New λ/NA scaling equations for resolution and depth-of-focus

ABSTRACT The Rayleigh's equations for resolution and depth of focus(DOF) have been the two pillars of optical lithography, defmingthe dependency of resolution and DOF to wavelength and to the numerical aperture(NA) of the imaging system'. Scaling ofresolution and DOF as well as determination of the engineering-based constants k, and k2 have been depending on these twoequations. However, the Rayleigh's equation for DOF is a paraxial approximation. Solving the optical path difference as aftinction of wavelength and NA rigorously, produces a DOF dependency to the inverse of the square of the numerical halfaperture instead of the numerical full aperture. Using this new DOF scaling equation and a new coefficient of DOF k3, 10%and 20% of the previously determined DOF have been overestimated at NA of 0.6 and 0.8 respectively. The Rayleigh'sequation for resolution does not suffer from loss of accuracy at high NA but is ambiguous for immersion lithography. Animproved form removes the ambiguity.Keywords: Optical microlithography, microlithography, microlithography imaging, Rayleigh, depth of focus, resolutionscaling, depth of focus scaling.