Coupled-mode stop bands of acoustic phonons in semiconductor superlattices

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Abstract
Dispersion relations of acoustic phonons in the (001) GaAs/AlAs superlattice are calculated for arbitrary propagation directions using the continuum approximation with the elastic anisotropy included. We predict the existence of forbidden band gaps inside the folded Brillouin zone in addition to those at the zone boundary and the zone center. They occur by the mixing of different phonon modes having propagation directions oblique to the interfaces. The phonon transmission rates are calculated for superlattices with a finite number of periods, and significant dips are predicted for frequencies corresponding to zone-center, zone-boundary, and coupled-mode stop bands.