Genetic Algorithms in Mems Synthesis

Initial results have been obtained for automatic synthesis of MEMS mask-layouts using a genetic algorithm. An initial random population of mask-layouts is produced. An initial fabrication process sequence is also generated. The fabrication of each geometrically valid layout is simulated using a 3-D simulation of etching. The 3-D results of the fabrication simulation are compared to the desired 3-D shape. 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 (and fabrication processes) to introduce random shape (and process) variations. The procedure is then repeated until one or more simulated shape is sufficiently close to the desired shape to stop the iteration. INTRODUCTION Initial results have been obtained for automatic synthesis of MEMS mask-layouts using a genetic algorithm. 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-layouts is produced. These mask-layouts are checked to ensure that they are geometrically valid (non-self intersecting, etc.). An initial fabrication process sequence is also generated (initially limited to the duration of each of two dissimilar processes). The fabrication of each geometrically valid ∗corresponding author 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 either turning functions (Arkin, Chew, Huttenlocher, Kedem, and Mitchell, 1991), Frechet or Hausdorff distances between polygons (Alt and Godau, 1995)). 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 (and fabrication processes) to introduce random shape (and process) 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 etching, or by bulk-wet etching, or any other processes for which an accurate digital simulator exists. 1 Copyright  1998 by ASME