A simple technique for measuring the fracture energy of lithiated thin-film silicon electrodes at various lithium concentrations

We have measured the fracture energy of lithiated silicon thin-film electrodes as a function of lithium concentration using a bending test. First, silicon thin-films on copper substrates were lithiated to various states of charge. Then, bending tests were performed by deforming the substrate to a pre-defined shape, producing a variation of the curvature along the length of the electrode. The bending tests allow determination of the critical strains at which cracks initiate in the lithiated silicon. Using the substrate curvature technique, we also measured the elastic moduli and the stresses that develop in the electrodes during electrochemical lithiation. From these measurements, the fracture energy was calculated as a function of lithium concentration using a finite element simulation of fracture of an elastic film on an elastic-plastic substrate. The fracture energy was determined to be Γ = 12.0 ± 3.0 J m−2 for amorphous silicon and Γ = 10.0 ± 3.6 J m−2 for Li3.28Si, with little variation in the fracture energy for intermediate Li concentrations. These results provide a guideline for the practical design of high-capacity lithium ion batteries to avoid fracture. The experimental technique described in this paper also provides a simple means of measuring the fracture energy of brittle thin-films.