重力波偵測組織(Laser Interferometer Gravitational wave Observatory, LIGO)是利用大型麥克森干涉儀偵測重力波訊號，其系統架構藉由高反射鏡作為共振腔，提升重力波訊號之訊雜比。由雜訊頻譜圖得知，偵測最靈敏且雜訊最小的頻率區間約在40~400 Hz，其中約在100 Hz下，雜訊的主要來源為高反射鏡薄膜材料的熱擾動(Coating Brownian Noise)，此雜訊可藉由Fluctuation-Dissipation Theorem得知與材料的機械損耗為正比關係，故薄膜須具有低機械損耗的特性。而且，高反射鏡薄膜材料還須擁有良好的光學性質，故本實驗室主要開發低機械損耗和低光學吸收的薄膜材料。
先前藉由電漿輔助化學氣相沉積(plasma enhanced chemical vapor deposition, PECVD)鍍製不同製程氣體流量比之氮化矽薄膜(silicon nitride, SiNx)，其折射率(refractive index, n)落在1.78~2.85，為高折射率材料。而無氨氣製程薄膜(PECVD-NH3-free process)擁有最高的折射率，並大幅降低N-H鍵，使得低溫機械損耗(cryogenic mechanical loss, φ)可由10-4降至10-5，且無損耗峰值[11]。由於PECVD-SiNx的氫含量高，後續藉由低壓化學氣相沉積(low pressure chemical vapor deposition, LPCVD)方式鍍製沉積溫度高、氫含量低的SiNx薄膜，在1550 nm的消光係數(Extinction coefficient, κ)可降至5.5x10-6[16]，擁有最佳光學吸收。為了搭配高折射率材料製作堆疊膜，後續藉由PECVD鍍製不同成份比之氮氧化矽(silicon oxynitride, SiOxNy)薄膜，並透過退火製程降低材料的光學吸收與機械損耗。其中，PECVD-SiOxNy-Ratio-27薄膜藉由高溫純氮退火的方式降低薄膜的N-H鍵濃度，在1550 nm的κ可降至5.8x10-7[15]，是具有最低光學吸收之低折射率材料。低溫機械損耗則以補氫退火之PECVD-SiOxNy-Ratio-3薄膜為最低[14]。從以上結果可知，SiNx和SiOxNy皆無法找到一個同時兼具最低光學吸收和最佳機械損耗的薄膜。因此，很難從歷屆數據判斷最佳的single-material組合。
為了找出最佳的single-material組合，本論文前半部利用光學模擬軟體Essential Macleod設計不同溫度下的堆疊膜結構，再透過COMSOL模擬得到bulk和shear能量在矽懸臂振動模態中的占比，計算每組堆疊結構的熱雜訊(Coating Thermal Noise, CTN)，分析每組之堆疊層數、光學吸收與CTN，與重力波偵測器規格做比較，並評估製程的可行性。
由評估結果得知，使用同一沉積溫度且不退火的高、低折射率材料是製作堆疊膜之可行方式。PECVD-NH3-free-SiN0.33H0.58/SiON-Ratio-3堆疊膜適合作為10 K與20 K的高反射鏡結構，其CTN分別低於偵測器ET-LF、KAGRA反射鏡規格的1和1.45倍；120K的結構則可選用PECVD-NH3-free-SiN0.33H0.58/SiON-Ratio-27堆疊膜。最後，藉由multi-material結構改善堆疊膜的光學吸收，1550nm的光學吸收從29.88ppm降至3.5ppm，符合ET-LF的規格。然而，multi-material堆疊膜會因使用兩種不同機台而造成製程條件不匹配，不同沉積溫度和退火製程皆會減薄薄膜厚度，無法精確地控制每層厚度，不利於鍍製堆疊膜。為了避免此種情況的發生，需尋找相同製程溫度且未經過退火(As-deposited, AD)的堆疊材料。
在AD材料中，LPCVD-SiNx薄膜藉由高溫沉積且不退火的方式降低氫含量，其光學吸收可低於PECVD-SiNx薄膜[16]。且從文獻可知[17]，此薄膜的低溫機械損耗低於PECVD-NH3-free(SiN0.33H0.58)薄膜，其數值約在1×10-5~2×10-5，適合作為高折射率層。對於低折射率層，同樣期望得到一個低光學吸收且兼顧不減薄膜厚的SiOxNy薄膜，故需同樣地透過高溫LPCVD製程沉積。
在進行LPCVD-SiOxNy薄膜的製程之前，須先討論製程的可行性與需求，故本論文後半部規劃LPCVD-SiOxNy薄膜的製程並評估可行性。由文獻可知[62-68]，LPCVD-SiOxNy薄膜的氫含量為0.05x1022cm-3，且Eg約為6eV、矽懸鍵濃度在偵測極限以下。依據桂芳成學長的研究[12]，推測波長於1550nm下，κ可降至1.5x10-7，低於PECVD-SiOxNy-Ratio-27。根據此評估結果，可知LPCVD-SiOxNy薄膜具有極好的光學吸收特性，是一個值得研究的低折射率材料。因此，後續將針對高研究價值之LPCVD-SiOxNy薄膜，設計製程與規劃設備。製程機台預計使用水平爐管，製程溫度從860oC開始測試，製程壓力則在400mtorr[51, 52, 54, 55]。薄膜鍍製方式與機台運作流程參考LPCVD-SiNx製程，並考量可能遇到之困難與解決方式。期待未來於TSRI加裝N2O管路或是額外尋找無塵室建造製程設備，鍍製LPCVD-SiOxNy薄膜並搭配LPCVD-SiNx製作LPCVD堆疊膜，最後應用於下一世代低溫重力波偵測器。

Laser Interferometer Gravitational-Wave Observatory (LIGO) uses the large Michelson interferometer to detect gravitational wave signals and uses high-reflective mirrors as a resonant cavity to enhance the signal-to-noise ratio. According to the noise spectrum, the frequency range with the best sensitivity and the smallest noise is at 40-400 Hz. The Coating Brownian Noise (CTN) is the major noise for high-reflective QW coating which frequency is around 100 Hz. Because the CTN is proportional to the mechanical loss that known from the fluctuation-dissipation theorem, the mechanical loss of films must be low. Additionally, high-reflective QW coatings must have good optical characteristics. Therefore, our laboratory develops materials with low mechanical loss and low optical absorption.
We studied the amorphous silicon nitride (SiNx) films deposited by plasma-enhanced-chemical-vapor-deposition (PECVD) methods. By tuning the flow ratio of process gases, we obtained the refractive index (n) of SiNx varied from 1.78-2.85. The PECVD-NH3-free process increased the refractive index to 2.85 and dramatically reduced the cryogenic mechanical losses (φ) to 10-5 without loss peaks, correlated with the reduction in N-H bond concentration [11]. However, high optical absorption in the PECVD-SiNx films due to their high H content. To improve this disadvantage, we changed the process to the low-pressure-chemical-vapor-deposition (LPCVD) with high deposition temperature. The LPCVD-SiNx had the lowest extinction coefficients (κ) of all SiNx films, dropping to 5.5x10-6 at 1550 nm [16]. To coat the stacks with high-n materials, we fabricated the silicon oxynitride (SiOxNy) films and tuned the flow ratio to vary the n [13]. Besides, we reduced their κ and φ significantly by thermal annealing. The best κ at 1550 nm was 5.8x10-7, which annealed the PECVD-SiOxNy-Ratio-27 at a high temperature of 900 oC, correlated with the reduction of N-H bond concentration [15]. The lowest φ of SiOxNy film was PECVD-SiOxNy-Ratio-3 that annealed at 500 oC [14]. Above these results, we cannot find a material with the lowest optical absorption and best mechanical loss for both SiNx and SiOxNy films. Therefore, it is hard to know the best combination directly for a single-material (SiNx/SiOxNy) stack.
The first half of this thesis uses some ways to find the best combination at 10 K, 20 K and 120 K (for ET-LF, KAGRA and Voyager). First, we design the HR mirror structures at different temperatures by Macleod. Through COMSOL simulation, we get the bulk and shear energy ratios of the silicon cantilever vibration modes. The number of layers, optical absorption, and CTN of all structures are calculated and compared with the specifications of the gravitational wave detectors. We evaluate the feasibility of the process eventually.
The results show that the materials of the stack are at the same deposition temperature without annealing is a more workable way to coat the QW HR mirror. The CTN of PECVD-NH3-free-SiN0.33H0.58/SiON-Ratio-3 stack is about 1 and 1.45 times lower than the specifications of ET-LF and KAGRA. The PECVD-NH3-free-SiN0.33H0.58/SiON-Ratio-27 stack is suitable for 120 K because of its lower CTN. Finally, a multi-material structure design improves the optical absorption at 1550 nm of the single-material stack from 29.88 ppm to 3.5 ppm, which meets the specification of ET-LF. However, unmatched process conditions also occur in the multi-material stack process. Both the different deposition temperatures and thermal annealing lead to the thickness reduction that is not good to coat a stack. To avoid this situation, we should find other as-deposited (AD) materials that are at the same process temperature.
As mentioned previously, thermal anneal significantly reduced the optical absorption and mechanical loss, but it caused thickness reductions. Accordingly, we should choose other AD materials. For the high-n material, we achieved lower optical absorption of SiNx films through the LPCVD method without annealing due to higher deposition temperature than PECVD [16]. Besides, its cryogenic mechanical loss varied from 1×10-5 to 2×10-5 [17], which was lower than PECVD-NH3-free-SiN0.33H0.58. For the low-n material, SiOxNy, we also want to get lower optical absorption and avoid thickness reductions simultaneously. Thus, we should develop the LPCVD-SiOxNy film.
Before coating the LPCVD-SiOxNy film, we should discuss its feasibility of the process and plan the process requirements first. Consequently, the second half of this study is to plan the LPCVD-SiOxNy process and evaluate its feasibility. The reference mentions that the H content of LPCVD-SiOxNy film is 0.05x1022cm-3. Furthermore, the Eg is about 6.0 eV and concentration of dangling silicon bonds is below the cryo-detection limit [62-68]. From these results and previous research [12], the κ at 1550 nm is expected down to 1.5x10-7 which is lower than PECVD-SiOxNy-Ratio-27. Therefore, the LPCVD-SiOxNy film is worth researching.
Finally, we have to design the process and prepare the proper equipment for the LPCVD-SiOxNy film with significant value for scientific research. We use a horizontal furnace as the coater. Its process temperature starts at 860 oC and the pressure is at 400 mtorr [51, 52, 54-55]. Referring to the LPCVD-SiNx process, we plan the coating process, S.O.P of the machine, potential difficulties and the solutions. We look forward to coating LPCVD-SiOxNy through either increasing N2O piping in TSRI or building the equipment, even coating the stack with LPCVD-SiNx for the next-generation cryogenic gravitational wave detector.

Abstract I
摘要 IV
致謝 VII
目錄 IX
圖目錄 XI
表目錄 XIII
第一章 導論 1
1.1 前言 1
1.2 研究動機 3
第二章 氮化矽(SiNx)與氮氧化矽(SiOxNy)薄膜材料評估 7
2.1高折射率SiNx薄膜之光學吸收與機械損耗比較 7
2.2低折射率SiOxNy薄膜之光學吸收與機械損耗比較 11
第三章 SiNx/ SiOxNy堆疊膜評估 16
3.1 堆疊膜評估之動機 16
3.2 不同溫度下之堆疊膜結果分析 16
3.2.1 不同世代LIGO重力波偵測器規格介紹 16
3.2.2 CTN計算流程介紹 19
3.2.3 10K堆疊膜組合之層數、光學吸收、CTN分析 24
3.2.4 20K堆疊膜組合之層數、光學吸收、CTN分析 32
3.2.5 120K堆疊膜組合之層數、光學吸收、CTN分析 36
3.2.6 製程的可行性評估 44
3.2.7 小結:不同溫度下之堆疊膜CTN最低組合 46
第四章 利用Multimaterial結構改善堆疊膜光學吸收 48
4.1 Multimaterial結構設計 48
4.2 堆疊膜光學吸收與CTN比較 54
第五章 利用低壓化學氣相沉積法鍍製氮氧化矽薄膜之製程設計 57
5.1 LPCVD SiOxNy薄膜之製程設計動機 57
5.2 LPCVD SiOxNy薄膜之製程評估 57
5.3 LPCVD SiOxNy薄膜之設備系統規劃 65
5.3.1 製程機台規劃 66
5.3.2 無塵室配置與支援設備規劃 70
5.4 LPCVD SiOxNy薄膜之製程設計規劃 81
5.4.1 製程機台之運作流程規劃 81
5.4.2 薄膜製程參數規劃 82
5.4.3 薄膜鍍製方式規劃 84
5.4.4 製程上可能遇到之困難與解決方案 85
第六章 總結與未來工作 86
6.1 總結 86
6.2 未來工作 88
6.2.1 LPCVD-SiOxNy薄膜製程機台架設 88
6.2.2 LPCVD-SiOxNy薄膜製程與相關量測分析 88
附錄A LPCVD SiOxNy設備估價資訊 89
附錄B 應用於LPCVD製程之單晶矽懸臂基板之模擬 91
附錄C 應用於LPCVD製程之單晶矽懸臂基板之室溫扭力測試 101
參考文獻 104

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