Dispersion of confined optical phonons in semiconductor nanowires in the framework of a continuum approach

Confined optical phonons are discussed for a semiconductor nanowire of the Ge (Si) prototype on the basis of a theory developed some years ago. In the present work this theory is adapted to a nonpolar material and generalized to the case when the phonon dispersion law involves both linear and quadratic terms in the wave vector. The treatment is considered along the lines of a continuous medium model and leads to a system of coupled differential equations describing oscillations of mixed nature. The nanowire is modeled in the form of an infinite circular cylinder and the solutions of the fundamental equations are found. We are thus led to a description of long-wavelength optical phonons, which should show a closer agreement with experimental data and with calculations along atomistic models. The presented theory is applied to the calculation of optical phonons in a Ge nanowire. We have found the dispersion curves for various optical phonon modes. We also normalize the modes and discuss the electron-phonon ...