In this article, we continue our mathematical study of organic solar cells
(OSCs) and propose a two-scale (micro- and macro-scale) model of heterojunction
OSCs with interface geometries characterized by an arbitrarily complex
morphology. The microscale model consists of a system of partial and ordinary
differential equations in an heterogeneous domain, that provides a full
description of excitation/transport phenomena occurring in the bulk regions and
dissociation/recombination processes occurring in a thin material slab across
the interface. The macroscale model is obtained by a micro-to-macro scale
transition that consists of averaging the mass balance equations in the normal
direction across the interface thickness, giving rise to nonlinear transmission
conditions that are parametrized by the interfacial width. These conditions
account in a lumped manner for the volumetric dissociation/recombination
phenomena occurring in the thin slab and depend locally on the electric field
magnitude and orientation. Using the macroscale model in two spatial
dimensions, device structures with complex interface morphologies, for which
existing data are available, are numerically investigated showing that, if the
electric field orientation relative to the interface is taken into due account,
the device performance is determined not only by the total interface length but
also by its shape
