Abstract

Understanding the interaction of light with particles or other three-dimensional structures on surfaces is of interest in the semiconductor industry for both contamination inspection and lithography. Light scattering from a particle in free space can be calculated by means of the coupled-dipole method.¹ In this method the object, which may be irregularly shaped, is modeled as a collection of dipoles that interact with one another and with the incident electromagnetic field. We have extended this method for use in the presence of a surface by modifying the interaction matrix to include both the direct contribution of a dipole and its reflection from the surface. The reflected dipole fields must be computed by means of the Sommerfeld integral expressions. The method permits full three-dimensional calculations of light scattering from dielectric structures on a surface. The calculation is efficient for structures as large as a wavelength. We have calculated light scattering from several objects, including polystyrene spheres on silicon with diameters as great as 0.85 λ, with varying angles of incidence. In addition, the method maybe applied to lithography structures and layered substrates.

© 1990 Optical Society of America