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

The dependence of physically observable quantities such as electron-phonon scattering rates on the boundary conditions for the optical phonons confined in polar semiconductor quantum wells, quantum wires, and quantum dots are examined within the dielectric continuum approach. Calculations of the confined phonons and of their contributions to the scattering rates are made using the boundary conditions of Maxwell's equations at the interfaces and the condition that the ionic displacements go to zero there. These results are compared with the results obtained using only the condition that Maxwell's equations be satisfied (the usual dielectric continuum model). We find that in the absence of phonon dispersion the rates of scattering by the confined phonons in these two cases are identical even though the individual phonons differ. We attribute this result to the fact that physically observable quantities involve sums over complete sets of states. As a part of the present work we have derived an interesting relation between the contributions of the confined phonons and the interface phonons to the scattering rates in nanostructures. This relation is useful in, for example, obtaining the rates of scattering by the confined modes for geometries of low symmetry where straightforward sums are difficult.