Anomalous Thermoelectric Power as Evidence for Two-Valence Bands in SnTe

The thermoelectric power ($\alpha$) of $p$-type SnTe has been measured between room temperature and 450°C for apparent hole concentrations ($p^{*}=\frac{1}{e{R}_{300}}$) between 1×${10}^{20}$ and 1.8×${10}^{21}$ ${\mathrm{cm}}^{-3\mathrm{}}$. At room temperature, $\alpha$ does not decrease monotonically with increasing $p^{*}$ in the usual manner for a $p$-type semiconductor. Instead, it increases from 5-8 μV/deg at $p^{*}=1-2\mathrm{}\times {10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$ to a maximum of 34μV/deg at $p^{*}=8\mathrm{}\times {10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$, after which it decreases to 20.5 μV/deg at $p^{*}=1.8\mathrm{}\times {10}^{21}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The maximum gradually disappears with increasing temperature. At 400 and 450°C, $\alpha$ decreases monotonically with increasing $p^{*}$. By means of numerical calculations for a particular set of band parameters, it is shown that this type of anomalous variation in $\alpha$ can be exhibited by a $p$-type semiconductor with two nondegenerate valence bands. It is found that the observed properties of SnTe, including the variation of Hall coefficient with temperature and carrier concentration, are qualitatively consistent with a two-valence-band model, but are difficult to explain on the assumption that SnTe is a semimetal. However, it has not been possible to obtain a quantitative fit to the data with a two-band model in which both bands are of simple parabolic form.