S-Shaped ${I}$ – ${V}$ Characteristics of Organic Solar Cells: Solving Mazhari’s Lumped-Parameter Equivalent Circuit Model

Abstract

We explain how to obtain closed-form analytic solutions from the set of equations that describe the three-diode lumped-parameter equivalent circuit model proposed by Mazhari [1] to portray the undesirable S-shape often observed in ${I}$ – ${V}$ characteristics of illuminated organic solar cells (OSCs), and occasionally seen in other types of solar cells. This allows quick extraction of the model’s parameter values by directly fitting the resulting closed-form solution to the cell’s measured ${I}$ – ${V}$ data. Such mathematical simplification of the extraction procedure facilitates individually studying the effect of each parameter on the illuminated OSC ${I}$ – ${V}$ characteristics, and thus on its power generation capacity. We illustrate application of the direct extraction procedure to measured ${I}$ – ${V}$ characteristics of an experimental OSC, which exhibits the illumination intensity-dependent S-shapes. The usefulness of the analytic solution to assess the effect of the model parameters is further corroborated by graphically illustrating the progression of a series of hypothetical synthetic ${I}$ – ${V}$ characteristics generated by this analytic solution using gradually changing the parameter values. Analysis of the results, in this case, indicates that activation of the diode that represents recombination is the key factor responsible for the emergence of the illuminated ${I}$ – ${V}$ curve’s S-shape.