An overview of level set methods for etching, deposition, and lithography development

Abstract

The range of surface evolution problems in etching, deposition, and lithography development offers significant challenge for numerical methods in front tracking. Level set methods for evolving interfaces are specifically designed for profiles which can develop sharp corners, change topology, and undergo orders of magnitude changes in speed. They are based on solving a Hamilton-Jacobi type equation for a level set function, using techniques borrowed from hyperbolic conservation laws. Over 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 etching, 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 (1996), can track the three-dimensional photoresist process through a 200/spl times/200/spl times/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 (1995), can be used to handle problems in which the speed of the interface delicately depends on the 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 development, etching/deposition problems under the effects of masking, visibility, complex flux integrations over sources, nonconvex sputter deposition problems, and simultaneous deposition and etch phenomena.