Data-driven exploration and first-principles analysis of perovskite material

Machine learning and genetic algorithm (crystal structure generation)

The MAGUS software is employed to generate new crystal structures of GdScO₃ using a combination of machine learning and density functional theories by leveraging evolutionary strategies. The genetic algorithm [Supplementary Materials] to obtain new crystal structures of GdScO₃ is initiated with (1) a set of preliminary random crystal structures and (2) different Vienna ab-initio simulation package (VASP)^[30] input parameters (INCAR) to fully account for the impacts of software geometrical optimization details and intrinsic crystal structures on the resulting crystal structures. The starting population undergoes iterative cycles of selection, with operations including crossover and mutation to evolve new generations of crystal structures. At each iteration, the crystal structures are evaluated based on their energy and stability using first-principles calculation, with the lower-energy configurations being preferentially selected for subsequent generations. The following hyperparameters are used: initSize = 20; popSize = 20; numGen: 10; saveGood = 3, min_n_atoms = 5; spacegroup = 2-230; d_ratio = 0.6; volume_ratio = 3. The preliminary DFT calculation involves Perdew-Burke-Ernzerhof (PBE) functional, 380 eV cutoff energy and convergence criteria (forces) of 0.01 eV/Å for atoms and 0.001 eV/Å for electrons. Four distinct k-spacing values expressed in different VASP input files are considered during the genetic process: KSPACING = 1.256000, KSPACING = 0.942, KSPACING = 0.618, and KSPACING = 0.314. These different input files act as the starting population to facilitate the genetic process. Full structural relaxation including unit cell parameters is performed, allowing the atomic positions and lattice parameters to adjust until the forces on the atoms are minimized and the total energy converges to stable values. Higher quality DFT calculations are executed based on these initial optimized structures. Through this combined approach of machine learning-driven genetic algorithms and DFT calculations, a diverse set of GdScO₃ structures are generated and their electronic structures are further analyzed in detail.

New structure screening

The obtained structures based on the previous step are ranked according to their relative energy and direct visual inspection in the structural integrity. The top ten candidates with decent stabilities are compared with entries stored in publicly available crystallographic databases, including Materials Project, Jarvis, Open Quantum Materials Database (OQMD) and Atomly^[31-33]. This process eliminates repetitive and existing GdScO₃ crystal structures, resulting in three new crystal structures 1-3 [Table 1 and Figure 2]. The data associated with this article is provided and is publicly available. The optimized atomic structures are provided at https://github.com/Zhang-NJ-Lab/GdScO3_CSP/tree/main/Crystal_Structures/OptimizedStructures. The initial input files for these four k-spacing values are available on the GitHub repository at: https://github.com/Zhang-NJ-Lab/GdScO3_CSP/tree/main/inputFold. The MAGUS input files (scripts) are provided at https://github.com/Zhang-NJ-Lab/GdScO3_CSP/blob/main/input.yaml (MAGUS yaml scripts) and https://github.com/Zhang-NJ-Lab/GdScO3_CSP/tree/main/inputFold (VASP input files). The code and the NLP model are provided on the GitHub website: https://github.com/Zhang-NJ-Lab/NJmatNLP/blob/main/NLP.py and https://figshare.com/articles/software/NJmatML/24607893?file=45863628.

Figure 2. Crystal structures of three new predicted GdScO₃ with different viewpoints. (A) The monoclinic structure 1; (B) The hexagonal structure 2; (C) The orthorhombic structure 3. GdScO₃: Gadolinium scandate.

Post-hoc first-principles electronic structure calculation

DFT calculations are performed using the CASTEP^[34,35] software package. Structural optimizations and property calculations are performed based on the three new crystal structures identified in the previous genetic+DFT step. The convergence criteria in the post-hoc DFT initial geometry optimization step are set to 1.0 × 10^-5 eV for the energy, 0.01 eV/Å for the force, 0.02 GPa for the stress and 5.0 × 10^-4 Å for the displacement, with PBE functional, 530 cutoff energy, ultrasoft pseudopotential and a 5 × 5 × 2 k-point set. Subsequently, a 9 × 9 × 4 k-point set is adopted to obtain the electronic properties such as its band structures, density of states (DOS) and UV-vis absorption spectra. The optimized crystal structure and the Magus parameter files are provided on the GitHub website (publicly available): https://github.com/Zhang-NJ-Lab/GdScO3_CSP. For example, the three crystal structures (after geometrical optimization) are provided at https://github.com/Zhang-NJ-Lab/GdScO3_CSP/tree/main/Crystal_Structures/OptimizedStructures.

Literature language model

The NLP workflow to construct the language model involves several essential steps: preparing the literature database, preprocessing, training the literature model, and performing dimensional reduction and clustering for visualization purposes. The construction of the language model analyzes the ontology of GdScO₃ from an alternative machine learning point-of-view based on the abstracts of 1.18 million scientific articles published in Springer Nature from 1960 to 2024 [Supplementary Materials], which corresponds to a concise summary of scientific information. This makes them a versatile data source despite some information loss compared to full texts. The searching criteria are associated with subjects in the domain of materials science, physics and chemistry. Additional preprocessing tasks include sentence splitting, tokenization, custom dictionary creation, spell checking, part-of-speech tagging, lemmatization, stemming, and tokenization. These steps are executed using the Natural Language Toolkit (NLTK) and verified with ChemDataExtractor for appropriate named entity recognition. The literature model is trained using Word2Vec with the following parameters: vector_size set to 100, window size of 10, sg set to 1, sample set to 1 × 10^-3, and trained over five epochs. Additionally, t-distributed stochastic neighbor embedding (t-SNE) is employed to reduce the dimensionality of the word vectors, with hyperparameters set to n_components = 2 and random_state = 42. The cosine similarity is calculated to demonstrate the evaluation of the potential applications of the perovskite material as follows:

Here, A_i and B_i represent the word vectors of the material formula and the target vocabulary in the language model. Cosine similarity ranges from -1 to 1, where a cosine similarity of 1 indicates that the angle between the two vectors is zero (more likelihood that the material can be used for certain applications), a cosine similarity of 0 indicates that the angle is 90°, and a cosine similarity of -1 indicates complete dissimilarity with an angle of 180°.

Crystal structure prediction

Three new crystal structures of GdScO₃ (1-3) are predicted by the machine learning crystal structure prediction method assisted via genetic algorithm: 1 has a monoclinic lattice and Cm space group (a = 6.372 Å, b = 3.485 Å, c = 8.819 Å, α = 90°, β = 138°, γ = 90°); 2 has a hexagonal lattice and P6₃/mmc space group (a = 3.612 Å, b = 3.612 Å, c = 12.396 Å, α = 90°, β = 90°, γ = 120°); 3 has an orthorhombic crystal lattice and Pnma space group (a = 5.776 Å, b = 7.977 Å, c = 5.534 Å, α = 90°, β = 90°, γ = 90°). The atoms in the three crystal structures exhibit tilted octahedrons [Figure 2] that correspond to Jahn-Teller distortions with longer equatorial bonds and shorter vertical bonds. In 1, the Sc–O bond lengths range from 2.04 to 2.09 Å, while the Gd–O bond lengths vary from 2.27 to 2.41 Å. In 2, the Sc–O bond lengths span from 2.07 to 2.09 Å, and the Gd–O bond length is 2.33 Å. In the structure, the planar Gd–O layers are interconnected by ScO₆ octahedrons, forming a quasi-layered architecture that may benefit the solar-rechargeable battery application^[36,37]. In addition, 3 exhibits Sc–O bond lengths from 2.10 to 2.13 Å, while the Gd–O bond lengths range from 2.28 to 2.67 Å. To sum up, the crystal structures of 1-3 differ from those reported in available crystal databases and their electronic and optical properties will be further evaluated.

Electronic structures

The band structures of the three new crystal structures of GdScO₃ predicted via genetic algorithms are examined to understand their electronic properties [Figure 3 and Supplementary Figure 1]. The band structures reveal a semimetallic pattern with a minority of band lines crossing the Fermi level near the Γ point before bending back. However, the semimetal feature is not significant and they can be considered as shallow defects that minimally influence the electronic excitation between valence band and conduction band in many cases^[38,39]. Several semimetal materials have been demonstrated to deliver bulk photovoltaic effects and generate shift and injection photocurrents allowed by noncentrosymmetry^[40]. Specifically, the monoclinic phase 1 characterized by the Cm space group exhibits an electronic band structure with a forbidden gap of 0.48 eV between 0.259 and 0.735 eV; this refers to a single band line ranging from -0.136 to 0.259 eV passing through the Fermi energy, and a nearby band line ranging from 0.735 to 0.974 eV is available. As a result, the band structure shows an energy gap between the neighboring bands near the Fermi level and the defect is considered to be shallow. The semimetallic behavior of the monoclinic phase suggests potential applications in spintronics and thermoelectric devices, where high electrical conductivity and thermoelectric efficiency are desirable. The hexagonal phase 2 of GdScO₃, characterized by the P6₃/mmc space group, exhibits a similar band structure feature showcasing the semimetallic behavior. For 2, multiple band lines pass through the Fermi energy level, such as one ranging from -0.064 to 0.086 eV and a second band line ranging from -0.058 to 0.122 eV. Meanwhile, there is no distinctive energy gap near the Fermi energy level, and the metallic behavior of 2 is suggested to be stronger than 1. In addition, the orthorhombic phase 3 of GdScO₃ characterized by the Pnma space group exhibits a band structure indicating slight semimetallic behavior; e.g., a forbidden gap of 0.851 eV is available for 3 between 0.056 and 0.907 eV and the empty states at 0.056 eV is considered to be shallow defects^[41-43]. The semimetal feature observed in these structures can be considered as shallow defects. This is based on the fact that these defects, akin to those observed in perovskite materials, introduce energy levels close to the band edges. As a result, they have a negligible effect on electronic excitation processes, which is crucial for maintaining efficient charge transport in applications such as photovoltaics. The shallow nature of these defects ensures that they do not act as major recombination centers, aligning with the established behavior of similar defects in perovskite materials. To sum up, the genetic algorithm identifies three distinct crystal structures of GdScO₃ with minor semimetallic features corresponding to shallow defects toward optoelectronic applications.

Figure 3. Band structures of new GdScO₃ crystal structures, including (A) the monoclinic structure 1; (B) the hexagonal structure 2; and (C) the orthorhombic structure 3. The Fermi level corresponding to the highest occupied state is set at 0 eV. GdScO₃: Gadolinium scandate.

The PDOS spectra of 1-3 [Figure 4] further illustrate the details of the electronic properties of the genetic-predicted new crystal structures of GdScO₃. An energy gap is available for 1-3 near 0.5 eV. The semimetallic feature is more prominent for 2 because of the additional empty states near 0.4 eV. In contrast, the valence band and conduction band of 1 and 3 are more separated, suggesting a reduced possibility of charge recombination after light excitation. For 1 and 3, the Gd elements mainly contribute to the energy states near 0 eV while the Sr-d orbitals mainly contribute to the conduction band for 2. In addition, the oxygen-p orbitals are universally present in the valence bands of 1-3 and contribute strongly to the bands from -4 to -2 eV. It is expected that charge transfers such as Gd → Gd, Gd → Sr, O → Gd and O → Sc may occur upon light excitation. In the X-ray photoelectron spectroscopy (XPS) and DFT analysis in the literature^[44], the O 2p states are observed in the region from -3 to -5.5 eV, which is consistent with the present research. The Gd 4f states appear in a more localized region, and this spatial and energetic proximity suggests interactions between the O 2p and Gd 4f orbitals, indicating a potential charge transfer from oxygen to gadolinium. Additionally, the presence of Gd 5p states and Sc 3p states provides further evidence of charge distribution involving Gd and Sc atoms. The consistency between these XPS features and DFT calculations supports the proposed charge transfer pathways, particularly O → Gd and O → Sc. As a result, the optoelectronic performance of these new crystals of GdScO₃ is considered to be decent, and further structural engineering is required to further optimize the optoelectronic properties of these crystals.

Figure 4. PDOS spectra of the GdScO₃. (A-D) Total DOS (total) and projected DOS (s, p and d) of 1; (E-H) Total DOS and projected DOS of 2; (I-L) Total DOS and projected DOS of 3. PDOS: Partial density of states; GdScO₃: gadolinium scandate; DOS: density of states.

The simulated UV-vis absorption spectra of 1-3 [Figure 5] demonstrate distinctive absorption bands in the UV-vis region. The absorption intensity is higher for 3 between 450 and 700 nm in the visible region (reaching 30,000 at the peak wavelength of 525 nm). However, 1 displays a strong absorption band near 800 nm, which is distinctive among the three. The absorption intensity of 2 in the visible region is comparatively inferior; however, 2 exhibits a large UV absorption intensity at 300 nm in the UV region. To conclude, the new GdScO₃ perovskite structures demonstrate decent absorption in the UV-vis region toward optoelectronic applications.

Figure 5. Simulated UV-vis absorption spectra of GdScO₃ crystal structures. UV-vis: Ultraviolet-visible; GdScO₃: gadolinium scandate.

Strain effects

The strain effects on the band structure of material 1 are evaluated by applying strains ranging from -10% to 10%, in increments of 2% [Figure 6]. This range includes both compressive (negative) and tensile (positive) strains, allowing for a comprehensive analysis of how different strain levels influence the material’s electronic properties. The band structures exhibit intricate changes as the strain is varied from compression (-10%) to tension (+10%). The symmetry of the band structures changes with strain; under compressive strain, the band lines show higher symmetry compared to those under tensile strain. In addition, the bandwidth changes with the strain values, with certain bands widening or narrowing significantly as the strain varies, highlighting the intricate sensitivity of the material’s electronic band structure to mechanical strain. (1) Applying compressive strain to GdScO₃ causes variation in the band lines that cross the Fermi level, resulting in a less pronounced crossing at the Γ and Y points in the Brillouin zone and potentially a reduction in the level of defects near the Fermi level toward optoelectronic application. In addition, this influences the effective mass of charge carriers as well as charge carrier mobility and electrical conductivity. The negative strain causes smaller energy separation between the neighboring empty band near 1 eV and the valence bands, leading to less pronounced semimetallic behavior under compressive strain; (2) Conversely, under tensile strain, the band line that crosses the Fermi level shifts upwards near the special points including M and A. Nevertheless, the level of defects near the highest occupied states is not prominent and the separation between the conduction band near 1 eV and the valence band near 0 eV is distinctive; this is associated with a shallow defect and desirable band gap formation in topological materials. Apart from that, the application of tensile and compressive strain often witnesses a reduction in the amount of empty states above the highest occupied states, signifying a possible minimization of undesirable defects near the valance band toward optoelectronic applications. These observations are crucial for photovoltaic applications where the material may be subjected to varying mechanical stresses, such as in flexible electronics or strain-engineered semiconductors.

Figure 6. Band Structure of the monoclinic structure 1 with strain level from -10% (compressive strain) to 10% (tensile strain): (A) -10%, (B) -8%, (C) -6%, (D) -4%, (E) -2%, (F) 0%, (G) 2%, (H) 4%, (I) 6%, (J) 8%, (K) 10%.

The simulated UV-vis absorption of 1 further displays the impacts of mechanical strain on the optoelectronic properties of GdScO₃ [Figure 7]. Three distinctive regions in the UV-vis spectra are clearly influenced by the strain: a band in the UV region centered at 350 nm; a second band in the visible region centered at 590 nm; a third band in the near-infrared region centered at 850 nm. For the first band in the UV region, shifting from the negative strain to the tensile strain (from -10% to 10%) results in a monotonic absorption intensity reduction (bleaching effects). Nevertheless, both bands peaked at 590 and 850 nm demonstrate an initial reduction in the absorption intensity but a subsequent upward shift in the intensity when the tensile strain is more prominent. The transition occurs at strain = -4% for the band peaked at 590 nm and strain = -2% for the band peaked at 850 nm. As a result, both tensile and compressive strains may lead to enhanced absorption intensity in the visible and near-infrared region, while the absorption intensity is higher for the compressive strain and lower for the tensile strain in the UV region. To sum up, the light absorption properties of the predicted GdScO₃ can be strongly influenced by external mechanical stimuli.

Figure 7. Strain effects on the simulated UV-vis absorption spectra of the monoclinic structure 1. (A) Negative strain effects; (B) Positive strain effects. UV-vis: Ultraviolet-visible.

Language model analysis of GdScO₃

The ontology of GdScO₃ material is comparatively insufficiently investigated and a holistic investigation is carried out in this study using language model employing 1.18 million scientific articles. The textual words are vectorized to evaluate the latent relationships between materials and their potential applications [Figure 8]. The NLP workflow for constructing the language model involves several key steps, including preparing the literature database, preprocessing, training the model using Word2Vec with a skip-gram approach, and performing dimensionality reduction for visualization [Supplementary Materials]. The literature database, built using the SpringerNature API, spans physics and chemistry publications from 1960 to 2020, covering abstracts from 1.18 million articles. In the skip-gram model, a shallow neural network is employed in an unsupervised manner to convert each word into a 200-dimensional vector. This model optimizes the probability P(w_c|w_t) of a context word w_c given a target word w_t, by minimizing the loss function J, where w_t is the center word and w_t-1, w_t-2, w_t+1, w_t+2 are the surrounding context words. To visualize the high-dimensional word vectors, t-SNE is used, which reduces the dimensionality by preserving the local structure of data, effectively mapping similar high-dimensional points to nearby points in lower dimensions. This method minimizes the divergence between probability distributions of points in the high-dimensional space and their corresponding low-dimensional representations. Finally, cosine similarity is calculated to evaluate the potential applications of materials, and they are ranked for photovoltaic applications. Known solar cell materials such as FAPbI₃, CIGS, MAPbI₃, GaAs, CdTe, and InP are identified. GdScO₃, with comparable cosine similarity, suggests potential as a promising photovoltaic material, as corroborated by the clustering effects observed after t-SNE dimensional reduction. Currently, the applications of GdScO₃ are mainly limited to high-k dielectric material in electronic devices, thin film capacitors and as a substrate for the epitaxial growth of materials in advanced electronic devices. However, the language model suggests that the GdScO₃ material is also recommended for various alternative applications related to semiconductors, photoconductivity, composites, photoemission, interfaces, devices and photovoltaics. For example, the language model recommends GdScO₃ for photovoltaic application; after t-SNE, GdScO₃ clusters with CIGS, CIGSe, GaAs and MAPbI₃ that are typical solar cell materials (dark region) [Figure 9 and Supplementary Figure 2]. In addition, the cosine similarity between GdScO₃ and photovoltaic is high, and the similarity value is comparable to that of typical solar cell materials such as CdTe and InP. This suggests the possibility of this perovskite oxide material for optoelectronic application. This, to some extent, contradicts the previous DFT calculations regarding the defects and semimetallic features of GdScO₃. However, the following two points are suggested to justify the suitability of GdScO₃ for photovoltaic applications. (1) The semimetallic features of 1-3 are not completely detrimental for photovoltaics evidenced by the apparent forbidden gap next to the band lines near the Fermi level, and the defects are considered to be shallow toward the light excitation; (2) Photovoltaic effects have been observed in several semimetal materials, including the colossal mid-infrared bulk photovoltaic effect in a Type-I Weyl semimetal, and optically induced thermal gradients via the Seebeck effect are suggested to benefit the current production provided with careful balance of the optical, electronic and thermal material properties^[40,45,46]. In addition, for perovskite-based materials (where the target word is perovskite and the cosine similarity is calculated between the material formula entity and the application entity), the GdScO₃ material clusters with MAPbI₃, FAPbI₃ and MAPbBr₃ that are typical hybrid perovskite materials toward photovoltaic applications. Meanwhile, the spatial distribution of GdScO₃ is far away from the comparatively inferior halide perovskite CsPbI₃ material toward the photovoltaic application, manifesting the potential of GdScO₃ toward this particular application. Moreover, the GdScO₃ material clusters well with CIGS, GaAs and InP for semiconductor application. Similarly, higher cosine similarity is observed between GdScO₃ and various applications such as photoconductivity, composite, photoemission, interfaces and devices. To sum up, the language model obtained via 1.18 million scientific articles suggests that GdScO₃ is a possible material for photovoltaic applications.

Figure 8. Language model analysis for GdScO₃. (A) Workflow of the language model construction and materials analysis, starting from scientific literature database and followed by preprocessing, model construction, dimension reduction and materials prediction. Here, the skip-gram method to predict textual words; (B) Ranking of exemplar materials identified by the language model toward photovoltaic application based on cosine similarity. GdScO₃: Gadolinium scandate.

Figure 9. Visualization of language model for analyzing GdScO₃ toward various potential applications, which are based on t-SNE dimension reduction from a language model using 1.18 million scientific articles. The following targets are evaluated: (A) perovskite, (B) semiconductor, (C) photovoltaic, (D) photoconductivity, (E) composite, (F) photoemission, (G) interfaces and (H) devices. GdScO₃: Gadolinium scandate; t-SNE: t-distributed stochastic neighbor embedding.