  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.
