Phonon modes and electron-phonon interactions in cylindrical quantum wires: Macroscopic and microscopic analyses for device applications

Abstract

The macroscopic and microscopic analyses of phonon modes that has been done in past works for two-dimensional quantum wells are developed in this work for one-dimensional quantum wires. Inconsistencies and errors in past works on phonon modes in quantum size structures are discussed including the correct form of the Lorentz factor that should be used and the proper quantization of the phonon modes. Connections between the macroscopic and microscopic approaches are described. Longitudinal optical and surface longitudinal optical phonon modes are calculated. The free polarization Hamiltonian and electron-phonon interaction Hamiltonian are developed. The application of this analysis to the development of high operating temperature quantum wire infrared photodetectors is discussed.