3D semiconductor grooves measurement simulations (scatterometry) using nonstandard FDTD methods

Hirokimi Shirasaki

doi:10.1117/12.773961

25 March 2008 3D semiconductor grooves measurement simulations (scatterometry) using nonstandard FDTD methods

Hirokimi Shirasaki

Proceedings Volume 6922, Metrology, Inspection, and Process Control for Microlithography XXII; 69223T (2008) https://doi.org/10.1117/12.773961
Event: SPIE Advanced Lithography, 2008, San Jose, California, United States

Abstract

In this paper, we analyze the nonstandard finite-difference time-domain (NS-FDTD) method for the rectangular prismatic and cylindrical medium mounts that are put on the substrate periodically. FDTD is useful for analyzing the light scattering from arbitrary shape grooves and mounts. Using the NS-FDTD algorithms, we can get the deep null in the dispersion error at the design frequency and the error is nearly sixth power of grid size with a same computational cost. First, the 3D NS-FDTD formulation is obtained from Maxwell equation for the conducting medium. We analyze structures of rectangular prismatic and cylindrical mounts on the substrate. We show the propagation characteristic calculated by NS-FDTD. Next, the standard (S) FDTD and NS-FDTD reflectance convergences are checked for the grid size h (=Δx=Δy=Δz) changes. The reflectance is compared with the RCWA results. For the case that the layer lattice and the substrate were the same silicon and had some extinction coefficient, the NS-FDTD reflectance convergences are better than the S-FDTD convergences. Finally, we calculate the reflectance from the cubic and cylindrical periodic mounts put on the silicon substrate.

Citation Download Citation

Hirokimi Shirasaki "3D semiconductor grooves measurement simulations (scatterometry) using nonstandard FDTD methods", Proc. SPIE 6922, Metrology, Inspection, and Process Control for Microlithography XXII, 69223T (25 March 2008); https://doi.org/10.1117/12.773961

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