Strained α-Sn/Ge superlattices: Geometrical structures and phonon spectra

The geometrical structures and phonon spectra of strained {α}-Sn/Ge superlattices grown pseudomorphically on (001)-oriented substrates are studied using a generalized Keating model. It is found that symmetrically strained {α}-Sn/Ge superlattices grown on properly chosen substrates can be approximately achieved, which renders the growth of superlattices with large thickness possible. The general features of phonon spectra are discussed. Ge-like confined LO modes can be well described by the bulk dispersion with the confinement length taken as deff=(n+1)a/4, where n is the number of Ge layers and a/4 is the Ge-Ge interplanar distance. The Sn-like LO modes are resonant and quasiconfined. No interface modes are found in the longitudinal polarization; however, such modes do appear in the transverse polarization around 232 cm^-1.