Modeling High Numerical Aperture Optical Lithography

Electromagnetic diffraction theory is applied to obtain a rigorous and comprehensive description of the imaging and exposure process in a projection optical system imaging a one-dimensional, periodic object in a planar layer of photoresist. The method is applicable to high numerical aperture and thick-photoresist systems, and accounts for the exposure dependent absorption characteristics of positive photoresists. It is used with the development simulator in SAMPLE to simulate the physical profile of the developed image. Theoretical and experimental results are given, which show asymmetrical variation of the developed image with focus. This asymmetry is found to depend on photoresist thickness, and the dependence is shown to be incompatible with the usual approximation of normal ray propagation in the photoresist.