Ionic and electronic polarization effects in horizontal hybrid perovskite device structures close to equilibrium

The electrical response of hybrid perovskite devices carries a significant signature from mobile ionic defects, pointing to both opportunities and threats when it comes to functionality, performance and stability of these devices. Despite its importance, the interpretation of polarization effects due to the mixed ionic-electronic conducting nature of these materials and the quantification of their ionic conductivities still poses conceptual and practical challenges, even for the equilibrium situation. In this study, we address these questions and investigate the electrical response of horizontal devices based on methylammonium lead iodide (MAPI) close to equilibrium conditions. We discuss the interpretation of DC polarization and impedance spectroscopy measurements in the dark, based on calculated and fitted impedance spectra obtained using equivalent circuit models that account for the mixed conductivity of the perovskite and for the effect of device geometry. Our results show that, for horizontal structures with a gap width between the metal electrodes in the order of tens of microns, the polarization behavior of MAPI is well described by the charging of the mixed conductor/metal interface, suggesting a Debye length in the perovskite close to 1 nm. We highlight a signature in the impedance response at intermediate frequencies, which we assign to ionic diffusion in the plane parallel to the MAPI/contact interface. By comparing the experimental impedance results with calculated spectra for different circuit models, we discuss the potential role of multiple mobile ionic species and rule out a significant contribution from iodine exchange with the gas phase in the electrical response of MAPI close to equilibrium. This study helps to clarify the measurement and interpretation of mixed conductivity and polarization effects in hybrid perovskites with immediate relevance to the characterization and development of transistors, memristors and solar cells based on this class of materials as well as other mixed conductors.