Light Intensity Modulated Photo-Electrochemical Methods and Distribution of Relaxation Times As Tools to Investigation Photovoltaic Materials
Authors: Vanysek Petr , Novak Vitezslav , Kreckova Jitka 
Published: July 2021

Electrical Impedance Spectroscopy (EIS, sometimes also Electrochemical Impedance Spectroscopy) found its place in material studies as a routine experiment. EIS proliferation became possible through advances in electronics. Current-voltage characteristics were standard features of potentiostats. Impedance techniques require additional components embedded into a potentiostat, namely signal generator and signal analyzer. Relatively simple devices are available, although dedicated instrumentation with little noise, broad frequency control and perhaps sample temperature control or automated sample handling are particularly desired and command premium in cost.
EIS as an electrical technique uses as the perturbing signal alternating electrical signal, either potential of current. In general, impedance studies are intended to study a transfer function and the input and output do not have to be only voltage-current or current-voltage as it would be in EIS. In mechanical engineering are for example useful studies focused on mechanical perturbation. Electrical response by its nature makes EIS amenable to study electrochemical systems.
Along with the impedance vs. frequency data collection comes also the need of meaningful data interpretation. This is typically done through data fitting to components of an equivalent electrical circuit. The acquired data -- real and imaginary impedance components gathered over a vast range of frequencies -- are evaluated by fitting to some equivalent circuit using nonlinear regression.
Oftentimes both finding the equivalent circuit and the physical component assignment are tedious, if not impossible. Recently a new approach to data reduction has been a treatment via distribution of relaxation times (DRT) [1, 2]. In principle, this approach has been outlined already in 1936 [3]. Its present use was made possible by available computation power of current PCs [4, 5]. While this is not a substitute to equivalent circuits and subsequent physical data interpretation, it is possibly a method, when used appropriately and in automated way, that can provide more information that simple comparison of the Bode or Nyquist graphs. This note is presenting some examples of this approach.
In the field of photovoltaic studies of light-gathering materials experimentation on systems responding to illumination makes use of impedance studies in which the perturbing signal is light of certain wavelength (or white light) with variable intensity. Here we will look at the link between EIS and electrical response spectroscopy induced by fluctuating light. This is sometimes for short dubbed as optical spectroscopy although it does make a use of the instruments for optical spectroscopy (such as UV-VIS, IR etc.) as they are known from analytical chemistry literature. Rather, an electric signal in a photoactive material is generated by intensity modulated light at different frequencies (similar range to electrical impedance spectroscopy) and a response (the magnitude and the phase shift) is analyzed. In this respect the magnitude and phase shift correspond to the magnitude and a vector of resistance on the polar plot of electrical impedance measurement. However, the data obtained serve a different purpose. For example, in a photovoltaic shorted system, the time constant associated with the response corresponds to mobility of the photogenerated charge in the material. For an open-circuit potential of such a photovoltaic system the measured time constant response corresponds to the rate of recombination of the generated hole-electron species.
Such materials of general structure (ABX3) could be replacements for silicon-based photovoltaic cells. These materials, due to the possible variability of both cations and anions in their composition, offer almost endless possibilities for synthetic preparation. For the active layer of a solar cell is often used the CH3NH3PbI3-2Cl2 perovskite structure, i.e., a structure containing an organic component. We have built and then tested such photovoltaic cells by static and dynamic methods using a unique photoelectric research instrument using the method CIMPS (Controlled Intensity Modulated Photocurrent Spectroscopy).
Acknowledgement
This work was supported through the support of The Czech Science Foundation (GACR), contract GA19-23718S.
References

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