Surface phonons of Ge(001) and their correlation with thep(2×1) andc(4×2) reconstruction as shown by Raman spectroscopy

Abstract

The $p$(2$\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}$1)/$c$(4$\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}$2) and the $c$(4$\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}$2) reconstruction of the Ge(001) surface have been studied by polarized Raman spectroscopy at 300 and 40 K, respectively. Raman spectra show several well-defined surface phonon modes related to the atomic structure of the Ge surface. Four modes are detected in the range between 5.70 and 28.15 meV. Their eigenenergies and polarization dependence agree with reported calculation results from the adiabatic bond charge model and from density-functional perturbation theory. The temperature-induced phase transition between both reconstructions is reflected in the symmetry selection rules. Moreover, our results reveal that in Raman scattering the impact of the well-known flipping of the buckled dimers in the $p$(2$\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}$1) reconstruction is fundamentally different from the time averaging, which occurs for low-energy electron diffraction (LEED) and scanning tunneling microscopy (STM). Since the phonon time scale is several orders of magnitude faster than the dimer flipping, the phonon oscillations and their Raman scattering are described consistently within the framework of quasistatic buckled dimers with a short-range antiferromagnetic in-row buckling order.