Introduction

Halides containing high-Z ns2 cations (with electron configurations of [d10]s2p0, e.g., Tl+, Pb2+, and Bi3+) have been found to possess unexpectedly good carrier transport properties. Depending on specific optical band gaps and other features of the band structure, they can be useful optoelectronic materials for various applications such as radiation detection, solar cells, etc.1,2,3,4,5,6 For instance, PbI2 and some Tl-based halides have shown excellent performance as semiconductor radiation detectors, in which carriers generated by γ-ray or X-ray radiation can be efficiently collected over millimeter or even longer distances.1,2,3,4 Meanwhile solar cells based on Pb-based organic–inorganic hybrid halide perovskites have achieved power conversion efficiency well above 20%.5,6 The prototypical material, CH3NH3PbI3, is exceptional in having an extremely large dielectric constant on the border of ferroelectricity, suitable band gap for solar absorber application, and low hole and electron effective masses.7,8,9,10,11,12,13,14 The physical mechanisms underlying these optoelectronic halide materials are not yet fully established, but can at least in part be attributed to the unique chemistry of the ns2 lone-pair state. Factors that have been discussed include formation of defects with lower charge states, high dielectric constants, and shallow defect levels, among others.7,8,9,10,11,12,13,14,15 Assessment can be made experimentally using time-resolved experiments for carrier lifetimes.14

In these compounds the cation-s state moves down in energy (forming the lone-pair state), separating from the cation-p states (due to the Mass-Darwin effect), so that there is substantial charge transfer only from the cation-p to anion-p states, rather than the cation-s to anion-p states. Thus, the valence bands are mainly formed by anti-bonding combinations of cation-s and anion-p states; the conduction bands are dominated by the spatially extended cation-p states, hybridizing also in the anti-bonding pattern with the anion-p states. This leads to simultaneously dispersive valence and conduction bands (favorable to high mobility), and defect tolerance. Furthermore, the resulting significant cross-band-gap hybridization gives rise to enhanced Born effective charges, analogous to classical ferroelectric materials, such as BaTiO3. This enhances the dielectric constant, which effectively screens defects and is beneficial for carrier transport.15,16

In addition to the ns2 cations containing halides, the corresponding oxyhalides and chalcohalides have been also considered as optoelectronic materials. In 2012, experimental studies by Hahn et al. found BiSI and BiSeI to be n-type, with high absorption coefficients.17,18 However, devices based on BiSI have up to now shown poor performances.18 Ganose et al., based on density functional calculations, attributed the poor performance in the reported BiSI-based devices to band misalignments and suggested alternative device architectures.19 Theoretical studies of Bi(III) chalcohalides have suggested n-BiSeBr, p-BiSI, and p-BiSeI as photovoltaic materials, BiSeBr and BiSI as room-temperature radiation detection materials, and BiOBr as a p-type transparent conducting material.10

The purpose of this paper is to explore these compounds more broadly seeking identification of new optoelectronic compounds and trends. Specifically, we assess a series of bismuth/antimony oxyhalides and chalcohalides. It is important to note the rich diversity of chemical compositions and geometrical structures in this class of compounds, which supports the notion that interesting properties are yet to be discovered in them. The compound-intrinsic properties (e.g., thermodynamic stability, electronic structure, effective masses of electron/hole, and optical absorption) of 36 relatively simple compounds obtained from the Inorganic Crystal Structure Database have been systematically investigated through density functional calculations. Based on the results, we found a series of candidates suitable for optoelectronic applications, including two types of compounds (BiSeCl/Br/I and Bi3Se4Br) as potential solar absorber materials, three types of compounds (Bi3Se4Br, BiSeCl/Br/I, and BiOI) as potential radiation detection materials, and three types of compounds (BiOCl/Br, SbOF, and Sb4O5Cl2/Br2) as potential p-type transparent conducting materials.

Results

Properties of the 36 Bi/Sb oxyhalides and chalcohalides

The calculated HSE + SOC band gaps of representative compounds are listed in Table 1, compared with available experimental results. One sees that the calculated gap values are in very good agreement with corresponding experimental data for most of the compounds except the tellurides, where the band gaps are overestimated compared to experiment with the HSE functional. In the following, we only consider the oxyhalides and chalcohalides not containing Te. It may also be noted that besides increasing the band gap relative to PBE + SOC, HSE + SOC calculations may lead to different band dispersions, for example, changes in the band curvatures and effective masses. We calculated HSE + SOC band structures to compare with PBE + SOC for some compounds, specifically the compounds that we identify as potential solar absorbers. As seen (Supplementary Fig. S1), while there are small differences, these changes are minor for the compounds studied.

Table 1 Calculated and experimental band gaps of some representative compounds considered in the current work
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The calculated formation energies, band gaps, and effective masses of electrons/holes for the 36 Bi and Sb-based compounds are given in Fig. 1 and Supplementary Table S1. Here, the formation energy is defined as the energy difference between a compound and its constituent elemental solids. It is seen that all the compounds possess negative formation energies (upper panel in Fig. 1), indicating that they are stable against decomposition to constituent elemental solids, as expected, considering that they are experimentally known compounds. Generally, the stabilities of the compounds increase as the halogens change from I to F or the chalcogens change from Te to O. This is the trend of increasing anion electronegativity, and therefore increasing electronegativity difference between anions and cations, which normally leads to increasing stability for ionic compounds. We also calculated the thermodynamic stability of the first category of compounds (BiSeCl/Br/I and Bi3Se4Br) with respect to competing phases, including structural optimization with inclusion of the van der Waals interaction based on the optB86 functional20 (important for the structure of the binaries) and find marginal stability against decomposition into binaries (Supplementary Table S2).

Fig. 1
figure 1

Formation energies per atom (upper panel), band gaps (middle panel), and effective masses of electron and hole (lower panel) for the 31 Bi and Sb-based compounds. The formation energy is defined as energy difference between the compound and constituent elemental solids. Red, green, and blue shaded areas in the middle panel indicate band gap ranges of 1.0–1.7, 1.5–2.2, and >3 eV, respectively. Gray shaded area in the lower panel indicates effective masses lower than the rest mass of electron (m0)

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As shown in the middle panel of Fig. 1, the calculated band gaps of these Bi and Sb-based compounds cover a wide range from ~1 to ~5 eV. There is a general trend of increasing band gap with increasing electronegativity difference between constituent cations and anions, as indicated in Fig. 2a. There is also a clear trend in the bond valence sum (BVS)21 plot shown in Fig. 2c, where the band gaps increase as the BVS values of Bi or Sb approach their the nominal valence of three, reflecting more ideal bonding geometries.

Fig. 2
figure 2

a Band gaps, b hole and electron effective masses as a function of average electronegativity discrepancy between anions and cations for the 31 Bi and Sb-based compounds; c band gaps, d effective masses of electron and hole as a function of bond valence sum of the cations

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The effective masses of electrons and holes of these compounds are shown in the lower panel of Fig. 1. In most cases the electron effective masses are lower than those of holes, but there is no obvious relationship between the effective masses, and the electronegativity difference (Fig. 2b) or the cation BVS (Fig. 2d). Strikingly, many of these compounds possess electron or hole effective masses lower than or around the rest mass of electrons (m0), indicating the possibility of good carrier mobility. The large span of the band gaps along with low electron or hole effective masses suggests opportunities for various optoelectronic applications based on compounds in this class.

The calculated dielectric constants, as obtained from PBE calculations, are also large for almost all of the compounds as shown in Fig. 3 (with the explicit numbers in Supplementary Table S3). Note that the main contributions to the dielectric constants are from the lattice, reflecting the mechanism discussed above. These high dielectric constants are then expected to lead to screening of defect potentials and suppression of point defect scattering.

Fig. 3
figure 3

Calculated dielectric constants (ε) of the considered bismuth/antimony oxyhalides and chalcohalides. We show total static dielectric constant (εst) and the component from phonon contribution (εphonon). Note that these compounds have generally high dielectric constants, mostly due to large phonon contributions

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Suitable optical band gap is a primary prerequisite for specific optoelectronic applications, e.g., gaps in range 1.0–1.7 eV are optimum for solar absorber materials. A larger gap, greater than 1.5 eV is essential for room-temperature radiation detection applications in order to minimize noise due to thermally generated carriers. Band gaps near to or larger than 3 eV are needed for transparent conducting materials. In addition, small effective mass of electrons or holes is also necessary for good carrier mobility. These two compound properties enable us to identify candidates as potential optoelectronic materials, which then deserve further theoretical or experimental studies concerning their dopability, dielectric, and other properties.

Potential solar absorbers

Four out of 36 compounds (BiSeCl, BiSeBr, BiSeI, and Bi3Se4Br) are found to possess optical band gaps in range of ~1.0–1.7 eV and electron or hole effective masses lower than m0. The band gaps and average carrier effective masses of the four compounds are given in histogram in Fig. 4a. There are two distinct crystal structures in this set of four compounds: BiSeCl, BiSeBr, and BiSeI possess a crystal structure of space group Pnma (No. 62), and Bi3Se4Br with space group C2/m (No. 12).

Fig. 4
figure 4

a Histogram of HSE + SOC band gaps, effective masses of electron and hole for BiSeCl, BiSeBr, BiSeI, and Bi3Se4Br. b Crystal structure, band structure, and partial density of states (DOS) of BiSeCl. c Crystal structure, band structure, and partial DOS of Bi3Se4Br. d Absorption spectra of BiSeCl, BiSeBr, BiSeI, and Bi3Se4Br

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The iso-structural compounds, BiSeCl, BiSeBr, and BiSeI, have similar electronic properties, including similar optical band gaps of approximately 1.47–1.48 eV, and similar transport effective masses of ~0.53–0.57 m0 and ~2.19–2.98 m0, for electrons and holes, respectively. This reflects the dominant role of the chalcogen in the upper valence band electronic structures. For comparison the cubic phase of CH3NH3PbI3 has reported effective masses of 0.35 m0 and 0.31 m0 for electrons and holes, respectively.7 As a representative, the crystal structure, band structure, and partial density of states (DOS) of BiSeCl are shown in Fig. 4b. The crystal structure has chains of atoms running along the c-axis. The band structure shows an indirect band gap with the conduction band minimum (CBM) located at Γ and valence band maximum (VBM) along the Γ-Z direction. The conduction bands are highly dispersive both parallel (Γ-Z direction) and perpendicular (Γ-X and Γ-Y direction) to the chain direction (kz), since they are mainly derived from the spatially extended Bi-p states. The valence bands are dispersive in direction parallel to the atomic chains (Γ-Z direction) but less so perpendicular (Γ-X and Γ-Y direction) to the chain. This is due to the weak Se–Se interchain coupling compared with that of intrachain coupling. The shortest interchain Se–Se distance is 4.32 Å, which is larger than intrachain Se–Se distance of 3.81 Å. We note that a prior density functional investigation10 also indicated that BiSeBr and BiSeI may have potential as a solar absorber materials consistent with the present results. The band structures are given in Supplementary Fig. S2. Within these three compounds the halogen-p states take an increasing role in the VBM as the halogen atomic number increases from Cl to I. For BiSeI, the nearest interchain I–I distance is slightly shorter than the intrachain distances, indicating a stronger interchain I–I coupling. This is reflected in the band structure. Thus, the valence bands of BiSeI are dispersive in direction both parallel and perpendicular to the atomic chains (Supplementary Fig. S2).

Bi3Se4Br is another candidate absorber identified in the present calculations. In contrast to the three compounds discussed above, it possesses simultaneously low electron and hole effective masses of 0.71 and 1.20 m0, respectively, indicating efficient transport of both electrons and holes. The crystal structure of Bi3Se4Br is depicted in the inset of Fig. 4c. It also has atomic chains, in this case along the b-axis. The calculated band structure shown in Fig. 4c indicates an indirect band gap (~1.69 eV) with the CBM at k-point along the Γ-M direction and VBM along the N-Z direction. As expected, not only the valance bands but also the conduction bands are dispersive. The partial DOS (Fig. 4c) shows that the valence band is dominated by anion-p states, as expected. These hybridize with Bi 6s orbital to form antibonding states, responsible for the dispersive valence bands. The conduction band is primarily derived from Bi 6p states.

We note that due to matrix elements and selection rules the magnitude of the electronic gap is not always indicative of strong absorption that is needed for solar applications, and calculations of absorption spectra are needed to assess their potential use in solar cells. The calculated absorption spectra for the four potential solar absorbers show strong absorptions near the band gap (Fig. 4d; note that these are direct (vertical) transitions so absorption onset is slightly above the indirect gap), consistent with high solar-energy capture efficiency.

Potential semiconductors for room-temperature radiation detection

Seven (BiSCl, BiSBr, BiSI, BiOI, Bi3Se4Br, SbSI, and SbSeI) of the 36 compounds show optical band gaps in range between 1.5 and 2.2 eV as well as electron or hole effective masses lower than m0. These are then potentially useful as room-temperature radiation detection materials as far as this screen is concerned. Since heavy atoms (high Z) are necessary for efficient absorption of high-energy radiation, five Bi-based compounds are favorable, whose band gaps and carrier effective masses are shown in Fig. 5a. Among the five compounds, Bi3Se4Br has been discussed above.

Fig. 5
figure 5

a Histogram of HSE + SOC band gaps, effective masses of electron and hole for BiOI, BiSCl, BiSBr, BiSI, and Bi3Se4Br. b Crystal structure, band structure, and partial DOS of BiSCl. c Crystal structure, band structure, and partial DOS of BiOI. d Phonon contribution to, and total static dielectric constant (εst = ε∞ + εphonon) for BiSCl, BiSBr, BiSI, BiOI, and Bi3Se4Br

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BiSCl, BiSBr, and BiSI adopt the same chain-like crystal structure as BiSeCl/Br/I with space group Pnma (No. 62). The band structure and partial DOS of BiSCl are shown in Fig. 5b as a representative, while those of BiSBr and BiSI are given in Supplementary Fig. S3. Generally, the band structures of BiSCl/Br/I are similar to those of BiSeCl/Br/I, except that the former have larger band gaps. This is attributable to the deeper S-p states as compared with Se-p states (recall the chalcogen-p VBM character). Within this group of compounds, the valence bands are mainly composed of anion-p states (S-p and halogen-p). The contributions from halogen-p states near the VBM increase as the halogen ion changes from Cl to I. In addition, there are also antibonding contributions from the Bi-s states. Despite this, the valence bands are still relatively flat leading to large hole effective masses, typically larger than m0. The conduction bands are always dominated by the spatially extended Bi-p states, leading to low electron effective masses, less than m0. The disparity between electron and hole effective mass may not be a prohibitive condition for radiation detection applications, as these devices are often designed to collect only one type of charge carrier.

BiOI is another candidate for radiation detection identified in this study. It crystallizes to a layered tetragonal structure of space group P4/nmm (No. 129). As depicted in the inset of Fig. 5c, each Bi is coordinated by four O atoms, while each O has four Bi neighbors, forming Bi–O layers. Each Bi–O layer is sandwiched by two iodine layers, stacking along the c-axis. The band structure of BiOI is shown in Fig. 5c. It has an indirect band gap. The CBM is at Γ point, while the VBM is at a k-point along the Z-R direction. The states near VBM are dominated by I-p states, while the states near CBM mainly derive from Bi-p states (Fig. 5c). The interlayer and intralayer I–I distances are 4.89 and 4.03 Å, indicating a weak interlayer interaction. This is responsible for the rather flat valence bands perpendicular to the atomic layers (Γ-Z and X-R directions). However, both valence and conduction bands along the Z-R are dispersive due to the strong interactions within the atomic layers. Remarkably, it possesses simultaneously low electron and hole effective masses, which raises the possibility of high mobility-lifetime (µτ) product for both type of charge carriers—a desirable characteristic for efficient charge collection and energy resolution in semiconductor detectors.

It is known that high dielectric constants are favorable for long carrier lifetime, large diffusion length, and the higher µτ values via effective screening of charged defects. The calculated static dielectric constants (εst, the high-frequency limit resulted from electronic polarization) for the five potential radiation detection materials are shown in Fig. 5d (see also Fig. 3; numerical values in Table S3). As seen all the materials exhibit rather large εst above 30, in spite of their sizable band gaps.

Compounds as potential transparent conductors

For transparent conducting materials, we focus on finding p-type (hole conducting) examples, since these are rather scarce compared to n-type.22,23,24,25,26 In addition to large band gap (>3 eV), low hole effective mass is a prerequisite since good conductivity is needed. While not reflecting a strictly intrinsic property, it should also be emphasized that successful development of a transparent conductor requires doping. This is a necessary criterion for a transparent conductor. The difficulty in doping most oxides p-type has been an important challenge in this field.23 It has been overcome through specific chemistries, such has that of monovalent Cu and divalent Sn, and through particularly stable crystal structures such as that of BaSnO3.22,23,24,25 Five compounds (BiOCl, BiOBr, SbOF, Sb4O5Cl2, and Sb4O5Br2, Fig. 6) are found to possess optical band gaps larger than 3 eV as well as reasonable hole effective masses (below 1.5 m0 except for BiOBr with ~1.7 m0). These may be potential transparent conducting materials, if they can be doped. All of them contain oxygen as the chalcogen, reflecting the fact that the high electronegativity of O is favorable for a large band gap.

Fig. 6
figure 6

a Histogram of HSE + SOC band gaps, effective masses of electron and hole for BiOCl, BiOBr, SbOF, Sb4O5Cl2, and Sb4O5Br2. b Crystal structure, band structures, and partial DOS of BiOCl. c Crystal structure, band structure, and partial DOS of SbOF. d Crystal structure, band structure, and partial DOS of Sb4O5Br2. e Calculated absorption spectra of BiOBr, BiOCl, Sb4O5Br2, Sb4O5Cl2, and SbOF

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BiOCl and BiOBr possess the same crystal structure of space group P4/nmm (No. 129) as that of BiOI. The band structures and partial DOS of BiOCl are shown in Fig. 6b, and those of BiOBr are shown in Supplementary Fig. S4. Their band structures display similar features as that of BiOI, partially reflecting the fact that these compounds adopt the same crystal structure. However, the band gap increases as the halogen ion changes from I to Cl because of the lowering of the halogen-p states, following the electronegativity. Moreover, the dispersion of the relatively flat conduction bands along Γ-Z (perpendicular to the atomic layers) also changes when going from I to Cl, leading to a shift in the CBM from Γ to Z point. The VBMs of the three compounds are always along the Z-R direction (parallel to the atomic layers). Due the strong intralayer halogen–halogen coupling, the valence bands are highly dispersive along Z-R direction, leading to low hole effective masses.

SbOF has a chain-like structure with space group Pnma (No. 62). The atomic chains extend along the b-axis (inset of Fig. 6c). Although it has the same symmetry as the BiSeCl/Br/I and BiSCl/Br/I compounds discussed earlier, the bonding pattern in SbOF is distinct. The Sb–O bonds in SbOF are almost in the plane of the atomic chains, while the Bi–Se/S bonds are not. The band structure and partial DOS of SbOF are shown in Fig. 6c. It has an indirect band gap of 3.95 eV with VBM at Γ and CBM at Y. The VBM is dominated by O-2p states. Since the nearest interchain O–O distance (4.77 Å) is much larger than that of intrachain distance (2.47 Å), the interchain O–O coupling is rather weak. This is responsible for the flat valance bands in direction perpendicular to the chain (Γ-X). However, the valence bands are highly dispersive along the chain direction (Γ-Y) due to the strong intrachain interactions.

Sb4O5Cl2 and Sb4O5Br2 adopt same layered structure with space group P21/c (No. 14) and atomic layers stacked along a-axis. Among these, Sb4O5Br2 was previously suggested as p-type transparent conducting material based on density functional calculations.24 The band structures of the two compounds shown in Fig. 6d (Sb4O5Br2) and Supplementary Fig. S5 (Sb4O5Cl2) are very similar. Both have indirect band gaps, VBM at Γ and CBM at Z. Interestingly, although they have a layered structure, the valence bands are dispersive in direction perpendicular to the atomic layers (Γ-Z direction). As seen in the DOS (Fig. 6d), the states near the VBM are dominated by halogen-p states. The intralayer halogen–halogen distances (5.10 and 5.13 Å for Sb4O5Cl2 and Sb4O5Br2, respectively) are much larger than those of interlayer ones (4.47 and 4.39 Å for Sb4O5Cl2 and Sb4O5Br2, respectively). This leads to strong interlayer halogen–halogen interactions and explains the dispersive valence bands in the Γ-Z direction.

Discussion

Motivated by recent results on halide semiconductors, and theoretical arguments about the origin of their performance, we selected a group of 36 chalcohalides and oxyhalides containing ns2 Bi3+ or Sb3+ cation. Density functional results for band gap, effective mass of electrons and holes, and optical absorption are reported. BiSeCl/Br/I and Bi3Se4Br are found to possess optical band gaps of 1.47–1.69 eV and low electron or hole effective masses. They are promising solar absorber materials. Bi3Se4Br, BiSCl/Br/I, and BiOI have band gaps in the range 1.69–2.08 eV, and low effective mass of electrons or holes, suitable for use as room-temperature radiation detection materials. BiOCl/Br, SbOF, and Sb4O5Cl2/Br2 have larger band gaps (>3.0 eV) and low hole effective mass, which makes them potential candidates as p-type transparent conducting materials. This suggests further study of the identified materials to assess other properties relevant to applications, such as dopability in the case of transparent conductors, and the possibility for obtaining high resistivity in the case of semiconductors for radiation detection.

There are several common themes in the electronic structure of the identified compounds. The band gap is controlled by positions of the anion-p states which form the valence bands. The Bi or Sb s-states hybridize in antibonding combinations with halogen-p and chalcogen-p states near respective VBMs favoring high dispersion and lower hole effective mass. The CBM of the compounds is formed primarily from Bi or Sb p-states. There is also a tendency toward cross-gap hybridization between the cation-p and anion-p states (band structure and DOS; Figs. 3–5). Cross-gap hybridization indicates covalency in the otherwise ionic materials, and possibility of large Born effective charge and static dielectric constant. The identified compounds do as a result have high dielectric constants. These large static dielectric constants are favorable for effective screening of charged defects and high mobility. Despite the complex chain or layered structures of these compounds, the valence and conduction band dispersion is a consequence of hybridization among the anion or cation-p states, favoring low carrier effective mass. The current work proposes a promising series of Bi and Sb-based oxyhalides and chalcohalides, which may be appropriate for various optoelectronic applications. Further theoretical and experimental investigations will be necessary to ascertain their dopability, defect and dielectric behavior, the possibility of obtaining high resistivity for radiation detection, as well as device-level properties.

Methods

All calculations are performed within the framework of density functional theory using plane-wave pseudopotential method as implemented in the VASP code.27 The electron–ion interaction is described by means of projector-augmented wave pseudopotentials.27,28 Valence electron configurations of ns2np3 for Sb/Bi, ns2np4 for O/S/Se/Te, and ns2np5 for F/Cl/Br/I are employed along with the Perdew–Burke–Ernzerhof generalized gradient approximation.29 A plane-wave basis set with an energy cutoff of 500 eV and the Monkhorst-Pack k-point mesh with grid spacing of ~2π × 0.03 Å−1 are used for total energy minimization and ground-state electronic structure calculations. Once the basic properties were obtained in this way, we then calculated electronic structures using the hybrid Heyd–Scuseria–Ernzerhof (HSE)30 functional, with the standard 25% non-local Fock exchange. Spin–orbit coupling (SOC) is included. This is important for these heavy p-electron element containing compounds. The carrier effective mass (m*) tensors for transport are directly calculated using the BoltzTraP code.31 For this purpose, the PBE + SOC eigenvalues on a dense k-point grid (2π × 0.015 Å−1 or less), with a carrier concentration of 1018 cm−3 and temperature of 300 K. This takes into account effects of non-parabolicity, anisotropy of bands, multiple bands, and other band structure effects, to obtain a single effective mass tensor for carrier transport. The quoted average values are from the direction average of the inverse transport effective mass.

Data availability

Additional data that support the conclusions in this paper are available by contacting the corresponding authors. All relevant data are available from the authors.