Phonon frequency and energy of electron-phonon interactions at the band gap of InAs, InP, GaP, and GaN semiconductors

The effects of phonon energy on the temperature dependence of energy of electron-phonon interactions at the band gap of InAs, InP, GaP, and GaN are studied in this paper. In the models of temperature dependence of the width of the band gap such as Fan’s formula, Bose-Einstein model, Manoogian and Leclerc’s equation, and O’Donnel and Chen’s equation, the Bose-Einstein occupation factor with phonon energy is included. Therefore, phonon energy plays important roles on the temperature dependence of energy of phonon-electron interactions at the band gap of semiconductors. The model for temperature-dependent band structures is employed to analyze the phonon frequency and energy of electron-phonon interactions at the band gap of InAs, InP, GaP, and GaN. The results show that the frequency of phonon energy of electron-phonon interactions at the band gap of InAs, InP, GaP, and GaN approximates the energy at the Debye temperature of these semiconductors. It is also revealed that the decrease of band-gap energy with temperature from 0 K is equal to the energy of electron-phonon interactions at the band gap of semiconductors with the phonon frquency corresponding to the Debye temperature.