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

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(1). Scaling of resolution and DOF as well as determination of the engineering-based constants k(1) and k(2) 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 equation and a new coefficient of DOF k(3), 10% and 20% 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 form removes the ambiguity.