On Including Manufacturing Constraints in the Topology Optimization of Surface-Micromachined Structures

Topology optimization of structures sometimes gives designs that cannot be economically manufactured without postprocessing. Because post-processing of topology solutions might lead to suboptimal designs, it is useful to include manufacturing constraints at the outset. In this work, we present a method for the topology optimization of micromachined devices by including surface micromachining constraints. Instead of explicitly including manufacturing constraints, we propose a novel design parameterization that implicitly restricts the design space so that it consists of only the manufacturable designs for a chosen surface-micromachining foundry process. In surface-micromachining, the photolithographic masks determine the geometry of surface-micromachined structures. Therefore, we use the masks themselves as the design variables in topology optimization. By using the continuous mask opacities as the design variables, we developed a virtual material movement model (VMMM) in which the material from a layer deposited on top of a putatively porous layer will move down. Consequently, the virtual density of material in the design domain changes depending on the opacity values of the masks in different cells. This virtual density is similar to the fictitious density assumed in Simple Isotropic Material with Penalty (SIMP) and other material interpolation techniques. The difference is that the opacity values of the masks are design variables here whereas the densities of the cells themselves are design variables in SIMP. In this manner, surface-micromachining constraints are implicitly satisfied in this design parameterization. An optimality criteria method aided by sensitivity analysis is implemented in Comsol MultiPhysics platform. Micromachined foundry processes such as MUMPs and SUMMiT are considered in the examples presented to demonstrate the efficacy of the method. An added benefit of the new method is that lithography mask layouts are readily generated in addition to manufacturable optimal topologies. Several examples are solved and discussed to show how the optimal manufacturable solutions compare with non-manufacturable ones.