Theory of Dendritic Crack Growth in Ceramic Solid-State Batteries

Abstract

In solid-state batteries, ceramic solid electrolytes are penetrated by dendrites when plating above a critical current density $J_{\mathrm{crit}}$. A dendrite will propagate by metal deposition at a pre-existing dendrite tip if the mechanical energy required to crack the ceramic open is less than the electrical energy (Joule heating) wasted by forcing the current to detour around the dendrite to the flat electrode surface. Based on this principle of minimal power dissipation, a dependence of $J_{\mathrm{crit}}\propto c_{\max }^{3/2}$ is derived in an analytical fashion. $c_{\max }$ is the length of the longest pre-existing, sufficiently thin interfacial defect. Consequentially, scattering of dendrite growth between samples must follow a Weibull-distribution, similar to the tensile strength of ceramic components but at smaller Weibull-modulus.

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