Mask-Layout Synthesis Through An Evolutionary Algorithm1 Category: Design, Modeling and Synthesis Aids

This paper reports an automatic method for synthesizing MEMS mask-layouts. This method incorporates a forward simulation of fabrication into a general evolutionary algorithm loop as shown in Figure 1. An initial random population of mask-layouts is generated. The fabrication of each layout is simulated through a digital process simulator to produce a 3D fabricated shape, which is compared to a user-specified desired shape. Each evolutionary loop governs the stochastic searching behavior such that the mask-layouts whose simulated shapes are closer to the desired shape are more likely to survive. More importantly, the “better” masks are more likely to be evolved among those survived mask-layouts for the next loop. Through such evolutionary iterations, a near global “optimum” mask-layout is likely to be found [2]. By using this evolutionary approach, we are able to take use of existing simulations of fabrication processes to achieve those mask-layout synthesis where reversing a fabrication process simulation (so that a 2D mask-layout might be produced) appears not to be possible. The general evolutionary loop mainly consists of a mask genetics module, an evolutionary technique module and a MEMS simulation module. The mask genetics module provides heuristic genetic operations on mask-layouts, which includes random mask generation, random crossovers and mutations, and local exploitations. The evolutionary technique module contains stochastic selection schemes, hybrid searching schemes and other stochastic schemes to control the searching convergence. The MEMS simulation module is the user input module, which requires a MEMS fabrication simulation and user-specified desired shape. In the mask genetics module, mask-layouts are geometrically treated as 2D simple polygons, which form the underlying searching space. Each mask-layout is encoded into two real strings called angle string and distance string. The angle string contains edge directional angles and the distance string contains edge lengths. The size of each string is equal to the number of polygon sides. Two elements from each string with the same element position describe an edge of the mask-layout. A crossover scheme is applied to two mask-layouts with the same sides each time. The two mask-layouts are geometrically aligned first. Two random linear blendings are applied to the directional angles and lengths of each pair of aligned edges respectively. Heuristics are used to ensure the simplicity (non-self intersection between non-adjacent edges) of the mask-layouts during the initial random generation and crossover. In the simulation module, the 3D shape is expressed through a series of horizontal polygon layers. The same polygon layers of different shapes are ensured to have the same vertical location. The shape closeness of any two shapes is the weighted sum of the shape closeness of each vertically paired polygon layer. The shape closeness of two polygon layers is measured by the L1 distance of their turning functions [1]. A test loop is constructed for the bulk wet etching mask synthesis by incorporating a 3D wet etching simulation [3]. Initial results shown in Figure 2 demonstrate the feasibility of this approach to mask-layout synthesis. Each cell in the figures includes two shapes. The right one is the user-specified shape which is all the same throughout the cells. The left one is the synthesized mask-layout (indicated by the darker outline) and its etched shape. The iteration numbers and the shape mismatch values are presented to show the converging search process.