Dielectric susceptibility model for optical phonons in superlattices

Abstract

The form of the long-wavelength optic-phonon modes in semiconductor superlattices is described using a dielectric susceptibility model. This model only requires knowledge of the frequencies and eigenvalues for LO and TO modes propagating along the superlattice growth direction $z.$ From these, the principal-axis dielectric susceptibilities ${\ensuremath{\varepsilon}}_{\mathrm{zz}}(\ensuremath{\omega})$ and ${\ensuremath{\varepsilon}}_{\mathrm{xx}}(\ensuremath{\omega})$ can be obtained, and so a full description of the optic phonons is possible for any phonon propagation direction. Calculations of confined LO and TO mode frequencies and displacements are made for GaAs/AlAs superlattices. The susceptibilities and mode displacements are compared using a simple continuum model and a microscopic linear-chain model. The susceptibilities are also used to model nonresonant Raman-scattering spectra, and are shown to give results that are in close agreement with published micro-Raman measurements.