  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 non polar 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 modelled 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 interaction within the deformation potential
approximation.
