ABSTRACT
Optical lithography modeling began in the early 1970s when Rick Dill started an effort at IBM Yorktown Heights Research Center to describe the basic steps of the lithography process with mathematical equations. The combination of the models described provides a complete mathematical description of the optical lithography process. Modeling strategies for optical lithography have historically relied on the continuum approximation to describe the physical world being simulated. The mathematical description of the resist process incorporated in the lumped parameter model uses a simple photographic model relating development time to exposure, while the aerial image simulation is derived from the standard optical parameters of the lithographic tool. Modeling has always been used as a tool for quantifying optical proximity effects and for defining algorithms for geometry-dependent mask biasing. Most people would consider modeling to be a required element of any optical proximity correction scheme.
