Theoretical and Experimental Particle Size Response of Wafer Surface Scanners

Abstract

The particle size response of wafer surface scanners is experimentally and theoretically studied. The basis for the theoretical predictions is the angular relative-intensity distributions obtained by three different methods: a numerical solution of Maxwell's electromagnetic wave equations for a polystyrene latex (PSL) sphere on a silicon surface, and two approximate models that superimpose the Mie scattering from the sphere and the Fresnel reflection at the wafer surface. The predicted scattered intensities are averaged over the geometry of the collection optics to yield the theoretical size responses that are compared with the experimental results. The experimental size response calibrations of the Tencor Surfscan models 4000 and 5500 are obtained by using uniformly deposited monodisperse PSL spheres on a bare silicon wafer. There is good agreement between the experimental data and the size response obtained from numerical solutions of Maxwell's equations. Compared to these numerical results, the two approximate models are found to give inexpensive and fairly reasonable solutions for the theoretical response calibration. The experimental and numerical PSL data show that the range of the multivalued response is very broad for wafer surface scanners because of the interactions between the scattering sphere and the reflecting wafer surface. The experimentally indicated response of a Surfscan model 5500 to silicon dust is also studied by depositing monodisperse silicon particles generated by the mobility classification-inertial impaction method. The experimental silicon dust size response shows a surprisingly good agreement with the approximate theoretical predictions