Application of the discrete dipole approximation for dipoles embedded in film

An implementation of the discrete dipole approximation for dipoles embedded in film on substrate is derived. It is capable of predicting the scattering response from various types of subsurface features such as trenches and contact-vias. An arbitrarily shaped subsurface feature is modeled with dipoles inside the film material on top of a substrate. Relative polarizability, direct interactions, and reflection interactions are derived and applied to construct a system of equations that are solved with an iterative method. The far-field scattering response is computed from the dipole moment solution of the system matrix with the help of the reciprocity theorem. The validity of the proposed method is compared with that of other existing theories, and the effect of film structure on far-field scattering is shown with high-aspect-ratio cylindrical contact-via models.