Calculation of the Temperature Dependence of the Energy Gaps in PbTe and SnTe

Abstract

The empirical pseudopotential method is modified to calculate the temperature dependence of the first direct gap $E_g$ of PbTe at the $L$ point of the Brillouin zone. The same set of form factors which had given a reasonable band structure throughout the Brillouin zone and which adequately explains the optical properties of PbTe gives both the correct positive sign and magnitude for ${\left(\frac{\partial E_g}{\partial T}\right)|}_P$. The same method when applied to SnTe gives very unusual results, namely, a negative temperature coefficient for the region in the Brillouin zone near the minimum gap but a positive temperature coefficient for gaps slightly removed from the minimum gap. This appears to be consistent with the negative temperature coefficient obtained from tunneling experiments and the positive temperature coefficients obtained from optical measurements. The origin of the temperature dependence of conduction and valence levels at the gap is discussed in detail.