Rigorous calculation of the Seebeck coefficient and mobility of thermoelectric materials

Abstract

The Seebeck coefficient of a typical thermoelectric material is calculated without recourse to the relaxation time approximation (RTA). To that end, the Boltzmann transport equation is solved in one spatial and two k-space coordinates by a generalization of the iterative technique first described by Rode. Successive guesses for the chemical potential profile are generated until current continuity and charge-neutrality in the bulk of the device are simultaneously satisfied. Both the mobility and Seebeck coefficient are calculated as functions of the temperature and the agreement to experimentally obtained values is found to be satisfactory. Comparison is made with the less accurate RTA result, which has the sole advantage of giving closed form expressions for the transport coefficients.