Exciton dissociation at heterojunctions in photovoltaic devices is not completely understood despite being fundamentally necessary to generate electrical current. One of the fundamental issues for ab initio calculations is that hybrid interfaces combining materials with Wannier-Mott excitons and those with Frenkel excitons can easily require thousands of atoms to encompass the exciton-wave function. The problem is further exacerbated by a large permittivity difference at the interface, which requires meso-scale boundary conditions to accurately predict electrostatic potentials. For these reasons, we have constructed a model of excited states at hybrid interfaces based on an effective mass Schroedinger equation. In this continuum model, carrier wave functions are represented by their envelope function rather than resolving the atomic scale variations. Electrostatic interactions are accounted for using the Poisson equation. For our model system, we use a pentacene/silicon interface. Because carrier mobility is low in pentacene relative to silicon, the hole is frozen such that it only interacts with the electron though an immobile positive charge density. The inputs to this model are as follows: dielectric permittivities, electron effective masses, interfacial width, band alignment, and the hole wave function. We find that the energetic favorability of charge transfer states relative to bulk excitons is most easily controlled by band alignment. However, when both states have similar energies, interface proximity and electrostatics become important secondary means of tuning the relative stability of these states.
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