Electronic structure of the $\mathrm{Si}\left(111\right)\sqrt{3}\times \sqrt{3}R{30}^{\circ }\text{−}\mathrm{B}$ surface from theory and photoemission spectroscopy

The $\mathrm{Si}\left(111\right)\sqrt{3}\times \sqrt{3}R{30}^{\circ }\text{−}\mathrm{B}\left[\mathrm{Si}\left(111\right)\text{−}\mathrm{B}\right]$ surface has evolved into a particularly interesting surface in the context of on-surface molecular self-assembly. Photoemission spectroscopy is a powerful tool to understand the interaction between the surface and the adsorbates. Previous studies of $\mathrm{Si}\left(111\right)\text{−}\mathrm{B}$ contain many inconsistencies with regard to the Si $2p$ core level and valence-band dispersion. Here we employ synchrotron-based core-level and angle-resolved photoemission spectroscopy measurements in combination with density functional theory (DFT) calculations to address these issues. DFT calculations of the Si $2p$ core-level spectra accurately identify contributions from one bulk and five surface components, which allows us to obtain a comprehensive understanding of the spectra recorded at different photon energies. As an archetypal example, this refined decomposition is employed to understand the changes in Si $2p$ spectra upon the adsorption of cobalt phthalocyanine molecules. Regarding the valence-band dispersion of the clean $\mathrm{Si}\left(111\right)\text{−}\mathrm{B}$ surface, our comprehensive DFT and photoemission investigations are able to reconcile the inconsistencies appearing in previous studies and reveal several yet unreported surface states. Furthermore, we are able to theoretically and experimentally resolve the distribution of these surface states in constant energy plots.

Figure 1

Schematic sideview of the $\mathrm{Si}\left(111\right)\text{−}\mathrm{B}$ surface. The notations for the corresponding surface components in Si $2p$ core-level spectra are denoted (in progressively higher binding energy) as $\mathrm{S}1–\mathrm{S}5$. The dashed blue oval indicates the Si adatom and its four nearest neighbors.

Figure 2

(a) Calculated Si $2p$ spectrum of $\mathrm{Si}\left(111\right)\text{−}\mathrm{B}$ using CLS calculated exemplarily with LDA and assuming only contributions from the surface atoms, i.e., no bulk signal, with Voigt profile broadening similar as used to fit the experimental spectra (i.e., a Lorentzian broadening of 0.085 eV and a Gaussian broadening of 0.2–0.3 eV). The total spectrum, which comprises a three-peak structure ($\mathrm{P}1–\mathrm{P}3$), is decomposed into five surface components $\mathrm{S}1–\mathrm{S}5$ in ratios of $\frac{2}{3}$ monolayer (ML), $\frac{1}{3}$ ML, $\frac{1}{3}$ ML, 1 ML, and $\frac{2}{3}$ ML, respectively, whereas attenuation effects due to the photoelectron mean free path were not considered. (b)–(d) Experimental Si $2p$ spectra measured using photon energies of (b) $h\nu =130\mathrm{eV}$, (c) $h\nu =160\mathrm{eV}$, and (d) $h\nu =200\mathrm{eV}$. Guided by the calculations, each spectrum is fitted as shown in Table 1.

Figure 3

(a) DFT modeling of an ideal 20% CoPc submonolayer coverage on $\mathrm{Si}\left(111\right)\text{−}\mathrm{B}$ in the most stable structure. Surface supercells of dimensions $4\sqrt{3}\times 4\sqrt{3}$ were used. The azimuthal orientation of the molecular LA with respect to the $\langle 110\rangle$ direction of the surface is denoted as $\varphi$. (b) Schematic sideview of CoPc adsorbed on the $\mathrm{Si}\left(111\right)\text{−}\mathrm{B}$ surface, showing the surface regions, which are differently perturbed by the molecule adsorption. Underneath the central Co where the molecule anchors to the Si adatom, the interaction is strongest. Thereby, the adatom is shifted upwards by $d_1$, whereas the Si atom in the third layer underneath the B atom is shifted downwards by $d_2$ (note the original positions given in lighter colors). There are other Si atoms underneath the molecule but weakly perturbed by the CoPc adsorption (W). At the considered low submonolayer coverages, areas of unperturbed surface also still exist. This region is denoted as U. (c)–(g) Separate spectra for the five Si $2p$ surface components, each including proportions of strongly perturbed, weakly perturbed, and unperturbed surface regions. (h) Calculated Si $2p$ spectrum for a 20% surface coverage with CoPc, obtained by adding the components for the different regions.

Figure 4

(a) Generated Si $2p$ spectra assuming different CoPc surface coverages between 10% and 50% and starting from the calculated one for 20%. Here, only the surface components (S1–S5) are considered. The small peak ($\mathrm{P}{1}^{*}$) originates from the $p_{3/2}$ structure of the atoms in the third layer beneath the B atoms (of S2 type). As a result of anchoring the Co atoms, a charge accumulation between the B atom and the Si atom beneath takes place. As a result, the BE of these Si atoms is shifted to lower values. However, the intensity of peak $\mathrm{P}{1}^{*}$ is too small to be detected experimentally. (b)–(d) Measured changes in Si $2p$ spectra upon increasing the CoPc coverage from 10% to 50% for photon energies of (b) 130, (c) 160, and (d) 200 eV.

Figure 5

Band dispersion for the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}\text{−}\overline{M^{\prime }}$ and $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ directions. (a) and (b) The left halves of each panel show the calculated band structures of $\mathrm{Si}\left(111\right)\text{−}\mathrm{B}$. Gray shaded areas indicate the bulk-projected bands. Blue dots indicate states localized on atoms nearest to the adatoms as indicated by the dashed ellipse in Fig. 1. The right halves show the $k$-resolved density of states projected on atoms in the surface region (defined here as the top four Si layers plus adatoms). (c)–(f) Experimental ARPES data taken with a photon energy of 62 eV as (c) and (d) intensity plots of the dispersion and (e) and (f) as spectra taken at individual $k_{\parallel }$ values. In the plots, surface and bulk related features are indicated by dashed and dotted lines, respectively. High-symmetry points of the $\sqrt{3}\times \sqrt{3}(1\times 1)$ cell are indicated in red (gray) (cf. Fig. 6).

Figure 6

Wave functions of selected states via isosurface plots of ${\left|\psi \right|}^2$ (at 1/3 of their maximum value). The character of $A_1$ is quite independent of $k$. The SBZ is also shown.

Figure 7

Constant energy slices through the whole surface Brillouin zone. Left: experimental data. Right: $k$-resolved DOS, projected on atoms in the surface region. The SBZ of the $\sqrt{3}\times \sqrt{3}$ and $1\times 1$ cells are shown in red and gray, respectively.