The complex defect chemistry of antimony selenide

Antimony selenide, Sb2Se3, is a highly promising solar absorber material with excellent optoelectronic properties; solar cell efficiencies are now poised to exceed 10%, after a rapid rise over the past few years. However, the open-circuit voltage (Voc) of most cells remains low, and such a high Voc deficit, along with defect spectroscopy studies, suggest that recombination via deep trap states may be a limiting factor. A comprehensive study of all the intrinsic defects in Sb2Se3 is warranted – in this article, we calculate the formation energies and transition levels of these defects using hybrid Density Functional Theory. Our results demonstrate that cation–anion antisite defects have low formation energies, and possess multiple mid-gap transition levels, making them the most likely candidates for previously observed trap states, and possible recombination centres. Suppressing these dominant defects will be crucial for future cell development – thus we also present potential methods to counteract their detrimental effects and allow further improvement in efficiencies.


Introduction
Photovoltaics (PV) have developed over the past few decades as one of the most promising sustainable energy generation technologies available, and as the cost of cells and modules continues to decrease, parity in $ per W with fossil fuels at utility scale becomes ever more achievable. 1 Still, alternative architectures beyond traditional silicon-based panels, such as building-integrated PV or exible devices, as well as diversication of materials should be considered to further enable widespread usage of photovoltaics in the future. Established thin-lm technologies such as CdTe and Cu(In, Ga)Se 2 are well situated to be used in such devices, 2 however the drawbacks of scarcity and expense (for In and Te) or toxicity (Cd) remain concerns for large-scale deployment. As such, emergent thin lm solar absorbers remain of signicant scientic and economic interest. 3 Antimony selenide, Sb 2 Se 3 , possesses a number of optimal properties for use as a solar absorber: a near-ideal 1.2 eV to 1.3 eV band gap, strong optical absorption, a binary stoichiometry (simplifying synthesis), and its pseudo-one-dimensional crystal structure has been proposed to demonstrate signicantly reduced grain-boundary recombination in comparison with traditional absorbers due to a lack of dangling bonds. 4 Prior theoretical calculations have reaffirmed the optimal band gap and absorption, 5,6 while calculation of thin-lm efficiency metrics have demonstrated particularly high and promising values for Sb 2 Se 3 , even for very thin layers of material. 7,8 Prior to the past few years, Sb 2 Se 3 was most of interest for use in 'extremely thin absorber' (ETA) cells, as a sensitizer to TiO 2 , however efficiencies remained near 3%. [9][10][11][12] Over the past ve years, however, creation of heterojunction cells, with careful control of growth conditions to align the Sb 2 Se 3 chains perpendicular to the substrate, and optimization of the junction interface has rapidly improved cell performance, with a recently published record efficiency of 9.2%, 13 cementing it as a highly promising PV material. Additionally, as devices fabricated using techniques such as closed-space sublimation (CSS) or rapid thermal evaporation (RTE) that retain efficiencies above 5% further demonstrate the potential scalability of the technology. 4,8,14 Nevertheless, a common theme through both ETA and heterojunction Sb 2 Se 3 cells has been a relatively large V oc decit: despite its 1.3 eV optimal band gap, many cells demonstrate V oc below 0.4 V 4,15 and the record published V oc is 0.45 V. 8 If Sb 2 Se 3 is to breach 10% efficiency and become a competitive solar absorber, this decit must be addressed: while some improvement is likely to be possible through choice of contacts, the possibility of deep defects enabling high levels of Shockley-Read-Hall (SRH) recombination is a signicant concern, especially in light of the detection of multiple trap states through Deep-level Transient Spectroscopy (DLTS), as published by Tang and coworkers. 16 Previous theoretical studies by Tumelero et al. 17 and Liu et al. 18 have examined the defect properties of the antimony chalcogenides, however they have done so using Density Functional Theory (DFT), employing standard functionals which require corrections to the band gap, and can also incorrectly describe the underlying defect physics, 19 and they do not include certain, crucial defects. In this article, we present theoretical defect calculations performed with hybrid DFT to enable a complete picture of the intrinsic defect chemistry of Sb 2 Se 3 , identify potential detrimental trap states, and discuss their implications for the future of the material as a solar absorber.

Computational methods
All calculations were performed using periodic density functional theory within the Vienna Ab Initio Simulation Package (VASP), using scalar relativistic PAW pseudopotentials. [20][21][22][23] The structure of Sb 2 Se 3 , as well as the elemental phases of Sb and Se, were relaxed using the HSE06 hybrid DFT functional, 24 with the addition of the D3 Grimme dispersion correction 25 to account for the interactions between the chains in the pseudo-1D structure of Sb 2 Se 3 . This method has been previously shown to give highly accurate structural properties in comparison with experiment, and also results in a predicted band gap that lies within 10 meV of a 0 K Varshni t to experimental measurements. 8,26 Defect calculations were also performed using the HSE06+D3 method on a 1 Â 3 Â 1 supercell (60 atoms) with a G centered 2 Â 2 Â 2 kpoint mesh and a plane-wave energy cutoff of 350 eV. All structures were optimized until the forces on each atom were below 0.02 eVÅ À1 . Spin-orbit coupling effects were not included in these calculations due to their expense and minimal structural effects; the relativistic renormalisation at the k-points considered is also small ($0.05 eV). A comprehensive description of the defect formation formalism is given in the ESI. † To account for the 'nite size effects' of the supercell and restore the dilute defect model, three corrections were used. Firstly, a correction is necessary to ensure that the electrostatic potential of the host and defect supercells are aligned. 27 Secondly, defects within supercells may interact with their own periodic images, causing the formation of a defect band; if this defect level is shallow, it may interact with a conduction or valence band, leading to erroneous lling with electrons and affecting the total energyto counteract this, a 'band lling' correction is applied. 28 Thirdly, charged defects may interact with each other coloumbically, due to the long range behaviour of such effects, and so a further 'image charge' correction is required. In this report, we use the formalism of Murphy et al., as this accounts for anisotropy in the dielectric constant of the material, an effect which is strong for Sb 2 Se 3 . 29 All transition levels are included in Tables 2 and 3 of the ESI, † and all optimized supercell structures are provided in an online repository (https://github.com/SMTG-UCL/Sb2Se3_intrinsic_defects). The VESTA program was used for the visualization and gures of the Sb 2 Se 3 crystal structure. 30

Results
Sb 2 Se 3 has no stable competing phases, and so its chemical potential space is solely bounded by the elements and its own formation enthalpy (À1.495 eV); the chemical potential (m) limits are thus given by the Sb-rich (A, m Sb ¼ 0 eV) and Se-rich (B, m Se ¼ 0 eV) extremes. The transition level (TL) diagrams of Sb 2 Se 3 , calculated using the HSE06+D3 method described in the Computational methods, are depicted for these two chemical potential limits in Fig. 2. Individual sites are marked by subscripts aer the atom label, and reference the positions marked in the labelled crystal structure depicted in Fig. 1. In both diagrams, it is clear that calculating defects for all possible sites is necessary, but especially for Se, as their behaviour can differ signicantlythis can be rationalised by the very different local environments for each Se position. Under Sb-rich conditions, there are numerous defects with formation energies under 1.5 eV, and thus are likely to be present in the sample in reasonable concentrations, including V Se (all sites), Sb Se (all sites) and the Sb interstitial. In this instance, the dominant defects are V Se,2 and Sb Se,1 , which will compensate each other at a Fermi level $0.58 eV above the valence band maximum (VBM), and pin the Fermi level at that point. At this position, all of the above defects will be present, and all possess deep transition levels: all three V Se , regardless of site, act as deep donors (as also seen in both PBE studies) 17,18 while all three Sb Se are amphoteric, with the (+1/À1) transition level of Sb Se,1 and (+3/À1) of Sb Se,3 standing out as a possible trap states for both holes and electrons. This amphoteric behaviour was not explored in either of the previous studies, yet appears to be crucial to the understanding of this defectboth in its potential pinning effect on the Fermi level, and with a mid-gap transition level, possibility to act as a site of efficient SRH recombination.
In the Se-rich regime, however, many of these previously problematic defects are moved to higher formation energies. While the neutral charge states of both V Sb remain high in formation energy, the À3 charge states are relevant elsewhere in the Fermi level rangethey intercept the +1 charge states for each Se Sb antisite in the middle of the gap; again these will act to compensate each other and likely pin the Fermi level mid-gap ($0.62 eV above the VBM). For this Fermi level position, far fewer defects have a formation energy below 1.5 eV: only the Se Sb and V Sb already noted, in addition to the Se interstitial. Of these, Se i has multiple transition levels deep within the band gap, that could plausibly act as hole or electron traps. V Sb acts as a deep acceptor, with all transition levels lying close to, but further than 0.025 eV from, the VB edge; the separation by site reveals that the À2 and À1 charge states are stabilised for V Sb,2 , which has a more regular coordination environment, compared to V Sb,1 , where only the (À3/0) transition level is observed. Both Se Sb defects however, are amphoteric, with an ultra-deep (+1/ À1) transition level; lying in the middle of the gap, these are particularly likely to act as recombination centres, as they will likely have similar carrier capture cross-sections for both electrons and holes, and thus are potentially highly detrimental to photovoltaic performance.
To attempt to validate some of these results, we can compare the positions of these expected trap states with those found in a recent DLTS study of Tang and co-workers on cells produced by RTE and vapour transport deposition; 16 in both cases, the traps were observed to appear in similar positions albeit with different densities. Comparing to the vapour transport deposition values rst, the two hole traps lie at 0.48 AE 0.07 eV and 0.71 AE 0.02 eV above the valence band maximumthese align almost exactly with our calculated HSE06+D3 (+1/À1) TLs of Sb Se,1 (VBM + 0.494 eV) and Se Sb,2 (VBM + 0.697 eV) respectively. A similar agreement is found with the RTE-synthesised cell DLTS values too (the hole traps lying at 0.49 AE 0.03 eV and 0.74 AE 0.04 eV above the valence band maximum) and these are represented pictorially in the Fig. 3. A recent study found that variation of ionization energies with temperature can cause disparities between defect transition levels and the actual likely activation energies seen in experimental DLTS studies in GaN (highly dependent on the defect itselffor 300 K, a variation of $60 meV was seen for V Ga -O N -2H, while a signicant $250 meV shi was seen for C N ), 31 and as such this agreement between our simulations and DLTS could be fortuitous. In both prior, PBE-based defect studies of Sb 2 Se 3 , however, no transition levels align well with these DLTS levels, even considering a large temperature effect (neither study gives a possible hole trap within 0.3 eV of the 0.71 eV hole trap position, and the closest transition levels are at least 0.1 eV from the rst hole trap)this does seem to demonstrate the necessity for a hybrid functional, as well as a comprehensive study of all possible charge states to properly describe the material's complex defect chemistry. A recent study has found that even hybrid DFT energies, if based on defect geometries relaxed using standard DFT functionals, can lead to signicant uncertainty in the defect level. 19 For the electron trap (E1), a further level of uncertainty is introduced through the renormalization of the conduction band position with temperaturehowever, using the calculated gap of 1.300 eV for the position of the conduction band minimum (CBM) the trap (0.61 AE 0.03 eV below the CBM) is predicted to lie at essentially the same position as the second hole trap (H2), and as an amphoteric defect, Se Sb,2 (CBM -0.603 eV) is the most likely candidate for this trap also. The proposition that these may in fact be the same defect state is not too unlikelyits position near the middle of the gap could lead to very similar capture cross-sections for both holes and electrons, 32 and E1 and H2 were found to have similar concentrations to each other for both sampled cells. While it is clear further validation may be necessary, both cation-anion and anion-cation intrinsic antisites seem to be the strongest candidates for the trap states in Sb 2 Se 3 , given our calculations.

Discussion
The identication of potential recombination centres at both chemical potential limits has implications not only for the use of Sb 2 Se 3 as a solar absorber but also other applications that might utilise its high absorption, but also need specic purity, such as radiation detection. The detrimental effect of these trap states could be alleviated, however, by targeted passivation: an analogy might be made to another popular, earth abundant solar absorber, Cu 2 ZnSnS 4 (CZTS), which had plateaued in efficiency due to a large V oc decitwhich some studies have related partly to intrinsic antisite defects or cation disorder, with varying reports of Cu Zn , Cu Sn or Sn Zn . [33][34][35] Some improvement in CZTS cells has been observed, however, through targeted doping with Na, suppressing the effect of intrinsic defects, and increasing carrier lifetimes. [36][37][38] For Sb 2 Se 3 , a possible strategy may be to favour Se-rich synthesis or treatments, combined with extrinsic doping on the Sb sites to suppress the formation of Se Sb defects.
Alternatively, we might note that the multiple deep acceptors and donors in both chemical potential limits suggest that Sb 2 Se 3 will resist signicant p or n-type doping, and that a more effective cell may be possible through synthesising Sb 2 Se 3 as close to stoichiometry as possible, resulting in a compromise that maximises the formation of both antisite defects, and forming a p-i-n architecture with Sb 2 Se 3 as an intrinsic layer. In this case, efforts may be necessary to nd optimal contact materials to account for the limited accessible range in Fermi level.
As well as their potential impact on the photovoltaic behaviour of Sb 2 Se 3 , the presence of low formation energy, deep antisite defects bears discussion within the wider context of  16 Green bars represent the hole traps, and orange represents the electron trap, and the defect labels are identical to those in Fig. 2. The diagram is plotted at the Se-rich chemical potential limit, in accordance with Wen et al.'s expected synthesis conditions, however the actual chemical potential conditions during synthesis are difficult to determine and likely to be closer to stoichiometry than our extreme limitsas such, the formation energies are only loosely considered when identifying the trap states. defects in functional energy materials. With the rise of the hybrid lead halide perovskites in PV, a number of publications have discussed the topic of 'defect tolerance' [39][40][41] in semiconductors, whereby materials are resistant to the formation of defects within them, or that such defects' detrimental effects are minimised. Some studies have directly linked defect tolerance with an electronic structure that has a VBM of antibonding character 39,40 (demonstrated in materials with ns 2 'lone pair' cations such as Pb 2+ , Sb 3+ or Bi 3+ ) 42-45 and a high dielectric constant. In our previous work, we found Sb 2 Se 3 to possess both of these characteristic properties, 8 however this study, along with the V oc decit in cells, suggests that Sb 2 Se 3 is far from defect tolerant. This is consistent with recent research suggesting that defect tolerance has signicant dependence on other factors, such as crystal structure and cation valence. 46,47 On the other hand, from a chemist's point of view, the presence of such cation-anion antisites in Sb 2 Se 3 is perhaps not surprisingthe amphoteric, 'so' chemical behaviour of both antimony and selenium is well known, and thus the relative stability of such antisites, and multiple charge states therein, might naively be expected to be possible. Indeed, previous studies in the chemically-related bismuth tetradymite structures (Bi 2 Se 3 , Bi 2 Se 2 Te) found that cation-anion antisite defects were also low in formation energy and could act as limits to performance. 48 Regardless, it is clear that close investigation of the defect behaviour of Sb 2 Se 3 is necessary for its future usage in energy applications.

Conclusions
In this study, we have calculated the intrinsic defects in the candidate solar absorber Sb 2 Se 3 using hybrid Density Functional Theory and including all defect sites to attempt to perform a complete assessment of its defect behaviour. We have found that, regardless of chemical potential limit, there will be low formation energy cation-anion anisite defects with mid-gap transition levels that could act as recombination centres. By noting the alignment of our calculated transition levels with published DLTS results, we propose that these Se Sb and Sb Se defects are most likely to be the trap states present in devices, and the potential barrier to improving device efficiencies. In order for Sb 2 Se 3 to further improve as a useful optoelectronic material, it is critical that these defects must be suppressed, perhaps through targeted passivation by extrinsic dopants.

Conflicts of interest
There are no conicts of interest to declare.