The complex defect chemistry of antimony selenide

Abstract

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 (V_oc) of most cells remains low, and such a high V_oc 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.

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1 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 flexible devices, as well as diversification of materials should be considered to further enable widespread usage of photovoltaics in the future. Established thin-film technologies such as CdTe and Cu(In, Ga)Se₂ 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 film solar absorbers remain of significant scientific and economic interest.³

Antimony selenide, Sb₂Se₃, 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 significantly 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-film efficiency metrics have demonstrated particularly high and promising values for Sb₂Se₃, even for very thin layers of material.^7,8 Prior to the past few years, Sb₂Se₃ was most of interest for use in ‘extremely thin absorber’ (ETA) cells, as a sensitizer to TiO₂, however efficiencies remained near 3%.^9–12 Over the past five years, however, creation of heterojunction cells, with careful control of growth conditions to align the Sb₂Se₃ 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 Sb₂Se₃ cells has been a relatively large V_oc deficit: 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 Sb₂Se₃ is to breach 10% efficiency and become a competitive solar absorber, this deficit 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 significant concern, especially in light of the detection of multiple trap states through Deep-level Transient Spectroscopy (DLTS), as published by Tang and co-workers.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 Sb₂Se₃, identify potential detrimental trap states, and discuss their implications for the future of the material as a solar absorber.

2 Computational methods

All calculations were performed using periodic density functional theory within the Vienna Ab Initio Simulation Package (VASP), using scalar relativistic PAW pseudopotentials.^20–23 The structure of Sb₂Se₃, 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 correction²⁵ to account for the interactions between the chains in the pseudo-1D structure of Sb₂Se₃. 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 fit to experimental measurements.^8,26 Defect calculations were also performed using the HSE06+D3 method on a 1 × 3 × 1 supercell (60 atoms) with a Γ centered 2 × 2 × 2 k-point mesh and a plane-wave energy cutoff of 350 eV. All structures were optimized until the forces on each atom were below 0.02 eV Å⁻¹. 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 ‘finite 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 filling with electrons and affecting the total energy – to counteract this, a ‘band filling’ 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 Sb₂Se₃.²⁹ 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 figures of the Sb₂Se₃ crystal structure.³⁰

3 Results

Sb₂Se₃ has no stable competing phases, and so its chemical potential space is solely bounded by the elements and its own formation enthalpy (−1.495 eV); the chemical potential (μ) limits are thus given by the Sb-rich (A, μ_Sb = 0 eV) and Se-rich (B, μ_Se = 0 eV) extremes. The transition level (TL) diagrams of Sb₂Se₃, 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 after 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 significantly – this 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/−1) transition level of Sb_Se,1 and (+3/−1) 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 defect – both 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.

Fig. 1 Crystal structure of Sb₂Se₃, with individual site labels. Antimony atoms are depicted in gold and selenium in light green.

Fig. 2 Defect transition level diagram for Sb₂Se₃ under limiting chemical potential conditions ((A) Sb-rich; (B) Se-rich), plotting defect formation energy (eV) against position of Fermi level above the VBM. Defect labels are given in the legend, charge states are given by labels adjacent to lines, with lines of the same slope representing the same charge state, and transition levels are represented by the filled dots.

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 −3 charge states are relevant elsewhere in the Fermi level range – they 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 −2 and −1 charge states are stabilised for V_Sb,2, which has a more regular coordination environment, compared to V_Sb,1, where only the (−3/0) transition level is observed. Both Se_Sb defects however, are amphoteric, with an ultra-deep (+1/−1) 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 first, the two hole traps lie at 0.48 ± 0.07 eV and 0.71 ± 0.02 eV above the valence band maximum – these align almost exactly with our calculated HSE06+D3 (+1/−1) 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 ± 0.03 eV and 0.74 ± 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 itself – for 300 K, a variation of ∼60 meV was seen for V_Ga–O_N–2H, while a significant ∼250 meV shift 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 Sb₂Se₃, 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 first 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 significant 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 temperature – however, using the calculated gap of 1.300 eV for the position of the conduction band minimum (CBM) the trap (0.61 ± 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 unlikely – its 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 Sb₂Se₃, given our calculations.

Fig. 3 Defect transition level diagrams for Sb₂Se₃ with the position of the DLTS trap levels recorded by Wen et al. for (a) a VTD-synthesised and (b) a RTE-synthesised cell marked on, with the experimental uncertainty given by the bar width.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 limits – as such, the formation energies are only loosely considered when identifying the trap states.

4 Discussion

The identification of potential recombination centres at both chemical potential limits has implications not only for the use of Sb₂Se₃ as a solar absorber but also other applications that might utilise its high absorption, but also need specific 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, Cu₂ZnSnS₄ (CZTS), which had plateaued in efficiency due to a large V_oc deficit – which some studies have related partly to intrinsic antisite defects or cation disorder, with varying reports of Cu_Zn, Cu_Sn or Sn_Zn.^33–35 Some improvement in CZTS cells has been observed, however, through targeted doping with Na, suppressing the effect of intrinsic defects, and increasing carrier lifetimes.^36–38 For Sb₂Se₃, 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 Sb₂Se₃ will resist significant p or n-type doping, and that a more effective cell may be possible through synthesising Sb₂Se₃ 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 Sb₂Se₃ as an intrinsic layer. In this case, efforts may be necessary to find optimal contact materials to account for the limited accessible range in Fermi level.

As well as their potential impact on the photovoltaic behaviour of Sb₂Se₃, the presence of low formation energy, deep antisite defects bears discussion within the wider context of 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’^39–41 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 ns² ‘lone pair’ cations such as Pb²⁺, Sb³⁺ or Bi³⁺)^42–45 and a high dielectric constant. In our previous work, we found Sb₂Se₃ to possess both of these characteristic properties,⁸ however this study, along with the V_oc deficit in cells, suggests that Sb₂Se₃ is far from defect tolerant. This is consistent with recent research suggesting that defect tolerance has significant 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 Sb₂Se₃ is perhaps not surprising – the amphoteric, ‘soft’ 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 (Bi₂Se₃, Bi₂Se₂Te) 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 Sb₂Se₃ is necessary for its future usage in energy applications.

5 Conclusions

In this study, we have calculated the intrinsic defects in the candidate solar absorber Sb₂Se₃ 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 Sb₂Se₃ 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 conflicts of interest to declare.

Acknowledgements

The authors would like to thank Dr Ben Williamson and Dr John Buckeridge for useful discussions. The authors acknowledge the use of the UCL Legion and Grace High Performance Computing Facility (Legion@UCL and Grace@UCL) in the production of this work. This work was also performed on the ARCHER UK National Supercomputing Service, via our membership of the UK's HEC Materials Chemistry Consortium, funded by EPSRC (EP/L000202). CNS is grateful to the Department of Chemistry at UCL for the provision of a DTA studentship (ref no. 1492829). DOS acknowledges support from the SUPERSOLAR Solar Energy Hub (EP/J017361/1), EPSRC (EP/N01572X/1), and membership of the Materials Design Network.

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Footnote

† Electronic supplementary information (ESI) available: Lattice parameter comparison, theoretical defect formalism, thermodynamic transition levels. See DOI: 10.1039/c9ta02022e

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