Pseudo-spectral frequency-domain method with background field decomposition and Green's function preconditioner for electromagnetic scattering problem in EUV lithography

Abstract

We provide an accelerated computational framework to solve electromagnetic scattering problems in planarly layered media arising from extreme ultraviolet (EUV) lithography. To achieve this, we reformulate the EUV scattering problem into a scattering problem on a homogeneous background, in which the electromagnetic contribution of the layered media is captured by a recursively updated reflection of the layered stack. The system is numerically solved by employing the pseudo-spectral frequency-domain method paired with an iterative solver, whose iterative convergence is expedited by a free-space Green's function preconditioner. The proposed framework is evaluated on EUV mask geometries and multilayer mirror stacks, demonstrating a significant speedup over the conventional pseudo-spectral frequency-domain method.