Theory of Impedance and Capacitance Spectroscopy of Solar Cells with Dielectric Relaxation, Drift-Diffusion Transport, and Recombination

Semiconductor photovoltaic devices currently investigated, such as hybrid organic inorganic lead halide perovskite based solar cells, have shown a high dielectric polarization combined with ambipolar carrier transport. In this work, we present a new model that takes into account both features by combining the classical drift-diffusion equation with a generalized Poisson equation that involves a density and frequency dependent dielectric constant that accounts for the polarization of the medium. We derive the corresponding transmission line (TL) and analyze the associated complex plane impedance spectroscopy (IS) and capacitance spectra. The standard dielectric constant is replaced by the dielectric relaxation element that depends on the frequency, which provides a dielectric relaxation subcircuit in the middle rail of the TL. After simplification of the TL, three arcs can be observed: the first one, at low frequency, is associated with the dielectric relaxation process, the second one, at intermediate frequency, is the drift-diffusion/recombination arc, and the last one, at high frequency, corresponds to the geometric capacitance in parallel with transport resistances for both electrons and holes. In the case in which only two semicircles are observed, the parameters that can be extracted are the recombination and dielectric relaxation resistances along with the chemical and dielectric relaxation capacitances. The density dependent static dielectric constant gives rise to current generators that produce exotic impedance spectra associated with inductive behavior. These results provide a major tool for the determination of physical characteristics of lead halide perovskite solar cells.