EFFECTS OF BOUNDARY-CONDITIONS ON CONFINED OPTICAL PHONONS IN SEMICONDUCTOR NANOSTRUCTURES

The dependence of physically observable quantities such as electron-ph onon scattering rates on the boundary conditions for the optical phono ns confined in polar semiconductor quantum wells, quantum wires, and q uantum dots are examined within the dielectric continuum approach. Cal culations of the confined phonons and of their contributions to the sc attering rates are made using the boundary conditions of Maxwell's equ ations at the interfaces and the condition that the ionic displacement s go to zero there. These results are compared with the results obtain ed using only the condition that Maxwell's equations be satisfied (the usual dielectric continuum model). We find that in the absence of pho non dispersion the rates of scattering by the confined phonons in thes e two cases are identical even though the individual phonons differ. W e attribute this result to the fact that physically observable quantit ies involve sums over complete sets of states. As a part of the presen t work we have derived an interesting relation between the contributio ns of the confined phonons and the interface phonons to the scattering rates in nanostructures. This relation is useful in, for example, obt aining the rates of scattering by the confined modes for geometries of low symmetry where straightforward sums are difficult.