Effect of electron-hole pairs on phonon frequencies in Si related to temperature dependence of band gaps

The direct and indirect gaps between valence and conduction bands in semiconductors usually decrease with temperature. This effect is related by thermodynamic identities to the influence of electron-hole pairs on the lattice vibration frequencies. We show that the surprisingly large magnitude of the effect in Si and similar semiconductors is related to the sensitivity of the transverse-acoustic modes to covalent bonding. We are able to account for the magnitude of the effect from zero to the melting temperature. We also account for anomalous temperature variation in HgTe and related cases and mention other applications of the theory.