Surface phonons of the $\mathrm{Si}\left(111\right):\mathrm{In}\text{−}(4\times 1)$ and $(8\times 2)$ phases

The reversible phase transition of the $\mathrm{Si}\left(111\right):\mathrm{In}\text{−}(4\times 1)$ surface has been studied using Raman spectroscopy and the symmetry, frequencies, and linewidths of the surface phonon modes have been determined. Dramatically different behavior has been identified for vibrational motion in the direction of the In chains and orthogonal to them. The differences in the Raman spectra of the room and low temperature surface are discussed in terms of the Peierls transition model and a recent dynamical soft shear distortion model. The measurements are found to be consistent with the former model, while some difficulties arise for the latter model. A combined Peierls transition and soft shear distortion model is consistent with the data, but is lacking detail. The Raman spectra presented here represent a challenge in developing theoretical models of this complex system.

Figure 1

(Color online) Schematic of the (a) $(4\times 1)$ and (b) $(4\times 2)$ structures from the model of Wang et al. (Ref. 7). The unit cells are marked as well as the 6 (12) atoms in the first double layer that dominate the low frequency microscopic surface modes.

Figure 2

Raman spectra of the $(4\times 1)$ and $(8\times 2)$ phases taken in $A^{\prime }$ and $A^{″}$ symmetries, using an incident laser energy of $1.91\mathrm{eV}$. The positions of the Raman modes are marked by dotted lines (see also Table ). New $(8\times 2)$ modes, assigned to backfolding of the phonon branches, are indicated by gray lines, while blueshifting of modes on cooling is marked by black arrows. The spectral range from $240\text{to}370{\mathrm{cm}}^{-1}$ is omitted as it is dominated by the bulk Si 2TA structure.

Figure 3

(Color online) Raman spectra of the $(4\times 1)$ (bottom) and $(8\times 2)$ phases (top). The integration time for the high quality measurements was $20\min$. The spectra taken during cooling at $-1\mathrm{K}∕\min$ used a $4\min$ integration time to enable the phase transition to be monitored (examples are shown at 250 and $60\mathrm{K}$, with the overall intensity expressed as a gray scale).

Figure 4

Spectra of the $\mathrm{Si}\left(111\right):\mathrm{In}\text{−}(4\times 1)$ and $(8\times 2)$ surfaces taken at different incident laser energies. The spectra are normalized by the intensity of the Si bulk phonon mode, which was corrected for the variation in penetration depth and the bulk resonance response.

Figure 5

Low energy region of the $A^{\prime }$ symmetry spectrum in the temperature range between 150 and $50\mathrm{K}$. The gray scale is changed from Fig. 3 to improve the contrast. The dotted lines mark the position of the phonon modes at $150\mathrm{K}$ for the $(4\times 1)$ phase and at $50\mathrm{K}$ for the $(8\times 2)$ phase. The spectrum in the temperature range from $120\text{to}80\mathrm{K}$ appears to be a simple linear combination of the two distinct Raman spectra.