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12 December 2009 Using transmission line theory to calculate equivalent refractive index of EUV mask multilayer structures for efficient scattering simulation by finite-difference time-domain method
Yen-Min Lee, Jia-Han Li, Philip C. W. Ng, Ting-Han Pei, Fu-Min Wang, Kuen-Yu Tsai, Alek C. Chen
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Proceedings Volume 7520, Lithography Asia 2009; 75200W (2009) https://doi.org/10.1117/12.837150
Event: SPIE Lithography Asia, 2009, Taipei, Taiwan
Abstract
The Finite-Difference Time-Domain (FDTD) method is used to study the scattering effects of extreme ultraviolet (EUV) mask. It requires significant amounts of memory and computation time as the fine grid size is needed for simulation. Theoretically, the accuracy can be increased as the mesh size is decreased in FDTD simulation. However, it is not easy to get the accurate simulation results for the multilayer (ML) structures by FDTD method. The transmission line theory is used to calculate the equivalent refractive index for EUV mask ML to simulate the ML as one layer of bulk artificial material. The reflectivities for EUV light with the normal incidence and small-angle oblique incidence in the bulk artificial material and EUV mask ML are simulated by FDTD method. The Fresnel's equation is used to evaluate the numerical errors for these FDTD simulations, and the results show good agreement between them. Using the equivalent refractive index material for EUV multilayer mask can reduce the computation time and have the accuracy with tolerable numerical errors. The ML structure with periodic surface roughness is also studied by this method, and it shows that only half of computation time is needed to substitute ML to a bulk equivalent refractive index material in FDTD simulations. This proposed method can accelerate the simulations of EUV mask designs.
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Yen-Min Lee, Jia-Han Li, Philip C. W. Ng, Ting-Han Pei, Fu-Min Wang, Kuen-Yu Tsai, and Alek C. Chen "Using transmission line theory to calculate equivalent refractive index of EUV mask multilayer structures for efficient scattering simulation by finite-difference time-domain method", Proc. SPIE 7520, Lithography Asia 2009, 75200W (12 December 2009); https://doi.org/10.1117/12.837150
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KEYWORDS
Finite-difference time-domain method
Extreme ultraviolet
Computer simulations
Reflectivity
Refractive index
Error analysis
Molybdenum
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