Structure and vibrational dynamics of interfacial Sn layers in Sn/Si multilayers

The structure and vibrational dynamics of room-temperature-grown nanoscale Sn/amorphous $(a$-)Si multilayers have been studied by x-ray diffraction, Raman scattering, ¹¹⁹Sn M\"ossbauer spectroscopy, and ¹¹⁹Sn nuclear-resonant inelastic x-ray scattering (NRIXS) of synchrotron radiation. With increasing Sn-layer thickness, the formation of β-Sn was observed, except at the Sn/Si interfaces, where a 10-{}-thick metastable pure amorphous-α-Sn-like layer remains stabilized. By means of NRIXS we have measured the Sn-projected vibrational density of states (VDOS) in these multilayers (in particular, at the interfaces), and in 500-{}-thick epitaxial α-Sn films on InSb(001) as a reference. Further, the Sn-specific Lamb-M\"ossbauer factor $(f$ factor), mean kinetic energy per atom, mean atomic force constant, and vibrational entropy per atom were obtained. The VDOS of the amorphous-α-Sn-like interface layer is observed to be distinctly different from that of (bulk) α-Sn and β-Sn, and its prominent vibrational energies are found to scale with those of amorphous Ge and Si. The observed small difference in vibrational entropy (ΔS/kB=+0.17±0.05 per atom) between α-Sn and interfacial amorphous-α-like Sn does not account for the stability of the latter phase.