Calibration of polarization effects for the focusing lens pair in a micro-spot Mueller matrix ellipsometer

Abstract

With the urgent demands of characterizing the optical properties and thicknesses of nano-films in some micron-scale trenches usually emerging in integrated circuit manufacturing, the micro-spot Mueller matrix ellipsometer (M-MME) has attracted increasingly more attention. While using a lens pair to enable a probing spot with a micron scale in the M-MME, the additional polarization effects caused by the lens pair usually degrade the measurement precision of the instrument. Therefore, it is of great significance to calibrate the polarization effects of the lens pair for measurement precision improvement. In this work, a parametric model based on the Mueller matrix decomposition has been proposed to fully describe the polarization effects of a focusing lens pair in the M-MME. A single lens in the focusing lens pair could be optical equivalent to a cascade system consisting of a circular retarder with slight diattenuation, a linear retarder with small diattenuation, a rotator, and a depolarizer. Correspondingly, a comprehensive calibration method combining an initial offline and a subsequent in-situ calibration was proposed to achieve the ingenious correction of polarization effects for the lens pair in the self-built M-MME. Meanwhile, in order to demonstrate the effectiveness and feasibility of the proposed method, a series of thickness measurement experiments on SiO2 films have been carried out. The corresponding results indicate that the proposed calibration method could improve the relative deviation between the thickness measured by the self-built M-MME and those measured by the commercial MME to within 1.6% for those SiO2 films with thickness larger than 25 nm.