Disorder effects in the linear chain compound TiS3

~

Solid State Comunicatlons, Printed in Great Britain.

Vol.46,No.7,

pp.505-507,

1983.

0038-|098/83/190505-03503.00/0 Pergamon Press Ltd.

DISORDER EFFECTS IN THE LINEAR CHAIN COMPOUND TiS 3 Pei-Ling Hsieh, C. M. Jackson, Department

of Physics,

and G. Gr~ner

University of California,

Los Angeles,

California 90024

(Received 25 February 1983 by A. Zawadowski) Conductivity (0) and thermoelectric power (S) measurements are reported in the linear chain trichalcogenide TiS 3. The de conductivity shows a non-exponential temperature dependence below the conductivity maximum, and o is also strongly frequency dependent. This, together with the anomalous temperature dependence of S is suggestive for disorder effects in this compound.

T r a n s i t i o n metal trichalcogenides, formed from groups V t r a n s i t i o n m e t a l s Nb or Ta and chalcogens S or Se are metals at high temperatures. Some members of this group u n d e r g o a phase transition, associated with the formation of charge density waves (CDW's), and display spectacular field and frequency dependent transport phenomena due to the collective response of CDW's.I The most p r o m i n e n t m e m b e r of this group is NbSe3, but the orthorhombic and monochlinic forms of TaS3, and one form of NbS 3 also show CDW transitions and collective transport phenomena. In contrast to this situation, transition metal triehalcogenides of group IV metals, like VS 3 or HfS3, are band semiconductors with large single particle gaps A. The semiconducting b e h a v i o r is the consequence of the tetravalent b o n d i n g c o n f i g u r a t i o n of the transition metal ions. An e x c e p t i o n to this rule is TiS 3 where the dc c o n d u c t i v i t y has a m a x i m u m around 200 K. 2 Above the maximum o decreases with increasing temperature T, and below the maximum o decreases with decreasing T, and is interpreted 2 as due to a small single particle gap. X-ray studies show no superlattice at low temperatures, indicating the absence of Peierls distortion in this material. We have measured the temperature, frequency, and field dependence of the c o n d u c t i v i t y o and the thermoelectric power S in an attempt to understand the reason for the anomalous behavior of the dc conductivity. We observe a large frequency dependence below the conductivity maximum, and a n o n - e x p o n e n t i a l t e m p e r a t u r e d e p e n d e n c e of the dc conductivity, and a large thermoelectric power. These observations, together with the small value of the dc c o n d u c t i v i t y , strongly suggest that the transport properties are determined by disorder induced localization in TiS 3 . TiS 3 was prepared by direct reaction of the c o m p o n e n t s at high temperature. The de conductivity, s h o w n in Fig. I, m e a s u r e d by four probe m e t h o d along the long d i r e c t i o n of the thin fibrous crystals agrees with p r e v i o u s measurements. The t h e r m o e l e c t r i c power was m e a s u r e d by equipment similar to that described in Ref. 3. T h e m i c r o w a v e c o n d u c t i v i t y was m e a s u r e d by a cavity perturbation technique b,5 at 9.14 GHz. The c o n d u c t i v i t y and dielectric

.... l"

l

l

i

i

i

i

2.0

TiS 3

1.0

OO +++ O O O O O

x

0.5

+ +

+

+

O O

~ 0.2 O O

-6 0.t

O 05

+ 9 GHz odc

02

'

Fig. I.

8

'

t'2

1~ IO00/T (K)

20

'

24

Temperature dependence of the normalized dc and microwave conductivity in Tis 3 .

constant are evaluated from the measured shift and a b s o r p t i o n of the cavity resonance, o (9 GHz) is also shown in Fig. I. The dielectric constant at low temperatures is e = 20, and it is w e a k l y temperature dependent. The room temperature c o n d u c t i v i t y , m e a s u r e d by the microwave m e t h o d gave ~ (300 K) = 0.4 0 -~ cm -I which agrees, w i t h i n the e x p e r i m e n t a l error associated with the measurement of the sample dimensions, with the dc value. We have normalized, therefore, the dc and m i c r o w a v e conductivity together at T = 300 K. It is apparent that t h e r e is no f r e q u e n c y d e p e n d e n c e above the c o n d u c t i v i t y maximum, and a strong dispersion d e v e l o p s in the low t e m p e r a t u r e "semiconducting" region. We also note that the dc conductivity cannot be fitted with a single exponential b e h a v i o r o(T) ffi o 0 exp(-A/kT) as expected for a b a n d s e m i c o n d u c t o r , but an e x p r e s s i o n

505

Vol. 46, No. 7

DISORDER EFFECTS IN THE LINEAR CHAIN COMPOUND TiS 3

506

o(T) = o0 e x p ( - T o / T ) l]m (1) m

=

2,

to

3

often used 6 for describing change transport in d i s o r d e r e d c o n d u c t o r s where a(T) is determined by a t e m p e r a t u r e d e p e n d e n t m o b i l i t y , rather than by a temperature dependent carrier number. We have also searched for nonlinear effects on the dc c o n d u c t i v i t y . Experiments performed using a pulse technique to avoid heating e f f e c t s did not show any d e v i a t i o n from Ohms law up to electric fields of 300 V/cm. We first note that the small absolute value of the conductivity at room temperature immediately rules out any interpretation in terms of band transport mechanism. The mean free path for a one dimensional narrow band metal is given by

The frequency dependence of a and the d i e l e c t r i c constant are in agreement with this interpretation. The low temperature dielectric constant ¢ ~ 20 is approximately a factor of 25 smaller than in Qn(TCNQ) 2 where ¢(4.2 K) = 500. At low temperatures ¢ is g i v e n by8, 9 ¢ = nx 2

where X is the l o c a l i z a t i o n length. Assuming that A is the same in both compounds (because of the similar Tma x values), n is approximately a factor of 25 smaller in TiS 3 than in Qn(TCNQ)2, in agreement with the conclusion b a s e d on the m a g n i t u d e of the c o n d u c t i v i t y . The strong frequency dependence observed at t e m p e r a t u r e s T < Tma x is an additional strong evidence for disorder induced localization effects. At T = 0, arguments which lead to Eq. (2) lead also to

= axh/2Ne2a0 where N is the number of electrons/atom and a0 is the lattice constant along the chain direction. A s s u m i n g that all e l e c t r o n s contribute to the conductivity, and the electron density n ~ I021 cm -3 (as in NbSe 3 or TaS3), we obtain ~ 10 -2 a0, orders of magnitude smaller than a m e a n free path % > a0 needed for band transport theory to be appropriate. This strongly suggests that disorder plays a fundamental role, and both the magnitude and temperature dependence of o r e f l e c t s t r a n s p o r t due to charge transfer between localized electron states. The reason for the low conductivity can be twofold: either the number of carriers is much smaller than n ~ 1021 cm -I, or disorder induced l o c a l i z a t i o n is v e r y strong in this material. Indeed, in Eq. (I) the characteristic temperature T O is the measure of the strength of the localization. 5 An overall d e s c r i p t i o n of o(T) including the maximum of o suggests 7 that the average height of the random p o t e n t i a l s which lead to localization is of the order of kTma x where Tma x is the temperature where o has a maximum. Above Tma x transport is d i f f u s i v e , while below Tma x it is determined by random, thermally assisted hopping between localized states. Tma x ~ 200 K observed for TiS 3 is approximately the same as that observed for v a r i o u s organic linear chain compounds, of which quinolinium ditetracyanoquinodimethanide, Q n ( T C N Q ) 2 , is the prime example.6, 7 Thus, the overall strength of the random potentials, and c o n s e q u e n t l y the mobility should be similar in the two compounds. The conductivity, however, is two orders of magnitude less in TiS 3 than in Qn(TCNQ) 2 and similar compounds leading to the c o n c l u s i o n that the number of carriers is small in TiS 3 . The reason for the small number of carriers may be the following: In the absence of disorder, TiS 3 would be a band semiconductor as the other m e m b e r s of this group such as VS 3 of HfS 3. D i s o r d e r leads to band tailing and to a small number of carriers at the Fermi level, and it is these carriers which d e t e r m i n e the conductivity; e x c i t a t i o n s across the single p a r t i c l e gap do not contribute to the transport process.

(2)

a(~)

~ ~2 nk2

(3 )

w h i l e at finite t e m p e r a t u r e s r a n d o m h o p p i n g b e t w e e n localized states is the dominant source of the f r e q u e n c y dependence. Although various m o d e l s were proposed to describe ~(~) in this t e m p e r a t u r e region,8, 9 detailed experiments at f r e q u e n c i e s b e t w e e n dc and 9 GHz would be required to make a direct comparison with these theories. Additional evidence for the small number of carriers is provided by the thermoelectric power. The temperature dependence of S is shown in Fig. 2. Both the temperature d e p e n d e n c e and the magnitude of S are in strong contrast to what is expected for a band semiconductor where current is carried by -80C

I

I

0 0 o 0O 0

0 0o

0 o

•

O0 ° 000000000 O00c

OOO0

Oo 000

D

o~O OtJ

•

OQ

0

-60~ 0 O')

B

TiS 3

o~ 3=

• somple t o somple 2

E

== -4(~

0 @

-~0

0

n

I

t00

200

3OO

"rIK~

F i g . 2.

Temperature dependence of the thermoelectric power in TiS 3.

DISORDER EFFECTS IN THE LINEAR CHAIN COMPOUND

Vol. 46, No. 7 extended electron conductor. I0 kB [ S = - -~

states

~e - ~hh] ~e +

for

A k-T + A

a

band

semi-

(4)

where ~e and ~h are the e l e c t r o n and hole mobilities and k B is the B o l t z m a n n constant, A is a c o n s t a n t d e p e n d i n g on the d e t a i l s of the s c a t t e r i n g process. Equation (4) l e a d s to a s t r o n g l y increasing S with d e c r e a s i n g t e m p e r a t u r e in contrast to what is observed. W h e n c h a r g e transport is due to hopping b e t w e e n l o c a l i z e d states, then S is independent of t h e t e m p e r a t u r e , a n d II S = - ~- ~.n where atom.

0

is the Equation

log average (5)

(5) number of electrons per is a result of entropy

considerations. A small n u m b e r of carriers then leads to a large (and temperature i n d e p e n d e n t ) t h e r m o p o w e r as o b s e r v e d at high temperatures. The strongly decreasing S below I00 K m a y be due to the freezing out of the entropy, as also observed in the other highly anisotropic disordered conductors. 12 We also note that the absence of nonlinear effects up to high electric fields is an a d d i t i o n a l e v i d e n c e for localization effects,

TiS 3

507

in contrast to charge d e n s i t y wave phenomena, w h i c h lead to both ~(~) and c(E) in the CDW state. I In conclusion, on the basis of, first, the m a g n i t u d e of the c o n d u c t i v i t y and the thermopower, second, the frequency dependence of the conductivity, and third, the t e m p e r a t u r e dependence of the c o n d u c t i v i t y and the thermopower, we argue that in TiS 3 disorder plays an important role in d e t e r m i n i n g transport properties. The source of the disorder in this m a t e r i a l is not clear at present. It may arise from imperfections, vacancies in the structure, or disorder associated with weak interchain coupling and r a n d o m local distortion. Further structural studies are required to clarify this point. Finally, we note that the strong dependence observed here is due to single particle effect, in contrast to those observed in NbSe 3 or TaS 3 where o(w) represents the response of the pinned CDW mode. Extreme care has to be taken, therefore, when a(~) experiments alone are used 13 to argue for collective transport effects in low dimensional materials. We wish to thank A. J ~ n o s s y and A. Zettl for u s e f u l d i s c u s s i o n s . This r e s e a r c h was s u p p o r t e d by the National Science Foundation grant DMR 81-21394.

References I.

2.

3. 4.

5. 6.

7.

See, for example, G. Gr~ner, Couments in Solid State Phys. IO, 183 (1983) and references listed therein. S. Kikkawa, M. Koizumi, S. Yamanaka, Y. Onuki, and S. Tanuma, Phys. Stat. Sol. A 61, K55 (1980). P . M . Chaikin and J. F. Kwak, Rev. Sci. Instrum. 46, 218 (1975). L. I. Burav---ov and I. F. Shchegolev, Prib. Tekh. Exsp. 14, 171 (1971), Instrum. Exp. Tech. (USSR) 14, 528 (1971). A. Zettl, C. M. Jackson, and G. Gruner, Phys. Rev. B 26, 5773 (1982). A. N. Block, B. R. Weisman, and C. M. Varma, Phys. Rev. Lett. 28, 753 (1972); I. F. Shchegolev, Phys. Stat. Sol. A 12, 9 (1972). S. Alexander, J. Bernasconi, W. R. Schneider, R. Billet, W. G. Clark, G. Gruner, R. Orbach, and A. Zettl, Phys. Rev. B 24, 7474 (1981).

8. 9. 10. II. 12.

13.

M. J. Rice and J. Bernasconi, Phys. Lett. 38A, 277 (1972). R. L. Bush, Phys. Rev. B 13, 805 (1976). G. Mihaly, G. Said, G. Gruner, and M. Kertesz, Solid State Comm. 21, 1115 (1977). V. V. Kosarev, Soy. Phys. Semicond. 8, 897 (1975). See, for example, G. Beni, J. F. Kwak, and P. M. Chaikin, Solid State Comm. 17, 1549 (1975). G. Verma, N. P. Ong, S. K. Khanna, J. C. Eckert, and J. W. Savage, Phys. Rev. B (to be published). N. P. Ong, G. X. Tessema, G. Verma, J. C. Eckert, and S. K. Khanna, Mol. Cryst. Liq. Cryst. 81, 41 (1982).