The effect of metallic barriers in inhibiting copper ion transport in low-k dielectrics: Implications for time-to-failure

In this article we study the effect of metallic barriers in inhibiting copper ion drift/diffusion into low-k dielectrics through a mathematical analysis. We extend our previous drift/diffusion model for copper ion drift without barriers to include the effect of metallic barriers. The addition of the barrier changes the boundary condition at the barrier/dielectric interface and results in a time dependent flux and concentration at the interface. The results show that for a given dielectric, a metallic barrier needs to have both a lower ionic solubility and lower ionic diffusivity for optimal effectiveness.