Temperature dependence of the energy gap in semiconductors

It is shown that the equation ΔE = αT²/(T + β), which is commonly used to describe the temperature variation of energy gaps in semiconductors, is a second order approximation of the electron–phonon interaction term in the recently proposed equation ΔE = UT^s + Vθ[coth (θ/2T) – 1]. The calculation shows that the parameters α and β of the approximate equation can describe the characteristics of semiconductors only if the relation [Formula: see text] holds, with the validity limited by the magnitude of the existing dilation effect. In this case it is found that β = θ/2 where θ is the effective Einstein vibrational frequency, in temperature units, of the phonon spectrum in the material. A comparison of the two equations when fitted to experimental data is presented and discussed.