Temperature Dependence of Electron Energy Levels in Solids

In many crystalline insulators there is a temperature proportional displacement of the long wave-length absorption limit towards longer wave-lengths. These are crystals which have a broad, nearly structureless absorption which is caused by the transition of an electron from a full to an empty electron band. Previous attempts to explain this phenomenon have shown that the effects of thermal expansion are far too small to account for the observed shift. In this paper it is shown that there is a broadening of electron energy levels due to collisions with the thermally vibrating lattice which results in reducing the effective width of the "forbidden" energy region between occupied and conducting bands. Calculations indicate that, in polar crystals for which the observations have been made, this effect is of the proper magnitude to explain the experimental data. In non-polar crystals the effect would be very small. However, no absorption shift in non-polar crystals has been observed.