  In this article we address the theoretical study of a multiscale
drift-diffusion (DD) model for the description of photoconversion mechanisms in
organic solar cells. The multiscale nature of the formulation is based on the
co-presence of light absorption, conversion and diffusion phenomena that occur
in the three-dimensional material bulk, of charge photoconversion phenomena
that occur at the two-dimensional material interface separating acceptor and
donor material phases, and of charge separation and subsequent charge transport
in each three-dimensional material phase to device terminals that are driven by
drift and diffusion electrical forces. The model accounts for the nonlinear
interaction among four species: excitons, polarons, electrons and holes, and
allows to quantitatively predict the electrical current collected at the device
contacts of the cell. Existence and uniqueness of weak solutions of the DD
system, as well as nonnegativity of all species concentrations, are proved in
the stationary regime via a solution map that is a variant of the Gummel
iteration commonly used in the treatment of the DD model for inorganic
semiconductors. The results are established upon assuming suitable restrictions
on the data and some regularity property on the mixed boundary value problem
for the Poisson equation. The theoretical conclusions are numerically validated
on the simulation of three-dimensional problems characterized by realistic
values of the physical parameters.
