Fast electrical-thermal co-simulation using multigrid method for 3D integration

In this paper, a fast electrical-thermal co-simulation method based on multigrid approach is proposed for simulating 3D systems. Using the proposed approach, accurate voltage/current distribution with temperature effect as well as temperature distribution with Joule heating effect can be obtained efficiently. By ensuring smoothly stretched gridding between die region and package region, fast convergence of multigrid method can be reached for both DC voltage drop and thermal simulations. The effect of nonuniform gridding on the convergence of multigrid is studied. The temperature effect on voltage drop and Joule heating effect on localized hotspot are discussed.