Electrochemical Impedance Spectroscopy with Discrete Transmission Line Model and Electric Circuit Simulation for Current Distribution in Electrode of All Solid–State Battery

Abstract

The commercialization of all solid–state batteries (ASSBs) incorporating inorganic solid electrolyte (SE) is an earnest desirefor energy–sustainable mobility because of their higher energy density and safer behavior compared to lithium–ion batteries (LIBs).One of the challenges for practical application of ASSBs is to fabricate thick electrode. The transport number of lithium-ions in ASSBs is nearly equal to 1, which theoretically could facilitate a fast charge-discharge reactions during cycling and ignore the overvoltage derived from the concentration gradient of lithium ions in the cell. However, the battery performance with ASSBs typically decreases with an increase in the electrode thickness. Besides active materials and electrical conductive materials, SEs are generally added as an anode/cathode material to promote the ionic conductivity. Unlike liquid electrolytes, it is hard to make a good reaction interface between SE and active materials in ASSBs, which might be the reason for the poor battery performance in thick electrode. However, the bottle–neck part of electrochemical reactions in thick electrodes are still under debate as it stands right now. Electrochemical impedance spectroscopy (EIS) is widely used for the analysis of LIB electrodes, which can divide complicated electrochemical reaction into elemental processes of electrochemical reaction based on their characteristic time constants. We have reported 3D structured electrodes can be analyzed by optimizing equivalent circuits [1–3]. For the most part, a transmission line model has been used to analyze electrodes with reaction distribution in depth-direction. This model is based on the assumption where each resistivity such as ionic resistance and charge transfer resistance is constant regardless of the location in the electrode. Therefore, it cannot express the real situation if the resistance changes by the locations in depth-direction.In this study, we firstly applied a discrete transmission line model (DTLM), in which all parameters in the equivalent circuit are variable for the evaluation of thick electrode. In addition, we simulated the current distribution in the electrode by using calculated parameters from DTLM.EIS measurement was carried out for the all solid–state half–cell composed of NMC cathode (~45 μm-thick)/sulfide–based SE/InLi counter electrode, and the obtained impedance was analyzed using DTLM. In DTLM, we divided the cathode into three layers and set the equivalent circuit as shown in Figure 1 (a). The current distribution in the cathode was also simulated by LTSPICE software.Figure 1 (b) shows Nyquist plots of the solid–state half–cell. The result confirms that Nyquist plots from experimental data were fitted well using the equivalent circuit with DTLM. The parameters obtained by the fitting are used for simulation of the current distribution. In order to adapt for electrical circuit simulation, the equivalent circuit with the parallel connection of R-C series circuits was designed instead of diffusion impedance expressed as constant phase element (CPE). In this case, the simulated current distribution indicates that the current in the cathode preferably flows near the SE side and deceases with approaching to the current collector.In the presentation, we will show the more details in current distribution and demonstrate DTLM can be an promising analytical tool to understand the bottle–neck electrochemcal reactions in ASSBs.