Theoretical analysis of Raman spectra of finite-stage Si/Si-Ge Fibonacci superlattices

Raman-scattering results for acoustic phonons in Si/${\mathrm{Ge}}_{\mathrm{x}}$ ${\mathrm{Si}}_{1\mathrm{-}\mathrm{x}}$ Fibonacci superlattices with low-stage numbers are analyzed and shown to have significant deviations from the infinite-stage assumption implicit in standard theoretical models. We show that a quantitative description of the observed spectra is possible only with a ‘‘sample-specific’’ theory which takes into account the presence of the substrate and the free surface. A nearest-neighbor linear-chain model is used to calculate Raman spectra which are in good agreement with experiment.