臺灣博碩士論文加值系統

陀螺儀作為其中一種傳感器，在各種大型器械或是精密儀器中相當常見，在MEMS(microelectromechanical systems)的尺度下，圓盤形陀螺儀DRG (disk resonator gyroscope)的發展行之有年，本論文主要討論近年來於MEMS尺度下蓬勃發展的半球殼形陀螺儀HRG (hemispherical resonator gyroscope)。而陀螺儀的基本性能由品質因數Q(quality factor)影響最深， 值是基於各種物理損耗機制所帶來的能量損耗總和，其中包含熱彈性阻尼損耗、錨固定損耗、電極損耗等。經由陀螺儀結構的最佳化，可以使其他機械損耗都降至最低，但是由材料性質所主導的熱彈性阻尼損耗卻無法經由結構設計去降低，完全取決於材料本身的性質，於是就成為了左右Q值的重要損耗項，此時材料選用對於陀螺儀及各式諧振器會造成很大的影響，最常見的材料為二氧化矽。本文欲探討在MEMS的尺度下，以各式半導體材料取代二氧化矽，並且於其中能貢獻最大Q值的β-Ga2O3作主要的說明與相關分析，並且討論半導體材料相對於一般材料的優勢以及提升陀螺儀性能的前景，本論文使用有限元素分析軟體ANSYS與微機電分析軟體CoventorWare對不同的諧振陀螺儀進行分析並且求取Q值，配合上Q值的解析解相互對照比較，最後也會設計實驗步驟來收集β-Ga2O3樑諧振器的實際Q值以佐證材料的優勢性。

As one of the sensors, gyroscope is quite common in various large-scale instruments or precision instruments. At the scale of microelectromechanical systems (MEMS), the development of disk resonator gyroscope (DRG) has been in progress for many years. Here we want to disscuss the hemispherical resonator gyroscope (HRG) that has flourished in the MEMS scale in recent years. The basic performance of the gyroscope is most affected by the quality factor Q. Q-1 is the sum of the energy losses caused by various physical loss mechanisms, including the thermoelastic damping, the anchor loss, and the electrode loss. Through the optimization of the gyroscope structure, other mechanical losses can be minimized, but thermoelastic damping dominated by the material properties can not be reduced by structural design, it depends on the property of the material itself, so it becomes the most important loss term of Q. For the reasons above, material selection will have a great impact on the gyroscope and various resonators, the most common material for which is silicon oxide. In this thesis, we will discuss the substitution of silicon oxide with various semiconductor materials at the MEMS scale, especially β-Ga2O3 which can contribute to enhanced Q, and discuss the advantages of semiconductor materials relative to insulting materials. Finite element analysis software ANSYS and the MEMS analysis software CoventorWare are used to analyze different resonant gyros and obtain the Q values. Experimental procedures were performed to collect the actual Q of β-Ga2O3 beam resonators.

摘要 I
Abstract III
誌謝 VI
目錄 VII
表目錄 X
圖目錄 XI
第一章 緒論 1
1-1前言 1
1-2陀螺儀基本原理 3
1-3半導體基本原理 9
1-4研究動機與方法 13
1-4-1研究動機 13
1-4-2模擬軟體ANSYS介紹 14
1-4-3模擬軟體CoventorWare介紹 14
1-4-4樑諧振器求取Q值實驗方法 15
1-5論文架構 16
第二章 諧振器陀螺儀運作之基本原理 18
2-1樑諧振器基本原理 18
2-1-1樑運動方程式與自然頻率推導 18
2-1-2有限元素分析軟體之自然頻率模擬 22
2-2圓盤形陀螺儀(DRG)運作基本原理 29
2-2-1圓盤形陀螺儀(DRG)基本介紹 29
2-2-2運動方程式與自然頻率推導 34
2-2-3有限元素分析軟體之自然頻率模擬 41
2-3半球殼形陀螺儀(HRG)運作基本原理 46
2-3-1半球殼形陀螺儀(HRG)基本介紹 46
2-3-2運動方程式與自然頻率推導 49
2-3-3有限元素分析軟體之自然頻率模擬 59
2-4陀螺儀相關性能參數指標 64
2-4-1品質因數Q 64
2-4-2分辨率 65
2-4-3比例因子 67
第三章 Q值與半導體材料β-Ga2O3應用 68
3-1品質因數Q的推導 68
3-1-1 Q值的基本定義 68
3-1-2熱彈性阻尼損耗 69
3-1-3錨固定損耗 71
3-1-4電極損耗 72
3-1-5 AKE損耗 74
3-2半導體材料β-Ga2O3之應用 76
3-2-1 β-Ga2O3介紹 76
3-2-2 β-Ga2O3應用於陀螺儀的優勢 79
第四章 模擬結果與實驗分析結果 81
4-1 CoventorWare模擬分析材料之Q值 83
4-1-1樑諧振器QTED解析解與模擬解比較 83
4-1-2半球殼形陀螺儀QTED模擬解比較 88
4-1-3模擬之結果與討論 96
4-2樑諧振器Q值之實驗 97
4-2-1器材介紹與實驗流程 97
4-2-2實驗結果 101
第五章 結論與未來展望 104
參考文獻 105

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