Correlation effects at ideal $\mathrm{SiC}\left\{0001\right\}\text{−}(1\times 1)$ surfaces

We report on studies of the surface band structure of clean and unreconstructed $6H\text{−}\mathrm{SiC}\left\{0001\right\}\text{−}(1\times 1)$ surfaces by angle-resolved photoelectron spectroscopy (ARPES). Using light induced desorption of hydrogen from the H-terminated, unreconstructed $6H\text{−}\mathrm{SiC}\left\{0001\right\}$ surfaces we were able to prepare these highly metastable surfaces. On both Si face and C face we observe a surface band with $(1\times 1)$ periodicity derived from the unsaturated surface dangling bonds. In both cases the surface band is located below the Fermi level indicating a semiconducting surface. On the (0001) surface the Si dangling bond band is located $\approx 0.8\mathrm{eV}$ above the valence-band maximum (VBM), whereas the C dangling bond band is located $\approx 0.2\mathrm{eV}$ above the VBM. The dispersion of the surface bands amount to 0.2 and 0.7 eV, respectively. The experimental observations are discussed in the light of earlier theoretical studies on the surface electronic structure of hexagonal SiC surfaces. It is suggested that the electronic properties of these surfaces are governed by strong correlation effects.

Figure 1

ARPES spectra taken along $\overline{\Gamma \mathrm{M}}$ of the H terminated (a) and clean (b) $6H\text{−}\mathrm{SiC}\left(0001\right)$ surface. The photon energy was 65 eV. Energies are given with respect to $E_F$. Spectra are shown for emission angles ranging from 0° to 40° in 1° steps.

Figure 2

(Color online) The Si dangling bond derived band dispersion $\left(D_{\mathit{Si}}\right)$ measured on the $6H\text{−}\mathrm{SiC}\left(0001\right)$ surface along $\overline{\Gamma \mathrm{M}}$ and $\overline{\Gamma \mathrm{K}}$ at photon energies of 65 eV (circles) and 110 eV (triangles), respectively. Also included is the calculated Si dangling-bond surface state band (Refs. 25, 37). The dashed vertical lines indicate the boundaries of $(1\times 1)$ surface Brillouin zone (SBZ). The horizontal line shows the position of the calculated Fermi level. Experimentally the Fermi level is located $(2.5\pm 0.2)\mathrm{eV}$ above the VBM.

Figure 3

(Color online) Angular dependence of the intensities of the two surface states $D_{\mathit{Si}}$ (full thin line) and $D_C$ (dashed thin line) on the Si and C face, respectively, together with the expected dependence derived from Eq. (1) for a $p_z$ orbital (shaded bold line). Origin of the polar angle is the sample normal.

Figure 4

(Color online) Comparison between the ARPES spectra of the H terminated and dehydrogenated surfaces for two selected angles corresponding to emission close to the $\overline{M}$ point of the $(1\times 1)$ SBZ. $S_1$ and $S_2$ are the H-induced states (see text), $D_{\mathit{Si}}$ is the Si dangling-bond state.

Figure 5

(Color online) Energy dispersion $E\left(k_{\Vert }\right)$ for azimuths $\overline{\Gamma \mathrm{M}}$ and $\overline{\Gamma \mathrm{K}}$ of the $(1\times 1)$ surface Brillouin zone derived from ARPES spectra taken at a photon energy of 65 eV on (a) H-terminated $6H\text{−}\mathrm{SiC}\left(0001\right)$ and (b) dehydrogenated $6H\text{−}\mathrm{SiC}\left(0001\right)$. The surface states and the bulk related features are indicated by open and full symbols, respectively. The spot size is roughly proportional to the intensity of the respective peak. The shaded areas are the projected bulk band structure and solid lines are the calculated electronic structures of the hydrogenated surface and the relaxed unreconstructed H-free surface of $6H\text{−}\mathrm{SiC}\left(0001\right)$ from Ref. 37.

Figure 6

ARUPS spectra taken along $\overline{\Gamma \mathrm{M}}$ of the H-terminated (a) and the clean (b) $6H\text{−}\mathrm{SiC}\left(000\overline{1}\right)$ surface. Photon energy was 65 eV. The energy is given with respect to $E_F$. Spectra are shown for emission angles ranging from 0° to 40° in 1° steps. Note that for comparison spectra for dehydrogenated surface (b) should be shifted by 0.65 eV downwards to compensate for the surface band bending (see text).

Figure 7

ARUPS spectra taken along $\overline{\Gamma \mathrm{K}}$ of the H-terminated (a) and clean (b) $6H\text{−}\mathrm{SiC}\left(000\overline{1}\right)$ surface. Spectra are shown for emission angles ranging from 0° to 40° in 1° steps. Note that for comparison spectra for dehydrogenated surface (b) should be shifted by 0.65 eV downwards to compensate for the surface band bending (see text).

Figure 8

(Color online) The dispersion of the C dangling-bond derived surface band $D_C$ on the $6H\text{−}\mathrm{SiC}\left(000\overline{1}\right)$ surface along $\overline{\Gamma \mathrm{M}}$ and $\overline{\Gamma \mathrm{K}}$ measured at a photon energy of 65 eV. Also included is the calculated C dangling-bond surface state band (Refs. 25, 37). The dashed vertical lines indicate the boundaries of $(1\times 1)$ SBZ. Experimentally, the Fermi level is located $(1.95\pm 0.20)\mathrm{eV}$ above the VBM.

Figure 9

(Color online) Comparison between the ARPES spectra of the H terminated and dehydrogenated $6H\text{−}\mathrm{SiC}\left(000\overline{1}\right)$ surfaces for several selected electron emission angles: normal emission (lower panel), 16° along $\overline{\Gamma \mathrm{M}}$ (middle panel), and 15° along $\overline{\Gamma \mathrm{K}}$ (upper panel) corresponding to emission close to the $\overline{\Gamma },\overline{M}$, and $\overline{K}$ points of the $(1\times 1)$ SBZ, respectively. The features $S_1\text{−}{S}_4$ are discussed in the text; $D_C$ is carbon the dangling-bond state. The spectra for the dehydrogenated surface are shifted towards higher binding energies by 0.65 eV to compensate for band bending.

Figure 10

(Color online) Energy dispersion $E\left(k_{\Vert }\right)$ for azimuths $\overline{\Gamma \mathrm{M}}$ and $\overline{\Gamma \mathrm{K}}$ of the $(1\times 1)$ surface Brillouin zone derived from ARPES spectra taken at a photon energy of 65 eV on (a) H-terminated $6H\text{−}\mathrm{SiC}\left(000\overline{1}\right)$ and (b) dehydrogenated $6H\text{−}\mathrm{SiC}\left(000\overline{1}\right)$. The spot size is roughly proportional to the intensity of the respective peak. The shaded areas are the projected bulk band structure and solid lines are the calculated surface electronic structures of the hydrogenated and the relaxed unreconstructed surface of $6H\text{−}\mathrm{SiC}\left(000\overline{1}\right)$ from Ref. 37.

Figure 11

(Color online) The experimental and theoretical values of the width of the Si dangling-bond orbital as a function of $1∕d^2$ ($d$ is the distance between dangling bonds) for different reconstructions [$3\times 3,(\sqrt{3}\times \sqrt{3})R30°$, and $1\times 1$] obtained on the $6H\text{−}\mathrm{SiC}\left(0001\right)$ surface. See text for details.