Boundary integral spectral element method analyses of extreme ultraviolet multilayer defects.

Extreme ultraviolet (EUV) lithography is an emerging technology for high-density semiconductor patterning. Multilayer distortion caused by mask defects is regarded as one of the critical challenges of EUV lithography. To simulate the influence of the defected nanoscale structures with high accuracy and efficiency, we have developed a boundary integral spectral element method (BI-SEM) that combines the SEM with a set of surface integral equations. The SEM is used to solve the interior computational domain, while the open boundaries are truncated by the surface integral equations. Both two-dimensional (2D) and three-dimensional (3D) EUV cases are simulated. Through comparing the performance of this method with the conventional finite element method (FEM), it is shown that the proposed BI-SEM can greatly decrease both the memory cost and the computation time. For typical 2D problems, we show that the BI-SEM is 11 and 1.25 times more efficient than the FEM in terms of memory and CPU time, respectively, while for 3D problems, these factors are over 14 and 2, respectively, for smaller problems; realistic 3D problems that cannot be solved by the conventional FEM can be accurately simulated by the BI-SEM.