Limitation of the Kirchhoff boundary conditions for aerial image simulation in 157-nm optical lithography

The aerial images of half-wavelength features with 0 degrees and 180 degrees phases obtained by using the Kirchhoff boundary conditions are compared with those obtained by using rigorous electromagnetic field computation for 248-nm lithography and 157-nm lithography, The discrepancies between the aerial images computed by the two methods are large at both wavelengths, but they are much larger for TM polarization at the wavelength lambda = 157 nm, These discrepancies are due to diffraction effects in the aperture regions, which are more pronounced at lambda = 157 nm because of the larger ratio of the thickness of the chromium absorber to the wavelength required at lambda = 157 nm for a given attenuation factor. This shows that diffraction effects in the aperture regions must be included when simulating aerial images in 157-nm lithography.