We describe a continuum model of optical phonons in GaAs/AlAs superlattices which consists of a linear combination of LO, TO, and interface modes. The model describes the mixing of confined and interface modes as the in-plane phonon wave vectors are varied. We derive an analytical expression for the dispersion relation and a detailed comparison is made with two different microscopic models. Excellent agreement is found for [111] superlattices and good agreement is found with [100] superlattices, especially if we take into account that the mechanical vibrations are not quite confined to the nominal GaAs layers.
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Chamberlain et al. (1993) studied this question.
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