Scanning tunneling microscopy of gate tunable topological insulator Bi${}_2$Se${}_3$ thin films

Electrical-field control of the carrier density of topological insulators (TIs) has greatly expanded the possible practical use of these materials. However, the combination of low-temperature local probe studies and a gate tunable TI device remains challenging. We have overcome this limitation by scanning tunneling microscopy and spectroscopy measurements on in situ molecular-beam epitaxy grown Bi${}_2$Se${}_3$ films on SrTiO${}_3$ substrates with prepatterned electrodes. Using this gating method, we are able to tune the Fermi level of the top surface states within a range of ≈250 meV on a 3-nm-thick Bi${}_2$Se${}_3$ device. We report field effect studies of the surface-state dispersion, band gap, and electronic structure at the Fermi level.

Figure 1

3D computer-automated drawings of the high-temperature sample holder with in situ back gating capability. (a) Top view. (b) Cross-sectional view. Part list: (1) alumina sample holder, (2) W source/drain electrode (tunnel bias), (3) W source/drain electrode, (4) SrTiO${}_3$ substrate, (5) Pt electrodes on SrTiO${}_3$, (6) Pt back gate electrode on SrTiO${}_3$, (7) W spring clip to hold SrTiO${}_3$, (8) W back gate electrode.

Figure 2

Characterization of the SrTiO${}_3$ substrate and TI growth. (a) AFM image, $1\mu \mathrm{m}\times 1\mu \mathrm{m}$, of SrTiO${}_3$ after thermal processing as detailed in the text showing large atomically flat terraces separated by single atomic-height steps. The AFM topographic height is shown in a color scale from dark to bright covering a range of 5.9 nm. (b) RHEED pattern of SrTiO${}_3$ prior to TI growth. (c) RHEED pattern of three-QL Bi${}_2$Se${}_3$ film grown on SrTiO${}_3$. (d) STM topographic image, 81 nm$\times$81 nm, of three-QL Bi${}_2$Se${}_3$ film grown by MBE on the gated sample holder in Fig. 1. The arrow indicates the position of $dI/dV$ mapping of quasiparticle scattering in Fig. 5. Tunneling parameters: $V_{\mathrm{B}}$ $=$ 1.5 V, $I=30$ pA. Inset: 10 nm$\times$10 nm atomic resolution image of three-QL Bi${}_2$Se${}_3$. Tunneling parameters: $V_{\mathrm{B}}=0.5$ V, $I=30$ pA. The STM topographic height is shown in a color scale from dark to bright covering a range of 2 nm for (d) and 0.03 nm for the inset.

Figure 3

Transport properties of three-QL Bi${}_2$Se${}_3$ film. (a) Bi${}_2$Se${}_3$ film (three QL) two-terminal film resistance versus temperature. (b) Bi${}_2$Se${}_3$ film (three QL) two-terminal film resistance versus gate voltage. The resistance in (a) and (b) is the total film resistance using contacts 2 and 3 in Fig. 1 and therefore includes contact resistance contributions.

Figure 4

Electric-field effect of Bi${}_2$Se${}_3$. (a) $dI/dV$ spectra of three-QL Bi${}_2$Se${}_3$ film versus gate voltage. The spectra are shifted vertically for clarity. The dashed lines are guides to the eye to indicate the approximate positions of the quantum well state peak (QW, black), the Dirac point, or more strictly, the middle of the hybridized gap (DP, purple), and the hump peak that defines the surface band gap (HP, green). Tunnel parameters: $I$ $=$ 100 pA, $V_{\mathrm{B}}$ $=$ 0.3 V, $V_{\mathrm{mod}}$ $=$ 10 mV. (b) The shift of the leftmost QW peak versus gate voltage. The error bars are one standard deviation uncertainty in the peak position obtained by fitting the QW peak to a Lorentzian function. The solid line is a linear fit yielding the gating efficiency of (1.2 ± 0.1) mV/V. The uncertainty in slope is one standard deviation uncertainty determined from the linear fit.

Figure 5

Bi${}_2$Se${}_3$ quasiparticle interference (QPI) patterns from the step edge indicated in Fig. 2d). $dI/dV$ maps of QPI patterns at $V_{\mathrm{G}}$ $=$ 0 V (a)–(e) and $V_{\mathrm{G}}$ $=$ −100 V (f)–(j) at the indicated sample biases. $dI/dV$ intensity is given by the color scale from low (dark) to high (bright) in arbitrary units. The oscillations in the $dI/dV$ maps are used to determine the energy momentum dispersion in Figs. 6 and 7. Tunneling parameters: $I$ $=$ 50 pA, $V_{\mathrm{B}}$ indicated in each panel, $V_{\mathrm{mod}}$ $=$ 15 mV.

Figure 6

Quasiparticle scattering and LDOS oscillations from Bi${}_2$Se${}_3$ as a function of back gating. (a) Real-space Bi${}_2$Se${}_3$ (111) surface lattice. Step edges occur along closed-packed directions indicated along the $a_1$ unit-cell vector. (b) Corresponding reciprocal-space lattice and surface Brillouin zone (blue hexagon). Scattering at the step edges correspond to scattering in the $\overline{\Gamma }$-$\overline{M}$ direction. (c) Fermi-surface contours given by Eq. (1) for energies relative to the Dirac point of 0.1–1.1 eV. Scattering oscillations are dominated by the vector $q_2$ connecting extremal parts of the Fermi contours along the $\overline{\Gamma }$-$\overline{M}$ direction. (d) $dI/dV$ intensity oscillations from scattering at the step edge in Fig. 2d obtained from the map in Fig. 5d at $V_{\mathrm{B}}$ $=$ 0.3 V and $V_{\mathrm{G}}$ $=$ 0 V. A smooth background was subtracted from the raw intensity to determine the oscillatory part (red data points), which was fit to a function $A$ cos($qx$)/$x^{3/2}$ (blue line), where amplitude $A$ and scattering vector $q$ are fitting parameters. (e) Energy versus scattering vector obtained from $dI/dV$ intensity oscillations as in (d) for gate voltages of 0 V and −100 V. The solid lines are linear fits to the data. The error bars are one standard deviation uncertainty in the scattering vector determined from fitting the intensity oscillations in (d).

Figure 7

Bi${}_2$Se${}_3$ energy-momentum dispersion along the $\overline{\Gamma }$-$\overline{M}$ direction determined from quasiparticle scattering oscillations from step edges. The $E$ vs $q$ data in Fig. 6e at different gate voltages are reported with energies relative to the Dirac point at $V_{\mathrm{B}}=-0.4$ V for $V_{\mathrm{G}}=0$ V and $V_{\mathrm{B}}=-0.27$ V for $V_{\mathrm{G}}=-100$ V. The momentum $k$ is determined from the scattering vector as $q_2=1.5$ $k$ following Ref. 34. The data from the different gate voltages collapse onto the same dispersion. The solid line is a linear fit yielding a velocity $=$ (1.11 ± 0.09) × 10${}^6$ m/s. The error in the velocity is one standard deviation uncertainty from the linear fit.