Theoretical analysis of coma aberration measurement for aerial image sidelobe peaks

Abstract

By analyzing aerial images, we characterize the lowest order coma aberration measurements for the projection optics of a microlithography exposure apparatus based on scalar diffraction theory. Our developed method for measuring the coma aberration exploits the intensity difference between the sidelobe peaks appearing near the boundaries of the bright field ("negative") single-line or plural-line patterns. Our method further demonstrates linearity between the intensity difference of the sidelobe peaks and the amount of residual lowest order coma aberration. We analyze the coma aberration sensitivity formula and determine the duty ratio of the line-and-space pattern that realizes the highest aberration sensitivity.

Parity decomposition theory of full wavefront aberration measurement using the intensity differences of aerial images in microlithography

“…Using parity decomposition and the perturbative approach with regard to aberration, the image intensity can be expressed with terms classified by the two types of parity: illumination pupil and wavefront aberration. In Section 3, we derive the generalized intensity difference formula in the same manner as that developed in previous studies [11,12]. In Section 4, after performing the Zernike polynomial expansion on the derived intensity difference formula, simultaneous linear equations for estimating the Zernike coefficients (except for Z 2 and Z 3 ) are established, and the validity of this measurement is numerically confirmed under practical lithography conditions.…”

“…Moreover, we cannot apply interferometer measurements to the "lens-onbody" situation in which the projection optics have already been installed in the exposure apparatus. On the other hand, alternative methods based on images projected by the optical system, which are called aerial images in this work, have been actively suggested [2][3][4][5][6][7][8][9][10][11][12] and could be utilized in lens-on-body aberration measurements at the cost of the measurement accuracy.…”

“…Recently, we have proposed a new method for realizing highly sensitive coma (odd) aberration measurements by measuring the intensity difference between the sidelobe peaks [11,12]. This method utilizes one-dimensional measurement patterns consisting of single-or multibars.…”

“…This method utilizes one-dimensional measurement patterns consisting of single-or multibars. Applying the perturbative approach with regard to aberration to the Fourier imaging formula, we have derived an aberration sensitivity formula in the coherent illumination case [11] and in the partially coherent illumination case [12].…”

“…In this study, we propose a new type of aerial image-based full wavefront measurement, including not only odd aberration but also even aberration, by extending our coma aberration measurement using the intensity difference [11,12]. We call this method the wavefront aberration measurement of parity decomposition (WAMPD).…”