A two-dimensional fast Fourier transform technique is proposed for accelerating the computation of scattering characteristics of features on surfaces by using the discrete-dipole approximation. The two-dimensional fast Fourier transform reduces the CPU execution time dependence on the number of dipoles N from O(N2) to O(N log N). The capabilities and flexibility of a discrete-dipole code implementing the technique are demonstrated with scattering results from circuit features on surfaces.

The ability to predict angle-resolved light scattering characteristics of surface features, including particle contaminants and circuit structures, is identified as an important tool for the development of next generation wafer inspection systems. A model and associated code based on the coupled-dipole method used to model the light scattering is described. Then, predicted scattering signatures for polystyrene latex spheres and silicon dioxide features (nominal 1 micrometer size) on smooth silicon surfaces are reported. The surface features of interest were from the ASU/SRC block of the SEMATECH Patterned Wafer Defect Standard die developed by VLSI Standards, Inc. Finally, the computational results are compared with scattering measurements from individual particles and features. A coherent beam incident of the features on the surface had a wavelength of 632.8 nm, 7 mm beam spot size, and was at an incident angle of 45 degrees. A ringed photodetector centered on the specular reflection was used to measure the angle-resolved scatter. Over the range of scattering angles studied (10 degrees to 60 degrees), the results for differential scattering cross-section agreed to within a factor of 3 or 4.