Comparison of finite element approaches for Si wafer buckling calculation

During the manufacturing process of the wafer, in particular during temperature changes, because of the different properties of the deposited films, the wafer can buckle, which induces a change of shape. This bifurcation can be anticipated analytically and by numerical computation via the finite element method. The models released allow in particular to compute the value of the critical load, the temperature at which the film/substrate system buckles, and to calculate the behaviour of the wafer after the bifurcation. A common numerical approach is to implement an additional perturbation force to trigger buckling. This method is non-physical and here compared to another method, this one physical but less commonly implemented in models, which consists in considering a geometrically imperfect wafer. This second approach uses the buckling modes of the wafer, previously calculated, in order to generate a realistic geometric defect and allows the calculation of the post-bifurcation path. The comparison shows that both numerical methods reached the same results.