CAPACITANCE TRANSIENT SPECTROSCOPY OF STATES LOCALISED AT DISLOCATIONS

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CAPACITANCE TRANSIENT SPECTROSCOPY OF STATES LOCALISED AT DISLOCATIONS

W. Schröter, M. Seibt

To cite this version:

W. Schröter, M. Seibt. CAPACITANCE TRANSIENT SPECTROSCOPY OF STATES LO- CALISED AT DISLOCATIONS. Journal de Physique Colloques, 1983, 44 (C4), pp.C4-329-C4-337.

�10.1051/jphyscol:1983439�. �jpa-00223058�

JOURNAL DE PHYSIQUE

Colloque C4, supplément au n°9, Tome 44, septembre 1983 page C4-329

CAPACITANCE TRANSIENT SPECTROSCOPY OF STATES LOCALISED AT DISLOCATIONS

W. Schroter and M. Seibt

IV. Physikalischea Institut dev Universitat Gottingen and

Sonderforschungsbeveioh 12,6 Gottingen-Clausthal, Bunsenstrasse 11-15, 3400 Gottingen, F.R.G.

Résumé

Le présent travail est une application de la DLTS aux défauts étendus à multi-êlectrons et une interprétation des spectres mesurés en terme de défauts ponctuels.

Comme exemple, nous discutons les spectres des états de coeur des dislocations dans le silicium du type n et ceux des images de défauts ponctuels autour des dislocations dans le germanium de.

type n également. En comparant ces résultats aux calculs théo- riques récents, nous concluons à la possibilité

d' observation dans le silicium des états de coeur d'une dis- location partielle à 60 incomplètement reconstruite.

abstract

This work is concerned with deep level transient spectroscopy (DLTS) of extended many-electron defects and a qualitative interpretation of measured spectra as compared to that of point defects. As examples the spectra of dislocation core states in n-type silicon and of point defect clouds surrounding the dislocation in n-type germanium are discussed. From a comparison of these results with recent theoretical calculation it is concluded, that in silicon possibly the core states of incompletely reconstructed 60° - partial dislocation have been observed.

Introduction

Dislocations in semiconductors are extended, many-electron centers whose experimental characteristics show pronounced differences to those of isolated point defects. The Coulomb interaction of the captured elec- trons among each other and between them and the bulk semiconductors gives rise to a long-range potential, which affects the coupling be- tween dislocation and bulk. In chapter I we describe how the long- range potential at a charged dislocation establishes itself experi- mentally in capacitance transient spectroscopy (DLTS). In chapter II we give a qualitative interpretation of these effects and indicate how the microscopic parameters of the dislocation might be derived from measured spectra. In chapter III we compare spectra obtained for de- formed n-type silicon and germanium, with recent theoretical predic- tion and arrive at the proposal, that in silicon it might be the core states at the 60°-partial dislocation which are responsible for a line observed by DLTS.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983439

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I D i s l o c a t i o n c o r e s t a t e s i n DLTS

To make more p r e c i s e t h e problem which we a r e d e a l i n q w i t h we b r i e f l y o u t l i n e t h e m a t h e m a t i c a l e q u a t i o n s which r e l a t e d e f e c t p a r a n e t e r s t o measured c a p a c i t a n c e t r a n s i e n t s d C ( t )

.

Ref e r r i n g t o t h e n o t a t i o n s

i n t r o d u c e d i n f i g . 1 , we have f o r t h e time- and p o s i t i o n - d e p e n d e n t o c c u p a t i o n f ( z , t ) o f t h e d e f e c t :

Sf ^(%t)

3 k

⁼

c,

^in(a,t)(j - ! ( E , & ) )

- en f [a, t)

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

f o r d i s l o c a t i o n s p a r a l l e l t o t h e S c h o t t k y c o n t a c t .

I n a r i g i d - b a n d approximation af

.kT

i s t h e h e i g h t of t h e long- r a n g e p o t e n t i a l a t t h e d i s l o c a t i o n . P l e a s e n o t e t h a t beyond t h i s appro- x i m a t i o n , e . g . i n t h e c a s e , t h a t t u n n e l i n g becomes r a t e c o n t r o l l i n g , a l s o t h e t e r m i n e q u a t i o n ( 2 ) d e s c r i b i n g e m i s s i o n becomes n o n - l i n e a r .

F i g . 1: E l e c t r o n t r a n s f e r r a t e s ( e m i s s i o n and c a p t u r e ) between t h e c o n d u c t i o n band and a deep p o i n t d e f e c t ( a ) o r a d i s l o c a t i o n

(b). n i s t h e f r e e e l e c t r o n d e n s i t y o u t s i d e the long-range p o t e n t i a l s u r r o u n d i n g t h e d i s 1 o c a t i o n . d

= d ( h , , , ~ ~ )

i s depen- d e n t o f t h e screevsing l e n g t h

AD

and an i n n e r c u t - o f f r a d i u s

E q u a t i o n ( 1 ) i s l i n e a r i n any d e v i a t i o n h f . f r o = t h e s t a t i o n a r y s t a t e ( A f , = f - f under r e v e r s e b i a s V0! A f l = -f d u r i n g t h e f i l l i n g p u l s e a t b i g s V1 = Vo

- A

V ) and 1s e a s i l y s o l v e d

P

Afi

Lilt) = n F i ( z \ b i

WP(-

I n s e r t i n g t h i s s o l u t d o n i n t o an e x p r e s s i o n , d e r i v e d from P o i s s o n ' s

e q u a t i o n : _hl

F i g . 2 : ( a ) Band edge of t h e c o n d u c t i o n band E

,

Fermi l e v e l and deep d e f e c t l e v e l ET w i t h i n t h e s p a c e cfiarge r e g i o n ( e x t e n s i o n w o r w under r e v e r s e biasVo and b i a s V1 = V

-

i j V d u r i n g tRe f i l l i n g p u l s e , r e s p e c t i v e l y ) o f t h e s c h o t ? k y c g n t a c t . The c r o s s - o v e n between

p

and ET a r e a t w

-h

^{o r w4}

- A .

Note t h a t E i s measured a s t h e f r e e e n t R a l p y of e l e c t r o n e m i s s i o n

A & .

F i g . 2 :(b) According t o a c o n c e p t g i v e n by Pons t h e s t a t i o n a r y occupa- t i o n f and f l u n d e r b i a s V and V , can be approximated by s t e p f z n c t i o n . During t h e B i l l i n g p u l s e of d u r a t i o n t t h e o c c u p a t i o n of f i l l e d t r a p s f ( t ) i s a l s o a s t e p functBon, p r o c e e d i n g t o t h e l e f t w i t h i n g r e a s i n g t

P'

(N d e n s i t y o f deep d e f e c t s t a t e s ) y i e l d s t h e d e s i r e d r e l a t i o n between

XC

^{( t )} and t h e d e f e c t p a r a m e t e r s . Pons ( 4 / 5 ) has developped a s i m p l e c o n c e p t o f how one may v i s u a l i z e t h e f i l l i n g F r o c e s s . I t i s g i v e n i n f i g . 2.

C4-332 JOURNAL DE PHYSIQUE

Equation ( 2 ) i s n o n - l i n e a r i n f and c o n s e q u e n t l y t h e r e i s no g e n e r a l a n a l y t i c s o l u t i o n . T h i s h a s made s e v e r a l a u t h o r s (6-8) a n a l y z e t h e i r r e s u l t s o b t a i n e d f o r d i s l o c a t i o n s i n terms of t h e formulas d e r i v e d f o r i s o l a t e d p o i n t d e f e c t s . However, t h e p a r a m e t e r s d e r i v e d i n t h i s way remain dubious i n t h e i r p h y s i c a l meaning. I n c h a p t e r I11 we s h a l l s k e t c h a p o s s i b l e a n a l y t i c p r o c e d u r e v a l i d f o r d i s l o c a t i o n s .

C a p a c i t a n c e t r a n s i e n t s h C ( t ) o f S c h o t t k y c o n t a c t s c o n t a i n i n g a s m a l l amount o f deep p o i n t o r e x t e n d e d d e f e c t s ( s m a l l : c o n c e n t r a t i o n o f c h a r g e c a r r i e r s t r a n s f e r r e d t o t h e deep c e n t e r s d c d o p i n q c o n c e n t r a t i o n

Ned)

a s measured a s a f u n c t i o n of t e m p e r a t u r e T and r e g i s t e r e d by a l o c k - i n a m p l i f i e r w i t h f r e q u e n c y vL w i l l be c h a r a c t e r i z e d i n t h e f o l l o w i n g .

The main c h a r a c t e r i s t i c o f t h e e m i s s i o n from deep c e n t e r s can be s e e n i n f i g . 3 ( 9 ) . There t h e l i n e shape o f DLTS f o r an e x t e n d e d d e f e c t , i n t r o d u c e d by p l a s t i c d e f o r m a t i o n a t 810° C i s compared t o t h a t a s s o - c i a t e d w i t h an i s o l a t e d p o i n t d e f z c t (dashed l i n e ) . Due t o i t s s t a b i - l i t y t o a n n e a l i n g up t o 900° C ( = .68 Tm, Tm m e l t i n g t e m p e r a t u r e ) t h e l i n e h a s been a t t r i b u t e d t o d i s l o c a t i o n c o r e s t a t e s ( 6 , 7 ) .

F i g . 3 : The l i n e a s s o c i a t e d w i t h d i s l o c a t i o n s i n n-type s i l i c o n shows a t a i l on t h e low-temperature s i d e and d e v i a t e s t h e r e a p p r e c i a b l y from t h a t o f a p o i n t d e f e c t (dashed c u r v e ) . Note t h a t t h e r e i s a s m a l l a d d i t i o n a l l i n e DE1 a s s o c i a t e d w i t h a p o i n t d e f e c t , which h a s t o be s u b t r a c t e d t o o b t a i n t h e l i n e a t t r i b u t e d t o d i s l o c a t i o n s .

The l o n g t a i l s a t t h e low-temperature s i d e have been a l s o observed i n p l a s t i c a l l y deformed germanium ( 1 0 ) and cadmium t e l l u r i d e ( 1 1 ) . I t has been d e m o n s t r a t e d by r e c o r d i n g t h e t r a n s i e n t s A C ( t ) by a s i g n a l - a v e r a g e r ( 9 ) , t h a t t h e t i m e law o f e m i s s i o n i s e x p o n e n t i a l a l s o f o r extended d e f e c t s above a b o u t t h e t e m p e r a t u r e , where t h e t a i l s s e t i n , n o t f o r t h e t a i l r e g i o n .

F i g . 4 and 5 compare t h e c a p t u r e c h a r a c t e r i s t i c s o f p o i n t and e x t e n - ded d e f e c t s . For i s o l a t e d p o i n t d e f e c t s AC ( t ) a s a f u n c t i o n o f t

,

t h e d u r a t i o n of t h e f i l l i n g p u l s e , approaches a q u a s i - s a t u r a t i o n P a c c o r d i n g t o t h e law 6 C ( t ) -(I

-

exp ( - c n t

)J,

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

4 C ~ l t n h a s been found i n a r a n g e o? s m b 1 t ( 7 , 9 , 1 2 ) . For b o t h t y p e s of g e f e c t s

h c

a s a f u n c t i o n o f t h e f i l l i n 5 p u l s e v o l t a g e A V h a s been found t o be l i n e a r i n A V w i t h a t h r e s h o l d AV; ( 9 ) .

P

P

F i g . : C a p t u r e c h a r a c t e r i s t i c s & . C ( t n ) f o r a p o i n t d e f e c t (

- .

-

~ , . h = ) 0 - 5 5 - 4 and f o r h i s l o c a t i o n s i n n-type s i l i c o n ( - - - ) ( f o r parameters s e e f i g . 3 )

While f o r p o i n t d e f e c t s t h e a n a l y t i c p r o c e d u r e d e s c r i b e d above, y i e l d s , i f a p p l i e d t o t h e e m i s s i o n and c a p t u r e c h a r a c t e r i s t i c s , a c o n s i s t e n t s e t of p a r a m e t e r s o f t h e d e f e c t , it does n o t f p r d i s l a c t i o n s .

JOURNAL DE PHYSIQUE

Fig. 5: Capture c h a r a c t e r i s t i c s LC ( A V ) f o r a p o i n t d e f e c t ( a ) and f o r d i s l o c a t i o n s i n n-type silBcon (b).

I1 Q u a l i t a t i v e I n t e r p r e t a t i o n

I f A C i s e x p o n e n t i a l i n t i m e d u r i n g e m i s s i o n , t h e e m i s s i o n r a t e e n a t t h e t e m p e r a t u r e of t h e l i n e maximum Tmax i s p r o p o r t i o n a l t o t h e l o c k - i n f r e q u e n c y v

=.

F o r p o i n t d e f e c t s t h e p r i n c i p l e of d e t a i l e d ba- l a n c e a l l o w s t o e x p r e s s e a s a f u n c t i o n of c n , A Hn and

A s n

and from t h e measured r e l a t i o n e n ?T,,,) one d e r i v e s A H n and c: = c n e x p ( + s n / k )

( 3 ) . The t h r e s h o l d

A

V + , o b s e r v e d i n t h e c a p t u r e c h a r a c t e r l s t l c L C ( A V , t ) marks t h e point: where t h e s t e p f u n c t i o n f ( z , t ) ( s e e

f i g . 2 )Pgo& o v e r t h e p o s i t i o n wo

- A

( s e e f i g .

2

)

. ^A

^G,, t h e F r e e en- t h a l p y of e l e c t r o n e m i s s i o n , c a n be d e r i v e d f r o m A ~ + . F u r t h e r m o r e t h e d e f e c t c o n c e n t r a t i o n NT and cn i s o b t a i n e d f r o m p ~ ( A V p , t p ) . I n what f o l l o w s we g i v e an o u t l i n e of an a n a l y t i c p r o c e d u r e of capa- c i t a n c e t r a n s i e n t s p e c t r a f o r d i s l o c a t i o n s . I t i s b a s e d on a n a p p r o x r m a t i v e e v a l u a t i o n o f t h e s t a t i o n a r y v a l u e s of f i ^{( 2 )} and on a s o l u - t i o n of e q u a t i o n ( 2 ) i n t h e l i m i t i n g c a s e t / t e - v O ( t e d u r a t i o n o f t h e e m i s s i o n p e r i o d ) . The example d i s c u s s e 8 r e f e r s t o d i s l o c a t i o n s i n n-type s i l i c o n a s s o c i a t e d w i t h an empty band i n t h e upper h a l f o f t h e band gap. I t i s assumend t h a t a t any p o s i t i o n w i t h i n t h e s p a c e c h a r g e r e g i o n of t h e S c h o t t k y c o n t a c t w e have N d f i & Ncdr where Nd i s t h e d e n s i t y of s t a t e s a s s o c i a t e d w i t h t h e d i s l o c a t i o n . The d i s - l o c a t i o n and i t s s c r e e n i n g c h a r g e i s p r e s e n t e d a s a d e f e c t w i t h an o c c u p a t i o n - d e p e n d e n t c a p t u r e c o e f f i c i e n t c n . e x p (-d f ) ( s e e equ. ( 2 ) ), w h i l e t h e e l e c t r o n d e n s i t y i n t h e c o n d u c t i o n band i s assumed t o f o l l o w t h e p o t e n t i a l of t h e u n d i s t u r b e d S c h o t t k y b a r r i e r . The r e s u l - t i n g f u n c t i o n s f i ( z ) a r e shown i n f i g . 6 . Note, t h a t t h e o c c u p a t i o n remains r a t h e r s m a l l ( - 0 . 1 ) and t h a t t h e t r a n s i t i o n from t h e b u l k v a l u e t o z e r o i s smeared o u t , s o t h a t f i ( z ) c a n n o t be approximated by s t e p f u n c t i o n a s i n t h e c a s e o f p o i n t d e f e c t s .

F i g . 6: S t a t i o n a r y o c c u p a t i o n f o and f l of d i s l o c a t i o n s under r e v e r s e b i a s V and V1 i n n - t y p e s i l i c o n . An empty narrow band i n t h e upper h a l f

09

t h e band gap h a s been a s s o c i a t e d w i t h d i s l o c a t i o n . The assumed v a l u e f o r d i s 1 5 0 , which i s n e a r t o t h a t r e a l i z e d i n t h e e x p e r i m e n t s w i t h n-type s i l i c o n ( s e e f i g . 3)

.

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The e q u a t i o n which r e l a t e s A H and cf w i t h t h e measured e ( T m a x ) of t h e e m i s s i o n p r o c e s s , i s f 8 r d i s l k c a t i o n s t h e same a s f o r p o l n t d e f e c t s e x c e p t f o r a f a c t o r , which a c c o u n t s f o r t h e d i f f e r e n t

s c r e e n i n g of t h e l i n e c h a r g e i n t h e s p a c e ( s c ) r e g i o n of t h e S c h o t t k y c o n t a c t and i n t h e b u l k ( b ) . T h i s f a c t o r i s o f t h e o r d e r

e x p [ a s c d b ) . f,

,

b u t i s v e r y d i f f i c u l t t o e s t i m a t e w i t h some p r e c l s l o n .

During c a p t u r e and e m i s s i o n t h e o c c u p a t i o n f ( z , t ) w i l l i n g e n e r a l l i e somewhere between f o and f

,

a p p r o a c h i n g f ( z ) f o r t / t --i> 0

and f ( z ) f o r s u f f i c i e n t l y l a r g e v a l u e s o f

?

/te. We s g a l f d i s c u s s t h e f i r s t c a s e h e r e , b u t we mention a l s o t h a t tRe second c a s e a l l o w s f o r an e a s y e s t i m a t i o n o f Nd. The d e v i a t i o n A f i from t h e s t a t i o n a r y s t a t e f o r t /te -P 0 w i l l be s m a l l d u r i n g t h e e m i s s i o n p e r i o d compared t o t h a t duryng t h e c a p t u r e p e r i o d : b f o L

4

f

Approximating 1

-

f by 1 and assuming&Af,C~lthe s o l u t i o n of e q u a t i o n ( 2 ) f o r t h e e m i s s i o n i s :

and f o r t h e end of t h e c a p t u r e p e r i o d :

Note that

~ f ~ ( & ~ - k 4 ~ ~ ~ )

⁼

(4, -fD) - ^A~?[O!')

From f i g . 6 it can b e s e e n , t h a t t h e e x p o n e n t i a l

i n

e q u a t i o n ( 4 ) d e c r e a s e s a b r u p t l y , where f o ( z ) b e g i n s t o grow. T h i s i s due t o t h e f a c t , t h a t t h e c a p t u r e r a t e d e c r e a s e s e x p o n e n t i a l l y w i t h i n c r e a s i n g

f , ( z ) .

The s o l u t i o n ( 5 a ) h a s been d e r i v e d under t h e c o n d i t i o n

ol

e n f I . A l o g a r i t h m i c dependence on t i s e x p e c t e d i f e x p ( d A f l ) ~ e n . f t L

) I

i n t h e r a n g e , where f o Z O . wePthen have I P

( 5 1 The p l a y i n g t o g e t h e r of e q u a t i o n s ( 4 ) and ( 5 ) may be v i s u a l i z e d a s f o l l o w s : f o l l o w i n g n ( z )

,

c r o s s e s t h e z - a x i s a t a p o i n t which p r o c e e d s from z = w., t o

tijt~;f:

and l e a d s t o a measurable c o n t r i b u - t i o n A C ( t ) a s soon a s t h i s p o i n t c r o s s e s t h e s t e e p d e c r e a s e of

4

^{f o ( Z , t )}

.

^{I f tp} i s k e p t c o n s t a n t , a f i n i t e t h r e s h o l d v o l t a g e

A V

+

1s needed, b e f o r e a s i g n a l

A C

( t ) can be d e t e c t e d . While f o r i s o l a e e d p o i n t d e f e c t s t h e t h r e s h o l d i s d i r e c t l y r e l a t e d t o t h e p o i n t p = A G n , i t i s f o r d i s l o c a t i o n s d e p e n d e n t onAGn and c n (ju t h e Fermi l e v e l i n t h e b u l k ) .

A c o n s i s t e n c y check of t h i s d e s c r i p t i o n i s p o s s i b l e by performing t h e i n t e g r a t i o n i n e q u a t i o n ( 3 ) w i t h t h e s o l u t i o n s ( 4 ) a n d ( 5 ) , d e t e r - mining Nd and c from AC ( A

v

, t o ) and comparing t h e dependencies and v a l u e of cn w i d t h e experimk?ntally e s t a b l i s h e d ones and w i t h t h e v a l u e of c, o b t a i n e d from t h e c r o s s o v e r , r e s p e c t i v e l y .

111. Core s t a t e s and p o i n t d e f e c t c l o u d s a t d i s l o c a t i o n s i n s i l i c o n and germanium

The deformation-induced d e f e c t - i n n-type s i l i c o n , which g i v e s r i s e t o a deep l e v e l w i t h A a n - - 0.37 eV, has been a s s o c i a t e d w i t h d i s l o - c a t i o n c o r e s t a t e s b e c a u s e o f i t s s t a b i l i t y on a n n e a l i n g a t 900° C

( c

0.68 T,). Are t h e r e i n d i c a t i o n s t o what t y p e of d i s l o c a t i o n s t h e s e s t a t e s belong?

I n n-type germanium by d e f o r m a t i o n a t 420° C

( 2

0.57 T ) a d e f e c t w i t h AHnc0.29 e V i s i n t r o d u c e d , which shows t h e asymmevric l i n e s h a p e characteristic of a n e x t e n d e d d e f e c t , b u t n o l o g - a r i t h m i c t i m e depen- d e n c e i n t h e c a p t u r e c h a r a c t e r i s t i c ( 1 0 ) . On a n n e a l i n g a t 580° C

( s

0 . 7 Tm) f o r 70 min t h e l i n e a m p l i t u d e d e c r e a s e s by a n o r d e r of m a g n i t u d e , A H n r e m a i n s unchanged, b u t t h e c a p t u r e c h a r a c t e r i s t i c i s now t h a t of an i s o l a t e d p o i n t d e f e c t .

To e x p l a i n t h e s e f i n d i n g s , t h e a u t h o r s ( 1 0 ) c l a i m t h a t t h e low-tem- p e r a t u r e d e f o r m a t i o n ( L 0 . 6 Tm) h a s i n t r o d u c e d p o i n t d e f e c t c l o u d s s u r r o u n d i n g t h e d i s l o c a t i o n , which a r e u n s t a b l e on a n n e a l i n g . T h e r e a r e no f u r t h e r l i n e s i n DLTS, s o t h a t o n e may c o n c l u d e t h a t t h e d i s - l o c a t i o n t y p e , whose c o r e s t a t e s g i v e r i s e t o a l i n e i n n - t y p e s i l i - c o n , d o e s n o t i n t r o d u c e any s t a t e s i n t h e u p p e r h a l f o f t h e band g a p o f germanium. A c c o r d i n g t o r e c e n t c a l c u l a t i o n s by Veth and T e i c h l e r

( 1 3 , 1 4 ) t h i s s i t u a t i o n i s e x p e c t e d f o r t h e i n c o m p l e t e l y r e c o n s t r u c t e d 6 0 O - ~ a r t i a l , i n whose c o r e d a n g l i n g bonds and s t r e t c h e d bonds r e m a i n w i t h a p e r i o d i c i t y l e n g t h o f 6.8 AO i n s i l i c o n . The s t r e t c h e d b o n d s , n o t a f f e c t e d by a c h e m i c a l s h i f t , l h t r o d u c e a n empty band i n t o t h e u p p e r h a l f o f t h e band g a p i n s i l i c o n and r e s o n a n c e s t a t e s i n t h e c o n d u c t i o n band o f germanium.

Acknowledgement

The a u t h o r s a r e g r a t e f u l t o K. Ahlborn f o r computer c a l c u l a t i o n s and t o M. Gbk and G. Z i r o f o r p r e p a r i n g t h e m a n u s c r i p t .

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