The Rayleigh's equations for resolution and depth of focus (DOF) have been the two pillars of optical lithography, defining the dependency of resolution and DOF to wavelength and to the numerical aperture (NA) of the imaging system. Scaling of resolution and DOF as well as determination of the engineering-based constants k₁ and k₂ have been depending on these two equations. However, the Rayleigh's equation for DOF is a paraxial approximation. Solving the optical path difference as a function of wavelength and NA rigorously, produces a DOF dependency to the inverse of the square of the numerical half aperture instead of the numerical full aperture. Using this new DOF scaling education and a new coefficient of DOF k₃, 10 percent and 20 percent of the previously determined DOF have been overestimated at NA of 0.6 and 0.8 respectively. The Rayleigh's equation for resolution does not suffer from loss of accuracy at high NA but is ambiguous for immersion lithography. An improved from removes the ambiguity.

Date Published: 5 July 2000
PDF: 6 pages
Proc. SPIE 4000, Optical Microlithography XIII, (5 July 2000); doi: 10.1117/12.389068

Published in SPIE Proceedings Vol. 4000:
Optical Microlithography XIII
Christopher J. Progler, Editor(s)