Electron Energy Bands in Tellurium

Abstract

The method of pseudopotentials was used to calculate the electron band structure of tellurium along the $k_Z$ axis. The calculation was performed in two stages. First, a model pseudopotential, based on the free-atom data of Herman and Skillman, was used to compute a preliminary band structure. Perturbation theory was then used to estimate the changes in the band structure caused by corrections to the model pseudopotential. The calculated band structure shows a direct energy gap at the top of the Brillouin zone ($k_Z=\frac{\pi }{c}$) and an indirect gap of about the same magnitude between the valence band edge at $k_Z=0\mathrm{}$ and the conduction band edge $k_Z=\frac{\pi }{c}$. It was found that $s-p$ mixing is significant in the important valence and conduction bands. Because of this mixing, spin-orbit splitting, which was calculated in a second-order perturbation approximation, is much smaller than the corresponding splitting of the $5p$ free-atom level. The calculated band structure is consistent with the major features of the experimental infrared absorption spectrum including the 11-μ peak observed by Caldwell and Fan.