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 TE material. The method utilises the SPB model and 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 (an end member of the highly popular Mg2(Si,Sn) solid solutions), chosen due to its low band gap and the availability of experimental data in a wide range of dopant concentrations. Using the experimental data for p- and n-type Mg2Sn from literature, a two-band model was obtained and optimum carrier concentration and maximum zT were predicted. At 650 K, pronounced differences between the SPB and the two-band model, which could prevent realisation of maximum zT, were observed demonstrating the practical necessity to model the effect of minority carriers.

Analyzing the Performance of Thermoelectric Generators with Inhomogeneous Legs: Coupled Material–Device Modelling for Mg2X-Based TEG Prototypes

“…The new method presented here, CPIM, is easy to implement, as SPB-based material models are available for several relevant thermoelectric material systems [54,65,66] and the often-implemented CPM methodology needs to be adjusted only marginally. A further improvement of the presented approach would be to employ a two-band model [67] to overcome the limitations of the SPB model and Finite Element Modelling to cross-check and deepen the understanding of the results presented in this work.…”

Material descriptors for thermoelectric performance of narrow-gap semiconductors and semimetals

“…34,35 While this is a reasonable approximation for materials with band gaps that are wide enough to avoid significant bipolar conduction, or even ''gapped metals'' where a single charge carrier type dominates transport, 36 it breaks down in materials where both electrons and holes are present in high concentrations, such as narrow-gap semiconductors and semimetals. [37][38][39] Bipolar conduction increases the electrical conductivity while simultaneously decreasing the Seebeck coefficient and increasing the electronic thermal conductivity. 40 As such, material descriptors for predicting the TE performance of narrow-gap semiconductors and semimetals must account for effects arising from bipolar conduction.…”

Material Descriptors to Predict Thermoelectric Performance of Narrow-gap Semiconductors and Semimetals

“…31,32 While this is a reasonable approximation for materials with band gaps that are wide enough to avoid significant bipolar conduction, it breaks down in materials where high concentrations of both electrons and holes are present, such as narrow-gap semiconductors and semimetals. [33][34][35] Bipolar conduction increases the electrical conductivity while simultaneously decreasing the Seebeck coe cient and increasing the electronic thermal conductivity. 36 As such, material descriptors for predicting the TE performance of narrow-gap semiconductors and semimetals must account for e↵ects arising from bipolar conduction.…”