Effect of the heavy hole band on the thermoelectric figure-of-merit of heavily doped $p$-type lead telluride
The thermoelectric properties of heavily doped $p$-type PbTe have been theoretically studied in the temperature range from 300 to 900 K. The calculations are based on a three-band model of the PbTe electron energy spectrum taking into account the transport of electrons and light holes in the $L$-extrema and heavy holes in the $\Sigma$-extrema. The thermoelectric quantities turned out to be very sensitive to the parameters of the heavy-hole band. The best agreement with the experiment is reached at $m_{hh}=5m_0$ and $E_{g\Sigma}=0.5$ eV, where all calculated thermoelectric quantities agree well with the available experimental data within the entire interval from 300 to 900 K. The calculation confirms a significant increase of the value of the thermoelectric figure-of-merit to $ZT\approx1.2$ that has been recently observed experimentally in heavily doped $p$-PbTe samples. The maximum of $ZT$ corresponds to the temperature at which the band edges of light and heavy holes coincide in energy so that the steepest singularity in the density of states in the valence band is formed.