Computationally efficient standard-cell FEM-based thermal analysis

Abstract

Thermal analysis of integrated circuits (IC) is a high performance computing problem because the nanoscale spatiotemporal features of the problem result in a large discrete problem. In previous works, compact models of ICs were introduced to speed up the modeling process. However, such methods have limited accuracy as they approximate the underlying physics. They are also ill-suited to simulate the thermal characteristics of an IC at the cell-level. The finite element method (FEM) is an appropriate computational technique for providing both fast and accurate thermal analyses. Considering that the number of cells in modern ICs is on the order of millions, thermal analysis at this abstraction level is a formidable task. Consequently, handling the computational meshes and computing thermal profiles of an IC at the cell-level requires substantial computing power. In order to provide accurate cell-level thermal simulations at a lower computational cost, this work introduces advanced techniques that judiciously trade off mesh granularity with simulation accuracy which allows fast analysis of cell-level floorplans. The proposed cell-homogenization techniques start with a flat cell-level floorplan and a related power trace and produce reduced order meshes that accelerate thermal simulations with a negligible loss in accuracy. Results show that the proposed techniques achieve up to a 90% reduction in the number of nodes in the mesh with less than 5% error in the temperature compared to the full scale mesh. The simulation time is also reduced by an order of magnitude.