Multiscale thermal reduced order model for transient ic analysis

Abstract

In one embodiment, several reduced order models (ROMs), each at a different scale, are developed to create a multiscale ROM for a given system, which can include one or more integrated circuits (ICs), for simulating thermal responses (e.g., heating in the ICs and the system) as a result of usage scenarios of the IC and system (in which power is applied on the IC and in the system) over time. An IC, package and system can be thermally characterized to determine transient temperature response to a power source in each IC; this characterization can use simulations of the power source to simulate temperature responses at points in the IC, package and system, and these responses provide a set of thermal training data. An algorithm generates a linear time-invariant (LTI) state-space thermal macromodel or ROM at each of the different scales on-chip and in system, from the set of thermal step response training data, and combines them into a multiscale ROM, which can be distributed and solved on many CPUs. When the multiscale ROM is used, power accounting can be used across the scales to conserve power. On IC symmetry and inverse heat transfer properties can be used to reduce the amount of thermal characterization operations.