本實驗室參與重力波觀測組織 (LIGO, Laser Interferometer Gravitational wave Observatory) 的研究計畫，其利用大型麥克森干涉儀量測重力波訊號，由於重力波訊號相當微弱，難以偵測，因此量測時必須盡可能減少額外雜訊。由雜訊頻譜中可知，在 40-400Hz 左右，雜訊來源主要為薄膜熱擾動 coating Brownian noise，此雜訊為薄膜產生且難以直接量測得到，但經由 fluctuation dissipation theorem 可知該雜訊與薄膜本身之機械損耗成正比關係，因此透過量測高反射鏡薄膜機械損耗去探討薄膜熱擾動為本實驗主要研究重點。
先前本實驗室利用 PECVD 開發出氮化矽薄膜材料SiN0.33H0.58，其具備高折射係數、低且平坦的低溫機械損耗，但薄膜的光學吸收偏高；低折射係數方面，開發出透過 N 原子取代 O 原子來抑制因Si-O-Si鍵之two-level system造成的低溫機械損耗峰值，形成不同於 SiO2 非晶結構的氮氧化矽 SiO0.85N0.27H0.45(ratio3) 薄膜，不僅改善了 SiO2 的低溫機械損耗峰值問題，還保有低折射率、低光學吸收的特性。因此選用SiN0.33H0.58 與 SiO0.85N0.27H0.45(ratio3) 作為重力波高反射鏡薄膜材料。
本研究前半部分探討四分之一 1550nm 波長 SiON(ratio3)/SiN0.33堆疊膜之室溫機械損耗。1-pair、2-pair 及 4-pair 堆疊膜損耗量測結果相近，表示 SiON(ratio3)/SiN0.33 介面對機械損耗影響不大。頻率於 100Hz 之機械損耗約為10-5 order，此結果低於目前室溫重力波探測器 aLIGO 所使用的高反射鏡材料 TiO2-doped Ta2O5/SiO2 約下降了 2 倍。後半部分透過光學模擬軟體 Essential Macleod 設計氮氧化矽/氮化矽堆疊高反射鏡的堆疊結構並評估其光學穿透與吸收，再透過 Bulk and shear loss angle 評估氮氧化矽/氮化矽堆疊高反射鏡結構的熱雜訊(coating thermal noise)，將這些評估結果與重力波偵測器規格做比較，結果說明氮氧化矽/氮化矽堆疊高反射鏡結構的熱雜訊低於現今室溫重力波偵測器 aLIGO 反射鏡規格約 1.5 倍。

Our laboratory has participated in the research project of the Laser Interferometer Gravitational Wave Observatory(LIGO), which detects the gravity wave signal by large Michelson interferometer. Due to that the signal of gravitational wave is extremely weak and difficult to detect, it’s necessary to reduce the another noise during measurement. According to the noise spectrum, the sensitivity of interferometer is mostly limited by coating Brownian noise at 40-400Hz. The noise is generated by the thin film and is difficult to directly measure. The coating Brownian noise, which is proportional to mechanical loss stated by fluctuation-dissipation theorem. Therefore, the main research focus is to investigate the thermal noise of the film by measuring the mechanical loss.
Our research group developed NH3-free silicon nitride thin film, SiN0.33H0.58, which had a high refractive index and low cryogenic loss without loss peak, however, slightly higher optical absorption. In terms of low refractive index, we have developed the use of N atoms to replace O atoms to suppress the cryogenic loss peak caused by the two-level system of Si-O-Si bonds, forming silicon oxynitride SiO0.85N0.27H0.45 which is different from the amorphous SiO2 structure. Silicon oxynitride not only improves the cryogenic loss peak problem of SiO2, but also still have low refractive index and low optical absorption characteristic. Therefore, SiN0.33H0.58 and SiO0.85N0.27H0.45(ratio3) are selected as the materials for high reflection mirror coating.
The first half of this study is that discusses the room-temperature mechanical loss of SiON(ratio3)/SiN0.33 quarter-wave (QW) stacks. The mechanical loss results of 1-, 2- and 4-pair stacked samples are similar, indicating that the SiON(ratio3)/SiN0.33 interface has little effect on the mechanical loss. The loss is in 10-5 order at 100 Hz, this result is lower than the mirror coating TiO2-doped Ta2O5/SiO2 used in aLIGO about 2.2 times lower. The second half of this study is the optical simulation software Essential Macleod were used for designing the HR mirror structures of the silicon oxynitride/silicon nitride evaluate its optical transmission and absorption. The bulk and shear loss angle were used to evaluate the thermal noise of the silicon oxynitride/silicon nitride stacked structure. These results are compared with the specifications of the gravitational wave detectors and it showed that the thermal noise of the silicon oxynitride/silicon nitride stacked structure is about 1.5 times lower than the aLIGO specification of room temperature gravitational wave detector.

[1] A. Einstein, “Die grundlage der allgemeinen relativitätstheorie, Annalen der Physik”, 49, 769 (1916).
[2] R. A. Hulse et al., “Discovery of a pulsar in a binary system”, The Astrophysical journal 195 (1975) L51.
[3] B. P. Abbott et al., Observation of Gravitational Waves from a Binary Black Hole Merger, PRL, 116, 061102 (2016).
[4] B. P. Abbott et al., “GW151226: Observation of Gravitational Wavess from a 22-Solar-Mass Binary Black Hole Coalescence”, Phys. Rev. Lett. 116, 241103 (2016).
[5] B. P. Abbott et al., “GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2”, Phys. Rev. Lett. 118, 221101 (2017).
[6] B. P. Abbott et al., “GW170814: A Three-Detector Observation of Gravitational Wavess from a Binary Black Hole Coalescence”, Phys. Rev. Lett. 119, 141101 (2017).
[7] B. P. Abbott et al., “GW170817: Observation of Gravitational Wavess from a Binary Neutron Star Inspiral”, Phys. Rev. Lett. 119, 161101 (2017).
[8] B. P. Abbott et al., “GW190521: A Binary Black Hole Merger with a Total Mass of 150 M⊙”, Phys. Rev. Lett. 125, 101102 (2020).
[9] LIGO Scientific Collaboration, Instrument Science White Paper 2019, LIGO Document: LIGO-T1900409-v2 (2019).
[10] H. B. Callen, T. A. Weltont. Irreversibility and generalized noise. Phys. Rev., Jul. 83, 34-40 (1951).
[11] ET Science Team, “Einstein gravitational wave telescope conceptual design study: ET-0106C-10” (European gravitational observatory, Cascina Italy, (2011) https://tds.virgo-gw.eu/?call_file=ET-0106C-10.pdf .
[12] K. Somiya, “Detector configuration of KAGRA–the Japanese cryogenic gravitational-wave detector”, Class. Quantum Grav. 29, 124007 (2012).
[13] R. Adhikari et al., “LIGO III Blue Concept LIGO”, LIGO Report No. LIGO-G1200573 (2012) http://dcc.ligo.org/LIGO-G1200573-v1/public .
[14] LIGO Scientific Collaboration, “Advanced LIGO”, Classical Quant. Grav. 32, 074001 (2015).
[15] G. Vajente, L. Yang, A. Davenport, M. Fazio, et al., “Low Mechanical Loss TiO2∶GeO2 Coatings for Reduced Thermal Noise in Gravitational Wave Interferometers”, Phys. Rev. L. 127, 071101 (2021).
[16] I. W. Martin et al., “Comparison of the temperature dependence of the mechanical dissipation in thin films of Ta2O5 and Ta2O5 doped with TiO2”, Class. Quantum Grav. 26, 155012 (2009).
[17] I. W. Martin et al., “Low temperature mechanical dissipation of an ion-beam sputtered silica film, Class. Quantum Grav”, 31, 035019 (2014).
[18] Z. L. Huang, “The optical properties of PECVD silicon nitride films after thermal annealing, and the optical and mechanical properties of NH3-free PECVD silicon nitride films”, Master thesis, National Tsing Hua University (2019).
[19] W. J. Tsai, “Study of the optical and mechanical properties of silicon oxynitride thin films fabricated by plasma enhanced chemical vapor deposition”, Master thesis, National Tsing Hua University (2020).
[20] 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 (2013).
[21] 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 (2013).
[22] B. A. Walmsley, Y. Liu, X. Z. Hu, M. B. Bush, J.M. Dell, and L. Faraone, Poisson’s ratio of low-temperature PECVD silicon nitride thin films, J. Microelectromech. Syst. 16, 622 (2007).
[23] J. Thurn and R. F. Cook, Stress hysteresis during thermal cycling of plasma-enhanced chemical vapor deposited silicon oxide films, J. Appl. Phy. 91, 1988 (2002).
[24] Jessica Steinlechner, Iain W. Martin, Jim Hough, et al., “Thermal noise reduction and absorption optimization via multimaterial coatings”, Phys. Rev. D 91, 042001 (2015).
[25] S. T. Thornton, J. B. Marion, “Classical dynamics of particles and systems”, Brooks Cole, 5: 109-121 (2003).
[26] D. R. M. Crooks, “Mechanical loss and its significance in test mass mirrors of gravitational wave detectors”, Ph.D. thesis, University of Glasgow, 121-123 (2002).
[27] X. Liu, R. O. Pohl, “Low-energy excitations in amorphous films of silicon and germanium”, Phys. Rev. B, Oct. 58: 9067-9081(1998).
[28] 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).
[29] H. C. Tsai, W. Fang, “Determining the Poisson's ratio of thin film materials using resonant method”, Sensors and Actuators A, 103: 377-383 (2003).
[30] J. S. Oul, “Setup of room temperature mechanical loss measurement and preliminary measurement results on fused silica and silicon cantilevers”, Master thesis, National Tsing Hua University (2012).
[31] C. 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).
[32] R. Nawrodt , A. Zimmer, S. Nietzsche, M. Thürk, W. Vodel, P. Seidel, “A new apparatus for mechanical Q-factor measurements between 5 and 300 K”, Cryogenics 46, 718-723 (2006).
[33] A. S. Nowick et al., “Anelastic relaxation in crystalline solid”, New York: 101 Academic Press (1972).
[34] Jessica Steinlechner, Iain W. Martin, Jim Hough, et al., “Thermal noise reduction and absorption optimization via multimaterial coatings”, Phys. Rev. D 91 , 042001 (2015).
[35] M.R. Abernathy, X. Liu, T.H. Metcalf, An overview of research into low internal friction optical coatings by the gravitational wave detection community, Mat. Res. 21 (suppl.2) (2018).
[36] T. Hong, H. Yang, E. K. Gustafson, R. X. Adhikari, and Y. Chen, “Brownian thermal noise in multilayer coated mirrors”, Phys. Rev. D 87, 082001 (2013).
[37] H. W. Pan, “Study of silicon nitride and silica films fabricated by a plasma enhanced chemical vapor deposition method for low thermal noise mirror coating of laser interferometer gravitational wave detectors”, PhD Thesis, National Tsing Hua University (2018).
[38] W. Yam, S. Gras, and M. Evans, “Multimaterial coatings with reduced thermal noise”Phys. Rev. D 91, 042002 (2015).
[39] J. Steinlechner and I. W. Martin, “Thermal noise from icy mirrors in gravitational wave detectors”, Phys. Rev. Research1, 013008 (2019).
[40] M. M. Fejer, S. Rowan, G. Cagnoli, D. R. M. Crooks, A. Gretarsson, G.M. Harry, J. Hough, S. D. Penn, P. H. Sneddon, and S. P. Vyatchanin, “Thermoelastic dissipation in inhomogeneous media: loss measurements and displacement noise in coated test masses for interferometric gravitational wave detectors”, Phys. Rev. D 70, 082003 (2004)
[41] P. W. Baumeister, “in Optical Coating Technology”, SPIE press, Bellingham, Ch. 5.3.1, p. 5–19 (2004)
[42] H. A. Macleod, “in Thin-Film Optical Filters 2nd ed”, Bristol. Hilger, Ch.5, p. 165 (2001).
[43] Y. H. Kao, “Study the reduction of optical absorption of the oxynitride thin film fabricated by plasma enhanced chemical vapor deposition”, Master thesis, National Tsing Hua University (2021).
[44] D. L. Tsai, “Study of the material properties of silicon nitride thin films fabricated by low pressure chemical vapor deposition for mirror coating of laser interferometer gravitational waves detector, Master thesis”, National Tsing Hua University (2021).
[45] D. R. Southworth, R. A. Barton, S. S. Verbridge, B. Ilic, A. D. Fefferman, H. G. Craighead, and J. M. Parpia, “Stress and silicon nitride: A crack in the universal dissipation of glasses”, Phys. Rev. Lett. 102, 225503 (2009).
[46] G.E. Jellison, Jr et al., “Spectroscopic ellipsometry characterization of thin-film silicon nitride”, Thin Solid Films, 313-314, 193-197 (1998).
[47] G.E. Jellison, Jr et al., “Parameterization of the optical functions of amorphous materials in the interband region”, Appl. Phys. Lett., 69, 371 (1996).
[48] M. A. Hopcroft, W. D. Nix, and T.W. Kenny, “What is the Young’s modulus of silicon?”, J. Microelectromech. Syst. 19, 229 (2010).
[49] L. C. Kuo, “Strain energy in the coating material”, lab file, National Tsing Hua University (2019).
[50] L. C. Kuo, “公式整理” , lab file, National Tsing Hua University (2019).