Topology optimization using multistep mapping from 2D photomask to 3D structure for designing reinforcing rib

• We proposed an improved method of topology optimization suitable for MEMS, which implements fabrication processes as a topology restriction
• The proposed method was utilized for designing a reinforcing rib to reduce residual stress deformations.
• We experimentally evaluated the validity of not only the initial and the optimized designs, but also the intermediate topologies.
• The experimental variation of the deformation agreed well with the calculation result of the topology optimization.

We developed a topology optimization method for designing a two-dimensional (2D) photomask. The optimization employs multistep mapping compatible with micromachining processes to improve the characteristics of a three-dimensional (3D) MEMS fabricated by the photomask. We used this method in the development of an electrostatic micromirror to design the most effective reinforcing rib shape that reduces the deformation caused by internal residual stress. Employing a dot-array pattern as the initial topology, the optimization calculation converged after 300 iterations for predicted 79.1% reductions in maximum displacement. To verify this result, micromirror structures were fabricated and their deformations were experimentally measured. The experimental deformations were reduced by 87.1%. The calculated results agree well with the experimental results and demonstrate the effectiveness of the proposed method.