KINK FORMATION AND MIGRATION AS DEPENDENT ON THE FERMI LEVEL

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KINK FORMATION AND MIGRATION AS DEPENDENT ON THE FERMI LEVEL

P. Haasen

To cite this version:

P. Haasen. KINK FORMATION AND MIGRATION AS DEPENDENT ON THE FERMI LEVEL.

Journal de Physique Colloques, 1979, 40 (C6), pp.C6-111-C6-116. �10.1051/jphyscol:1979623�. �jpa- 00219039�

JOURNAL D E PHYSIQUE CoLZoque C6, suppZ4ment cac n06, tune 40, juin 1973, page C6-Ill

KINK FORMATION AND MIGRATION AS DEPENDENT ON THE FERMI LEVEL P . Haasen

I n s t i t u t fiir MetaZZphysik, University Gottingen, F.R.G.

Resume.- Les d i s l o c a t i o n s dans l e s semiconducteurs de s t r u c t u r e diamant se deplacent par l a formation e t m i g r a t i o n des decrochements. Ces processus sont analyses theoriquement e t dans l e u r s manifesta- t i o n s experimentales : selon l e dopage e t l a temperature, une charge e l e c t r i q u e a i d e a l a formation des decrochements. Cela a des consequences importantes pour l a deformation sous i l l u m i n a t i o n e t dans un e l e c t r o l y t e .

Abstract.- D i s l o c a t i o n s i n the diamond c u b i c s t r u c t u r e (D.S.) move by t h e formation and spreading o f k i n k s . These processes are analysed both t h e o r e t i c a l l y and i n t h e i r experimental manifestations. De- . pending on doping and temperature a charge on t h e d i s l o c a t i o n s helps i n k i n k formation. This has im-

p o r t a n t consequences f o r deformation under i l l u m i n a t i o n and i n an e l e c t r o l y t e .

1. I n f l u e n c e of D i s l o c a t i o n S t r u c t u r e . - As i n d i c a t - ed i n o t h e r l e c t u r e s a t t h i s Conference and w e l l documentedin the l i t e r a t u r e /1,2,3,4/ d i s l o c a t i o n s i n D.S: c r y s t a l s , i . e . S i and Ge, are d i s s o c i a t e d i n t o p a r t i a l s . The d i s s o c i a t i o n i s , however, n o t complete : Depending on deformation temperature (perhaps a l s o on s t r a i n and h e a t i n g / c o o l i n g time) one observes l o c a l c o n s t r i c t i o n s , p e r f e c t d i s l o c a - t i o n segments, o r segments o f anomalous d i s s o c i a t i o n /2,4,5/. F i g u r e 1 shows by way o f t h e a p p r o p r i a t e imaging c o n d i t i o n s o f t h e weak beam technique such anomalies i n Ge, deformed 1.2% a t 600°C and 0 . 7 % a t 400°C, w i t h subsequent annealing o f 2 h a t 450°C.

F i g u r e 2 demonstrates by two almost orthogonal views o f the same edge d i s l o c a t i o n ( d i p o l e ) t h a t most of t h e c o n s t r i c t i o n s are a c t u a l l y (super) jogs, some l e a d i n g from the g l i d e s e t i n which t h e d i s l o c a t i o n d i s s o c i a t e s t o t h e s u f f l e set, t h e obvious p o s i t i o n o f t h e complete d i s l o c a t i o n . Blanc /6/ argues t h e r - modynamically t h a t t h i s t r a n s i t i o n leads under emission of vacancies t o t h e w e l l known s h u f f l e s e t c o n f i g u r a t i o n w i t h a row o f dangling bonds. Accor- d i n g t o Packeiser /5/ t h i s t r a n s i t i o n occurs by thermal evaporation o f vacancies above T, = 600°C as evidenced by a spacing L between c o n s t r i c t i o n s

which decreases w i t h i n c r e a s i n g temperature ( o f

SOOA *

deformation o r annealing), f i g u r e 3. Below Tc t h e u

spacing L increases w i t h T, perhaps by annealing o f deformation produced j o g s . L does n o t d i f f e r much

f o r edge and screw d i s l o c a t i o n s (whose widths o f F i g . 1 : D i s l o c a t i o n i n ( I l l ) f o i l o f Ge under (a) g = P2q and (b) g = [?2C the l a t t e r t i l t e d d i s s o c i a t i o n a r e d i f f e r e n t however /4,5/). N e i t h e r abou 8, showing widening

hi,

t h e c o n s t r i c t i o n s . These c o n s t r i c t i o n s most l i k e l y h i n d e r t h e motion o f d i s l o c a t i o n s i n D.S. c r y s t a l s .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979623

C6-112 JOURNAL DE PHYSIQUE

F i g . 2 : D i s l o c a t i o n d i p o l e i n Ge, deformed a t 450°C and cooled under load, viewed i n < I l l > and <110>

d i r e c t i o n s , shows superjogs a t c o n s t r i c t i o n s (G. Packeiser) .

F i g . 3 : Mean d i s t a n c e s between c o n s t r i c t i o n s as a f u n c t i o n o f annealing temperature (G. Packeiser) (Arrow i n d i c a t e s d i s t a n c e a f t e r deformation (0.35%

a t 600°C + 1,15% a t 450°C).

2.2. Kink Formation i n t h e P e i e r l s P o t e n t i a l .- ^There

a r e good reasons t o b e l i e v e t h a t d i s l o c a t i o n s i n D.S. c r y s t a l s encounter a r e l a t i v e l y s t r o n g P e i e r l s p o t e n t i a l ; i .e. d i s l o c a t i o n s 1 i e para1 l e l t o c l o s e packed d i r e c t i o n s i f t h e deformation temperature i s n o t t o o high. A t f i n i t e temperatures double k i n k s are nucleated on t h e d i s l o c a t i o n and spread along i t . Thermally a c t i v a t e d double k i n k f o r m a t i o n i s the obvious mechanism f o r d i s l o c a t i o n movement i n Ge and S i . I t i s c l e a r t h a t f o r a p p l i e d stresses T>T,, t h e s t r e s s by which t h e two p a r t i a l s o f a d i s s o c i a t - ed d i s l o c a t i o n s i n t e r a c t among each other, the p a r t i a l s have t o overcome t h e p e i e r l s p o t e n t i a l inde- pendently. The P e i e r l s p o t e n t i a l has been c a l c u l a t e d o n l y f o r complete screw d i s l o c a t i o n s so f a r /7,8/ as has been t h e energy t o form a double k i n k . M'dller /9/ has r e c e n t l y formulated a t h e o r y o f k i n k nuclea- t i o n and m i g r a t i o n f o r d i s s o c i a t e d d i s l o c a t i o n s

(see the f o l l o w i n g a r t i c l e ) . I t i s based on Rybin and O r l o v ' s / l o / theory f o r t h e movement o f complete d i s l o c a t i o n s . These authors have recognized t h a t i t i s n o t p o s s i b l e t o e x p l a i n t h e complicated s t r e s s dependence o f t h e measured d i s l o c a t i o n v e l o c i t y i n Ge /11/ and S i /12/

V = 6-rmexp(-E'/~T) ( 1 )

(m = 1 f o r h i g h T and ^T, m > 1 otherwise)

j u s t by t h e process o f k i n k n u c l e a t i o n and m i g r a t i o n . They i n t r o d u c e d s o - c a l l e d weak obstacles t o be over- come by thermal a c t i v a t i o n o f the spreading k i n k s . We a r e now i n c l i n e d t o i d e n t i f y these weak obstacles w i t h the observed c o n s t r i c t i o n s although t h e i r mean spacing a t T = 600°C o f a z (0.4-0.7) pm i s somewhat smal l e r than t h e one needed i n t h e t h e o r y o f M i l l e r /9/ a

-

Rybin and Orlov consider t h e weak obstacles t o anneal o u t t h e r m a l l y ( P a c k e i s e r ' s low T mechanism) according t o

L = R o e x p ( - s / ~ T ) (2)

P u t t i n g t h i s i d e a i n t o t h e expression / l o / f o r t h e d i s l o c a t i o n v e l o c i t y (under t h e c o n d i t i o n o f k i n k - k i n k a n n i h i l a t i o n )

where a = p e r i o d o f t h e P e i e r l s p o t e n t i a l , Tab1 vK = k i n k v e l o c i t y

-

kT

Jc = k i n k n u c l e a t i o n r a t e p e r u n i t l e n g t h o f a d i s - l o c a t i o n c o n t a i n i n g weak obstacles

a" ^T

= Joexp(-EDK- ( 1 + f ) exp (-T,/T), EDK = double k i n k formation energy -. a'&-

P' Ed = a c t i v a t i o n energy o f weak o b s t a c l e E ~ , a b l ,

T = P e i e r l s s t r e s s , b = Burgers v e c t o r P

Jo, v o = frequency constants

Expression (3) a p p l i e s i n a s i t u a t i o n where f u r t h e r k i n k s a r e formed before one k i n k reaches the end o f a (macroscopic) d i s l o c a t i o n segment o f l e n g t h L, i . e . 3,L2 >>4vK. Otherwise V would depend on L (2200 um) which i s n o t observed /11/. Also ^T < T~ i s assumed, i . e . c o r r e l a t e d k i n k f o r m a t i o n i n both p a r t i a l s ; o t h e r w i s e see /9/. The d i s l o c a t i o n v e l o c i t y then has t h e form

v = Acexp((-ED,- a' - Ed - ~ ) / 2 k T ) * ( l + -;j TI% e x p ( - 2 ) (4) . ^,

which u n f o r t u n a t e l y c o n t a i n s 4 parameters Ac = - 2a x

, EDK; Ed and E. The a n a l y s i s i n t h e range Jii

T > T~ r e q u i r e s two more constants, A, and

EL^

u n c o r r e l a t e d k i n k f o r m a t i o n on a p a r t i a l d i s l o c a t i o n /9/. Mdl l e r shows, however, t h a t a l a r g e ensemble o f

data V ( T , T) f o r screw and 60°C d i s l o c a t i o n s i n Ge and S i can be f i t t e d i n d e t a i l ' w i t h a l i m i t e d choice o f the constants (see t h e f o l l o w i n g paper).

~ y p i c a l l y ( ' ) ~ ~ ~

-

t o remove t h i s j o g i n a t h e r m a l l y a c t i v a t e d process ! Also M i l l e r /9/ f i n d s from t h e h i g h s t r e s s v e l o c i t y data t h a t the energy

EL^

3. Comnents on v a r i o u s Experimental Methods /11,12, 13/.- I n r e c e n t years techniques f o r t h e measurement -

o f v e l o c i t i e s o f d i s l o c a t i o n s i n semiconductors have been developed t o an e x t r a o r d i n a r y degree o f p e r f e c - t i o n . Etch p i t t i n g as w e l l as X-ray topography are used t o measure v e l o c i t i e s between and l o - ' cm/s as stresses between 5 and 60 ~ / m m ~ a r e a p p l i e d . The r e s u l t s o f both methods g e n e r a l l y agree w e l l w i t h each o t h e r demonstrating t h a t surface e f f e c t s a r e _,.., n o t importantt'! I s o l a t e d d i s l o c a t i o n h a l f loops are introduced by s c r a t c h i n g o f the s u r f a c e i n c r y s t a l - l o g r a p h i c d i r e c t i o n s and a p p l i c a t i o n o f a s t r e s s t o t h e whole specimen. The s c r a t c h i s then removed and t h e movement o f the remaining deep h a l f loops i s f o l l o w e d d u r i n g o r a f t e r successive s t r e s s pulses.

The Burgers v e c t o r and t h e o r i e n t a t i o n s o f t h e l o o p arms a r e w e l l known by topography. An e f f e c t o f the d i s l o c a t i o n l i n e t e n s i o n and o f t h e image f o r c e s a t t h e f r e e s u r f a c e i s observed i f t h e d i s l o c a t i o n i s heated w i t h o u t a p p l i e d s t r e s s : t h e h a l f l o o p shrinks and rounds o f f . Superposed s t r e s s e s o f t h e order o f

he values quoted here d i f f e r f r o m t h o s e given i n /9/ as explained by M i j l l e r a t t h i s Conference.

( 2 ) ~ u c h a value i s a l s o obtained from TEM-measure- ments of a(T) /5L.

( 3 ) ~ e s u l t s o f Erofeev e t a l . /14/ on Si a t small r a r e e x c e p t i o n a l see /12/.

1 ~ / m n ~ stop such movements f o r loops o f about 600 pm diameter i n Ge; loops o f 100 urn diameter are s t a b i - l i z e d by a s t r e s s T = 6 ~ / m m ~ . f i l l e r /13/ has s t u - d i e d t h e k i n e t i c s o f d i s l o c a t i o n s under such small

l i n e t e n s i o n and image f o r c e s or/and a p p l i e d s t r e s - ses. He f i n d s a v e l o c i t y f o l l o w i n g equation ( 1 ) w i t h m = 1 b u t an a c t i v a t i o n energy EZ = 1.45 eV f o r Ge,

i . e . s l i g h t l y l e s s than h a l f t h a t o f forward move- ment under l a r g e r stresses. EZ i s analysed i n s i m i l a r

terms as equation (4) w i t h a formation energy Ek = EDK/2 corresponding t o the f o r m a t i o n o f a s i n g l e k i n k a t t h e s u r f a c e ( t h e o t h e r h a l f o f t h e double k i n k being i t s image) i n c o n t r a s t t o t h e h i g h e r s t r e s s double k i n k f o r m a t i o n i n the volume. The sur- face-generated k i n k s e v i d e n t l y move L = (170 + 15)11m i n t o the i n t e r i o r where they p i l e up and o f t e n form a l a r g e k i n k , f i g u r e 4 . The n a t u r e o f these "strong"

obstacles l i m i t i n g t h e f r e e path o f k i n k s i s n o t y e t known. Other disturbances o f d i s l o c a t i o n movements near a surface a r e c l i m b and cross s l i p processes /11,12/. These e f f e c t s are t r e a t e d i n another paper a t t h i s meeting.

F i g . 4 : X-ray topogram o f d i s l o c a t i o n h a l f l o o p i n Ge, a f t e r annealing 15 min a t 550°C w i t h o u t load;

the arms o f some d i s l o c a t i o n s are kinked about 100um from s u r f a c e o r l o o p corner (H.J. M o l l e r ) .

Measurements on 111-V o r I 1 IV-compounds n o t o n l y deal w i t h 60' and screw d i s l o c a t i o n s b u t a l s o have t o d i f f e r e n t i a t e between a and 0 t y p e 60" d i s - l o c a t i o n s , ending t h e i r e x t r a h a l f plane by rows o f lower o r h i g h e r v a l e n t atoms, r e s p e c t i v e l y , i t they are i n the s h u f f l e set, v i c e versa i n t h e g l i d e set, /15, 16, 17, 18/. The d i f f i c u l t y w i t h these measure- ments t r e a t e d i n d e t a i l a t t h i s conference are t h e p a r t i c u l a r l y small m o b i l i t i e s o f 0 and screw d i s l o - c a t i o n s r e l a t i v e t o a. The macroscopic s t r a i n r a t e o f such a c r y s t a l i s given by 6 = b ~ J r q where

N = Na = N i s t h e mobile d i s l o c a t i o n d e n s i t y /18/.

0

C6-1 14 JOURNAL DE PHYSIQUE

I n t e r n a l f r i c t i o n measurement on deformed O.S.

c r y s t a l s a l s o p r o v i d e s i n f o r m a t i o n on a) t h e move- ment o f geometrical k i n k s on d i s l o c a t i o n s which are n o t p a r a l l e l t o a P e i e r l s v a l l e y , b) the f o r m a t i o n o f k i n k s . A s t r i k i n g f e a t u r e o f two r e c e n t s t u d i e s on Ge and S i 119, 20/ a t 15 Hz below 450 K and a t 70 kHz below 150 K i s t h e extremely small energy l o s s , Q-' = 5x10-' and < 5 ~ 1 0 - ~ , r e s p e c t i v e l y ,

observed even f o r d i s l o c a t i o n d e n s i t i e s N > 1 0 ' ~ m - ~ , According t o the v i b r a t i n g s t r i n g model ( w i t h o u t i n e r t i a l e f f e c t s ) the r e l a x a t i o n s t r e n g t h o f N seg- ments o f l e n g t h R should be about NR' = 1 f o r

9. = 1 um w h i l e t h e above mentioned losses l e a d t o 2 = (50 - 8 0 ) i /19, 20/. This i s d i f f i c u l t t o under*

stand even w i t h Packeiser's low temperature cons- t r i c t i o n distances. The r e l a x a t i o n times correspon- d i n g t o two peaks i n Q - ' ( T ) observed i n t h e measu- rements o f Ohori and Sumino /20/ on Ge a t 64 K and 97 K y i e l d a c t i v a t i o n energies o f 0.08 and 0.13 eV, r e s p e c t i v e l y . The authors i n t e r p r e t these i n terms o f stress-induced k i n k m i g r a t i o n over t h e P e i e r l s p o t e n t i a l o f the second k i n d ( k i n k p o t e n t i a l ) on screw and 60" d i s l o c a t i o n s . Labusch has c a l c u l a t e d t h i s f o r t h e complete screw i n Ge t o 0.04 eV. A t h i g h e r temperatures t h e same authors /21/ f i n d two f u r t h e r and much l a r g e r peaks n o t observed i n /19/

f o r deformed Ge. The a c t i v a t i o n energies are 0.62 eV (Q;:~ = 2x10-') and 0.85 eV (Q;ix = 5 ~ 1 0 - ~ a f t e r annealing). The i d e n t i f i c a t i o n o f t h e f i r s t peak w i t h t h e movement o f k i n k s o v e r j o g s agrees w i t h W l l e r ' s /9/ v a l u e o f Ed = 0.7 eV ( i n s t e a d o f 0.62 eV); t h a t o f t h e second w i t h s i n g l e k i n k forma- t i o n a t surfaces i s t o be compared w i t h t h e value e x t r a c t e d from back movement /13/ EK = 1.0 eV ( i n s - tead o f 0.85eV). More a m b i g u i t i e s a r i s e w i t h i n t e r n a l f r i c t i o n r e s u l t s o f InSb /22/ t r e a t e d i n another paper a t t h i s Conference.

4. Kink f o r m a t i o n on charged d i s l o c a t i o n s . - The l i n e charge on a d i s l o c a t i o n i n t h e D.S. i s a w e l l esta- b l i s h e d concept b o t h t h e o r e t i c a l l y /23,24/ and expe- r i m e n t a l l 2 /25,26/. I t depends s o l e l y on t h e p o s i - t i o n o f t h e Fermi l e v e l EF r e l a t i v e t o t h a t Eo o f the d i s l ' o c a t i o n band which i n t u r n depends on t h e 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 . A number o f papers a t t h i s meeting t r e a t t h i s problem e x t e n s i v e l y , p a r t i - c u l a r l y w i t h r e s p e c t t o the e l e c t r o s t a t i c s e l f i n - t e r a c t i o n o f .the charge (on t h e d i s l o c a t i o n 1 i n e . E x p e r i m e n t a l l y t h e H a l l e f f e c t f y i e l d s t h e d i s l o c a - t i o n charge Q p e r u n i t l e n g t h a t low temperatures.

To apply i t i n t h e temperature range where d i s l o c a - t i o n s a r e mobile, the changes i n EF(T) and i n Eo

due t o the thermal v a r i a t i o n o f t h e band gap must be taken i n t o account.

The charge on the d i s l o c a t i o n e x p l a i n s i n our o p i n i o n t h e 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 on doping i n the e x t r i n s i c range /27/. There i s a w e a l t h o f experimental r e s u l t s o f t h i s type which cannot be understood i n terms o f the c l a s s i c a l d i s l o c a t i o n / s o l u t e i n t e r a c t i o n s : Sizeable changes i n v(T) r e s u l t a l r e a d y from doping w i t h an atom f r a c t i o n l e s s than

lo-", and the v e l o c i t y sometimes increases b u t w i t h o t h e r dopants decreases (depending on t h e accompa- n y i n g changes i n EF ! ) . Therefore a l s o t h e model o f p r e f e r e n t i a l k i n k n u c l e a t i o n a t (perhaps charged) s o l u t e atoms used i n bcc metals /28/ does n o t work i n our m a t e r i a l s , see 1291. I t i s however easy t o ;

see t h a t any charge on a s t r a i g h t d i s l o c a t i o n des- t a b i l i s e s i t and so decreases t h e energy t o form a (double) k i n k /27/. This i s t r u e a l s o f o r d i s s o c i a - t e d d i s l o c a t i o n s i n which both p a r t i a l s may be ( d i f f e r e n t l y ) charged. One can show t h a t t h e w i d t h o f d i s s o c i a t i o n i s s t i l l determined by a balance o f s t a c k i n g f a u l t a t t r a c t i o n and e l a s t i c r e p u l s i o n f o r c e s K ? ~ r e l a t i v e t o which t h e e l e c t r o s t a t i c i n - t e r a c t i o n KY2 between t h e charged p a r t i a l s remains comparatively small, i .e.

f o r a 6 " - d i s l o c a t i o n ( p = shear modulus,v= Poisson's r a t i o , E = d i e l e c t r i c constant). I n p a r t i c u l a r f o r a screw d i s l o c a t i o n i n i n t r i n s i c Ge a t 500°C Q 1 = Qz =

- 0.07 /26/ and K?,/KY, z 3 . 7 ~ 1 0 - ~ . For a disso- c i a t e d 60' d i s l o c a t i o n t h i s r a t i o most l i k e l y i s by a f a c t o r 6 l a r g e r .

Assuming screened Coulomb i n t e r a c t i o n ( w i t h a Debye screening d i s t a n c e A ) the decrease i n e l e c t r o - s t a t i c s e l f energy o f a charged d i s l o c a t i o n on f o r - mation o f a double k i n k o f amplitude a, w i d t h d i s ( " ) ( F i g . 5)

Q 2 cos8dx2e q2a2 7 ^dxz

AE = -2 2 dx, I ^{- - 2} -

o r c o

-a/2A

f o r a << d ( 6 ) A t t h e deformation temperatures (500°C f o r Ge /30/, 600°C f o r S i /31,32/) and the h i g h e s t dopings Nc

-

l o 1 9cm-3 i n v e s t i a a t e d

('11 am g r a t e f u l t o P e t e r H i r s c h f o r p o i n t i n g o u t an e r r o r i n my e a r l i e r c a l c u l a t i o n f o r A + /27/.

The i n t e r a c t i o n between the two k i n k s themselves and between'each o f them and t h e s t r a i g h t d i s l o - c a t i o n segments a r e neglected i n equation ( 6 ) .

F i g . 5 : Double k i n k i n charged d i s l o c a t i o n used f o r c a l c u l a t i o n o f e l e c t r o s t a t i c d e s t a b i l i z a t i o n . w h i l e t h e p e r i o d o f t h e P e i e r l s p o t e n t i a l a = 0.86 b, so t h a t t h e exponential (6) i s always near t o one.

The degree o f occupation f i s r e l a t e d t o t h e charge Q = - e f / b and can be determined from t h e Fermi energy by /24/

Here Eo i s t h e l i m i t o f occupation o f the n e u t r a l d i s l o c a t i o n a t t h e deformation temperature, ro th e r a d i u s o f t h e wave f u n c t i o n i n t h e d i s l o c a t i o n core, S t h e c o n f i g u r a t i o n a l entropy o f t h e e l e c t r o n s on t h e d i s l o c a t i o n , being o f importance o n l y f o r t h e f u l l and empty bands o f t h e screw (S, = k l n f / ( l - f ) . These parameters a r e known t o a f i r s t approximation from e l e c t r i c a l measurements and a r e f i t t e d t o t h e v e l o c i t y data v(T, Nc) i n doped S i and Ge (30-32/

r e l a t i v e t o t h e v e l o c i t y vi o f i n t r i n s i c m a t e r i a l according t o equations (4) and (6)

v = exp

&

where fi i s t h e occupancy o f t h e i n t r i n s i c d i s l o c a - t i o n and atheor = e2a/€b2 = 0.19 eV f o r Ge, 0.26 eV f o r S i . F i g u r e 6 shows t h e degree o f occupation vs.

deformation temperature and doping f o r 60" d i s l o c a - t i o n s i n S i c a l c u l a t e d from t h e known Fermi l e v e l w i t h the h e l p of equation (8), assuming Eo = 0.34 eV

- B(T-300 K) , 6 = 6 . 1 x 1 0 - ~ e ~ / ~ , ro = 3.8 1 . The f i t o f equation ( 9 ) t o t h e d a t a /31,32/ on S i does n o t work as w e l l as a previous attempt i n which a i n equation (6) was replaced by d. Such an e m p i r i c a l r e l a t i o n perhaps i n d i c a t e s a n i n t e r a c t i o n between t h e two k i n k s themselves. A s i m i l a r e v a l u a t i o n has been attempted f o r d i s l o c a t i o n s i n Ge /30/ and screws i n S i and f o r d i s l o c a t i o n s i n GaAs and InSb /27/.

5. Manipulation o f t h e d i s l o c a t i o n charge by i l l u m i - n a t i o n o r e l ' e c t r i c f i e l d s .- The degree o f occupation by e l e c t r o n s on t h e d i s l o c a t i o n may be changed from i t s e q u i l i b r i u m value by i l l u m i n a t i o n w i t h l i g h t o f

s u f f i c i e n t energy t o populate t h e d i s l o c a t i o n band b u t n o t s u f f i c i e n t f o r h e a t i n g t h e c r y s t a l ( b r i d g i n g t h e energy gap). This gives r i s e t o t h e s o - c a l l e d

"photomechanical e f f e c t " i f the r a t e o f k i n k forma- t i o n depends on f : Such an e f f e c t i s described i n d e t a i l a t t h i s meeting f o r I 1 V I - compounds where however more l o c a l i z e d i n t e r a c t i o n s o f t h e (charged) d i s l o c a t i o n w i t h a l i o v a l e n t i o n s may determine t h e d i s l o c a t i o n v e l o c i t y

7 XyX-X-

- ^{0.2 L}

750 800 850 goo 950 TCKI

F i g . 6 : Degree o f occupation o f d i s l o c a t i o n i n S i a t v a r i o u s temperatures and dopings c a l c u l a t e d by W. Schroter doping : (1) 1.4x1019, (2) 6x10''

( 3 ) 1 . 2 ~ 1 0 ' ~ ; (4) i n t r i n s i c , p doping : ( 5 ) z . ? x ~ o ~ ~

(6) 6.8x1017, ( 7 ) 8 ~ 1 0 ' ~ c m - ~ .

W i t h i n a Debye screening d i s t a n c e from t h e surface t h e d i s l o c a t i o n charge may be manipulated from t h e outside, e.g. by p o l a r i z a t i o n o f an e l e c t r o - l y t e . This leads t o band bending near t h e surface ( F i g . 7) and a change o f occupation o f d i s l o c a t i o n s t a t e s i n a near-surface l a y e r . I f again d i s l o c a t i o n m o b i l i t y i s determined by i t s charge one observes a

"chemomechanical e f f e c t " f o r near-surface d i s l o c a - t i o n s as a r e u s u a l l y observed i n v e l o c i t y measure- ments ( s e c t i o n 3 above).

F i g . 7 : Band s t r u c t u r e a t s u r f a c e which i s n e g a t i - v e l y charged. D i s l o c a t i o n band and valence band c a r r y p o s i t i v e charge near surface.

C6-I 16 JOURNAL DE PHYSIQUE

Such an e f f e c t i s w e l l known f o r i o n i c c r y s t a l s /28/ Sato, A. and Meshii, M., Acta M e t a l l . - 21 (1973) which a r e d u c t i l e a t e l e c t r o l y t e temperatures b u t 753.

,,,here the dis.ocat.on mobility is limited by inte- /29/ Schroter, W., Labusch, R. and Haasen, P., Phys.

Rev. 6, 15 (1977). - - r a c t i o n w i t h charged i m p u r i t i e s /33/.

/30/ P a t e l , J.R. and Chaudhuri, A.R., Phys. Rev. - 143 (1966) 601.

Acknowledgement.- Thanks are due t o W. Schroter and /31/ Erofeev, V.N. and N i k i t e n k o , V . I . , Sov. Phys.

S i r P e t e r H i r s c h f o r h e l p f u l discussions. S o l i d S t a t e 13 (1971) 116. - /32/ George, A., ThSse Nancy (1977).

/33/ MacMillan, N.H., Huntington, R.D. and Westwood,

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