A transient self-adaptive technique for modeling thermal problems with large variations in physical scales

The concurrent electro-thermal design of three-dimensional integrated circuits characterized by submicron geometric features requires thermal modeling that can comprehend geometric complexities, multiple materials, temperature-dependent material properties, and multiple spatial and temporal scales. The computational time required for a full-scale transient simulation with traditional discretization schemes far exceeds what is practical for concurrent design practices. A new computational paradigm for a transient, multiple-grid, solution technique has been developed, which adaptively handles the wide ranges of spatial and temporal scales associated with the thermal modeling of high-performance integrated circuits (ICs). As the grid is automatically refined over selected regions of the computational domain, the solution becomes invariant to further reductions in grid spacing and time step size. The use of this self-adaptive approach reduces the computational requirements for transient thermal modeling by over two orders of magnitude, making it possible for the first time to simultaneously perform both the electrical and thermal analysis and design of real ICs.