Method of Images for the Fast Calculation of Temperature Distributions in Packaged VLSI Chips

TL;DR

This paper introduces an efficient method combining the method of images with power blurring to accurately compute temperature distributions in complex packaged VLSI chips with minimal FEA simulations.

Contribution

It presents a novel approach that accounts for thermal boundary symmetry, reducing FEA simulations to only two, improving speed and accuracy in temperature modeling.

Findings

Achieves temperature profile accuracy within 0.5% error.

Requires only two finite element simulations for complex profiles.

Effective for realistic VLSI chip packaging scenarios.

Abstract

Thermal aware routing and placement algorithms are important in industry. Currently, there are reasonably fast Green's function based algorithms that calculate the temperature distribution in a chip made from a stack of different materials. However, the layers are all assumed to have the same size, thus neglecting the important fact that the thermal mounts which are placed underneath the chip can be significantly larger than the chip itself. In an earlier publication, we showed that the image blurring technique can be used to calculate quickly temperature distribution in realistic packages. For this method to be effective, temperature distribution for several point heat sources at the center and at the corner and edges of the chip should be calculated using finite element analysis (FEA) or measured. In addition, more accurate results require correction by a weighting function that will need several FEA simulations. In this paper, we introduce the method of images that take the symmetry of the thermal boundary conditions into account. Thus with only "two" finite element simulations, the steady-state temperature distribution for an arbitrary complex power dissipation profile in a packaged chip can be calculated. Several simulation results are presented. It is shown that the power blurring technique together with the method of images can reproduce the temperature profile with an error less than 0.5%.