A combined diffusion/rate equation model to describe charge generation in phase-separated donor-acceptor blends

TL;DR

This paper introduces an analytical model combining exciton diffusion and Marcus theory-based charge transfer to better understand charge generation in phase-separated donor-acceptor blends, highlighting the importance of exciton lifetime.

Contribution

The model provides a new analytical framework for analyzing charge generation dynamics considering exciton diffusion and rate equations, advancing understanding of organic solar cell efficiency.

Findings

Intrinsic exciton lifetime is crucial for efficient charge generation.

Charge generation times are shorter than exciton diffusion times in low-offset systems.

Y6 domain size estimated at 25nm from the model.

Abstract

The power conversion efficiency (PCE) of organic solar cells (OSCs) has been largely improved by the introduction of novel non-fullerene acceptors (NFAs). Further improvements in PCE require a more comprehensive understanding of the free charge generation process. Recently, the small PCE of donor-acceptor blends with low offsets between the relevant frontier orbitals was attributed to inefficient exciton dissociation. However, another source of photocurrent loss is the competition between exciton diffusion and decay, which is particularly relevant for bilayers or bulk heterojunction blends with phase separated morphology. Here, we present an analytical model that combines exciton diffusion with a set of rate equations based on Marcus theory of charge transfer. An expression for the charge generation efficiency is derived from the steady-state solution of the model. Thereby, the intrinsic exciton lifetime is identified as a pivotal parameter to facilitate efficient charge generation in spite of a vanishing driving force for exciton dissociation. The dynamic formulation of the model is used to elucidate the characteristic time scales of charge generation. It is found that for low-offset systems, the pure diffusive times are considerably shorter than those associated with charge generation. It can therefore be concluded that when estimating domain sizes via exciton diffusion measurements, the assumption that excitons are instantaneously quenched at the donor-acceptor interface is only valid when a high driving force for exciton dissociation is present. The model is applied to the transient absorption dynamics of a PM6:Y6 blend. It is demonstrated that the charge generation dynamics are determined by the interplay between exciton diffusion and hole transfer kinetics, with an estimated Y6 domain size of 25nm, while interfacial charge transfer (CT) states separate rapidly into free charges.