Thermoelastic Solutions for a Finite Substrate With an Electronic Device

Abstract

Sneddon and Lockett obtained a fairly general solution to the steady-state thermoelastic problem for the thick plate (Sneddon and Lockett, 1960). In particular, they have obtained the exact solutions for axially symmetrical temperature distributions on the upper surface of the thick plate. In this note, their exact solution will be applied to an electronic problem, namely, a chip on a substrate with finite thickness. Emphasis is placed on the generation of dimensionless charts for the temperature, displacement, and stress distributions in the substrates. These charts are not only useful for designing substrates but also can be used to verify finite element analysis procedures.