Phonon dynamics of theSn∕Ge(111)surface at room temperature and low temperature determined by helium-atom scattering

Abstract

We report on a high-resolution helium atom scattering study of the surface lattice dynamics, for both the room temperature $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})\mathrm{R}30\ifmmode^\circ\else\textdegree\fi{}$ and the low-temperature $(3\ifmmode\times\else\texttimes\fi{}3)$ structures formed by $1∕3$ of a monolayer of Sn on Ge(111). At room temperature a pronounced lowering of the energy of the transversally polarized phonons along the $\overline{\ensuremath{\Gamma}\mathrm{M}}$ direction is observed for wave vectors in the vicinity of $Q=0.6\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{\ensuremath{-}1}$, the $\overline{\mathrm{K}}$ point of the room temperature $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})\mathrm{R}30\ifmmode^\circ\else\textdegree\fi{}$ structure. The temperature dependence of this mode is analyzed between 140 and 300 K. We conclude that the softening of this mode is related with the $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})\mathrm{R}30\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\leftrightarrow}(3\ifmmode\times\else\texttimes\fi{}3)$ phase transition. Phonon distributions curves are determined for both phases and the two high symmetry directions. The experimental data are explained from the backfolding of the slightly modified $\mathrm{Ge}(111)\ensuremath{-}(1\ifmmode\times\else\texttimes\fi{}1)$ Rayleigh wave and from the modes related to the Sn induced superstructures, in good agreement with first-principles calculations.