Non-axisymmetric models for light scattering from a particle on or near a plane surface

Abstract

The communication is devoted to semi-analytical approaches for analyzing the scattering by a non-axisymmetric structure consisting of a nonspherical particle and a plane surface. On the basis of the discrete sources method and the T-matrix method, numerical schemes were developed and implemented in computer programs. Numerical results related to the influence of particle shape on the scattering characteristics are discussed. We will show that even for particles much smaller than the wavelength the scattering characteristics are still sensitive to the particle shape.

Introduction

The foregoing miniaturization of microchips come to be a real factor of a technical progress in semiconductor manufacturing. Being a first-step chain for the chip manufacturing, silicon wafers demand an extra care of their purity, which is determined by certain defects of real wafers: contaminating micro-particles, pits, subsurface bulks (crystal originated particles), scratches, etc. Therefore, the control of silicon wafer surface defects is of prime significance in semiconductor manufacturing. The purity monitoring is being carried out through optical surface scanners. The design of the surface scanner includes a laser source of light and collector's system to capture the intensity scattered by a micro-particle. Problems of surface scanner's operating include both false counts of non-existing contaminants detected, and missing counts of real defects not detected by the instrument. As the minimum line width of wafer structures continues to decrease, the importance of proper detection and characterization of scattering features grows. One response to this problem is the use of increasingly sophisticated models to predict light scatter signals using mathematical modeling and computer simulation analysis.

Several studies have addressed the scattering problem by spherical micro-particles 1, 2, 3, 4. In 5, 6, 7, 8the scattering by axisymmetric particles on a silicon substrate has been investigated in the framework of the discrete sources method and the T-matrix method. The analysis was restricted to an axisymmetric model by assuming that the particle symmetry axis coincides with the normal direction to the plane interface. Unfortunately, real contaminating particles are not axisymmetric. In this context the elaboration of mathematical models for such kind of applications appears to be of great interest in the design of surface scanners.

In the present communication, we extend our previous models [8]to a non-axisymmetric structure consisting in a nonspherical particle deposited on a plane surface. The aim of our analysis is to investigate the influence of the micro-particle shape on the scattering characteristics.