A Deterministic Limit for Photovoltaic Efficiency: Deriving the Critical Defect Capture Radius via Carrier Diffusion

The prediction of non-radiative energy loss in advanced photovoltaics, particularly regarding Shockley-Read-Hall (SRH) recombination at lattice defects, relies heavily on empirical carrier lifetimes and bulk statistical capture cross-sections. While these macroscopic frameworks estimate aggregate quantum efficiency and fill-factor degradation, they fail to deterministically define the exact spatial boundary where localized electrostatic defect trapping triggers irreversible carrier loss. This paper introduces a continuum framework for solid-state recombination dynamics. By modeling the semiconductor lattice as a dynamic balance between charge transport (carrier diffusion) and localized electrostatic capture (defect trapping), we derive a universal critical capture radius (Rcapture). We demonstrate that efficiency loss is not a probabilistic decay but an exact deterministic limit where localized defect trapping overpowers the advective carrier-sweeping capacity of the surrounding crystal. We propose a blueprint for Defect-Immune Photovoltaics, utilizing nanoscale photoluminescence mapping to apply targeted spatial passivation solely to defects that breach the geometric stability threshold.