PHONON INDUCED ANOMALOUS RESISTIVITY IN STRUCTURAL PHASE TRANSITION OF PbSnTe

(1)

HAL Id: jpa-00221307

https://hal.archives-ouvertes.fr/jpa-00221307

Submitted on 1 Jan 1981

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

PHONON INDUCED ANOMALOUS RESISTIVITY

IN STRUCTURAL PHASE TRANSITION OF PbSnTe

T. Suski, S . Katayama

To cite this version:

(2)

JOURNAL DE PHYSIQUE

CoZZoque C6, supp2dment au n o 12, Tome 42, ddcembre 1981 page c6-758

PHONON INDUCED ANOMALOUS RESISTIVITY I N STRUCTURAL PHASE TRANSITION O F

PbSnTe

T. Suski and S. ~atayama*

High Pressure Research Center, Polish Academy of Sciences, Warsaw, SokoZowska

29, Poland

*

_{Department of Physics, Osaka University,}_{1-1 Machikane-yma, Toyonaka, 560}

Japan A b s t r a c t .

-

LJe r e p o r t a n anomalous e l e c t r i c a l r e s i s t i v i t y i n c r e - ment A p o n PbSnTe n e a r t h e v i c i n i t y of t h e s t r u c t u r a l p h a s e t r a n s i t i o n t e m p e r a t u r e Tc. Applying h y d r o s t a t i c p r e s s u r e lowers Tc and l e a d s t o a d e c r e a s e o f A p . I t i s r e a s o n a b l y i n t e r p r e t e d t h a t A p i s due t o t h e f r e e c a r r i e r s c a t t e r i n g from t h e s o f t TO phonon. The o b s e r v e d i n i t i a l s l o p e o f Tc w i t h i n c r e a s i n g p r e s - s u r e is a l s o d i s c u s s e d by u s i n g t h e L i t t l e w o o d formula.

1. I n t r o d u c t i o n . - The I V - V I compound s e m i c o n d u c t o r s such a s (Pb ,Ge,Sn)- Te a l l o y s e x h i b i t a s t r u c t u r a l phase t r a n s i t i o n from r o c k s a l t s t r u c - t u r e t o rhombohedrally d i s t o r t e d s t r u c t u r e . The s o f t e n i n g of t h e t r a n s v e r s e o p t i c a l (TO) phonon a t q=O i n d i c a t e s the s t r u c t u r a l i n s t a - b i l i t y i i l t l l e s e s m a l l gap m a t e r i a l s . A sequence o f r e c e n t e x p s r i x s n t s have e l u c i d a t e d t h e n a t u r e o f i n s t a b i l i t y a s s o c i a t e d w i t h t h e i n t e r - band electron-phonon c o u p l i n g . 2 I n p a r t i c u l a r PbSnTe h a s a t t r a c t e d o u r a t t e n t i o n on t h e " z e r o " gap n a t u r e a s w e l l a s on t h e phase t r a n s i t i o n . The p u r p o s e o f p r e s e n t paper i s t o r e p o r t t h e e l e c t r i c a l t r a n s p o r t measurements o n P b 1-x S n T e x (x=0.44, 0.54, 0.80 and 0.86) f r o m 4 . 2 t o 150 K by a p p l y i n g h y d r o s t a t i c p r e s s u r e . From t h e anomalous p o r t i o n o f r e s i s t i v i t y n e a r Tc under p r e s s u r e , we e x p l o r e t h e p r e s s u r e dependence o f Tc a s w e l l a s t h e f r e e c a r r i e r s c a t t e r i n g mechanism g i v i n g rise t o A P .

2. Experiments.- Measurements o f H a l l c o e f f i c i e n t and r e s i s t i v i t y p

were made f o r s o l u t i o n grown s i n g l e c r y s t a l by u s i n g t h e t e c h n i q u e o f h e l i u m gas compression t o produce the h y d r o s t a t i c p r e s s u r e s . D e t a i l s o f c r y s t a l c h a r a c t e r i z a t i o n were g i v e n e l s e w h e r e . 3,4

(3)

Fig. 2 : Temperature dependence of

0

20

40

60

80

A p a t f o u r p r e s s u r e s . S o l i d l i n e s

Temperature

(K)

_{experiments which a r e o b t a i n e d by}and denote c a l c u l a t i o n s and

Fig. 1 : p vs. T a t f o u r p r e s s u r e s . s u b t r a c t i n g t h e smooth background from p i n Fig. 1.

There appears a prominent c u s p - l i k e anomaly A p f o r each p r e s s u r e . The lowering peak s h i f t with i n c r e a s i n g p r e s s u r e corresponds t o d e c r e a s e of Tc. According t o e a r l i e r t h e o r e t i c a l a n a l y s i s on ~ n ~A p e i n PbSnE ~ , may a l s o be due t o t h e c a r r i e r s c a t t e r i n g from t h e s o f t TO mode. ExpLic-

it form of r e s i s t i v i t y by t h e TO phonon s c a t t e r i n g pTO i s given by 8

2 2

where wTO ( q ) i s t h e TO phonon frequency a s w 2 ( q ) = wTO ( T )

+

Aq

,

k F I

TO

N(EF) and mTO, r e s p e c t i v e l y , a r e t h e Fermi wave number, t h e d e n s i t y of s t a t e a t t h e Fermi l e v e l EF and t h e m a t r i x element i n v l o v i n g t h e i n t e r

-+

band electron-phonon deformation p o t e n t i a l E I f we used a high tem- cv'

p e r a t u r e e x p r e s s i o n f o r t h e Planck d i s t r i b u t i o n f u n c t i o n a s n(w)=GT/liw i n Eq. (1) I pTO i s p r o p o r t i o n a l t o T. Figure 2 shows t h e c a l c u l a t e d pTO by Eq.

(1) and t h e experimental p o i n t s from Fig.1 a s a f u n c t i o n of T a t f o u r pres- s u r e s on Pb0.56Sn0,44Te. The v a l u e of

1 / / A

i s e s t i m a t e d t o be 2 . 4 4 ~ 1 0 ' ~ cv- eVcm l s e c which i s o b t a i n e d by f i t t i n g -e

pTO with Ap a t 1 b a r . The o v e r a l l fea-

z1

-

t u r e i n Ap i s w e l l reproduced by pTO s o

1 ,

,

t h a t Ap mainly comes from t h e s o f t mode

OO 0.5 1

.o

1.5 s c a t t e r i n g . Note t h a t t h e c u s p - l i k e Pressure (KMr) _{anomaly around}_Tc _{i n}_pTO _{i s}_{produced by}

F i g . 3 : A p ( T c ) v s . p r e s s u r e . the mean f i e l d behavior of w a s

(4)

C6-760 JOURNAL DE PHYSIQUE

2

wTO=ci (T-TC) f o r T I T and w 2 =2a (Tc-T) f o r T<Tc. I n F i g . 3, we p l o t t e d

c TO

Ap a t Tc; A p ( T c ) v s . p r e s s u r e f o r a l l samples. The s o l i d c u r v e s denote t h e c a l c u l a t i o n s by u s i n g pTO(Tc)=gTc w i t h t h e observed v a l u e s of Tc. g is a d j u s t e d f o r each c u r v e t o a g r e e w i t h A p a t 1 b a r . W e ignored the

p r e s s u r e dependence o f t h e energy gap E e f f e c t i v e mass m* and Awhich

'ir'

g i v e g i n some combination. This approximation may b e p e r m i t t e d a s long

I I a s we a r e concerned W i t \ t h e c a r r i e r c o n c e n t r a t i o n s h i g h e r t h a n 1 0 l ~ c m - ~ a s

&

L

,

-

w e l l a s low p r e s s u r e l e s s t h a n 1 Kbar.

e s t i m a t e d t o be -14.5, -15.1, -13.4 and -15.0 K / I ~ a r f o r x=0.44, 0.54,

E

z80

2

P:

I- 5 4 0 -

.-

.c_ $20 I - ,

0

9 0.80 and 0.86, r e s p e c t i v e l y . P-ccording t o t h e Littlewood formula

,

dTJdp f o r x=0.44, 0 -54, 0 -80 and 0.86, r e s p e c t i v e l y , a r e -12.5, -11.6, -11.8 and

-11,9K/Kbar. The t r e n d and o r d e r of magnitude a g r e e w e l l w i t ; ? -ts. Ok 0.5 0.6 0.7 0.8 0.9 1.0 v a l u e s e s t i m a t e d by i n t e r - and extrapo-

x

l a t i o n a r e p l o t t e d . The observed i n i t i a l Fig. 4 : Tc vs. x under p r e s s u r e . s l o p e of T~ w i t h i n c r e a s i n g p r e s s u r e are

I

bar

,"

-

I

-

,

0 / P--;

-

,

'

,.

/

P

-

* - - *

,'

_,

,

, /

1 Kbar,

,

.d , '

1.5Kbar

-

w ' ' m - ,&'

-

,!<

-

4

-

I I I I I

I n c o n c l u s i o n we reemphasize t h a t t h e observed behavior of Ap under We can s e e a good c o r r e l a t i o n between d a t a and c a l c u l a t i o n s . There appears a s m a l l d i s c r e p a n c y above 0.5 Kbar which may be a t t r i b u t e d t o o u r i g n o r i n g of t h e p r e s s u r e dependence of E m* and A.

g '

I n Fig.4, w e summerized Tc v s . t i n compositions x a t 0.001, 1 and 1.5 Kbar i n t h e f o u r compositions w i t h adding Tc= 98.5 K i n SnTe a t 1 bar.5 When w e d o m t have d a t a j u s t a t 1 and 1.5 Kbar, t h e

p r e s s u r e i n PbSnTe n e a r T i s w e l l understood by assuming t h e s o f t TO

C

phonon s c a t t e r i n g w i t h wTO d e s c r i b e d by t h e mean f i e l d scheme.

The i m p o r t a n t c o n t r i b u t i o n of Dr.M.Baj i s g r a t e f u l l y acknowledged. One of us (S.K.) thanks Prof .K.&lurase f o r h i s f r u i t f u l d i s c u s s i o n s . We a r e a l s o i n d e b t e d t o D r s

.

I<. L

.

I. Kobay a s h i and K

.

I?. Komatsubara f o r s u p p l y i n g specimens.

References

1. See t h e r e c e n t a r t i c l e by K-Murase, J.Phys.Soc.Jpn.,

2

Supp1.A (1980) 725, and t h e r e f e r e n c e s contained t h e r e i n .

H.Kawamura, Proc.Int.Summer School on Narrow Gap Semiconductors, Nimes 1979 ( B e r l i n , S p r i n g e r Verlag, 1 9 8 0 ) .

K.L.I.Kobayashi, Y.Kato and K.F.Komatsubara, Prog.Crysta1 Growth Charact.

1

(1978) 117.

T.Suski, L.Dmowski and M.Baj, S o l i d S t a t e Commun.,

38

(1980) 59. K.L.I.Kobayashi, Y.Kato, Y.Katayama and IC.F.Komatsubara, S o l i d S t a t e Commun.,

17

(1975) 875.

S.Takaoka and K.Murase, Phys. Rev., B g (1979) 2623.

T.Suski, M.Baj, W.Zuczkowski, I<.L.I.Kobayashi and K.F.Komatsubara, S o l i d S t a t e Commun., 30 (1979) 77.

S.Katayama and D . L . M ~ ~ ~ s , Phys. Rev., B z (1980) 336.