We develop a framework to understand the performance of tandem organic photovoltaic (OPV) cells consisting of a series-connected stack of an arbitrary number of sub-cells. The power conversion efficiency penalty, Δη, is defined as the loss incurred when the tandem cell is at its maximum power point (MPP) but one or more sub-cells are not operating at their individual MPPs. To minimize Δη, the current at the MPP for each sub-cell must be equal. We also develop a method to calculate the tandem cell spectral mismatch factor and fill factor, showing that they are related to both the fill factors and short circuit currents of all the constituent sub-cells. By including the current generated in the dark, exciton dissociation at the donor-acceptor heterojunction, and photoconductivity, along with current losses due to polaron-pair and bimolecular recombination, we simulate the operation of small molecule bilayer and mixed-layer sub-cells used in the tandem, and from these results derive the behavior of the integrated device. This analysis is used to understand and optimize tandem OPV cell performance.
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