掃描式白光干涉儀應用在量測薄膜之光學常數

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姓名

李孟錡(Meng-Chi Li) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

掃描式白光干涉儀應用在量測薄膜之光學常數
(Application of white-light scanning interferometer on optical thin film constant measurement)

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摘要(中)

本論文提出以掃描式白光干涉技術量測光學薄膜之厚度、折射率
以及色散常數。薄膜反射光譜可藉由白光干涉圖之傅立葉振幅而推得，
並利用基因演算法反推薄膜光學常數。在未知的薄膜特性，利用基因
演算法以全域式之搜尋方法，求得最佳的數值解。並針對在量測傅立
葉振幅可能造成之誤差來源，包括波數精準性以及光源在時間和空間
上的變化，進行研究和改善。隨著誤差的減少和演算法的改進，量測
光學薄膜厚度和折射率的結果與橢圓偏振儀比較，其差異皆在 1%以
內。搭配白光干涉儀量測大範圍的反射振幅和單點薄膜之特性，可以
快速重建二維的薄膜厚度，並且延伸至量測多層膜之厚度。

摘要(英)

A method to measure thin film thickness, refractive index and
dispersion constants based on white light interferometry is described. The
thin film property is retrieved from the Fourier amplitude of the white
light correlogram and genetic algorithms with elitism to avoid falling into
the local minimum due to the parameter convergence and maintain the
capability to search the global minimum solution. Besides, the sources of
errors in Fourier amplitude, which include the accuracy of wave-number,
light source variation in time, and illumination non-uniformity, are
investigated. With all these errors reduced, the film thicknesses and
refractive indices of four samples measured by white light interferometry
are within 1% of the ellipsometry results. As the accuracy of
measurement improved, the amplitude based method could be capable to
measure thickness profiler of thin-film as well as multi-layer films.

關鍵字(中)

★ 白光干涉儀
★ 光學薄膜
★ 厚度
★ 折射率
★ 基因演算法

關鍵字(英)

★ white-light interferometer
★ thin-film
★ thickness
★ refractive index
★ genetic algorithm

論文目次

V

目錄
摘要 ............................................................................................................. I
ABSTRACT ............................................................................................. II
致謝 .......................................................................................................... III
目錄 .................................................................................................... V
圖目錄 ................................................................................................... VIII
表目錄 ........................................................................................................ X
第一章緒論 ............................................................................................... 1
1.1 前言 ................................................................................................... 1
1.2 研究動機 ........................................................................................... 3
1.3 本文架構 ........................................................................................... 5
第二章薄膜光學基本理論 ...................................................................... 7
2.1 光學常數 ........................................................................................... 7
2.2 光的色散 ......................................................................................... 11
2.3 薄膜光學之反射與透射理論[7] .................................................... 12
2.3.1 光學導納 .................................................................................. 12
2.3.2 單介面的反射與透射理論 ..................................................... 15
2.3.3 單層膜的反射與透射理論與膜矩陣 ...................................... 16
2.3.4 多層膜的反射與透射理論 ..................................................... 20
第三章光學常數量測法 ........................................................................ 23
3.1 破壞性量測技術 ............................................................................ 23
3.2 光學量測方法 ................................................................................ 25
3.2.1 光度法 ...................................................................................... 25
3.2.2 橢圓偏振儀 .............................................................................. 31

VI

3.2.3 白光干涉技術 ............................................................................. 35
第四章白光干涉技術 ............................................................................ 36
4.1 干涉顯微技術的發展 ..................................................................... 36
4.2 干涉顯微鏡..................................................................................... 38
4.2.1 Mirau 干涉顯微鏡 .................................................................... 38
4.2.2 Michelson 干涉顯微鏡 ............................................................. 40
4.2.3 Linnik 干涉顯微鏡 ................................................................... 41
4.3 干涉量測技術 ................................................................................. 44
4.3.1 相移干涉技術 .......................................................................... 44
4.3.2 垂直掃描干涉技術 .................................................................. 45
4.4 WLSI 應用於薄膜量測 .................................................................. 48
4.5 白光干涉理論 ................................................................................ 50
4.6 決定膜厚和其光學常數 ................................................................ 56
第五章基因演算法 ................................................................................ 58
5.1 基因演算法之演化機制 ................................................................. 58
5.2 初始化 ............................................................................................. 61
5.3 適應函數 ......................................................................................... 62
5.4 編碼 ................................................................................................. 63
5.5 基因運算子..................................................................................... 64
5.5.1 選擇 .......................................................................................... 64
5.5.2 交配 .......................................................................................... 65
5.5.3 突變 .......................................................................................... 67
5.6 終止條件 ......................................................................................... 70
5.7 傳統最佳化與基因演算法最佳化之比較 .................................... 71
第六章掃描式白光干涉系統 ................................................................ 74

VII

6.1 白光 MICHELSON 干涉儀 ................................................................ 74
6.2 基因演算法之各項參數設定 ........................................................ 78
6.2.1 初始化 ...................................................................................... 79
6.2.2 薄膜之適應函數 ...................................................................... 80
6.2.3 編碼 .......................................................................................... 80
6.2.4 選擇 .......................................................................................... 80
6.2.5 交配 .......................................................................................... 81
6.2.6 突變 .......................................................................................... 81
6.2.7 終止條件 .................................................................................. 81
6.3 薄膜量測結果 ................................................................................ 84
6.4 系統誤差分析 ................................................................................ 88
6.4.1 波數精確性 ............................................................................... 88
6.4.2 光源照度之影響 ...................................................................... 90
6.4.3 基板的折射率 .......................................................................... 93
6.5 二維薄膜之測量 ............................................................................ 96
6.6 多層膜之測量 .............................................................................. 100
第七章結論 ........................................................................................... 102
參考文獻 ................................................................................................. 104

參考文獻

104

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指導教授

李正中(Cheng-Chung Lee)

審核日期

2012-12-3

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