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研究生：	蔡修安 Tsai, Shiou-An
論文名稱：	調變式橢圓偏光儀於光學材料分析之研究 Modulated Ellipsometer for the Determination of the Properties of Optical Materials
指導教授：	羅裕龍 Lo, Yu-Lung
學位類別：	碩士 Master
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2010
畢業學年度：	98
語文別：	英文
論文頁數：	96
中文關鍵詞：	橢圓偏光儀、橢偏參數、調變
外文關鍵詞：	Ellipsometry, Ellipsometric parameters, Modulate
相關次數：	點閱：90 下載：0
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本研究建立發展一偏光光譜分析系統，使用調變頻率可達數百kHz之電光調變器(Electro-optic modulator)結合波片來取代傳統調變頻率只有數十到數百Hz之直流馬達旋轉偏振片之調變方式，並將共路徑外差偏光量測技術結合此光譜析系統擴展成調變式之橢圓偏光量測系統；接著量測材料之橢偏參數(Δ, ψ)，透過我們所發展之調變式橢圓偏光儀之數學模型，可使橢偏參數(Δ, ψ)的動態量測範圍達到全域量測，接著利用反射光的橢偏參數(Δ, ψ)來帶入程式即可得到樣本之厚度。
然而利用相位差來求橢偏參數雖具有快速及穩定之優點，此調變式橢圓偏光儀藉由擷取兩相位差來達到量測橢偏參數(Δ, ψ)的目標，雖較以往之調變式橢圓偏光儀之實驗次數較少，但其量測值之誤差對於所求出參數影響頗大。且目前方法不須連續旋轉待測材料，雖可降低因機械調變以及旋轉時光點偏移所造成的誤差，但仍需旋轉光學元件以得到足夠之數據以供求解，因此旋轉所造成之誤差仍無法完全避免。在實驗結果中，Ψ的標準差為 0.1313 o，Δ的標準差為0.6829 o，由Ψ和Δ計算出材料厚度的標準差為0.9355 (nm)。
此外我們還利用所提出之調變式橢圓偏光儀來發展全場式的量測系統：經調變系統及通過樣本後由CCD擷取各個波長之影像訊號，接著搭配高複雜度可程式控制器(CPLD，Complex Programmable Logic Device)，並且利用影像處理的演算法來達到全場量測之目的，而此方法我們已發展成功並得到初步之結果。初步結果也顯示出此全場量測系統之可行性。未來這也將會是我們致力於發展之方向。

In this research, we propose a scheme to measure the ellipsometric parameters of the materials, and construct an analytic model which is composed of the 4x4 method and signal processing system. And the simulation results and experimental initial results confirms that the feasibility of the proposed the modulated ellipsometry system which is combined with a heterodyne interferometer. The frequency of the saw tooth signal from a function generator that applied to the EO modulator was 1 kHz. In the experimental results, we have shown that the standard deviation of Ψ is 0.1313o, the standard deviation of Δ is 0.6829o, and the standard deviation of thickness is 0.9355(nm).
In addition, we also show the feasibility of the full-field measurement by using the modulated ellipsometry we proposed. However, it’ll combine an image processing algorithm based on a three-integrating-bucket method and a heterodyne interferometer. The pre-experimental results have shown that the ellipsometric parameters (Ψ and Δ) have slight difference on the pattern of the solar cell.
In this study, the measurement based on the modulated ellipsometry has been developed. Moreover, the proposing system has the ability to measure the full range of the ellipsometric parameters form the detected area of materials. However, this new proposed measurement system has two special characteristics. Unlike the other previous studies, we propose the scheme to measure the ellipsometric parameters of the materials by taking the two phases from the optical model. In addition, the presence of environmental disturbances via the use of a common-path configuration for the interferometer system cannot affect the measurement results by eliminating the DC component of the output light intensity signal in the signal processing algorithm.

Abstract in English........................................I
Abstract in Chinese......................................III
Table of Contents..........................................V
List of Figures...........................................IX
List of Tables..........................................XIII

Chapter 1 Introduction.....................................1
    1.1 Preface	1
    1.2 Review of Ellipsometry.............................2
    1.3 Review of Modulated Ellipsometry...................6
    1.4 Overview of Chapters...............................7

Chapter 2 Optical Properties of Materials.................12
    2.1 The Optical Properties of Birefringence...........12
    2.2 Phase Retardation.................................18

Chapter 3 The Heterodyne Interferometer...................23
    3.1 Preface...........................................23
    3.2 Principle of Traditional Interference.............23
    3.3 Basic Theory of Heterodyne Interference...........24
    3.4 Common-Path Heterodyne Interferometry.............26
    3.5 The Modulating Technique of Electro-Optic Modulator	..................................................27
        3.5.1 Electric-Optic Effect.......................28
        3.5.2 Electric-Optic Modulation...................29
            3.5.2.1 Amplitude Modulation..................29
            3.5.2.2 Phase Modulation......................34

Chapter 4 Basic Theory of Ellipsometry....................37
    4.1 Fresnel Equations.................................37
    4.2 Principles of Ellipsometry........................39
        4.2.1 Jones of Samples............................40
    4.3 4×4 Matrix Method.................................42
        4.3.1 General Transfer Matrix.....................44
        4.3.2 Partial Transfer Matrix.....................47
        4.3.3 Incident Matrix.............................50
        4.3.4 Exit Matrix.................................51

Chapter 5 Measurement of the Silicon substrate coated with the SiO2 Thin Film by Using the New Modulated Ellipsometry52
    5.1 Theoretical Analysis in the New Modulated Ellipsometry..............................................52
    5.2 Simulation Results................................57
        5.2.1 Simulation Results of the material..........57
        5.2.2 Simulation Results of Ψ and Δ Error Analysis	..................................................61
            5.2.2.1 Simulation Results of Ψ and Δ Error Analysis In θi Error =±0.01o..............................62
               5.2.2.2 Simulation Results of Ψ and Δ Error Analysis In the Phase Error =±0.01o.......................64
            5.2.2.3 Simulation Results of Ψ and Δ Error Analysis In θi Error =±0.01o and the Phase Error =±0.01o...................................................66
    5.3 Experimental Setup and Experimental Results.......68
        5.3.1 Experimental Setup..........................68
        5.3.2 Experimental Results........................70

Chapter 6 Full-Field Measurement Using the New Modulated Ellipsometry..............................................77
    6.1 Theoretical Analysis in the Full-Field Measurement by Using the New Modulated Ellipsometry...................77
    6.2 Experimental Setup and Pre-Experimental Results...80
        6.2.1 Experimental Setup..........................80
        6.2.2 Pre-Experimental Results....................83
            6.2.2.1 Full-Field Measurement of the Silicon substrate coated with Aluminum Thin Film by Using the New Modulated Ellipsometry....................................83
            6.2.2.2 Full-Field Measurement of the silicon substrate coated with polycrystalline silicon (The Solar Cell) by Using the New Modulated Ellipsometry.............85

Chapter 7 Conclusions and Future Work.....................87
    7.1 Conclusions.......................................87
          7.1.1 Conclusions of Measurement of the Silicon substrate coated with the SiO2 Thin Film by Using the New Modulated Ellipsometry....................................87
        7.1.2 Conclusions of Full-Field Measurement Using the New        Modulated Ellipsometry.....................88
    7.2 Future Work.......................................89
Bibliography	90
Autobiography	96

                                    

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