Optical Reflectivity of the Si(111)-(2×1) Surface — The Role of the Electron–Hole Interaction

Abstract

We calculate the optical reflectivity of the Si(111)‐(2×1) surface from first principles. To this end, we first calculate the quasiparticle band structure of the surface within the GW approximation for the electronic self energy. The band structure exhibits two surface bands inside the fundamental bulk band gap. Thereafter the electron–hole interaction is computed for transitions between the relevant bands, the Bethe‐Salpeter equation for coupled electron–hole excitations is solved and the optical response is evaluated. In the energy range below the fundamental bulk band gap, the reflectivity spectrum is dominated by a surface exciton at 0.43 eV with an excitonic binding energy of 0.26 eV. Our calculated spectrum is in very good agreement with experimental data from differential reflectivity spectroscopy.

Extended Hückel theory for band structure, chemistry, and transport. II. Silicon

“…As second example, we look at the surface bandstructure of reconstructed Si(111) 2x1 as shown in Figure 6 using the EHT-parameters in Table 28 . Similar to the previous case, the overall shape of the π-and π * -surface bands match qualitatively well with DFT-GW calculations of Rohlfing et al 35 . In Table III we compare our EHT-bandedges and gaps (1st column) at two specific points J and K of the 2D-Brillouin zone with DFT-GW calculations 35,36 and PES/IPES experiments.…”

“…Similar to the previous case, the overall shape of the π-and π * -surface bands match qualitatively well with DFT-GW calculations of Rohlfing et al 35 . In Table III we compare our EHT-bandedges and gaps (1st column) at two specific points J and K of the 2D-Brillouin zone with DFT-GW calculations 35,36 and PES/IPES experiments. The values for the bandedges as well as for the gaps agree quantitatively well among all three calculations, and show also a good agreement with PES/IPES experiments, where the error in the energy resolution is typically 150 − 200 meV depending on temperature and incident energy of the electrons.…”

“…A more extended comparison with PES/IPESexperiments turns out to be very limited, since the π-and the π * -bands are not as well experimentally determined as in the case of silicon (100) (2x1). Contrary to the pre- vious case of Si(100) (2x1), we find for Si(111) (2x1) that both π * -and π-band calculated in EHT agree quantitatively very well with DFT-GW calculations of Northrup et al 36 and in particular with Rohlfing et al 35 over the entire range of the Brillouin zone as shown in Figure 7. EHT (Table 28 ) DFT-GW 36 DFT-GW 35 In the two previous cases we explored the transferability of the EHT-parameters, cf.…”

Surface electronic structure calculations using the MBJLDA potential: Application to Si(111)2 × 1

“…Consistent with earlier work, we observe that the system is semiconducting with two surface state bands spanning the Fermi energy (indicated by the dashed line). These surface state bands are quite dispersive in the direction parallel to the π‐bonded chains (Γ‐J and K‐J′), and more localized perpendicular to the chains (J‐K and J′‐Γ).…”

“…This variation is related to uncertainty about the magnitude of excitonic effects associated with this surface, with some work suggesting that these effects are small, while other research has indicated that the quasiparticle gap may differ significantly from the optical gap . GW calculations have yielded electronic structures for the Si(111)2 × 1 π‐bonded chain surface in good agreement with experiment. However, such calculations are very computationally demanding.…”