Weakly guiding approximation of a three-dimensional waveguide model for extreme ultraviolet lithography simulation

Abstract

A three-dimensional (3D) waveguide model is applied in extreme ultraviolet (EUV) lithography simulations. The 3D waveguide model is equivalent to rigorous coupled-wave analysis, but fewer field components are used to solve Maxwell’s equations. The 3D waveguide model uses two components of vector potential, A x and A y , corresponding to the two polarizations. The electric field of the A x polarization is approximately parallel to the x axis, and the electric field of the A y polarization is approximately parallel to the y axis. The 3D waveguide model solves a coupled vector wave equation for two polarizations. The refractive index of conventional EUV absorbers is close to that of vacuum. The weakly guiding approximation in optical fiber theory is applied to the 3D waveguide model. The coupled vector wave equations for the two polarizations are decoupled into two independent scalar wave equations. Maxwell’s equations are simplified to a set of scalar wave equations. The weakly guiding approximation reduces the computation time to solve the equations. The computation time required to solve the weakly guiding approximation is about 1/5 of the time to solve the original 3D waveguide model.