An Overview of Level Set Methods for Etching, Deposition, and Lithography
J.A. Sethian and D. Adalsteinsson
to appear, IEEE Transactions on Semiconductor Devices, Feb. 1997.
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
In the case of more complex etching and deposition,
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.
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