Applicability of the empirical Varshni relation for the temperature dependence of the width of the band gap

We have carried out a comparison of relations used to describe the temperature dependence of the width of the band gap in crystals. It is shown that for kT≫ℏω the well-known Varshni relation can be obtained from the non-empirical Fan expression in explicit form taking account of the phonon statistics. We have calculated the temperature coefficient bof the width of the band gap for a number of materials in the range where the high-temperature condition is not met. We have found that the Varshni relation overestimates β, whereas calculations based on the Fan expression agree with experiment.

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