Analytical thermal response of a multiple-layer device under the semi-infinite approximation

An analytical method for the analysis of the transient thermal response of a multiple-layer semi-infinite solid-state device is described. The method uses the Laplace transform to obtain solutions of the coupled partial differential equations. The solutions indicate the time limits for which the
t^{1/2}
dependance of the surface temperature is valid. The temperature distribution within the layers indicates that an exponential type distribution results. As an example, computations were carried out on the structure of a typical soft-soldered power transistor, using a digital computer.