Abstract

Ellipsometry is a powerful method for measuring the optical constants of materials and is very sensitive to surface roughness. In previous ellipsometric measurement of optical constants of solid materials with rough surfaces, researchers frequently used effective medium approximation (EMA) with roughness already known to fit the complex refractive index of the material. However, the ignored correlation length, the other important parameter of rough surfaces, will definitely result in fitting errors. Hence it is necessary to consider the influence of surface roughness and correlation length on the ellipsometric parameters $\mathrm{\Delta }$ (phase difference) and $\mathrm{\Psi }$ (azimuth) characterizing practical systems. In this paper, the influence of roughness of two-dimensional randomly microrough surfaces (relative roughness $\sigma /\lambda$ ranges from 0.001 to 0.025) of silicon on ellipsometric parameters was simulated by the finite-difference time-domain method which was validated with experimental results. The effects of incident angle, relative roughness, and correlation length were numerically investigated for two-dimensional Gaussian distributed randomly microrough surfaces, respectively. The simulated results showed that compared with the smooth surface, only tiny changes of the ellipsometric parameter $\mathrm{\Delta }$ could be observed for microrough silicon surface in the vicinity of the Brewster angle, but obviously changes of $\mathrm{\Psi }$ occur especially in the vicinity of the Brewster angle. More differences between the ellipsometric parameters of the rough surface and smooth surface can been seen especially in the vicinity of the Brewster angle as the relative roughness $\sigma /\lambda$ increases or correlation length $\tau$ decreases. The results reveal that when we measure the optical constants of solid materials by ellipsometry, the smaller roughness, larger correlation length and larger incident wavelength will lead to the higher precision of measurements.

© 2016 Optical Society of America

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