A Scale-Invariant Geometric Threshold for Exciton Diffusion: Deriving the Absolute Efficiency Limit of Bulk Heterojunctions via Spatial Propagation Dynamics

The Internal Quantum Efficiency (IQE) of organic photovoltaics (OPVs) is fundamentally bottlenecked by the short diffusion length of photogenerated excitons, typically restricted to ∼10 nm before spontaneous recombination occurs. Current fabrication paradigms rely on empirical morphological tuning of the donor-acceptor bulk heterojunction (BHJ) to approximate this scale. This paper introduces a deterministic topo-dynamical framework that replaces statistical exciton lifespans with a strict geometric boundary. By modeling exciton transport as a continuous spatial propagation operator competing against localized radioactive structural decay, we derive a scale-invariant geometric threshold (Λ∗). We mathematically demonstrate that this invariant defines the absolute physical maximum domain size for the BHJ lattice. By actively formulating polymer blend phase separation to strictly match this geometric limit, we outline a generalized, parameter-free methodology for engineering maximum-efficiency exciton harvesting in advanced organic photovoltaics and light-emitting diodes.