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Lead-halide perovskites (LHPs) have shot to prominence as efficient energy conversion materials that can be processed using cost-effective fabrication methods. A widely-quoted reason for their exceptional performance is their ability to tolerate defects, enabling long charge-carrier lifetimes despite high defect densities. Realizing defect tolerance in broader classes of materials would have a substantial impact on the semiconductor industry. Significant effort has been made over the past decade to unravel the underlying origins of defect tolerance to design stable alternatives to LHPs comprised of nontoxic elements. However, it has become clear that understanding defect tolerance in LHPs is far from straightforward. This review discusses the models proposed for defect tolerance in halide perovskites, evaluating the experimental and theoretical support for these models, as well as their limitations. We cover attempts to apply these models to identify materials beyond the lead-halide system that could also exhibit defect tolerance, and the successes and pitfalls encountered over the past decade. Finally, a discussion is made of some of the important missing pieces of information required for a deeper understanding and predictive models that enable the inverse design of defect tolerant semiconductors., Comment: 64 pages, 4 figures, 3 boxes, 1 table

The structures and properties of organic-inorganic perovskites are influenced by the hydrogen bonding between the organic cations and the inorganic octahedral networks. This study explores the dynamics of hydrogen bonds in CH$_3$NH$_3$PbBr$_3$ across a temperature range from 70 K to 350 K, using molecular dynamics simulations with machine-learning force fields. The results indicate that the lifetime of hydrogen bonds decreases with increasing temperature from 7.6 ps (70 K) to 0.16 ps (350 K), exhibiting Arrhenius-type behaviour. The geometric conditions for hydrogen bonding, which include bond lengths and angles, maintain consistency across the full temperature range. The relevance of hydrogen bonds for the vibrational states of the material is also evidenced through a detailed analysis of the vibrational power spectra, demonstrating their significant effect on the physical properties for this class of perovskites., Comment: 26 pages, 14 figures

Empirical A-site cation substitution has advanced the stability and efficiency of hybrid organic-inorganic lead halide perovskites solar cells and the functionality of X-ray detectors. Yet, the fundamental mechanisms underpinning their unique performance remain elusive. This multi-modal study unveils the link between nanoscale structural dynamics and macroscopic optoelectronic properties in these materials by utilising X-ray diffuse scattering, inelastic neutron spectroscopy and optical microscopy complemented by state-of-the-art machine learning-assisted molecular dynamics simulations. Our approach uncovers the presence of dynamic, lower-symmetry local nanodomains embedded within the higher-symmetry average phase in various perovskite compositions. The properties of these nanodomains are tunable via the A-site cation selection: methylammonium induces a high density of anisotropic, planar nanodomains of out-of-phase octahedral tilts, while formamidinium favours sparsely distributed isotropic, spherical nanodomains with in-phase tilting, even when crystallography reveals cubic symmetry on average. The observed variations in the properties of dynamic nanodomains are in agreement with our simulations and are directly linked to the differing macroscopic optoelectronic and ferroelastic behaviours of these compositions. By demonstrating the influence of A-site cation on local nanodomains and consequently, on macroscopic properties, we propose leveraging this relationship to engineer the optoelectronic response of these materials, propelling further advancements in perovskite-based photovoltaics, optoelectronics, and X-ray imaging., Comment: Main text and supplementary information. Main text 16 pages, 4 figures. Supplementary information 42 pages, 36 figures

Two-dimensional hybrid organic-inorganic metal halide perovskites offer enhanced stability for perovskite-based applications. Their crystal structure's soft and ionic nature gives rise to strong interactions between charge carriers and ionic rearrangements. Here, we investigate the interaction of photo-generated electrons and ionic polarizations in single-crystal 2D perovskite butylammonium lead iodide, varying the inorganic lammelae thickness in the 2D single crystals. We determined the directionality of the transition dipole moments of the relevant phonon modes (in the 0.3-3 THz range) by angle-and-polarization dependent THz transmission measurements. We find a clear anisotropy of the in-plane photoconductivity, with a 10% reduction along the axis parallel with the transition dipole moment of the most strongly coupled phonon. Detailed calculations, based on Feynman polaron theory, indicate that the anisotropy originates from directional electron-phonon interactions., Comment: 50 pages, 5 figures main text, 13 figures in supplementary information

Solid-state sodium batteries require effective electrolytes that conduct at room temperature. The Na$_3$SbS$_4$ (Pn = P, Sb; Ch = S, Se) family have been studied for their high Na ion conductivity. The population of Na vacancies, which mediate ion diffusion in these materials, can be enhanced through aliovalent doping on the pnictogen site. To probe the microscopic role of extrinsic doping, and its impact on diffusion and phase stability, we trained a machine learning force field for Na$_{3-x}$W$_{x}$Sb$_{1-x}$S$_4$ based on an equivariant graph neural network. Analysis of large-scale molecular dynamics trajectories shows that an increased Na vacancy population stabilises the global cubic phase at lower temperatures with enhanced Na ion diffusion, and that the explicit role of the substitutional W dopants is limited. In the global cubic phase we observe large and long-lived deviations of atoms from the averaged symmetry, echoing recent experimental suggestions. Evidence of correlated Na ion diffusion is also presented that underpins the suggested superionic nature of these materials.

Crystal structures are indispensable across various domains, from batteries to solar cells, and extensive research has been dedicated to predicting their properties based on their atomic configurations. However, prevailing Crystal Structure Prediction methods focus on identifying the most stable solutions that lie at the global minimum of the energy function. This approach overlooks other potentially interesting materials that lie in neighbouring local minima and have different material properties such as conductivity or resistance to deformation. By contrast, Quality-Diversity algorithms provide a promising avenue for Crystal Structure Prediction as they aim to find a collection of high-performing solutions that have diverse characteristics. However, it may also be valuable to optimise for the stability of crystal structures alongside other objectives such as magnetism or thermoelectric efficiency. Therefore, in this work, we harness the power of Multi-Objective Quality-Diversity algorithms in order to find crystal structures which have diverse features and achieve different trade-offs of objectives. We analyse our approach on 5 crystal systems and demonstrate that it is not only able to re-discover known real-life structures, but also find promising new ones. Moreover, we propose a method for illuminating the objective space to gain an understanding of what trade-offs can be achieved., Comment: Accepted GECCO 2024

Defects are a universal feature of crystalline solids, dictating the key properties and performance of many functional materials. Given their crucial importance yet inherent difficulty in measuring experimentally, computational methods (such as DFT and ML/classical force-fields) are widely used to predict defect behaviour at the atomic level and the resultant impact on macroscopic properties. Here we report doped, a Python package for the generation, pre-/post-processing, and analysis of defect supercell calculations. doped has been built to implement the defect simulation workflow in an efficient and user-friendly -- yet powerful and fully-flexible -- manner, with the goal of providing a robust general-purpose platform for conducting reproducible calculations of solid-state defect properties.

The identification of materials with exceptional properties is an essential objective to enable technological progress. We propose the application of \textit{Quality-Diversity} algorithms to the field of crystal structure prediction. The objective of these algorithms is to identify a diverse set of high-performing solutions, which has been successful in a range of fields such as robotics, architecture and aeronautical engineering. As these methods rely on a high number of evaluations, we employ machine-learning surrogate models to compute the interatomic potential and material properties that are used to guide optimisation. Consequently, we also show the value of using neural networks to model crystal properties and enable the identification of novel composition--structure combinations. In this work, we specifically study the application of the MAP-Elites algorithm to predict polymorphs of TiO$_2$. We rediscover the known ground state, in addition to a set of other polymorphs with distinct properties. We validate our method for C, SiO$_2$ and SiC systems, where we show that the algorithm can uncover multiple local minima with distinct electronic and mechanical properties.

Antimony selenide (Sb2Se3) is at the forefront of an emerging class of sustainable photovoltaic materials. Despite notable developments over the past decade, the light-to-electricity conversion efficiency of Sb2Se3 has reached a plateau of ~10%. Is this an intrinsic limitation of the material or is there scope to rival the success of metal halide perovskite solar cells? Here we assess the trap-limited conversion efficiency of Sb2Se3. First-principles defect analysis of the hole and electron capture rates for point defects demonstrates the critical role of vacancies as active recombination centres. We predict an upper limit of 25% efficiency in Sb2Se3 grown under optimal equilibrium conditions where the concentrations of charged vacancies are minimised. We further reveal how the detrimental effect of Se vacancies can be reduced by extrinsic oxygen passivation, highlighting a pathway to achieve high-performance metal selenide solar cells close to the thermodynamic limit.

Defects dictate the properties of many functional materials. To understand the behaviour of defects and their impact on physical properties, it is necessary to identify the most stable defect geometries. However, global structure searching is computationally challenging for high-throughput defect studies or materials with complex defect landscapes, like alloys or disordered solids. Here, we tackle this limitation by harnessing a machine-learning surrogate model to qualitatively explore the defect structural landscape. By learning defect motifs in a family of related metal chalcogenide and mixed anion crystals, the model successfully predicts favourable reconstructions for unseen defects in unseen compositions for 90% of cases, thereby reducing the number of first-principles calculations by 73%. Using CdSe$_x$Te$_{1-x}$ alloys as an exemplar, we train a model on the end member compositions and apply it to find the stable geometries of all inequivalent vacancies for a range of mixing concentrations, thus enabling more accurate and faster defect studies for configurational complex systems.

Inorganic semiconductors based on heavy pnictogen cations (Sb3+ and Bi3+) have gained significant attention as potential nontoxic and stable alternatives to lead-halide perovskites for solar cell applications. A limitation of these novel materials, which is being increasingly commonly found, is carrier localization, which substantially reduces mobilities and diffusion lengths. Herein, the layered p\v{r}\'ibramite CuSbSe2 is investigated and discovered to have delocalized free carriers, as shown through optical pump terahertz probe spectroscopy and temperature-dependent mobility measurements. Using a combination of theory and experiment, it is found that the underlying factors are: 1) weak coupling to acoustic phonons due to low deformation potentials, as lattice distortions are primarily accommodated through rigid inter-layer movement rather than straining inter-atomic bonds, and 2) weak coupling to optical phonons due to the ionic contributions to the dielectric constant being low compared to electronic contributions. This work provides important insights into how pnictogen-based semiconductors avoiding carrier localization could be identified., Comment: 47 pages, 4 figures

Photovoltaics (PVs) are a critical technology for curbing growing levels of anthropogenic greenhouse gas emissions, and meeting increases in future demand for low-carbon electricity. In order to fulfil ambitions for net-zero carbon dioxide equivalent (CO2eq) emissions worldwide, the global cumulative capacity of solar PVs must increase by an order of magnitude from 0.9 TWp in 2021 to 8.5 TWp by 2050 according to the International Renewable Energy Agency, which is considered to be a highly conservative estimate. In 2020, the Henry Royce Institute brought together the UK PV community to discuss the critical technological and infrastructure challenges that need to be overcome to address the vast challenges in accelerating PV deployment. Herein, we examine the key developments in the global community, especially the progress made in the field since this earlier roadmap, bringing together experts primarily from the UK across the breadth of the photovoltaics community. The focus is both on the challenges in improving the efficiency, stability and levelized cost of electricity of current technologies for utility-scale PVs, as well as the fundamental questions in novel technologies that can have a significant impact on emerging markets, such as indoor PVs, space PVs, and agrivoltaics. We discuss challenges in advanced metrology and computational tools, as well as the growing synergies between PVs and solar fuels, and offer a perspective on the environmental sustainability of the PV industry. Through this roadmap, we emphasize promising pathways forward in both the short- and long-term, and for communities working on technologies across a range of maturity levels to learn from each other., Comment: 160 pages, 21 figures

Defects determine many important properties and applications of materials, ranging from doping in semiconductors, to conductivity in mixed ionic-electronic conductors used in batteries, to active sites in catalysts. The theoretical description of defect formation in crystals has evolved substantially over the past century. Advances in supercomputing hardware, and the integration of new computational techniques such as machine learning, provide an opportunity to model longer length and time-scales than previously possible. In this Tutorial Review, we cover the description of free energies for defect formation at finite temperatures, including configurational (structural, electronic, spin) and vibrational terms. We discuss challenges in accounting for metastable defect configurations, progress such as machine learning force fields and thermodynamic integration to directly access entropic contributions, and bottlenecks in going beyond the dilute limit of defect formation. Such developments are necessary to support a new era of accurate defect predictions in computational materials chemistry.

The traditional display of elements in the periodic table is convenient for the study of chemistry and physics. However, the atomic number alone is insufficient for training statistical machine learning models to describe and extract composition-structure-property relationships. Here, we assess the similarity and correlations contained within high-dimensional local and distributed representations of the chemical elements, as implemented in an open-source Python package ElementEmbeddings. These include element vectors of up to 200 dimensions derived from known physical properties, crystal structure analysis, natural language processing, and deep learning models. A range of distance measures are compared and a clustering of elements into familiar groups is found using dimensionality reduction techniques. The cosine similarity is used to assess the utility of these metrics for crystal structure prediction, showing that they can outperform the traditional radius ratio rules for the structural classification of AB binary solids., Comment: 7 pages, 8 figures

Thermoelectric devices can directly convert waste heat into electricity, which makes them an important clean energy technology. The underlying materials performance can be evaluated by the dimensionless figure of merit ZT. Metal halides are attractive candidates due to their chemical flexibility and ease of processing; however, the maximum ZT realized (ZT = 0.15) falls far below the level needed for commercialization (ZT > 1). Using a first-principles procedure we assess the thermoelectric potential of copper halide CsCu2I3, which features 1D Cu-I connectivity. The n-type crystal is predicted to exhibit a maximum ZT of 2.2 at 600 K along the b-axis. The strong phonon anharmonicity of this system is shown by locally stable non-centrosymmetric Amm2 structures that are averaged to form the observed centrosymmetric Cmcm space group. Our work provides insights into the structure-property relations in metal halide thermoelectrics and suggests a path forward to engineer higher-performance heat-to-electricity conversion., Comment: 12 pages, 10 figures

Metal halide perovskites have shown extraordinary performance in solar energy conversion technologies. They have been classified as "soft semiconductors" due to their flexible corner-sharing octahedral networks and polymorphous nature. Understanding the local and average structures continues to be challenging for both modelling and experiments. Here, we report the quantitative analysis of structural dynamics in time and space from molecular dynamics simulations of perovskite crystals. The compact descriptors provided cover a wide variety of structural properties, including octahedral tilting and distortion, local lattice parameters, molecular orientations, as well as their spatial correlation. To validate our methods, we have trained a machine learning force field (MLFF) for methylammonium lead bromide (CH$_3$NH$_3$PbBr$_3$) using an on-the-fly training approach with Gaussian process regression. The known stable phases are reproduced and we find an additional symmetry-breaking effect in the cubic and tetragonal phases close to the phase transition temperature. To test the implementation for large trajectories, we also apply it to 69,120 atom simulations for CsPbI$_3$ based on an MLFF developed using the atomic cluster expansion formalism. The structural dynamics descriptors and Python toolkit are general to perovskites and readily transferable to more complex compositions., Comment: 10 figures

Building on the extensive exploration of metal oxide and metal halide perovskites, metal nitride perovskites represent a largely unexplored class of materials. We report a multi-tier computational screening of this chemical space. From a pool of 3660 ABN$_3$ compositions covering I-VIII, II-VII, III-VI and IV-V oxidation state combinations, 279 are predicted to be chemically feasible. The ground-state structures of the 25 most promising candidate compositions were explored through enumeration over octahedral tilt systems and global optimisation. We predict 12 dynamically and thermodynamically stable nitride perovskite materials, including YMoN$_3$, YWN$_3$, ZrTaN$_3$, and LaMoN$_3$. These feature significant electric polarisation and low predicted switching electric field, showing similarities with metal oxide perovskites and making them attractive for ferroelectric memory devices

Metal halide perovskites are multifunctional semiconductors with tunable structures and properties. They are highly dynamic crystals with complex octahedral tilting patterns and strongly anharmonic atomic behaviour. In the higher temperature, higher symmetry phases of these materials, several complex structural features have been observed. The local structure can differ greatly from the average structure and there is evidence that dynamic two-dimensional structures of correlated octahedral motion form. An understanding of the underlying complex atomistic dynamics is, however, still lacking. In this work, the local structure of the inorganic perovskite CsPbI$_3$ is investigated using a new machine learning force field based on the atomic cluster expansion framework. Through analysis of the temporal and spatial correlation observed during large-scale simulations, we reveal that the low frequency motion of octahedral tilts implies a double-well effective potential landscape, even well into the cubic phase. Moreover, dynamic local regions of lower symmetry are present within both higher symmetry phases. These regions are planar and we report the length and timescales of the motion. Finally, we investigate and visualise the spatial arrangement of these features and their interactions, providing a comprehensive picture of local structure in the higher symmetry phases.

The phenomenon of negative-U behavior, where a defect traps a second charge carrier more strongly than the first, has been established in many host crystals. Here we report the case of four-carrier transitions for both vacancy defects in Sb2Se3. A global structure searching strategy is employed to explore the defect energy landscape from first-principles, revealing previously-unrealized configurations which facilitate a major charge redistribution. Thermodynamic analysis of the accessible charge states reveals a four-electron negative-U transition (delta q = 4) for both V_Se and V_Sb and, by consequence, amphoteric behavior for all intrinsic defects in Sb2Se3, with impact on its usage in solar cells. To the best of our knowledge, four-electron negative-U behavior has not been previously explored in this or other compounds. The unusual behavior is facilitated by valence alternation, a reconfiguration of the local bonding environments, characteristic of both Se and Sb.

The competition between corner, edge and face-sharing octahedral networks is a cause of phase inhomogeneity in metal halide perovskite thin-films. Here we probe the charged iodine vacancy distribution and transport at the junction between cubic and hexagonal polytypes of CsPbI$_3$ from first-principles materials modelling. We predict a lower defect formation energy in the face-sharing regions, which correlates with a longer Pb$-$I bond length and causes a million-fold increase in local defect concentration. These defects are predicted to be more mobile in the face-sharing regions with a reduced activation energy for vacancy-mediated diffusion. We conclude that hexagonal phase inclusions or interfaces will act as defect sinks that could trap charges and enhance current-voltage hysteresis in perovskite-based solar cells and electrical devices.

Point defects are a universal feature of crystalline materials. Their identification is often addressed by combining experimental measurements with theoretical models. The standard approach of simulating defects is, however, prone to missing the ground state atomic configurations associated with energy-lowering reconstructions from the idealised crystallographic environment. Missed ground states compromise the accuracy of calculated properties. To address this issue, we report an approach to efficiently navigate the defect configurational landscape using targeted bond distortions and rattling. Application of our workflow to a range of materials ($\rm CdTe$, $\rm GaAs$, $\rm Sb_2S_3$, $\rm Sb_2Se_3$, $\rm CeO_2$, $\rm In_2O_3$, $\rm ZnO$, anatase-$\rm TiO_2$) reveals symmetry breaking in each host crystal that is not found via conventional local minimisation techniques. The point defect distortions are classified by the associated physico-chemical factors. We demonstrate the impact of these defect distortions on derived properties, including formation energies, concentrations and charge transition levels. Our work presents a step forward for quantitative modelling of imperfect solids.

Antimony sulfide (Sb2S3) and selenide (Sb2Se3) are emerging earth-abundant absorbers for photovoltaic applications. Solar cell performance depends strongly on charge carrier transport properties but these remain poorly understood in Sb2X3. Here we report band-like transport in Sb2X3 by investigating the electron-lattice interaction and theoretical limits of carrier mobility using first-principles density functional theory and Boltzmann transport calculations. We demonstrate that transport in Sb2X3 is governed by large polarons with moderate Fr\"ohlich coupling constants (~ 2), large polaron radii (extending over several unit cells) and high carrier mobility (an isotropic average of > 10 for both electrons and holes). The room temperature mobility is intrinsically limited by scattering from polar phonon modes and is further reduced in highly defective samples. Our study confirms that the performance of the Sb2X3 solar cells is not limited by intrinsic self-trapping.

Conventional wisdom of materials modelling stipulates that both chemical composition and crystal structure are integral in the prediction of physical properties. However, recent developments challenge this by reporting accurate property-prediction machine learning (ML) frameworks using composition alone without knowledge of the local atomic environments or long-range order. To probe this behavior, we conduct a systematic comparison of supervised ML models built on composition only vs. composition plus structure features. Similar performance for property prediction is found using both models for compounds close to the thermodynamic convex hull. We hypothesize that composition embeds structural information of ground-state structures in support of composition-centric models for property prediction and inverse design of stable compounds., Comment: 18 pages, 8 figures

Ferroelectricity in crystals is associated with the displacement of ions or rotations of polar units. Here we consider the dipole created by donor doping ($D^+$) and the corresponding bound polaron ($e^-$).A dipole of 6.15 Debye is predicted, from Berry phase analysis, in the Ruddlesden-Popper phase of ${\rm Sr_3Ti_2O_7}$. A characteristic double-well potential is formed, which persists for high doping densities. The effective Hubbard $U$ interaction can vary the defect state from metallic, a two-dimensional polaron, through to a zero-dimensional polaron. The ferroelectric-like behavior reported here is localized and distinct from conventional spontaneous lattice polarization.

Covalent organic frameworks (COFs) offer a high degree of chemical and structural flexibility. There is a large family of COFs built from 2D sheets that are stacked to form extended crystals. While it has been common to represent the stacking as eclipsed with one repeating layer ("AA"), there is growing evidence that a more diverse range of stacking sequences is accessible. Herein, we report a computational study of layer stacking in two prototypical COFs, Tp-Azo and DAAQ-TFP, which have shown high performance as Li-ion battery electrodes. We find a striking preference for slipped structures with horizontal offsets between layers ranging from 1.7 \r{A} to 3.5 \r{A} in a potential energy minimum that forms a low energy ring. The associated symmetry breaking results in a pronounced change in the underlying electronic structure. A band gap opening of 0.8 - 1.4 eV is found due to modifications of the underlying valence and conduction band dispersion as explained from changes in the $\pi$ orbital overlap. The implications for the screening and selection of COF for energy applications are discussed.

The efficiency of a solar cell is often limited by electron-hole recombination mediated by defect states within the band gap of the photovoltaic (PV) semiconductor. The Shockley-Read-Hall (SRH) model considers a static trap that can successively capture electrons and holes. In reality however, true trap levels vary with both the defect charge state and local structure. Here we consider the role of metastable structural configurations in capturing electrons and holes, taking the tellurium interstitial in CdTe as an illustrative example. Consideration of the defect dynamics, and symmetry-breaking, changes the qualitative behaviour and activates new pathways for carrier capture. Our results reveal the potential importance of metastable defect structures in non-radiative recombination, in particular for semiconductors with anharmonic/ionic-covalent bonding, multinary compositions, low crystal symmetries or highly-mobile defects., Comment: Submitted to Faraday Discussions, to be presented at the RSC Faraday Discussion on 'Emerging inorganic materials in thin-film photovoltaics' in Bath, UK, July 2022: https://www.rsc.org/events/detail/46796/emerging-inorganic-materials-in-thin-film-photovoltaics-faraday-discussion

The lifetime of non-equilibrium electrons and holes in semiconductors is crucial for solar cell and optoelectronic applications. Non-adiabatic molecular dynamics (NAMD) simulations based on time-dependent density functional theory (TDDFT) are widely used to study excited-state carrier dynamics. However, the calculated carrier lifetimes are often different from experimental results by orders of magnitude. In this work, by revisiting the definition of carrier lifetime and considering different recombination mechanisms, we report a systematic procedure for calculating the effective carrier lifetime in realistic semiconductor crystals that can be compared directly to experimental measurements. The procedure shows that considering all recombination mechanisms and using reasonable densities of carriers and defects are crucial in calculating the effective lifetime. When NAMD simulations consider only Shockey-Read-Hall (SRH) defect-assisted and band-to-band non-radiative recombination while neglect band-to-band radiative recombination, and the densities of non-equilibrium carriers and defects in supercell simulations are much higher than those in realistic semiconductors under solar illumination, the calculated lifetimes are ineffective and thus differ from experiments. Using our procedure, the calculated effective lifetime of the halide perovskite CH3NH3PbI3 agrees with experiments. It is mainly determined by band-to-band radiative and defect-assisted non-radiative recombination, while band-to-band non-radiative recombination is negligible. These results indicate that it is possible to calculate carrier lifetimes accurately based on NAMD simulations, but the directly calculated values should be converted to effective lifetimes for comparison to experiments. The revised procedure can be widely applied in future carrier lifetime simulations., Comment: 30 pages, 5 figures

A deep understanding of defects is essential for the optimisation of materials for solar energy conversion. This is particularly true for metal oxide photo(electro)catalysts, which typically feature high concentrations of charged point defects that are electronically active. In photovoltaic materials, except for selected dopants, defects are considered detrimental and should be eliminated to minimise charge recombination. However, photocatalysis is a more complex process where defects can play an active role, for example, by stabilising charge separation and mediating rate-limiting catalytic steps. Here, we review the behaviour of electronic defects in metal oxides, paying special attention to the principles underpinning the formation and function of trapped charges in the form of polarons. We focus on how defects alter the electronic structure, statically or transiently upon illumination, and discuss the implications of such changes in light-driven catalytic reactions. Finally, we consider the applicability of lessons learned from oxide defect chemistry to new photocatalysts based on carbon nitrides, polymers and metal halide perovskites., Comment: Review paper. Nat Rev Mater (2022)

Antimony sulfide (Sb2S3) and selenide (Sb2Se3) have emerged as promising earth-abundant alternatives among thin-film photovoltaic compounds. A distinguishing feature of these materials is their anisotropic crystal structures, which are composed of quasi-one-dimensional (1D) [Sb4X6]n ribbons. The interaction between ribbons has been reported to be van der Waals (vdW) in nature and Sb2X3 are thus commonly classified in the literature as 1D semiconductors. However, based on first-principles calculations, here we show that inter-ribbon interactions are present in Sb2X3 beyond the vdW regime. The origin of the anisotropic structures is related to the stereochemical activity of the Sb 5s lone pair according to electronic structure analysis. The impacts of structural anisotropy on the electronic and optical properties are further examined, including the presence of higher dimensional Fermi surfaces for charge carrier transport. Our study provides guidelines for optimising the performance of Sb2X3-based solar cells via device structuring based on the underlying crystal anisotropy.

Improvement in the optoelectronic performance of halide perovskite semiconductors requires the identification and suppression of non-radiative carrier trapping processes. The iodine interstitial has been established as a deep level defect, and implicated as an active recombination centre. We analyse the quantum mechanics of carrier trapping. Fast and irreversible electron capture by the neutral iodine interstitial is found. The effective Huang-Rhys factor exceeds 300, indicative of the strong electron-phonon coupling that is possible in soft semiconductors. The accepting phonon mode has a frequency of 53 cm$^{-1}$ and has an associated electron capture coefficient of 10$^{-10}$cm$^3$s$^{-1}$. The inverse participation ratio is used to quantify the localisation of phonon modes associated with the transition. We infer that suppression of octahedral rotations is an important factor to enhance defect tolerance.

The thermodynamic limit of photovoltaic efficiency for a single-junction solar cell can be readily predicted using the bandgap of the active light absorbing material. Such an approach overlooks the energy loss due to non-radiative electron-hole processes. We propose a practical ab initio procedure to determine the maximum efficiency of a thin-film solar cell that takes into account both radiative and non-radiative recombination. The required input includes the frequency-dependent optical absorption coefficient, as well as the capture cross-sections and equilibrium populations of point defects. For kesterite-structured Cu$_2$ZnSnS$_4$, the radiative limit is reached for a film thickness of around 2.6 micrometer, where the efficiency gain due to light absorption is counterbalanced by losses due to the increase in recombination current., Comment: 5 pages; 3 figures

CdTe is a key thin-film photovoltaic technology. Non-radiative electron-hole recombination reduces the solar conversion efficiency from an ideal value of 32% to a current champion performance of 22%. The cadmium vacancy (V_Cd) is a prominent acceptor species in p-type CdTe; however, debate continues regarding its structural and electronic behavior. Using ab initio defect techniques, we calculate a negative-U double-acceptor level for V_Cd, while reproducing the V_Cd^-1 hole-polaron, reconciling theoretical predictions with experimental observations. We find the cadmium vacancy facilitates rapid charge-carrier recombination, reducing maximum power-conversion efficiency by over 5% for untreated CdTe -- a consequence of tellurium dimerization, metastable structural arrangements, and anharmonic potential energy surfaces for carrier capture.

We study the effects of bismuth doping on the crystal structure and phase transitions in single crystals of the perovskite semiconductor methylammonium lead tribromide, MAPbBr3. By measuring temperature-dependent specific heat capacity (Cp) we find that, as Bi doping increases, the phase transition assigned to the cubic to tetragonal phase boundary decreases in temperature. Furthermore, after doping we observe one phase transition between 135 and 155 K, in contrast to two transitions observed in the undoped single crystal. These results appear strikingly similar to previously reported effects of mechanical pressure on perovskite crystal structure. Using X-ray diffraction, we show that the lattice constant decreases as Bi is incorporated into the crystal, as predicted by density functional theory (DFT). We propose that bismuth substitutional doping on the lead site is dominant, resulting in BiPb+ centers which induce compressive chemical strain that alters the crystalline phase transitions., Comment: 19 pages, 4 figures

Batteries are the most abundant form of electrochemical energy storage. Lithium and sodium ion batteries account for a significant portion of the battery market, but high-performance electrochemically active materials still need to be discovered and optimized for these technologies. Recently, tin(II) oxide (SnO) has emerged as a highly-promising battery electrode. In this work, we present a facile synthesis method to produce SnO nanoparticles whose size and shape can be tailored by changing the solvent nature. We study the complex relationship between wet chemistry synthesis conditions and resulting layered nanoparticle morphology. Furthermore, high-level electronic structure theory, including dispersion corrections to account for van der Waals forces, are employed to enhance our understanding of the underlying chemical mechanisms. The electronic vacuum alignment and surface energies are determined, allowing the prediction of the thermodynamically-favoured crystal shape (Wulff construction) and surface-weighted work function. Finally, the synthesized nanomaterials were tested as Li-ion battery anodes, demonstrating significantly enhanced electrochemical performance for morphologies obtained from specific synthesis conditions.

Lead-halide perovskites have demonstrated astonishing increases in power conversion efficiency in photovoltaics over the last decade. The most efficient perovskite devices now outperform industry-standard multi-crystalline silicon solar cells, despite the fact that perovskites are typically grown at low temperature using simple solution-based methods. However, the toxicity of lead and its ready solubility in water are concerns for widespread implementation. These challenges, alongside the many successes of the perovskites, have motivated significant efforts across multiple disciplines to find lead-free and stable alternatives which could mimic the ability of the perovskites to achieve high performance with low temperature, facile fabrication methods. This Review discusses the computational and experimental approaches that have been taken to discover lead-free perovskite-inspired materials, and the recent successes and challenges in synthesizing these compounds. The atomistic origins of the extraordinary performance exhibited by lead-halide perovskites in photovoltaic devices is discussed, alongside the key challenges in engineering such high-performance in alternative, next-generation materials. Beyond photovoltaics, this Review discusses the impact perovskite-inspired materials have had in spurring efforts to apply new materials in other optoelectronic applications, namely light-emitting diodes, photocatalysts, radiation detectors, thin film transistors and memristors. Finally, the prospects and key challenges faced by the field in advancing the development of perovskite-inspired materials towards realization in commercial devices is discussed.

The bandgap tunability of mixed-halide perovskites makes them promising candidates for light emitting diodes and tandem solar cells. However, illuminating mixed-halide perovskites results in the formation of segregated phases enriched in a single-halide. This segregation occurs through ion migration, which is also observed in single-halide compositions, and whose control is thus essential to enhance the lifetime and stability. Using pressure-dependent transient absorption spectroscopy, we find that the formation rates of both iodide- and bromide-rich phases in MAPb(BrxI1-x)3 reduce by two orders of magnitude on increasing the pressure to 0.3 GPa. We explain this reduction from a compression-induced increase of the activation energy for halide migration, which is supported by first-principle calculations. A similar mechanism occurs when the unit cell volume is reduced by incorporating a smaller cation. These findings reveal that stability with respect to halide segregation can be achieved either physically through compressive stress or chemically through compositional engineering.

Various thin-film I$_2$-II-IV-VI$_4$ photovoltaic absorbers derived from kesterite Cu$_2$ZnSn(S,Se)$_4$ have been synthesized, characterized, and theoretically investigated in the past few years. The availability of this homogeneous materials dataset is an opportunity to examine trends in their defect properties and identify criteria to find new defect-tolerant materials in this vast chemical space. We find that substitutions on the Zn site lead to a smooth decrease in band tailing as the ionic radius of the substituting cation increases. Unfortunately, this substitution strategy does not ensure the suppression of deeper defects and non-radiative recombination. Trends across the full dataset suggest that Gaussian and Urbach band tails in kesterite-inspired semiconductors are two separate phenomena caused by two different antisite defect types. Deep Urbach tails are correlated with the calculated band gap narrowing caused by the (2I$_\mathrm{II}$+IV$_\mathrm{II}$) defect cluster. Shallow Gaussian tails are correlated with the energy difference between the kesterite and stannite polymorphs, which points to the role of (I$_\mathrm{II}$+II$_\mathrm{I}$) defect clusters involving Group IB and Group IIB atoms swapping across \textit{different} cation planes. This finding can explain why \textit{in-plane} cation disorder and band tailing are uncorrelated in kesterites. Our results provide quantitative criteria for discovering new kesterite-inspired photovoltaic materials with low band tailing.

Halide double perovskites have gained significant attention, owing to their composition of low-toxicity elements, stability in air and long charge-carrier lifetimes. However, most double perovskites, including Cs2AgBiBr6, have wide bandgaps, which limit photo conversion efficiencies. The bandgap can be reduced through hallowing with Sb3+, but Sb-rich alloys are difficult to synthesise due to the high formation energy of Cs2AgSbBr6, which itself has a wide bandgap. We develop a solution-based route to synthesis phase-pure Cs2Ag(SbxBi1-x)Br6 thin films, with the mixing parameter x continuous varying over the entire composition range. We reveal that the mixed alloys (x between 0.5 and 0.9) demonstrate smaller bandgaps (as low as 2.08 eV) than the pure Sb- (2.18 eV) and Bi-based (2.25 eV) compounds, with strong deviation from Vegard's law. Through in-depth computations, we propose that bandgap lowering arises from the Type II band alignment between Cs2AgBiBr6 and Cs2AgSbBr6. The energy mismatch between the Bi and Sb s and p atomic orbitals, coupled with their non-linear mixing, results in the alloys adopting a smaller bandgap than the pure compounds. Our work demonstrates an approach to achieve bandgap reduction and highlights that bandgap bowing may be found in other double perovskite alloys by pairing together materials forming a Type II band alignment., Comment: 28 pages, 4 figures

Point defects in metal halide perovskites play a critical role in determining their properties and optoelectronic performance; however, many open questions remain unanswered. In this work, we apply impedance spectroscopy and deep-level transient spectroscopy to characterize the ionic defect landscape in methylammonium lead triiodide ($MAPbI_3$) perovskites in which defects were purposely introduced by fractionally changing the precursor stoichiometry. Our results highlight the profound influence of defects on the electronic landscape, exemplified by their impact on the device built-in potential, and consequently, the open-circuit voltage. Even low ion densities can have an impact on the electronic landscape when both cations and anions are considered as mobile. Moreover, we find that all measured ionic defects fulfil the Meyer--Neldel rule with a characteristic energy connected to the underlying ion hopping process. These findings support a general categorization of defects in halide perovskite compounds.

The relative permittivity of a crystal is a fundamental property that links microscopic chemical bonding to macroscopic electromagnetic response. Multiple models, including analytical, numerical and statistical descriptions, have been made to understand and predict dielectric behaviour. Analytical models are often limited to a particular type of compounds, whereas machine learning (ML) models often lack interpretability. Here, we combine supervised ML, density functional perturbation theory, and analysis based on game theory to predict and explain the physical trends in optical dielectric constants of crystals. Two ML models, support vector regression and deep neural networks, were trained on a dataset of 1,364 dielectric constants. Shapley additive explanations (SHAP) analysis of the ML models reveals that they recover correlations described by textbook Clausius-Mossotti and Penn models, which gives confidence in their ability to describe physical behavior, while providing superior predictive power., Comment: 14 pages, 4 figures, 4 tables

Defects influence the properties and functionality of all crystalline materials. For instance, point defects participate in electronic (e.g. carrier generation and recombination) and optical (e.g. absorption and emission) processes critical to solar energy conversion. Solid-state diffusion, mediated by the transport of charged defects, is used for electrochemical energy storage. First-principles calculations of defects based on density functional theory have been widely used to complement, and even validate, experimental observations. In this `quick-start guide', we discuss the best practice in how to calculate the formation energy of point defects in crystalline materials and analysis techniques appropriate to probe changes in structure and properties relevant across energy technologies., Comment: 6 pages, 4 figures, and 1 table

Solar cells are semiconductor devices that generate electricity through charge generation upon illumination. For optimal device efficiency, the photo-generated carriers must reach the electrical contact layers before they recombine. A deep understanding of the recombination process and transport behavior is essential to design better devices. Halide perovskite solar cells are commonly made of a polycrystalline absorber layer, but there is no consensus on the nature and role of grain boundaries. This review paper concerns theoretical approaches for the investigation of extended defects. We introduce recent computational studies on grain boundaries, and their influence on point defect distributions, in halide perovskite solar cells. We conclude the paper with discussion of future research directions., Comment: 9 pages, 4 figures

Halide perovskites exhibit slow rates of non-radiative electron-hole recombination upon illumination. Chu et al. [Sci. Adv. 6 7, eaaw7453 (2020)] use the results of first-principles simulations to argue that this arises from the nature of the crystal vibrations and leads to a breakdown of Shockley-Read-Hall theory. We highlight flaws in their methodology and analysis of carrier capture by point defects in crystalline semiconductors., Comment: 3 pages, 1 table

Mixing iodide and bromide in halide perovskite semiconductors is an effective strategy to tune their bandgap, therefore mixed-halide perovskites hold great promise for color-tunable LEDs and tandem solar cells. However, the bandgap of mixed-halide perovskites is unstable under (sun-)light, since the halides segregate into domains of different bandgaps. Using pressure-dependent ultrafast transient absorption spectroscopy, we show that high external pressure increases the range of thermodynamically stable halide mixing ratios. Chemical pressure, by inserting a smaller cation, has the same effect, which means that any iodide-to-bromide ratio can be thermodynamically stabilized by tuning the crystal volume and compressibility. We interpret this stabilization by an alteration of the Helmholtz free energy via the largely overlooked PdeltaV term.

The Shockley-Queisser (SQ) limit provides a convenient metric for predicting light-to-electricity conversion efficiency of a solar cell based on the band gap of the light-absorbing layer. In reality, few materials approach this radiative limit. We develop a formalism and a computational method to predict the maximum photovoltaic efficiency of imperfect crystals from first principles. Our scheme includes equilibrium populations of native defects, their carrier-capture coefficients, and the associated recombination rates. When applied to kesterite solar cells, we reveal an intrinsic limit of 20% for $\mathrm{Cu_2ZnSnSe_4}$, which falls far below the SQ limit of 32%. The effects of atomic substitution and extrinsic doping are studied, leading to pathways for enhanced efficiency of 31%. This approach can be applied to support targeted-materials selection for future solar-energy technologies., Comment: 12 pages, 8 figures, 2 tables

Lattice vibrations of point defects are essential for understanding non-radiative electron and hole capture in semiconductors as they govern properties including persistent photoconductivity and Shockley-Read-Hall recombination rate. Although the harmonic approximation is sufficient to describe a defect with small lattice relaxation, for cases of large lattice relaxation it is likely to break down. We describe a first-principles procedure to account for anharmonic carrier capture and apply it to the important case of the \textit{DX} center in GaAs. This is a system where the harmonic approximation grossly fails. Our treatment of the anharmonic Morse-like potentials accurately describes the observed electron capture barrier, predicting the absence of quantum tunnelling at low temperature, and a high hole capture rate that is independent of temperature. The model also explains the origin of the composition-invariant electron emission barrier. These results highlight an important shortcoming of the standard approach for describing point defect ionization that is accompanied by large lattice relaxation, where charge transfer occurs far from the equilibrium configuration.