ADAPTIVE MODELING OF THE TRANSIENTS OF SUBMICRON INTEGRATED-CIRCUITS

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 h andles multiple materials and temperature-dependent thermal conductivi ty. The meshing technique is adaptive in both space and time, is indep endent of the initial grid size, and allows the user to specify the de sired accuracy requirements, Based on the steady-state solution of a g iven problem and the predicted error fields, a template of nest levels is identified which resolves the physics everywhere in the computatio nal domain to within the specified accuracy criterion, The nesting tem plate is then used to solve the transient problem over the nested grid s with automatically determined adaptive time steps. The application o f this spatially and temporally adaptive system reduces the computatio nal time requirements by two orders of magnitude over conventional tra nsient methods. Consequently, concurrent electrical and thermal design of high-performance integrated circuits becomes, For the first time, both possible and practical.