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Abstract：
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.
摘要：
在这项工作中,我们通过绘制状态图，讨论了有效介质近似（EMA）模型在光谱椭圆偏振（SE）数据分析中的精度。通过严格的耦合波分析求解了EMA模型的SE参数Φ（振幅比）和Δ（相位差）。用时域有限差分法模拟了具有微粗糙度的实际表面的电磁响应,实验结果验证了这一点。通过将实际值与模型值进行比较，绘制了与EMA模型的SE参数以及光学常数n（折射率）和k（消光系数）相关的状态图。我们发现，使用EMA对具有高吸收的微粗糙表面进行建模可以导致振幅比和消光系数的更高精度。Φ的精度，Δ,n和k随着相对粗糙度σ/λ(σ：均方根粗糙度，λ:入射波长)减小。Φ的精度影响k的精度，Δ的精度影响n的精度。仅改变σ对SE参数和光学常数的相对误差的状态图影响不大。绘制状态图的优越优点是它能够清楚地确定EMA是否能够对粗糙表面建模。
