This paper reports a three-dimensional nonlinear numerical model developed for the deep submicron interconnects that carry high current densities in integrated circuits. This model can solve a thermoelectrically coupled field to analyze resistance variation and Joule heating as a function of electromigration-induced voiding in various interconnect structures. As a result, the model can identify the critical void volume that is directly related to the time to electromigration failure. The model is particularly useful as an analytical tool that can quantitatively evaluate the effects of the architecture and physical properties of various refractory films and diffusion barriers on the electromigration reliability.