A First-Principle Calculation of the Temperature Dependence of the Indirect Band Gap of Silicon

We have evaluated the contribution to the temperature dependence of the indirect band gap of silicon arising from electron-phonon interactions using a first-principle pseudo-potential technique. This represents the first parameter-free calculation of the temperature dependence of the band gap of a real material. Numerical results are in reasonable agreement with experiment. At high temperatures we find that each phonon branch gives approximately the same contribution to the temperature dependence of the gap.