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    Deconvoluting the Impedance Response of Halide Perovskite Single Crystals: The Distribution of Relaxation Time Method
    (Amer Chemical Soc, 2023) Pandey, Siddhi Vinayak; Parikh, Nishi; Mahapatra, Apurba; Kalam, Abul; Akin, Seckin; Satapathi, Soumitra; Prochowicz, Daniel
    Electrochemical impedance spectroscopy (EIS) has beenemergingas a promising tool to study the core mechanisms occurring withinmetal halide perovskites (MHPs). Generally, MHPs show one or two semicirclesin the Nyquist spectra in the probed frequency range. However, inthe presence of external stimuli, often a Warburg diffusion or aninductive loop is observed at low frequencies. In such cases, a comparisonof low-frequency parameters in both cases cannot be drawn becauseof the lack of a unique electrical circuit (EC). To overcome the issueof lack of EC, transformation of the frequency-domain technique tothe time domain is carried out. In this work, we investigated threedifferent cases of MAPbI(3), MAPbBr(3), and surface-passivatedMAPbBr(3) single crystals (SCs), which showed one suppressedsemicircle, two semicircles, and a Warburg-like diffusion, respectively,in the Nyquist response of EIS. Next, we transformed these spectrainto the time domain using the distribution of relaxation times (DRT)technique, a machine-learning-assisted tool. The obtained resultssuggest that in the case of Nyquist spectra with one semicircle (thecase of MAPbI(3) SCs), the observed time constants usingEC and DRT are close enough. However, in the case of MAPbBr(3) SC, three different time constants are obtained, associated withhigh, medium, and low frequencies, although the Nyquist response showedtwo semicircles. At last, in the presence of surface-passivated SCs,the Warburg-like feature changes significantly for different passivationtimes. Interestingly, the DRT spectra showed almost similar time constants,through which reliable information on the low-frequency RC can beextracted. Thus, DRT can pave the way for the easy and reliable interpretationof EIS spectra, which is not possible using EC.