Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources

Abstract

In the current optical lithography processes for semiconductor manufacturing, differently shaped illumination sources have been widely used for the need of stringent critical dimension control. This paper proposes a technique for in situ measurement of lens aberrations with generalized formulations of odd and even aberration sensitivities suitable for arbitrarily shaped illumination sources. With a set of Zernike orders, these aberration sensitivities can be treated as a set of analytical kernels which succeed in constructing a sensitivity function space. The analytical kernels reveal the physical essence of partially coherent imaging systems by taking into account the interaction between the wavefront aberration and the illumination source, and take the advantage of realizing a linear and analytical relationship between the Zernike coefficients to be measured and the measurable physical signals. A variety of mainstream illumination sources with spatially variable intensity distributions were input into the PROLITH for the simulation work, which demonstrates and confirms that the generalized formulations are suitable for measuring lens aberrations up to a high order Zernike coefficient under different types of source distributions. The technique is simple to implement and will have potential applications in the in-line monitoring of imaging quality of current lithographic tools.

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

“…6, where the total wavefront aberration root-mean-square (rms) is 0.0142λ rms; the rms of the wavefront aberration is over 0.0100λ rms, assuming a typical well-tuned projection lens [7,8]. Previously, the total rms of residual wavefront aberration for the immersion ArF exposure apparatus has been reported at about 0.0050λ rms [27].…”

“…(8). Such an odd functional spectrum is realized in the phase shift mask [28,29], where we neglect the phase factor, which induces uniform translation of the image.…”

“…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.…”

“…For example, the odd aberration leads to a lateral shift of the total aerial image, and the even aberration shifts the best focus position in the z axis. Therefore, the wavefront aberration can be estimated by measuring the qualities of these aberration-induced characteristics [2][3][4][5][6][7][8]. However, in the measurement of the best focus shift, we must obtain at least three defocused images at different z-axis positions.…”

“…(7) and (8). The kernel function K ξ 1 ; ξ 2 is assumed to be any term appearing in the TCC expansion in Eqs.…”