THE TEMPERATURE DEPENDENCE OF EBIC CONTRAST FROM INDIVIDUAL DISLOCATIONS IN SILICON

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THE TEMPERATURE DEPENDENCE OF EBIC CONTRAST FROM INDIVIDUAL DISLOCATIONS

IN SILICON

A. Ourmazd, P. Wilshaw, G. Booker

To cite this version:

A. Ourmazd, P. Wilshaw, G. Booker. THE TEMPERATURE DEPENDENCE OF EBIC CON-

TRAST FROM INDIVIDUAL DISLOCATIONS IN SILICON. Journal de Physique Colloques, 1983,

44 (C4), pp.C4-289-C4-295. �10.1051/jphyscol:1983434�. �jpa-00223053�

THE TEMPERATURE DEPENDENCE OF EBIC CONTRAST FROM INDIVIDUAL DISLOCATIONS IN SILICON

A. Ourmazd , P.R. Wilshaw and G.R. Booker**

"Department of Electronics, The University, Southampton, U.K.

""Department of Metallurgy and Science of Materials, Parks Road, Oxford, U.K.

Résumé. - On peut, en principe, lier le contraste des images obtenues par EBIC de défauts étendus dans les semiconducteurs a la section de capture pour les porteurs minoritaires et donc au comportement précis en recombinaison de défauts individuels.

La mesure du contraste en EBIC en fonction de la température et de la concentration en impuretés est donc proposée comme méthode pour obtenir les positions des niveaux énergétiques associes à"

des dislocations individuelles bien caractérisées. Quelques résultats d'une telle étude sont présentes en vue de démontrer que les interprétations théoriques actuelles du contraste sont incapables de décrire correctement la variation observée du contraste en fonction de la température. Des modifications qui pourraient permettre aux traitements théori ques de mieux

décrire les résultats expérimentaux sont suggérées.

Abstract.'- The EBIC contrast from extended defects in semi- conductors can, in principle, be related to the defect capture cross-section for minority carriers and hence to the details of the recombination behaviour of individual defects. The

monitoring of EBIC contrast as a function of temperature and dopant concentration is proposed as a possible method for deducing the positions of energy levels associated with well- characterised, individual dislocations. Some results of such an investigation are presented to show that current theoretical interpretations of the EBIC contrast are unable to describe correctly the observed temperature - dependent properties of the contrast. Possible modifications, which may enable

theoretical treatments to describe better the experimental results, are suggested.

1. INTRODUCTION

The Electron Beam Induced Current (EBIC) mode of the SEM has long been used to reveal the presence of electrically active dislocations in semiconductor specimens. Only in recent years, however, have attempts been made to deduce quantitative information from this technique / l , 2, 3/ and relate such information to the details of the recombination process at individual defects / 4 / . A major advantage of the EBIC technique is its high spatial resolution and thus its ability to yield electrical data from individual extended defects.

Fig. 1(a) is a TEM micrograph of a widely dissociated screw dislocation obtained with a forbidden reflection of the type

1/3 (422) , where the stacking fault ribbon between the 30° partials of the dislocation is showing bright contrast / 5 / . Fig. 1(b) is the corresponding EBIC image, where the individual 30° partials are

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983434

C4-290 JOURNAL DE PHYSIQUE

Fig. 1 ( a ) TEM f o r b i d d e n r e f l e c t i o n and ( b ) EBIC micrograph o f a w i d e l y d i s s o c i a t e d screw d i s l o c a t i o n . The 300 p a r t i a l s a r e d i r e c t l y r e s o l v e d i n ( b ) . Note t h e a b s e n c e o f any E B I C c o n t r a s t from t h e s t a c k i n g f a u l t r i b b o n between t h e p a r t i a l s .

d i r e c t l y r e s o l v e d f o r t h e f i r s t time. S i n c e t h e u l t i m a t e s p a t i a l r e s o l u t i o n of an e l e c t r i c a l t e c h n i q u e i s e s s e n t i a l l y d e t e r m i n e d by t h e Debye s c r e e n i n g l e n g t h , which i n t h e sample o f Fig. 1 i s

a p p r o x i m a t e l y O . l p r n , it i s c l e a r t h a t EBIC i s c a p a b l e o f a p p r o a c h i n g t h i s r e s o l u t i o n l i m i t .

The q u a n t i t a t i v e p a r a m e t e r , which d e s c r i b e s t h e e l e c t r i c a l i n f o r m a t i o n o b t a i n e d from d e f e c t s by EBIC i s t h e s o - c a l l e d c o n t r a s t C = ( I b - I d ) / I where I b and I r e f e r t o t h e v a l u e s o f t h e c u r r e n t o b t a i n e d w i t h t k & e l e c t r o n beam P a r from and a t t h e d e f e c t r e s p e c t i - v e l y . The c o n t r a s t can be r e l a t e d , a l b e i t s u b j e c t t o v a r i o u s

a p p r o x i m a t i o n s , t o t h e c a p t u r e c r o s s - s e c t i o n o f t h e d e f e c t f o r m i n o r i t y c a r r i e r s / 4 , 6-9/. I t i s , i n a d d i t i o n , dependent on g e o m e t r i c a l f a c t o r s and t h e t h e o r i e s o f Donolato and Pasemann have been s p e c i a l l y s u c c e s s f u l i n a c c u r a t e l y d e s c r i b i n g t h e i n f l u e n c e of geometry on t h e EBIC c o n t r a s t .

I g n o r i n g t h e i n f l u e n c e o f geometry f o r t h e moment, t h e EBIC c o n t r a s t can b e c o n s i d e r e d a f u n c t i o n o f t h e d e f e c t c a p t u r e c r o s s - s e c t i o n

C = C ( o ) . The c a p t u r e c r o s s - s e c t i o n i s i n t u r n d e t e r m i n e d by t h e c h a r g e s t a t e o f t h e d e f e c t i . e . t h e p o s i t i o n o f t h e d e f e c t e n e r g y l e v e l Eo w i t h r e s p e c t t o t h e Fermi e n e r g y E f , and a l s o t e m p e r a t u r e ; C = C ( E o , E , ^{T ) .} I n samples c o n t a i n i n g n o t t o o h i g h d i s l o c a t i o n d e n s i t i e s , t i e F e m i e n e r g y i s d e t e r m i n e d by t h e dopant c o n c e n t r a t i o n Nd and T. Thus one may w r i t e C = C ( E o , Nd,T). Such a f u n c t i o n a l dependence p r o v i d e s , i n p r i n c i p l e , a means f o r

d e t e r m i n i n g e n e r g y l e v e l Eo, w i t h sub-micron s p a t i a l r e s o l u t i o n , by m o n i t o r i n g t h e EBIC c o n t r a s t a s a f u n c t i o n o f t e m p e r a t u r e and dopant c o n c e n t r a t i o n . I n p r a c t i c e one would m o n i t o r t h e EBIC c o n t r a s t from a p a r t i c u l a r d e f e c t , s a y i n n - t y p e m a t e r i a l , a s t h e Fermi e n e r g y i s moved from t h e v i c i n i t y o f t h e c o n d u c t i o n band edge t o w a r d s mid-gap by means o f r a i s i n g t h e sample t e m p e r a t u r e from a low v a l u e (- 100K) .

The n e g a t i v e c h a r g e on t h e d e f e c t would r a p i d l y d e c r e a s e when t h e Fermi energy i s lowered towards mid-gap t h r o u g h t h e d e f e c t e n e r g y l e v e l . A major r e d u c t i o n i n t h e m i n o r i t y c a r r i e r ( h o l e ) c a p t u r e c r o s s - s e c t i o n and hence E B I C c o n t r a s t would t h e r e f o r e s i g n i f y t h e n e a r c o - i n c i d e n c e o f t h e Fermi e n e r g y and t h e n e u t r a l p o s i t i o n o f t h e d e f e c t e n e r g y l e v e l . However, a s p o i n t e d o u t above, t h e EBIC

c o n t r a s t i s a l s o dependent on g e o m e t r i c a l f a c t o r s , such a s t h e d e f e c t d e p t h , and b e f o r e comparisons can be made between t h e b e h a v i o u r s o f d i f f e r e n t d e f e c t s , a s a t i s f a c t o r y method must b e found t o " n o r m a l i s e "

t h k s geometry dependence.

I n t h i s p a p e r we r e p o r t t h e r e s u l t s o f an on-going i n v e s t i g a t i o n

d e s i g n e d t o y i e l d t h e e n e r g y l e v e l s a s s o c i a t e d w i t h i n d i v i d u a l ,

w e l l - c h a r a c t e r i s e d , d i s l o c a t i o n s i n s i l i c o n by t h e EBIC t e c h n i q u e a s

-

'Ym Plan- view

Fig. 2 P l a n view ( a ) and c r o s s - s e c t i o n a l ( b ) TEM micrographs o f t h e deformation-induced d i s l o c a t i o n network.

o u t l i n e d above. I n o r d e r t o h i g h l i g h t t h e f u r t h e r advances needed i n t h e t h e o r e t i c a l d e s c r i p t i o n o f t h e E B I C c o n t r a s t , t h e r e s u l t s w i l l be r e s t r i c t e d t o t h e sample geometry and dopant c o n c e n t r a t i o n

d e s c r i b e d i n s e c t i o n 2 . The r e s u l t s o f s e c t i o n 3 w i l l be d i s c u s s e d i n s e c t i o n 4 t o i l l u s t r a t e t h e i r p o s s i b l e i m p l i c a t i o n s a s f a r a s c u r r e n t t h e o r i e s o f E B I C a r e concerned.

2. EXPERIMENTAL

The FZ s i l i c o n samples ( k i n d l y deformed and p r o v i d e d by t h e group o f P r o f . H. Alexander o f Cologne U n i v e r s i t y ) were phosphorus doped t o a c o n c e n t r a t i o n o f 1015 and deformed by a two-stage p r o c e d u r e a t 8 5 0 ~ ~ and 4 2 0 ~ ~ t o produce a d i s l o c a t i o n d e n s i t y o f

l o 7 ~ m - ~ . EPR examination o f t h e s e samples (performed by

D r . E. Weber o f Cologne U n i v e r s i t y ) have shown them t o c o n t a i n no EPR c e n t r e s o t h e r t h a n Si-K7 /lo/.

The samples were p o l i s h e d and f a b r i c a t e d i n t o S c h o t t k y d i o d e s by means o f a Au/Pd s u r f a c e m e t a l l i s a t i o n l a y e r d e p o s i t e d a t room t e m p e r a t u r e . The EBIC e x a m i n a t i o n s were performed by means o f a c o m p u t e r i s e d l o c k - i n E B I C system /11, 1 2 / , o v e r t h e t e m p e r a t u r e r a n g e 100-400K. I t was found t h a t , i n o r d e r t o o b t a i n r e p r o d u c i b l e r e s u l t s , t h e i r r a d i a t i o n t i m e o f t h e a r e a o f i n t e r e s t must be k e p t t o a

minimum. The u s e o f a computer f o r f a s t d a t a c o l l e c t i o n i s t h e r e f o r e e s s e n t i a l .

3. RESULTS

Fig. 2 ( a ) i s a plan-view TEM micrograph o f t h e d i s l o c a t i o n s

s t u d i e d . The d i s l o c a t i o n s l i e a l o n g <110> d i r e c t i o n s i n (111) p l a n e s

and are_ a l l c h a r a c t e r i s e d by a s i n g l e B u r g e r s v e c t o r o f t h e t y p e

a/2 <110>. The c r o s s - s e c t i o n a l TEM micrograph o f Fig. 2 ( b ) shows

t h e d e p t h d i s t r i b u t i o n o f t h e s e d i s l o c a t i o n s . I t i s c l e a r t h a t t h e

network c o n s i s t s of p l a n a r d i s l o c a t i o n a r r a y s l y i n g a t d i f f e r e n t

d e p t h s b e n e a t h t h e s u r f a c e .

C4-292 JOURNAL DE PHYSIQUE

Fig. 3 i s an EBIC micrograph o f a p a r t o f t h e network. Although i n d i v i d u a l d i s l o c a t i o n s a r e e a s i l y r e s o l v e d , q u a n t i t a t i v e c o n t r a s t measurements a r e n e c e s s a r y

b e f o r e d i f f e r e n t 4

d i s l o c a t i o n s can b e compared. I t must be

b o r n e i n mind t h a t

d i s l o c a t i o n s a t d i f f e r e n t

d e p t h s w i l l e x h i b i t Fig. 3 EBIC micrograph o f t h e d i f f e r e n t v a l u e s o f d i s l o c a t i o n network.

c o n t r a s t .

F i g . 4 i s a p l o t o f E B I C c o n t r a s t v s

t e m p e r a t u r e f o r two d i f f e r e n t d i s l o c a t i o n s i n t h e s e samples. The d i f f e r e n c e s i n t h e magnitudes o f c o n t r a s t may b e due t o a d e p t h e f f e c t . Donolato has shown t h a t t h e c o n t r a s t from a d i s l o c a t i o n can be w r i t t e n i n t h e form -

where

i s t h e r a d i u s o f " c y l i n d e r o f i n f l u e n c e " o f t h e d i s l o c a t i o n , T~ i s t h e l i f e t i m e i n s i d e t h i s c y l i n d e r , L i s t h e b u l k d i f f u s i o n l e n g t h , d t h e d e f e c t d e p t h and R t h e e l e c t r o n r a n g e /13/.

F d e n o t e s a f u n c t i o n a l dependence. Thus t h e " g e o m e t r i c a l i n f o r - mation" i s e n t i r e l y c o n t a i n e d by t h e f u n c t i o n F ( L , d, R ) .

A c c o r d i n g l y , it s h o u l d be p o s s i b l e t o e l i m i n a t e t h e g e o m e t r i c a l dependence o f t h e c o n t r a s t by c o n s i d e r i n g t h e E B I C c o n t r a s t

n o r m a l i s e d by i t s room t e m p e r a t u r e v a l u e CRT p r o v i d e d t h a t t h e b u l k d i f f u s i o n l e n g t h L i s t e m p e r a t u r e - i n d e p e n d e n t , which h a s been measured t o be t h e c a s e i n t h e s e samples /12/. For t h e n

- ⁼ and, t h e

'RT RT s

h

n o r m a l i s e d c o n t r a s t 3 C/CRT c o n t a i n s no

g e o m e t r i c a l dependence - ⁸

and must be t h e same f o r .- _In

a l l i d e n t i c a l d i s l o c a -

t i o n s . T h i s c o n c l u s i o n ... 2

remains v a l i d even i f o

d i f f e r e n t d i s l o c a t i o n s o f t h e same c h a r a c t e r a r e 2

a l l o w e d t o c o n t a i n

d i f f e r e n t c o n c e n t r a t i o n s 2

o f r e c o m b i n a t i o n c e n t r e s ,

f o r one can t h e n w r i t e 4

C . = n y F(L, d, R) and 100 150 2 00 250 300

a g a i n

c

., Temperature

& = _ ' I

which i s

'RT YRT

i n d e p e n d e n t o f geometry Fig. 4 A p l o t o f EBIC c o n t r a s t v s

and c o n c e n t r a t i o n o f t e m p e r a t u r e f o r two d i s l o c a t i o n s .

recombination c e n t r e s n.

t h a t t h e t e m p e r a t u r e Temperature

dependence o f t h e c o n t r a s t s

from d i f f e r e n t d i s l o c a t i o n s

can b e d e s c r i b e d by an Fig. 5 A p l o t o f n o r m a l i s e d EBIC e q u a t i o n o f t h e form: c o n t r a s t v s t e m p e r a t u r e f o r two

d i s l o c a t i o n s . The c o n t r a s t i s

dc =

d ~ "'RT

( 3 ) n o r m a l i s e d t o t h e v a l u e a t 100k.

F i g . 6 i s a p l o t o f dC/dT v s C f o r a number o f d i s l o c a t i o n s ; t h e a c c u r a c y w i t h which e q u a t i o n (qy ^{i s obeyed i s} remarkable.

t e m p e r a t u r e f o r two e

d i f f e r e n t d i s l o c a t i o n s

1.6 shows t h a t t h e n o r m a l i s a t i o n

p r o c e d u r e d e s c r i b e d above

i s u n a b l e t o e l i m i n a t e t h e 2 1.45

d i f f e r e n c e s between m

d i f f e r e n t d i s l o c a t i o n s o f

t h e same c h a r a c t e r . I t 1.3 must t h e r e f o r e be .-

concluded t h a t t h e " s t a n d - -

a r d " t h e o r y of E B I C 1.1 5 c a n n o t a d e q u a t e l y d e s c r i b e

t h e t e m p e r a t u r e dependence z ,.0

4. DISCUSSION

-

-

-

-

I I a

I t i s i m p o r t a n t a t t h i s s t a g e t o e s t a b l i s h t h a t t h e s t a n d a r d t h e o r y o f EBIC a s p r e s e n t e d i n r e f e r e n c e s 6 - 9 i s u n a b l e t o r e p r o d u c e t h e form o f e q u a t i o n ( 3 ) above. From (1)

o f E B I C c o n t r a s t .

I t t u r n s o u t , however, 100 150 200 250 300

C = Y F ( L , d, R)

= % F ( L , d l R) 36 dT

2 d c - 2 % ²⁸

CRT dT - Y RT dT

d ~ d ~ a C R T ( 4 ) d T dC i . e . - = 1 dy

a~ (G ^{ZF) 'RT 2 0}

-

o r

dT

l 2 Thus " s t a n d a r d " t h e o r y

p r e d i c t s t h a t a p l o t o f dC/dT v s CRT s h o u l d p a s s t h r o u g h t h e o r i g i n , a 4 p r e d i c t i o n which i s c o n t r a - dieted by experiment.

- ^Theory

Experiment

-

I I I

^, 7

-

I I

- :

8 8 I I

-,I' t I

J I : I

Furthermore, t h e h i g h e r

o r d e r c o r r e c t i o n t e r m s 0 4 8 12

s u g g e s t e d by Paseman / 9 / 'RT

a l s o seem u n a b l e t o

reproduce t h e form o f F i g . 6 A p l o t o f t h e r a t e o f change e q u a t i o n ( 3 ) . ^{o f E B I C} c o n t r a s t w i t h t e m p e r a t u r e ,

dC/dT v s room t e m p e r a t u r e c o n t r a s t C R T .

C4-294 JOURNAL DE PHYSIQUE

I t i s t h e r e f o r e i n t e r e s t i n g t o e n q u i r e what p o s s i b l e m o d i f i c a t i o n s t o t h e s t a n d a r d t h e o r y may be c a p a b l e o f r e p r o d u c i n g t h e non-zero i n t e r c e p t B o f e q u a t i o n ( 3 ) . A b a s i c assumption i n t h e t r e a t m e n t p r o v i d e d i n r e f e r e n c c s 6 - 9 i s t h a t t h e bulk d i f f u s i o n l e n g t h L i s c o n s t a n t t h r o u g h o u t t h e sample. Such an assumption i s c l e a r l y n o t v a l i d i n t h e c a s e o f samples w i t h an inhomogeneous d i s t r i b u t i o n o f p o i n t d e f e c t s and/or i m p u r i t i e s and may a l s o be v i o l a t e d i n t h e v i c i n i t y o f d i s l o c a t i o n s due t o t h e s t r a i n f i e l d s s u r r o u n d i n g them. A p o s s i b l e m o d i f i c a t i o n , t h e r e f o r e , i s a l l o w i n g t h e

d i f f u s i o n l e n g t h L t o b e d i f f e r e n t a t p o i n t s f a r from and c l o s e t o t h e d i s l o c a t i o n s . I f t h e d i f f u s i o n l e n g t h f a r from t h e d e f e c t i s d e s i g n a t e d by Lb, t h e c u r r e n t c o l l e c t e d w i t h t h e beam f a r from t h e d e f e c t ( t h e background c u r r e n t ) can be w r i t t e n a s :

I, = g ( 5 ) e - ' / ~ b dV ( 5 ) ( s e e r e f . 1 3 ) The c u r r e n t c o l l e c t e d when t h e beam i s a t t h e d e f e c t i s g i v e n by:

where C i n d i c a t e s i n t e g r a t i o n i n s i d e t h e c y l i n d e r o f i n f l u e n c e o f d e f e c t /13/ and t h e b u l k d i f f u s i o n l e n g t h Lb h a s been r e p l a c e d by a d i f f e r e n t v a l u e L. Thus t h e E B I C c o n t r a s t can be w r i t t e n a s :

C = 1 - F(L, Lb, R) + y G (L, Lb, R, d )

But G = (CRT - ¹ + ^F)/yRT

dC - 1

Thus - - - (CRT - ¹ + ^F) , which can b e w r i t t e n a s :

dT YRT

Thus a l l o w i n g t h e v a l u e o f t h e b u l k d i f f u s i o n l e n g t h t o v a r y o v e r t h e sample i s c a p a b l e o f r e p r o d u c i n g t h e o v e r a l l f e a t u r e s o f t h e e x p e r i m e n t a l r e s u l t s d e s c r i b e d i n s e c t i o n 3. One-dimensional c a l c u l a t i o n s s u g g e s t t h a t t h e v a r i a t i o n o f L can indeed c o r r e c t l y d e s c r i b e t h e o b s e r v e d r e s u l t s . However, d e t a i l e d t h r e e - d i m e n s i o n a l c a l c u l a t i o n s a r e r e q u i r e d t o c o n f i r m t h i s h y p o t h e s i s a s t h e o r i g i n of t h e e x p e r i m e n t a l o b s e r v a t i o n s and t h e p r e c e d i n g d i s c u s s i o n can o n l y be t r e a t e d a s i n d i c a t i v e a t t h i s s t a g e .

5. CONCLUSIONS

I t a p p e a r s t h a t t h e s t a n d a r d t h e o r i e s o f E B I C a r e u n a b l e t o

t h e o r y o f EBIC i s n e c e s s a r y b e f o r e t h e t e m p e r a t u r e - d e p e n d e n c e o f c o n t r a s t can b e used t o deduce q u a n t i t a t i v e i n f o r m a t i o n w i t h r e g a r d t o r e c o m b i n a t i o n a t i n d i v i d u a l d e f e c t s . A p o s s i b l e mechanism, which a t t h i s s t a g e a p p e a r s c a p a b l e o f e x p l a i n i n g t h e e x p e r i m e n t a l o b s e r v a t i o n s , i s a change o f t h e b u l k d i f f u s i o n l e n g t h a s t h e e l e c t r o n beam i s p l a c e d a t and f a r away from t h e d e f e c t . REFERENCES

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The a u t h o r s a r e g r a t e f u l t o D r . C. D o n o l a t o o f C.N.R./LAMEL,

Bologna and Messrs. R. B. Mears a n d M. P. Varnham o f Southampton

U n i v e r s i t y f o r u s e f u l d i s c u s s i o n s . F i n a n c i a l s u p p o r t from t h e

SERC i s acknowledged.