The Two Faces of Capacitance: New Interpretations for Electrical Impedance Measurements of Perovskite Solar Cells and Their Relation to Hysteresis
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(2018)cite arxiv:1807.00954.

Perovskite solar cells are notorious for exhibiting transient behaviour not seen in conventional inorganic semiconductor devices. Significant inroads have been made into understanding this fact in terms of ion migration, now a well-established property of the prototype photovoltaic perovskite MAPbI$_3$ and a likely feature in the newer mixed compositions. Here we study the manifestations of ion migration in frequency-domain small-signal measurements, focusing on the popular technique of Electrical Impedance Spectroscopy (EIS). We provide new interpretations for a variety of previously puzzling features, including giant photo-induced low-frequency capacitance and negative capacitance in a variety of forms. We show that these apparently strange measurements can be rationalized by the splitting of AC current into components associated with charge-storage and carrier recombination. The recombination-induced contribution to the capacitance can take either a positive or a negative sign, and is potentially very large when slow processes such as ion migration are at play. Using numerical drift-diffusion semiconductor models, we show that the slow process of ion migration can manifest as giant photo-induced capacitance, inductive loop features, and low-frequency negative capacitance, all via the oft-neglected recombination contribution to the capacitance. In doing so, we unify the understanding of EIS measurements with the comparably well-developed theory of rate dependent current-voltage (I-V) measurements in perovskite cells. Comparing the two techniques, we argue that EIS is more suitable for quantifying I-V hysteresis than conventional methods based on I-V sweeps, and demonstrate this application on a variety of cell types.
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