Deconvoluting the Impedance Response of Halide Perovskite Single Crystals: The Distribution of Relaxation Time Method

Electrochemical impedance spectroscopy (EIS) has been emerging as a promising tool to study the core mechanisms occurring within metal halide perovskites (MHPs). Generally, MHPs show one or two semicircles in the Nyquist spectra in the probed frequency range. However, in the presence of external stimuli, often a Warburg diffusion or an inductive loop is observed at low frequencies. In such cases, a comparison of low-frequency parameters in both cases cannot be drawn because of the lack of a unique electrical circuit (EC). To overcome the issue of lack of EC, transformation of the frequency-domain technique to the time domain is carried out. In this work, we investigated three different cases of MAPbI 3, MAPbBr 3, and surface-passivated MAPbBr 3 single crystals (SCs), which showed one suppressed semicircle, two semicircles, and a Warburg-like diffusion, respectively, in the Nyquist response of EIS. Next, we transformed these spectra into the time domain using the distribution of relaxation times (DRT) technique, a machine-learning-assisted tool. The obtained results suggest that in the case of Nyquist spectra with one semicircle (the case of MAPbI 3 SCs), the observed time constants using EC and DRT are close enough. However, in the case of MAPbBr 3 SC, three different time constants are obtained, associated with high, medium, and low frequencies, although the Nyquist response showed two semicircles. At last, in the presence of surface-passivated SCs, the Warburg-like feature changes significantly for different passivation times. Interestingly, the DRT spectra showed almost similar time constants, through which reliable information on the low-frequency RC can be extracted. Thus, DRT can pave the way for the easy and reliable interpretation of EIS spectra, which is not possible using EC.