Temperature Prediction on Substrates and integrated Circuit Chips

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Abstract
This work deals with application of semianalytical methods for evaluation of temperature distribution on substrates and integrated circuit chips. This approach is based on a method proposed by Hein and Lenzi in 1969 which is a combination of Fourier transform. Green's function, and surface-element methods. The application of the method has evolved from a model that predicts the steady-state temperature on one-layer structures with lead connectors (modeled as lumped thermal resistances) and planar-discrete sources to a model that includes the effects of multiple layers and anisotropic thermal conductivity. Further generalization of the method to three new cases is presented. The first includes the transient thermal behavior in the one-layer structures with planar-discrete sources and anisotropic conductivity. The second deals with the steady-periodic behavior of two-layer structures with planar-discrete-periodic sources and anisotropic conductivity. The third case solves for the steady-state temperature in multilayer structures in which the conductivity of the bottom layer is larger than that of the upper layers (i.e., copper substrate); the thermal contact resistance between the bottom layer and its adjacent is also taken into account. Comparison between the finite-element (FE) method and this method is presented for one case.

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