Influence of surface optical phonons on exciton binding energies of a quasi-one-dimensional wurtzite GaN-based nanowire: Quantum size effect

Abstract

Based on the surface optical phonon states and their electron-phonon coupling functions obtained recently, the surface polaronic exciton states in a quasi-one-dimensional (Q1D) wurtzite nanowire (NW) are investigated by using the variational method and Lee-Low-Pines transform. In order to reflect the different confined features of Q1D wurtzite NWs in axial and radial directions and anisotropy of wurtzite nitride crystals, a two-parameter variational approach is proposed and applied to describe the polaronic exciton states in the NWs. Numerical calculations are performed for GaN NWs. The quantum size effects on the binding energies of polaronic exciton and the contributions of surface phonon modes are analyzed in detail. Our results show that the binding energy of polaronic exciton and surface phonon contribution in the wurtzite GaN NWs reaches 190 and 95 meV, respectively, which are one or two orders of magnitude larger than those in cubic GaAs-based quantum wells and NWs with the same radius. This is mainly ascribed to the strong electron-phonon interaction, the large effective masses of carriers and relatively small dielectric constants in GaN material. The numerical results also show that the two-parameter variational approach is reasonable and necessary for the description of polaronic exciton states in Q1D wurtzite GaN NWs. Moreover, the behaviors of the two variational parameters for the polaronic exciton states are quite different from those for the bound polaron states in Q1D wurtzite NWs.