening by recovery processes i n t h e course o f p l a s t i c deformation. Besides t h e c r o s s - s l i p mechanism which i s n o t i m p o r t a n t f o r the experiments described i n t h i s paper, two b a s i c recovery processes have been d e a l t w i t h i n t h e l i t e - r a t u r e : t h e c l i m b o f edge d i s l o c a t i o n s /1/ and t h e dragging o f j o g s on screw d i s l o c a t i o n s /2/. Both mechanisms have been shown t o be r a t e c o n t r o l l i n g i n creep experiments, i . e . c o n s t a n t - s t r e s s deformation t e s t s , i n t h e steady-state regime. I n t h i s region, deformation has reached a s t a b l e s t a t e o f dynamic e q u i l i b r i u m : t h e r a t e o f hardening i s then compen- sated by t h e r a t e o f recovery. The steady-state creep r a t e dc as a f u n c t i o n o f temperature T and a p p l i e d s t r e s s T has been d e r i v e d f o r the c l i m b mechanism /1,3/ as

and f o r t h e jog-dragging mechanism /2/ as

Here, A,, AZ and V are constants, k i s Boltzmann's constant, n and m are t h e s t r e s s exponents, b i s t h e Burgers v e c t o r and QSD i s the a c t i v a t i o n energy and Dothe preexponential f a c t o r o f s e l f - d i f f u s i o n . Both equations s i g n i f i c a n t l y d i f f e r i n t h e i r s t r e s s dependence. Formula (1) has been d e r i v e d f o r small s t r e s s w h i l e formula (2) i s n o t r e s t r i c t e d i n s t r e s s .

The most i m p o r t a n t aspect o f both equations i s t h a t t h e temperature dependence o f . t h e creep r a t e i s c o n t r o l l e d by t h e a c t i v a t i o n energy o f s e l f - d i f f u s i o n . T h i s means t h a t creep experiments can be

ted by a c o m p i l a t i o n /4/ showing t h e a c t i v a t i o n ener- g i e s o f s e l f - d i f f u s i o n and o f steady-state creep t o c o i n c i d e f o r v a r i o u s m a t e r i a l s a t temperatures above two t h i r d s o f t h e absolute m e l t i n g p o i n t . ' A t lower temperatures, p i p e - d i f f u s i o n may become r a t e c o n t r o l - l i n g .

2. Experimental r e s u l t s . - Steady-state creep e x p e r i - ments i n S i /5/ and Ge /6/ y i e l d e d a c t i v a t i o n ener- g i e s o f 5.6 eV and 4.5 eV, r e s p e c t i v e l y . Though f o r S i t h e r e may be a rough coincidence w i t h values o f about 5 eV f o r Q~~ a t h i g h temperatures /7/, t h e r e i s no agreement i n Ge, where Q~~ was found t o be 3.0 eV /8/. A r e - e v a l u a t i o n o f t h e same creep data, however, l e d t o a c t i v a t i o n energies o f about 3.7 eV and 3.0 eV f o r S i and Ge, r e s p e c t i v e l y /9/. On t h e o t h e r hand, creep t e s t / l o / i n S i a t very low s t r e s s l e v e l s y i e l d e d an a c t i v a t i o n energy o f about 1.7 eV, which was a s c r i b e d t o t h a t f o r d i s l o c a t i o n movement.

Recovery processes are a l s o i m p o r t a n t i n stage I 1 1 o f c r y s t a l s deformed i n a dynamic experiment, i . e . a t constant s t r a i n r a t e . Contrary t o metals where c r o s s - g l i d e o f screw d i s l o c a t i o n s i s t h e b a s i c mechanism, i n S i and Ge t h e recovery processes d i s - cussed above are r a t e c o n t r o l l i n g /4,11,13/. Both equations ( 1 ) and (2), can be used f o r t h e i n t e r p r e - t a t i o n o f t h e experiments by simply i n v e r t i n g them and by r e p l a c i n g T and ic by T~~~ and dIII, t h e s t r e s s and t h e s t r a i n r a t e a t the beginning o f r e - gion 111, though the p r e f a c t o r s may be d i f f e r e n t .

The r e s u l t s o f the TIII-measurements obtained i n compression t e s t s a r e presented i n f i g u r e 1 f o r S i /11/ and Ge / 4 / , where according t o equation '(1) t h e s t r e s s T ~ ~ ~ , n ~ r ~ m a l i z e d t o t h e shear modulus, has been o l o t t e d as a f u n c t i o n o f t h e temoerature-com- used t o e v a l u a t e d i f f u s i o n data. This view i s suppor-

pensated strain rate. Such a plot has the advantage

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979636

(3)

C 6 - 178 JOURNAL D E PHYSIQUE

t h a t a l l data p o i n t s f i t a s i n g l e curve f o r each t o t h e same p r e f a c t o r A, f o r both m a t e r i a l s . Then, m a t e r i a l , if an a p p r o p r i a t e v a l u e f o r t h e a c t i v a t i o n according t o equation ( I ) , both curves i n f i g u r e 1 energy QSD i s chosen. This i s t h e case f o r S i w i t h d i f f e r o n l y by t h e i r preexponential f a c t o r s Do.

QSD = 3.6 eV and f o r Ge w i t h QSD = 3.0 eV. The de- Taking D, f o r Ge t o be about 10 cm2/s /8/, t h e d i f f e - v i a t i o n s from l i n e a r i t y a t h i g h stresses are n o t rence between b o t h curves i n f i g u r e 1 i s taken i n t o compatible w i t h equation ( 1 ) . A computer f i t o f account by a Do-value f o r S i o f 0.5 cm2/s.

equation (2) t o the data l e d t o a reasonable agree- 3. Discussion.- The r e s u l t s on dynamical recovery i n ment y i e l d i n g a c t i v a t i o n energies Q~~ of 3.6 eV and S i and Ge a r e compatible w i t h s e l f - d i f f u s i o n by a

2.8 eV f o r S i and Ge, r e s p e c t i v e l y . I n f i g u r e 1, monovacancy mechanism /4,11/. At l e a s t f o r Ge t h i s

mono measurements

f o r Ge taken from the l i t e r a t u r e conclusion cannot be questioned, as t h e measured /12, 13/ are i n c l u d e d : The d a t a obtained i n com- a c t i v a t i o n energy corresponds t o t h a t found by t h e p r e s s i o n t e s t s /12/ (marked by crosses) f i t w e l l our t r a c e r method /8/. I n S i where our measurements were curve w h i l e t h e data from t e n s i o n t e s t s /13/ (dashed performed a t temperatures between 850°C and llDO°C, l i n e ) a r e s h i f t e d t o h i g h e r Stress l e v e l s , most proba- t h e r e i s a q u a l i t a t i v e agreement w i t h models /16,17/

b l y on account o f t h e d i f f e r e n t methods O f deformatior.. which c l a i m vacancy d i f f u s i o n w i t h a c t i v a t i o n ener- These data are compatible w i t h equation ( 1 ) y i e l d i n g g i e s about 4 eV t o be dominant a t temperatures below an a c t i v a t i o n energy of 2.9 eV. The s t r i k i n g d i f f e - about 1050°C. The discrepancies between these models rences between compression and tension t e s t s which i n t h e high-temperature regime concerning t h e ques- have been observed i n Creep experiments /5,6,14/ do t i o n whether i n t e r s t i t i a l s /16/ o r vacancies i n d i f - n o t occur i n stage I 1 1 of t h e dynamical deformation f e r e n t charge s t a t e s /17/ c o n t r o l s e l f - d i f f u s i o n

t e s t . w i t h a c t i v a t i o n energies o f about 5 eV /7/ cannot

be r e s o l v e d by our present measurements. F u r t h e r i n - v e s t i g a t i o n s o f dynamical recovery i n t h e high-tem- p e r a t u r e regime and of t h e doping dependence may h e l p t o c l a r i f y these problems.

Acknowledgments.- The author i s indebted t o W.Schr5- t e r and H.G. B r i o n from GGttingen f o r t h e i r c o n t i - nuous cooperation.

F i g . 1 : Modulus-corrected s t r e s s a t t h e beginning o f stage I 1 1 as a f u n c t i o n of t h e temperature-com- pensated s t r a i n r a t e i n S i (QSD = 3.6 eV) and i n Ge (QSD = 3.0 eV). Data from t h e l i t e r a t u r e f o r Ge /12,13/ a r e i n d i c a t e d by t h e crosses (compression t e s t ) and by t h e dashed 1 in e ( t e n s i o n t e s t ) .

I n p r e v i o u s work /4,11/, t h e preexponential f a c t o r Do o f t h e d i f f u s i o n c o e f f i c i e n t had been r o u g h l y 'estimated f o r S i . A more r e l e v a n t value can be deduced i n t h e f o l l o w i n g way : By a n a l y s i n g a g r e a t v a r i e t y o f creep data, i t has been shown i n t h e l i t e r a t u r e /15/ t h a t t h e constants Al and n i n equation ( i ) a r e r e l a t e d by

n = 3.0 + 0.3 l o g 1 0 A l

Assuming h i s r e l a t i o n t o be v a l i d f o r Ge and S i and t a k i n g i n t o account t h e same n-value ( a c t u a l l y , n = 3.63 f o r S i /11/ and n = 3.66 f o r Ge /4/) leads

(4)

H . S i e t h o f f

References

/1/ Weertman, J., J. Appl. Phys. 26 (1955) 1213

/2/ B a r r e t t , C.R. and Nix, W.D., Acta M e t a l l .

13

(1965) 1247.

/3/ Mukherjee, A.K., B i r d , J.E. and Dorn, J.E., Trans.

ASM 62 (1969) 155.

/4/ Brion, H.G., Schroter, W. and S i e t h o f f , H., Defects and Radiation E f f e c t s i n Semiconductors 1918 ( I n s t i t u t e o f Physics Conference S e r i e s

-

No 46, t o be p u b l i s h e d ) .

/5/ Myshlyaev, M.M., Nikitenko, V . I . and Nesterenko, V . I . , Phys. S t a t u s S o l i d i 36 (1969) 89.

/6/ Myshlyaev, M.M. and Khodos, I.I., Phys. S t a t u s S o l i d i (b), 43 (1971) 83.

/7/ Mayer, H.J., Mehrer, H. and Maier, K., L a t t i c e Defects i n Semiconductors 1976 ( I n s t i t u t e o f Phy- s i c s Conference S e r i e s No. 31), p. 186.

/8/ Widmer, H. and Gunther-Mohr, G.R., Helv. Phys.

Acta,

3

(1961) 635.

/9/ S i e t h o f f , H., Phys. Status S o l i d i ( a ) , 5 (1978) K 135.

/ l o / Taylor, T.A. and B a r r e t t , C.R., Mater. S c i . E n g . g (1972) 93.

/11/ S i e t h o f f , H. and Schroter, W., P h i l o s . Mag. A 37

(1978) 711.

/12/ Schafer, S., Dip1 oma Thesis, Gottingen, (1963).

/13/ A1 exander, H. and Haasen, P., Acta Y e t a l l ., 2

(1961) 1001.

1141 Myshlyaev, M.M. and Khodos, I . I . , M e t a l l o f i z i k a (Kiev), 68 (1977) 76.

/15/ Stocker, R.L. and Ashby, M.F., Scr. M e t a l l .

1

(1973) 115.

/16/ Seeger, A. and Chik, K.P., Phys. S t a t u s S o l i d i 2

(1968) 455.

/17/ F a i r , R.B., Semiconductor S i l i c o n 1977, H.R. R u f f and E. S i r t l , eds. (The Electrochemical S o c i e t y ) 1977, p. 968.