LIGO（Laser Interferometer Gravitational-Wave Observatory）是一個先進的科學觀測站，用於探測重力波。下一代重力波探測器將在低溫下量測，以減少背景熱雜訊。干涉儀兩臂共振腔內的高反射鏡薄膜扮演著關鍵的角色，它可增加光束的傳輸效率。薄膜的性能顯著影響LIGO儀器的靈敏度和精度。

然而，薄膜的設計和應用也面臨了許多挑戰。首先，這些薄膜必須具有高反射率和低吸收率，以及低機械損耗，以減少能量損失。在之前的實驗中，我們透過改變SiH2Cl2/NH3氣體流量比，並使用在台灣半導體研究中心的LPCVD（Low-Pressure Chemical Vapor Deposition）調變不同的退火溫度來優化SiN薄膜。令人鼓舞的是，SiN在低溫下沒有機械損耗的峰值，這與LIGO目前使用的Ta2O5相比有顯著的進步。此外，我們透過使用氣體流量比為1和退火1.5小時的比例鍍製SiN，在雷射波長1550nm下測得了1.3×10-6 [2]的吸收值，這是使用LPCVD方法獲得的最佳吸收值。

因此，本研究旨在測量SiN薄膜在低溫下的機械損耗，並確定它們是否同時具有低光吸收和低機械損耗特性。此外，我們正在開發一個用於機械損耗測量的GNS（Gentle Nodule Suspension) 系統。相比之前的低溫系統，GNS具有更多優勢，因為相較於原本的低溫系統它減少了夾持面積，並且簡化了樣品製作過程，顯著的減少了額外的損耗並提高了測量精確度。因此，我將講述GNS開發的最新進展以及探討開發過程中遇到的雜訊問題，期望能夠成功地開發GNS系統。

LIGO (Laser Interferometer Gravitational-Wave Observatory) is an advanced scientific observatory dedicated to detecting gravitational waves. The upcoming generation of gravitational wave detectors, known as LIGO Voyager, will operate at low temperatures to minimize background thermal noise. High reflectivity mirror coatings are pivotal components within the resonant cavities in an interferometer, enhancing the transmission efficiency of the laser beams. The effectiveness of these coatings has a substantial impact on the sensitivity and precision of the LIGO instruments.
However, designing and applying these coatings also presents several challenges. Firstly, the coatings must exhibit high reflectivity, low absorption, and minimal mechanical loss to minimize energy dissipation. In previous experiments, we optimized SiN (Silicon Nitride) coatings by modulating the SiH2Cl2/NH3 gas flow ratio and utilizing Low-Pressure Chemical Vapor Deposition (LPCVD) at the Taiwan Semiconductor Research Institute with varying annealing temperatures.
Encouragingly, SiN exhibited no mechanical loss peaks at low temperatures, representing a significant improvement over the current Ta2O5 coatings used in LIGO. Furthermore, we achieved the best absorption value of 1.3×10-6 [2] at a laser wavelength of 1550 nm using LPCVD, with a gas flow ratio of 1 and an annealing time of 1.5 hours.
Therefore, this study aims to measure the mechanical loss of SiN coatings at low temperatures and determine whether they exhibit both low optical absorption and minimal mechanical loss characteristics. Furthermore, we are in the process of developing a Gentle Nodule Suspension (GNS) system for conducting mechanical loss measurements. In comparison to the previous low-temperature system, the GNS system offers several advantages, including a reduced clamping area and simplified sample preparation. These advancements significantly minimize additional losses and enhance measurement precision.
Thus, I will present the latest developments in GNS development and discuss the noise issues encountered during the development process, hoping to successfully realize the GNS system.

Abstract I
摘要 III
Acknowledgments IV
List of Figures VIII
List of Tables XI
Chapter1 Introduction 1
Chapter 2 The Science of Gravitational Wave Observation 4
2-1 Observation of Gravitational Waves 4
2-2 Reducing noise in coating research. 7
Chapter 3 Motivation 12
Chapter 4 Measurement of mechanical loss at low temperatures. 17
4-1 Fabrication of SiN using LPCVD 17
4-2 Sample fabrication 18
4-3 Introduction to low-temperature equipment. 20
4-4 Calculation of mechanical loss 21
4-5 The results of the mechanical loss measurements 22
4-6 Discussion 25
Chapter 5 Development of Gentle Nodule Suspension System 30
5-1 Introduction 30
5-2 Thickness measurement of coated wafer 30
5-3 COMSOL simulation of resonant frequency 33
5-4 Measurement of resonant frequency 35
5-4-1 Overview of measurement setup 35
5-4-2 Readout and control of system 36
5-5 Results 37
Chapter 6 Upgrade of Gentle Nodule Suspension System 40
6-1.1 Design of Interferometer 41
6-1.2 The Principle of Interference and the Quarter-Wave Plate 42
6-2 Actuator design 44
6-3 Introduction to External Control Instruments of GNS (Second-generation setup) 47
6-4 Measurement Results and Discussion (Second-generation setup) 50
Chapter 7 Conclusion& Future Work 53
7-1 Conclusion 53
7-2 Future Work 55
Reference 56
Appendix A 59
Appendix B (Steps to simulate resonant frequency in COMSOL) 60
Appendix C (Comprehensive summary of high and low refractive index materials) 69

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