Temperature dependence of the energy gap of semiconductors in the low-temperature limit

The temperature dependence of the electronic states and energy gaps of semiconductors is an old but still important experimental and theoretical topic. Remarkably, extant results do not clarify the asymptotic T --> 0 behavior. Recent breakthroughs in the spectroscopy of enriched Si-28 allow us to measure changes in the band gap over the liquid He-4 temperature range with an astounding precision of one part in 10(8), revealing a T4.0+/-0.2 decrease with increasing T. This is in excellent agreement with a theoretical argument predicting an exponent of 4. This power law should apply, in the low temperature limit, to the temperature dependence of the energies of all electronic states in semiconductors and insulators.