High-throughput and data-driven search for stable optoelectronic AMSe₃ materials

Abstract

The rapid advancement in emerging optoelectronic technologies demands highly efficient, affordable, and ecofriendly materials. In this context, ternary chalcogenides, especially ternary selenides, show early promise as a material class due to their stability and remarkable electronic, optical, and transport properties. Herein, we integrate first-principles-based high-throughput computations with machine learning (ML) techniques to predict the thermodynamic stability and optoelectronic properties of 920 valency-satisfied selenide compounds. Through investigating polymorphism, our study reveals the edge-sharing orthorhombic Pnma phase (NH₄CdCl₃-type) as the most stable structure for most ternary selenides. High-fidelity supervised ML models are trained and tested to accelerate stability and band gap predictions. These data-driven models pin down the most influential features that dominantly control key material characteristics. The multistep high-throughput computations identify the ternary selenides with optimal direct band gaps, light carrier masses, and strong optical absorption edges. The extensive materials screening considering phase stability, toxicity, and defect tolerance, finally identifies the seven most suitable candidates for photovoltaic applications. Two of these final compounds, SrZrSe₃ and SrHfSe₃, have already been synthesized in a single-phase form, with the latter showing an optically suitable band gap, aligning well with our findings. The non-adiabatic molecular dynamics reveal sufficiently long photoexcited charge carrier lifetimes (on the order of nanoseconds) in some of these selected selenide materials, indicating their exciting characteristics. Overall, our study suggests a robust in silico framework that can be extended to screen large datasets of various material classes for identifying promising photoactive candidates.

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Dibyajyoti Ghosh

Dr Dibyajyoti Ghosh has been an Assistant Professor at the Indian Institute of Technology (IIT) Delhi since July 2021, specializing in computational materials science and condensed matter physics. He completed his PhD from the JNCASR, Bangaluru, India, in 2016 and then worked at the University of Bath, UK, and Los Alamos National Laboratory, USA, as a post-doctoral fellow until 2021. His work employs advanced computational techniques, such as density functional theory, ab initio and non-adiabatic molecular dynamics and machine learning, to discover new materials and tailor their properties for technological applications. He is actively involved in teaching and mentoring students, fostering a collaborative research environment.

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Introduction

Efficient optoelectronic technologies, such as solar cells and light-emitting devices (LEDs), are emerging as one of the most promising responses to the pressing global energy crisis and the environmental impact of fossil fuel dependence. Over the past few decades, various optoelectronic materials have been discovered and extensively optimized for highly efficient device performance.^1–4 Prominent examples include silicon and CdTe,^5–7 extensively used in solar photovoltaic technologies, and traditional III–V semiconductors, commonly used in LEDs.^8,9 While silicon-based photovoltaics currently dominate the global market, ongoing efforts focus on identifying alternative cost-effective semiconductors with superior performances.^10–15 Metal halide perovskites have garnered considerable interest in the last decade as viable options for solar applications owing to their outstanding optoelectronic features and cost-efficient production process.^16,17 However, the intrinsic instability under environmental conditions and the ubiquitous presence of toxic Pb adversely impact their commercialization.¹⁸ Recently, toxic-element-free ternary chalcogenides have attracted considerable research interest due to their excellent optoelectronic properties and superior structural stability under ambient conditions.^19–21 The general chemical formula of these compounds is AMX₃, where A and M are cations with oxidation states ranging from +1 to +5 and X is a chalcogen, either S or Se. The possibility of accommodating A and M with several oxidation state pairs provides an opportunity to enumerate large chemical space, finding the most suitable chalcogenides for targeted applications.

The predominant covalent character of chalcogenides frequently gives rise to narrow band gaps, which are beneficial for efficient solar energy harvesting for photovoltaics and photocatalysis.²² Furthermore, the AMX₃ compounds exhibit a unique bonding nature due to the moderate electronegativity of S and Se, which are less electronegative than oxygen and halogens but more so than that of non-metal elements like Si and Ge. Sun et al. employed density functional theory (DFT) to find suitable optoelectronic properties of several chalcogenides while exploring the perovskite phase of AMX₃ (A = Ca, Sr, Ba; M = Ti, Zr, Hf; X = S, Se).²³ Extensive high-throughput computational screening of ternary sulfides (AMS₃) by Kuhar et al. identified candidates with suitable electronic and optical properties for photoactivity. Their study reported the synthesis and characterization of a LaYS₃ thin film that shows a direct band gap of 2 eV.²⁴ Zhang et al. computationally found and experimentally verified that the perovskite phase of LaScSe₃ is thermodynamically stable with a slightly wider band gap of ∼2.2 eV.²⁵ Driven by their emerging attractive photoactivity, several ternary chalcogenides are now being synthesized as single crystals, thin films, and colloidal nanocrystals.²² In addition to traditional high-temperature solid-state reactions, approaches like magnetron sputtering,²⁶ pulsed laser deposition,²⁷ molecular beam epitaxy,²⁸ and chemical solution deposition²⁹ are gaining popularity in synthesizing high-quality chalcogenides under relatively mild experimental conditions. Regarding direct characterization, Niu et al. found comparable and better external and internal luminescence efficiency for SrZrS₃ than traditional semiconductors, suggesting their potential optoelectronic applications. The minimal shift in the photoluminescence peak of the LaYS₃ thin film indicates its attractive photoactivity.³⁰ Moroz et al. employed optical diffuse reflectance measurements to find a band gap of ∼1 eV for SrHfSe₃ that has been synthesized through a high-temperature solid-state reaction.³¹

Despite these recent remarkable advancements,^{14,15,20,22,23,27–29,32–37} ternary chalcogenides, especially selenides, remain largely underexplored. Their pronounced polymorphism, which is an ability to form different structural phases of the same AMX₃ compound, raises a critical challenge for their long-term phase stability. It is worth mentioning that most of the reports so far have focused on the corner-sharing orthorhombic perovskite phase of sulfides as they closely resemble halide perovskites.^23,24,32 However, this geometry often appears thermodynamically unstable or metastable compared to other non-perovskite phases, indicating limited stability under ambient conditions. A comprehensive computational study, encompassing the entire chemical space and accounting for other stable perovskite/non-perovskite phases, is essential to tap into the potential of these ternary chalcogenides for optoelectronic applications.

In this work, we integrate several atomistic simulation techniques such as DFT, ab initio molecular dynamics (AIMD), non-adiabatic molecular dynamics (NAMD) and Machine Learning (ML)-based models to identify promising ternary selenide AMSe₃ compounds for photovoltaics and other applications. While AMS₃ compounds have been extensively studied using high-throughput approaches,³⁸ AMSe₃ systems remain relatively underexplored despite their frequent demonstration of thermodynamic stability and promising optoelectronic properties. On the other hand, AMTe₃ compounds, although intriguing, often exhibit poor structural stability and have never been reported experimentally, which diminishes their practical relevance and makes them less attractive for computational studies.³⁹ The available chemical space and valency consideration provide an initial dataset of 920 distinct combinations of AMSe₃. Rigorous phase stability analysis of randomly selected candidates identifies the most commonly realized ground-state structure. The extensive in silico study of thermodynamic stability and band gap analyses substantially narrowed down the list of potential materials for optoelectronic applications. The complete dataset has been provided as a separate file. We train and test high-accuracy ML models to predict the formation energy, hull stability, and electronic band gaps for AMSe₃ compounds. Subsequent multi-stage material filtering considering crucial properties, such as the direct band gap, low carrier effective mass, eco-friendliness, and defect tolerance, yields a list of the most suitable ternary selenides for optoelectronics. Finally, NAMD simulations reveal extended excited carrier lifetimes in three of these AMSe₃, indicating their superior properties. The identification of already synthesized SrHfSe₃ and SrZrSe₃ in the final list of potential candidates suggests the feasibility of experimentally realizing other screened compounds.

Results

Ternary selenide chemical space

Our primary focus is to explore the entire chemical space of ternary selenide materials, AMSe₃, by varying atomic species A and M throughout the periodic table. The exclusion of inert gases, lanthanides (except La), actinides, and post-actinides results in 54 × 53 = 2862 possible ternary selenide compounds, excluding two-component A₂Se₃ or B₂Se₃ species (ESI Fig. S1†). Additionally, we confine ourselves to A–M combinations that maintain the overall charge neutrality of AMSe₃. Thus, A and M can have the following pairs of oxidation states (+1, +5) (+2, +4) (+3, +3) (+4, +2) and (+5, +1), ensuring that the sum of the valences of cations and anions vanishes. These criteria yield 920 ternaries in total and are open for further investigation (ESI Fig. S1†). Note that any pair of suitable elements X and Y define distinct XYSe₃ and YXSe₃ structures in our dataset due to non-equivalent Wyckoff positions of A and M sites and their dissimilar oxidation states and ionic radii.

Phase stability. Ternary chalcogenides feature polymorphism where each structural type exhibits a distinct bonding pattern.²² With 920 materials, the challenge lies in identifying the most stable phase for each AMSe₃ composition using conventional crystal structure prediction approaches like CALYPSO⁴⁰ and USPEX.⁴¹ Thus, we search for the most stable structure using the prototype structure approach as employed previously.^38,42 The available experimental structures depict that AMX₃ (X = S, Se) compounds mostly crystallize in a few distinct phases: (i) GdFeO₃-type orthorhombic Pnma structure, a perovskite with corner-sharing octahedra, (ii) NH₄CdCl₃-type orthorhombic Pnma structure, a non-perovskite with edge-sharing octahedra (needle-like phase), (iii) FePS₃-type monoclinic C12/m1 structure, a layered non-perovskite with edge-sharing octahedra, and (iv) PbPS₃-type monoclinic P1c1 structure with no octahedra. Fig. 1a–d display these representative structures. To assess the relative phase stability of AMSe₃, we compute the total energy (see the Methods section) of a subset of 200 randomly chosen compounds, which are optimized in these four different phases (ESI Table S1†).

Fig. 1 Representative structures of (a) GdFeO₃-, (b) NH₄CdCl₃-, (c) FePS₃-, and (d) PbPS₃-type phases of AMSe₃ compounds. (e) Phase stability investigation of 200 randomly selected AMSe₃. The heatmap depicts the calculated energy difference (ΔE) between the NH₄CdCl₃-type orthorhombic phase and the most stable phase. Special markers: white circles represent compounds with ΔE = 0 (stable in NH₄CdCl₃-type orthorhombic phase) and white hollow squares represent compounds with 0 < ΔE < 0.1 eV (metastable in NH₄CdCl₃-type orthorhombic phase). Here, ΔE is defined as the difference between the NH₄CdCl₃-type orthorhombic phase and the most stable phase energy.

Computed total energies of AMSe₃ in various crystal structure motifs reveal that the NH₄CdCl₃-type orthorhombic phase is most frequently stable (56.5%), followed by PbPS₃-like monoclinic P1c1 (20.5%), FePS₃-like monoclinic C12/m1 (14.5%), and GdFeO₃-like orthorhombic Pnma (8.5%) structures, see Fig. 1e. Furthermore, 32% of AMSe₃ compounds that are less stable in the NH₄CdCl₃-type structure are found to be metastable, within 0.1 eV per atom of the ground-state geometry. Thus, 88.5% of selected AMSe₃ are either mostly stable or marginally metastable in the orthorhombic non-perovskite phase. Previous studies have also identified a NH₄CdCl₃-type structure of AMSe₃ as the most stable phase (ESI Section S2.1†).^34,36 The frequent phase stability of edge-sharing polyhedron-containing structures demonstrates that ternary selenides do not obey Pauling's third rule.⁴³ We note that dominant covalent bonding and the subsequent weak coulombic repulsion between B-site cations in adjacent polyhedra facilitate the stabilization of the NH₄CdCl₃-type phase. Given these observations, we next structurally optimize and explore the remaining AMSe₃ candidates (720 out of 920), focusing exclusively on the NH₄CdCl₃-type orthorhombic phase.

Crystal structure of the NH₄CdCl₃-like orthorhombic phase. Fig. 1b and S2 ESI† show a prototype of AMSe₃ in the NH₄CdCl₃-like orthorhombic phase. The edge-sharing MSe₆ octahedra, which form 1D chains along the x-axis, remain stacked through electrostatic interactions between A cations and Se anions along the other axes (y and z). Thus, these AMSe₃ compounds exhibit inherent structural anisotropy due to their dissimilar crystal packing along different crystal directions. The distribution of lattice constants for the entire dataset suggests that the parameter ‘a’ varies significantly less than the parameters ‘b’ and ‘c’ (ESI Fig. S3†). The 1D-chains of MSe₆ edge-sharing octahedra lead to a limited variation along the a-axis. In contrast, the less dense stacking of octahedra along the ‘b’ and ‘c’ axes with more intervening space results in broader fluctuations across the chemical space. More detailed discussion is included in ESI Section S2.2.†

Thermodynamic stability. In silico assessment of thermodynamic stability is a key step for accelerated materials screening and selection.^44,45 To identify stable AMSe₃ compounds from the dataset, we compute two well-established properties, namely formation energy (E_f) and hull distance (E_h). Among them, E_f is a relatively relaxed criterion compared to E_h for screening stable compounds (ESI Section S3.1†). Thus, E_f is initially used to segregate AMSe₃ into two distinct categories: formable (E_f ≤ 0 eV per atom) and non-formable (E_f > 0 eV per atom). We find that 93% of AMSe₃ compounds are formable, which implies the frequent stability of ternary selenides relative to their elemental standard states of A, M, and Se (Fig. 2 and S4a ESI†). These formable compounds are further split into three groups based on the hull distance (E_h): phase stable with E_h ≤ 0.1 eV per atom, metastable with 0.1 < E_h ≤ 0.2 eV per atom, and unstable with E_h > 0.2 eV per atom (Fig. 2 and S4c ESI†). This classification reveals that 24%, 36%, and 33% of AMSe₃ candidates are hull stable, metastable, and unstable, respectively (ESI Fig. S4c†). Thus, about one-third of ternary selenides that are stable against their constituent elemental phases can decompose into relatively more stable binary or ternary phases. This underpins the importance of computing E_h alongside E_f for reliable prediction of material stability, as these two quantities do not exhibit any noticeable correlation (ESI Fig. S4d†). Our study identifies 25 AMSe₃ candidates with E_h = 0 eV per atom, depicting their stability against competing structural phase(s) and all possible decomposed constituting phases (Fig. 2 and Table S2 ESI†).

Fig. 2 A composition map of A/M elements depicting energy above hull (E_h) values across the entire chemical space. White rings denote highly stable compositions with E_h ≤ 0.01 eV per atom and E_f ≤ 0 eV per atom. Crosses (✗) represent AMSe₃ compounds with E_f > 0 eV per atom. Boxes marked with a ‘tick’ indicate compounds with E_f ≤ 0 eV per atom and E_h > 0.01 eV per atom. The gradient color bars highlight different stability classes of AMSe₃.

Traditionally, materials with E_h > 0 eV per atom have been considered synthetically challenging and prone to long-term stability due to spontaneous decomposition into other phases.⁴⁶ However, advancements in solid-state synthesis procedures, including improved control over experimental conditions, have made it possible to realize metastable materials in their stable form.^47–50 Moreover, the present stability data are computed at 0 K, without considering the entropy contribution to the free energy at finite temperatures. Such an entropy factor can potentially further stabilize the selenide compounds with marginally positive hull stability. Therefore, using relaxed criteria for thermodynamic stability, E_h ≤ 0.1 eV per atom, allow us to identify metastable yet functionally promising AMSe₃ compounds during in silico screening. ESI Section S3.2† provides a brief discussion of the recent progress in synthesizing metastable phases of materials.

The thermodynamic stability maps in Fig. 2 and S5 ESI† further categorize the entire chemical space according to common elemental groups. The map reveals that most AMSe₃ compounds with alkaline earth metals as M exhibit high formability but poor hull stability. In contrast, post-transition metals/non-metals as A and transition metals/post-transition metals as M emerge with much more frequent phase stability. AMSe₃, compounds with transition metals in both A and M positions, exhibit relatively lower stability (ESI Fig. S5†). Overall, we do not find strong trends in chemically stable regions for these compounds, underscoring their complex relation between stability and composition.

Commonly used radius ratios, such as the Goldschmidt tolerance factor, octahedral factor, and modified tolerance factor, are effective for classifying stability regions for perovskite and non-perovskite phases.^51,52 However, those metrics perform poorly in identifying the stability range for NH₄CdCl₃-type orthorhombic phases of AMSe₃ (ESI Fig. S6†). This fundamental limitation is attributed to the prevailing covalent character of M–Se bonds, which contrasts with the predominantly ionic bonding typically found in oxides and halides for which these geometric factors were formulated.⁵³ The intricate chemical bonding prompts moving beyond simple geometric descriptors and developing more robust ML models for accurately predicting the thermodynamic stability of these ternary selenides.

ML model for stability. We next train and test supervised ML models that can quantitatively predict the formation energies and hull stability for the complete AMSe₃ dataset. These models use relevant data calculated using the computationally affordable semi-local PBE-GGA functional. Two types of initial ML models are developed: (1) models based solely on elemental and compositional features and (2) models including lattice parameters of the crystal as additional features.

Formation energy

First, we trained and tested regression models for E_f using various elemental and compositional features. We selected gradient-boosting algorithms due to their proven effectiveness in handling complex, nonlinear relationships in materials science datasets. These ensemble methods combine multiple weak learners (typically decision trees) to form a strong predictive model, which is particularly suitable for capturing intricate patterns in formation energy data. Among these models, the gradient boosting regressor⁵⁴ achieves the best prediction accuracy with an MAE of 0.067 eV per atom for the test set (ESI Fig. S7a†). Other models, including the histogram-based (hist) gradient boosting regressor⁵⁵ and extreme gradient boosting regressor,⁵⁶ also efficiently predict E_f for ternary selenides (ESI Fig. S7b†). These specific ML models are robust against overfitting and handle mixed data types, as shown in previous materials property predictions.^56,57

In the next step, the regression models are trained with lattice parameters (a, b, and c) as features. Previous studies have highlighted the necessity of incorporating structural information to construct reliable ML models for material stability predictions.⁵⁸ However, these structural parameters are only available once the ground-state geometry is known, which limits the applicability of trained ML models for predicting stability in entirely new compositions. To minimize the dependence on structural information, we train ML models using only the lattice parameters as features. Among the tested models, the gradient boosting regressor achieves the highest accuracy for predicting E_f with a test MAE of 0.06 eV per atom (Fig. 3a). The E_f prediction errors are comparable to or even better than those of previously reported models.^59–61 Thus, our results indicate that incorporating structural parameters as features reduces the MAE and improves the prediction accuracy of E_f by approximately 11%.

Fig. 3 The supervised regression models for structural stability are illustrated with parity plots: (a) formation energy predictions using the gradient boosting regressor model and (b) hull distance predictions using the histogram-based (hist) gradient boosting regressor model. These ML models include lattice parameters as features to improve the prediction accuracy. The feature importance ranking for these formation energies and hull stability prediction models are shown in panels (c and d), respectively.

Hull stability

As hull stability (E_h) depends on the energetics of competing compounds, its accurate prediction through ML models is more challenging than evaluation of E_f.^58,62 Our study illustrates that including lattice parameters along with compositional and elemental features is essential for a reliable prediction of E_h (ESI Section S4.1†). The hist gradient boosting regressor model achieves the best performance among all tested models, with a test MAE of only 0.04 eV per atom when lattice parameters are included as features. The performance of other models and the impact of including structural information in ML models are further discussed in ESI Section S4.1.†

Here, we note that the ML models including E_f and excluding lattice parameters as features exhibit similar predictive performance for E_h (ESI Fig. S8†). Thus, despite poor direct correlations between E_f and E_h (see ESI Fig. S4(d)†), the ML models reveal the crucial role of E_f values in predicting the E_h of AMSe₃ compounds. These findings further suggest that access to high-fidelity E_f data is sufficient for predicting E_h without structure information for AMSe₃.

Feature importance of the best performing ML model

We conduct feature importance analyses using permutation feature importance, a model-agnostic technique, for the best-performing regression models (ESI Section S4.2†). As depicted in Fig. 3c, elemental features such as the minimum value of work function (min_phi), electronegativity (min_Electronegativity), and Mendeleev number (min_MendeleevNumber) are the most influential features for E_f prediction. Structural features, such as lattice parameter ‘b’, also appear in the top ten most important features; however, their significance is notably lower than that of the top ones. The relatively weaker importance of structural features justifies the marginal improvement in the model performance when they are incorporated during training. In contrast, the lattice constants emerge as highly important features in predicting E_h, where all three parameters appear in the top five on the feature list (Fig. 3d). The high importance of lattice parameters aligns with the much-improved model accuracy of machine-learned E_h predictions, when these features are included in training and testing. Note that other models exhibit similar or worse accuracy in predicting E_h and similar stability indicators without structural input while considering much larger datasets.^52,58,63

Materials screening based on stability

The high-throughput materials screening of AMSe₃ employs thermodynamic stability criteria of E_f < 0 eV per atom and ΔE_h < 0.1 eV per atom. These relatively strict criteria separate ternary selenides that are stable and most likely do not need special synthesis approaches. Out of the initial 920 AMSe₃ candidates, only 222 appear structurally stable (Fig. 2). Consequently, 76% of selenides in the entire dataset are discarded, underscoring the importance of computing thermodynamic stability early in the high-throughput materials screening protocol.

A careful check reveals that the screened stable candidates include most of the AMSe₃ compounds previously reported in the literature. Notably, hull stable candidates SrHfSe₃ and SrZrSe₃ have been synthesized in the NH₄CdCl₃-type orthorhombic phase.^31,64 Ong et al. employed evolutionary methods to find the ground state structure of BaZrSe₃ in the same phase.³⁴ Moreover, Adhikari et al. and Sun et al. explored the phase stability of a few AMSe₃ (A = Ca, Sr, Ba; M = Zr, Hf) compounds, with most of the compounds computationally predicted to be stable in the NH₄CdCl₃-type phase.^23,36

Electronic properties

The photovoltaic efficiency of absorber semiconductors intimately depends on their band gap values, as described by the Shockley–Queisser limit.⁶⁵ Therefore, finding optimal band gap systems through DFT-based high-throughput screening and, more recently, ML-based models, has emerged as the elementary step for the in silico design of optoelectronic materials. To develop a reliable ML model for band gap (E_g) prediction, we compute the electronic structures of AMSe₃ using the semi-local GGA-PBE functional and the more accurate hybrid HSE06 functional, regardless of their thermodynamic stability.

Band gap distribution

Fig. 4 shows the calculated HSE06 band gap values for all 920 AMSe₃ candidates. There are ∼37% of candidates (339 systems) with band gap values of E_g ≤ 0.05 eV that are not suitable for optoelectronic applications. These AMSe₃ compounds mostly populate the chemical space where both A and M are transition metals (Fig. 4). The AMSe₃ candidates with E_g > 0.5 eV are ∼34% of the total dataset (315 systems) and are potentially relevant for photovoltaics. These ternary selenides predominantly emerge from the chemical space where A and M are nonmetals.

Fig. 4 The elemental map displaying the band gap data obtained with the HSE06 functional for all 920 AMSe₃ compounds. The band gap values are represented by three different colored bars shown in the right. Black circles highlight compounds with E_h < 0.1 eV and HSE06 bandgap > 0.5 eV, while white squares overlaid on black circles denote AMSe₃ compounds with direct band gaps.

We next examine the relationship between the material stability and electronic band gap in these ternary selenides. Fig. 5a illustrates that 82% (258 systems) of wide band gap AMSe₃ (with E_g > 0.5 eV) are stable or metastable (E_f ≤ 0 eV per atom and E_h ≤ 0.2 eV per atom). In contrast, only 25% of metastable and unstable AMSe₃ appear as wide band gap candidates, illustrating their prevalent metallic/narrow band gap characteristics (Fig. 5a). Our data-driven analysis suggests potential labor-intensive experimental efforts required to stabilize these materials through a synthetic optimization process if low-band gap compounds from this family are needed for optoelectronic applications.

Fig. 5 (a) The stability, metastability, and instability distribution for semiconducting and metallic AMSe₃ compounds. Parity plots for high-fidelity HSE06 band gap prediction using the (b) hist gradient boosting regressor model that includes E_h and E_f as features and (c) artificial neural network (ANN) model which relies on the GGA-PBE band gap as a feature. (d) Feature importance analysis for the band gap regression model as presented in (b), highlighting the key contributors to the prediction accuracy.

ML models for band gap prediction

We train, cross-validate, and rigorously test several supervised regression models for predicting the high-fidelity HSE06 band gap of AMSe₃ with and without structural features (see ESI Section S5.1† for details). The best-performing ML model with only compositional and elemental features achieves reasonable accuracy with a MAE of 0.24 eV (ESI Fig. S9a†), comparable to other reported band gap prediction models.^66–69 The large chemical space and relatively small dataset limit further show improvements in prediction accuracy. In the next step, the models are trained and tested, including the lattice parameters as additional features. However, unlike stability prediction, incorporating structural information does not significantly improve the band gap prediction accuracy, indicating its relatively weak influence on electronic properties (ESI Fig. S9b†). To further improve the prediction accuracy, stability parameters E_f and E_h are incorporated as features for training the ML models. The best-trained hist gradient boosting regressor model achieves a reduced MAE of 0.19 eV for predicting high-fidelity HSE06 band gaps (Fig. 5b).

Despite these improvements, we observe that traditional regression models plateaued in performance, likely due to their limited capacity to capture complex nonlinear relationships inherent in electronic property predictions. The band gap determination involves intricate interactions between atomic orbitals, electronic configurations, and quantum effects, which are not easily modeled by linear or even simple nonlinear regression techniques.⁷⁰ To address this challenge, we explore the use of artificial neural networks (ANNs), which are well-suited for modeling complex, nonlinear relationships due to their layered architecture and nonlinear activation functions.^71–73 ANNs can capture high-level abstractions and interactions between features that traditional models often miss. In our case, incorporating the low-fidelity GGA-PBE band gaps as a feature within an ANN framework allows the model to learn the nonlinear mapping between the inexpensive GGA-PBE calculations and the high-fidelity HSE06 band gaps efficiently. The ANN model exhibits the best performance with an MAE of 0.16 eV (Fig. 5c), outperforming the regression models. This accurate predictive model surpasses the performance of several ML models reported previously.^66–69 The use of GGA-PBE band gaps, which are significantly faster (∼80–85 times for our systems) to compute compared to hybrid HSE06 simulations, provides practical advantages. As most computational databases contain GGA-PBE band gaps, our developed ML models can readily be extended to predict more accurate HSE06-level band gaps for other material datasets.

Feature importance

The feature importance for hist gradient boosting regressor model reveals that E_f and E_h thermodynamic stability features are the most significant features for predicting the HSE06 band gaps of AMSe₃ (Fig. 5d). Other elemental features like maximum ionization energy (max_ion_energy) and maximum work function (max_phi) between A and M also rank highly in importance. The high feature importance for stability parameters is non-trivial. However, these stability features are somewhat correlated to the electronic properties of AMSe₃, as shown in Fig. 5d. Moreover, the Spearman and Pearson Correlation analyses^74,75 reveal negative correlations between E_f or E_h and E_g, suggesting lower or vanishing band gaps for relatively less stable AMSe₃ compounds (ESI Fig. S10a and b†). For the best-performing ANN model, the feature importance predictably illustrates the much higher importance of the GGA-PBE band gap in predicting HSE06 counterparts (ESI Fig. S11a†). This is consistent with the strong correlation observed between GGA-PBE and HSE06 band gaps, as shown in ESI Fig. S11b.†

Materials screening with band gaps

We apply the criterion E_g > 0.5 eV to further down-select thermodynamically stable AMSe₃ compounds for prototypical optoelectronic applications. Out of the initial 222 stable compounds, 137 AMSe₃ meet the band gap specification (Fig. S12†). Thus, the adopted dual-filtering strategy integrating thermodynamic stability with electronic performance effectively narrows the candidate pool by ∼85%, significantly accelerating the high-throughput materials screening process.

In the subsequent step, compounds with direct band gaps, which are usually desirable for optoelectronic applications, are identified. This screening step further narrows the number of potential candidates to 51 (Fig. 4). The frequent indirect band gaps in NH₄CdCl₃-type AMX₃ (X = S, Se) can potentially originate from factors like MSe₆ tilting due to edge-sharing coordination and atomic orbital contribution to the band edge states.²² The compositions of these screened AMSe₃ candidates remain broadly distributed across the periodic table (Fig. 4).

Chemical trends in band gaps and band edges

The projected density of states (pDOS) of AMSe₃ compounds depicts that the Se 4p orbitals mainly contribute to the valence band maximum (VBM), whereas the conduction band minimum (CBM) comprises contributions from Se 4p and M-site orbitals (ESI Fig. S13†). We further explore the chemical nature of band edge states of these screened selenides. AMSe₃ materials with transition metals as the M-site exhibit CBM predominantly composed of the nd-orbitals (n = 3, 4, 5) (ESI Fig. S13†). Therefore, the band gap widens as M progresses from 3d to 4d to 5d elements. For example, BMSe₃ compounds have band gaps of 1.34, 1.54, and 1.94 eV for M = Co (3d), Rh (4d), and Ir (5d), respectively (ESI Fig. S14†). A similar trend is observed for other transition metals, with Hf(5d)-based selenides consistently exhibiting higher band gaps than Zr(4d)-based ones, in agreement with findings reported by Sun et al.²³ (ESI Fig. S15a†). In other chemical spaces, compounds with non-metal M-sites construct the CBM from M-np and Se-4p orbitals (Fig. S14b†). Whereas the selenides with rare earth elements (e.g., Sc, La, and Y) as A and M exhibit CBM states mostly contributed by nd orbitals (ESI Fig. S15c†). These results highlight the chemical versatility of the band edge states of NH₄CdCl₃-type AMSe₃ materials while maintaining the optoelectronically suitable direct band gap (ESI Section S5.2†). Additionally, the significant influence of M on electronic properties suggests that strategic alloying at the M-sites could be a promising approach for band gap tuning in ternary selenides, a strategy that has already been successfully demonstrated for sulfides.^33,35

The band gaps of the screened AMSe₃ compounds align well with previously reported values from experimental and computational studies, as listed in ESI Table S3.† For instance, Moroz et al. found an experimental band gap of 1.0 eV for SrHfSe₃, which matches our calculated HSE06 band gap.³¹ The E_g data from other in silico studies also agree with our calculations.³⁶

Carrier effective masses. The efficient photogenerated charge separation and mobility are essential in high-performance optoelectronic materials. To simplify the evaluation process and avoid computationally intensive calculations, we focus on electron and hole carrier effective masses, and , that are inversely related to their corresponding carrier mobilities, μ_e and μ_h (ESI Section S1†). Optoelectronically promising materials are expected to possess smaller , typically indicative of superior transport characteristics.^76–79 To refine the candidate pool, we choose the most frequently considered criteria of and , identifying ternary selenides with low electron and hole masses. This crucial screening step leads to 30 candidates with suitable carrier transport characteristics (ESI Table S4†).

Light absorbance in the context of photovoltaic performance metric. For the subsequent screening step, we compute the Spectroscopic Limited Maximum Efficiency (SLME) of screened AMSe₃ candidates to assess their light absorption potential, for example when serving as the absorbing layer for solar cells. The SLME represents the highest achievable efficiency of a light-absorbing material and can be considered the theoretical maximum photoconversion efficiency of a single p–n junction solar cell.⁸⁰

We set the selection criterion as SLME > 22% (for a film thickness of 1 μm), resulting in the identification of 22 AMSe₃ materials with promising power conversion efficiencies. The higher SLME threshold compared to other studies guarantees the promising photovoltaic properties of screened materials.^81,82 As depicted in Fig. 6a, these screened materials achieve SLME values ranging from 22.8% to 30.1%, surpassing many other well-explored higher efficiency light absorbers.⁸¹ The dense electronic states at the band edges of these selenides result in strong optical absorption, as shown in ESI Fig. S16,† ultimately boosting their power conversion efficiency.

Fig. 6 (a) SLME values of 30 AMSe₃ compounds with low effective masses. The ‘✗’ symbol marks AMSe₃ materials that contain toxic elements. The ternary selenides with red bars indicate their potential phase instability compared to other competing phases. The spin-polarized densities of states for (b) CaZrSe₃ and (c) BRhSe₃ with neutral selenide defects are also presented. In contrast to BRhSe₃, all defect levels for CaZrSe₃ lie within 0.1 eV of the band-edge states and can be considered as shallow defect states.

Elemental toxicity. In the following step, we implement a stringent refinement step to evaluate the environmental and health implications of the screened compounds. Recognizing the potential hazards associated with certain elements, we exclude compounds containing arsenic (As) and lanthanum (La) from further consideration (marked with a cross in Fig. 6a). This refinement ensures that the final selection includes compounds both excelling in efficiency and stability and adhering to strict safety and environmental standards. As a result, 17 ternary selenides with high SLME are toxic-element free and should not directly pose environmental threats. Note that the discarded compounds can reduce the concentration of toxic elements through compositional engineering without compromising photovoltaic characteristics. This strategy has been successfully demonstrated for toxic Pb-based halide perovskites.^18,83

Phase stability. We next explore the thermodynamic phase stability of screened AMSe₃ materials. As detailed in ESI Section S1,† the total energies of these compounds are calculated across all commonly reported prototypical crystal structures (Fig. 1a). Consistent with our initial findings, the edge-sharing orthorhombic Pnma phase emerges as the most stable structure for most of the cases (12 out of 17 or 71%) (ESI Table S5†). Ternary selenides that exhibit stable phases other than the NH₄CdCl₃-type are marked with red bars in Fig. 6a. These results validate our initial approach of considering only the most frequently stable phase, which substantially reduces the computational expense and accelerates the screening process.

Defect tolerance. The screened candidates are further scrutinized to elucidate their point-defect resilience. Point-defect-induced in-gap states frequently degrade the optical performance of semiconductors. These additional electronic states may act as recombination centers and become traps for photo-generated carriers (electrons and holes), which in turn degrade the carrier mobility, shorten their lifetime, and reduce the charge separation efficiency.

We consider atomic vacancy defects, including A, M, and Se vacancies, which often exhibit low defect-formation energies. Our goal is to qualitatively assess the presence of deep-defect states, focusing exclusively on neutral defects to establish a clear foundation without the added complexity of charged states. While the use of a semi-local exchange–correlation functional introduces some limitations, such as band gap underestimation and delocalization errors, it provides an efficient and reliable starting point for identifying key trends in defect behavior. Other defect types, such as anion interstitials and cation anti-site defects, can significantly determine the defect tolerance and overall optoelectronic performance of chalcogenide materials, particularly in complex ternary and quaternary systems.⁸⁴ Advanced methods like hybrid functionals or GW calculations, while capable of greater accuracy, are better suited for future studies aiming to resolve defect levels with higher precision.

The pDOS plots in Fig. 6b, c and S17 ESI† summarize the defect properties of AMSe₃ compounds. Seven defect-tolerant candidates stand out that they do not introduce deep trap levels despite hosting A, M, and Se vacancies. For instance, as shown in Fig. 6b and S17 ESI,† the defects arising from Ca, Zr, and Se vacancies in CaZrSe₃ do not create in-gap states. Meanwhile, the BRhSe₃ material shows defect intolerance as the Se-defects introduce deep trap levels within the band gap (Fig. 6c). Since anion vacancies primarily contribute to deep defect states, mitigating such defects can improve the characteristics of these ternary selenides. These seven AMSe₃ candidates, as summarized in Table 1, emerge as the final materials that we find highly promising for photovoltaic applications. A brief overview of our multi-step screening process and the number of surviving AMSe₃ compounds after each step is schematically shown in Fig. 7.

Table 1 Characteristics of the final seven AMSe₃ candidates pertinent to their potential photovoltaic applications

Compound	HSE06 band gap (eV)			SLME (%) (1 μm)
BaZrSe3	0.99	0.482	−0.587	27.80
CaZrSe3	1.11	0.479	−0.306	29.81
GeZrSe3	0.85	0.406	−0.525	26.74
ScYSe3	1.43	0.569	−0.639	29.60
SrHfSe3	1.0	0.401	−0.536	26.64
SrZrSe3	0.84	0.968	−0.558	25.67
YScSe3	0.96	0.679	−0.63	26.75

---

Fig. 7 Procedural outline of the multi-step screening process employed to select AMSe₃ with promising optoelectronic properties.

Among the screened materials, polycrystalline SrHfSe₃ and SrZrSe₃ have already been synthesized and structurally characterized in the NH₄CdCl₃-type phase.^31,64 However, transport measurements and optoelectronic device fabrications from these materials have yet to be reported. We also note that sulfur analogs of most of these final AMSe₃ compounds have been experimentally synthesized.^22,85 With the rapid recent advancements in low-temperature synthetic routes for ternary chalcogenides, we anticipate that the remaining selenides will be realized soon.²²

Thin-film photovoltaics. The thickness-dependent SLME in ESI Fig. S18† depicts that the final candidates reach near-maximum conversion efficiency within 1 μm thickness, suggesting their potential application in thin-film solar cells. Thin absorbing layers enable photogenerated carriers to traverse shorter distances to reach the contacts, thereby reducing their recombination losses. We note that conventional thin-film absorbers like GaAs usually require thicknesses greater than 2 μm to absorb enough sunlight.^86,87 Thus, the thinner absorbing layers of these newly explored ternary selenides can introduce solar cells with better structural flexibility and affordability compared to currently commercialized technologies.

Structural integrity. To confirm the dynamic stability of selected candidates, we perform phonon calculations on our selected candidates, as depicted in Fig. S19.† Moreover, to evaluate the structural integrity and thermal stability of screened AMSe₃ compounds, we employ ab initio molecular dynamics (AIMD) simulations under ambient conditions, as detailed in ESI Section S1.† Given the heavy computational expense, the current study explores three representative compounds with high SLME: BaZrSe₃, ScYSe₃, and SrHfSe₃. These candidates are selected to represent distinct A and M elements and address different chemical spaces. Fig. 8a illustrates that the potential energies of these materials fluctuate around their average values over time and remain confined within a narrow range despite the inherent structural distortions. The temperatures over time in these systems also fluctuate around the desired value, 300 K, see ESI Fig. S20.† The selected snapshots of AMSe₃ structures confirm their robustness, see the inset in Fig. 8a and S21 ESI.† To further assess the structural rigidity of the AMSe₃ compounds, we calculate the pair distribution functions (g(r)) for M–Se bonds. As depicted in Fig. 8b, the g(r) profiles exhibit sharp peaks, signifying well-maintained atomic arrangements in the edge-sharing orthorhombic structures at 300 K. Overall, our AIMD simulations confirm the strong bonding interactions and structural integrity of the ternary selenides, validating their thermal stability.

Fig. 8 The structural stability of three representative AMSe₃ systems, BaZrSe₃, ScYSe₃, and SrHfSe₃, evaluated at 300 K. (a) The total energy per formula unit of three AMSe₃, where variations reflect thermal fluctuation in a narrow energy range, (b) the g(r) of M–Se feature sharp peaks, evidencing the retained material crystallinity at 300 K, and (c) the time-dependent population of non-radiatively recombined electron–hole pairs. The function f(t) = 1 − exp(−t/τ) is used to fit the population rise with time; here, τ is the effective electron–hole recombination time. (d) Average NAC values and calculated average band gaps for these compounds.

Excited carrier dynamics and lifetime. Finally, we study the excited carrier dynamics and non-radiative recombination processes under ambient conditions in these three AMSe₃ compounds. The Time-Domain Density Functional Theory (TD-DFT) combined with Non-Adiabatic Molecular Dynamics (NAMD) simulations are utilized to evaluate the charge carrier lifetime, a key parameter for photovoltaic performance.⁸⁸ As detailed in ESI Section S1,† these methods qualitatively track the time-dependent increase in carrier population in the ground state due to non-radiative charge recombination across the band gap. The rate of population growth is inversely proportional to the photoexcited carrier lifetime. Fig. 8c reveals the calculated slow non-radiative carrier relaxation rates in these AMSe₃ compounds, evidencing potential long carrier lifetimes in the excited state. The calculated lifetimes for BaZrSe₃, ScYSe₃, and SrHfSe₃ are 2.1, 4.2, and 1.18 ns, respectively. The photoexcited lifetimes on the nanosecond scale are quite comparable to the measured values for other inorganic materials, including halide perovskites like CsPbBr₃ (Table 2).^89,90

Table 2 Comparison of non-radiative carrier lifetimes of representative systems

	BaZrSe3	ScYSe3	SrHfSe3	CsPbBr3 (ref. 89)
Recombination lifetime (ns)	2.1	4.2	1.18	1.45

---

The band gap variations and non-adiabatic coupling (NAC) strengths under ambient conditions are known to decisively impact photoexcited carrier lifetimes in semiconductors.^91,92Fig. 8d depicts the time-average band gaps and NAC values closely correlating with the observed trend in carrier lifetimes for SrHfSe₃, BaZrSe₃, and ScYSe₃. Among these three candidates, the highest band gap and the weakest NAC give rise to the longest carrier lifetime in ScYSe₃. During non-radiative carrier relaxation and recombination, the photoexcited carriers dissipate excess energy via electron–phonon coupling, exciting various lattice phonon modes. Higher band gap and weak NACs in ScYSe₃ partially suppress such energy dissipation processes, extending the excited state lifetime. More details on modeling the carrier dynamics and recombination processes are provided in ESI Section S8.†

Discussion

Ternary chalcogenides are often explored to search for stable materials in conventionally photoactive phases featuring corner-shared MSe₆ octahedra. However, a comprehensive exploration over available chemical space reveals the exciting photoactivity and carrier transport characteristics of AMSe₃ emerging in an often thermodynamically stable NH₄CdCl₃-type orthorhombic phase. High-quality films or single crystals of these selenides can eventually enable promising optoelectronic devices with long-term stability. In this regard, robust ambient stability of chalcogenides at room temperature suggests less extensive post-processing of these materials for practical device applications.

Our accurate ML models reveal the most crucial elemental and structural features that substantially control the stability of AMSe₃ materials and their fundamental electronic properties. These insights are useful for further tuning the core material properties through compositional engineering. For example, the high feature importance of lattice parameters in stability and band gap prediction models suggests that applying controlled lattice strain in AMSe₃ could be an effective tool for modifying these characteristics. Lattice compression and expansion have already been extensively used to optimize the optoelectronic properties of photoactive materials including chalcogenides,^93,94 highlighting the potential of this approach for AMSe₃ systems.

In this study, we have highlighted our procedure to downselect materials suitable for solar cell applications, given the well-established performance metric for photovoltaics. In addition to their potential in photovoltaics, ternary selenides show remarkable versatility across several other optoelectronic and energy-related applications. For instance, light-emitting diodes (LEDs) represent a promising avenue, where the impressive luminescent properties, efficient carrier transport, defect tolerance, and robust environmental stability of these AMSe₃ can make them superior candidates.⁹⁵ Moreover, due to their efficient photo-excited electron–hole pair generation and suitable band alignments, these chalcogenides can be promising photocatalysts for various chemical reactions.⁹⁶ Furthermore, these ternary selenides can be suitable for photochemical water splitting owing to their wide band gaps (∼2 eV) and high carrier mobilities. In this context, Kuhar et al. investigated the sulfide analogue of AMS₃ and proposed a few candidates as potential water-splitting materials with wide band gaps.¹⁹ AMSe₃ compounds also exhibit features such as low lattice thermal conductivity, which makes them suitable for thermoelectric applications. Cao et al. identified quasi-ductile thermoelectric compounds, reporting six n-type and six p-type candidates with ZT > 0.3 at 300 K.⁹⁷ The high-quality dataset presented here as separate file can readily be used to screen ternary selenides for other targeted applications.

Conclusions

In conclusion, our study introduces an advanced data-driven framework, integrated with high-throughput ab initio simulations, to systematically screen ternary selenides for optoelectronic applications. Among several common polymorphs, the edge-shared orthorhombic NH₄CdCl₃-type phase (Pnma) emerges as the most frequently stable structure for AMSe₃ compounds. By exploring the relevant chemical space, we develop and publish an extensive in silico dataset comprising optimal geometries and high-fidelity electronic structures for 920 candidates in this orthorhombic phase. Reliable supervised ML models are trained and tested for accelerated screening, using thermodynamic stability parameters and electronic band gap values as criteria. Feature importance analysis from these models suggests specific design approaches to boost the stability and key photovoltaic properties of ternary selenides. We further establish a multi-tiered high-throughput materials screening workflow incorporating stringent materials characteristics. This systematic screening identifies tenths of new ternary selenides with desired functional properties such as hull stability, direct band gap spanning a wide range, low charge carrier mass, and high SLME. Our staged selection process finally identifies seven AMSe₃ compounds with promising photovoltaic properties. The AIMD and NAMD simulations on three of these selenides reveal their thermal stability and long carrier lifetimes, indicating their potential optoelectronic applications. This application screens materials suitable for photovoltaics. However, we note that exceptional functional properties of AMSe₃ materials suggest their versatility in a wide variety of applications ranging from photocatalysis to light emission to thermoelectric. This work emphasizes the importance of exploring traditionally overlooked but thermodynamically stable non-perovskite phases of ternary chalcogenides to uncover their exciting functional characteristics for advanced optoelectronic technologies.

Methods

In this work, all the DFT-based calculations and AIMD simulations were performed using the Vienna Ab initio Simulation Package (VASP).^98,99 The Perdew–Burke–Ernzerhof (PBE) version of the exchange–correlation functional¹⁰⁰ within the Generalized Gradient Approximation (GGA), projector-augmented wave (PAW)¹⁰¹ method and the plane wave basis sets¹⁰² were employed for structure relaxation and other static calculations. In some instances, the hybrid HSE06 functional^103,104 was employed to determine the band gaps of ternary selenides, aiming for quantitative agreement with experimental values. Geometric relaxation of the structures was performed using the PBE functional. Crystal structures were optimized with an energy convergence criterion of 1 × 10⁻⁵ eV, employing a kinetic energy cutoff of 400 eV for the plane-wave basis. Relaxation of structures continued until atomic forces reached below 0.04 eV Å⁻¹. To ensure consistency and accuracy in formation energy and convex hull calculations, parameters identical to those in the OQMD¹⁰⁵ dataset were adopted. Spin polarization was explicitly included in all calculations to account for the magnetic effects of 3d transition metal elements. However, spin–orbit coupling (SOC) was not considered due to the significant computational cost associated with high-throughput calculations of the large AMSe₃ dataset.

To ensure a consistent and accurate description of the AMSe₃ compounds, we employed the HSE06 hybrid functional, which is well known for reliably capturing the electronic structure of transition metal chalcogenides without the need for empirical Hubbard U corrections.¹⁰⁶ While the inclusion of Hubbard U parameters can improve the localization of d-electrons, their selection is highly system-dependent and requires rigorous benchmarking. This makes their application impractical for high-throughput computational studies. Specific details about various types of calculations – convex hull distance, formation energy, effective charge carrier masses, SLME, phase stability, defect calculations, phonon calculations, AIMD, and NAMD – are given in ESI Section S1(a).†

The machine learning methodology for predicting the thermodynamic stability of ternary selenides involves constructing a dataset with 348 features from elemental properties (MAGPIE)¹⁰⁷ and structural attributes. Feature engineering eliminates features with >10% missing data, low variance, or high correlation (≥0.95) and selects relevant ones using Recursive Feature Elimination (RFE).¹⁰⁸ Regression and classification tasks predict the formation energy, hull distance, and band gap, with an 80/20 train–test split. Baseline models are tested with Lazy Predict, followed by hyperparameter tuning and advanced models like artificial neural networks (ANN). Permutation feature importance identifies key features driving model performance. Further details on data science computational methods are included in ESI Section S1(b).†

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

D. G. acknowledges the IIT Delhi SEED Grant (PLN12/04MS), the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), India, for the Start-up Research Grant SRG/2022/00l234, CSIR-Human Resource Development Group (HRDG) for ExtraMural Research-II Grant 01/3136/23/EMR-II and the IIT Delhi HPC facility for computational resources. The research presented in this article was supported by the Laboratory Directed Research and Development program of Los Alamos National Laboratory (LANL) under project number 20190656PRD4 and 20240590ECR. This work was performed in part at the Center for Integrated Nanotechnology (CINT) at LANL, a U.S. DOE and Office of Basic Energy Sciences user facility. This research used resources provided by the LANL Institutional Computing Program. LANL is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001).

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta08867k

‡ These authors contributed equally.

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