Numerical strategies for the prediction of patterned wafer warpage during manufacturing process

A manufacturing process consists of the deposit of thin films at different temperatures which produce in-plane stress loading. The presence of these mechanical stresses in different layers induces deformation of the wafer. In this sense, wafer warpage usually occurs which can cause unexpected large and critical deformations of the structure, including symmetrical (spherical) and asymmetrical deformed shapes. A wafer usually represents the repetition of many identical substructures (patterns) which are obtained by photo-lithography and etching steps. The magnitude of the deformed shape of a wafer could be high enough to prevent the manufacturing process. Then the prediction of the warpage phenomenon becomes crucial at the early stage of the design process. To predict wafer deformation accurately, analytical approaches do not seem suitable whereas standard finite element techniques based on 3D elements require excessive computational resources. Efficient alternative numerical approaches are therefore needed for the prediction of wafer warpage at affordable times. In this paper, comparisons are proposed between two kinds of alternative approaches, namely the homogenization technique and the FETI-DP method. Numerical simulations conducted on simple test-cases show that both these approaches are promising to achieve accurate results and strong time reduction compared to a full 3D analysis.