Vibration eigenmodes of the Au-$(5\times 2)$/Si(111) surface studied by Raman spectroscopy and first-principles calculations

Ordered submonolayers of adsorbate atoms on semiconductor surfaces constitute a playground for electronic correlation effects, which are tightly connected to the local atomic arrangement and the corresponding vibration eigenmodes. We report on a study of the vibration eigenmodes of Au-covered Si(111) surfaces with $(5\times 2)$ reconstruction using polarized Raman spectroscopy and first-principles calculations. Upon Au coverage, the vibration eigenmodes of the clean reconstructed Si(111)-$(7\times 7)$ surface are quenched and replaced by new eigenmodes, determined by the Au-$(5\times 2)$ reconstruction. Several polarization-dependent surface eigenmodes emerge in the spectral range from 25 to $120{\mathrm{cm}}^{-1}$, with the strongest ones at 29, 51, and $106{\mathrm{cm}}^{-1}$. In our first-principles calculations we have determined the vibration frequencies, the corresponding elongation patterns, and the Raman intensities for two different structure models currently discussed in the literature. The best agreement with the experimental results is achieved for a model with 0.7 monolayer coverage and seven Au atoms per unit cell, proposed by S. G. Kwon and M. H. Kang [Phys. Rev. Lett. 113, 086101 (2014)].

Figure 1

Structural models of the Au/Si(111)Au surface within (a) the EBH model (0.6-ML coverage) [5] and (b) the KK model (0.7-ML coverage) [8]. Yellow balls represent gold atoms, while green and dark blue balls identify the Si honeycomb chain and the remaining Si surface atoms, respectively. Si atoms of the underlying bulk layer are colored light blue. The $(5\times 2)$ surface unit cell is outlined in red. Si adatoms are not included.

Figure 2

The $(5\times 2)$ LEED pattern recorded at an electron energy of 45 eV. The green circles on the edges of the blue $(1\times 1)$ rhomb indicate the superstructure reflexes. Together with the streaks, marked by the arrow labeled “x2,” they document the $(5\times 2)$ superstructure.

Figure 3

Polarized Raman spectra of Au-$(5\times 2)$/Si(111) (red) and the aged Au/Si(111) surface (black). Polarization configurations are (a) $z\left(yx\right)\overline{z}$, (b) $z\left(xy\right)\overline{z}$, (c) $z\left(yy\right)\overline{z}$, and (d) $z\left(xx\right)\overline{z}$, where $x$ is the Au-chain direction $\left(1\overline{\text{1}}0\right)$. Excitation wavelength is 660 nm, and temperature is 300 K.

Figure 4

Intensity difference between the Raman spectra of the Au-$(5\times 2)$/Si(111) reconstruction and the aged case in Fig. 3, yielding the Au-$(5\times 2)$-induced vibration modes. Polarization configurations are (a) $z\left(yx\right)\overline{z}$, (b) $z\left(xy\right)\overline{z}$, (c) $z\left(yy\right)\overline{z}$, and (d) $z\left(xx\right)\overline{z}$, where $x$ is the Au-chain direction $\left(1\overline{\text{1}}0\right)$.

Figure 5

Measured difference spectra of the Au-$(5\times 2)$/Si(111) reconstruction (black) along with the calculated Raman spectra within the KK and EBH models (red and blue, respectively). The spectra are depicted within the polarization configurations $\left(yy\right),\left(xx\right)$, and $\left(yx\right)$, which is equivalent to $\left(xy\right)$. The intensity scales (in arbitrary units) are equal within each row.

Figure 6

Schematic displacement patterns of the most dominant phonon modes within the $\left(yy\right)$ polarization of the KK model, corresponding to the theoretical Raman peaks in Fig. 5. White and yellow balls represent Si and Au atoms, respectively. Single-headed arrows indicate a rigid translation; double-headed arrows indicate a dimerization motion.