Adaptive modeling of the transients of submicron integrated circuits [monolithic microwave devices]

The development and application of a transient, multiple-grid solution system are shown to lead to a dramatic decrease in the computational time requirements for complex three-dimensional (3-D) thermal problems. A multiple-grid solution technique is presented which successfully handles multiple materials and temperature-dependent thermal conductivity. The meshing technique is adaptive in both space and time, is independent of the initial grid size, and allows the user to specify the desired accuracy requirements. Based on the steady-state solution of a given problem and the predicted error fields, a template of nest levels is identified which resolves the physics everywhere in the computational domain to within the specified accuracy criterion. The nesting template is then used to solve the transient problem over the nested grids with automatically determined adaptive time steps. The application of this spatially and temporally adaptive system reduces the computational time requirements by two orders of magnitude over conventional transient methods. Consequently, concurrent electrical and thermal design of high-performance integrated circuits becomes, for the first time, both possible and practical.