Computational modeling has become an indispensable tool for understanding and predicting the properties of perovskite semiconductors. These materials, characterized by their ABX3 structure, exhibit exceptional optoelectronic properties, making them promising candidates for solar cells, light-emitting diodes, and other devices. Theoretical approaches such as density functional theory (DFT), molecular dynamics (MD), and machine learning (ML) provide deep insights into their electronic structure, stability, and transport mechanisms without the need for experimental synthesis.

Density functional theory is the most widely used method for studying perovskites at the atomic scale. DFT simulations enable the calculation of key properties such as band structure, density of states, and charge distribution. For hybrid organic-inorganic perovskites like MAPbI3 (MA = methylammonium), DFT reveals the role of spin-orbit coupling in reducing the bandgap, which is critical for photovoltaic efficiency. Generalized gradient approximation (GGA) functionals often underestimate bandgaps, but hybrid functionals like HSE06 or GW approximations yield more accurate results. For example, the bandgap of MAPbI3 is calculated as 1.6 eV with HSE06, closely matching experimental observations. DFT also predicts the impact of halide substitution, showing how replacing iodine with bromine or chlorine tunes the bandgap from 1.5 eV to 2.3 eV.

Defect formation energies are another critical aspect studied using DFT. Point defects such as vacancies, interstitials, and antisite substitutions influence charge carrier lifetimes and recombination rates. In lead halide perovskites, iodine vacancies exhibit low formation energies, making them common defects that act as shallow traps. DFT calculations demonstrate that these vacancies introduce defect states near the valence band, facilitating non-radiative recombination. Similarly, lead vacancies are deep-level defects that degrade performance. Defect passivation strategies, such as incorporating potassium or cesium, can be modeled to assess their effectiveness in reducing trap densities.

Phase stability is a major concern for perovskites, particularly under environmental stressors like moisture and heat. DFT-based phonon calculations and ab initio molecular dynamics (AIMD) simulations evaluate thermodynamic stability by analyzing formation enthalpies and phase transition barriers. For instance, cubic-to-tetragonal phase transitions in MAPbI3 occur around 330 K, and AIMD simulations capture the dynamics of MA cation rotation during this transition. Entropic contributions are also critical; Gibbs free energy calculations reveal that entropy stabilizes the cubic phase at higher temperatures. Additionally, DFT predicts how strain engineering or alloying can enhance stability, such as by mixing formamidinium (FA) and cesium to suppress phase segregation.

Molecular dynamics simulations extend beyond static DFT calculations by modeling time-dependent atomic interactions. Classical MD with force fields like ReaxFF or polarizable models captures ion migration, a key degradation mechanism in perovskites. Simulations show that halide ions diffuse through vacancies, with activation energies ranging from 0.1 to 0.5 eV depending on the crystal phase. AIMD provides higher accuracy by incorporating electronic effects, revealing that ion migration is coupled with lattice distortions. These insights guide the design of more stable compositions, such as 2D Ruddlesden-Popper perovskites, where bulky organic spacers suppress ion diffusion.

Carrier transport models combine DFT and MD results with Boltzmann transport theory or non-adiabatic dynamics to predict mobility and recombination rates. Electron-phonon coupling is a dominant factor, with Fröhlich interactions limiting mobility to around 100 cm²/Vs in MAPbI3. Quantum dynamics simulations further show that hot carriers cool within picoseconds, while charge localization occurs at grain boundaries or defects. Kinetic Monte Carlo methods simulate larger-scale transport, quantifying how grain size and morphology affect device performance.

Machine learning accelerates property prediction by bypassing expensive quantum calculations. Trained on datasets from DFT or experiments, ML models predict bandgaps, formation energies, and defect tolerances for vast chemical spaces. Descriptors such as ionic radii, electronegativity, and tolerance factors are used to screen potential perovskites. For example, random forest models identify Cs2AgBiBr6 as a stable lead-free alternative with a predicted bandgap of 1.8 eV. Neural networks also optimize doping concentrations by learning defect-energy relationships from high-throughput DFT data.

Challenges remain in computational modeling. DFT struggles with strongly correlated systems, requiring advanced methods like DFT+U or dynamical mean-field theory. MD simulations face trade-offs between accuracy and computational cost, while ML models depend on data quality and diversity. Future directions include integrating multi-scale simulations and active learning to explore uncharted perovskite compositions.

In summary, computational modeling provides a powerful framework for understanding perovskites. DFT reveals electronic and defect properties, MD uncovers dynamic processes, and ML enables rapid material discovery. These methods collectively advance the design of high-performance, stable perovskite semiconductors for next-generation technologies.