A stress-based effective film technique for wafer warpage prediction of arbitrarily patterned films

Initially flat silicon wafers are prone to warp due to the high levels of intrinsic stress of deposited films, particularly metallic films. Processing and handling of warped wafers in the fab is a challenge. One of the ways to control the degree of warpage is by limiting the amount of metallization allowed on the wafer. However, this imposes a constraint on the silicon designers, and can lead to decreased performance of the IC. Therefore, there is a need to accurately predict the amount of wafer warpage caused by a proposed layout in order to give designers the most freedom to develop IC solutions while ensuring that the processed wafers meet the manufacturing equipment requirements. The metal artwork (in addition to other materials, layer thicknesses, processing parameters, etc.) is an important factor in determining wafer curvature. Simple analytical methods, such as Stoney's Formula, cannot capture the non-uniform warpage due to these patterned films. On the other hand, numerical methods which require detailed modeling of the film patterns across the whole wafer are computationally expensive. Thus, a new finite element modeling technique was developed in which the entire patterned film stack is represented as a uniform effective orthotropic film bonded onto a silicon substrate. The orthotropic properties are determined from a small set of virtual experiments using a unit-cell model that is characteristic of the actual pattern. The resultant effective film, despite using a very course mesh, is able to capture the non-uniform surface stress induced by a patterned multi-layer film stack, and thus results in very similar wafer warpage as in the conventional detailed model. Several example film patterns will be presented here, where the warpage difference between the detailed model and the effective film model are less than a few percent across the whole wafer.