The electronic band structure of PbS

Abstract

The cellular method has been applied to the determination of electronic wave functions of the Bloch type in PbS. In each cell ψ is expanded in terms of ‘Kubic harmonics', and a table of these functions (for a NaCl type of lattice) for prominent points in momentum space is included. An attempt has been made to establish a self-consistent field, by treating only the electrons with k = 0, but results have shown that this approximation is not very good. Methods of matching the wave functions at the boundaries between the cells are described, based either on least square fitting or on expansion of ψ in terms of functions which are orthogonal over the boundaries. These methods have been tested with the empty lattice test. Curves are given showing the approximate band structure in two prominent crystallographic directions. The resulting width of the full band is about 6 eV, that of the conduction band about 7 eV. The forbidden energy gap is very small (< 0.3 eV). The lowest allowed optical transition has a wave-length of 0.9 μ. These results are in agreement with the observed absorption spectrum and suggest that its tail is due to forbidden transitions. The calculated rate of change with temperature of the energy gap is 2 x 10 -4 eV /degree, about half the experimental value.