Bismuth and Antimony Based Oxyhalides and Chalcohalides as Potential Optoelectronic Materials

In the last decade the ns$^2$ cations (e.g., Pb$^{2+}$ and Sn$^{2+}$) based halides have emerged as one of the most exciting new classes of optoelectronic materials, as exemplified by for instance hybrid perovskite solar absorbers. These materials not only exhibit unprecedented performance in some cases, but they also appear to break new ground with their unexpected properties, such as extreme tolerance to defects. However, because of the relatively recent emergence of this class of materials, there remain many yet to be fully explored compounds. Here we assess a series of bismuth/antimony oxyhalides and chalcohalides using consistent first principles methods to ascertain their properties and obtain trends. Based on these calculations, we identify a subset consisting of three types of compounds that may be promising as solar absorbers, transparent conductors, and radiation detectors. Their electronic structure, connection to the crystal geometry, and impact on band-edge dispersion and carrier effective mass are discussed.


INTRODUCTION
Halides containing high-Z ns 2 cations (with electron configurations of [d 10 ]s 2 p 0 , e.g., Tl + , Pb 2+ and Bi 3+ ) 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-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 ns 2 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 lonepair 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 antibonding 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 ns 2 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 ptype 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 (ICSD) 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.

Properties of the 36 Bi/Sb oxyhalides and chalcohalides
The calculated HSE+SOC band gaps of representative compounds are listed in Table I, 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.
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 form 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 (BiSe/Cl/Br/I and Bi2Se4Br) with respect to competing phases, including structural optimization with inclusion of the van der Waals interaction based on the optB86 functional 35 (important for the structure of the binaries) and find marginal stability against decomposition into binaries (Supplementary Table S2).
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. 2(a). There is also a clear trend in the bond valence sum (BVS) 36 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.
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. 4 As a representative, the crystal structure, band structure and partial density of states (DOS) of BiSeCl are shown in Fig. 4(b). 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  and valence band maximum (VBM) along the -Z direction. The conduction bands are highly dispersive both parallel (-Z direction) and perpendicular (-X and -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 (-Z direction) but less so perpendicular (-X and -Y direction) to the chain. This is due to the weak Se-Se interchain coupling compared with that of intra-chain coupling. The shortest inter-chain Se-Se distance is 4.32 Å, which is larger than intra-chain Se-Se distance of 3.81 Å. We note that a prior density functional investigation 10 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 inter-chain I-I distance is slightly shorter than the intra-chain distances, indicating a stronger inter-chain 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 insert of Fig. 4(c). It also has atomic chains, in this case along the b axis. The 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. 4(d); 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 1.5-2.2 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. 5(a).
Among the five compounds, Bi3Se4Br has been discussed above.
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. 5 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 (st, the high-frequency limit resulted from electronic polarization) for the five potential radiation detection materials are shown in Fig. 5(d) (see also Fig. 3; numerical values in Table S3). As seen all the materials exhibit rather large st 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. [37][38][39][40][41] 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. 38 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. [37][38][39][40] 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 expect for BiOBr with ~1.7 m0). These may be potential transparent conducting materials, if they can be is much larger than that of intra-chain distance (2.47 Å), the inter-chain O-O coupling is rather weak. This is responsible for the flat valance bands in direction perpendicular to the chain (-X). However, the valence bands are highly dispersive along the chain direction (-Y) due to the strong intra-chain 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. 39 The band structures of the two compounds shown in Fig. 6(d) (Sb4O5Br2) and Supplementary Fig. S5 (Sb4O5Cl2)  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 (DFT) using plane-wave pseudopotential method as implemented in the VASP code. 42 The electron-ion interaction is described by means of projector-augmented wave pseudopotentials. 42 Table S3. Calculated total static dielectric constant (εst), the high-frequency limit of dielectric constant (ε∞) and the component from phonon contribution (εphonon ) for the 31 bismuth/antimony oxyhalides and chalcohalides.