Numerical calibration of the angle of incidence in ellipsometers

Abstract

The experimental error in the angle of incidence strongly affects the film optical constants and thickness sought from the ellipsometric data, particularly when the film is thinner than 200 Å. This angle should therefore be accurately measured and this has been a frequently faced difficulty, especially in fixed-angle-of-incidence and in situ ellipsometers. We describe in this paper two numerical calibration procedures evaluating the angle of incidence from the ellipsometric data and measured on well-identified film - substrate reflecting structures either with a known or with an unknown film refractive index. The procedures rapidly determine the angle of incidence independently of the film thickness. An error analysis shows that the angle of incidence can thus be determined with an uncertainty of a few hundredths of a degree from ellipsometers inducing the same order of angular errors. The thickness ranges of films yielding such lower uncertainties are deduced from the error analysis. The effect of substrate real index error on this uncertainty is studied in particular. The supplementary results produced therein may be used in data interpretation while checking the angle of incidence if it is accurately measured by some other method. The procedures may also be easily adopted to variably damped least-squares (VDLS) algorithms employed in real-time monitoring of films during growth. The calibration procedures are illustrated for all these aspects with experimental data from real reflecting systems.