AN OVERVIEW OF LEVEL SET METHODS FOR ETCHING, DEPOSITION, AND LITHOGRAPHY DEVELOPMENT

The range of surface evolution problems in etching, deposition, and li thography development offers significant challenge for numerical metho ds in front tracking. Level set methods for evolving interfaces are sp ecifically designed for profiles which can develop sharp corners, chan ge topology, and undergo orders of magnitude changes in speed, They ar e based on solving a Hamilton-Jacobi type equation for a level set fun ction, using techniques borrowed from hyperbolic conservation laws. Ov er the past few years, a body of level set methods have been developed with application to microfabrication problems, In this paper, we give an overview of these techniques, describe the implementation in etchi ng, deposition, and lithography simulations, and present a collection of fast level set methods, each aimed at a particular application, In the case of photoresist development and isotropic etching/deposition, the fast marching level set method, introduced by Sethian in [39], [40 ], can track the three-dimensional photoresist process through a 200x2 00x 200 rate function grid in under 55 s on a Sparc10. In the case of more complex etching and deposition, the narrow band level set method, introduced in Adalsteinsson and Sethian in [2], can be used to handle problems in which the speed of the interface delicately depends on th e orientation of the interface versus an incoming beam, the effects of visibility, surface tension, reflection and re-emission, and complex three-dimensional effects, Our applications include photoresist develo pment, etching/deposition problems under the effects of masking, visib ility, complex flux integrations over sources, nonconvex sputter depos ition problems, and simultaneous deposition and etch phenomena.