Domain decomposition methods for the electromagnetic simulation of scattering from three-dimensional structures with applications in lithography

An integrated methodology has been developed for the computer simulation and modeling of the electromagnetic scattering from large, non-periodic, two-dimensional layouts of advanced photomasks (masks with optical proximity correction and phase shifting masks). The name domain decomposition method (DDM) was used, since it describes the central mechanism of the method.; Domain decomposition consists of three important steps: First, by virtue of the linearity of the Kirchhoff-Fresnel diffraction integral, the mask layout is decomposed into a set of constituent single-opening masks. Secondly, the rigorous electromagnetic simulation of each three-dimensional structure from the set of these single-opening masks is circumvented, and instead, the result for the scattered field is synthesized based on two two-dimensional rigorous electromagnetic simulations that model the mask geometry in two cross-sectional planes. Subsequently, based on the results of the electromagnetic scattering from these two-dimensional geometries, compact equivalent source models are used to describe the scattered fields on a reference plane. These models are constructed in such a way as to minimize the error in the part of the diffraction spectrum that is passing through the projection system allowing accurate and efficient image simulation.; Excellent accuracy in the calculation of the near scattered fields of better than 99% (in a normalized mean square error sense) compared with the fully rigorous mask model has been achieved, accompanied by speed-up factors for the total simulation time in excess of 200. A further revision of the method consisting of the decomposition of the layout into edges (edge-DDM) allows for easier algorithmic implementation. The algorithm of the edge-DDM was programed in the MATLAB environment and together with TEMPEST cross-sectional simulations resulted in speed-up factors for the total simulation time of 172,800 (1sec. vs. 2days) using a library of pre-calculated edge-diffraction simulations. The normalized mean square error of the near field results between the edge-DDM and full three-dimensional simulation is less than 1%. A 12μm by 16μm layout of a three level alternating PSM, that is out of reach for fully rigorous methods, was simulated in under 1min.; The domain decomposition method was extended in two ways: Energy cross-coupling between neighboring apertures in alternating phase shift masks was modeled through simulation, enabling the accurate modeling of masks with large vertical topography. Another revision of the domain decomposition method suitable for handling the case of scattering from masks when phase defects are present was also realized, enabling rapid defect printability assessment.; Finally, useful engineering design data relevant to the design of optical proximity correction were produced and the electromagnetic behavior of isolated phase defects was examined to understand their interaction with layout features.