我們提出了一個製造寬頻帶抗反射（AR）塗層的新方法，
並使反射的影響達到最小。我們採用二項式多斷阻抗匹配方法去確定
每個匹配層的厚度和折射率，而這些層可以通過亞波長矽
通孔陣列製作全介電可調變折射率的超材料並進一步實現抗反射鍍膜於於THz頻段中。根據填充率，孔徑尺寸和周期寬度，有效地調製近似線性
變化的等效折射率。 基於此方案，我們為被廣泛使用的矽晶片設計了
10層AR塗層。我們設計的AR塗層厚度是1656μm且形式是矽晶片雙面成，能夠將THz透射率不管是TE偏振或TM偏振THz光束的提升到
95.00％以上 , 而入射角度只要低於50 o仍有不錯的穿透率表現。

A novel approach of fabricating a broadband anti-reflection (AR) coating is proposed to minimize the effect of unwanted reflections. The binomial multi-section transformer is employed to efficiently determine the thickness and the refractive index of each matching layer, while those layers can be further realized by manufacturing the subwavelength silicon through-hole arrays as an all-dielectric gradient index metamaterial with broadband THz operation. Depending on the fill-factor, hole-size and period, the effective index was linearly modulated in THz region. Based on this scheme, we design a ten-layer AR coating for widely used silicon wafer. The designed AR coatings are double-sided integrated with a 1656-μm-thick silicon wafer, which is able to enhance the overall THz transmission to higher than 95.00% from 0.250 THz to 0.919 THz for either TE-polarized or TM-polarized THz beam incident from arbitrary angle below 50o.

目錄
Acknowledgements............................................i
Abstract....................................................ii
摘要........................................................iii
目錄........................................................iv
圖目錄......................................................vi
List of Tables..............................................viii
第一章 緒論.................................................1
1.1 抗反射鍍膜之介紹....................................1
1.2 抗反射鍍膜於可見與紅外光之應用......................2
1.3 抗反射鍍膜於兆赫波頻段之介紹........................3
1.3.1 兆赫波的簡介........................................4
1.3.2 兆赫波的應用研究....................................4
1.3.3 抗反射鍍膜於兆赫波之文獻回顧........................6
1.4 研究動機............................................9
第2章 理論基礎..............................................10
2.1 兩介質界面之穿透與反射..............................10
2.2 多層介質界面之穿透與反射............................11
2.2.1 傳遞矩陣法介紹(transfer matrix method)..............12
2.2.2 傳遞矩陣法於多層介質上之運用........................12
2.3 斜向入射至多層介質..................................14
2.3.1 橫向電場(Transverse Electromagnetic Wave)...........15
2.3.2 橫向磁波(Transverse Magnetic Wave)..................16
2.4 單層抗反射鍍膜理論推導..............................18
2.4.1 厚度之選擇..........................................18
2.4.2 折射率之選擇........................................19
2.5 多層抗反射鍍膜之理論推導............................21
2.5.1 二項式響應(Binomial Multi-Section Transformer)......22
2.5.2 柴比雪夫響應(Chebyshev Multi-Section Transformer)...23
2.5.3 比較兩種不同類型的阻抗匹配的結果....................26
2.6 超材料( Metamaterial ).................................28
2.6.1 人造材料幾何參數之介紹..............................28
2.6.2 等效折射率於特定週期寬度下調變填充率之變化..........29
2.6.3 等效折射率於特定孔徑下調變週期寬度之變化............30
2.6.4 等效折射率於特定填充率下調變週期寬度之變化..........31
第3章 多層雙邊抗反射鍍膜設計與實現方法......................32
3.1 優化抗反射鍍膜之層數與厚度..........................33
3.1.1 分析抗反射鍍膜層數與穿透率和頻寬之間的關係..........34
3.1.2 抗反射鍍膜之層數可行性分析與討論....................36
3.1.3 抗反射鍍膜之厚度可行性分析與討論....................38
3.1.4 抗反射鍍膜之各項設計之參數表........................39
3.2 斜向入射之穿透率模擬分析............................40
3.2.1 斜向入射之TE mode穿透率模擬.........................40
3.2.2 斜向入射之TM mode穿透率模擬.........................41
3.3 抗反射鍍膜實現之製程方法............................42
第4章 實驗結果..............................................44
4.1 等效折射率之理論與實驗比較.............................44
4.2 透過掃描電子顯微鏡之微結構圖分析理論模擬與實驗結果.....49
第5章 結論................................................55
References..................................................56

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