Extension of the Hopkins theory of partially coherent imaging to include thin-film interference effects

摘要

In this paper, we extend the Hopkins formulation to take into account high numerical aperture and thin-film interference effects by introducing a new TCC function for each depth inside the photoresist, which completely characterizes the lens/thin-film system with respect to partial coherence, aberrations, defocus and interference effects at the given depth within the photoresist. The basis of the new formulation lies in the fact that, in the presence of the thin- film stack, each point on the exit pupil of the optical system maps linearly not into a single plane wave, but into a family of multiply reflected and generally obliquely propagating plane waves, when bleaching induced scattering effects are neglected. The response within the photoresist due to each incident plane wave is calculated by the method of thin-film optics. The results are then used in the calculation of a new, matrix pupil function of the lens/thin- film system for each depth within the photoresist. Obliquity factors appropriate to high-NA systems are included in the new pupil function. For the Koehler illumination commonly used in reduction projection systems, it is shown that the total irradiance at each depth within the photoresist is expressible in terms of a matrix TCC in the limit when the rays incident on the mask are all nearly vertical, as is the case in a 5X reduction system.