Analyzing and modeling methods for warpages including cylindrical deformations are discussed in large-area dies with redistribution layers (RDLs) and thin 50-µm-thick Si substrates. The buckling behavior of warpage, a deformation transition from spherical to cylindrical, strongly depends on the lateral sizes of the dies and the RDL structures, and can be calculated using the analytical model of the nonlinear plate theory. The equivalent stress values are introduced to simplify RDL structures by applying the model to measured curvatures of homogeneous patterned samples. Area densities of Cu are a good index for evaluating die warpage even for inhomogeneous patterned RDLs.
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