Abstract
The effective medium approximation (EMA) model may cause a large deviation in the data analysis of spectroscopic ellipsometry (SE) for solid materials with randomly micro-rough surfaces since it ignores the influence of the lateral irregularities of the rough surfaces on the electromagnetic scattering. In this work, a novel inversion framework is developed to extract optical constants from the SE parameters for solid materials with randomly micro-rough surfaces. Our approach enables the integration of the Levenberg-Marquardt optimization algorithm and the first-principles calculations of electromagnetic scattering. In each iterative step, the electromagnetic interactions with rough surfaces are accurately obtained from first-principles calculations without using the EMA model for rough estimation, which significantly guarantees the precision and wide applicability of our method for actual surfaces without a perfectly Gaussian height distribution. Furthermore, a superior advantage of our approach is that its error can be feasibly evaluated from the instrumental errors of the surface morphology detectors and the SE.
Highlights
The optical constants of materials are essential data and closely connected with many fields, such as photocatalysis [1,2], the solar desalination of sea water [3,4], thermophotovolatic emitters [5,6], and thin film materials in photonics [7,8]
Based on the convergence of calculations, a mesh size of λ/400 was used for this case, which could reproduce the morphology of the rough surfaces well
The effective medium approximation (EMA) model cannot build accurate mappings between the optical constants and the spectroscopic ellipsometry (SE) parameters for micro-rough surfaces since it neglects the large effect of the correlation length on the electromagnetic scattering from rough surfaces
Summary
The optical constants of materials are essential data and closely connected with many fields, such as photocatalysis [1,2], the solar desalination of sea water [3,4], thermophotovolatic emitters [5,6], and thin film materials in photonics [7,8]. The referred surface roughness is usually much smaller than the wavelength of incident light in practical experiments, SE is capable of detecting the large deviation between ellipsometric responses from micro-rough and smooth surfaces since it is highly sensitive to surface structures [14,15,16] Such a deviation will yield pseudo optical constants. The EMA model cannot build the accurate mappings between the optical constants and the SE parameters, because it considers only the height irregularities and it neglects the large effect of the lateral characteristic dimensions on the electromagnetic scattering from rough surfaces. By combining the first-principles calculations of electromagnetic scattering and the Levenberg-Marquardt optimization algorithm, we present a novel inversion method to obtain the optical constants of solid materials with micro-rough surfaces from SE measurements. In the last part of this work, we demonstrate the experimental validation of our method with the available SE experimental data for rectangular gratings and a real SiO2 randomly rough surface
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