Rigorous simulation of alignment for microlithography

As the dimensions of semiconductor devices continue to shrink, mask alignment becomes increasingly important and difficult. The required accuracy of alignment is only a few percent of the used wavelengths. In optical projection lithography, the position of a wafer with respect to a mask is determined by the analysis of the light that is diffracted from an alignment mark on the wafer. The profile shape, depth, and asymmetry of the alignment mark significantly affect the observed alignment signal. In order to predict the influence of these factors, the simulation of the alignment system becomes necessary. We compare rigorous methods for the simulation of light diffraction from the alignment mark, such as the finite-difference time-domain method, rigorous coupled wave analysis, and the waveguide method (WG) to the Fresnel method that has been used in the past. It is shown that the three rigorous methods used in this study demonstrate a good convergence. For the specific geometry and material parameters of the alignment mark used in our investigations, WG is most appropriate for fast work. The difference between Fresnel and rigorous methods becomes important when the height of the alignment mark exceeds 30% of the wavelength of the alignment system.