雷射干涉重力波偵測站(LIGO, Laser Interferometer Gravitational Wave Observatory)以大型麥克森干涉儀進行重力波偵測，並運用於觀測天文現象。重力波訊號相當微弱，因此需要降低系統與環境的雜訊干擾才能量測，目前重力波偵測系統整體雜訊最低處於100 Hz，主要受限於反射鏡薄膜的熱擾動雜訊(thermal noise)。由統計力學中的Fluctuation-dissipation theorem間接得到，薄膜熱擾動雜訊與機械損耗成正比，故我們可以藉由量測薄膜機械損耗得知薄膜熱擾動雜訊的程度。機械損耗量測方式，可以透過激發矽懸臂的共振頻率，讓其自然衰減並測量衰減時間，進而得知其機械損耗。此外，由定理公式亦可知系統溫度與熱擾動雜訊成正比，因而期望得知薄膜材料在低溫下的特性。為了提高偵測系統之靈敏度，必須減少反射鏡上薄膜的thermal noise，故我們致力於研究機械損耗小的薄膜材料，且於低溫環境下進行機械損耗量測，以尋找低溫環境下機械損耗小的薄膜材料。
本論文第一部分主要說明低溫機械損耗量測系統架設，並針對基頻模態為100 Hz之矽懸臂基板設計量測流程，包含系統溫度與系統壓力穩定之判斷方式、探討夾具材料與夾持扭力對機械損耗之影響；並加入自動化程式，使得量測效率更佳。此低溫機械損耗系統的量測溫度範圍從5 K-300 K，量測頻率範圍概括整個重力波偵測器系統中最靈敏的頻率區間40~400 Hz，進行初步量測結果分析。
第二部分利用熱退火的方式降低奈米多層膜的薄膜機械損耗，分析退火溫度對薄膜機械損耗之影響。高反射鏡主要以高低折射係數材料推疊成QWL(quarter wave length)，如TiO2/SiO2。然而，參考文獻顯示在不結晶的前提下，退火溫度愈高可以使機械損耗愈低。但TiO2結晶溫度受薄膜厚度影響，膜層愈薄結晶溫度愈高，為了提高退火溫度，我們利用奈米多層膜結構(nano-layer)取代高反射鏡中的高折射係數層(TiO2)，而nano-layer是以TiO2/SiO2堆疊而成。在薄膜總厚度相同且等效折射係數不變的前提下，nano-layer層數愈多，則各別單層TiO2厚度愈薄，即可承受愈高的退火溫度。再將奈米多層膜中11、15、19 layer各結構經過不同溫度的熱退火處理，探討各結構經熱退火後對機械損耗之影響。

The Laser Interferometer Gravitational Wave Observatory (LIGO) detects gravitational waves with a large Michaelson interferometer and is used to observe astronomical phenomena. Signal of gravitational wave is weak, it is important that the noises should be reduced. The sensitivity of the Laser Interferometer Gravitational wave Observatory (LIGO) is mainly limited by coating Brownian noise at 100 Hz. This noise comes from the high reflective optical coating on the mirror. According to the fluctuation-dissipation theorem, noise of the film is proportional to mechanical loss, thus the level of thermal noise can be known from measuring the mechanical loss of the film. To measure mechanical loss, one can let an excited silicon cantilever ring down decay, while observing the decay time to obtain mechanical loss. Furthermore, from Fluctuation-dissipation theorem, it can also be known that system temperature is proportional to thermal noise, thus it is desirable to know the property of the film material under low temperature. To increase the system's sensitivity, thermal noise on the reflecting film must be minimized; therefore, we attempt to search for a material for the film that has low mechanical loss, and can be measured at low temperature.
The first part of the paper describes a new cryogenic apparatus which allows the measurement of the mechanical Q-factor – as a measure of internal losses – in a temperature range from 5 K up to 300 K. This closed-loop cryogenic system is able to measure mechanical loss of the coatings on the cantilevers. And the whole measurement process is fully automatic without human attendance. The second part is crystallization following thermal annealing of thin film stacks consisting of alternating nm-layer(Titania/Silica) was investigated. Coatings of the mirror is composed of pairs of alternating high and low refractive index thin films with thickness of quarter-wavelength. Currently, the materials used in the coatings are silica and Titania in amorphous. It was found that thermal annealing also reduces coating mechanical losses, and thermal noise . However, excessive thermal annealing eventually leads to crystallization. Mechanical losses due to friction among crystallites, as well as scattering from the grain boundaries, make the coatings unsuitable. It was found that the Titania layers eventually crystallized forming the Anatase phase. However, progressively thinner layers exhibited progressively higher threshold temperatures for crystallization onset. Accordingly it can be expected that composites with thinner layers will be able to sustain higher annealing temperatures without crystallizing. In order to increase the annealing temperature, we use nano-multilayer film structure to replace the high reflector of the high refractive index layer. The structure of nano-layer has the same total optical thickness. Notice that nano-layer with more numbers of layers has thinner TiO2 layer thickness, which translates into tolerance for higher annealing temperature. Then, apply different thermal annealing processes to the structure of the 11,15,19 layer of the nano-layer and discuss how the annealing of each structure affects mechanical loss.
Key word: mechanical loss, cantilever, closed-loop cryogenic system, low vibration noise, temperature gradient, clamping torque

摘要 I
誌謝 III
目錄 IV
圖目錄 VII
表目錄 IX
第一章、導論 1
1.1 前言 1
1.2 研究動機 3
第二章、低溫機械損耗系統設計及建置 7
2.1 機械損耗理論 7
2.2 低溫系統結構介紹 12
2.2-1 真空系統及抽氣系統 12
2.2-1-1 封閉式降溫系統與抽氣系統 12
2.2-1-2 Rubber bellow 震動隔絕 14
2.2-2 真空腔內組件設計 17
2.2-3 非接觸式光學量測系統 22
2.2-3-1 量測方式說明 22
2.2-3-2 雷射光路設計與光斑修正 24
2.3 低溫機械損耗系統特性介紹 30
2.3-1 系統溫度與壓力穩定 30
2.3-1-1 溫度穩定 30
2.3-1-2 壓力穩定 35
2.3-2 光學量測系統之雷射加熱對矽懸臂溫度梯度之影響 37
2.3-3 夾具材料與夾持扭力對機械損耗之影響 39
2.3-3-1 黃銅材料夾具之扭力量測結果分析 39
2.3-3-2 黃銅材料與不鏽鋼材料夾具之機械損耗比較 44
2.3-4 溫度循環對機械損耗之影響 46
2.4 流程設計與說明 48
2.4-1 前置準備作業 48
2.4-2 機械損耗量測 53
2.4-3 待機 55
2.5 低溫系統設置之結論 56
第三章、低溫機械損耗初步量測結果與分析 58
3.1 矽懸臂基板之低溫機械損耗量測結果與分析 58
3.2 二氧化鈦薄膜機械損耗量測結果與分析 61
3.3 奈米多層膜退火後機械損耗量測結果與分析 64
第四章、奈米多層膜介紹與室溫機械損耗量測結果 71
4.1 奈米多層膜簡介 71
4.1-1 奈米多層膜結構介紹 71
4.1-2 薄膜退火溫度對結晶影響 71
4.1-3 薄膜製程簡介 73
4.1-4 基板製程簡介 76
4.2 矽懸臂室溫機械損耗量測 78
4.2-1 室溫機械損耗量測系統介紹 78
4.2-2 矽懸臂於夾持時是否清潔對機械損耗量測之影響 80
4.2-3 矽懸臂基板退火後對機械損耗量測之影響 83
4.3 奈米多層膜之不同層數退火前後對機械損耗量測結果 84
第五章、結論與未來展望 89
5.1 結論 89
5.2未來展望 90
參考文獻 91

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