Insertion-induced expansion of a thin film on a rigid substrate

The local volume expansion due to the insertion of lithium into electric anode in a lithium-ion battery determines the structural durability and reliability of the battery. The coupling between diffusion and stress was incorporated in analyzing the insertion-induced expansion of an elastic thin film on a rigid substrate. The results showed that the stress-assisted diffusion is an important mechanism controlling the diffusion of lithium cations in silicon films. Under the action of a constant diffusion flux, semi-analytical relations were obtained for the temporal evolution of the insertion-induced expansion of a Si film and the hydrostatic stress in the Si film. The surface displacement of the Si film is proportional to the film thickness and the square of the electric current density for small diffusion time.