Optimizing Perovskites for Solar Cells with AI and DFT

By Soham NandiReviewed by Susha Cheriyedath, M.Sc.May 19 2024

In an article published in the journal Nature, researchers focused on designing B-site-alloyed ABX₃ multi-element metal halide perovskites (MHPs) with enhanced stability and optoelectronic properties.

By integrating density functional theory (DFT) and machine learning (ML), the authors screened 41,400 MHPs to identify 10 promising compounds. CsGe_0.3125Sn_0.6875I₃ and CsGe_0.0625Pb_0.3125Sn_0.625Br₃ were highlighted as potential photon absorbers for solar cells, demonstrating a novel framework for optimizing MHPs.

Background

MHPs with the ABX₃ formula, where A, B, and X represent monovalent organic/inorganic cations, divalent metal cations, and monovalent halide anions respectively, have gained significant attention for their exceptional optoelectronic properties, low cost, and ease of fabrication. These attributes make MHPs promising materials for photovoltaics, light-emitting diodes (LEDs), lasers, and photodetectors.

However, challenges such as the toxicity of lead (Pb) and instability under adverse conditions have hindered their commercialization. Traditionally, MHPs with methylammonium (MA) or formamidinium (FA) at the A-site and Pb at the B-site have shown the best optoelectronic properties, but the Pb content and stability issues remain problematic.

To address these issues, substitutional alloying has been proposed, where different elements are doped or mixed at each site in the MHPs to improve stability and reduce Pb content. High-entropy alloying, which involves mixing multiple elements to enhance thermodynamic stability, has shown promise in improving MHP performance.

Despite these advancements, the vast compositional space of MHPs with multiple alloying elements makes experimental exploration impractical. Previous computational approaches, such as DFT and ML, have been used to screen potential MHP compositions. However, these methods often do not guarantee the most stable atomic configurations.

This paper introduced a DFT/ML-combined framework using a crystal graph convolution neural network (CGCNN) to predict stability and electronic band structures of B-site-alloyed MHPs, addressing the gaps in previous studies. By exhaustively exploring all possible atomic configurations, the framework identified the most stable configurations and expanded the compositional space to include quaternary phases, providing more accurate predictions for potential MHP candidates.

Computational Methods for Generating and Analyzing B-Site Mixed Metal Halide Perovskites

The training data for this study were generated using DFT calculations with the Perdew–Burke–Ernzerhof functional for solids (PBEsol) functional. A crystal structure comprising four formula units of ABX₃ was used, focusing on multi-element mixing at the B-site. Monovalent alkali cations, cesium (Cs), potassium (K), rubidium (Rb) and halogen anions, bromine (Br), chlorine (Cl), iodine (I) were employed at the A- and X-sites, while six divalent metal cations, cadmium (Cd), germanium (Ge), mercury (Hg), Pb, tin (Sn), zinc (Zn) were considered for B-site mixing. This led to 1134 unique ABX₃ compositions and 3159 unique B-site-mixed structures for training.

A CGCNN was trained using these data. The input geometry was unrelaxed, predicting properties of the relaxed structures based on the well-known CsPbI3 structure. The data were divided into training, validation, and test sets in a 7:1:2 ratio. Model parameters were determined through early stopping.

Thermodynamic stability was assessed using decomposition enthalpy, which compared the energy of ABX3 with the most stable AX and BX₂ phases. The mixing entropy was calculated based on the ideal solid solution model. Additionally, the band type and bandgap were calculated using PBEsol to evaluate photovoltaic applications, distinguishing between indirect and non-indirect bandgaps.

The tolerance factor was used to predict perovskite stability. All DFT calculations were performed using the Vienna ab initio simulation package (VASP), employing projector-augmented wave pseudopotentials and optimizing cell parameters and atomic coordinates. Band structures were calculated for training data and selected compounds, with the hybrid functional (PBE0) providing more accurate bandgap predictions. Effective masses of electrons and holes, as well as optical absorption spectra, were also calculated to further evaluate the materials' properties.

Comprehensive Analysis and Screening of Mixed Metal Halide Perovskites for Photovoltaic Applications

The study's design strategy highlighted the workflow and use of PBEsol data to train three CGCNN models. These models independently predicted three target properties: decomposition enthalpy, bandgap, and band type classification. For band type classification, non-indirect and indirect band types were labeled as positive and negative classes, respectively.

To explore multi-element MHPs, a larger structure with 16 B-sites was used, enabling finer compositional resolution and alloying up to quaternary systems. The CGCNN-predicted decomposition enthalpy was used to identify stable atomic configurations, incorporating the mixing entropy term at 298 Kelvin. Bartel’s tolerance factor was employed to classify perovskites, showing better accuracy than Goldschmidt’s factor.

For solar-cell applications, compositions with direct bandgaps under 0.5 electron volt (eV) were selected, aiming for PBE0-calculated bandgaps of 1.0-2.0 eV, ideal for photovoltaics. Selected compounds underwent further PBEsol and PBE0 validation to assess stability and band structure. The spectroscopic limited maximum efficiency (SLME) was calculated using optical absorption spectra and bandgaps, assuming an air mass 1.5 global solar spectrum.

The training dataset analysis revealed trends in thermodynamic stability, with lower decomposition enthalpy for Ge-containing alloys. The researchers found positive correlations between Bartel’s tolerance factor and stability, despite some inconsistencies. Validation of the CGCNN models demonstrated promising accuracy in predicting stability, bandgap, and band type, despite a class imbalance in the data.

For B-site mixed MHPs, 41,400 compositions were explored using the CGCNN model. Screening criteria identified 110 compounds for solar-cell potential, further narrowed down to 31 candidates with direct bandgaps. Ultimately, 10 compounds were highlighted as promising for photovoltaic applications, with bandgaps and stability close to ideal values.

Conclusion

In conclusion, the researchers designed B-site-alloyed ABX₃ multi-element MHPs with enhanced stability and optoelectronic properties by integrating DFT and ML. Screening 41,400 MHPs, they identified 10 promising compounds, highlighting CsGe_0.3125Sn_0.6875I₃ and CsGe_0.0625Pb_0.3125Sn_0.625Br₃ as potential solar cell photon absorbers.

This novel framework addressed the challenges of Pb toxicity and stability, expanding the compositional space to include quaternary phases, providing accurate predictions for potential MHP candidates, and advancing the design of perovskite alloys for photovoltaic applications.