Contribution of strain-induced modulation to the sound velocity in lattice-mismatched quasiperiodic superlattices.

The propagation of longitudinal-acoustic waves through a quasiperiodic superlattice composed of layers belonging to the cubic symmetry group is explored in terms of the interfacial strain effects. The results show features that seem unique to the lattice-mismatched superlattices. We find that the strain-induced modification of the propagation velocity in this type of superlattice is more pronounced and may be positive or negative, depending only on the velocity difference in the respective media. We also obtain universal formulas for the effective elastic coefficient and average and effective sound velocities, as well as the relevant modulation amplitude, which depends on the quasiperiodic index p. These expressions are applied to analyze the folded acoustic-phonon spectra of semiconductor Si-${\mathrm{Ge}}_{\mathit{x}}$${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$ and GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quasiperiodic Fibonacci superlattices. Our predictions for peak positions of the Raman spectra are in reasonable agreement with the experimental data.