First-principles study of structural and dynamical properties of α-Sn(0 0 1)-(2 × 1)

We have investigated the structural and vibrational properties of the α-Sn(0 0 1)-(2 × 1) surface using the density functional perturbation theory and the pseudopotential method. The dimer is tilted by about 22° and has a characteristic length slightly larger than the bulk bond length. The surface sustains phonon modes below the bulk continuum, modes in stomach gaps (gap regions within the bulk continuum) and above the bulk continuum. Energy locations and polarization characteristics of rocking, dimer stretch and surface back bond phonon modes have been determined. A brief comparison of these features is made with the silicon and germanium surfaces.