Solar cells offer a clean, renewable energy source because of the huge amount of solar energy received on earth from the sun. Organic solar cells are a viable technology to capture the solar radiation because of many advantages including light weight, flexibility, ability to adapt to a variety of surfaces such as roofs, and simple and low manufacturing costs [1]. However, for large scale manufacturing of organic solar cells with predictable performance, accurate physics-based engineering models are needed. Therefore, in this paper, we propose an analytical model to describe the current-voltage characteristics of organic bulk heterojunction (BHJ) solar cells. The model includes boundary conditions for the free charge density at the interfaces, expressed as a power function of the current density [2]. As the interfaces control the injected and the extracted current density, these boundary conditions play an important role in the determination of key parameters such as the open-circuit voltage V_oc or the short-circuit current J_sh. The model uses a previously developed idea of analytically solving the drift-diffusion equations for organic BHJ solar cells in which different assumptions are made. In particular, physical variables, such as the electric field, the charge carrier mobility, the generation rate, and the bimolecular recombination rate are considered uniform along the device for each applied voltage [3]. Despite this common starting point with other analytical expressions, our proposal solves different problems that still persist in previous analytical models, such as the use of constant boundary values for the electron and hole densities at the metal-organic interfaces [3-4] or the need of developing a previous numerical solution of the transport equations in order to provide initial guess values for some of the variables found in these equations [3].

In previous works, we demonstrated that non-constant values for the electron and hole densities at the interfaces of organic devices are required for the interpretation of current-voltage J-V curves [5-6]. In single-carrier metal-organic contacts under drift-dominated transport, we observe that the charge concentration at the interface, p(0), due to injection, follows a power-law function of the current density. This boundary condition for the charge density keeps information about the limited recombination velocity at the contacts and the contribution from space charge limited conduction (SCLC) in the bulk. In diffusion-dominated transport, at low bias close to the diode's built-in voltage, the charge density at the contact is almost constant with the current. The complete relation between charge and current for injecting electrodes, extracted from the analysis of single-carrier diodes, can be used as boundary condition in bipolar devices, which are the basis of organic solar cells [2].

In this work, we have incorporated our power law relation p(0)-J in the analytical expression of the J-V characteristics of organic solar cells (OSCs). Incorporating of the power law relation p(0)-J in the analytical expression adds information about the interfaces. Nevertheless, it introduces new parameters into the model. A parameter extraction procedure is also provided in order to fully characterize the J-V characteristics of OSCs. We have tested the expression in OSCs in dark and under illumination. We have checked that the use of non-constant values for the free charge density at the interfaces is especially important close to the V_oc and in the high voltage region. In the low voltage region, a parasitic shunt resistance must be added in order to consider recombination losses. Finally, a complete verification of the parameter extraction procedure is done.

This work has been supported by MINECO under research Project MAT2016-76892-C3-3-R.

[1] M.J. Deen, “Organic Semiconductor Devices,” Wiley Encyclopedia of Electrical and Electronics Engineering, Editor, J.G. Webster, John Wiley and Sons, Inc., 17 pp (Published on-line 15 Dec 2014).

[2] P. López-Varo, J.A. Jiménez-Tejada, O. Marinov, C.H. Chen, M.J. Deen, Org. Electron. , 35, 74 (2016).

[3] Inche Ibrahim, M. L.; Ahmad, Z. and Sulaiman, K. AIP Advances, 5, 027115 (2015).

[4] A. Cheknane, et al. Microelectron. J., 39, 1173 (2008).

[5] P. López-Varo, J.A. Jiménez Tejada, J.A. López Villanueva, M J. Deen, Org. Electron., 15, 2526 (2014).

[6] P. López-Varo, J.A. Jiménez Tejada, J.A. López Villanueva, M.J. Deen, Org. Electron., 15, 2536 (2014).