Direct Imaging of Band Structure for Powdered Rhombohedral Boron Monosulfide by Microfocused ARPES

Abstract

Boron-based two-dimensional (2D) materials are an excellent platform for nanoelectronics applications. Rhombohedral boron monosulfide (r-BS) is attracting particular attention because of its unique layered crystal structure suitable for exploring various functional properties originating in the 2D nature. However, studies to elucidate its fundamental electronic states have been largely limited because only tiny powdered crystals were available, hindering a precise investigation by spectroscopy such as angle-resolved photoemission spectroscopy (ARPES). Here we report the direct mapping of the band structure with a tiny (∼20 × 20 μm²) r-BS powder crystal by utilizing microfocused ARPES. We found that r-BS is a p-type semiconductor with a band gap of >0.5 eV characterized by the anisotropic in-plane effective mass. The present results demonstrate the high applicability of micro-ARPES to tiny powder crystals and widen an opportunity to access the yet-unexplored electronic states of various novel materials.

Developing functional two-dimensional (2D) materials is a current central challenge in materials science, stimulated by the discovery of the quantum Hall effect in graphene.¹ Two-dimensional materials consisting of boron (B) are now attracting particular attention since boron-based materials are expected to exhibit novel electronic properties distinct from those of carbon-based materials. A typical example of B-based 2D materials is hexagonal boron nitride (h-BN),² which has a flat honeycomb lattice similar to graphene but a large insulating gap in contrast to the zero-gap semiconducting behavior of graphene. The insulating gap in h-BN is regarded as a great advantage in realizing exotic quantum phenomena when in contact with other 2D materials such as graphene and transition-metal dichalcogenides.³⁻⁸ Furthermore, B-based 2D sheets themselves also serve as a useful platform to realize exotic quantum states, as exemplified by (i) the high-temperature superconductivity in MgB₂⁹ with honeycomb B sheets, (ii) Dirac fermions in a 2D borophene sheet,^10,11 (iii) potential high-temperature superconductivity (T_c ≈ 22 K) in borophene/Ag(111),¹² and (iv) efficient H₂ storage in hydrogen borides (HB).¹³ It is thus of great importance to explore the electronic states of various B-based 2D materials to realize the novel functionalities in the 2D sheets.

Rhombohedral boron monosulfide (r-BS) is attracting great attention as a new type of layered boride. As shown in Figure 1a, r-BS has a unique crystal structure with R3̅m symmetry, characterized by the periodic stacking of 2D sheets consisting of B and S atoms. The unit BS layer can be regarded as a transition-metal disulfide layer where a transition-metal atom is replaced with a covalently bonded B–B pair, and adjacent BS sheets are weakly coupled via the van der Waals force.^14,15 Due to the rhombohedral nature, r-BS layers are stacked in the A–B–C stacking manner so that the bulk crystal contains three layers in the unit cell, leading to the long c-axis length of 20 Å. Due to this long c-axis length, the bulk Brillouin zone (BZ) is short in the direction of the c* axis. One can adopt hexagonal BZ (Figure 1b) by taking into account the convenience to compare the band structure between the bulk and thin films. It has been theoretically predicted that the 2D BS sheet exhibits various functional properties such as high hydrogen storage,¹⁶ high thermal conduction,¹⁷ and efficient photocatalysis.¹⁸ Furthermore, theoretical predictions of spin current control in the MoS₂/r-BS junction and high-T_c superconductivity over 20 K in δ-BS (orthorhombic structure with Pmma symmetry) make the BS system even more attractive.¹⁹ Recent successful fabrication of the bulk r-BS crystal^14,15 as well as isolation of a monolayer BS sheet from bulk crystal^20,21 opened a door to examining such intriguing predictions. On the other hand, despite these theoretical studies that suggest the sensitivity of electronic states to the configuration, stacking sequence, and number of BS layers,^17,19−21 no experimental outputs on the basic electronic states have been obtained even for bulk r-BS. This is primarily because obtained bulk single crystals are very small and powder-like (a photograph is shown in Figure 1c; the typical powder size is less than 30 μm), hindering access by spectroscopy techniques such as photoemission spectroscopy (PES).

Figure 1.

(a), (b) Schematics of the crystal structure and the first BZ of r-BS, respectively. (c) Photograph of r-BS powders. (d) Schematics of (1) sample mounting on an Au substrate, (2), (3) cleaving by Kapton tape, and (4) micro-ARPES measurements.

In this Letter, we report the band structure of the r-BS powder crystal studied by microfocused angle-resolved photoemission spectroscopy (μ-ARPES). Although the determination of band structure for such a tiny powder crystal with conventional ARPES is almost impossible, we have overcome this difficulty by utilizing a microfocused photon beam²² and carefully selecting a tiny single-crystal piece among many islands of powders stamped on a gold (Au) substrate by spatial photoelectron imaging. As a result, we have succeeded in mapping out the 3D band structure of r-BS and have compared it with calculations. We emphasize that the experimental scheme established in this study can be widely applicable to elucidate the electronic band structure of many other powder crystals.

To perform ARPES measurements with a tiny r-BS crystal, we at first dispersed r-BS powders on a polycrystalline Au substrate with a thickness of ∼0.3 mm attached to the sample holder in the atmosphere (Figure 1d, ①), and installed it into an ultrahigh vacuum (UHV) chamber connected to the ARPES chamber. Next, we pasted a piece of Kapton tape onto the Au substrate (Figure 1d, ②) and removed it to cleave the powder samples under UHV (Figure 1d, ③). For details of sample fabrication and characterization, see Supporting Information S1. An optical microscope image after cleavage is shown in Figure 2a, where several r-BS clusters are seen as white areas enclosed by purple line. To distinguish r-BS crystals from the Au substrate, we performed scanning μ-PES measurements (Figure 1d, ④) with a 100 μm step and mapped out the spatial distribution of photoelectron intensity at a binding energy (E_B) of 185.5–192.5 eV where the B 1s core-level peak is expected to appear (blue curve in Figure 2b). The result shown in Figure 2c signifies that the weak intensity area with blue color shows good matching with the area where high-density r-BS clusters are seen in the optical microscope image in Figure 2a. This is opposite to an intuitive expectation that the higher-density area of r-BS powders should show a stronger B 1s intensity. However, this unexpected result can be well explained in terms of the strong charging effect of the sample caused by the poor electrical contact due to the high density and/or thick nature of r-BS clusters. Actually, the charging behavior is recognized in the PES spectrum measured in the blue color region as a strong suppression of the spectral weight (red curve in Figure 2b). From these experimental results, we concluded that the sample area where white-colored r-BS clusters are clearly visible (Figure 2a) is not suitable for observing the intrinsic electronic states of r-BS because the PES spectrum suffers from the strong charging effect due to the insulating nature of r-BS.^14,15,20,21 We then looked for smaller pieces of r-BS powder with lower density to obtain reliable PES signals. We chose a sample area (green dashed box in Figure 2c) where the photoelectron intensity is relatively strong and carried out the spatial mapping of photoelectron intensity with a finer step of 20 μm (Figure 2d). The strong intensity region (red color) shows a good correspondence with the area of the exposed Au substrate observed in the magnified optical microscopy image (Figure 2e). This is also confirmed by the experimental result that the ARPES intensity at point 1 in Figure 2d is relatively strong at E_B ≈ 2.5, 4, and 6 to 7 eV (Figure 2f) where the Au 5d bands are expected to appear.²³ The nondispersive feature of PES intensity indicates that the Au substrate is polycrystalline. The reason that the B 1s signal is not visible in Figure 2d is that it is covered by the strong-intensity background from the Au substrate as seen in Figure 2b. To enhance the signal from the B 1s peak, we integrated the photoelectron intensity within a narrower window covering only the B 1s peak (188.0 ≤ E_B ≤ 189.5 eV; see vertical dashed lines in Figure 2b), and the result is shown in Figure 2g. Now, one can identify the strongest intensity appearing in a single pixel of 20 × 20 μm² marked as point 2, which was overlooked in the PES-intensity mapping in a wider E_B integration window shown in Figure 2d. We found from the laser microscope image in Figure 2h that such a small area is characterized by a flat and mirror-like surface suitable for ARPES measurements. In fact, we were able to obtain high-quality ARPES data at point 2 as shown in Figure 2i (see also Supporting Information S2 and S3; note that an overall reproducibility of experimental band structure was confirmed by measuring a few different flakes as detailed in Supporting Information S4). These bands originate from the r-BS crystal because the PES spectrum of a wider energy range of E_B = 0–200 eV (Figure 2j) signifies not only the B 1s peak but also the spin–orbit satellites of S 2p_1/2 and S 2p_3/2 core-level peaks, besides weaker Au 4f peaks from the Au substrate. Moreover, the composition ratio of B and S is estimated from the spectral weight of the B 1s and S 2p peaks by taking into account that the photoionization cross-section²⁴ is 1.1 ± 0.1, consistent with the expected value of 1.0. It is emphasized here that, to efficiently find an appropriate sample position for ARPES measurements, it is essential to carry out high-spatial-resolution mapping with a pixel size comparable to that of powder crystals.

Figure 2.

(a) Optical microscope image of r-BS powder crystals on a Au substrate after exfoliation with Kapton tape. (b) Representative PES spectra around the B 1s core level at three representative sample positions where the B 1s core-level peak is clearly recognized (blue curve), the strong signal from the Au substrate dominates (green curve), and the strong charging effect is seen (on white-colored r-BS clusters) (red curve). (c) Spatial mapping of photoemission intensity integrated over the E_B range of 185.5–192.5 eV, measured with hv = 250 eV in the same spatial region as the microscopy image of (a). (d) Same as (c) but for a smaller spatial region enclosed by a green dashed box (0.8 × 0.8 mm²) in (c) measured with a finer step of 20 μm. (e) Optical microscope image corresponding to (d). (f) ARPES intensity in the valence-band region as a function of E_B and the wave vector measured with hv = 100 eV at point 1 in (d). (g) Same as (d) but with a narrower E_B window of 188.0 ≤ E_B ≤ 189.5 eV which covers only the B 1s peak as indicated by vertical dashed lines in (b). Points on the sample where ARPES measurements were carried out are indicated as squares in (d) and (g) (points 1 and 2). (h) Enlarged laser microscope image around point 2. (i) Same as (f) but measured at point 2. (j) PES spectrum in a wider E_B range (E_B = 0–200 eV) measured with hv = 250 eV. The inset shows the magnified view in the B 1s and S 2p core-level region.

Now that the scheme to access the band structure of r-BS powder crystal is established, we present the 3D band structure obtained at point 2 in more detail. To clarify the three-dimensionality of the electronic states, we investigated the band structure along the wave vector perpendicular to the surface (k_z) by varying the photon energy in ARPES measurements. We carried out the in-plane band-dispersion mapping at selected k_z planes. Figure 3a shows EDCs measured along the ΓKM cut (k_y cut) at k_z ≈ 0 plane with hν = 105 eV at T = 300 K. (Note that the direction of high-symmetry lines was determined by the symmetry and periodicity of the FS mapping shown in Figure 4e.) One can recognize several dispersive bands. For example, sharp peaks located at 2 and 2.5 eV seen in the normal-emission EDCs have a hole-like dispersion centered at the Γ point and rapidly disperse toward higher E_B on moving away from the Γ point. The band dispersion is better visualized in the corresponding ARPES intensity plot in Figure 3b, which signifies that the hole-like band rapidly disperses up to 7 eV midway between the Γ and K points and then disperses back again toward E_F on further approaching the K point. After passing the K point, this band moves further upward and becomes nearly flat at ∼2.5 eV around the M point. One can see a weak intensity above 2 eV midway between the Γ and K points as indicated by a black arrow. This band is likely connected to the 2 eV peak at the Γ point to form an M-shaped band centered at the Γ point as predicted in the calculation (details in Figure 4). Besides such a highly dispersive band, there exist less dispersive features, such as a weakly dispersive electron-like band that bottoms out at 9 eV at the Γ point and a band located at 4 eV with small wiggling along the E_B axis. (Note that weak features located at 2.5 eV and 6 to 7 eV are assigned to the background from the Au substrate.) When the photon energy is increased to hν = 125 eV to probe the k_z ≈ π plane (Figure 3c,d), the uppermost valence band moves upward and shows a holelike dispersion with its top at 0.5 eV at the A point, which corresponds to the valence band maximum. (Note that the A point coincides between triple-layer- and single-layer-based BZs.) The absence of the E_F crossing of bands signifies the semiconducting nature of r-BS. As shown in Figure 3d, besides the topmost valence band, there exists another band that bottoms out at 6 eV at the Γ point which does not have a corresponding feature in the k_z ≈ 0 plane (Figure 3b). Except for these bands, most of the bands (e.g., band tops out at 2.5 eV at the M point and bottoms out at 9 eV at the Γ point) show a similar overall dispersive feature between k_z ≈ 0 and π, supporting the quasi-2D nature of r-BS, consistent with the existence of a van der Waals gap between adjacent BS sheets in the crystal.

Figure 3.

(a), (b) EDCs and corresponding ARPES intensity plot measured along the ΓKM cut (k_z = 0 plane) with hv = 105 eV. Gray arrows show a weak spectral signature from the topmost valence band. (c), (d) Same as (a) and (b), but measured along the AHL cut (k_z = π plane) with hv = 125 eV. There exist notable differences in the ARPES intensity plot between the k_z = 0 and π planes, such as the energy position of the hole-band top at the Γ/A point and the absence/appearance of a U-shaped band that bottoms out at 6 eV at the Γ/A point.

Figure 4.

(a), (b) Comparison of ARPES-intensity plot (same as Figure 2e, but in gray scale) with calculated band structure (red curves) along the ΓKM cut. (c), (d) Same as (a) and (b) but along the AHL cut. Bands are labeled A–G. (e) ARPES-intensity plot as a function of in-plane wave vectors, k_x and k_y, for representative E_B slices measured with hv = 125 eV corresponding to the AHL plane, overlaid with the calculated equi-energy contours (red curves). (f), (g) ARPES intensity plots along the AL and AH cuts, respectively, together with the experimental band dispersion (purple circles) and the result of numerical fittings with a parabolic function (blue curve).

To obtain further insights into the characteristics of observed bands, we directly compare the ARPES intensity along the ΓKM cut (the same as Figure 3b but plotted with gray scale) and the calculated band structure in Figure 4a,b. We also compare the experimental and calculated band structures for the AHL cut in Figure 4c,d. Calculated bands are shifted as a whole so as to align the energy position of the topmost valence band at the Γ/A point. One can recognize very good agreement between the experiment and calculation. For example, (A) a highly dispersive holelike band at the Γ point in the E_B range of 2–7 eV, (B) a nearly flat band that tops out at ∼2.5 eV around the M point, and (C) an electronlike band that bottoms out at 8 to 9 eV at the Γ point are commonly recognized in both ΓKM and AHL cuts. In addition, (D) a weak M-shaped band for the topmost valence band which exists only along the ΓKM cut corresponding to the ARPES feature indicated by black arrows in Figure 3a,b, (E) a weakly dispersive band at 4 eV along the ΓKM cut, and (F) an electron-like band that bottoms out at 6 eV and (G) a topmost valence band that tops out at 0.5 eV along the AHL cut are nicely reproduced in the calculation. According to the calculation, all of these bands are assigned to the hybridized B 2p and S 3p orbitals. Among them, the topmost valence band originates from the hybridized B 2p_z and S 3p_z orbitals in which the electronic wave function extends along the c axis. Since the bandwidth along the k_z axis is sensitive to the magnitude of interlayer hopping, exfoliation of the r-BS crystal down to a few layers may cause a dramatic influence on the size of the band gap.^20,21 To discuss the energy dispersion of the topmost valence band in more detail, we show in Figure 4e the energy counter plot as a function of the in-plane wave vectors, k_x and k_y, obtained at the k_z ≈ π plane at some representative E_B values. One can recognize from the intensity plot at E_B = E_F the absence of ARPES intensity, which confirms the semiconducting nature of r-BS. At E_B = 0.5 eV, a small spot, corresponding to the valence band maximum, starts to appear at the A point. Upon increasing E_B, the small spot gradually enlarges and evolves into a large circular-shaped contour and eventually becomes a large hexagon at E_B = 1.75 and 2.25 eV. These features well reflect the symmetry of BZ and show good agreement with the calculated equi-energy contours overlaid by red curves. (Note that the energy position of the topmost valence band is aligned between the experiment and calculation.) It is noted that the band gap value in the occupied region estimated from the present ARPES experiment (0.5 eV) is less than half of the band gap estimated by other experiments such photoluminescence (1.8–2.5 eV) and ultraviolet diffuse reflectance (3.4 eV), as well as the calculated band gap (2.7 eV).^14,20,21 This suggests that r-BS is a hole-doped p-type semiconductor.

The observed hexagonal (noncircular) contour in Figure 4e suggests an anisotropic in-plane effective mass (m*). To estimate the m*, we at first extracted the experimental band dispersion for the topmost valence band from the peak position of EDCs measured along the AL and AH cuts, as shown by red circles in Figure 4f,g. Then, we performed numerical fittings to the experimental band dispersion with a parabolic function and estimated the m*/m₀ (m₀: free electron mass) value along the AL and AH cuts to be −1.30 ± 0.02 and −0.93 ± 0.02, respectively, which indicates an anisotropy of ∼40%. It is remarked that the average m*/m₀ value of r-BS is twice as large as that of bulk h-BN (−0.49),²⁵ and there is also a sizable difference in the band gap magnitude (the band gap of h-BN is ∼6 eV).^2,14,20,21 This would point to a different usability as a semiconductor device in the application. It is noted that the m* value of monolayer r-BS is predicted to be enhanced by 10 times compared to that of its bulk counterpart due to the possible formation of a relatively flat valence band associated with the band quantization.^16,20 As a next step, it would be challenging to carry out the band-structure investigation of monolayer r-BS and its band-structure engineering with electrical gating and/or chemical doping to search for exotic quantum states predicted for flat-band 2D materials.^5,6,26,27

Finally, we briefly discuss the implications of the present results in both material and spectroscopy aspects. Two-dimensional semiconductors are useful in a broad range of applications such as optoelectronics and spintronics. A majority of so-far-identified 2D semiconductors are n-type due to the electron doping from intrinsic impurities and/or defects (e.g., electron-doped MoS₂ and WS₂ with chalcogen vacancies), whereas p-type 2D semiconductors are still limited (e.g., black phosphorus,²⁸ tellurium,²⁹ and α-MnS). To develop functional devices based on 2D semiconductors, it would be indispensable to find a new p-type 2D semiconductor in both bulk and monolayer forms to make a p–n junction. Our finding of the p-type semiconducting nature of bulk r-BS would be useful in this respect. In the spectroscopy aspect, we have established concrete methodology to elucidate the band structure of tiny powder crystals by μ-ARPES. This technique can be widely applicable to a variety of materials whose large single crystal has been difficult to synthesize.

In conclusion, we reported a direct visualization of the 3D band structure of the r-BS power crystal by utilizing scanning micro-ARPES. Our key findings are (i) the existence of a band gap exceeding 0.5 eV, supportive of the p-type semiconductor nature of r-BS, (ii) the large effective mass of valence electrons twice as large as that of h-BN, and (iii) the anisotropic nature of the in-plane effective mass. The present results open a pathway toward investigating the band structure and fermiology of a wide variety of powder crystals for which the application of electron spectroscopy techniques has been limited.

Glossary

Abbreviations

2D

two-dimensional

3D

three-dimensional

BZ

Brillouin zone

E_F

Fermi level

E_B

binding energy

DFT

density functional theory

UHV

ultrahigh vacuum

PES

photoemission spectroscopy

ARPES

angle-resolved photoemission spectroscopy

EDC

energy distribution curve

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.2c04048.

• Synthesis of r-BS, micro-ARPES measurements, choice of substrates, microscopic measurements, first-principles band calculations, reproducibility, and photon-energy dependence of ARPES data (PDF)

Author Contributions

This work was planned and proceeded by discussion among K.S., S.-i.O., T. Kondo, and T.S. H.K., M.M., T. Taniguchi, and T. Kondo carried out the fabrications of samples and their characterization. K.S., A.H., T. Kawakami, K.Y., S. Souma, K.N., M.K., K.H., and H.K. performed micro-ARPES measurements. M.T. and S. Saito carried out the band-structure calculations. K.S., T. Takahashi, and T.S. finalized the manuscript with input from all of the authors.

The authors declare no competing financial interest.