A novel mixture rule for multi-layer plates with thermal bending and twisting effects applied to FOCoS devices

Abstract

A novel approach for reducing the simulation time of highly complex fan-out chip on substrate (FOCoS) structures was developed. Based on the Uflyand-Mindlin plate theory and using the multi-layer plate technique, we have successfully obtained the effective elastic and thermal expansion constants incorporating with the effects of bending and twisting for a two-layer plate structure. The newly developed approach was then applied to simulate, by the finite element method, a variety of cases commonly encountered in practice, such as a slightly asymmetric substrate, an extremely asymmetric rigid structure, and an extremely asymmetric soft structure, with a maximum error of only 3 μm. Remarkably, applying the present mixture rule to simulate the complete FOCoS structure has resulted in an error of only 10 μm with up to 75 % of reduction in the number of mesh elements. The present approach, hence, provides an effective and reliable means for simulating the ever increasingly important FOCoS structures in the rapidly evolving information technology applications.