Atomic and electronic structure of the cleaved $6\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(11\overline{2}0\right)$ surface

We present a combined cross-section scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) and ab initio simulations study of the nonpolar $\left(11\overline{2}0\right)$ cleaved surface of 6H-SiC. The experimental results show an unreconstructed surface in agreement with theory. Upon truncation, two surface bands appear inside the semiconductor band gap: one empty band localized on the Si atoms and one filled band on the C atoms. According to the STS experimental results on $n$-doped samples, the Fermi energy is pinned at the surface inside the band gap. By comparison of STM filled and empty states topographies we propose that on the fresh cleaved surface the Fermi level lies at the bottom of the Si-like band. The calculated STM images reproduce the experimental contrast of the 6H stacking sequence and its bias dependence very well.

Figure 1

(Color online) Constant current topography $(i=0.1\mathrm{nA})$ of a $(35\mathrm{\AA }\times 35\mathrm{\AA })$ area on $6\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(11\overline{2}0\right)$ at $U_{\exp }=-2.2\mathrm{V}$. The $z$ range varies between $-7.5$ and $7.5\mathrm{pm}$. The surface unit cell and the 6H-SiC atomic stacking sequence (hereafter defined as a zigzag chain) are also shown: C (Si) atoms are indicated with black (orange) dots.

Figure 2

(Color online) Top view of the hexagonal truncated (a) and relaxed (b) supercell considered. Numbers label the outermost atoms. The different planes sketched are the first surface layer and the second layer in the slab. Outermost C (Si) atoms are indicated with black (orange) dots, while atoms in the underlayer are represented with sticks of the same colors. The coordinate system is oriented so that the $\left(xy\right)$ plane representing the surface is the one described by directions $\left[\overline{1}100\right]$, [0001] and the surface normal $z$ corresponds to the $\left[11\overline{2}0\right]$ direction.

Figure 3

(Color online) Side view of the hexagonal truncated (a) and relaxed (b) supercell considered. The different planes sketched are the first surface layer, and the second layer in the slab. Outermost C (Si) atoms are indicated with black (orange) dots, while atoms in the underlayer are represented with sticks of the same colors. The coordinate system is oriented so that the $\left(xy\right)$ plane representing the surface is the one described by directions $\left[\overline{1}100\right]$, [0001] and the surface normal $z$ corresponds to the $\left[11\overline{2}0\right]$ direction.

Figure 4

Experimental constant current topographies $(10\mathrm{\AA }\times 15\mathrm{\AA })$ of the filled states at $0.1\mathrm{nA}$: $U_{\exp }=-2.2\mathrm{V}$ (a), $U_{\exp }=-2.0\mathrm{V}$ (b), and $U_{\exp }=-1.8\mathrm{V}$ (c). Gray scale with black denoting minimal and white denoting maxima tip height (the $z$ range is different in the images) with the $\left[\overline{1}100\right]$ direction along $x$ and the [0001] along $y$.

Figure 5

Experimental constant current topographies $(10\mathrm{\AA }\times 15\mathrm{\AA })$ of the empty states at $0.1\mathrm{nA}$: $U_{\exp }=+1.9\mathrm{V}$ (a), $U_{\exp }=+2.1\mathrm{V}$ (b), and $U_{\exp }=+2.5\mathrm{V}$ (c). Gray scale with black denoting minimal and white denoting maxima tip height (the $z$ range is different in the images).

Figure 6

(Color online) Experimental constant current $\left(0.1\mathrm{nA}\right)$ filled (a) and empty (b) topographies $(10\mathrm{\AA }\times 15\mathrm{\AA })$ in multibias mode, i.e., quasisimultaneous measure of the filled and empty states $U_{\exp }=-2.2\mathrm{V}$ and $U_{\exp }=+2.2\mathrm{V}$, respectively. Superposition of filled and empty states topographies (c).

Figure 7

Experimental STS spectra on the fresh cleaved $6\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(11\overline{2}0\right)$ surface averaged over an area of $(1\mathrm{nm}\times 20\mathrm{nm})$: characteristic $I=I\left(U_{\exp }\right)$ (a), differential conductivity $dI∕d{U}_{\exp }$ (b), and normalized differential to total conductivity $(dI∕d{U}_{\exp })∕(I∕U_{\exp })$ or DOS (c).

Figure 8

Surface DOS (left) and band structure (right) of the relaxed $6\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(11\overline{2}0\right)$ surface. The shaded areas show the projected bulk band structure. The DOS is obtained through a convolution with a $0.8\mathrm{eV}$ wide Gaussian.

Figure 9

(Color online) Relaxed $6\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(11\overline{2}0\right)$ plane (a) and corresponding STS simulated images at $\simeq 1.5\mathrm{\AA }$ above the ideal truncated plane with decreasing bias from $U_{\mathrm{th}}=0$ (b) to $U_{\mathrm{th}}=-1.2\mathrm{V}$ (h) in steps of $0.2\mathrm{V}$ ($U_{\mathrm{th}}=0$ is the surface highest occupied molecular orbital (HOMO), at $E=0.4\mathrm{eV}$ in Fig. 8). The calculations have been carried out using the Tersoff-Hamman approximation (Ref. 25).

Figure 10

(Color online) STM simulated images at constant current changing $U_{\mathrm{th}}$ from $\simeq -1.0\mathrm{V}$ (a) to $-0.2\mathrm{V}$ (e) with steps of $0.2\mathrm{V}$ ($U_{\mathrm{th}}=0$ is the surface HOMO).

Figure 11

(Color online) Representative simulated STM images for filled (a) and empty (b) states present complementary localization in space, since they are localized, respectively, on C and Si atoms, as can be clearly visualized in the sum image (c). The filled states STM image is calculated at $U_{\mathrm{th}}=-0.6\mathrm{V}$ from HOMO, the empty states image at $U_{\mathrm{th}}=+0.2\mathrm{V}$ from LUMO at the $\overline{\Gamma }$ point of the Brillouin zone.

Figure 12

Bias dependent scheme of tunneling experiment on the fresh cleaved $6\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(11\overline{2}0\right)$ surface. The STM topographies have been measured at $i=0.1\mathrm{nA}$. The position of the vacuum level at equilibrium (c) is fixed according to the work function of tungsten tip ${\varphi }_T=4.5\mathrm{eV}$ and the calculated electron affinity of $6\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(11\overline{2}0\right)$ ${\chi }_S=I_S-E_S^{\text{gap}}\approx 2.6\mathrm{eV}$ (with calculated ionization energy $I_S\approx 5.6\mathrm{eV}$). The Fermi energy level of the tip and the sample are denoted with $E_{\mathrm{FT}}$ and $E_{\mathrm{FS}}$ respectively; the conduction band minimum of the sample is indicated with CBM and the valence band maximum with VBM.