Effects Of Electron-Phonon Interaction And Hydrostatic Pressure On The Surface States In Nitride Semiconductors

A variational approach is used to study the surface states of electrons insemi-infinite wurtzite nitride semiconductor, by including the effects of theelectron-Surface-Optical-phonon interaction. The effective Hamiltonian and thesurface-state levels as functions of the surface potential barrier V₀ are derived byadopting the LLP-like theory.The numerical computation has been performed for the energies of the electronicsurface states, the electron-Surface-Optical-phonon-interaction energies, and theaverage penetrating depths d of surface state wave functions as functions of thesurface potential V₀ in wurtzite GaN, AlN and InN, respectively. The differencesbetween the wurtzite and zinc-blende structural materials are also discussed. Theresults show that the surface-state energies are linear increased with increasing of V₀. It is clearly that the electron-Surface-Optical-phonon interaction lowers thesurface-state levels. The energy of the electron-Surface-Optical-phonon interaction isalmost independent of surface potential barrier. The electronic surface-state levels inthe wurtzite material are lower than that in the corresponding zinc-blende one forhundreds of meV. The numerical computation has been also performed for theelectronic surface-state energies as function of the composition x in wurtziteAl_xGa_1-xN, Al_xIn_1-xN and In_xGa_1-xN by using linear interpolation method, respectively.It is found that the electronic surface-state levels are decreased with increasing ofcomposition x.Furthermore, the surface states of electrons in semi-infinite nitridesemiconductors are discussed under hydrostatic pressure by considering thevariations of lattice constants, dielectric constants, bulk LO (TO)-phonon energies,anisotropic effective band masses of electrons, and forbidden band gaps withhydrostatic pressure. The shifts of the surface-state levels, which caused by theeffects of electron-Surface-Optical-phonon interaction, are becomes larger underpressure. The variations of electron-Surface-Optical-phonon interaction energy withpressure are obviously. It is indicated that the effects of the electron-phononinteraction and hydrostatic pressure on the electronic surface-state energy can not beneglected, especially, for the materials with stronger electron-phonon coupling andbroad band gap.