Modified Stoney formula for in-situ lithiation stress measurement in thin-film Si electrode

The multi-beam optical stress sensor method combined with Stoney equation is an effective approach to measure in-situ average stress in thin film electrodes upon lithiation / delithiation. However, the classic Stoney formula is applicable only at low stress states. A modified Stoney formula for stress measurement in thin-film Si electrodes was applied to account for the combined effects of the Li concentration-dependent material properties and large substrate curvature change. The numerical results based on three-dimensional non-linear finite element model for the full coupling of large deformation and Li diffusion confirm the accuracy of the modified Stoney equation. Further, a critical condition for the curvature bifurcation was discussed, which should be avoid when using the modified Stoney equation.