Interface phonons of quantum wires

Abstract

We have used the continuum dielectric approach to study the optical-interface-phonon modes of a quantum-wire structure consisting of one material buried within another. Wires with a number of cross-sectional shapes have been studied. Analytical results are presented for wires with elliptical cross sections, of which the circular cross section is a special case. Numerical results using an integral-equation approach are given for wires with arbitrary cross-sectional shapes including rectangles having rounded corners. The dependence of the modes on the wire cross sections and their relation to the vibrational modes of planar quantum wells are discussed. For large wave vectors parallel to the wire or around the wire circumference, the modes are found to approach those of the planar interface. Modes are found to be localized in the corners of the wires or regions of high curvature, and the degree of localization is found to increase with the increasing sharpness of the corners.