Study of the electronic band structure of thermoelectric (TE) materials is fundamental to both its understanding and further development. Currently theoretical models which assume a single-band-based charge transport are utilized due to their predictive capabilities and ease of implementation. However, most good thermoelectric materials have complex band structures with multiple bands near the band edge. The extent of applicability of single-band models in such systems is questionable and forms the objective of this study. To check this, we have chosen five well-known TE materials and modeled their room temperature properties using the single parabolic band (SPB) model and the single Kane band (SKB) model. The room temperature experimental data for these materials were extracted from literature reports, and the analysis was carried out on a relatively large sample set (with over 350 data points spread across the various materials). Our analysis indicates the failure of single-band models in situations where multiple near-degenerate bands are present close to the band extrema. The associated errors are in the estimated density of states effective mass (m D *), Lorenz number (L), and lattice thermal conductivity (κ L ), which in turn result in erroneous predictions of the optimum charge carrier concentration and zT values. We also find that identifying whether the band edge is parabolic is difficult from a visual comparison of the SPB and SKB Pisarenko plots since the observed variations are well within the acceptable limits of experimental error. To overcome this problem, we propose an error analysis technique which can be used to find the best fit model. The error analysis can also be useful in identifying the dominant charge carrier scattering mechanism as shown from our study. Overall, our work highlights the need for implementation of multiband modeling while working with materials with complex band structures.

No abstract

Thermoelectric (TE) devices operate under large temperature differences, but material property measurements are typically accomplished under small temperature differences. Because of the issues associated with forming proper contact between the test sample and the electrodes and the control of heat flux, there are very few reports on large temperature difference measurements. Therefore, practically relevant performance parameters of a device, namely, power output and efficiency, are estimated by temperature averaging of material properties, whose accuracy is rarely validated by experimental investigations. To overcome these issues, we report an apparatus that has been designed and assembled to measure the TE properties—Seebeck coefficient, electrical conductivity, thermal conductivity, and power output and efficiency of a single thermoelectric material sample over large temperature gradients. The sample holder—a unique feature of this design—lowers the contact resistance between the sample and the electrodes, allowing for more accurate estimates of the sample’s properties. Measurements were performed under constant temperature differences ranging from 50 to 300 K with the hot side reaching 673 K on a metallized Mg2Si0.3Sn0.7 leg synthesized in the laboratory. To simulate practical operating conditions of a continuously loaded generator, continuous current flow measurements were also performed under large temperature differences. The temperature-averaged TE properties from standard low temperature difference measurements and the experimental TE properties agree with each other, indicating that the designed setup is reliable for measuring various thermoelectric generator properties of single TE legs when subjected to temperature gradients between 50 and 300 K.

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.