Atomic relaxations at the (0001) surface of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ single crystals and ultrathin films

We present a surface x-ray analysis of the atomic structure of the (0001) surface of the topological insulator ${\mathrm{Bi}}_2{\mathrm{Se}}_3$, which was grown as a single crystal and as an ultrathin film on Si(111) using molecular beam epitaxy (MBE). In general we find that the top Se-Bi layer spacing is expanded between 2% and 17% relative to the bulk, while deeper layers and the first van der Waals gap are unrelaxed. The top layer expansion is directly related to the amount of surface contamination by carbon and oxygen. The near-surface structures of the single crystal and the MBE-grown thin film differ in the degree of (static) disorder: for the former an overall Debye parameter ($B$) per quintuple layer (QL) of $5{\AA }^2$ is found to decrease slowly with depth. MBE-grown ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ films exhibit the opposite scenario, characterized by an increase in $B$ from about $10{\AA }^2$ for the topmost QL to values of $B=20–40 {\AA }^2$ for the fourth QL. This is attributed to the lattice misfit to the Si(111) surface. Ab initio calculations reveal carbon to act as an $n$-dopant, while the first interlayer spacing expansion induces a shift of the Dirac point towards the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ bulk conduction band minimum.

Figure 1

LEED images of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (0001) surface. (a) Bulk and (b) MBE samples.

Figure 2

Differential Auger electron spectra (primary electron energy, 3 keV) for a bulk (B) and two MBE (M)–grown ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ samples. Several AES transitions are indicated. Note that one Bi-NNO transition at $E\approx 268$ eV almost coincides with the C-KLL line ($E\approx 272$ eV). While sample M4 can be considered “clean,” samples M2 and B1 can be viewed as being heavily contaminated with carbon and oxygen.

Figure 3

Powder diffraction pattern for bulk ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. Circles (red) and black line correspond to the measured and fitted intensity, respectively. The difference is shown by the bottom horizontal (blue) line on the same scale. Reflection positions are indicated by the vertical (green) bars for the silicon standard (upper panel) and ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ (lower panel).

Figure 4

Ball-and-stick model of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. Small (red) and large (blue) balls represent selenium and bismuth atoms, respectively. The interstitial carbon atom is shown by the smallest, dark ball. Interlayer distances are labeled $d_{i,i+1}$ (see Table 2). The arrow emphasizes the expansion of the top layer spacing.

Figure 5

(a) Schematic of the intensity distribution along the ($10L$) and the ($01L$) rod of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001). Bright (yellow) and dark (green) color represents high and low intensity, respectively. (b), (c) Snapshots of detector images for a single crystal (b) and a thin-film sample (c).

Figure 6

Experimental (symbols) and calculated (lines) structure factor intensities along several crystal truncation rods for the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) bulk crystal.

Figure 7

Experimental (symbols) and calculated (lines) structure factor intensities for the MBE-grown film. For details, see text.

Figure 8

Interlayer relaxations for (a) bulk and (b) MBE-grown samples. Color coding refers to Fig. 2.

Figure 9

Debye parameter versus depth expressed by the number of the quintuple layer (QL) for samples M1 and B3. $\mathrm{QL}=1$ indicates the QL at the sample surface. Uncertainties are $<10\%$. Note that $B$ is shown on a log scale.

Figure 10

Calculated band structure of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$(0001) surface along $\overline{K}-\overline{\Gamma }-\overline{M}$. Left: pristine surface ($\Delta d_{12}/d_{12}=0\%$). Center: perturbed surface ($\Delta d_{12}/d_{12}=15$%) without doping. Right: perturbed surface ($\Delta d_{12}/d_{12}=15$%) with carbon doping.