(Invited) Role of the Metal-Organic Interfaces in the Dark Current-Voltage Characteristics of Organic Solar Cells
Authors: Jiménez Tejada J. a. , López Varo P. , Marinov O. , Deen M. Jamal 
Published: February 2020

Abstract. We present a model for the current-voltage curves of organic solar cells (OSCs), operating at dark conditions. The model relates the free charge density at the contact interface with the current density in OSCs. The strength and novelty of the model lie in the use of appropriate and physically-based boundary conditions for the charge and potential at the metal-organic interfaces. These boundary conditions contain information for the doping close to interfaces and for built-in voltage and band bending due to asymmetric contacts. We show that the values for the boundary conditions obtained from symmetric single-carrier diodes can be successfully used also for asymmetric double-carrier devices, such as OSCs, irrespectively of the dominant limit (space-charge, injection or diffusion) in the charge transport.

Motivation. Organic solar cells (OSCs) are a promising alternative for powering portable devices directly from sunlight [1]. To support these applications, analyses and physical modeling of OSCs are required. In particular, the electrical conduction of the OSCs is described by the drift-diffusion differential equations. However, the solutions of these equations depend on the boundary conditions (BCs) at the contacts.

Model and BCs. OSCs are asymmetric, with contacts to materials with different work functions, which result in built-in voltage Vbi
and generate a voltage V between the contacts under illumination. Previously in [2-4], by relating to the charge density at interfaces, we have proposed a model for the current density – voltage (J-V) curves of single-carrier organic diodes, considering high bias and conduction limited by space-charge (SCLC) and injection (ILC). However, the OSCs are double-carrier devices, and their photovoltaic operation is at low bias, 0<V<Vbi
, for which the diffusion dominates in the charge transport. We are now validating the model from [2-4] also for the diffusion regime at low bias of double-carrier diodes.
In our model, the boundary conditions for charge concentrations at their respective injecting contacts are Eqs. (1), where p and n are the hole and electron concentrations, respectively, and the model parameters K­
1p
, K­
1n
, mp, mn, K2p
and K2n
depend on the organic materials, energy barriers at interfaces and doping [5]. These parameters can be extracted from experimental J-V curves (symbols in Fig. 1) for electron-only Yb/PPV/Ca and hole-only ITO/Ag/PPV/Ag devices [6], by fitting the experimental J-V curves with the curves obtained from the numerical solutions of the transport equations, using (1) as boundary conditions at the injection interfaces.
The carrier densities at their respective extracting electrodes are assumed constant (2), since p(L) and n(0) are small, owing to the large Φ
4
/kT>>1 and Φ

1
/kT>>1, where, Φ
1

to Φ
4
are the barriers seen at the interfaces, (see inset of Figure 1) and NC
is the density of sites. Then, the charge boundary conditions extracted from single-carrier devices are introduced in the model of the double-carrier device.
Inspecting equations and results from numerical simulations, the potential distribution in the semiconductor V(x) can be approximated by a linear function (3), where b, b=kT/q[ln(q
2
NcL
2/2kTε)-2], is a band-bending related parameter [7]. This suggests that the hole Jp
and electron Jn
current densities are (4) and (5).
With the above boundary conditions, our J−V model (solid lines in Fig. 1) is in an excellent agreement with published experimental results at dark conditions, both for the aforementioned single-carrier devices and for the double-carrier Ag/PPV/Ca diode.

Conclusions. In this work, we present a model for J-V curves of OSCs that highlights the importance of the carrier density at interfaces. The model is valid for single- and double-carrier organic devices at dark conditions.

Acknowledgments. This work was supported by the Project mP_TIC_5 from Campus de Excelencia Internacional BioTic Granada.
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Figure 1