Locating the Frequency of Turnover in Thin-Film Diffusion Impedance

Abstract

The impedance of diffusion is an important tool to investigate a wide variety of systems, including electrochemical devices such as Li-ion batteries, porous electrodes, and solar cells. The classical impedance model for diffusion in a thin layer with a blocking boundary contains two separate regimes: Warburg diffusion at high frequency and capacitive charging at low frequency. Here, we provide a physical criterion for the transition between these two regimes, as the point of closest approach between early-and latetime approximations of the exact diffusion current. The resulting frequency is (π 2 /2)ω d with respect to the natural frequency ω d = D n /L 2 , with D n being the diffusion constant and L being the thickness of the layer.

Impedance Spectroscopy of Metal Halide Perovskite Solar Cells from the Perspective of Equivalent Circuits

“…According to the transmission line model, , for an ion-blocking boundary, there is a transition of two features, from a 45° Warburg feature at high frequency, to a vertical feature associated with capacitive charging, indicated in Figure c. The diffusion coefficient can be determined from the characteristic frequency of the transition and the thickness of the sample For a permeable boundary, the low-frequency property is not vertical but rather an arc depending on the charge transfer rate at the boundary, as shown in Figure d. This pattern is similar to the Gerischer impedance in Figure c, but the interpretation is quite different.…”

“…For a deeper insight into the analysis of ionic diffusion, it is recommended to prolong the measurement to very low frequency in order to obtain the information about the patterns of Figure . If the turnover frequency is observed, then it is straightforward to derive the diffusion coefficient by eq …”

“…If the turnover frequency is observed, then it is straightforward to derive the diffusion coefficient by eq 33. 152 The full diffusion impedance associated with ionic transport has been in fact observed for low doped monocrystalline MAPbBr 3 samples in the dark, contacted with gold electrodes, as shown in Figure 47. 103 The method aims at minimizing the electronic conductivity using dark conditions and V dc = 0 V. A distortion of the impedance pattern is observed by including an organic layer, as expected for a partially absorptive boundary, as indicated in Figure 47e,f.…”

Hysteresis in Organic Electrochemical Transistors: Distinction of Capacitive and Inductive Effects

“…The equivalent circuit of Figure e is inherent to the operation of the OECT, so that it forms a “minimal model” that can be complemented with additional effects as mentioned in the introduction. For example, in the case that Warburg impedances are observed, the impedance model has to be extended including spatial diffusion by solving eq . , …”

“…For example, in the case that Warburg impedances are observed, the impedance model has to be extended including spatial diffusion by solving eq 16. 55,56 In summary, the hysteresis and more generally the time transient and impedance characteristics of the OECT have been described based on a simple model that takes into account several effects: the transversal electronic and vertical ionic currents, leading to charging of the film and ion diffusion; the electrolyte resistance and surface capacitance of the film; and the disorder effects that produce a specific form of the chemical capacitance. By combining these factors, we can classify different types of hysteresis, either capacitive or inductive, associated with the chemical inductor effect of ion diffusion in the organic film.…”