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

• Published in: Sensors (Basel, Switzerland) Vol. 24; no. 4; p. 1242
• Main Authors: Huang, Meijiao, Guo, Liang, Jiang, Fengyi
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 15.02.2024; MDPI
• Subjects: Analysis; Approximation; effective medium approximation; Electromagnetism; ellipsometry; Microscopy; Morphology; regime map; rough surfaces; Simulation; Thin films; effective medium approximation; regime map; rough surfaces; ellipsometry
• ISSN: 1424-8220; 1424-8220
• DOI: 10.3390/s24041242

In this work, we discuss the precision of the effective medium approximation (EMA) model in the data analysis of spectroscopic ellipsometry (SE) for solid materials with micro-rough surfaces by drawing the regime map. The SE parameters ψ (amplitude ratio) and Δ (phase difference) of the EMA model were solved by rigorous coupled-wave analysis. The electromagnetic response of the actual surfaces with micro roughness was simulated by the finite-difference time-domain method, which was validated by the experimental results. The regime maps associated with the SE parameters and optical constants n (refractive index) and k (extinction coefficient) of the EMA model were drawn by a comparison of the actual values with the model values. We find that using EMA to model micro-rough surfaces with high absorption can result in a higher precision of the amplitude ratio and extinction coefficient. The precisions of ψ, Δ, n and k increase as the relative roughness σ/λ (σ: the root mean square roughness, λ: the incident wavelength) decreases. The precision of ψ has an influence on the precision of k and the precision of Δ affects the precision of n. Changing σ alone has little effect on the regime maps of the relative errors of SE parameters and optical constants. A superior advantage of drawing the regime map is that it enables the clear determination as to whether EMA is able to model the rough surfaces or not.