Modeling Nonradiative Recombination in CsPbI₃ and Ge-Doped Perovskites Via Deep Learning with CNN and Transformer Architectures

Nonradiative electron-hole recombination is a key factor in the performance bottleneck of perovskite optoelectronic devices, and its rate is highly dependent on nonadiabatic (NA) coupling and electron coherence. Traditional first-principles-based NA coupling calculations have the problems of high computational overhead and low efficiency, which limit their wide application in complex systems such as doping regulation. This work adopts a CsPbI₃ and Ge-doped system as the research object, combines density functional theory with nonadiabatic molecular dynamics (NAMD), uses Hammes-Schiffer-Tully (HST) and norm-preserving interpolation (NPI) strategies to systematically evaluate four types of NA couplings, and introduces a variety of deep learning models (including four convolutional neural networks and three Transformer structures) to achieve efficient prediction. Among them, the ResNetPlus model achieved the highest average determination coefficient R² (0.915) in each task and the TSTPlus model performed best in the Transformer class. After embedding the predicted coupling into the NAMD simulation, the nonradiative recombination lifetime obtained is highly consistent with the direct calculation. Further analysis of spatially localized modes and pure decoherence functions revealed that the enhanced localized vibration frequency caused by Ge doping reduced the coherence time from 9.20 to 4.81 fs, accelerating the decoherence process of the system. At the same time, the enhanced localization of the conduction band minimum and valence band maximum charge distribution led to a significant weakening of the NA coupling strength (HST decreased from 0.296 to 0.171 meV; NPI decreased from 0.832 to 0.407 meV), and the synergistic effect of the two effectively delayed nonradiative recombination (HST lifetime increased from 18.96 to 61.44 ns, while NPI lifetime extended from 1.16 to 6.94 ns). This work not only reveals the microscopic regulation mechanism of Ge doping on the nonequilibrium recombination process but also provides theoretical guidance for the construction of efficient and stable perovskite materials and demonstrates the broad application prospects of deep learning in the modeling of complex excited-state processes.