Electron-phonon interactions and lattice dynamics of optic phonons in semiconductor heterostructures

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Abstract
Slab vibrations, reformulated slab vibrations, and guided vibrations have been proposed by various authors as the confined polar-optic-phonon modes in heterostructures. It is shown, with reference to these three cases, that both the intrasubband and intersubband electron-phonon scattering rates are independent of the basis set used to describe the phonon modes, as long as this set is orthogonal and complete. Earlier conflicting results are attributed to the use of basis sets that do not satisfy these criteria, and to scattering potentials that do not obey the correct boundary conditions. Nearly all the scattering is by modes that are well described by continuum models. A dispersive continuum theory of the lattice dynamics is developed. Without recourse to microscopic theory, we derive the connection rules that relate fields on either side of an interface, and identify the circumstances in which each above-mentioned set of vibrations corresponds to the normal modes. The controversy over whether the normal modes satisfy electromagnetic or mechanical boundary conditions is resolved. The design of lattice properties to minimize electron-phonon scattering rates is discussed.