FDTD-Based Study on Equivalent Medium Approximation Model of Surface Roughness for Thin Films Characterization Using Spectroscopic Ellipsometry

Abstract

Spectroscopic ellipsometry (SE) is an effective method to measure the optical constants of thin film materials which is very sensitive to the surface topography of thin films. When performing ellipsometric measurements of the optical constants of solid materials with rough surfaces, the equivalent medium approximation (EMA) model is often used to characterize the surface topography. The EMA model is determined by two parameters of equivalent thickness dEMA and the void volume fraction f. In most applications, the void volume fraction parameter f is always set to an empirical 50% without any instructions, and then the thickness parameter dEMA is determined by fitting. In order to improve the accuracy of the fitting results, it is necessary to validate the construction law of the EMA model in the ellipsometry analysis considering characteristic parameters of the actual surface topography. In this paper, the influence of the surface topographical parameters on EMA model is analyzed. The method of FDTD (finite difference time domain) is employed to simulate the SiO2 films with different topographical parameters and EMA model are carried out on these samples. The analysis results show that the EMA model constructed with dEMA = σ + 0.80 h (σ: the root mean square height, h: the average height) can better fit the SE parameters. The proposed method can facilitate a better understanding and utilization of the EMA model in SE application.

Regime Map of the Effective Medium Approximation Modelling of Micro-Rough Surfaces in Ellipsometry

“…The parameter ∆ represents the difference in phase experienced upon reflection by p-and s-polarizations. The amplitude ratio Ψ and the phase difference ∆, which are known as the SE parameters, are defined by [20]:…”

“…The parameter Δ represents the difference in phase experienced upon reflection by p- and s-polarizations. The amplitude ratio Ψ and the phase difference Δ, which are known as the SE parameters, are defined by [ 20 ]: where ρ is the ellipsometric ratio; E rp and E ip represent the reflected and the incident electric field intensity of p-polarizations, respectively; and E rs and E is denote the reflected and the incident electric field intensity of s-polarizations, respectively.…”

“…Liu et al [ 19 ] reported that d EMA has a linear relationship with σ 2 / τ and the proportionality coefficient and intercept change with the materials. Yu et al [ 20 ] found that the EMA model constructed with d EMA = σ + 0.80 h ( σ represents the root mean square height and h represents the average height, respectively) better fits the SE parameters. Above all, using EMA to model rough surfaces has the drawback that the formulas of the film thickness are undefined and the precision of the model is difficult to determine.…”

Investigation of Surface Defects in Optical Components Based on Reflection Mueller Matrix Spectroscopy

“…Based on the principle that different physical properties of the surface defects of optical elements lead to a different modulation of the polarization state of the reflected light, this paper proposes a new method for the optical identification of surface roughness [14,16], pockmarks, dirty particles above the surface, and SSBDs [17] in optical elements using RMMS. In this method, firstly, the combination of the BRDF and the Rayleigh-Rice vector scattering theory is innovatively proposed to construct the pBRDF model for various types of defects on the surface of optical elements, and then the BRDF is numerically analyzed to obtain the optimal detection conditions for defects on the surface of optical elements.…”