Mixed-Mode Fracture Analysis of a Patterned Si Electrode during Lithiation/Delithiation

We investigate the mechanical degradation of patterned Si based on large deformation theory and mixed-mode failure. Mode I debonding at the center of Si is found to suddenly increase and lead to crack initiation during the early stages of lithiation. The generated crack propagates to the surface and hinders Li diffusion, thus increasing the inhomogeneity of Li within Si. During delithiation, very little Mode I and Mode II debonding occur near the center of the patterned Si; however, both Mode I and Mode II debonding develop considerably at the surface. In addition, the effects of the charge/discharge rate are considered. A very low state of charge induces crack initiation at the center of Si, regardless of the charge rate. The charge/discharge rate is correlated with the total crack length, which is directly proportional to the charge rate. Based on our simulation results, we propose a new shape of the patterned Si with a hole in order to enhance mechanical stability. The hole prevents crack growth by releasing the internal stress, and Mode I debonding at the center of the patterned Si becomes significantly lower, with much slower increases during lithiation.