Evolutionary Techniques in Mems Synthesis

Initial results have been obtained for automatic synthesis of MEMS mask-layouts using a genetic algorithm. An initial random population of geometrically valid mask-layouts (non-self intersecting 2D polygons) is produced. The fabrication of each layout is simulated using a 3-D simulation of etching. The 3-D results of the fabrication simulation are compared to a desired 3-D shape specified by users. A genetic algorithm is applied to this initial population to iteratively search for a global optimum mask-layout whose fabricated 3-D shape is sufficiently close to the desired shape. During each iteration of the genetic algorithm, the mask-layouts with fabricated 3-D shapes close to the desired shape are more likely to survive. Random shape variations with ensured geometrical validity are applied to the surviving masklayouts to produce the mask-layouts for the next iteration. The procedure is then repeated until one or more simulated shape is sufficiently close to the desired shape to stop the iteration. Initial results demonstrate the feasibility of this approach to masklayout synthesis. INTRODUCTION We have developed an evolutionary approach to synthesis of mask-layouts for MEMS. Figure 1 illustrates the overall approach. The process begins with a desired 3-D shape, represented by a series of planar contours, with each contour parallel to the surface of the wafer. An initial random population of mask∗corresponding author layouts is produced. These mask-layouts are checked to ensure that they are geometrically valid (non-self intersecting, etc.). The fabrication of each geometrically valid layout is simulated using a computationally efficient geometrically accurate 3-D simulation of etching called Segs (Hubbard and Antonsson, 1996; Li, Hubbard, and Antonsson, 1998), built on earlier geometric (Hubbard and Antonsson, 1994) and cellular automata (Hubbard and Antonsson, 1997) methods. The 3-D results of the fabrication simulation are compared to the desired 3-D shape (by comparing individual contours using the turning functions of two polygons (Arkin, Chew, Huttenlocher, Kedem, and Mitchell, 1991)). Resulting 3-D shapes that are determined to be sufficiently close to the desired shape are kept in the candidate population. A genetic algorithm is applied to each member of the remaining population of mask-layouts to introduce random shape variations. The procedure is then repeated until one or more simulated shape is sufficiently close to the desired shape to stop the iteration. Because reversing a fabrication process simulation (so that a 2-D mask-layout might be produced) appears not to be possible, and because each fabrication process would require (if possible) a reverse simulator to be developed, an approach using existing simulations of fabrication processes in an iterative refinement loop has been adopted, shown in Figure 1. One of the primary benefits of this approach is that any fabrication process can be utilized with the synthesis approach described here, as long as an efficient digital simulation of the process exists. Thus synthesis can be performed on devices to be fabricated from deposition, patterning and removal of surface layers by wet or dry 1 Copyright  1998 by ASME