Effect of Strain on the Secondary Band Extrema of PbS, PbSe, PbTe, and SnTe

The energy levels associated with the secondary extrema in the energy-band structure of PbS, PbSe, and PbTe, at $\overrightarrow{\mathrm{k}}=\left(\frac{\pi }{a}\right)(\frac{4}{5},\frac{4}{5},0)$, are calculated using the augmented-plane-wave method. The resulting wave functions, along with those previously calculated for SnTe, are used to obtain isotropic and uniaxial deformation potentials for all the energy levels at this point in the Brillouin zone. The results are compared with the temperature coefficients of the various gaps in the "two-band model" for the galvanomagnetic properties of these compounds. The sign of the calculated $\frac{d{E}_g}{\mathrm{dT}}$ and $\frac{d\Delta E_v}{\mathrm{dT}}$ for the lead chalcogenides are in agreement with the experimental results. The agreement for the magnitudes, although not uniformly good for all cases, is satisfactory and presents a coherent picture for the relationship between these compounds.