Topology optimization method using multistep mapping from 2D photomask to 3D MEMS

We have developed a topology optimization method for designing a two-dimensional (2D) photomask. It employs micromachining-process-like multistep mapping to analytically improve the characteristics of a three-dimensional (3D) MEMS fabricated by the photomask. We used this method to design reinforcing ribs for an electrostatic micromirror to reduce deformation caused by internal residual stress. Employing a dot-array pattern as the initial topology, the optimization calculation converged after 300 iterations. It predicts a 79.1% reduction in the maximum displacement. To verify this result, micromirror structures were fabricated and their deformations were measured. The deformation was reduced by 87.1% in this experiment. The calculation results agree well with the experimental results, demonstrating the effectiveness of the proposed method.