Thermoelectric characteristics of heavily doped $p$-type lead telluride at different heavy-hole band depths

The full set of thermoelectric parameters of heavily doped $p$-PbTe in the temperature range of 300–1200 K at an acceptor doping level of $N_ a$ = 1 $\times$ 10$^{19}$–4 $\times$ 10$^{20}$ cm$^{-3}$ and a heavy-hole band depth ranging from 0.36 to 0.7 eV is calculated. The figure-of-merit value $Z$ is found to be highly sensitive to the doping level and increased by a factor of 1.5 with an increase in the dopant concentration from 1 $\times$ 10$^{19}$ to 5 $\times$ 10$^{19}$ cm$^{-3}$; the maximum $Z$ value is found to correspond to $N_ a$ = (1–2) $\times$ 10$^{20}$ cm$^{-3}$. It is demonstrated that the change in the heavy-hole band depth leads to a noticeable shift of the $Z$ maximum position along the temperature axis without noticeable $Z$ maximum variation. The temperature corresponding to the maximum $Z$ value is similar to that at which the top of the light-hole band crosses the Fermi level. The maximum calculateded $ZT$ value is shown to be 1.64. At a heavy-hole band depth of 0.5 eV, the calculated results agree well with the available experimental data.