A MECHANISM FOR THE EFFECT OF DOPING ON DISLOCATION MOBILITY

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A MECHANISM FOR THE EFFECT OF DOPING ON DISLOCATION MOBILITY

P. Hirsch

To cite this version:

P. Hirsch. A MECHANISM FOR THE EFFECT OF DOPING ON DISLOCATION MOBILITY.

Journal de Physique Colloques, 1979, 40 (C6), pp.C6-117-C6-121. �10.1051/jphyscol:1979624�. �jpa-

00219040�

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JOURNAL DE PHYSIQUE CoZZoque CF, s u p p l h e n t au n06, tome 40, j u i n 1979, page C6-117

A MECHANISM FOR THE EFFECT OF DOPING ON DISLOCATION M O B I L I T Y P.B. H i r s c h

Department of Metallurgy and Science o f Materials, University o f Oxford, Parks Road, Oxford, England

Resume.- Un modele nouveau e s t propose pour l ' a c t i o n des impuretes e l e c t r i q u e s sur l a v i t e s s e des d i s l o c a t i o n s dans l e s semiconducteurs c o o r d i n a t i o n tetrahPctri,que

.

La s t r u c t u r e e l e c t r o n i q u e des p a r t i e l l e s 8 30" e t 90°, l e s q u e l l e s sont l e s c o n s t i t u a n t s des di'slocations v i s e t 8 60'. e s t suppos@e se composer d'une bande complete e t d'une bande v i d e d ' e n e r g i e p l u s haute dans l ' e t a t n e u t r e . Les " k i n k s " sont suppos&s S t r e associ@s 8 des niveaux l o c a l i s @ s d 1 @ n e r g i e e n t r e l e s deux bandes de d i s l o c a t i o n s . L ' a c t i o n des impuretes e s t due

a

l a d i m i n u t i o n de l ' e n e r g i e l i b r e du systeme p a r l a t r a n s i t i o n d ' u n @ l e c t r o n / t r o u de l a bande de conduction/bande de valence, ou des bandes de d i s l o c a - t i o n s aux "kinks". Le modele expl i q u e raisonnablernent l a v a r i a t i o n de l a v i tesse des d i s l o c a t i o n s avec l a c o n c e n t r a t i o n des impuretes, 8 une temperature f i x e , e t donne des v a l e u r s de l ' e n e r g i e pour l e s niveaux l o c a l i s 6 s des " k i n k s " dans Ge e t S i , lesquels sont comparables aux niveaux d 1 6 n e r g i e associes avec l e s d i s l o c a t i o n s c o i n , determinges par des mesures e l e c t r i q u e s .

Abstract.- A new model i s proposed f o r t h e e f f e c t of doping on d i s l o c a t i o n v e l o c i t y i n t e t r a h e d r a l l y coordinated semiconductors. The e l e c t r o n i c s t r u c t u r e o f 30° and 90" p a r t i a l s , which a r e the compo- n e n t s of screw and 60' d i s l o c a t i o n s , i s assumed t o c o n s i s t o f a f u l l donor band an empty ( h i g h e r energy) acceptor band i n t h e n e u t r a l s t a t e . Kinks a r e thought t o be associated w i t h l o c a l i s e d acceptor/donor l e v e l s w i t h i n the gap of t h e d i s l o c a t i o n bands. The doping e f f e c t i s considered t o be due t o t h e r e d u c t i o n of t h e f r e e energy o f t h e system by t h e t r a n s i t i o n o f an e l e c t r o n / h o l e fkom t h e conduction/valence band, o r from t h e d i s l o c a t i o n bands, t o the k i n k s i t e s . The model accounts reasonably w e l l f o r t h e observed v a r i a t i o n o f d i s l o c a t i o n v e l o c i t y w i t h dopant c o n c e n t r a t i o n a t a g i - ven temperature, and y i e l d s values f o r t h e energies of the l o c a l i s e d k i n k s t a t e s i n Ge and Si, which a r e o f t h e same order as t h e energy l e v e l s associated w i t h edge d i s l o c a t i o n s as determined from e l e c t r i c a l measurements.

1. I n t r o d u c t i o n . - The i n f l u e n c e o f doping on d i s l o - c a t i o n v e l o c i t y i n Ge and S i and some 111-V com- pounds i s w e l l e s t a b l i s h e d /1-9/. The e f f e c t has been a t t r i b u t e d t o t h e i n f l u e n c e o f l i n e charge on the generation o f double k i n k s /3/, /6-9/. The theory o f F r i s c h and Pate1 /3/ i s phenomenological i n t h a t the authors assume 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 pro- p o r t i o n a l t o t h e f r a c t i o n o f charged d i s l o c a t i o n s i - tes; i n Haasen's /8/ t h e o r y t h e e f f e c t i s due t o a r e d u c t i o n i n a c t i v a t i o n energy o f double k i n k forma- t i o n due t o a decrease i n e l e c t r o s t a t i c energy o f a d i s l o c a t i o n r e s u l t i n g from t h e f o r m a t i o n o f a double k i n k . The a c t u a l formula used by Haasen /8/, which p r e d i c t s a change i n e l e c t r o s t a t i c energy p r o p o r t i o - nal t o t h e l e n g t h o f t h e double k i n k i s however i n e r r o r , and, a f t e r c o r r e c t i o n seems t o p r e d i c t t o o small an e f f e c t . Both t h e o r i e s (as published) seem t o assume t h a t t h e same basic mechanism operates f o r double k i n k generation on charged and uncharged d i s - l o c a t i o n s . This assumption leads t o t h e p r e d i c t i o n t h a t the change i n d i s l o c a t i o n v e l o c i t y i s t o be a t t r i b u t e d t o a change i n a c t i v a t i o n energy, w i t h o u t a p p a r e n t l y changing the pre-exponential f a c t o r . However, t h e experimental r e s u l t s f o r Ge and S i / I / , /6/ show f o r example t h a t t h e r a t i o o f t h e v e l o c i t y o f di'slocations i n doped n type t o t h a t i n undoped m a t e r i a l i s expected t o be, according t o t h e change

i n a c t i v a t i o n energy, about 100 times g r e a t e r than a c t u a l l y observed. I n t h i s paper we suggest how t h e doping e f f e c t may a r i s e from the n a t u r e o f t h e e l e c - t r o n i c s t a t e s associated w i t h t h e k i n k s formed i n t h e p a r t i a l d i s l o c a t i o n s .

2. M o b i l i t y and double k i n k formation.- 2.1.

Screw gl?locafjgns. -

2.1.1

.Sg:ggf !~g=;~~=gzgcgu=1g_up1~=gf

kighi2.- According t o Wagner and Haasen

/ l o / ,

screw d i s l o c a t i o n s , i .e. 30' p a r t i a l s , i n Ge a r e associated ( i n t h e n e u t r a l s t a t e ) w i t h a f u l l donor band a t 0.035 eV and an empty acceptor band a t 0.59 eV r e s - p e c t i v e l y above the valence band. For a wide range o f Ferrni l e v e l s w i t h i n t h e gap the d i s l o c a t i o n s w i l l t h e r e f o r e c a r r y l i t t l e charge. The presence o f a k i n k along t h e d i s l o c a t i o n d i s t u r b s t h e p e r i o d i c i t y and leads t o l o c a l i s e d s t a t e s w i t h i n the gap. F i g u r e 1 shows t h e p o s s i b l e s t r u c t u r e s o f t h e two types of k i n k i n a 30' p a r t i a l ; t h e s t r u c t u r e s o f t h e two k i n k s are d i f f e r e n t , b u t f o r s i m p l i c i t y we s h a l l assume t h a t they a r e b o t h associated w i t h s i m i l a r l o c a l i s e d s t a t e s , energy EBa

,

EBd f o r t h e acceptor and donor l e v e l s .

2.1-2 ~ ~ ~ ~ ~ ~ ~ ~ ~ D - x ~ ~ ~ ~ ~ ~ Y ~ - c o D ~ ~ P ~ ~ I : ~ = ~ u ~ M D E ~ P ~ ~ ~ ~

$i$kk.-

F o l l o w i n g H i r t h and Lothe /13/, and assuming t h a t the mean f r e e p a t h o f t h e k i n k s i s determined by a n n i h i l a t i o n by o t h e r s moving i n t h e o p p o s i t e d i - r e c t i o n , t h e p a r t i a l d i s l o c a t i o n v e l o c i t y vp i s

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979624

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C6-1 18 JOURNAL DE PHYSIQUE

given by

where ao i s t h e r e s o l v e d shear s t r e s s a c t i n g on t h e p a r t i a l , h t h e d i s t a n c e jumped forward by t h e d i s l o - c a t i o n , Fk the f o r m a t i o n energy o f one h a l f double kink, Dk t h e k i n k d i f f u s i v i t y .

F i g . 1 : P o s s i b l e s t r u c t u r e s of k i n k s i n 90' and 30" p a r t i a l s viewed normal t o t h e s l i p plane. The atoms i n t h e centres o f the k i n k s A and C, and adja- c e n t t o t h e two c e n t r e atoms i n k i n k B c o u l d t a k e up s l i g h t l y d i f f e r e n t p o s i t i o n s .

I n t h e steady s t a t e t h e v e l o c i t i e s o f both p a r t i a l s are the same, and i f t h e parameters a, Dk, Fk a r e d i f f e r e n t t h e s e p a r a t i o n D between t h e p a r t i a l s changes so t h a t an e f f e c t i v e s t r e s s

tk %

a c t s t o speed up one and t o r e t a r d t h e o t h e r p h i a l , so t h a t t h e two v e l o c i t i e s a r e equal. (Wi i s t h e i n - t e r a c t i o n energy p e r u n i t l e n g t h , i n c l u d i n g t h e f a u l t energy, between t h e two p a r t i a l s )

.

Assuming t h a t t h e s t r e s s term i n Fk can be neglected the steady s t a t e d i s l o c a t i o n v e l o c i t y vo i s

vo =

-

^2'effh2 ^Dk exp(-Fk/kT)

8 k ~ (2)

where oeff = 1 dWi

* E ~

1

(3)

Equation ( 2 ) gives t h e v e l o c i t y o f d i s l o c a t i o n s w i t h uncharged kinks, w i t h

Dk = bT2 v D exp(-Wm/kT)

where bT i s t h e t o t a l Burgers v e c t o r , v D the Debye frequency and Wm t h e a c t i v a t i o n energy f o r m i g r a t i o n o f an uncharged k i n k . Fk may i n c l u d e an e l e c t r o s t a - t i c term due t o t h e reducJion i n e l e c t r o s t a t i c energy due t o t h e f o r m a t i o n o f a k i n k (8), i . e . we can w r i t e

where Q i s the l i n e charge o f t h e d i s l o c a t i o n and ^E

t h e d i e l e c t r i c constant. T h i s e l e c t r o s t a t i c term w i l l be neglected i n what f o l l o w s .

2.1.3. E f f e c t of-chgyged-blDks.-

...

The f o r m a t i o n o f a double k i n k on a 30' p a r t i a l i s considered t o l e a d t o t h e generation o f acceptor/donor l e v e l s i n t h e gap (see 2.1.1.). The r e a c t i o n between an uncharged k i n k s i t e K and e.g. an e l e c t r o n e

K

+

e + K - ( 6 )

i s d r i v e n t o t h e r i g h t by i n c r e a s i n g the donor con- c e n t r a t i o n . Since t h e c o n c e n t r a t i o n o f t h e uncharged k i n k s i s expected t o be constant the t o t a l concentra- t i o n o f k i n k s increases, and since t h e d i s l o c a t i o n v e l o c i t y i s p r o p o r t i o n a l t o t h e c o n c e n t r a t i o n o f k i n k s ( i . e . t h e exponential term i n equation ( 2 ) ) t h i s provides a mechanism f o r t h e e f f e c t o f doping on d i s l o c a t i o n v e l o c i t y . If t h e Fermi energy EF>EBa2 EBd, the acceptor/donor l e v e l s o f t h e k i n k s , these w i l l tend t o be n e g a t i v e l y charged, and t h e r a t i o o f the concentrations o f n e g a t i v e l y charged and n e u t r a l k i n k s (-ck. o ~ k ) i n thermodynamic e q u i l i b r i u m i s determined by Fermi-Dirac s t a t i s t i c s t o be

where eV i s t h e e l e c t r o s t a t i c energy o f t h e ( s l i g h t l y ) charged d i s l o c a t i o n ( i n c l u d i n g t h e k i n k s ) . The e f f e c t o f t h e Fermi energy on d i s l o c a t i o n v e l o c i t y i s appa- r e n t from ( 7 ) . Equation ( 7 ) may a l s o be regarded as g i v i n g the r a t i o o f the c o n c e n t r a t i o n o f h a l f , doubly n e g a t i v e l y charged, double k i n k s , t o t h a t o f n e u t r a l h a l f double kinks.

Since t h e v e l o c i t y o f t h e d i s l o c a t i o n i s pro- p o r t i o n a l t o t h e c o n c e n t r a t i o n o f k i n k s ( o r o f h a l f double k i n k s ) through t h e exponential (-Fk/kT) term i n ( 2 ) , we can w r i t e f o r t h e v e l o c i t y o f t h e d i s l o - c a t i o n c o n t r o l l e d by n e g a t i v e l y charged double k i n k s

where AWm i s t h e d i f f e r e n c e i n m i g r a t i o n energy f o r charged and uncharged k i n k s . S i m i l a r l y , f o r p o s i t i - v e l y charged double kinks, i .e. f o r EF < EBd,

The t o t a l d i s l o c a t i o n v e l o c i t y due t o charged and uncharged k i n k s i s vo

+

v, o r vo

+

vp. I n o r d e r t o i n t e r p r e t t h e experimental r e s u l t s we need t o consi- d e r t h e temperature dependence o f EF. I n what f o l - lows we s h a l l n e g l e c t t h e term AWm. Using t h e usual approximate r e l a t i o n s f o r EF f o r i n t r i n s i c and n

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P.B. H i r s c h C6-1 19

t y p e m a t e r i a l , we f i n d f o r i n t r i n s i c m a t e r i a l :

i "'dh 3~ 1

-

_v =

(-1

^{exp (2Eg}

-

^EBa

-

^eV)/kT

o mde

where mdh9 mde a r e t h e e f f e c t i v e masses o f holes and e l e c t r o n ; n type m a t e r i a l :

--

-

N~

vo N ~ ( T / ~ o o ) ~ / ~ exp ( E

-

^EBa

^-

^eV)/kT

g

where ND i s t h e c o n c e n t r a t i o n o f donor atoms; p type m a t e r i a l :

v Nv(T/30O)%

I P

-

- -

exp

-

^(EBa

+

eV)/kT

0 A

where NA i s the c o n c e n t r a t i o n o f acceptor atoms. For valence band t r a n s i t i o n s f o r p type m a t e r i a l :

.A?=

v

N~

y2 exp(EBd + eV)/kT (13)

vo Nv(T/300)

I n s e r t i n g t y p i c a l values, t h e pre-exponential f a c - t o r s i n (11)

,

(13) a r e

%lo-'-

t h e r e i s an a d d i t i o n a l f a c t o r due t o t h e temperature dependence o f Eg and EB; eV w i l l a l s o vary w i t h temperature.

The charged k i n k mechanism w i l l t h e r e f o r e predomi- n a t e i f t h e exponential f a c t o r outweighs t h e pre- exponential f a c t o r , i . e . f o r s u f f i c i e n t l y l a r g e ND, NA i n ( l l ) , (13), and below a c r i t i c a l temperature.

It f o l l o w from ( l l ) , (12), (13) t h a t a t cons- t a n t T

l o g

-

= l o g ND

+

const.

0

(14) v

l o g

3

=

-

^{l o g}^N,

+

const.

vo (15

v

l o g

3

= l o g N~

+

const.

vo (16)

The r e s u l t s f o r screw d i s l o c a t i o n s i n n-type S i due t o P a t e l , T e s t a r d i and F r e e l and /6/ fit equation (14) w e l l over a range o f values (see f i g u r e 2 based on data from t h e i r paper).

The i n t e r c e p t made by t h e l i n e on t h e l o g ND a x i s i s c o n s i s t e n t ~ i t h known values f o r Nc and assuming a l i n e a r temperature dependence f o r Eg-EBa, s i m i l a r t o and scaled t o t h a t f o r Eg. The f i t w i t h equation (16) f o r p t y p e m a t e r i a l i s n o t q u i t e so good, b u t t h e r e s u l t s show c l e a r l y t h a t the mechanism o f equa- t i o n (13), n o t t h a t o f equation (12) operates. T h i s suggests t h a t EBd i s s u b s t a n t i a l . I n i n t e r p r e t i n g t h e a c t i v a t i o n energies, t h e temperature dependence o f t h e parameters Eg, EBa,d must be taken i n t o account. Assuming t h a t Eg, EBa,d v a r y l i n e a r l y w i t h temperature, t h e experimental data y i e l d values .corresponding t o T = 0 K. The changes i n a c t i v a t i o n

energy AF, r e l a t i v e t o t h a t f o r uncharged kinks, are given by the term i n t h e exponentials i n equations (10)

-

(13).

F i g . 2 : Logarithm of the r a t i o o f screw d i s l o c a t i o n v e l o c i t y i n n t y p e Si(vln) t o t h a t i n i n t r i n s i c S i ( v , i ) as a f u n c t i o n o f t h e l o g a r i t h m o f t h e donor c o n c e n t r a t i o n N

,

a t 600°C. A s t r a i g h t l i n e o f u n i t slope (see equa?ion (14) i s f i t t e d i n t h e range o f l o g l o N % 18.5-19.5. Data from P a t e l , T e s t a r d i and

~ r e e 1 an! /6/.

Thus

-

^(AF,,

-

^AFIi) ⁼7Eg-(eV)n+(eVfi 1 (17)

-

⁽^FZP

-

^Fli) ⁼^EBd+EBa

-

%g+(e~)p+(e~)i(18) Table I shows t h e r e s u l t s . The experimental value f o r

-

(AF,,-AF,i) i s i n good agreement w i t h 1/2 E suggesting t h a t the values o f eV a r e small. Assum~ng

s'

t h a t i n p type m a t e r i a l d i s l o c a t i o n s a r e p o s i t i v e l y chzrged, and i n n t y p e m a t e r i a l n e g a t i v e l y charged, t h e terms (eVb and (eV)i i n (18) w i l l cancel t o some e x t e n t . Assuming f u r t h e r t h a t EBd a EBa, t h e d a t a y i e l d a v a l u e o f EBa a EBd % 0.5 i 0.15 eV.

2.2. 60" DjslWcatjops

.-

^2.2.1. Effect-of-charged

---

kinks.- The 60' d i s l o c a t i o n c o n s i s t s o f a 30" and a

--- ---

90" p a r t i a l . The e l e c t r o n i c s t r u c t u r e o f t h e 90"

p a r t i a l i s u n c e r t a i n /ll/. We s h a l l assume here t h a t t h e r e i s a s u b s t a n t i a l gap between acceptor and do- n o r l e v e l s , t h a t t h e charge on t h e d i s l o c a t i o n i s r e l a t i v e l y small f o r a wide range o f Fermi l e v e l s , and t h a t deep acceptor/donor 1 eve1 s a r e associated w i t h t h e kinks, which l i e between t h e acceptor/donor l e v e l s f o r the 90" p a r t i a l . The s t r u c t u r e o f these k i n k s (A i n Fig. 1) has some s i m i l a r i t y t o t h a t o f t h e B type k i n k i n t h e 30" p a r t i a l ( F i g . 1 ) . We s h a l l assume f o r simp1 i c i ty t h a t t h e energy l e v e l s o f t h e l o c a l i s e d k i n k s t a t e s a r e the same as those assumed f o r both t h e k i n k s i n t h e 30" p a r t i a l , Eba,d.

I t f o l l o w s t h a t t h e change i n a c t i v a t i o n energy should be s i m i l a r t o t h a t f o r screw d i s l o c a t i o n s . Table I shows t h a t f o r S i t h e e x p e r i m e n t a l l y d e t e r - mined values of AF a r e indeed s i m i l a r t o those f o r

screw d i s l o c a t i o n s , t o w i t h i n t h e experimental e r r o r

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JOURNAL DE PHYSIQUE

Table I

I

Screw d i s l o c a t i o n i n s i l i c o n (600°C, 3 kg/mm2)

I

I I I

I

Derived o r

!

^Fexpt

i

^E~ ( A F - A F i ) e x ~ t

:

c a l c u l a t e d values

:

(eV) (eV) I (eV) I ^I (eV)

I 6 I I

I I I I

p type 8 ~ 1 0 ~ ' c m - ~ B

:

^1.7(2.15)

:

^{4 . 0 4} -0.452 .15 EBa,EBd4.5i0.15

I I I I

i n t r i n s i c

:

2.15 0.49 I 0 ^II

n-type 5 .5x101 'CIII-~AS 1.6 0.87 -0.55+ .15

-

^-$g1 ⁼^-0.58

Eg ( 0 K) = 1.16eV

(Experiments o f P a t e l , T e s t a r d i and Freeland /6/; t h e r e s u l t s f o r p type m a t e r i a l a r e f o r T

<

600°C; those i n b r a c k e t s f o r T 2 600°C).

60" d i s l o c a t i o n i n s i l i c o n (600°C, 12 k g / m 2 )

i

^Fexpt

I

^E~

I (eV)

:

(eV) (eV)

I 6

p t y p e 10' ' c ~ - ~ B

:

1.8 0.12

I I

i n t r i n s i c

:

^2.1 ^0.49

:

⁰ ^I

I I I I

n type 10' ' ~ m - ~ ~ s / S b

:

^1.5

1

0.77 -0.6?0.1

E (0 K) = 1 . 1 6 e V

I

Î Î Î

9 Î Î Î

(Experiments o f Erofeev and ~ i k i t e n k o /5/)

. '

I I

60' d i s l o c a t i o n i n germanium (500°C, 6 kg/mm2)

A A i e x p t (:%:

I E~

,

i

^Fexpt

I (eV) (eV)

i

⁽^eV⁾

I I

I I I

p type 2 ~ 1 0 ' ~ c m - ~ G a

:

1.75

:

%0.02 I 0

I I I

i n t r i n s i c

:

1.57 0.24

:

-0.18t0.15

:

<0.19+.15

t t I 1

n type 10' ' ~ m - ~ A s

1

1.2

:

^0.38

:

-0.5520.15

1

10.19t.15

Eg (0 K ) = 0.741 eV

:

ÎÎ ÎÎ ÎÎ

(Experiments o f Pate1 and ~ h a u d h r i / I / ) .

'

^I ¹

( t h e r e s u l t s i n ( 5 ) a r e s t a t e d t o be accurate t o a p p l i e s i n t h e p type region, 0.05 eV). The experimental value f o r -(AF,,-bFli) i s -(AFn

-

AF ) = E

-

EBa

-

eV

1 P 9

again i n good agreement w i t h

$ .

w h i l e EBa%EBd%

9 -(AFi

-

AF ) = -ZEg 1

-

EBa

-

^eV

0.44+0.1 eV. P

For Ge, t h e v a r i a t i o n o f v e l o c i t y w i t h doping c o n c e n t r a t i o n a t a given temperature f o r n type ma- t e r i a l i s c o n s i s t e n t w i t h t h a t p r e d i c t e d from t h e r a t i o o f equation (11) t o equation ( l o ) , i . e . s i m i - l a r t o t h a t o f equation (14), r e p l a c i n g vo by v, i and f o r p type m a t e r i a l w i t h t h a t p r e d i c t e d from t h e r a t i o o f equations (12) t o ( l o ) , i .e. s i m i l a r t o t h a t o f equation (15), r e p l a c i n g vo by v,

.

^(See

f i g u r e 3,' based on f i g u r e 1 o f /9/). The i n t e r c e p t s made by t h e l i n e s on t h e l o g ( i m p u r i t y c o n c e n t r a t i o n ) a x i s f o r l o g ( v e l o c i t y r a t i o ) = 0 a r e i n good agreement w i t h e s t a b l i s h e d values f o r Nc, Nv, Eg, mdh, mde. Contrary t o t h e case'of S i , f o r Ge t h e acceptor/

donor l e v e l s must be very c l o s e 'to t h e valence band, so t h a t t h e mechanism o f equation (12) operates.

Using t h e value o f Eg a t 0 K f o r Ge (= 0.741 ,eV), and assuming t h a t t h e uncharged k i n k mechanism vo

t a b l e I shows t h a t EBa<0.19+.15 eV.

3. Conclusions.- The simple t h e o r y presented e x p l a i n s reasonably w e l l t h e v a r i a t i o n o f d i s l o c a t i o n v e l o c i - t y w i t h dopant c o n c e n t r a t i o n . As regards t h e values o f a c t i v a t i o n energy, t h e l i m i t s o f e r r o r are r a t h e r l a r g e . Nevertheless t h e s i m i l a r i t y between the va- l u e s o f EBa%EBd<(0.19k0.15) eV f o r Ge, and o f EBa%EBd%

(0.45_+0.15)eV f o r Si, w i t h t h e energy l e v e l s f o r a h a l f f i l l e d band obtained by t h e Gottingen group from H a l l c o n d u c t i v i t y data, suggests t h e p o s s i b i l i t y t h a t the l a t t e r may be c o n t r o l l e d by edge d i s l o c a - t i o n s (60" p a r t i a l s ) , o r by geometric kinks, and t h a t t h e 90° p a r t i a l s have a band gap. I t should be noted t h a t t h e s t r u c t u r e o f t h e A and B type k i n k s i s r a t h e r s i m i l a r t o t h a t o f t h e atoms w i t h i n one p e r i o d o f the 60' p a r t i a l /11/. I t should a l s o be p o i n t e d o u t t h a t t h e s t r u c t u r e o f t h e 60° p a r t i a l

(6)

P.B. H i r s c h

shown i n f i g u r e 4 i n /11/ can be r e c o n s t r u c t e d i n two ways;

17 18 19 20

log IMPURITY CONCENTRATION

Fig. 3 : Logarithm o f the r a t i o o f 60" d i s l o c a t i o n v e l o c i t y i n n and p t y p e Ge t o t h a t i n i n t r i n s i c Ge as a f u n c t i o n o f t h e l o g a r i t h m o f t h e i m p u r i t y con- c e n t r a t i o n , a t 500°C. S t r a i g h t l i n e s w i t h u n i t s l o - pes have been f i t t e d t o t h e data reproduced from f i g u r e 1 o f Pate1 and T e s t a r d i /9/.

F i r s t l y , by j o i n i n g i n each p e r i o d (JJbT) t h e two atoms i n t h e 90' p a r t i a l c o n f i g u r a t i o n , l e a v i n g one d a n g l i n g bond p e r p e r i o d ; secondly, by j o i n i n g neighbouring atoms along t h e d i s l o c a t i o n i n p a i r s , which r e s u l t s i n one r e c o n s t r u c t e d bond o f t h e 90' p a r t i a l type, p l u s two o f t h e 30' p a r t i a l type per double p e r i o d (2J5bT), ( i .e. one 30" p a r t i a l p l u s one h a l f 90' p a r t i a l bond p e r p e r i o d ( f i b T ) ) . If t h e c a l c u l a t i o n s o f Marklund and Jones /14,15/ a r e c o r r e c t , and t h e l o w e r i n g o f t h e energy i s substan- t i a l l y g r e a t e r f o r t h e r e c o n s t r u c t i o n of the 90' p a r t i a l than f o r the 30° p a r t i a l bond, t h e f i r s t t y p e o f r e c o n s t r u c t i o n suggested above f o r t h e 60' p a r t i a l may have lower energy, and a h a l f f i l l e d band, w i t h one d a n g l i n g bond per p e r i o d ( f i b T ) r e - s u l t s .

References

/I/ P a t e l , J.R. and Chaudhuri, A.R., Phys. Rev.

143

(1966) 601.

/2/ P a t e l , J.R. and Freeland, P.E., Phys. Rev. L e t t . 18 (1967) 833.

-

/3/ F r i s c h , H.L. and P a t e l , J.R., Phys. Rev. L e t t . 18 (1967) 784.

-

/4/ P a t e l , J.R. and F r i s c h , H.L., Appl

.

Phys. L e t t . 13 (1968) 32.

-

/5/ Erofeev, V.N. and N i k i t e n k o , V . I . , Sov. Phys.

S o l i d S t a t e

13

(1971) 116.

/6/ P a t e l , J.R., . T e s t a r d i , L.R. and Freeland, P.E., p h y s . - ~ e v . ~ 1 3 (1976) 3548. See a l s o phys. Rev. ,:

B15

-

(1977) 4 n 1 .

/7/ Alexander, H., and Haasen, P., S o l i d S t a t e Phys.

22 (1968) 28.

-

/8/ Haasen, P . , Phys. Status S o l i d i ( a ) - 28 (975) 145.

/9/ P a t e l , J.R. and Testardi, L.R., Appl. Phys. ' L e t t . 30 (1977)

-

3.

/ l o /

Wagner, R. and Haasen, P., L a t t i c e Defects i n Semiconductors, I n s t . Phys. Conf. Ser. No.

23

(1975) 387.

/11/ H i r s c h , P.B., ( t h i s conference).

/12/ Labusch, R. and Schr8ter. W., L a t t i c e Defects

, . ^. ^.

i n ~ e m i c o n d u c t o r s , I n s t . Phys. Conf. Ser. No.23

(1975) 56.

-

/13/ H i r t h , J.P. and Lothe, J., Theory o f D i s l o c a - t i o n s (New York : McGraw-Hill) 1968.

/14/ Marklund, S., ( t h i s conference).

/15/ Jones, R., ( t h i s conference).

Acknowledgement.- I should l i k e t o t h a n k p r o f e s s o r s P. Haasen, R. Labusch and W. Schroter, and Dr J.R.

P a t e l , f o r v e r y h e l p f u l discussions.