Acoustic phonons propagating parallel to the growth direction of a periodic superlattice composed of more than two different constituent layers are studied theoretically. We give general formulas for the phonon dispersion relation and the width {Δ}{ν} of frequency gaps existing at the center and boundary of the folded Brillouin zone. We also calculate the structure factor for phonons and find that {δ}-function peaks corresponding to Bragg reflection have prefactors proportional to {Δ}{ν}. This relation can be used to explain the relative magnitude of transmission dips found at frequencies satisfying the Bragg condition.
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Tamura et al. (1988) studied this question.
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