Size Dependence of the Longitudinal Optical and Surface Optical Phonon Modes in Cylindrical Quantum Wires

With the use of the classical macroscopic approach, we have derived the longitudinal optical (LO) and surface optical (SO) phonon modes in a cylindrical quantum wire (QW). The dispersion relation of the SO phonon modes in the QW is discussed explicitly. Having quantized the vibrational eigenmodes, we give the interaction Hamiltonian of the electron with the LO and SO phonon modes in QW.