Fig. 1: The apparent dielectric constant of a MAPbI₃ thin film.

a As a function of frequency, obtained by impedance spectroscopy (black solid line). The red stars correspond to the apparent dielectric constant at the voltage scan rates used in the simulations (Sim values) in Fig. 3. b Temperature dependence of the apparent dielectric constant (red filled stars) at 0.0575 Hz (dashed line in Supplementary Fig. 1), corresponding to the scan rate of the temperature-dependent J–V measurements in Figs. 2 and 4. c Ion diffusion coefficient as a function of temperature, obtained from impedance spectroscopy (red circles). The measurements are fitted with an Arrhenius law with an activation energy of 0.42 eV (black line). The blue stars represent the ion diffusion coefficients used in the simulations.