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Perovskite solar cells are notorious for exhibiting transient behaviour notseen in conventional inorganic semiconductor devices. Significant inroads havebeen made into understanding this fact in terms of rapid ion migration, now awell-established property of the prototype photovoltaic perovskite MAPbI$_3$and strongly implicated in the newer mixed compositions. Here we study themanifestations 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 negativecapacitance in a variety of forms. We show that these apparently strangemeasurements can be rationalized by the splitting of AC current into twocomponents, one associated with charge-storage, and the other with thequasi-steady-state recombination current of electrons and holes. The lattercontribution to the capacitance can take either a positive or a negative sign,and is potentially very large when slow, voltage-sensitive processes such asion migration are at play. Using numerical drift-diffusion semiconductormodels, we show that giant photo-induced capacitance, inductive loop features,and low-frequency negative capacitance all emerge naturally as consequences ofion migration via its coupling to quasi-steady-state electron and holecurrents. In doing so, we unify the understanding of EIS measurements with thecomparably well-developed theory of rate dependent current-voltage (I-V)measurements in perovskite cells. Comparing the two techniques, we argue thatEIS is more suitable for quantifying I-V hysteresis than conventional methodsbased on I-V sweeps, and demonstrate this application on a variety of celltypes.

The Two Faces of Capacitance: New Interpretations for Electrical Impedance Measurements of Perovskite Solar Cells and Their Relation to Hysteresis