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研究生：	林柏亨 Po-Heng, Lin
論文名稱：	Optical Characterization of Nanofilms and Metalenses via Ellipsometry
指導教授：	王智明 Chih-Ming, Wang
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 光電科學研究所碩士在職專班 Executive Master of Optics and Photonics
論文出版年：	2025
畢業學年度：	113
語文別：	英文
論文頁數：	115
中文關鍵詞：	橢圓偏振量測、嚴格耦合波分析、先穎透鏡、色散模型
外文關鍵詞：	Ellipsometry, RCWA, Metalens, Dispersion model
相關次數：	點閱：29 下載：0
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本研究建立了一套整合橢圓偏振量測、Tauc–Lorentz 色散模型與嚴格耦合波分析法（RCWA）的完整工作流程，旨在全面性地表徵非晶矽薄膜以及奈米級週期性光柵結構。我們首先運用 Tauc–Lorentz 色散模型擬合非晶矽的橢圓偏振參數 Ψ 與 Δ 光譜，獲得最佳化的薄膜厚度（62.64 nm）與入射角度（60.52°）。所提取的介電常數進一步透過 Kramers–Kronig 關係驗證其物理自洽性。

接著，利用 RETICOLO, 一套使用在 MATLAB 的 RCWA 求解器，我們系統性探討 60°–70° 入射角範圍、佔空比（0.3–0.7）、蝕刻深度（91–111 nm）以及光柵週期（726 nm 與 1033 nm）對 TE/TM 反射率以及橢圓偏振參數 Ψ 與 Δ 在 250–1200 nm 波段與內的影響。模擬結果與實驗數據展現出極佳的一致性，顯示在布魯斯特角附近 TM 波顯著抑制。

最後，我們提出一套適用於先穎透鏡量測的多點、多角度量測策略：選擇 AOI = 60° 作為穩定的基線，以及 AOI = 70° 作為敏感檢測奈米級非均勻性的量測條件。此方法能為薄膜與奈米結構元件提供穩健的線上製程監控，並加速光柵與先穎透鏡的設計優化。

This work develops an integrated workflow combining spectroscopic ellipsometry, the Tauc–Lorentz dispersion model, and rigorous coupled-wave analysis (RCWA) to comprehensively characterize amorphous silicon thin films and nanoscale periodic grating structures.

We first employ the Tauc–Lorentz formalism to fit ellipsometric Ψ and Δ spectra of amorphous silicon, achieving optimized film thickness (62.64 nm) and incidence angle (60.52 ° ). Physical self ‐ consistency of the extracted refractive index and extinction coefficient is confirmed via Kramers–Kronig relations. Next, using the RETICOLO RCWA solver, we systematically investigate the influence of 60°–70° AOI, duty cycle (0.3–
0.7), etch depth (91–111 nm), and grating period (726 nm vs. 1033 nm) on TE/TM reflectance and ellipsometric parameters across 250–1200 nm. Simulation and experimental data exhibit excellent agreement, revealing pronounced TM suppression at Brewster’s angle. Finally, we propose a multi‐point, multi‐angle measurement strategy for metalens metrology: AOI = 60° for a stable baseline and AOI = 70° for sensitive detection of nanoscale nonuniformities. This methodology offers robust in‐line process monitoring for thin ‐ film and nanostructured photonic devices and accelerates design optimization of gratings and metalenses.

Chapter 1: Introduction, 1
1 Motivation, 1
2 Objective, 1
2.1.    Determination of Thin Film Optical Constants, 1
2.2.    Analysis of Periodic Structural Parameters, 2
3 Essay Structure,3 
3.1    Introduction, 3
3.2    Theoretical Foundations of Spectroscopic Ellipsometry, 3
3.3    Experimental Design and Methodology, 4
3.4    Data Analysis and Interpretation, 4
3.5    Conclusion and Prospective Research Directions, 5
Chapter 2: Literature Review, 5
1 Fundamental Principles of Spectroscopic Ellipsometry, 6
1.1    Core Concepts and Mathematical Formulation, 6
1.2    Ellipsometric Equations and Their Derivation, 7
1.3    Discussion, 8
2 Data Analysis Methodologies and Dispersion Models, 8
2.1    Optical Parameter Extraction, 8
2.2    Dispersion Models, 10
2.3    Model Comparison and Selection, 12
3 Computational Modeling of Periodic Structures, 13
3.1    Fundamentals of RCWA, 13
3.2    Numerical Implementation and Extensions, 14
3.3    Integration with Optimization Techniques, 16
3.4    Summary, 16
4 Global Optimization in Optical Modeling, 17
4.1    Overview of Global Optimization Methods, 17
4.2    Hybrid Optimization Strategies, 19
4.3    Integration with RCWA-Based Modeling, 20
4.4    Summary and Future Outlook, 21
5 Summary and Future Perspectives, 21
5.1    Summary of Key Points, 22
5.2    Future Perspectives and Trends, 23
5.3    Concluding Remarks, 25
Chapter 3: Theoretical Foundations of Spectroscopic Ellipsometry, 26
1 Fundamental Principles of Ellipsometry, 26
1.1    Core Concepts and Mathematical Formulation, 26
1.2    Derivation of the Ellipsometric Equations, 26
2 Data Analysis Methodologies, 32
2.1    Extraction of Optical Parameters, 32
2.2    Introduction to Dispersion Models, 36
2.3    Conclusion, 40
3 Computational Modeling of Periodic Structures, 40
3.1    Fundamentals of the Rigorous Coupled-Wave Analysis (RCWA), 40
3.2    Key Features of RCWA, 40
3.3    Advantages of RCWA, 41
3.4    Practical Implementation in Reticolo, 41
3.5    Conclusion, 43
4 Thin-Film Characterization, 43
5 Workflow for Simulating Ψ and Δ Spectra, 46
5.1    Data Import, 46
5.2    Define the Tauc-Lorentz Model Function, 47
5.3    Define the Ellipsometric Calculation Function, 48
6  Optimization Strategies for Model Fitting, 50
6.1    Define the Objective Function for Optimization, 50
6.2    Perform Optimization & Compute Final Optical Constants, 50
6.3    Calculate Final Results, 51
7  Optimization Strategies for Model Fitting, 52
7.1    Implementation Framework for RCWA Simulations, 54
Chapter 4: Data Analysis and Interpretation, 58
1 Analysis of Thin-Film Optical Properties, 58
1.1    Core Concepts and Mathematical Formulation, 58
1.2    Evaluation of AOI and optical constants, 59
1.3    Evaluation of Kramers–Kronig Relations, 60
2 Periodic Structure Simulation Analysis, 63
2.1    Influence of Structural Parameters on TE and TM Reflection, 63
2.2    Influence of Structural Parameters on Ψ and Δ, 68
3 Analysis of Grating measurement results, 75
3.1    Influence of Structural Parameters on Ψ and Δ, 75
3.2    Analysis of Δ Variation in Grating Structures, 78
3.3    Analysis of Simulation Results, 81
4 Analysis and Measurement Methodologies for Metalens Structures, 84
4.1    Analysis of Ψ Variation in Metalens Structures, 86
4.2    Analysis of Δ Variation in Metalens Structures, 88
4.3    Developing a Practical Metrology Methodology, 90
Chapter 5: Conclusions and Recommendation, 92
1 Key Findings and Discussion, 92
1.1    Discussion of Thin‐Film Optical Properties, 92
1.2    Periodic Structure Simulation vs. Experiment, 93
1.3    Validation of Metalens Measurement Methodology, 94
2 Limitations and Future Work, 94
2.1    Modeling and Numerical Simulation Limitations, 94
2.2    Experimental Measurement and Fabrication Variability, 95
2.3    Future Research Directions, 95
3 Practical Recommendations and Future Applications, 96
3.1    In‐Line Process Monitoring, 96
3.2    Photonic Device Design Optimization, 97
References List, 98

                                

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