Electromagnetic scattering by a finite strip on a substrate

Features on wafers manufactured by the semiconductor industry continue to decrease in size. Simulation is required to determine the dimensions of a feature from a microscope image when some of the dimensions are comparable to or significantly smaller than the wavelength of the light used in the microscope. Previously images of finite strips on a substrate have been approximated by those of infinite strips, which reduces to the solution of the two-dimensional scalar Helmholtz equations. If this simpler approach no longer gives accurate results, we have to consider scattering of monochromatic plane waves of circular frequency ω by finite strips, which requires the solution of the three-dimensional Maxwell equations. We use a generalization of the single-integral-equation formulation that reduces the number of unknowns on the interfaces in three-dimensional problems such as a particle in a layer, a doublet of spheres, and a finite strip on a substrate, where we show the integral equations for the unknown tangential vector fields on the boundaries and the simulation of image formation. Here we show details of the scattering by a finite strip, such as the parameters defining the configuration of an oblique strip, the handling of the surface divergence term, and the reduction to algebraic equations, including self-patch contributions.