Temperature coefficient of the refractive index of diamond- and zinc-blende-type semiconductors

We have calculated the temperature coefficient of the long-wavelength refractive index of several group-IV and III-V semiconductors, using the Penn model for the electronic contribution to the dielectric constant. The isotropic band gap of this model is identified with the band gap at the X point of the Brillouin zone, which can be simply expressed in terms of pseudopotential coefficients. The explicit temperature dependence of this gap is calculated by applying to these pseudopotential coefficients the appropriate Debye-Waller factors. The thermal expansion effect is obtained in the manner suggested recently by Van Vechten. Good agreement between the calculated and the observed temperature dependence of the long-wavelength refractive index is found.