Models of Bifurcation in a Semiconductor Wafer: A Comparison of the Analytical Solution vs. the ANSYS Finite Element Analysis

In this work we report a relationship between the curvature provided by the Stoney equation, considered in an "extended" linear regime, and the arithmetic average of the main curvatures of a bifurcated plain metalized circularly shaped wafer. ANSYS® Finite element analysis (FEA) methods have exploited to find out the substrate curvatures for the case of an 8" silicon (001) semiconductor substrates metalized with a 4.5 μm aluminium metal layer. We have explored the spherical and bifurcation cases. In particular, the bifurcation is induced in the wafer by applying a pair of weak forces acting normally with respect to the wafer surface as perturbations and along two perpendicular diameters. The resulting principal curvatures of the wafer have compared with the bifurcation diagram obtained from the theory. The FEA results also demonstrate a correlation between the Stoney slope extended in the bifurcation interval and the average of the simulated curvatures of the bifurcated wafer.