Surface phonon dispersion on hydrogen-terminated Si(110)-(1 × 1) surfaces studied by first-principles calculations

We studied the lattice constants, surface-phonon dispersion curves, spectral densities, and displacement vectors of the hydrogen-terminated Si(110)-(1 × 1) [H:Si(110)-(1 × 1)] surface using the first-principles calculations within the framework of density functional theory (DFT). The symmetry of the H:Si(110)-(1 × 1) surface belongs to the two-dimensional space group p2mg, which has two highly symmetric and orthogonal directions, Γ X ¯ and Γ X ′ ¯, with the glide planes along the Γ X ¯ direction. Because glide symmetry separates the even and odd surface phonon modes, we mapped the even surface modes in the first surface Brillouin zone (SBZ) and the odd surface modes in the second SBZ using the spectral densities and displacement vectors. The surface phonon modes were analyzed with respect to their physical origin, spatial localization properties, polarization, and the charge density of their electronic states. Our calculated surface phonon modes were in good agreement with recent high-resolution electron-energy-loss spectroscopy data in the first and second SBZs of the Γ X ¯ direction. In the SBZ of the Γ X ′ ¯ direction, our calculated surface phonon modes agree well with the data in the energy region below 65 meV but are not satisfactorily compatible with those in the stretching and bending modes. In addition, we discuss the microscopic nature of the surface phonon dispersion of the H:Si(110)-(1 × 1) surface using the phonon eigen modes.