# An Overview of Level Set Methods for Etching, Deposition, and Lithography Development

## to appear, IEEE Transactions on Semiconductor Devices, Feb. 1997.

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 Method , introduced by Sethian in 1996, can track the three-dimensional photoresist process through a $200 \times 200 \times 200$ rate function grid in under 80 seconds on a Sparc10. In the case of more complex etching and deposition, the narrow band method, introduced by Adalsteinsson and Sethian in 1995, can be used to handle problems in which the speed of the interface delicately depends on the orientation of the interface vs. 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, non-convex sputter deposition problems, and simultaneous deposition and etch phenomena.