Modeling Current Constriction at the Lithium Anode Interface in Solid-State Battery Cells

Abstract Contact loss between lithium anodes and solid electrolyte separators (SES) is a key challenge for solid-state batteries. The resulting current constriction (CCS) causes locally elevated current densities and additional overvoltages, which are critical for dendrite formation and for interpreting impedance measurements. This work quantifies these effects with three-dimensional finite element simulations. The current distribution across the remaining contact areas is highly inhomogeneous: for a remaining contact surface of 33 %, the 99.9 percentile of the local current density exceeds the average across the contact areas by a factor of about eleven when the ohmic resistance of the SES controls the current distribution, and by about two when the charge transfer resistance controls it. The governing parameter is a Wagner number, the ratio of charge transfer resistance to SES constriction resistance, determined by the exchange current density, ionic conductivity, effective contact pitch, relative contact surface, and temperature. The results agree with classical constriction theory for electrical contacts. Based on systematic parameter variations, practical estimation formulas are derived for the maximum local current density and for the additional overvoltage caused by CCS. They provide a framework for assessing dendrite-critical current densities and for interpreting measured charge transfer resistances in solid-state cells.