Lattice Dynamics of Grey Tin and Indium Antimonide

Abstract

We have measured the phonon-dispersion relations in symmetry directions for $\ensuremath{\alpha}\ensuremath{-}\mathrm{S}\mathrm{n}$ at 90 \ifmmode^\circ\else\textdegree\fi{}K and InSb at 300 \ifmmode^\circ\else\textdegree\fi{}K. A limited number of measurements were made at 240 \ifmmode^\circ\else\textdegree\fi{}K in $\ensuremath{\alpha}\ensuremath{-}\mathrm{S}\mathrm{n}$ to look for effects associated with the phase transition, but none were found. The two dispersion relations are qualitatively similar, the main differences arising from the lower symmetry and a slight general drop in frequency in going from $\ensuremath{\alpha}\ensuremath{-}\mathrm{S}\mathrm{n}$ to InSb. Systematic trends in the comparison with other group-IV and III-V semiconductors can be seen. We have found second-neighbor shell models which give a reasonable description of the dispersion relations but in which the parameters are poorly defined and apparently devoid of physical meaning. The microscopic implications of this fact are discussed.