Steady-state crack growth along a grain boundary in interconnects with a high electric field intensity

Abstract

A pre-existing microcrack is considered to grow in a steady state along a grain boundary of an interconnect line under the action of an applied electric field. Consistent with electromigration, the mechanism of crack growth is assumed via diffusive transport of atoms from both crack surfaces to the grain boundary. A set of second order nonlinear ordinary differential equations for the crack shape is derived from physical principles and solved numerically using the fourth-order Runge-Kutta method, coupled with a two-point shooting method. The results showed that the steady-state crack velocity V is proportional to the applied field E ₀ with an exponent of 1.5, that is V = AE ^1.5 ₀, in agreement with the previous analysis. However, the proportionality constant A is enhanced owing to electric field concentration at the crack tip.