  Provided is a comprehensive description of a band gap thermodynamic model,
which predicts and explains key features of photosegregation in lead-based,
mixed-halide perovskites. The model provides a prescription for illustrating
halide migration driven by photocarrier energies. Where possible, model
predictions are compared to experimental results. Free energy derivations are
provided for three assumptions: (1) halide mixing in the dark, (2) a fixed
number of photogenerated carriers funneling to and localizing in low band gap
inclusions of the alloy, and (3) the statistical occupancy of said inclusions
from a bath of thermalized photocarriers in the parent material. Model
predictions include: excitation intensity ($I_{\textrm{exc}}$)-dependent
terminal halide stoichiometries ($x_{\textrm{terminal}}$), excitation intensity
thresholds ($I_{\textrm{exc,threshold}}$) below which photosegregation is
suppressed, reduced segregation in nanocrystals as compared to thin films, the
possibility to kinetically manipulate photosegregation rates via control of
underlying mediators, asymmetries in forward and reverse photosegregation rate
constants/activation energies, and a preference for high band gap products to
recombine with the parent phase. What emerges is a cohesive framework for
understanding ubiquitous photosegregation in mixed-halide perovskites and a
rational basis by which to manage the phenomenon.
