Deformation in Multilayer Stacked Assemblies

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Abstract
A linear-elastic analytical model has been developed to describe the deformed geometry of a multi-layered stack assembly subject to thermal loading. The model is based on Timoshenko’s bimetal thermostat analysis [1] and consists of a series of first-order polynomial equations. The radius of curvature, bending moment, force, horizontal and vertical displacements can be determined numerically. These quantities match well with finite element analysis. Calculations for silicon power transistor stacks are presented in order to demonstrate the model capability. The results from this analyitcal model have been found to correlate well with experimental measurements when an appropriate secant modulus is used to represent the nonlinear stress-strain behavior of solder.

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