Energy Bands of PbTe, PbSe, and PbS

Because it is impossible to obtain first-principle crystal potentials of the lead salts with sufficient accuracy to calculate energy bands in agreement with experiment, we have developed a new pseudopotential containing only $2n+1$ adjustable parameters, where $n$ is the number of different atoms per unit cell. This pseudopotential contains all the important relativistic effects including spin-orbit interactions and yet requires only 5 parameters for the lead salts. We have chosen the parameters to fit the ordering of the six levels around the forbidden energy gap at the (\textonehalf{}\textonehalf{}\textonehalf{}) point on the Brillouin-zone face as well as two optically measured energy gaps presumed to be at the center of the zone. The energy bands obtained are in very good agreement with the rest of the optical data, the photoelectric data, and the pressure dependence of the forbidden gap. Reasonably good agreement is obtained between our calculated effective masses and $g$ values and the experimentally determined ones.