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研究生： 林堯竣
Lin, Yao-Jun
論文名稱： 應用多光束干涉法決定薄膜之厚度與折射率
Determination of Thin Film Thickness and Refractive Index by Using Multiple Beam Interferometry
指導教授： 陳元方
Chen, Terry Yuan-Fang
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： 2005
畢業學年度： 93
語文別： 中文
論文頁數： 108
中文關鍵詞： 多光束干涉 、快速光譜相關干涉法 、多層膜矩陣法 、對稱式三層公式 、薄膜厚度 、折射率 、等色階條紋
外文關鍵詞： Multiple Beam Interferometry, Fast Spectral Correlation Interferometry, Thickness of thin film, Refractive index, Symmetrical three-layer formula, Multilayer Matrix Method, Fringe of Equal Chromatic Order (FECO)
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    • 　　本文主要的目的是應用的多光束干涉所產生之等色階條紋來決定待測薄膜的厚度及折射率。其計算方法主要有兩種：一種為使用Israelachvili發表的對稱式三層公式；另一種為利用多層膜矩陣法與快速光譜相關干涉法計算。本文將會分別使用這兩種方法分析模擬的或實驗的等色階條紋來決定出薄膜的厚度及折射率，並比較兩種方法的優劣性，以及分析條紋性質，最後發展出完整的計算程式，進而表面力幫助分析儀的發展。

    　In this article, the main purpose is that using multiple beam interferometry to produce the Fringe of Equal Chromatic Order (FECO) and then using FECO to determine the thickness and refractive index of the thin film. There are two methods to determine the thickness and refractive index of the thin film: one is symmetrical three-layer formula from Israelachvili, the other is multilayer matrix method and fast spectral correlation interferometry. In this article, I used the two methods respectively to analysis the FECO from the simulation or from the experiment and then to determine the thickness and refractive index of the thin film. And I compared the two methods and analysis the property of FECO. Finally, I developed a completed program. Let the results in this article to aid our experiments in surface force apparatus.

    中文摘要.....................................................I 英文摘要....................................................II 致謝.......................................................III 目錄........................................................IV 圖目錄.....................................................VII 表目錄......................................................IX 符號說明.....................................................X 第一章 緒論.................................................1 1-1 研究目的與背景.........................................1 1-2 文獻回顧...............................................3 1-3 本文架構...............................................6 第二章 多光束干涉法之原理................................7 2-1 簡介...................................................7 2-2 對稱式三層干涉原理.....................................9 2-2-1 修正未考慮色散與相位改變的干涉公式................17 2-3 多層膜矩陣法（Multilayer Matrix Method）...................23 2-4 快速光譜相關干涉法（Fast Spectral Correlation Interferometry）..26 第三章 FECO條紋的模擬與薄膜厚度及折射率的決定.......30 3-1 FECO條紋的模擬.......................................30 3-2 應用對稱式三層公式決定薄膜厚度與折射率的方法....33 3-2-1 影像處理..........................................34 3-2-2 FECO條纹影像水平方向畫素位置對應波長之解析度的校 正................................................36 3-2-3 條紋階數的決定....................................38 3-2-4解非線性聯立方程組且判斷其解的正確性...............40 3-2-5 整體處理程序流程..................................42 3-3快速光譜相關干涉法的處理...............................45 第四章 結果與討論.........................................48 4-1 對稱式三層公式修正結果討論............................48 4-2 對稱式三層公式之量測範圍..............................51 4-3 對稱式三層修正公式與其簡化式模擬分析之比較.......53 4-4 對稱式三層修正公式對於實驗圖的分析..............59 4-5 快速光譜相關干涉的處理結果與討論......................66 4-6 對稱式三層公式與快速光譜相關干涉法之比較 .............69 第五章 結論與建議.........................................71 附錄A 金屬導體之光學係數............................73 附錄B 多層膜矩陣法其特徵矩陣及光強穿透率之推導......76 參考文獻...................................................90 自述................................................93

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