Investigation of ellipsometric parameters of 2D microrough surfaces by FDTD

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 Δ (phase difference) and Ψ (azimuth) characterizing practical systems. In this paper, the influence of roughness of two-dimensional randomly microrough surfaces (relative roughness σ/λ 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 Δ could be observed for microrough silicon surface in the vicinity of the Brewster angle, but obviously changes of Ψ 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 σ/λ increases or correlation length τ 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.

Atomic force microscopy analysis of nanoparticles in non-ideal conditions

Nanoparticles are often measured using atomic force microscopy or other scanning probe microscopy methods. For isolated nanoparticles on flat substrates, this is a relatively easy task. However, in real situations, we often need to analyze nanoparticles on rough substrates or nanoparticles that are not isolated. In this article, we present a simple model for realistic simulations of nanoparticle deposition and we employ this model for modeling nanoparticles on rough substrates. Different modeling conditions (coverage, relaxation after deposition) and convolution with different tip shapes are used to obtain a wide spectrum of virtual AFM nanoparticle images similar to those known from practice. Statistical parameters of nanoparticles are then analyzed using different data processing algorithms in order to show their systematic errors and to estimate uncertainties for atomic force microscopy analysis of nanoparticles under non-ideal conditions. It is shown that the elimination of user influence on the data processing algorithm is a key step for obtaining accurate results while analyzing nanoparticles measured in non-ideal conditions.