Hybridization of Surface Waves with Organic Adlayer Librations: A Helium Atom Scattering and Density Functional Perturbation Theory Study of Methyl-Si(111)

The interplay of the librations of a covalently bound organic adlayer with the lattice waves of an underlying semiconductor surface was characterized using helium atom scattering in conjunction with analysis by density functional perturbation theory. The Rayleigh wave dispersion relation of ${\mathrm{CH}}_3$- and ${\mathrm{CD}}_3$-terminated Si(111) surfaces was probed across the entire surface Brillouin zone by the use of inelastic helium atom time-of-flight experiments. The experimentally determined Rayleigh wave dispersion relations were in agreement with those predicted by density functional perturbation theory. The Rayleigh wave for the ${\mathrm{CH}}_3$- and ${\mathrm{CD}}_3$-terminated Si(111) surfaces exhibited a nonsinusoidal line shape, which can be attributed to the hybridization of overlayer librations with the vibrations of the underlying substrate. This combined synthetic, experimental, and theoretical effort clearly demonstrates the impact of hybridization between librations of the overlayer and the substrate lattice waves in determining the overall vibrational band structure of this complex interface.

Figure 1

A schematic of the methyl-terminated Si(111) surface, with the real space unit cell highlighted, showing the crystallographic orientations of the reciprocal lattice $\overline{\Gamma M}$, $⟨01\overline{1}⟩$, and $\overline{\Gamma K}$, $⟨11\overline{2}⟩$ (a). Diffraction spectra for both of these orientations are overlaid along with an inset displaying the reciprocal space unit cell (b). An overlay of TOF spectra from the ${\mathrm{CH}}_3\mathrm{\text{−}}\mathrm{Si}(111)$ surface at $T_S=150\mathrm{K}$ along $\overline{\Gamma K}$ (c). The arrows indicate single-phonon creation peaks, and the inset displays scan curves for each spectrum (colors). The black points indicate the energy and momentum transfers for the observed inelastic peaks, and the gray lines are the Rayleigh wave dispersion curves. (d) is the corresponding energy transfer spectra of the TOF data from (c), with inelastic peaks indicated by black arrows. Spectra are offset for clarity.

Figure 2

HAS single phonon data overlaid on the dispersion curves (black lines) obtained from DFPT calculations for (a) ${\mathrm{CH}}_3\mathrm{\text{−}}\mathrm{Si}(111)$ and (b) ${\mathrm{CD}}_3\mathrm{\text{−}}\mathrm{Si}(111)$. Multiple phonon scattering events are not shown here for improved clarity. The total sagittal displacement of the terminal ${\mathrm{CH}}_3$ and ${\mathrm{CD}}_3$ groups is presented in the color scale. The single phonon HAS data coincide with modes that contain significant sagittal displacements. Schematics of the displacement patterns for the rocking libration, the hindered rotation, and the RW are presented, with arrows proportional to the real components of the mode eigenvectors (c).

Figure 3

Overlay of the actual curves with the “frozen” calculations for ${\mathrm{CH}}_3$-, (a), and ${\mathrm{CD}}_3\mathrm{\text{−}}\mathrm{Si}(111)$, (b). (c) overlays the frozen curves with those obtained from H-Si(111) calculations.