多孔結構材料在光學薄膜應用的領域中是廣泛地被使用的材料。利用多孔結構之體積分率與結構特徵的可調整性，我們可以得到多種擁有不同光學特性的多孔結構光學薄膜。多孔結構可以由許多不同的材料所組成，包括合金、聚合物、矽等。在眾多技術中存在一種多孔結構薄膜的製程技術為利用離相分離法以及旋鍍塗佈法的方式，可以製造出在空間中無序的非晶相分離多孔結構。因為其無序的特性，使得該種結構擁有相較於晶體結構來說更加複雜並且有趣的結構性質。因此，研究各種結構特性所帶來在光學性質上的影響與變化與形成機制在這個部分的研究中是非常重要的。
在本研究中，我們將會利用數值模擬以及實驗結果來探討非晶相分離結構的等效光學性質。在模擬的結構建立中，我們在三維空間中帶入卡恩･希利亞德方程式來建造出模擬的相分離結構。在光學性質模擬方面我們使用時域有限差分法來做計算，其模擬的結果會與各種較常被使用的等效近似模組所計算的光學特性做比較。各種不同模組對於多孔結構薄膜光學特性的預測準確度與適用度會因為非晶相分離結構之結構性值而有所不同，同時這樣的變化也是本研究中討論的重點之一。此外，我們會藉由量測多孔結構薄膜樣品的反射率來討論其光學特性，並且將實驗結果與數值模擬以及等效模組計算結果三者做互相的比較。本研究的內容最終會給出非晶相分離結構之光學與結構特性的變化結論，並且給予在未來相關的元件設計上一定的理論依據與幫助。

Porous structures are widely used in optical thin film applications. Taking advantages of the adjustability of the volume fraction and structural features, we can obtain porous thin films with different optical properties. Porous structure can be made of different materials such as alloys, polymers, silicon, etc. One technique to form porous structure thin film is spinodal decomposition with phase separation method, where amorphous porous structures with spatially disordered can be obtained.
Owing to the disorder nature, the structure may exhibit complicated and interesting structural counterparts. Therefore, it is of great importance to understand the physics behind in order to tailor the optical properties. In this study, we numerically and experimentally investigate the effective optical properties of amorphous porous thin films. In our simulation, the porous structures are constructed by solving Cahn-Hilliard equation in a three-dimensional space. The optical properties are calculated by the Finite-Difference Time-Domain method. The simulated results are then compared with those predicted by commonly used effective medium approximations (EMA). The validity of different EMA models will be evaluated and discussed based on different morphologies of porous structures formed in various stages of phase separation. We further carry out experimental investigation to characterize the optical properties of porous films by measuring the reflectance. The experimental measurements are discussed and compared with the numerical simulation and EMA models. Our analysis provides general understanding of optical properties for porous thin films formed by phase separation, which gives great technical support on designing optical devices with porous structures.

目錄
摘要 I
Abstract II
目錄………………………………………………………………………………….III
第一章 緒論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 多孔結構之介紹 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 非晶結構 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 研究動機 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
第二章 實驗方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 結構建立及分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 非晶結構之分析方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 非晶結構之結構特性 . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 無序相分離結構光學特性模擬及量測 . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 時域有限差分法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 菲涅耳方程式 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 量測方法 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 薄膜干涉 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 CIE色彩空間 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
第三章 等效介質近似理論 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1 等效介質之近似原理 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.1 均質材料與多孔材料 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.2多孔結構之等效折射率 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 等效介質近似模組與理論基礎 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.1 Lichtenecker’s Logarithmic mixture Formula . . . . . . . . . . . . . 21
3.2.2 馬克士威-加奈特模組 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.3 布魯格曼模組 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.4 並聯模組與串聯模組 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.5 結果比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 薄膜之折射率分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.1 薄膜厚度與光的干涉 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3.2 薄膜反射率之計算與模擬 . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
第四章 非晶結構之可見光光學特性研究 . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1 多孔結構薄膜等效折射率匹配方法 . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.1 均質薄膜之反射率 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.2 均質薄膜與多孔薄膜之光譜比較 . . . . . . . . . . . . . . . . . . . . . . 43
4.2 週期結構薄膜之光學特性分析 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2.1 薄膜厚度與孔洞大小 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.2.2 孔洞分布 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3 非晶結構之結構參數 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.3.1 相分離時間 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3.2 初始濃度 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 非晶結構薄膜之光學特性分析 . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4.1 薄膜反射光譜模擬 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4.2 非晶結構與等效模組之匹配 . . . . . . . . . . . . . . . . . . . . . . . 58
4.4.3 實驗量測結果與比較 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.4.4 CIE色彩座標 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
第五章 結果與未來展望 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
參考文獻 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

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