Modal analysis of multi-layer structure for chemical mechanical polishing process

In this study, a three-dimensional finite element model was established to perform modal analysis of the chemical mechanical polishing process. The contact boundary conditions were considered in the wafer and pad, and the influence of the static load exerted on the carrier was considered in order to investigate dynamic behaviour of the wafer. The analysis was in two steps. Firstly, a given pressure was exerted on the carrier and the geometric nonlinear effect and large deformation theory were used to carry out static analysis. Secondly, the results of the analysis were used to perform modal analysis of the wafer. The results gave way to four conclusions. (1) Due to the offset configuration of the wafer and pad, the von Mises stress distribution was asymmetric. Therefore, the stress on the wafer appeared to be almost uniform near its centre, goes through a maximum near the edge, and decreased as the edge is approached. This tendency is similar to that of the removal rate profile experiment, which proved that the proposed finite element model for CMP is acceptable. (2) Due to the extremely thin thickness of the film, wafer and pad, most mode shapes are predominant in out-plane deformation. Furthermore, since the y-axis is symmetric in the three-dimensional model, there were double roots in some modes. (3) When the load was larger, the tangent stiffness and the natural frequency would also be reduced. The pressure changes did not have much affect on mode shape. (4) Since the soft materials of the pad and film have significantly different Young’s modulus’ than hard materials, the natural frequencies of harder materials for the pad and film increase.