Large Scale Numerical Simulations For Multi-Phase Fluid Dynamics With Moving Interfaces

This short communication presents our recent studies to implement numerical simulations for multi-phase flows on top-ranked supercomputer systems with distributed memory architecture. The numerical model is designed so as to make full use of the capacity of the hardware. Satisfactory scalability in terms of both the parallel speed-up rate and the size of the problem has been obtained on two high rank systems with massively parallel processors, the Earth Simulator (Earth simulator research center, Yokohama Kanagawa, Japan) and the TSUBAME (Tokyo Institute of Technology, Tokyo, Japan) supercomputers.

Coma measurement by use of an alternating phase-shifting mask mark with a specific phase width

The correlation between the coma sensitivity of the alternating phase-shifting mask (Alt-PSM) mark and the mark's structure is studied based on the Hopkins theory of partially coherent imaging and positive resist optical lithography (PROLITH) simulation. It is found that an optimized Alt-PSM mark with its phase width being two-thirds its pitch has a higher sensitivity to coma than Alt-PSM marks with the same pitch and the different phase widths. The pitch of the Alt-PSM mark is also optimized by PROLITH simulation, and the structure of p - 1.92 lambda/NA and pw = 2p/3 proves to be with the highest sensitivity. The optimized Alt-PSM mark is used as a measurement mark to retrieve coma aberration from the projection optics in lithographic tools. In comparison with an ordinary Alt-PSM mark with its phase width being a half its pitch, the measurement accuracies of Z(7) and Z(14) apparently increase. (C) 2009 Optical Society of America

Even aberration measurement of lithographic projection system based on optimized phase-shifting marks

In the present paper, we propose a novel method for measuring the even aberrations of lithographic projection optics by use of optimized phase-shifting marks on the test mask. The line/space ratio of the phase-shifting marks is optimized to obtain the maximum sensitivities of Zernike coefficients corresponding to even aberrations. Spherical aberration and astigmatism can be calculated from the focus shifts of phase-shifting gratings oriented at 0 degrees, 45 degrees, 90 degrees and 135 degrees at multiple illumination settings. The PROLITH simulation results show that, the measurement accuracy of spherical aberration and astigmatism obviously increase, after the optimization of the measurement mark. (C) 2008 Elsevier B.V. All rights reserved.