Mathematical treatment of condenser aberrations and their impact on linewidth control

Christof G. Krautschik; Masato Shibuya; Kenny K.H. Toh

doi:10.1117/12.354395

26 July 1999 Mathematical treatment of condenser aberrations and their impact on linewidth control

Christof G. Krautschik, Masato Shibuya, Kenny K.H. Toh

Proceedings Volume 3679, Optical Microlithography XII; (1999) https://doi.org/10.1117/12.354395
Event: Microlithography '99, 1999, Santa Clara, CA, United States

Abstract

While condenser aberrations under Koehler illumination were previously treated in the literature their mathematical derivation did not take conservation of radiance into consideration. Here we make use of a more rigorous derivation of the mutual intensity where the source deformation term is treated in the context of radiance conservation. The derivation predicts that condenser aberrations lead to radiance invariance while aberrations have a direct bearing on illumination uniformity and the angular extent of the local effective source. This result significantly contrasts with the previously established conclusion in the literature that condenser aberrations lead to a modification of the source radiance but preserves irradiance in the reticle plane. Source aberrations of first and third order are derived and then systematically explored both analytically and numerically. Aberration impact on linewidth control are further considered and quantified from the aerial image perspective. It is shown that third order coma has the most significant impact on CD control as a result of the asymmetry in the deformation of the source shape. Similarly coma also significantly impacts overall mask illumination uniformity.

Citation Download Citation

Christof G. Krautschik, Masato Shibuya, and Kenny K.H. Toh "Mathematical treatment of condenser aberrations and their impact on linewidth control", Proc. SPIE 3679, Optical Microlithography XII, (26 July 1999); https://doi.org/10.1117/12.354395

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