A Scattering Matrix Formalism to Model Periodic Heat Diffusion in Stratified Solid Media

TL;DR

This paper introduces a numerically stable scattering matrix formalism for modeling periodic heat diffusion in layered solids, overcoming instability issues of traditional transfer matrix methods at high frequencies and in thick structures.

Contribution

It develops a scattering matrix approach inspired by wave propagation models, providing enhanced numerical stability for heat diffusion analysis in stratified media.

Findings

The framework is validated against known solutions.

It demonstrates stability in complex chip architectures.

Synthetic experiments show improved thermal property extraction.

Abstract

The transfer matrix formalism is widely used in modeling heat diffusion in layered structures.Due to an intrinsic numerical instability issue, which has not yet drawn enough attention to the heat transfer community,this formalism fails at high heating frequencies and/or in thick structures. Inspired by its success in modeling wave propagation, we develop a numerically-stable scattering matrix framework to model periodic heat diffusion in stratified solid media.As a concreate example, we apply this scattering matrix methodology to the three omega method.We first validate our framework using various well-known solutions.Next, we demonstrate the numerical stability of the framework using a configuration that resembles the three-dimensional stacked architecture for chip packing. Last, we propose synthetic experiments to exhibit, under certain circumstances, the merits of the scattering matrix formalism in extracting thermal properties.