Band filling and disorder in molecular conductors

Solid State Communications, Vol. 27, pp. 325-329 •

© Pergamon Press Ltd. 1978.

0038-1098/78/0715-0325502.00/0

Printed in Great Britain.

BAND FILLING AND DISORDERIN MOLECULARCONDUCTORS Arthur J. Epstein and Joel S. Miller* Xerox Webster Research Center, Rochester, New York 14644, USA (Received on 19 April 1978 by J. Tauc)

We have systematically probed the roles of band f i l l i n g and disorder in molecular conductors utilizing the (NMP)x(Phen)I_x(TCNQ)(O.5 < x < l.O) system. Conductivity results show a semTconducting behavior with charge carriers activated to extended states with a large strongly tenq~erature dependent mobility. The energy gap is found to decrease with decreasing band f i l l i n g , varying as x2. The inconsistency of these results with various disorder models is indicated.

Two issuesl, 2 of central importance that have emerged for highly conducting quasi-onedimensional molecular conductors concern the roles of band f i l l i n g and disorder in determining their properties. We have recently synthesized 3 a new series of highly conducting quasione-dimensional materials, which allow for the f i r s t time direct and continuous control of disorder and a wide range of band f i l l i n g . We have found that for temperature, T, greater than 65K, these materials behave as semiconductors with an energy gap proportional to the degree of band f i l l i n g squared. Disorder is found to play a secondary role in this temperature range. The systems studied are based upon N-methylphenazinium 7,7,8,8-tetracyano- Equinodimethanide, (NMP)(TCNQ), and are achieved by substituting neutra] phenazine, Phen°, for the nontotally-symmetric NMP+ cation. The Phen° is of similar size, shape and polariza b i l i t y to NMP+ but is neutral, closed-shell and symmetric. Detailed analysis 3 has shown that the gross (NMP)(TCNQ) crystal structure remains unchanged even with Phen° replacement for NMP+ in amounts up to 50%. For each NMP+ replaced by Phen°, one electron is removed from the TCNQacceptor stacks. Consequently, TABLE I.

materials wlth between a one-half and a onequarter f i l l e d band can be selectively prepared. The disorder at each TCNQsite in (NMP)(TCNQ) arises from the random positive charge d i s t r i bution on the cation (due to the random methyl group locationW). The varying distance of this positive charge to the TCNQchains leads to a fluctuating electrostatic potential. Replacing NMP+ with Phen° increases the randomness in the potential at TCNQsites. We have measured the T-dependenceof the four-probe single crystal dc conductivity,-o, of (NMP)x(Phen)I_x(TCNQ) along the stack direction Ca-axis) as a function of x. Figure la shows ~(T) for four representative samples. The differences in o(2gSK), Table I, are not considered significant because of the errors involved in measuring the cross-sectional areas of the small samples (~l x 0.03 x 0.02 mm). The temperature for the maximum conductivity, Tm, is lower in Phen° doped samples than in (NMP)(TCNQ).5 The low te~erature behavior of these four sables is shown in Figure 2. While the conductivity decreases monotonically in all sables for T < Tm, there is a clear systematic behavior observed with on(T) = o(T)/a(295K) increasing with Increasing phenazine content.

Conductivity Parameters for (NMP)x(Phen)I.x(TCNQ)

x

o(295K)~ohm-lcm -1

°n(T m)

Tm,K

~

ArK

A~,K

1.00

200

1.17

220

4.1

900

500

0.94

100

1.27

205

3.9

800

400

0.81

100

1.85

155

3.7

575

275

0.63

70

1.26

175

2.2

400

200

-

* Present address, Rockwell International Science Center, Thousand Oaks, California g1360. 325

BAND FILLING AND DISORDER IN MOLECULAR CONDUCTORS

326

in Table I. Each o(T) curve in Figure la is thus transformed into a nearly T-independent ~(T) curve in Figure Ib, demonstrating that there is no change of transport mechanism for T > 65K in these materials. For T < 65K, the measured o(T) is greater than that predicted by Eq. [ l ] suggesting that another transport channel dominates at low temperatures (see below). As previously shown for (NMP)(TCNQ),s the excellent f i t to Eq. [ l ] suggests a model of a band semiconductor with two one-dimensional (I-D)

The a(T) curves in Figure la are similar. We have previously shown that for (NMP)(TCNQ)s and numerous other systems6,~ which feature a broad weak maximum in o(T) at Tm, a(T) can be explained as a product of an activated carrier concentration, n(T) and a temperature dependent mobility) p(T). We have found that we Fan f i t the an(T) data for (NMP)x(Phen)I_x(TCNQ) for 60K < T < 400K with on(T) = A T-¢ exp[-A(x)/T] [l]

~.0

I

i

a.

I

i

I

I

I

I

~

1.6-

Vol. 27, No. 3

I

o x = 1.00

f

"~1;~

zx x =0.94 o x =0.81 • x =0.63

.-. v~ 1.2 b 0.8

-.

(~ N~.

0.4 O0

-~

I

b.

,

I

)

i

I

I

I 3?.0

1 360

(NMP)x(PHEN)I-x(TCNQ)

4.0 3.2 2.4 I.E 40

Fig. I.

(a)

= 80

n I I I I 120 160 200 ?_40 280 TEMPERATURE, T(K)

Normalized four-probe a-axis conductivity versus temperature

for some representative (NMP)x(Phen)I_x(TCNQ) samples. The solid lines are computer f i t s to Eq. (1) with values given in Table I. The phenazine molecule is illustrated here. (b)

~(T) calculated from Eq. (I) with experimental a(T) and A(x)

from Table I.

with A(x) constant for all samples of the same phenazlne content and ~ a sample dependent constant in the range of 2 to 4, Table I. The constant A is fixed by an(295K) ~ I. The solid lines ~n Figures la and 2 show the f i t s obtained with these parameters in Eq. [ l ] . The good agreement above 65K is particularly impressive in view of the large variation in an(T) with x. Figure Ib is a plot of a as a function of T calculated from Eq. [ l ] by using for o the experimental values and for A(x), the values given

tight binding bands each of width co separated by a gap 2A(x). We have previously showns-7 that for Maxwell-Boltzmenn statistics this leads to _ n(T) = Tl/2 exp(-A/T) and ~ ~ I0(295/T) ~+0"5 cmZ/ volt-sec. Similar values of ~ are obtained for the phenazine substituted samples. Using the known molecular vibration frequencies and known electren-phonon coupling constants, 9 we have already quantitatively shown that the crystal optical modes (molecular vibrations) can determine the mobility in (NMP)(TCNQ),S,7 (quinolinium).

Vol.

27,

No. 3

327

BAND FILLING AND DISORDER IN If)LECITLAR CONDUCTORS

T(K)

,o, I I00 ~

,oo,

,

~ ~ P ) x ( P H E N ) I - x ( T C N Q )

I0-I~ --

b io_5~_

o x : Loo - x :o.~

/

lo-el-

\ -~,o \ \% \ "C

[] x :0.81

•

I

\

\

~

~

°o.

oOoo

,o-'I10-81 0

" °°o

I 5

I I0

I 15

I 20

I 25

I 3;0

I 35

I 40

o I 45

I O 0 0 / T ( K -I)

Fig. 2.

Experimental log[o(T)/o(295K)]

versus T"I for samples of Fig. 2,

and computer f i t s from Eq. (l) with parameters given in Table I. (TCNQ)26,7 and (tetrathiafulvalenium)(TCNq). 7,s The qualitative and quantitative extenslon of this microscopic model to (NMP)x(Phen)I_x(TCNQ) is straightforward. In Figure 3, the vartattqn of A with the square of the band f i l l i n g , xc, is shown. This result is i ~ o r t a n t in understanding the microscopic aspects of ]-D materials. The presence of a distortion of the underlying l a t t t c e with pertod 2a/x where a ts the average repeat unit along the TCNQ chatn would lead to an energy gap at the Fermi energy cF for all band f i l l i n g s . However, the evidence-for such a Peterls type distortion is not yet conclusive, l° A MottHubbard gap due to on-site Coulomb repulsion 11 would lead to a sendconductor gap for only x = l.O. The addition of nearest neighbor Coulomb interactions 12 leads to a gap at the 1/4 band level as wel], i n s u f f i c i e n t to explain the semtconductlng behavior of the tntemedtate x systems. We point out that part (or even a l l ) of A may be a mobility gap associated with localtzat!on of states at the band edges due to disorder. I t has a]so been suggested that long range tntrechatn Coulomb interactions may lead to a gap at CF for all x. 13 However, none of these models as yet explain the observed variation of A with x2. One mode], based on the e a r l i e r work of Noynarovtch, e t a ] . 14 is particularly appealing. In this model electrostatic tnterchatn i n t e r action between charge density waves stabilizes the charge density waves and leads to an energy gap at CF fop all band f i l l i n g s . The magnitude of this gap depends roughly on the square of the charge density (degree of charge transfer), In

agreement with experimental data, Ftgure 3. As fomulated 14 the ground state is no.nmegnettc although add|tton of on-stte or tntrechatn Coulomb repulsion would probably make the ground state megnettc. These results suggest that the observed activation energtes tn (NI~) (TCNO), (qutnoltntum)(TCNO)2 and related system, are not solely due to on-stte or near netghbor Coulomb tnteracttons. The questton artses whether a band semiconductor model ts comattble wtth the dtsorder expected to extst tn these cyrstals. What detemtnes the nature of conduction ts the length of the regton for whtch the wavefunctton ts extended, ~a.S,6, 7 At temperatures high enough for these s~ates to be s i g n i f i c a n t l y occupied, (T > 65K tn our samples) they wtll dominate the dc a. At low enough temperatures (depending on the property betng measured) electrons tn localIzed states my dominate the behavior. IncreasIng phenaztne content Increases the disorder, hence decreasing ~a. Ftgures lb and 2 show that the observed o(T) ts s~stemettcally larger than predicted by Eq. [ 1 ] for T ~ 65K. Assumtno that the mean free path ts ltmtted by tmpurttfes for T < 65K, o ( T ) = exp(-AI/T), for 65K > T > 3OK. The values of A~ found f o r each x are approxtmetely gtven by A/2, Table I. Thts suggests the presence of an Increasingly large number of localized states tn the gap produced by the Increased amount of Phen° as x ts decreased. Thus for 65K • T > 3OK, carrters exctted from the localized states at the Ferret energy in the center of the gap to the extended states with an activation energy A~ ~ A/2 would outnumber the I n t r i n s i c carrter

328

BAND FILLING AND DISORDER

population. For T < 33K, o(T) becomes less Tdependent, as well as increases with increasing Phen°, suggesting that hopping among the increas-

Vol. 27, No. 3

IN MOLECULAR CONDUCTORS

experiment. In sum, we have shown that (NMP)x(Phen)I-x(TCNQ) forms a continuous series of materials

X 0 I000

0.45

0.63

0.77 I

0,89 ~

1.00 I

8 0 0 --

m

600 -,w(

4 0 0 --

/ /

200 --

/

/

/ /

c 0

/

/

I 0.2

I 0.4

I 0.6

I 0.8

I 1,0

X2 F i g . 3.

Variation of activation energy, A, obtained for T )65K with fraction of NMP+, x.

ing number of localized states in the gap dominates for T < 3OK. The change in a(T) behavior at 65K may also be due to either the presence of a phase transition or a transition to hopping type transport for T < 65K. Additional efforts are necessary to distinguish these models. Several groups have attempted to quantitat i v e l y model o(T), T > 65K, for TCNQ salts assuming that the electrons hop among the localized states. Bloch, et al. is attributed o at low temperatures to variable-range phonon-assisted hopping, and at high temperature to diffusive hopping. Gogolin, et al. is quantitatively f i t o(T) with a disorder model u t i l i z i n g tntramolecular phonons for phonon-assisted hopping (T < Tm) and phonon localization (T > Tm). Attempts to apply these models to the (NMP)x(Phen)I_x(TCNQ) system lead to a prediction of increasing Tm with increasing phenazine content, at variance wlth experimental findings. Shante17 has recently proposed a model for anisotropic hopping conduction in (NMP)(TCNQ) which suggests similar behavior for phenazine substituted samples for T < lOOK in contrast with

with semiconducting )ehavior. Data analysis leads to A = (900K)xZ and a large strongly Tdependent mobility for T > 65K. The major effect of increased disorder is to give rise to additional strongly localized states at the band edges (bandtatltng) increasing the low temperature one-dimensional (hopping) conduction at low T. This system has broad implications for understanding the source of energy gaps and the role of disorder in molecular conductors. Additional physical data including magnetic s u s c e p t i b i l i t y , esr, and thermoelectric power confirm this continuous behavior as a function of x between that characteristic of (NMP)(TCNQ)(X = l.O) and that characteristic of Qn(TCNQ) 2(x = o.5). Acknowledgement -We are deeply indebted to Dr. D. J. Sandman for his extensive cooperation in synthesizing high quality samples for cond u c t i v i t y studies. We thank Drs. E. M. Conwell and D. J. Sandman for stimulating discussions and Prof. P. Chatktn fop providing laboratory facilities.

Vol. 27, No. 3

BAND FILLING AND DISORDER IN MOLECULAR CONDUCTORS References

1. 2.

PAL, L., GRUNER, G., OANOSSY, A. & S()LYOH, J . , edltors, Lecture Notes In Physics (1977), Sprtnger-Verlag, New York (1977); KELLER, H. J., editor, NATOAdvanced Study I n s t i t u t e Sertes B25 (1977), Plenum Press, New York (1977). HILLER, J. S. & EPSTEIN, A. J . , editors, Anna1 of the New York Academy of Sciences, 313 (1978).

3. 4. 5.

MILLER, J. S. & EPSTEIN, A. J . , Journal American Chemical Society lO0, 1639 (1978). FRITCHIE, C. J . , JR., Acta Crystallographtca 20, 892 (1966). EPSTEIN, A. J . , CONWELL, E. H., SANDMAN, D. J. & MILLER, J. S., Solid State Communications 23, 355 (1977).

6. 7. 8. 9.

EPSTEIN, A. J. & CONWELL, E. M., Solid State Communications 24, 627 (1977)o EPSTEIN, A. J., CONWELL, E. N. & MILLER, J. S., in Reference 2. CONWELL,E. M., Physical Review Letters 39, 777 (1977).

10.

LIPARI, N. 0., RICE, M. J . , DUKE, C. B., BOZIO, R., GIRLANDO, A. & PECILE, C., International Journal of Quantum Chemistry: Quantum Chemistry Symposium, 1_~], 583 (1977). UKEZ, K. & SHIROTANI, I . , Communications on Physics 2_, 159 (1977) report x-ray diffuse scattering to f i f t h order for (NMP)(TCNQ). This may be related to the coupled charge density waves rather than a periodic l a t t i c e d i s t o r t i o n . Their results suggest a charge transfer of 0.91 for (NNP)(TCNQ) which would not be inconsistent with the results presented here.

I I . EPSTEIN,A. J., ETEMAD,S., GARITO,A. F. & HEEGER,A. J., Physical Review B 5, 952 (1972). 12. HOLCZER,K., MIH~LY, C., J~NOSSY, A. & GRUNER,R., Molecular Crystals Liquid Crystals 32, 199 (1976). 13. GRANT,P. & HUBBARD,J., private comnmnication. 14. WOYNAROVICH,F., MIH~LY, L. & GRUNER,G., Solid State Communications 19, I189 (1976). 15. BLOCH,A. N., WEISMAN, R. B. & VARMA, C. M., Physical Review Letters 28, 753 (1972). 16. GOGOLIN,A. A., ZOLOTUKHIN,S. P., MELNIKOV, V. I . , RASHBA, E. I. & SHCHEGOLEV, I. F., JETP Letters 22, 278 (1975). 17. SHANTE,V. K. S., Physical Review BL6, 2597 (1977).

329