Effects of composition-dependent modulus, finite concentration and boundary constraint on Li-ion diffusion and stresses in a bilayer Cu-coated Si nano-anode

During the lithiation of a Si anode from pure Si to fully lithiated alloy, the volume expands four times and modulus varies by several tens of times. Thus, the Li-ion diffusion and the stress evolution can be strongly coupled, which may play a significant role in determining the anode performance. In this work, we present a theoretical study of the fully coupled diffusion and stresses in a nonequilibrium Li-Si system by taking into account the effects of composition-dependent modulus, finite concentration, and boundary constraint. The Li-ion diffusion and induced stresses in a bilayer Cu-coated Si anode at the nanometer scale is examined to show these important effects. The transient stress-assisted diffusion problem is solved numerically by a finite difference method, whilst the stress field is obtained analytically. It is shown that the modulus variation with composition plays a mild role in the Li-ion diffusion. In order to account for the finite concentration effect, a nonlinear flux equation is introduced that describes the Li-ion diffusion over the full range of concentration from dilute to near-saturation state in a unified, symmetric manner. The finite concentration effect is significant, especially during the early delithiation process. The boundary constraint effect is found to play an intriguing role in the chemical diffusion. The bending stress results in a resisting force to Li-ion flow preventing effectively the Si anode from full lithiation. The constraint effect is significant for a wide range of Cu thickness. (C) 2012 Elsevier B.V. All rights reserved.