Temperature Dependence of the Energy Gap in Semiconductors

The problem treated is the effect of lattice vibrations in producing a shift of the energy levels which results in a temperature dependent variation of the energy gap in semiconductors. Calculations for silicon and germanium give results of the same order of magnitude as the observed temperature dependent shift of the absorption band edge. The effect of lattice vibrations on the energy gap has been treated previously on the basis of broadening rather than shifting of the energy levels. The effect was found to be negligible for non-polar crystals, whereas according to our treatment it should be much larger. For polar crystals our result turns out to be essentially the same as was given by the previous treatment.