3D isolated and periodic grooves measurement simulations for the semiconductor circuits by scatterometry using the FDTD methods and the time shortening calculation method

Abstract

First, we establish numerical calculation techniques for the three-dimensional arbitrary cross section measurement equipment production using oblique incident light waves. In the 3D analysis, the enormous calculation times are problematic to analyze arbitrary cross sections using the FDTD (Finite Difference Time Domain) methods. Then, the sub-grids are used for the time shortening analysis. The sub-grid methods are carried out by the adoption to change the cell dimensions in some specific regions. The multilayer thin film parts are necessary to use the small lattice because we had to deal with the small shape changes. Second, the Gaussian beam incidence analysis for non periodic and isolated grooves is examined. The spot beams are needed for the analysis of the 3D isolation grooves. The scattering characteristics are examined using the spot size of 0.2-1.0 microns. Third, the cell size in the FDTD method must be small enough (<a tenth of wavelength) and the time-step size must satisfy the Courant stability condition. The alternating-direction-implicit (ADI) time-stepping algorithm is introduced to address this issue. This method is unconditionally stable and the Courant stability condition can be eliminated.