DIRECT-TRANSITION OPTICAL ABSORPTION IN PBS PBSE AND PBTE FROM RELATIVISTIC AUGMENTED-PLANE-WAVE FUNCTIONS

The optical absorption arising from the first five (six in PbTe) direct band-to-band transitions in each of the lead chalcogenides has been calculated from first principles, using the parabolic approximation. The major features of the absorption structure in these materials are accounted for by the direct transitions considered. Within the energy range of these transitions there also occur indirect transitions whose contributions cannot presently be calculated but are second-order and less important to the absorption structure. The direct-transition optical matrix elements, effective masses, and energy differences (threshold energies) were obtained from the results of relativistic augmented-plane-wave energy-band calculations whose only fit to experiment was to the value of the forbidden gap. All of the electric-dipole transitions which contribute occur at the point L. An indication of the applicability of relativistic augmented-plane-wave results to determinations of optical absorption in semiconductors is provided by comparing calculation with experiment. When the above parameters are employed in the theory of Elliott, calculation and experiment agree to within less than an order of magnitude. At the forbidden gap, where Elliott's theory is exact, calculation and experiment agree to within a factor of 3. The calculated absorption curves demonstrate that a direct-transition threshold energy can be accurately obtained only from the position of a discontinuity in slope, and not from the position of a shoulder or maximum. The agreement between the calculated and experimental curves indicates that the observed absorption in the lead chalcogenides arises predominantly from direct transitions at the point L. © 1969 The American Physical Society.