POD based reduced basis element method for use in thermal modeling of integrated circuits

With the decreasing sizes of transistors and the increasing integrated circuit (IC) density, heat dissipation can be a limiting factor in developing emerging semiconductor technologies, such as silicon-on-insulator (SOI) based transistors and 3D-stacked ICs. To overcome this challenge, accurate thermal simulations are needed. The goal of this investigation is to explore the use of proper orthogonal decomposition (POD)-based reduced basis element methods (RBEM) for performing fast and accurate thermal predictions of ICs. The reduced basis element method (RBEM) is new type of reduced order modeling that takes advantage of repeated geometrical features. The RBEM uses a reduced set of basis functions to approximate the solution of a PDE on some geometrical subdomain or “block”. Once a reduced order model (ROM) has been created for a particular geometrical block it is a matter of “gluing” multiple blocks together and solving for equations governing the combined system. In this study, we examine the appropriate choice of “block” for the RBEM simulation of an IC. To determine the trade-offs between these choices, RBEM thermal simulations using single device blocks are compared to RBEMs that span multiple devices. It was found that larger blocks are more computationally efficient; however the advantage decreases if the devices within a block receive independent signals.