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Since the beginning of the optical lithography simulation, the mask, though actually with limited thickness, is always considered as purely Two-Dimensional, or in other word, the mask thickness is infinitely small. This is always a good approximation for the real mask when the critical dimension is relative large and the Numerical Aperture of the optical imaging system is smaller than 0.7, for, the image distortion induced by the mask thickness and profile under such situation is negligible. Even adopting infinite thin mask approximation described by Kirchoff approach, accurate simulation results can be achieved. However, for higher NA microlithography process, the polarization of the illumination light and the profile of the mask become important factor that will be reflected in the final image formation. Thus, the infinite thin mask approximation will have larger deviation from real world process with the technology goes into 65nm node and beyond.
To describe the 3D mask effect exactly, Maxwell electric-magnetic filed equations should be adopted. However, to solve the Maxwell equations mathematically is obviously a horrible work, since the pattern on the mask can be extremely complicated. Fortunately, there are still a lot of algorithms through which numerical results of the Maxwell equations can be achieved. We have developed a tool based on the Finite-difference time-domain method (FDTD), which is developed by K. S. Yee in 1966. Second-order approximation of Mur’s absorbing boundary condition is used to enhance the convergence of the calculation. We here will demonstrate some simulation results given by our tool, including how the profile (footing, undercutting and so on) of the mask affects the final image formed on wafer level and the comparison of the results given by Kirchoff approach and FDTD approach. Brief summary will also given for the 3D Mask Effect in the image formation.
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