雷射干涉重力波組織(LIGO, Laser Interferometer Gravitational-Wave Observatory)為一大型麥克森干涉儀，其目的為量測重力波，2015年9月LIGO於Hanford, WA 及Livingston, LA的兩座觀測站第一次偵測到重力波訊號，提出以麥克森干涉儀偵測重力波的Weiss、Thorne、Barish更在2017年因此獲得諾貝爾物理學獎。以往人們藉由電磁波觀察天文現象，日後可望以重力波觀察更多電磁波觀察不到的現象。而重力波訊號對干涉儀之變化只有10-21，必須降低雜訊干擾以提高靈敏度， LIGO最靈敏之頻段在100Hz附近，其主要雜訊來源為quantum noise與coating Brownian noise，本實驗室致力於降低coating Brownian noise，此為干涉儀反射鏡上光學薄膜材料熱擾動造成之雜訊，根據fluctuation-dissipation theorem其與溫度及機械損耗成正比，藉由量測機械損耗可研究此雜訊。
本文第一部分探討以PECVD製作氮化矽薄膜之低溫機械損耗。低溫機械損耗隨氮矽比增加而增加，SiN0.40H0.79損耗最低、SiN0.87H0.93損耗最高且甚至在40K附近形成損耗峰，此峰可以活化能方式進行分析並解釋其產生原因。
本文第二部分探討四分之一1550nm波長SiN0.40H0.79/ SiO2堆疊膜之低溫機械損耗。4-pair及8-pair堆疊膜損耗量測結果相近，表示SiN0.40H0.79 /SiO2介面對低溫機械損耗影響不大。堆疊膜量測損耗值介於SiN0.40H0.79與SiO2之間，且在40K附近具有如SiO2之損耗峰，判斷此峰由SiO2造成。4-pair及8-pair在120K、675Hz之機械損耗為2.07×10-4及2.10×10-4，且其尚未退火，具有潛力應用於未來低溫LIGO之反射鏡光學薄膜材料。

Laser Interferometer Gravitational-Wave Observatory (LIGO) detected the gravitational wave came from two black holes merged in 2015. Weiss, Thorne and Barish received Nobel Prize because of their contribution. From now on we can observe astronomical phenomena using not only electromagnetic wave but also gravitational wave. Gravitational wave signal caused about 10-21 change to the arms of the interferometer. It was so small that LIGO couldn’t detect weaker signals came from other astronomical phenomena. This research is dedicated to enhancing the signal to noise ratio of LIGO. As the frequency of signal is about 100Hz, the noise is dominated by quantum noise and coating Brownian noise. Coating Brownian noise comes from the material coated on the mirrors of the interferometer. It is a kind of thermal noise which is proportional to mechanical loss and temperature according to Fluctuation-Dissipation Theorem. We can investigate this noise by measuring mechanical loss of materials.
In the first part of this thesis, we fabricated SiNxHy thin films by Plasma Enhanced Chemical Vapor Deposition (PECVD). We coated it on cantilevers and measured its cryogenic mechanical loss. The loss of SiN0.40H0.79 was lowest and SiN0.87H0.93 was largest. We deduced that loss increased as silicon to nitrogen ratio increased. There was a loss peak in SiN0.87H0.93 at around 40K. We used two level system to explain its loss mechanism and calculated its activation energy.
In the second part of this thesis, we fabricated 4-pair and 8-pair SiN0.40H0.79/SiO2 stacks by PECVD. Their cryogenic mechanical losses were similar. It was believed that SiN0.40H0.79/SiO2 interface would not cause too much extra cryogenic loss. There was a cryogenic peak in the stacks at around 40 K. We believed the loss peak was caused by SiO2. The mechanical loss of 4-pair and 8-pair stacks were 2.07×10-4 and 2.10×10-4 respectively at 675 Hz, 120K. SiN0.40H0.79/SiO2 stack was a potential material to be used for LIGO in the future.

[1] B. P. Abbott, et al. Observation of Gravitational Waves from a Binary Black Hole Merger. PRL 116, 061102, 2016.
[2] I. W. Martin, Studies of materials for use in future interferometric gravitational wave detectors, PhD thesis, University of Glasgow(2009)
[3] LIGO Scientific Collaboration Group. Instrument science white paper. Oct. 2016, LIGO-T15TBI-v1
[4] H. B. Callen, T. A. Weltont. Irreversibility and generalized noise. Phys. Rev., Jul. 1951, 83: 34-40
[5] R. F. Greene, H. B. Callen. On the formalism of thermodynamic fluctuation theory. Phys. Rev., Sep. 1951, 83: 1231-1235
[6] H. B. Callen, R. F. Greene. On a theorem of irreversible thermodynamics. Phys. Rev., Jun. 1952, 86: 702-710
[7] G. Sasso, Cryogenic Q-measurements on silicon, presentation at Friedrich Schiller University Jena (2006)
[8] Y. H. Juang. Stress effect on mechanical loss of the SiNx film deposited with PECVD method on silicon cantilever and setup for the loss measurement improvement. Master thesis, National Tsing Hua University, Aug. 2014
[9] Xiao Liu et al. Elastic Properties of Several Silicon Nitride Films. Mater. Res. Soc. Symp. Proc. Vol. 989, 2007
[10] C. W. Lee. Study of the material properties and the mechanical loss of the silicon nitride films deposited by PECVD method on silicon cantilever for laser interference gravitational wave detector application. Master thesis, National Tsing Hua University, Aug. 2013
[11] W. Y. Wang. Study of mechanical vibration and loss of silicon cantilever for development of the high-reflection mirror in the laser interference gravitational wave detector. Master thesis, National Tsing Hua University, Aug. 2013
[12] D. L. Smith, A. S. Alimonda, C. C. Chen, et al. Mechanism of SiNxHy deposition from NH3-SiH4 plasma. J. Electrochem. Soc., Feb. 1990, 137: 614-623
[13] J. N. Chiang, D. W. Hess. Mechanistic considerations in the plasma deposition of silicon nitride films. J. Electrochem. Soc., Jul. 1990, 137: 2222-2226
[14] Sami Franssila. Introduction to Microfabrication. John Wiley & Sons, 2004, Ch5.5:51-53, ISBN: 978-0-470-85106-7
[15] D. R. M. Crooks, Mechanical loss and its significance in test mass mirrors of gravitational wave detectors, Ph.D. thesis, University of Glasgow (2002)
[16] X. Liu, R. O. Pohl. Low-energy excitations in amorphous films of silicon and germanium. Phys. Rev. B, Oct. 1998, 58: 9067-9081
[17] B. E. W. Jr., R. O. Pohl. Thin films: stresses and mechanical properties V: Elastic properties of thin films. Mater. Res. Soc., Pittsburgh, Jun. 1995, No.356: 567-572, ISBN: 978-1-558-99257-3
[18] H. C. Tsai, W. Fang. Determining the Poisson's ratio of thin film materials using resonant method. Sensors and Actuators A, 2003, 103: 377-383
[19] Z. Z. Xie. Study of the optical-mechanical properties of amorphous silicon and silicon dioxide fabricated by Plasma Enhance Chemical Vapor Deposition (PECVD). Master thesis, National Tsing Hua University, Apr. 2015
[20] M. A. Hopcroft, W. D. Nix, T. W. Kenny. What is the Young’s modulus of silicon? Journal of Microelectromechanical system, Apr. 2010, 19: 229
[21] T. Y. Zhang, Y. J. Su, C. F. Qian, et al. Microbridge testing of silicon nitride thin films deposited on silicon wafers. Acta mater., Mar. 2000, 48: 2843-2857
[22] B. A. Walmsley, Y. Liu, X. Z. Hu, et al. Poisson’s ratio of low-temperature pecvd silicon nitride thin films. J. Microelectromechanical Syst., Jun. 2007, 16: 622-627
[23] V. Ziebart, O. Paul, U. Munch, et al. Thin-Films: stresses and mechanical properties VII: A novel method to measure Poisson’s ratio of thin films. Cambridge University Press, 1998, 27-32, ISBN: 978-1-107-41330-6
[24] C. L. Dai. A resonant method for determining mechanical properties of Si3N4 and SiO2 thin films. Materials Letters, Jun. 2007, 61: 3089-3092
[25] J. J. Wortman and R. A. Evans. Young's Modulus, Shear Modulus, and Poisson's Ratio in Silicon and Germanium. J. Appl. Phys. 36, 153 (1965)
[26] Chun Cheng. Cryogenic mechanical loss measurement system setup and annealing effect on the mechanical loss of the nano-layer coatings. Master thesis, National Tsing Hua University, 2015
[27] Meng-Yun Wu. Room Temperature Mechanical Loss of SiN0.40/SiO2 Quarter-wave Stacks Deposited by Plasma Enhanced Chemical Vapor Deposition Method. Master thesis, National Tsing Hua University, 2016
[28] Ling-chi Kuo, Huang-wei Pan et al. Errors on the Cryogenic Mechanical Loss Measurement in Cantilever Ring-down Method, LVC meeting, Glasgow, 2017, LIGO Document: LIGO-G1700301
[29] I Martin et al. Measurements of a low-temperature mechanical dissipation peak in a single layer of Ta2O5 doped with TiO2. Class. Quantum Grav. 25 (2008)
[30] R.J. Bruls et al. The temperature dependence of the Young's modulus of
MgSiN2, AlN and Si3N4. Journal of the European Ceramic Society 21, 2001
[31] A. Nowick, B. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, New York, 1972
[32] V. B. Braginsky, V. P. Mitrofanov, V. I. Panov, Systems with small dissipation, University of Chicago Press, Chicago, 1985.
[33] W. A. Phillips, Tunneling states in amorphous solids, Journal of Low Temperature Physics 7 (1972) 351–360.
[34] P. W. Anderson, Anomalous low-temperature thermal properties of glasses and spin glasses, Philosophical Magazine 25 (1972) 1–9.
[35] K. S. Gilroy, W. A. Phillips, An asymmetric double-well potential model for structural relaxation processes in amorphous materials, Philosophical Magazine B 43 (1981) 735–746.
[36] O. L. Anderson, H. E. Bommel, Ultrasonic absorption in fused silica at low temperatures and high frequencies, Journal of the American Ceramic Society 38 (1955) 125–131.
[37] D. J. McLachlan, L. L. Chamberlain, Atomic vibrations and melting point in metals, Acta Metallurgica 12 (1964) 571–576.
[38] R. E. Strakna, Investigation of low temperature ultrasonic absorption in fast-neutron irradiated SiO2 glass, Physical Review 123 (1961) 2020–2026.
[39] H. W. Pan et al. "Silicon nitride films fabricated by plasma enhanced chemical vapor deposition method for coatings of the laser interferometric gravitational waves detector" In preparation (2017) LIGO document number LIGO-P1700252-v2
[40] Paul B. Woller. The Conformational Analysis of n-Butane. Journal of the American Chemical Society, 1972
[41] Norman L. Allinger. Conformational Analysis. 130. MM2. A Hydrocarbon Force Field Utilizing V1 and V2 Torsional Terms. Journal of the american chemical society, 1977 https://openwetware.org/wiki/Todd:Chem3x11_ToddL1?ref=vidupdatez.com/
[42] Hsuan-Yu Ho. Annealing effect on the room temperature and cryogenic
mechanical loss of ion beam sputtered nano-layer coatings. Master thesis,
National Tsing Hua University, oct. 2017
[43] Jessica Steinlechner, Iain W. Martin, Jim Hough, et al. Thermal noise reduction and absorption optimization via multimaterial coatings. Phys. Rev. D 91 (Feb. 2015), 042001
[44] Peter G. Murray et al. Ion-beam sputtered amorphous silicon films for cryogenic precision measurement systems, Phys. Rev. D 92, 062001, 2015
[45] Gregory M. Harry et al. Thermal noise in interferometric gravitational wave detectors due to dielectric optical coatings. Class. Quantum Grav. 19, 897–917 , 2002
[46] Nai-chung Kang. Photothermal common-path interferometry system setup and study of the optical absorption of the silicon nitride films deposited by PECVD method. Master thesis, National Tsing Hua University, oct. 2017
[47] Hsin-cheih Chen. Annealing effect on the room temperature mechanical loss of the silicon nitride films deposited with PECVD on silicon cantilever. Master thesis, National Tsing Hua University, oct. 2017