Thermopower in amorphous As2Se3

Volume 38A, n u m b e r 1

PHYSICS

THERMOPOWER R. CALLAERTS

IN

LETTERS

AMORPHOUS

**, P. NAGELS

3 J a n u a r y 1972

As2Se

3 *

and M. DENAYER

Solid Slate Physics Depa)~lrne~tt, S. C.K./C. E.N., B-2400 Mol, Belgium,7 Received 15 November 1971

In the t e m p e r a t u r e range from 120 to 200Oc the thermopower of amorphous As2Se 3 v a r i e s as S -7.08 and E S = 1.01 :L 0.05 eV, which is the same activation energy as the one obtained from the conductivity curve.

(Iz/eI(Es/kT+B) w i t h B

T h e c u r r e n t m o d e l of c o v a l e n t a m o r p h o u s semiconductors assumes that the conduction and v a l e n c e b a n d s h a v e t a i l s of l o c a l i z e d s t a t e s . In either band a well-defined energy separates the r a n g e s of e n e r g y w h e r e t h e s t a t e s a r e e x t e n d e d or localized. Whether the current is carried by c a r r i e r s m o v i n g m a i n l y in o n e of t h e s e r a n g e s w i l l d e p e n d on t h e w i d t h of t h e t a i l s of l o c a l i z e d s t a t e s a n d on t e m p e r a t u r e . T h e r e a p p e a r s to b e widespread agreement that at the present status of t h e o r e t i c a l k n o w l e d g e of a m o r p h o u s s e m i c o n ductors the electrical conductivity and the thermoelectric power are the most reliable paramet e r s to g e t i n s i g h t i n t o t h e o r i g i n of c o n d u c t i o n . T h i s l e t t e r d e s c r i b e s m e a s u r e m e n t s of dc c o n d u c t i v i t y ~ a n d t h e r m o p o w e r S on a m o r p h o u s A s 2 S e 3 a s a f u n c t i o n of t e m p e r a t u 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 s of ~ a n d S h a v e p r e v i o u s l y b e e n m e a s u r e d b y Uphoff a n d H e a l y [1] on a m o r p h o u s A s 2 S e 3 a n d b y E d m o n d [2] on l i q u i d A s 2 S e 3. A c h a r a c t e r i s t i c f e a t u r e of t h e l o g cr v e r s u s 1 / T c u r v e s i s the a b s e n c e of a n y d i s c o n t i n u i t y on p a s s i n g f r o m t h e g l a s s y to t h e l i q u i d s t a t e . On t h e c o n t r a r y , t h e t h e r m o p o w e r d a t a , as reported by the previous authors, show an abrupt jump when passing from the amorphous to t h e l i q u i d s t a t e . T h e s l o p e of t h e c o n d u c t i v i t y c u r v e f o r l i q u i d A s 2 S e 3 w a s f o u n d b y E d m o n d to b e 1.06 eV, w h i l e t h e a c t i v a t i o n e n e r g y d e d u c e d from the thermopower curve S =f(1/T) was h i g h e r a n d e q u a l to 1.2 eV. T h e a c c u r a c y of t h e experimental results is probably not high enough to s a y w h e t h e r t h i s i s a r e a l d i s c r e p a n c y . On t h e o t h e r h a n d , Uphoff a n d H e a l y c o n c l u d e d to a l i n * Work p e r f o r m e d in Association A g r e e m e n t between S. C. K./C. E. N. Mol and R i j k s u n i v e r s i t a i r Centrum Antwerpen, Antwerp, Belgium. ** R i j k s u n i v e r s i t a i r Centrum Antwerpen, Antwerp, Belgium.

ear dependence S = f(T) for amorphous As2Se 3 but, within the broad limits of the estimated accuracy, their thermopower data can also be approximated by a variation linear in I/T with a slope equal to 0.47 eV. Samples of amorphous As2Se 3 were prepared by heating proper amounts of the elements in evacuated quartz ampoules at 700°C and quenching in air. The temperature differences and the Seebeck potentials were measured with the help of two chromel-constantan thermocouples which were fused into the material to a depth of about I ram. The reliability of the measurements was checked not only by changing the temperature difference across the specimen but also by reversing the cold and the hot point. The temperature gradients ranged from approximately 5 to 15°C. After completion of the thermopower measurements the samples were cut in platelets of I mm thickness and the dc electrical conductivity was determined by Van der Pauw's method. In the temperature range from 115 to 220°C t h e c o n d u c t i v i t y i s of t h e f o r m (7 = C e x p ( - E ~ / k T ) w i t h E(r = 0.98 eV a n d C = 6.6 × 103 ~ - 1 c m - 1 . T h e t h e r m o p o w e r , w h i c h is p o s i t i v e , c a n b e f i t t e d to a n e x p r e s s i o n of t h e f o r m S = ( k / e ) ( E s / k T + B ) (fig. 1), w h e r e E S = 1.01 i 0.05 eV and B = -7.08. For liquid As2Se3, Edmond found B = -10.6, whereas the thermopower data of Uphoff a n d H e a l y f o r a m o r p h o u s A s 2 S e 3 , w h e n replotted as S versus l / T , yield B ~ -2.8. Our thermopower data are much higher than the ones r e p o r t e d b y Uphoff a n d H e a l y a n d , w h e n e x t r a p o l a t e d to h i g h e r t e m p e r a t u r e s , a r e in good a g r e e m e n t w i t h E d m o n d ' s r e s u l t s f o r l i q u i d A s 2 S e 3. In t h e l i g h t of t h e p r e s e n t c o n c e p t s a b o u t t h e d i f f e r e n t w a y s of c u r r e n t t r a n s f e r in a m o r p h o u s s e m i c o n d u c t o r s , t h e m a j o r f e a t u r e of o u r r e s u l t s i s t h e e q u a l v a l u e of t h e a c t i v a t i o n e n e r g y 15

Volume 38A, n u m b e r 1

PIIYSICS

3 January 1972

ing t h a t E F l i e s in t h e m i d d l e of t h e g a p , b u t t h a t t h e t a i l of l o c a l i z e d s t a t e s i s w i d e r f o r t h e c o n d u c t i o n b a n d t h a n f o r t h e v a l e n c e b a n d , M o t t [6] favoured the possibility E F - E v E c - E F. F o r a h i g h e r n u m b e r of h o l e s a n d on t h e a s s u m p t i o n of a l i n e a r v a r i a t i o n of tile F e r m i l e v e l w i t h t e m p e r a t u r e t h e c o n d u c t i v i t y a n d tile t h e r m o power can be represented by:

7000,

c~

>

o K

LETTEIIS

- (~o exp (y k) e x p I - ( E F - EV) T = o / k T ]

l"

1001]1

and F-

i

1400, 7

S77

714

20

107 ( K 1} T

Fig. 1, 'Fhermopower of three samples of amorphous As2Se 3 as a function of the i n v e r s e absolute t e m p e r a ture. associated with the conductivity and thermop o w e r (1.0 eV). T h i s f e a t u r e s t r o n g l y s u g g e s t s t h a t in t h e i n v e s t i g a t e d t e m p e r a t u r e r a n g e c o n duction occurs via delocalized states. Indeed, if t h e c a r r i e r s m o v e b y h o p p i n g in t h e l o c a l i z e d states, the conductivity varies exponentially with temperature and the measured activation energy i s t h e s u m of t h e a c t i v a t i o n e n e r g i e s f o r c a r r i e r c r e a t i o n a n d f o r h o p p i n g . T h e r e f o r e , one e x p e c t s a d i f f e r e n c e in s l o p e b e t w e e n t h e c o n d u c tivity and thermopower curve, which has not b e e n o b s e r v e d f o r A s 2 S e 3. T h e h i g h v a l u e of t h e p r e - e x p o n e n t i a l C in t h e c o n d u c t i v i t y e x p r e s s i o n a l s o p o i n t s to c o n d u c t i o n in t h e e x t e n d e d s t a t e s . I n d e e d D a v i s a n d M o t t [3] s u g g e s t e d t h a t v a l u e s of C in t h e r a n g e of 1 0 2 - 1 0 4 ~ - 1 c m - 1 a r e t y p i c a l f o r t h i s t y p e of c o n d u c t i o n . In t h e g e n e r a l c a s e of e l e c t r o n a n d h o l e c o n t r i b u t i o n , t h e t h e r m o p o w e r f o r c o n d u c t i o n in t h e n o n - l o c a l i z e d s t a t e s i s g i v e n by [4, 5]: crS= ores e + CrhSh

( k / e ) [ ( E F - E v) y _ f f l e T - 7

k + 1].

In t h i s c a s e t h e t h e r m o p o w e r , w h e n p l o t t e d a s S versus 1 T, does show the same activation energy as the conductivity. This has been observed experimentally. The temperature coefficient 7 obtained from our thermopower data is 6.3 > 10 -4 eV K -1, w h e r e a s tile t e m p e r a t u r e c o e f f i c i e n t 13 of t h e o p t i c a l b a n d g a p f o u n d b y K o l o i n l e t s a n d P a v l o v [7] i s 1 1 × 10 -4 e V K -1 ( 3 ~ 2 7 ) . From the pre-exponential C ao exp (Z/k) o n e f i n d s cro ~ 2 f~-I c m - 1 . A s e c o n d p o s s i b i l i t y to e x p l a i n t h e p o s i t i v e s i g n of S i s g i v e n b y t h e c o n d i t i o n : E F - E v E c - E F a n d C h : Ce, w h i c h i s t h e r e q u i r e m e n t f o r i n t r i n s i c c o n d u c t i o n . In t h i s c a s e t h e r a t i o of t h e s l o p e s of t h e t h e r m o p o w e r a n d t h e c o n d u c t i v ity c u r v e s a l l o w s one to d e t e r m i n e (aoh - J o e )/' (~5oh + Poe); t h i s e x p r e s s i o n w i l l o n l y b e c l o s e to one for a high ratio ~oh/~oe. For As2Se 3 the s l o p e s a r e e q u a l w i t h i n t h e l i m i t s of p r e c i s i o n , w h i c h a m o u n t s to a b o u t 5%; t h e r a t i o (Croh- Poe ) / (aoh + ~oe) c a n t h e r e f o r e l i e w i t h i n t h e l i m i t s 0.95 a n d 1, w h i c h y i e l d s Croh L 50 ~oe" T h e p r e s e n t r e s u l t s , h o w e v e r , do n o t a l l o w u s to d e c i d e w h e t h e r t h e p o s i t i v e s i g n of S a r i s e s f r o m a h i g h e r n u m b e r of h o l e s o r f r o m a l a r g e r s h a r e of C h to t h e c o n d u c t i v i t y . T h e a u t h o r s w i s h to t h a n k L. V a n Gool a n d R. Jans for their technical assistance.

w i t h S e = - ( k / e ) [ ( E c - E F ) / k T + 11 ,

S h = (le/e)[(E F - E v ) / k Y + 1] Ucfe~cnce8 and

% = Ce exp[-(E c - EF)/kT], oh = C h e x p [ - ( E F - E v ) / l e T ]

w h e r e E e , E v s e p a r a t e t h e e n e r g i e s of l o c a l i z e d from extended states. For As2Se 3 the thermopower has a positive sign, which indicates that holes are the most numerous carriers (E F - E v < E e - EF) a n d / o r C h > C e. By a s s u m 16

[1] H.L. Uphoff and J . t t . Healy, J. Appl. Phys. 32 (1961) 950. [2] J . T . Edmond, Brit. J. Appl. Phys. 17 (1966) 49. [3] E. A. Davis and N. F. Mort, Phil. Mag. 22 (1970) 903. [4] M. Cutler and N . F . M o t t , Phys. Rev. 181 (1969) 1336. [5] N.K. Hindley, J. Non-Cryst. Sol. 5 (1970) 17. [6] N.F. Mott, Phil. Meg. 24 (1971) 1. {7] B. T. Kolomiets and B. V. Pavlov, Soy. Phys. - Semicond. ] (1967) 350.