Fast topography simulation using differential method

Sonny Y. Zinn; Sung-Hyuck Kim; Sung-Woon Choi; Jung-Min Sohn

doi:10.1117/12.485355

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26 June 2003 Fast topography simulation using differential method

Sonny Y. Zinn, Sung-Hyuck Kim, Sung-Woon Choi, Jung-Min Sohn

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Proceedings Volume 5040, Optical Microlithography XVI; (2003) https://doi.org/10.1117/12.485355
Event: Microlithography 2003, 2003, Santa Clara, California, United States

Abstract

The finite-difference time-domain (FDTD) is a standard method for simulating mask topography effects. Its algorithm is simple, robust, and easy to implement. However, the FDTD algorithm consumes a lot of computer memory and time. For full three-dimensional simulation of a small contact pattern, it takes several hours on a personal computer. To reduce computing time, we adopted the differential method (DM) which solves the Maxwell equations in spatial frequency domain. Speed is the main advantage of DM over FDTD. To verify the numerical accuracy of DM, we compared the aerial images of several line/space patterns whose topography effects are predicted by DM and FDTD. For the calculation of the aerial images, we used a vector model. For unpolarized light, the maximum intensities differ by about 7%. Having assessed the accuracy of DM, we now describe the simulation result of a two-dimensional pattern. The pattern mainly contains densely packed rectangles. The size of the simulation domain was taken to be 1.972 μm × 4.368 μm × 0.350μm on the mask scale where the first two numbers represent the size of the unit cell of the pattern. Illumination condition is KrF source, annular aperture of 0.85/0.55, and NA of 0.7. Estimated running time of FDTD for topography simulation was 180 days. However, DM took about 280 minutes. The resulting aerial image agreed within about 8% with an experimental image directly measured by an AIMS-FAB.

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Sonny Y. Zinn, Sung-Hyuck Kim, Sung-Woon Choi, and Jung-Min Sohn "Fast topography simulation using differential method", Proc. SPIE 5040, Optical Microlithography XVI, (26 June 2003); https://doi.org/10.1117/12.485355

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