Analytical approximations of the source intensity distributions

摘要

Diffractive optical elements and hard-stop blades are widely used in scanners to form off-axis illumination. They generate tapered illumination profiles, which have to be accurately represented in lithographical simulations. Typically these profiles are captured in measured source maps. The source maps are inconvenient for OPC applications, because the map files are bulky and often represent asymmetrical sources. We propose analytical formulas to approximate smooth intensity distributions across the illumination aperture for standard, annular, dipole and quadruple sources. The analytical representation is an efficient compression of the source map information, does not require large files, and conveniently regularizes source intensities. We demonstrate examples of fitting measured source maps with these formulas and analyze the induced simulation errors.