THIN-FILM INTERFERENCE EFFECTS IN PHOTOLITHOGRAPHY FOR FINITE NUMERICAL APERTURES

It is known that the energy coupled into a planar resist film atop a reflective substrate and illuminated from above has an oscillatory dependence on the resist thickness. We consider in detail the remarkable effects produced by oblique waves in the incident illumination for projection optical lithography with finite numerical apertures. A simple discussion reveals how significant corrections to thin-film interference phenomena in photolithography can occur relative to the case of normally incident illumination. Moreover, the criterion for the onset of these corrections is derived and is shown to be closely similar to that for the onset of bulk defocus effects. Rigorous modeling results are then presented, based on a finite element solution of the two-dimensional Helmholtz equation. A simplified oblique-propagation model is also introduced.