Effect of electron-phonon interaction on surface states in zinc-blende GaN, AlN, and InN under pressure

A variational approach is used to study the surface states of electrons in a semi-infinite polar semiconductor under hydrostatic pressure. The effective Hamiltonian and the surface-state levels are derived including the effects of electron-optical phonon interaction and pressure. The numerical computation has been performed for the surface-state energies versus pressure for zinc-blende GaN, AlN, and InN. The results show that the effect of electron-optical phonon interaction lowers the surface-state energy. It is also found that the effect of electron-surface optical phonon interaction is much bigger than the effect of electron-half space longitudinal optical phonon interaction for surface-state levels. It indicates that the surface-state energies and the influence of electron-phonon interaction increase with pressure obviously.