Developing a two-parabolic band model for thermoelectric transport modelling using Mg2Sn as an example

Abstract

Thermoelectrics is a field driven by material research aimed at increasing the thermal to electrical conversion efficiency of thermoelectric (TE) materials. Material optimisation is necessary to achieve a high figure of merit (zT) and in turn a high conversion efficiency. Experimental efforts are guided by the theoretical predictions of the optimum carrier concentration for which generally the single parabolic band (SPB) model is used which considers the contribution to electronic transport only from the majority carriers’ band. However, most TE materials reach peak performance (maximum zT) close to their maximum application temperature and when minority carrier effects become relevant. Therefore, single band modelling is insufficient to model the behaviour of TE materials in their most practically relevant temperature range. Inclusion of minority effects requires addition of the minority carrier band and necessitates the use of a two-band model—the simplest and, for most cases, sufficient improvement. In this study, we present a systematic methodology for developing a two-band model using one valence and one conduction band for any given TE material. The method utilises in part the SPB model and in part a simple cost function based analysis to extract material parameters like density of states masses, band gap, deformation potential constant etc., based on easily available experimental data. This simple and powerful method is exemplified using Mg2Sn, chosen due to its low band gap, the availability of experimental data in a wide range of dopant concentrations and its practical importance, being an end member of the highly popular Mg2(Si,Sn) solid solutions. Using the experimental data for p- and n-type Mg2Sn from literature, a two-band model was obtained. Optimum carrier concentration and maximum zT were predicted from both SPB and two-band models and at 650 K pronounced differences between the two models, which could prevent realisation of maximum zT, were observed, demonstrating the practical necessity to model the effect of minority carriers.