Transport and Thermal Properties

In this chapter the transport and thermal properties of fullerenes in the normal state are discussed. The superconducting properties are reviewed in Chapter 15. Since pristine solid C60 and C70 have no free carriers for transport, either doping, photoexcitation or some other mechanism must be used to generate carriers for electrical conduction.

The transport properties of doped fullerene solids are unusual for several reasons. First, the movement of an excess electron on the surface of a fullerene anion suffers relatively little scattering compared to that for movement of electrons from one fullerene anion to an adjacent neutral fullerene molecule. Increasing the distance between adjacent ions by selective donor doping gives rise to two competing processes regarding carrier transport: one process decreases the wave function overlap integral between adjacent fullerene ions and thereby sensitively decreases electronic transport, while the other increases the density of states at the Fermi level, thereby enhancing electronic transport. Because of the many types of vibrational modes in the lattice, the identification of the modes that dominate the scattering processes is of particular interest.

Second, metallic conduction seems to be restricted to a small range of stoichiometrics close to a half-filled LUMO-derived band, as discussed in §14.1.1. Simple one-electron arguments suggest that any partial occupation of the LUMO-derived conduction band would give rise to metallic conduction, thus indicating that many-body electron-electron correlation effects are important for describing the electronic states in alkali metal- and alkaline earth-doped fullerenes. These arguments are consistent with the large relative value of the Hubbard U (~l-2 eV), which is large compared to the electronic bandwidth W of the LUMO-derived bands (0.2-0.5 eV) in the undoped fullerite crystal (see §12.7.7). A third special feature of the doped-fullerene bands is the fact that there appears to be no observed metal-insulator transition for a half-filled band, as occurs for many highly correlated systems [14.1]. Yet another special feature of transport in the doped fullerenes is the role of merohedral disorder as a scattering mechanism in the fullerene host material, thereby reducing the low-temperature electrical conductivity. Disorder of the dopant also contributes to additional carrier scattering in doped fullerenes. These novel features of the transport properties of fullerenes are further discussed throughout this chapter.

The transport properties of fullerene solids that have been studied include electrical conductivity (dc up through microwave frequencies), Hall effect, magnetoresistance, photoconductivity, and thermoelectric power. Also included in this chapter is a review of the thermal properties, including specific heat, thermal conductivity, the temperature coefficient of lattice expansion, and differential scanning calorimetry.

14.1. Electrical Conductivity

In previous discussions of the electronic structure, the semiconducting behavior of crystalline C60 and C70 was emphasized (see §12.7). The room temperature resistivity of the undoped fullerene solids is high with p ~ 1014 fl-cm reported for undoped mixtures of C60 and C70 films exposed to air [14.2] and p ~ 108 il-cm for oxygen-free C60 films [14.3]. Almost no carriers are available for transport in C60 unless they are thermally or optically excited, or more importantly if carriers are introduced by the doping of donor (or perhaps acceptor) species. Until now, the most intensively studied donor dopants are the alkali metals, which are efficient in providing electron charge transfer to the fullerenes and in creating carriers near the Fermi level. In addition, a few studies have been reported on the electrical conductivity in the alkaline earth-doped C60 compounds (§14.1.3) as well as in the alkali metal-doped C70 compounds (§14.1.4). Because of the degenerate ground states of the fullerene anions and cations (see §12.4.2 and §12.4.3), Jahn-Teller distortions of the molecule may occur, thereby contributing to the overlap of the wave functions between adjacent fullerenes and to the enhancement of their transfer integral.

14.1.1. Dependence on Stoichiometry

Because of the high-resistivity of undoped C60, doping with alkali metals decreases the electrical resistivity p of C60 by many orders of magnitude.

As x in M,C60 increases, the resistivity p(x) decreases and eventually approaches a minimum at x = 3.0±0.05 [14.4,5], corresponding to a half-filled /Il(-derived (ilu-derived) conduction band. TTien, upon further increase in x from 3 to 6, p again increases, as is shown in Fig. 14.1 [14.5]. It should be noted that stable crystallographic K^C«, phases occur only for x = 0,1,3,4, and 6 (see §8.5). The compounds corresponding to filled molecular levels (C60 and M6C60) are the most stable and exhibit maxima in the resistivity of M^Qo (M = K, Rb) as a function of x, consistent with a filled band.

The measurements shown in Fig. 14.1 are also significant with regard to whether or not a band gap is formed at x = 3, corresponding to a half-filled band [14.6], The p(x) measurements in Fig. 14.1 yield a minimum resistivity very close to x = 3, where the stoichiometry was independently determined by the Rutherford backscattering (RBS) technique. The experimental results for p(x) do not give evidence for a band gap at this stoichiometry, although many-body theoretical arguments suggest that a strongly electron-correlated material (U > W) should undergo a metal-insulator transition at a half-filled band (see §12.7.7) [14.1,6,7]. More recent experiments than in Fig. 14.1 using a thin C^ film with a much larger grain size of ~1 jxm as the starting material before the doping [14.8] show a shoulder in p(x)

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