Relativistic electronic structure and band alignment of BiSI and BiSeI: candidate photovoltaic materials †

Bismuth-based solar absorbers are of interest due to similarities in the chemical properties of bismuth halides and the exceptionally e ﬃ cient lead halide hybrid perovskites. Whilst they both experience the same bene ﬁ cial relativistic e ﬀ ects acting to increase the width of the conduction band, bismuth is non-toxic and non-bioaccumulating, meaning the impact of environmental contamination is greatly reduced. Here, we use hybrid density functional theory, with the addition of spin orbit coupling, to examine two candidate bismuth containing photovoltaic absorbers, BiSI and BiSeI, and show that they possess electronic structures suitable for photovoltaic applications. Furthermore, we calculate band alignments against commonly used hole transporting and bu ﬀ er layers, which indicate band misalign-ments are likely to be the source of the poor e ﬃ ciencies reported for devices containing these materials. Based on this we have suggested alternative device architectures expected to result in improved power conversion e ﬃ ciencies.

Furthermore, we calculate band alignments against commonly used hole transporting and buffer layers, which indicate band misalignments are likely to be the source of the poor efficiencies reported for devices containing these materials. Based on this we have suggested alternative device architectures expected to result in improved power conversion efficiencies.
As the global demand for energy continues to grow inexorably, there is an increasing need for a clean energy source capable of providing indenite and sustainable economic growth. With a year's worth of sunlight providing almost two hundred times the energy of the world's entire known supply of fossil fuels, solar power is suitably positioned as a strong contender for utility-scale power generation. 1,2 Currently, the photovoltaic (PV) market is dominated by crystalline silicon panels, which, whilst relatively efficient, are subject to high synthesis and processing costs, limiting their potential for widespread application. 3,4 Other technologies, such as those containing Cu(In/Ga)Se 2 (CIGS) and CdTe absorbers, show efficiencies approaching 22% (ref. 5 and 6) but contain cadmium, which is toxic and indium, the price of which is highly volatile due to the limited number of suppliers. 7 The last 10 years have therefore seen a signicant research drive into low-cost materials containing only earth-abundant elements, [8][9][10][11] termed third-generation devices, from which hybrid halide perovskites emerged as a promising class of solar absorbers in 2009. 12,13 Currently, the highest performing hybrid perovskite is CH 3 NH 3 PbI 3 (MAPI), which can be easily solution processed allowing for dramatically reduced manufacturing costs. [14][15][16] Impressively, the power conversion efficiencies (PCEs) of MAPI-based devices have quickly overtaken all other thirdgeneration absorbers such as Cu 2 ZnSn(S,Se) 4 (ref. 17) and dyesensitised solar cells, 18 reaching 20.1% in only 6 years. 19,20 Unfortunately, the intrinsic stability of MAPI is still unresolved, and observations of facile decomposition upon contact with moisture have lead to concerns over long-term performance and the potential environmental risks due to leaching of toxic Pb. [21][22][23] There is therefore an urgent need to explore novel materials capable of replicating the signicant successes of hybrid perovskites, whilst employing rational design in order to prevent similar shortcomings.
Recently, bismuth-based PV materials have become of interest, in part due to similarities in the chemical properties of bismuth halides and lead hybrid perovskites. [24][25][26] Both Pb 2+ and Bi 3+ adopt a stable d 10 s 2 p 0 electronic conguration, 27 possess a similar so polarisability and form a wide range of compounds with rich structural diversity, 28,29 such as BiX 6 clusters, 25 1D ribbons, 30 and layered perovskite type structures. 26,31 Bismuth containing compounds also experience the same benecial large relativistic effects seen in MAPI, which act to stabilise the material against oxidation and increase the conduction band width through a signicant lowering of the conduction band minimum (CBM). [32][33][34] Importantly, bismuth is non-toxic and non-bioaccumulating, meaning the impact of environmental contamination is greatly reduced. 35,36 Whilst an increasing number of bismuth halides have been screened for solar absorber properties in recently months, such as BiI 3 (ref. 26 and 37) and A 3 Bi 2 I 9 (where A ¼ K or Rb, 25 Cs or CH 3 NH 3 , 38 and NH 4 (ref. 39)), research into the electronic properties of complex bismuth halides remains limited. As such, these compounds present an understudied class of earth-abundant and non-toxic materials, with signicant potential in PV applications.
Two such materials displaying promise as solar absorbers are BiSI and BiSeI. 24 Both crystallise in the ribbon structure shown in Fig. 1, in which [(BiChI) N ] 2 ribbons are held together by weak ionic or van der Waals-type forces (Fig. 1). 30,40 Recently, Zhou et al. have proposed that this type of geometry can provide several advantages: (i) by orientating the crystal such that the ribbons are vertically aligned on the substrate, a clear pathway is formed between the device contacts allowing for efficient carrier transport along the covalently bonded 1D axis, and (ii) by enforcing vertically aligned growth, any grain boundaries should occur parallel to the ribbons and therefore will not result in dangling bonds, substantially minimising recombination losses. 41 Furthermore, alloying of BiSI with BiSeI should not disrupt the connectivity of the conduction pathways and will simultaneously allow for precise tuning of the band gap. 42 These advantages have recently been demonstrated in another 1D solar absorber, Sb 2 Se 3 , in which controlled growth of a vertically aligned lm resulted in an increase in efficiency of over 2%, when compared to orientations that produced dangling bonds at grain boundaries. 41 In 2012, Hahn et al. screened BiSI and BiSeI for PV applications, nding them to be n-type materials, with high absorption coefficients and indirect band gaps of 1.57 eV and 1.29 eV, respectively. 42,43 However, an extremely low PCE (0.012%) was observed when BiSI was incorporated into a device containing CuSCN as a p-type hole transporting material and uorinedoped tin oxide (FTO) as the front contact. The authors note that hole diffusion lengths in BiSI samples were only 50 nm 43 and propose that effective screening of the electric eld at the heterojunction prevents efficient electron-hole separation, resulting in high levels of charge-carrier recombination in the neutral bulk. This is, however, in contrast to other materials with large dielectric constants, such as MAPI, where this screening does not appear to negatively affect charge separation and has instead been lauded as providing enhanced defect tolerance. 24,44,45 Instead, it is likely that the polycrystalline nature of the lms used in these devices precludes the formation of clear pathways for charge-carrier extraction and undermines the proposed benets of the ribbon structure. Regardless, these materials appear to possess many of the desired properties of efficient solar absorbers and, as such, warrant further analysis.
In this letter we study the fundamental electronic structure of BiSI and BiSeI, using hybrid density functional theory (DFT). We demonstrate: (i) that despite possessing indirect band gaps, in both cases the difference between the direct and indirect band gaps is small and should result in only marginal effects on performance, (ii) the valence band maximum shows largely anti-bonding character, which enhances band dispersion and may be of benet for the defect chemistry, and (iii) the mixing of the S/Se and I p states produces a diffuse conduction band in the directions along the ribbon structure, indicating that the material should show good conductivity in these directions. Lastly, we calculate the fundamental band alignments and accordingly suggest transparent conducting oxide and hole transporting materials likely to minimise interfaces losses in order to improve device efficiencies.

Computational methods
All calculations were performed using the Vienna Ab initio Simulation Package (VASP), 46-49 a periodic plane wave DFT code which includes the interactions between the core and valence elections using the Project Augmented Wave (PAW) method. 50 Both the plane wave basis set and k-point sampling were checked for convergence, with a cutoff of 520 eV and k-point grid of G-centred 3 Â 6 Â 2, for the 12 atom unit cells of BiSI and BiSeI, found to be sufficient. Geometry optimisations were tested using two functionals: the Perdew, Burke and Ernzerhof (PBE) functional 51 and the PBEsol functional, 52 a version of PBE revised for solids. Both functionals were trialled with and without the addition of Grimme's dispersion correction (D3), 53 however, we note that PBEsol oen accurately predicts the lattice constants for systems containing van der Waals interactions, without the need to treat them explicitly. 54 The structures were deemed to be converged when the forces on all the atoms totalled less than 10 meVÅ À1 . In order to accurately predict electronic properties, the Heyd-Scuseria-Ernzerhof (HSE06) hybrid DFT functional 55 with the addition of spin orbit effects (SOC) was used for density of states, charge density, and band structure calculations. 25,37,56,57 Crystal Orbital Hamilton Population (COHP) analysis was performed using the LOBSTER program. 58,59 In the plane wave formalism, due to the presence of periodic boundary conditions, the electrostatic potential of a crystal is not dened with respect to an external vacuum level and, as such, the absolute electronic eigenvalues from different calculations are not comparable. In order to align the energies to the vacuum level, a slab-gap model (20Å slab, 20Å vacuum) was constructed and the corresponding electrostatic potential averaged along the c-direction, using the MacroDensity package (Fig. 2). 60-62 HSE06 + SOC has previously been shown to provide accurate ionisation potentials for similar systems, 63 however, the large size of the surfaces precluded its use in this study. Instead the slab calculations were performed using the HSE06 functional with a correction for the valence band energy and band gap, taken from the HSE06 + SOC calculated bulk. The energy of the potential at the plateau was used as the external vacuum level when aligning the core-level eigenvalues. Based on similar work into SbSI, the (110) surface was chosen as it did not produce any dangling bonds and resulted in a low energy, nonpolar termination.

Geometry
BiSI and BiSeI both crystallise in the same structure as SbSI (space group Pnma), in which BiChI ribbons resulting from distorted edge-sharing pseudo-octahedra are formed from 3 Bi-Ch and 2 Bi-I bonds, with a vacant site occupied by the Bi lone pair. 30,40 Two Bi-Ch bonds lengths are observed depending on whether the bonds are parallel (Bi-Ch k ) or perpendicular (Bi-Ch t ) to the ribbons shown in Fig. 1b. The effect of functional on geometry optimisation was tested, with the full results provided in Table S1 of the ESI. † The PBEsol functional (without the inclusion of Grimme's dispersion) best reproduced the experimental lattice parameters and bond distances (within 1%, Table 1). In both BiSI and BiSeI, the a and b parameters were underestimated suggesting thermal effects will play a role in the structure, most likely in determining the distance between ribbons.

Electronic structure
The band structures of BiSI and BiSeI are presented in Fig. 3a and c. The effect of spin orbit coupling was tested, with the results provided in Fig. S1 of the ESI. † In both cases, the relativistic renormalisation of the conduction band was found to be over 0.6 eV, highlighting the importance of including spin orbit effects in modelling these systems. The band structures show broadly the same features, with the main difference being the position of the band edges. In BiSI, the valence band maximum (VBM) and CBM occur between Y-G and G-Z, respectively, whereas in BiSeI, the VBM occurs between G-Z and the CBM is situated at G. The calculated band gaps for BiSI and BiSeI are 1.78 eV and 1.50 eV, respectively and are noticeably overestimated compared to experiment (1.57 eV and 1.29 eV for BiSI and BiSeI), which is likely due to the absence of thermal effects, including lattice expansion and electron-phonon coupling, when performing the calculations. The band gaps are both indirect (E i g ), as expected of group 15 chalcohalide semiconductors, 65,66 however, as the direct band gap (E d g ) is more relevant for thin lm solar absorbers, due to the requirement for high absorption coefficients (vertical optical transitions), it is provided in Table 2. The difference between the direct and indirect band gaps is only $0.1 eV, indicating that these materials are still suitable for thin lm photovoltaic applications.
The partial (ion decomposed) density of states (DOS) are shown in Fig. 3b and d. The overall shape of the states is similar in both cases, with the main difference being the increase in energy of the of Se p orbital which acts to raise the VBM. The VBM is formed from mixing of I and S/Se p states with some and Bi s and p states, whilst the CBM is dominated by Bi p states with contributions from the I and S/Se p orbitals, similar to in other group 15 chalcohalide semiconductors. 56 The contribution of the Bi states to the VBM can be accounted for by the Bi lone pair. Like many of the heavier metals in groups 13 to 16, the stability of the d 10 s 2 p 0 electronic conguration means Bi prefers to adopt a valence state two lower than its group valence. Classical lone pair theory predicts   27 It has recently been suggested that these anti-bonding states help to ensure that dangling bonds, formed upon vacancy formation, will appear as resonances in the valence bands, signicantly improving point defect tolerance. 70,71 If these anti-bonding states contain a substantial cation s contribution, they can mix with unoccupied cation p states at the top of the valence band, resulting in a signicant stabilisation effect. It is this interaction which produces the asymmetric electron density responsible for the distortion of the pseudo-octahedra. [72][73][74] This effect is primarily mediated by the relative energies of the cation s and anion p states, as states closer in energy will increase the cation s contribution at the top of the valence band and result in stronger lone pairs. 27 As such, the lone pair effect is most prominent in oxides and lessens down the chalcogen group. A further reduction in lone pair strength is seen in Bi compounds due to the reduction in energy of the Bi 6 s states due to the scalar-relativistic contraction of the s-shell. 27,75 Consequently, BiSI and BiSeI possess lone pairs that are relatively diffuse, as evidenced by the charge density isosurfaces presented in Fig. 4, which show low electron density around the Bi ions at the top of the valence band. The strength of the lone pair is also indicated by the degree of pseudo-octahedral distortion in the lattice and can be calculated as the average deviation in the bond angles of the BiChI pseudooctahedra from the ideal angle of 90 , s oct . As expected, the distortion is seen to decrease when moving from BiSI to BiSeI, from 7.49 to 6.61 , respectively. We note that this distortion is Fig. 3 (a and c) Band structures along the high symmetry directions, and (b and d) ion decomposed partial and total density of states, for BiSI and BiSeI, respectively. In all cases the valence band maximum is set to zero eV. The valence bands and conduction bands of (a and c) are denoted by blue and orange respectively.  35.8 signicantly less than in materials with strongly stereoactive lone pairs, such as Sb 2 O 3 (s oct ¼ 21.82 ). 76 The effective masses of the CBM (m * e ) and VBM (m * h ) are given in Table 2, with the Brillouin zone for the Pnma space group, illustrating the relevant high symmetry points, provided in Fig. S3 of the ESI. † It is clear that conductivity will be highly anisotropic, with large values of m * e observed between G and Z (along [001]), reecting the weak bonding interactions between the [(BiChI) N ] 2 ribbons. The electron effective masses along the 1D ribbons (G / Y, along [100]) are signicantly smaller, suggesting that controlled growth of vertically oriented crystals has the potential to increase carrier mobilities. The smallest electron effective mass appears in BiSeI, in the direction from G to Y (0.51m 0 ). In BiSI the smallest electron effective mass is from the CBM toward Z (0.69 m e ). Hole effective masses are small in both cases (slightly larger in BiSI, due to the reduced dispersion of the VBM), indicating that holes should be mobile in this system, at variance with the small hole diffusion lengths observed experimentally in BiSI. 43 Furthermore, we note that similar to MAPI, 44 the hole effective masses are lower than the electron effective masses, likely resulting from the s antibonding orbital composition of the VBM. In both cases, the effective masses are similar to other bismuth based absorbers, such as BiI 3 (3 r ) and are increasingly considered a crucial factor in the high performance of hybrid perovskites. 24,44,79 A higher dielectric constant indicates an increased ability to screen charge and plays an important role in the charge capture cross-section of defects, with large constants resulting in smaller cross sections and, in turn, decreased scattering and recombination rates. 80 Furthermore, for simple 'hydrogenic' defects, lower dielectric constants result in larger defect binding energies (within effective mass theory, E b ¼ m * e / 23 r 2 ) 44,81 and, as a result, deeper defect states. The dielectric constants of BiSI and BiSeI were calculated to be 36.8 and 35.8, respectively. These are smaller than in MAPI (oen 60-70 or higher due to contributions from the organic cation) 45,82 but signicantly larger than other third-generation solar absorbers such as CZTS ($10). 83 As such, this combination of relatively large dielectric constants and low effective masses is expected to promote effective ionization of defect states, leading to fewer trap states deep in the band gap. 84 The calculated band alignments of BiSI and BiSeI are shown in Fig. 5. The valence band energies (ionisation potentials, IPs) of BiSI and BiSeI were found to be 6.4 eV and 6.2 eV below the vacuum level, respectively, and are noticeably larger than most other commonly used solar absorbers. 44,62,91 From the alignments it is apparent that the reduction in band gap from BiSI to BiSeI occurs due to a decrease in the IP of BiSeI, with concomitant lowering of the conduction band minimum relative to the vacuum level (an increase in the electron affinity, EA). The band alignments obtained experimentally by Hahn et al. are also included in Fig. 5, and show an increase in the IP upon doping with Se, from 6.1 AE 0.2 eV in BiSI to 6.3 AE 0.2 in BiSeI. 42 This downwards shi of the valence band maximum is unexpected as the increase in valence p orbital energy down the chalcogen group typically results in a higher valence band maximum upon anion substitution, as observed in CdS 1Àx Se x , 92 CdSe x Te 1Àx , 93 and Cu 2 ZnSn(S,Se) 4 . 94 The authors note, however, that this anomalous shi is likely the result of BiOI contamination on the surface of their samples. 42 The band alignments for a range of hole transporting materials and n-type transparent conducting oxides are also shown in    85,86 As such, a hole transporting material with a lower valence band maximum, such as poly(uorene-2,7-diyl) (F8, IP ¼ 5.7 eV), 87 is necessary to maximise the open-circuit voltage of the p-n junction and increase device efficiencies. Conversely, the conduction band minimum of FTO (EA x 4.4 eV) 88 occurs above the conduction band minimum of BiSI and BiSeI (EA ¼ 4.9 eV and 5.0 eV, respectively), indicating that there will be poor transfer of electrons to the window layer. A material with a larger electron affinity, such as indium tin oxide (ITO, EA x 5.2 eV) 89,90 or lead-doped tin oxide (Pb:SnO 2 , EA x 5.0 eV), 95 should therefore be used to promote efficient transport of photo-generated electrons. We note that our analysis only takes into account the fundamental band alignments and does include any effects arising from interfacial strain or chemical interactions occurring at the interface. Nonetheless, the need for developing new contact materials is clear.

Conclusions
We have demonstrated, using rst-principles relativistic electronic structure theory, that BiSI and BiSeI possess suitable electronic structures for solar energy applications, with only a small difference between the direct and indirect band gaps and low electron effective masses in the direction along the BiChI chains. Additionally, the presence of antibonding states at the top of the valence band, coupled with high dielectric constants, is expected to provide a high level of defect tolerance ideal for efficient solar absorbers. Previously, devices containing these materials have performed poorly, this is in part due to the 1D nature of the ribbon structure, which should be vertically oriented on the device in order to provide clear conduction pathways. Additionally, the large electron affinity of these materials (>4.9 eV) results in band misalignments with commonly used electron transport materials and, as such, we have suggested alternatives that are likely to increase device efficiencies.