A Theoretical study of the Thermoelectric Transport Coefficients of n-type PbTe
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A Theoretical study of the Thermoelectric Transport Coefficients of n-type PbTe
Jawaher Al-Otaibi, Gyaneshwar P. Srivastava School of Physics, University of Exeter, Stocker Road, Exeter, EX4 4QL, UK
ABSTRACT In this work we present a theoretical study of the transport coefficients of n-type PbTe. The electronic transport coefficients are calculated using the isotropic-nearly-free-electron approximation, including the effect of band non-parabolicity on electron-phonon scattering. The lattice thermal transport coefficient is computed by employing the isotropic continuum model for the dispersion relation for acoustic as well as optical phonon branches, an isotropic anharmonic continuum model for crystal anharmonicity, and the single-mode relaxation time scheme. The role of transverse optical (TO) phonon modes in anharmonic interactions will be discussed in detail. INTRODUCTION Lead telluride (PbTe) is a widely used material for energy applications in the intermediate operating temperature range of 400 - 800 K [1, 2]. The efficiency of thermoelectric power generators is determined by the figure of merit ZT = S 2 σT /(κmp + κbp + κph ), where S, σ, κmp (κbp ), κph , and T are, respectively, the Seebeck coefficient, the electrical conductivity, the electrical thermal conductivity from the monopolar (bipolar) component, the lattice thermal conductivity, and T is the (mean) temperature of the system [3]. This formula expresses the fact that a good thermoelectric material must have the ability to preserve the temperature gradient, i.e. should exhibit low lattice thermal conductivity. PbTe, which crystallises in the rock-salt structure, exhibits a low bulk lattice thermal conductivity value of κph ∼ 2 W m−1 K−1 at 300 K [4, 5, 6]. Anomalously large anharmonic interactions, involving optical and acoustic modes, have been noted for this material [1]. However, despite several reports of calculations of ZT for PbTe, detailed understanding of the role of optical phonons in its lattice thermal conductivity is missing. We present a theoretical study of the lattice thermal transport coefficient by employing the isotropic continuum model for the dispersion relation for acoustic as well as optical phonon branches, an isotropic anharmonic continuum model for crystal anharmonicity, and the single-mode relaxation time scheme. The role of transverse optical (TO) phonon modes in anharmonic interactions is discussed in detail. We compute the electronic transport coefficients within the isotropic-nearly-free-electron approximation, including the effect of band non-parabolicity on electron-phonon scattering. Our results for the thermoelectric transport coefficients and the figure of merit are compared and validated by the experimental data reported in Ref. [7].
THEORY The lattice thermal conductivity κph can be expressed, within the single mode relaxation time and the isotropic continuum approximations, as [8]: X Z ωD ~2 (1) κph = c2s ω 2 τ n (n + 1)g(ω)dω, 2 3V kB T s 0 where kB , ω = ω(qs), cs and V are Boltzmann’s constant, phonon frequ
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