5.3 Field Calculation over Nonplanar Topography

The growing complexity of the devices is mainly realized by decreasing the minimal feature size and simultaneously increasing the nonplanarity of the topography. Both trends contradict most of the stringent assumptions required for the simple planar imaging models. Second-order effects such as light scattering due to the inhomogeneity of the resist and especially the notching phenomenon due to a nonplanar reflective substrate have to be caught by the simulation. Hence rigorous EM methods are being developed that directly solve the Maxwell equations in either the spatial-, time- or frequency-domain. A survey over representative examples belonging to these basic categories is given below. However, as the chemical reaction of the resist is only understood to a certain depth and as the extreme computational requirements prohibit a quick everyday application of rigorous field solvers, approximate EM simulation techniques suited for nonplanar topography have been proposed recently. For the sake of completeness one promising approach based on the geometrical theory of diffraction will be described at the end of this chapter.