Ab initio pseudopotential calculations of the transverse and longitudinal phonon spectra of Ge, alpha-Sn, and alpha-Sn/Ge superlattices

A combination of a first-principles pseudopotential plane wave and the inte rplanar force constants (IPFC's) methods is used to calculate the transvers e (T) and longitudinal (L) phonon spectra along [001] of Ge and biaxially s trained alpha-Sn, which correspond to a coherent growth on alpha-Sn, alpha- Sn0.5Ge0.5 and Ge(001) substrates. The calculated sets of IPFC's are also u sed to investigate the phonon spectra of alpha-Sn/Ge superlattices (SL's) p seudomorphically grown on a Ge substrate. Our results for both the T and L phonon spectra of unstrained alpha-Sn are in good agreement with the experi mental data, and their variations with respect to the (001)-biaxial strain are predicted. Despite the large lattice mismatch between Ge and alpha-Sn, the calculated phonon spectra of alpha-Sn show a linear variation with resp ect to the strain state. The T and L confined and interface phonon modes in the alpha-Sn/Ge SL's are discussed, in comparison with the corresponding p honon spectra of bulk Ge and properly strained alpha-Sn. In particular, the Ge-like L- and T-optical confined modes in alpha-Sn-m/Ge-n SL's are well d escribed relative to the bulk dispersions of Ge by effective confinement le ngths equal to (n + 1)a(0)(Ge)/4 and (n + 3)a(0)(Ge)/4, respectively. [S016 3-1829(99)00926-1].