Fast 3-D thermal analysis of complex interconnect structures using electrical modeling and simulation methodologies

Accurate and fast estimation of VLSI interconnect thermal profiles has become critically important to estimate their impact on circuit/system performance and reliability, which is necessary for reducing product development time and achieving first-pass silicon success. Present commercial thermal analysis tools are incapable of simulating complex structures, particularly in the 3-D domain and are also difficult to integrate with existing design tools. Existing analytical thermal models are not perfect either: they are either not accurate enough or oversimplified. This paper uses a methodology, which exploits existing electrical resistance solvers for thermal simulation, to allow fast acquisition of thermal profiles of complex interconnect structures with good accuracy and reasonable computation cost. Moreover, for the first time, an accurate closed-form thermal model is developed. The model allows for an equivalent medium with effective thermal conductivity (isotropic or anisotropic) to replace the detailed material information in non-critical regions so that complex interconnect structures can be simulated. Using these techniques, this paper demonstrates the simulation of a very complex interconnect structure (~9000 objects or 15 million meshed unknowns after first order isotropic equivalent medium replacement), which is a first time achievement in the area of interconnect thermal analysis. On the other hand, it is shown that an anisotropic equivalent medium is a much better approximation of real interconnect structures from the point of view of accuracy and computation.