Vibration signatures of the structural phase transition of Sn/Ge(111) compared to Sn/Si(111)

A temperature driven structural phase transition between $\left(\sqrt{3}\times \sqrt{3}\right)$ and $\left(3\times 3\right)$ has been reported for Sn adsorbed on the Ge(111) surface, which does not occur for the analogous Sn/Si(111) system. This phase transition has been correlated to a softening of a low-frequency Sn vibration mode, referred to as dynamical fluctuation mode. We have determined the eigenfrequencies of the vibration modes of Sn/Ge(111) and Sn/Si(111) with high accuracy by in situ surface Raman spectroscopy in the temperature range between 300 and 40 K, and calculated the surface reconstructions and vibration eigenmodes by density functional theory. Our calculated vibration eigenfrequencies are in excellent agreement with the observed Raman peak positions and the calculated displacement patterns allow the assignment of all observed vibration modes. Our results for both adsorbate systems Sn/Ge(111) and Sn/Si(111) show the preservation of the global surface atom configuration over the whole investigated temperature range. The emergence of a backfolded Rayleigh wave at $\approx 50{\mathrm{cm}}^{-1}$ for Sn/Ge(111) below $\approx 200$ K is a clear signature of its transition to a static $\left(3\times 3\right)$ reconstruction. The gradual intensity increase of this mode upon further cooling suggests an order-disorder character of this transition.

Figure 1

Model of the atomic structure of the Sn-$\left(3\times 3\right)$/Ge(111) reconstruction (top view on the top and side view in $\left[\overline{1}10\right]$ direction at the bottom). The Sn atoms are shown as blue spheres (not in scale). The protruding ones on “up” positions induce the $\left(3\times 3\right)$ periodicity. Disregard of the height differences results in the $(\sqrt{3}\times \sqrt{3})R{30}^{\circ }$ reconstruction.

Figure 2

Polarized Raman spectra at room temperature (RT) of the Ge(111)-$\text{c}\left(2\times 8\right)$ reconstruction for the polarization configurations $z\left(xx\right)\overline{z}$ (red) and $z\left(xy\right)\overline{z}$ (green) and the unreconstructed surface (black). For the $\text{c}\left(2\times 8\right)$ reconstruction, additional features arise (shaded area) which are assigned to reconstruction-induced surface vibration modes.

Figure 3

Polarized surface Raman spectra of Ge(111)-$\text{c}\left(2\times 8\right)$ at low temperature (LT, $\approx 40$ K). The labels “RW” indicate backfolded Rayleigh waves.

Figure 4

Contour plot of the electronic charge density of Sn-$\left(\sqrt{3}\times \sqrt{3}\right)$/Si(111) (a) and Sn-$\left(\sqrt{3}\times \sqrt{3}\right)$/Ge(111) (b), calculated within DFT-LDA in the $\left(\overline{1}10\right)$ crystallographic plane containing one of the three equivalent Sn-Si(Ge) bonds.

Figure 5

Surface Raman spectra of the Sn/Si(111) surface at room temperature (RT) and at low temperature (LT, $\approx 40$ K) for $z\left(xx\right)\overline{z}$ and $z\left(xy\right)\overline{z}$ polarization configurations in the frequency range from 130 to $500{\mathrm{cm}}^{-1}$. The range below $130{\mathrm{cm}}^{-1}$ is covered in Sec. 3e.

Figure 6

Calculated displacement pattern and eigenfrequency of selected surface localized phonon modes in the Sn-$\left(\sqrt{3}\times \sqrt{3}\right)$/ Si(111) system. The arrows show the atomic displacement within the $\left(\sqrt{3}\times \sqrt{3}\right)$ surface unit cell. The double and triple frequency values in panels (d) and (f) correspond to different participation of underlying Si layers.

Figure 7

Surface Raman spectra of the Sn/Ge(111) surface at room temperature (RT) for both polarization configurations and at low temperature (LT, $\approx 40$ K) for $z\left(xx\right)\overline{z}$ polarization configuration. In the LT spectrum a fit with Voigt profiles is added to illustrate the decomposition of the peaks. The frequency range below $80{\mathrm{cm}}^{-1}$ is shown and discussed in more detail in Sec. 3e.

Figure 8

Calculated displacement patterns of selected surface localized phonon modes in the Sn-$\left(\sqrt{3}\times \sqrt{3}\right)$/Ge(111) system. The arrows show the atomic displacement within the $\left(\sqrt{3}\times \sqrt{3}\right)$ surface unit cell.

Figure 9

Low-frequency surface Raman spectra of Sn/Ge(111) at room temperature (RT) and low temperature (LT, $\approx 40$ K). Both polarization configurations are shown. The emerging shoulder (shaded area) on the low-frequency side of the main peak at LT is identified with a backfolded Rayleigh wave (RW) and acts as an indication for the structural phase transition. The inset shows the RW intensity development with temperature.

Figure 10

Calculated displacement pattern and eigenfrequency of selected surface localized phonon modes in the Sn-$\left(\sqrt{3}\times \sqrt{3}\right)$/ Si(Ge)(111) system. The arrows show the atomic displacement within the $\left(\sqrt{3}\times \sqrt{3}\right)$ surface unit cell. Rounded arrows represent the seesaw movement of the Si(Ge) trimer below the Sn atom.

Figure 11

Schematic representation of the calculated eigenmodes of the Sn-$\left(3\times 3\right)$/Ge(111) system, which are related to the dynamic fluctuation. The arrows show the atomic displacement within the $\left(3\times 3\right)$ surface unit cell.

Figure 12

Surface Raman spectra of Sn/Si(111) in the low frequency spectral range at room temperature (RT) and low temperature (LT, $\approx 40$ K). Both polarization configurations are shown.