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. 2019 Dec 27;9:19846. doi: 10.1038/s41598-019-56338-6

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© The Author(s) 2019

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Light intensity-dependent variations of effective capacitance C_eff (a) and exponents p (b) of the two CPEs in the inset of Fig. 2. Values of Q and p, defining CPE impedance Z_CPE = Q(jω)^-p, were determined from the fitting of impedance spectra to the equivalent circuit model. Effective capacitance C_eff,i was calculated by using the fitting-produced values of Q_i, p_i, and R_i: C_i = [(Q_i R_i)^1/p_i]/R_i for i = 1, 2. Each R-C pair represents a process with a characteristic time constant defined as τ_i = R_iC_i. Interestingly, C_eff,1 and p₁ varied only slightly with respect to intensity, and p₁ remained larger than 0.93. On the contrary, C_eff,2 and p₂ showed significant difference between low- and high-illumination ranges.