Mathematical model for silicon electrode – Part I. 2-d model

Abstract

This paper presents a 2-dimensional transient numerical model to simulate the electrochemical lithium insertion in a silicon nanowire (Si NW) electrode. The model geometry is a cylindrical Si NW electrode anchored to a copper current collector (Cu CC) substrate. The model solves for diffusion of lithium in Si NW, stress generation in the Si NW due to chemical and elastic strains, stress generation in the Cu CC due to elastic strain, and volume expansion in the Si NW and Cu CC geometries. The evolution of stress components, i.e., radial, axial and tangential stresses in different regions in the Si NW are presented and discussed. The effect of radius of Si NW and lithiation rate, on the maximum stresses developed in the Si NW are also discussed.