反射鏡的薄膜熱擾動是目前雷射重力波干涉儀最主要的雜訊之一，因此找尋低機械損耗的薄膜材料及薄膜結構，一直是下一世代觀測站研究的焦點。本論文提出使用奈米多層膜取代傳統高反射鏡中的四分之一波長薄膜。奈米多層膜同樣是使用兩種不同折射材料交替堆疊而成，但在奈米多層膜中每層的薄膜厚度僅為數奈米。奈米多層膜的等效光學常數和等效彈性常數具有可調整的特性，可通過改變奈米多層膜中兩材料厚度比例來調整。本篇研究發現兩種與厚度相關的現象並進行探討：首先是結晶的抑制，非晶薄膜材料的結晶溫度會隨著膜厚的減薄而增加，因此能承受更高的退火溫度更有效的降低機械損耗。其次為非晶薄膜材料低溫機械損耗的抑制，當薄膜減薄時低溫機械損耗也隨之下降。
論文中使用離子束濺鍍法，交替鍍製二氧化鈦與二氧化矽薄膜來堆疊各種結構的奈米多層膜。在結晶抑制的實驗中，主要針對二氧化鈦的結晶溫度與厚度進行分析，在膜厚約127nm時結晶溫度約為250℃，但將膜厚下降到1.8nm後結晶溫度可提高至800℃。最後，本論文對二氧化鈦與二氧化矽厚度分別為1.8nm 和3.6nm的奈米多層膜進行600℃的退火，並對退火對機械損耗進行量測，從量測結果發現室溫和低溫的機械損耗均有明顯改善。
論文中測量了兩種厚度比例相同，但單層膜厚不同的奈米多層膜。從量測結果中發現，奈米多層膜的低溫機械損耗量測值，均會低於理論的機械損耗值。且奈米多層膜中單層膜厚越薄，所量測到的機械損耗值也越低。認為是奈米多層膜結構能夠限制超出薄膜厚度原子團的轉換，使機械損耗降低。
最後針對奈米多層膜堆疊而成的高反射鏡進行光學模擬，從模擬得知當入射波長在可見光和近紅外範圍時，反射頻譜會與傳統四分之一光學厚度堆疊而成的反射鏡相同。表示在可見光和近紅外範圍下，奈米多層膜內部不會產生額外的干涉效應。

Thermal noise of the mirror coatings is one of the major noise sources for the laser interferometer gravitational waves detector at its most sensitive frequency about 100Hz. Searching for new thin film materials and layer structures for the mirror coatings with low mechanical loss and operate the instrument at cryogenic temperature are the main focuses for the coatings research of the next generation detector. In this study, a stack of alternately deposited films each with thickness in the nano-meter range is used to replace the quarter-wave layer in the conventional high reflector coatings. The effective optical constants and the effective elastic constants of the stack can be tuned by adjusting the thickness ratio of the nano-layers to optimize the optical and the mechanical properties of the coatings. Throughout the study, two thickness-related phenomena were discovered: the crystallization temperature of the amorphous thin film material was increased with decreased thickness, and the cryogenic mechanical loss of the amorphous thin film material was suppressed with decreased thickness. The former phenomenon enables the nano-layer stack to sustain the higher temperature of annealing to reduce the mechanical loss, and the later phenomenon provides a new layer structure for coatings of cryogenic operation.
Ion beam sputtering was used to deposit nano-layer stacks that consisted of amorphous titania and silica thin films with various thickness combinations. The crystallization temperature of the titania layer increased from 250oC for 127 nm thickness to 800oC for 1.8 nm. Subsequent thermal annealing of the titania/silica (1.8 nm/3.6 nm) nano-layer at 600oC revealed that room temperature and cryogenic mechanical losses were reduced significantly.
Cryogenic mechanical losses of the nano-layer stacks of titania/silica with the same thickness ratio were measured and found to be lower than that of the calculated titania/silica nano-layer using the mechanical loss of the thick films and furthermore, we experimentally verified that the titania/silica nano-layer with thinner silica thickness, but the same thickness ratio, has lower cryogenic mechanical loss than that of the nano-layer with thicker silica thickness. Suppression of the cryogenic mechanical loss of the silica by thinner thickness was evident. Suppression of the transitions of the two-level-system of the long-range group of atoms that exceeds the thickness of the silica film was proposed to account for the phenomena.
Optical simulation of the complete mirror coatings that consisted of nano-layer stacks showed that the transmittance spectrum in the visible and near IR range is identical to that of the conventional quarter-waves stack that consists of quarter-wave layers with effective refractive index and extinction coefficient of the nano-layer stack, indicating that there is no extra interference effect introduced by the nano-layer.

Abstract I
中文摘要 III
Acknowledgement IV
Contents VI
List of figures IX
List of Tables XIV
Ch.1 Introduction 1
1.1 Gravitational wave detection 1
1.2 Noise sources 3
1.3 Nano-layer introduction 5
Ch.2 Theory 9
2.1 Mechanical loss of film 9
2.2 Energy ratio 10
2.3 Effective Young’s modulus 12
Effective parallel Young’s modulus 13
Effective vertical Young’s modulus 15
2.4 Effective shear modulus 16
Effective parallel shear modulus 17
Effective vertical shear modulus 19
2.5 Mechanical loss of nano-layer 20
2.6 Effective refractive index and extinction coefficient 21
Ch.3 Deposition of nano-layer 24
3.1 Thickness design 24
3.2 Silicon substrate 25
3.3 Ion beam sputter 27
3.3.1 Sputtering parameter 27
3.3.2 Thickness control 28
3.3.3 Composition analysis 30
Ch.4 Mechanical loss measuring system 31
4.1 Room temperature 31
4.2 Cryogenic 33
4.2.1 Introduction of the structure 33
Closed-loop system for helium recycling 33
Measurement conditions 35
4.2.2 Clamping system for cantilever 37
Effect of clamping torque 37
Effect of re-clamping 38
4.2.3 Temperature control system 42
Temperature stabilization 42
Effect on pressure 43
Effect on the resonant frequency of the cantilever 46
Effect of temperature recycle 47
Effect of laser light source wavelength 48
Ch.5 Measurement results and analysis 51
5.1 Thickness-dependent crystallization of titania 51
5.1.1 Annealing procedure 51
5.1.2 X-ray diffraction measurement results 53
Measuring principle 53
Measurement result 54
5.1.3 TEM measurement results 60
5.1.4 Crystal size analysis 64
5.2 Thickness-dependent on mechanical loss 68
5.2.1 Mechanical loss of silica 68
5.2.2 Mechanical loss of titania 71
5.2.3 Mechanical loss of nano-layer 72
19-layer with the thickness ratio of 65% 72
19-layer with the thickness ratio of 32% and 75-layer with the thickness ratio of 33% 74
5.2.4 Suppression effect on silica 78
Two-level system 78
Suppression effect at cryogenic temperature 79
Suppression effect at room temperature 82
5.2.5 Suppression effect on titania 85
5.3 Annealing effect of nano-layer 87
5.3.1 Annealing effect on silicon substrate 87
5.3.2 Room-temperature mechanical loss 89
Nano-layer with the thickness ratio of 65% 89
Nano-layer with the thickness ratio of 33% 94
5.3.3 Cryogenic mechanical loss 96
5.4 Optical properties of nano-layer 101
5.4.1 Effective layer 101
5.4.2 Reflectance spectrum 101
5.4.3 Absorptance 104
Ch.6 Conclusion and future work 106
6.1 Conclusion 106
6.2 Future work 107
Appendix A: Silicon substrate mechanical loss database for cryogenic temperature 109
Appendix B: Annealing effect on extinction coefficient 112
Appendix C: Numerical analysis of the strain energy in the cantilever system 115
Reference 126

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