Diffusion-Reaction-Deformation Coupled Modeling of Large-Deformed Germanium Thin Film Anodes

Abstract

Germanium is known as a high-capacity material that reversibly stores large amounts of lithium, whereas the inevitable volume changes lead to mechanical failures and unstable reaction interfaces. According to the finite deformation theory, we establish a theoretical framework to capture the viscoplastic flow and the interfacial transfer kinetics during lithiation and delithiation under coupled diffusion-reaction-deformation environments. Many microcracks on the surface of germanium electrodes are observed by previous experiments, and we take this effect into consideration by associating the parameters of Li-Ge alloy with the degree of lithiation, such as the concentration-dependent elasticity modulus and yield stress. Subsequently, the framework is used to calculate the mechanical and electrochemical response of thin film electrodes during charge and discharge under the rigid substrate constraint. The results suggest that charge rate and electrode thickness determine the performance of thin film battery, which is in accordance with the experimentally observed phenomenon. The Cauchy stress in the thin film electrode is also subject to the effect of the inhomogeneous spatial distribution of stress, and the stress drop at the ends of the electrodes is the main source of material fracture failure.