Abstract
Despite the very different underlying physics of organic photovoltaics (OPVs), inorganic p-n junction’s Shockley’s diode equation is often applied to describe current density–voltage (JV) curves of OPVs. The model parameters, including the diode saturation current, diode ideality factor, series, and parallel resistances, are usually extracted and treated as constants in JV curve analyses. In this work, we develop a drift-diffusion bilayer interface (DD-BI) model for bilayer OPVs, which treats the donor–acceptor (D–A) heterojunction using the detailed balance between densities of polaron pairs, free electrons, and free holes. From the DD-BI model, we derive a diode equation, which is of Shockley’s equation form, but each parameter is explicitly written in terms of the D–A interface properties. We call this model the self-consistent diode (SCD) model as it is consistent with the DD-BI results provided that the key parameters are from the simulation data. By studying the effects of light intensity and carrier mobility, we find that the Shockley SCD parameters are voltage dependent because of space charge accumulation around the D–A heterojunction. Our models are successful in explaining the common discrepancies in OPV JV curve analyses, such as the validity of fitting for series resistance, deviation of ideality factor from the theoretical values, and different resistance values under light and dark conditions. The results provide a better understanding of OPVs with a D–A heterojunction and how we can capture its physics using the SCD equation.
Highlights
The Shockley equation (SE), which was derived for inorganic p-n junctions,[1] is often applied to describe current density–voltage (JV) curves of organic donor–acceptor (D–A) heterojunction (HJ) solar cells,[2,3,4,5,6] despite fundamental differences between the two systems.[7]
We develop a driftdiffusion bilayer interface (DD-BI) model for bilayer organic photovoltaics (OPVs), which treats the donor–acceptor (D–A) heterojunction using the detailed balance between densities of polaron pairs, free electrons, and free holes
This paper focuses on introducing the self-consistent diode (SCD) and DD-BI models, and showing how the voltage dependence of the SCD parameters reflect the fundamental physics of device models
Summary
The Shockley equation (SE), which was derived for inorganic p-n junctions,[1] is often applied to describe current density–voltage (JV) curves of organic donor–acceptor (D–A) heterojunction (HJ) solar cells,[2,3,4,5,6] despite fundamental differences between the two systems.[7] Important characteristics of organic D–A HJ solar cells that are different from inorganic cells are lower carrier mobilities[8,9] and lower dielectric permittivity. Lower dielectric constant results in larger exciton binding energy and bound charge-pair states at D–A interfaces, which are usually referred to as charge transfer states or polaron pairs (PPs), while low mobilities enhance the importance of space charge effects.[10] The generalized Shockley equation with parasitic resistances is usually written as. Equivalent electrical circuit models similar to the SE are successful in describing electrical responses of OSCs in impedance spectroscopy measurements and providing insights into carrier dynamics.[12,13] the Shockley parameters are not constants (i.e., they are functions of voltage, light intensity, and charge transport properties12–14), so accurate descriptions of the Shockley parameters’ behavior are needed
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