Trap-Controlled Ideality Factors in Metal–Halide Perovskite Solar Cells: A Unified Analytical Framework

Metal–halide perovskites display diode behavior that systematically deviates from classical Shockley theory, yet the physical origin of their noninteger ideality factors remains debated. Here, we derive a unified analytical framework that links the ideality factor nid to the energetic level and occupancy of defect states, the quasi-Fermi-level splitting at open circuit, and the detrapping kinetics of injected charge. By consistently treating illumination- and bias-dependent measurements, the framework clarifies why trap-assisted recombination in soft, defect-rich semiconductors generally yields 1 < nid < 2 and how nid evolves with trap-level energetics and voltage. The resulting expressions provide a physically transparent reinterpretation of widely used Voc–log(I) and Suns–Voc analyses in perovskite solar cells and offer a general route to quantify trap-controlled recombination in emerging semiconductor absorbers.