Electronic structures and unusually robust bandgap in an ultrahigh-mobility layered oxide semiconductor, Bi2O2Se

A new layered oxide semiconductor (Bi2O2Se) is found with excellent electronic properties for promising applications.


This PDF file includes:
Section S1. SdH quantum oscillation and effective mass in Bi 2 O 2 Se bulk crystal Section S2. Statistical result of Se-atom coverage on the cleaved Bi 2 O 2 Se surface Section S3. Determination of the high-symmetry points along k z and bulk band structure of Bi 2 O 2 Se Section S4. Potassium doping and the structure of electron pocket Section S5. Fitting of the electron and hole pockets Section S6. Calculation on the formation of surface dimer Section S7. Monte Carlo simulation and analysis of STM image Section S8. Density functional theory calculation on half Se coverage surface Fig. S1. SdH quantum oscillation and effective mass.

Section S1. SdH quantum oscillation and effective mass in Bi 2 O 2 Se bulk crystal
As illustrated in fig. S1a, the Bi 2 O 2 Se bulk crystal exhibits a very high residual-resistance ratio (RRR, R xx, 300 K /R xx, 2 K ) of 585, which is about one order higher than that of the typical CVDgrown 2D Bi 2 O 2 Se crystal (~60), thereby resulting in a superior Hall mobility at low temperature.
We note that the metallic R xx -T behavior here results from the residual carriers -which can be removed by electric gating, as can be seen in Ref. 19, where the Bi 2 O 2 Se field effect transistor shows an insulating behavior with top gating at room temperature ( Fig. 4( where ω c = eB/m*. The effective masses were estimated to be both 0.16±0.02 m 0 (m 0 is the mass of a free electron) at an external magnetic field of 6.02 and 6.69 T (fig. S1(c-d)), showing excellent consistency with the ARPES measurements and theoretical calculations. exhibiting a very high residual-resistance ratio (RRR, R xx, 300 K /R xx, 2K ) of 585. b, Longitudinal resistance (R xx ) as a function of the applied perpendicular magnetic field (B) measured at the temperature range from 2 to 16 K. c-d, Oscillation amplitude ∆R xx /R 0 as a function of temperature T using the Lifshitz-Kosevich formula fitting at 6.02 T and 6.69 T, respectively.

Section S2. Statistical result of Se-atom coverage on the cleaved Bi 2 O 2 Se surface
As the Bi-Se interlayer interaction along c-axis is much weaker than that of in-plane Bi-O bonds in layered Bi 2 O 2 Se, the cleavage of Bi 2 O 2 Se bulk crystals occurs on the Se-plane. As described in the manuscript, only half of the Se atoms remain on the cleavage surface. To verify that, the surface was carefully examined by STM. As indicated in fig. S2, distance between adjacent bright spots is measured to be ~0.39 nm, consistent with the crystal structure of the Se-Se atomic distance, therefore confirms the Se cleavage plane. Line-shape vacancies of atoms are randomly distributed on the cleaved surface. All four regions illustrated feature an average ~50 % occupancy of Se atoms on the cleavage surface.

Section S3. Determination of the high-symmetry points along k z and bulk band structure of Bi 2 O 2 Se
During the photoemission process, the horizontal momentum (k || ) of band electrons is obtained directly from the free-electrons based on the momentum conservation law. The vertical momentum (k z ) is not conserved. With the free-electron final state approximation and a potential parameter V 0 (also known as the inner potential) describing the energy difference of photoelectrons before and after passing the crystal surface, we can derive the k z as = √2 ( cos 2 + 0 ) ħ where θ is the emission angle and E k is the kinetic energy of the emitted electron, which satisfies where hν is the photon energy, w is the work function of the sample and E B is the electron binding energy.
As V 0 varies with compounds, we typically perform energy dependent ARPES by using a broad range of photon energies to ensure the full coverage of k z -span (ideally more than one Brillouin Zone (BZ)), and then use the high-symmetry points in the k || -k z plane of the BZ to identify the exact value of V 0 .
As for Bi 2 O 2 Se, the inner potential was determined to be V 0 = 12 eV, according to the k-space

Section S4. Potassium doping and the structure of electron pocket
The electron and hole pocket near the CBM and VBM are essential to the transport properties for n-and p-type Bi 2 O 2 Se, respectively. As the Fermi-level of the as-grown sample is very close to the CBM which makes its band dispersion difficult to resolve, we used the in situ potassium doser (see fig. S4a) inside the vacuum system to introduce the K atoms (thus free electrons) onto the surface of the cleaved sample. We effectively shifted the Fermi-level up by ~160 meV ( fig.   S4b), which enables us to acquire the detailed dispersion of the parabolic electron pocket, as illustrated in fig. S4c(ii).

Section S6. Calculation on the formation of surface dimer
On the cleavage surface of Bi 2 O 2 Se crystal, both Se atoms and vacancies dimerize and form 2×n structures ( Fig. 4a in manuscript). To understand these results, we performed ab-initio calculation to estimate the formation energies of different Se-atom and vacancy configurations, by using a slab model, as illustrated in fig. S6. Considering the 4-fold symmetry of the crystal, only x direction is considered here (configuration extended along y). The formation energy was calculated as following The configuration illustrated in the figure (Se-Se dimer with vacancy on each side) was calculated to have the lowest formation energy, therefore is most favorable. This explains the formation of Se-atom and vacancy dimers on the cleavage surface of Bi 2 O 2 Se bulk crystals.

Section S7. Monte Carlo simulation and analysis of STM image
As discussed in the manuscript, the chain of Se-Se dimer with one vacancy on each side proves to be the most energy favorable configuration. Therefore, 4×4 square building blocks (extended configuration in 2D space) was used for a Monte Carlo simulation (Tile model) to simulate the patterns on the half-Se-coverage surface ( fig. S7a). The assumption is that the building blocks have equal possibility to distribute along x or y direction, considering the 4-fold symmetry of the crystal. A 50×50 matrix is firstly generated with each element containing a random value (either 0 or 1 with equal possibility). Then the elements containing 0 or 1 were replaced by building blocks along x or y direction respectively. The simulated pattern is illustrated in fig. S7a, which highly matches the real situation.
To have a quantitative comparison, the possibility of different lengths of vacancy dimers was deduced from both simulated and real images. For the real STM image, as illustrated in fig. S7b, original image was firstly binarized with the local thresholding method. Different vacancy dimer chains were separated by computing the area connectivity. Length of each vacancy dimers chain was then calculated and a statistic distribution was obtained (Fig. 4b(ii) in manuscript). were projected to the top three Bi atoms for the Bi-top region, and to the top Se atom and underlying two Bi atoms for the Se-top region, as shown in the manuscript (Fig. 4c(ii)). In addition, we note that the seemingly direct energy gap at the Γ point in fig. S8 is due to the band folding of the supercell structure.