Analytical Framework Relating Capacitance-Frequency Measurements and Hysteresis in Perovskite Solar Cells

Mobile ion migration strongly influences the electrical response and current-voltage hysteresis of perovskite solar cells. However, quantitative determination of ionic transport parameters typically requires transient measurements, extensive numerical simulations, and/or fitting procedures involving multiple uncertain parameters. Here, we present an analytical model that establishes a direct relationship between capacitance-frequency (C-f) characteristics and ionic transport properties in perovskite solar cells, while accounting for interlayer effects. The model describes the transition from the ion-screened depletion capacitance at low frequencies to the geometric capacitance at high frequencies and demonstrates that the characteristic transition frequency provides a direct measure of the dielectric relaxation time for ions. Furthermore, the model establishes a quantitative connection between C-f characteristics and scan-rate-dependent current-voltage hysteresis, enabling prediction of the scan-rate window in which maximum hysteresis occurs. Drift-diffusion simulations show excellent agreement with the analytical predictions over wide ranges of ion density, ion mobility, transport-layer mobility and doping concentration. Experimental measurements confirm the predicted correlation between capacitance and hysteresis. By providing a direct, physically transparent, and computationally efficient route for extracting ionic transport parameters from routine impedance measurements, this work offers a practical tool for quantifying ion migration and understanding dynamic phenomena in perovskite solar cells.