IC thermal simulation and modeling via efficient multigrid-based approaches

The ever-increasing power consumption and packaging density of integrated systems creates on-chip temperatures and gradients that can have a substantial impact on performance and reliability. While it is conceptually understood that a thermal equivalent circuit can be constructed to characterize the temperature gradients across the chip, direct and iterative solutions of the corresponding three-dimensional (3-D) equations are often intractable for a full-chip analysis. Integrated circuit (IC)-specific multigrid (MG) techniques for fast chip level thermal steady-state and transient simulation are proposed. This approach avoids an explicit construction of the matrix problem that is intractable for most full-chip problems. Specific MG treatments are proposed to cope with the strong anisotropy of the full-chip thermal problem that is created by the vast difference in material thermal properties and chip geometries. Importantly, this paper demonstrates that only with careful thermal modeling assumptions and appropriate choices for grid hierarchy, MG operators, and smoothing steps across grid points can a full-chip thermal problem be accurately and efficiently analyzed. This paper further speeds up the large thermal transient simulations by incorporating reduced-order thermal models that can be efficiently extracted under the same MG framework. The experiments carried out in this work have shown that the proposed methodology provides sufficient efficiency in both runtime and memory usage.