Polarization eigenvectors of surface-optical phonon modes in a rectangular quantum wire

The polarization eigenvectors and dispersion relations for confined longitudinal-optical (LO) and surface-optical (SO) phonon modes in a rectangular quantum wire are derived within the continuum approximation. The SO and confined LO modes are compared for a quantum wire with a square cross-section in the limit of a vanishing phonon wave vector along the quantum-wire axis. For this case, it is demonstrated that the SO mode becomes dominant over the confined LO modes in interaction with electrons and must be taken into account in calculating the electron–optical-phonon scattering rate.