光學薄膜的熱擾動是高精度干涉儀測量的限制之一。為了測量微弱的信號如重力波，應盡可能降低熱擾動，以提高檢測靈敏度。根據Fluctuation-Dissipation theorem，薄膜的熱擾動與材料的機械損耗成正比關係。因此，我們只要量測材料的機械損耗，就可以得知由薄膜引起的熱擾動影響。本實驗室致力於研究材料的機械損耗以降低熱擾動。
我們透過離子束濺鍍法研究二氧化矽和二氧化鈦薄膜。對於傳統的高反射鏡，二氧化矽是不可缺少的低折射率材料。然而，二氧化矽具有高的低溫機械損失，會導致高的熱擾動影響。因此，我們將二氧化鈦做為二氧化矽薄膜的blocking layer。當減少二氧化矽的膜層厚度時，由於長範圍Two-level system的轉變被消除了，使二氧化矽的低溫損耗產生抑制效果。
對於另一種材料，二氧化鈦是一個難以在高溫下退火的材料。因此，我們將二氧化矽做為二氧化鈦的blocking layer。藉由此方式進行退火，二氧化鈦的結晶溫度有顯著提高。在最小膜層厚度的樣品中，其退火可以增加到600℃而不結晶。最重要的是該樣品在600℃退火機械損耗可以更有效地被減少。

Thermal noise from the optical coating in the cavities of the interferometer is the limiting factors for high-precision measurement. In order to measure weak signals such as gravitational-wave, the noise should be reduced as much as possible to improve detection sensitivity. According to Fluctuation-Dissipation theorem, the thermal noise is proportional to the mechanical loss of materials. Therefore, as long as we measure the loss, we can determine the noise effect of the films. The laboratory is committed to research the loss of materials to reduce the noise of the measurement system.
We investigated the silica and the titania films for high reflection coating by ion beam sputtering. For traditional high reflection mirrors, silica is an indispensable low refractive index material. However, silica has a high cryogenic mechanical loss and hence contributes to high thermal noise. Therefore, we stacked titania as a blocking layer for silica films. When reducing the thickness of the silica layers that eliminates the transitions of the long-range two-level systems. There had a suppression effect in cryogenic loss of silica layers.
In another material, titania is a material that difficult to anneal at high temperatures. Therefore, silica becomes a blocking layer for titania films. Annealing in this way, the crystallization temperature of titania was significantly improved. In the case of the sample which has the smallest film thickness. Annealing of the sample could increase to 600oC without crystallization. The most important is that the sample which annealing at 600oC could effectively decrease the mechanical loss.

[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, L51 (1975)
[3] H. B. Callen et al., Observation of Gravitational Waves from a Binary Blcak Hole Merger, Phys. Rev. Lett. Vol.116, 061102(2016)
[4] LIGO Scientific Collavoration Group. Instrument science white paper. LIGO-T1800133-v3, Oct.2018
[5] H. B. Callen et al., Irreversibility and generalized noise, Physical Review, Vol.83, 34-40(1951)
[6] R. F. Greene et al., On the formalism of thermodynamic fluctuation theory, Phy. Rev., Vol.83, 1231-1235(1951)
[7] H. B. Callen et al., On a theorem of irreversible thermodynamics, Phy. Rev., Vol.86, 702-710(1952)
[8] Wen-Hsiang Wang, Low loss optical mixed film and dielectric mirror, Ph. D. thesis, Taiwan( R. O. C. ), National Tsing Hua University(1999)
[9] Shun-Jin Wang, Fabrication and annealing study of the ion beam sputtered nano-layer structures in the high reflective dielectric mirror for the laser interference gravitational wave detector, Master thesis, Taiwan( R. O. C. ), National Tsing Hua University(2013)

[10] Sin Jhong Song, Study of the crystallite size for the nano-meter multilayer stack after thermal anneal, Master thesis, Taiwan( R. O. C. ), National Tsing Hua University(2015)
[11] Hsuan-Yu Ho, Annealing effect on the room temperature and cryogenic mechanical loss of ion beam sputtered nano-layer coatings, Master thesis, Taiwan( R. O. C. ), National Tsing Hua University(2017)
[12] Wei-Ya Wang, Study of mechanical vibration and loss of silicon cantilever for the high-reflection mirror in the laser interference gravitational wave detector, Master thesis, Taiwan( R. O. C. ), National Tsing Hua University(2013)
[13] Chia-Wei 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, Taiwan( R. O. C. ), National Tsing Hua University(2013)
[14] Wen Jeng Huang, Preparation of the ion beam sputter coater for coating the low loss thin films in LIGO mirror application, Master thesis, Taiwan( R. O. C. ), National Tsing Hua University(2012)
[15] Jeng-Shiun Oul, Setup of room temperature mechanical loss measurement and preliminary measurement results on fused silica and silicon cantilevers, Master thesis, Taiwan( R. O. C. ), National Tsing Hua University(2012)
[16] S. T. Thornton et al., Classical dynamics of particles and systems, Brooks Cole, fifth edition, 109-121(2003)
[17] K. Y. Yasumura et al., Quality Factors in Micron- and Submicron-Thick Cantilevers, journal of microelectromechanical systems, vol.9(2000)

[18] D. R. M. Crooks, Mechanical loss and its significance in test mass mirrors of gravitational wave dectors, Ph. D. thesis, University of Glasgow(2002)
[19] X. Liu, R. O. Pohl, Low-energy excitations in amorphous films of silicon and germanium. Phys. Rev. B, 58:9067-9081, Oct.1998
[20] B. E. W. Jr., R. O. Pohl, Thin films: stresses and mechanical properties V: Elastic properties of thin films. Mater. Res. Soc., Pittsburgh, No.356:567-572,ISBN:978-1-558-99257-3, Jun. 1995
[21] 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
[22] M. A. Hopcroft, W. D. Nix, T. W. Kenny, What is the Young’s modulus of silicon?, Journal of Microelectromechanical system, 19: 299, Apr. 2010
[23] 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)
[24] Chun Cheng, Cryogenic mechanical loss measurement system setup and annealing effect on the mechanical loss of the nano-layer coatings, Master thesis, Taiwan( R. O. C. ), National Tsing Hua University(2015)
[25] Han Wu, Cryogenic Mechanical Loss of SiNxHy and SiN0.40H0.79/SiO2 Stacks Deposited by Plasma Enhanced Chemical Vapor Deposition Method, Master thesis, Taiwan( R. O. C. ), National Tsing Hua University(2017)
[26] Hsin-Chieh Chen, Annealing effect on the room temperature mechanical loss of the silicon nitride films deposited with PECVD on silicon cantilever, Master thesis, Taiwan( R. O. C. ), National Tsing Hua University(2017)
[27] I. M. Pinto et al., Nanometer-layered SiO2:TiO2 mixtures for high reflectance/low noise coatings status update, Ligo document: LIGO-G1300321-v1(2013)
[28] S. Chao et al., Thickness-dependent crystallization on thermal anneal for titania/silica nm-layer composites deposited by ion beam sputter method, Opt. Exp. Vol.22, 29847-29854(2014)
[29] A. J. HAIJA et al., Effective characteristic matrix of ultrathin multilayer structure, Opt. Appl. XXXVI(2016)1
[30] A. Nowick, B. Berry, Anelastic Relaxation in Crystalline Solids, Academic Press, New York, 1972
[31] V. B. Braginsky, V. P. Mitrofanov, V. I. Panov, Systems with small dissipation, University of Chicago press, Chicago, 1985
[32] W. A. Phillips, Tunneling states in amorphous solids, Journal of Low temperature Physics7, 351-360(1972)
[33] P. W. Anderson, Anomalous low-temperature thermal properties of glasses and spin glasses, Philosophical Magazine25, 1-9(1972)
[34] I. W. Martin, Studies of materials for use in future interferometric gravitational wave detectors, Ph. D. thesis, University of Glasgow(2009)
[35] R. Hamdan, J. P. Trinastic, H. P. Cheng, Molecular dynamics study of the mechanical loss in amorphous pure and doped silica, The Journal of Chemical Physics 141, 054501 (2014)
[36] Hai-Ping Cheng, Origin of the second peak in the mechanical loss function of amorphous silica, Phy. Rev. B 95, 014109 (2017)
[37] A. Nakaruk, D. Ragazzon, C.C. Sorrell, Anatase-rutile transformation through high-temperature annealing of titania films produced by ultrasonic spray pyrolysis, Thin Solid Films 518, 3735-3742 (2010)
[38] B. E. Warren, X-Ray Diffraction, 251-258(1990)
[39] L. C. Kuo et al., LIGO Document: LIGO-G1700300-v2(2017)
[40] 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, Taiwan( R. O. C. ), National Tsing Hua University(2017)