Interconnect thermal modeling for accurate simulation of circuit timing and reliability

We apply three-dimensional finite element analysis to study the thermal coupling between nearby interconnects. We find that the temperature rise in current-carrying lines is significantly influenced by a dense array of lines in a nearby metal level. In contrast, thermal coupling between just two neighboring parallel lines is insignificant for most geometries. Design rules for average root-mean-square current density are provided for specific geometries given the requirement that the interconnect temperature be no more than 5 degrees C above the substrate temperature, Semi-empirical formulae for coupling effects are presented based on the numerical results. A procedure is proposed to implement the formulae in computer-aided design tools.