A STUDY OF THE GROUND STATE OF ACCEPTORS IN SILICON FROM THERMALTRANSPORT EXPERIMENTS

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A STUDY OF THE GROUND STATE OF ACCEPTORS IN SILICON FROM

THERMALTRANSPORT EXPERIMENTS

A. de Goër, M. Locatelli, K. Lassmann

To cite this version:

A. de Goër, M. Locatelli, K. Lassmann. A STUDY OF THE GROUND STATE OF ACCEPTORS IN

SILICON FROM THERMALTRANSPORT EXPERIMENTS. Journal de Physique Colloques, 1981,

42 (C6), pp.C6-235-C6-237. �10.1051/jphyscol:1981667�. �jpa-00221603�

JOURNAL DE PHYSIQUE

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&cembre 1981 page

A STUDY OF THE GROUND STATE OF ACCEPTORS I N S I L I C O N FROM THERMAL TRANSPORT EXPERIMENTS

A.M.

K.

Service des Basses Tempgratures, Laboratoire de Cryophysique, Centre drEtudes NucZgaires de GrenobZe, 85 X, 38041 GrenobZe Ceder, France

" PhysikaZisches I n s t i t u t , University of Stuttgart, 7000 Stuttgart 80, F.R.G.

ABSTRACT - Thermal c o n d u c t i v i t y measurements o f s i l i c o n c r y s t a l s doped w i t h B o r I n have shown t h e presence o f s e v e r a l phonon s c a t t e r i n g processes. The r e s o n a n t e f f e c t observed below 1 K i s a s c r i b e d t o t h e e x i s t e n c e o f a d i s - t r i b u t i o n o f s p l i t t i n g s N(6) o f t h e r8 ground s t a t e o f t h e a c c e p t o r , which c o u l d be r e l a t e d t o t h e presence o f oxygen and carbon i m p u r i t i e s . I n two cases, t h e maximum o f N(6) occurs f o r 6 max near 6 GHz, i n agreement w i t h p r e v i o u s u l t r a s o n i c s t u d i e s ( 6

4 GHz).

Samples and Experiments - The thermal c o n d u c t i v i t y o f f o u r S i s i n g l e c r y s t a l s doped w i t h B o r I n has been measured from 50 mK t o 200 K. Three c r y s t a l s have been s t u d i e d by u l t r a s o n i c a b s o r p t i o n i n S t u t t g a r t and some o f t h e s e r e s u l t s have been a l r e a d y p u b l i s h e d [11. The c h a r a c t e r i s t i c s o f t h e samples a r e g i v e n i n t a b l e 1.

TABLE 1

+ T h i s sample has been measured p r e v i o u s l y above 1 . 2 K [ 2 1

R e s u l t s and qua1 i t a t i v e d i s c u s s i o n - The e x p e r i m e n t a l r e s u l t s a r e d i s p l a y e d i n f i g . 1 i n a l o g - l o g p l o t and show t h a t t h r e e t e m p e r a t u r e ranges can be c o n s i d e r e d .

( i ) T

2 K Resonant phonon s c a t t e r i n g i s p r e s e n t i n t h e t h r e e samples measured i n t h i s t e m p e r a t u r e range. We a s c r i b e t h i s s c a t t e r i n g t o a d i r e c t process between t h e two energy l e v e l s a r i s i n g f r o m t h e r8 a c c e p t o r ground s t a t e , t h e s p l i t t i n g b e i n g v a r i a b l e f r o m s i t e t o s i t e due t o random s t r a i n s and e l e c t r i c f i e l d s . The d i s t r i -

C

Sample Dimensions (mrnxmm xmm ) Acceptor

(n cm) NA ( ~ m - ~ ) no (cm-3) nc (cm-3) Growth method

%ax. (GHZ)

S 87 d

3 . 0

3.0 x 34 B 2.5 5 . 4 l o i 5

z 2.1015

< 5.1015 F1. zone 1 . 3 S 80 g

2.6

3.0 x 35 B 10.8 1 . 2 1015 5 . 7 1017 4 . 1 l o L 6

Cz ( f r o m u l t r a s o n i c s ) > 4

i

S 5 2

2.3

3 . 0

14 I n 0 . 1 5.10

8 . 1 0

? C z

>

4

S 33 *

0.85 ~ 3 . 0 3

11 I n

2 5.10

7.10

?

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981667

JOURNAL

DE

F i g u r e 2. S o l i d l i n e s a r e not

c a l c u l a t e d

F i g u r e 1.

b u t i o n s N(6) have been s t u d i e d a t f r e q u e n c i e s l e s s t h a n 4 G H z by u l t r a s o n i c a t t e n u a - t i o n and r e l a t e d t o t h e presence o f carbon o r oxygen i m p u r i t i e s i n t h e c r y s t a l s [ I ] . The phonon r e l a x a t i o n r a t e due t o t h i s process i s g i v e n a p p r o x i m a t i v e l y by

?-I(,) =

i2 ^N(6=w)/PI

^{v 2 ( 1 )}

where D i s a mean v a l u e o f t h e c o u p l i n g c o n s t a n t , and t h e q u a l i t a t i v e shape o f N ( 6 ) i s g i v e n by t h e f u n c t i o n T 2 / ~ [ 3 1 . I n f i g . 2, T2/K i s p l o t t e d as a f u n c t i o n o f T f o r t h e t h r e e samples s t u d i e d . A maximum i s observed n e a r 0.19 K i n t h e case o f S i : I n (5.1017/cm3) and 0.09 K i n t h e case o f S i : B (1.2 1015/cm3), which would c o r r e s - pond v e r y c r u d e l y t o f r e q u e n c i e s 6rnax o f 15 and

G H z r e s p e c t i v e l y . I n t h e case o f S i : B ( 5 . 1 0 ~ ~ / c m 3 ) t h e maximum i s n o t reached a t t h e l o w e s t temperatures, so t h a t must be l e s s t h a n 4 G H z . These r e s u l t s a r e i n v e r y good q u a l i t a t i v e agree- ment w i t h t h o s e o b t a i n e d b y u l t r a s o n i c measurements and g i v e n i n t a b l e 1.

( i i ) 2

T

30 K A v e r y c l e a r d i p appears near 20 K i n t h e case o f t h e In-doped

samples, which has been a l r e a d y observed and a t t r i b u t e d t o an e x c i t e d J a h n - T e l l e r

l e v e l o f t h e a c c e p t o r n e a r 40 cm-I [2]. A s m a l l e f f e c t c o u l d be p r e s e n t n e a r 3 K i n

t h e more h i g h l y doped S i

B sample so t h a t t h e r a t i o o f t h e t r a n s i t i o n e n e r g i e s f o r

t h e two systems would be a b o u t 5, a v a l u e n o t i c e a b l y l a r g e r t h a n p r e v i o u s l y sup- posed [41.

( i i i ) T

30 K The d i p n e a r 40 K p r e s e n t i n t h e l i g h t l y doped S i : B c r y s t a l and n o t i n t h e h i g h l y doped one i s a t t r i b u t e d t o t h e presence o f i s o l a t e d oxygen i n t e r s - t i t i a l ~

t h e two c r y s t a l s c o n t a i n d i f f e r e n t amount o f oxygen (see t a b l e 1 ) and i n f a c t , t h e two curves c r o s s near 20 K. T h i s r e s o n a n t s c a t t e r i n g observed n e a r 40 K i s a l s o p r o b a b l y p r e s e n t i n t h e In-doped samples and c o u l d be r e l a t e d t o a t r a n s i t i o n n e a r 80 cm-l, i n r e a s o n a b l e agreement w i t h t h e energy l e v e l scheme o f oxygen deduced f r o m FIR a b s o r p t i o n measurements [51.

Q u a n t i t a t i v e a n a l y s i s - A p r e l i m i n a r y a n a l y s i s o f t h e r e s u l t s i n t h e temperature range T

1 K f o r t h e two samples c o n t a i n i n g oxygen and carbon has been c a r r i e d o u t w i t h i n t h e Debye a p p r o x i m a t i o n . Only boundary s c a t t e r i n g (rgS1

c o n s t a n t ) and s c a t - t e r i n g by t h e a c c e p t o r s as d e s c r i b e d by e q u a t i o n ( 1 ) have been c o n s i d e r e d . We have used an e x p r e s s i o n o f N(6) w h i c h g i v e s a s a t i s f a c t o r y d e s c r i p t i o n o f t h e d i s t r i b u - t i o n o b t a i n e d b y a Monte-Carlo c a l c u l a t i o n f o r p o i n t d e f e c t s such as carbon [ll.

The general 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 T2/K curves ( f i g . 2 ) can be d e s c r i b e d b y such an a n a l y s i s and, w i t h t h e parameters g i v e n i n t a b l e 2, t h e p o s i t i o n and i n t e n - s i t y o f t h e maximum a r e w e l l reproduced, b u t n o t t h e d e t a i l e d shape o f t h e c u r v e s . The values o f 6max o b t a i n e d f r o m t h e s e f i t s a r e s i m i l a r i n t h e two c r y s t a l s , i n c o n t r a s t w i t h t h e crude e s t i m a t i o n s f r o m t h e p o s i t i o n o f t h e p i c s g i v e n above.

TABLE 2

T h i s a n a l y s i s a l s o g i v e s values o f ~ ~ E ~ a n d , supposing t h a t a l l t h e a c c e p t o r s c o n t r i b u t e t o t h e s c a t t e r i n g , we o b t a i n t h e values o f D g i v e n i n t a b l e 2, which a r e n o t unreasonable. F u l l d e t a i l s w i l l be pub1 i s h e d e l sewhere.

References

[l] LASSMANN K. and ZEILE H, i n "Phonon S c a t t e r i n q i n Condensed M a t t e r " e d i t e d by MARIS H . J . , Plenum Press (1980), 369.

[ 2 ] DE COMBARIEU A. and LASSMANN K. i n "Phonon S c a t t e r i n g i n S o l i d s " e d i t e d by CHALLIS L.J. e t a1 . , Plenum Press (1976), 340.

[ 3 ] CHALLIS L.J., DE GOER A.M. and HASELER S.C., Phys. Rev. L e t t e r 2 (1977) 558.

[ 4 ] SIGMUND E. and LASSMANN K. i n "Phonon S c a t t e r i n g i n Condensed M a t t e r "

e d i t e d by MARIS H.J., Plenum Press (1980) 417.

151 HAYES W. and BOSOMWORTH D.R., Phys. Rev. L e t t e r s 23 (1969), 851.

- D ( e v ) 1.5 0.63 Sample

S i : B ( S 8 O g ) S i

I n (S 5 2 )

I

6maX (GHz) 6 . 2 k 0 . 4 5.6 k 0 . 4

~ ~ B ~ ( e r g ~ c ~ n - ~ ) 6.5

5.1

NA ( ~ m - ~ )

1.2 l 0 l 5

5.1017