能量耗散在微機電系統(Micro Electromechanicsystem : MEMS)及奈米機電系統(Nano Electromechanicsystem : NEMS)是一件相當嚴重的問題，過大的能量耗散會造成系統的效率低落及其性能(Performance)的不彰，因此，本研究將針對由雙邊固定樑所構成共振器(Resonator)做能量耗散機制的探討。共振器在射頻微機電系統(RF MEMS)是常見的元件之一，對於共振器來說，追求高頻、高品質因數(Quality factor)是非常重要的，將從外阻尼及內阻尼開始探討，外阻尼為擠壓膜阻尼(Squeeze Film Damping : SFD)，內阻尼為熱彈性阻尼(Thermoelastic Damping : TED)，此為兩種常見也相當重要的能量耗散機制。
一般在探討系統的總能量耗散機制時，都是先計算個別的能量耗散機制，再利用總品質因數的計算方式(1.2)所求得。但是，這是在各能量耗散相互不影響的情況下才會成立，但是，從有關SFD的研究(Bao and Yang 2007)中知道，SFD會影響系統的共振頻率，而從TED的研究中(Zener 1938)知道，TED會受到頻率的影響而變化，所以要是不考慮SFD與TED相互會影響的情況下，利用總品質因數的計算方式(1.2)來計算SFD與TED的總品質因數是有疑慮的，因此本研究將會特別探討SFD與TED耦合(SFD+TED)時的能量耗散機制，試圖分析在SFD與TED相互影響極為顯著時，總品質因數的計算方式(1.2)是否適用。
會對SFD與TED造成影響的物理參數有元件尺寸、環境壓力、擠壓膜厚度等，振動的模態也會影響SFD與TED。在環境壓力較低及擠壓膜厚度極小的情形下，會造成稀薄氣體效應的產生，此時SFD與TED的值會相當的接近，兩者間的變化，對於總能量耗散的影響是相當顯著的，故有探討的必要性。而在稀薄氣體效應之下，調節係數對於MEMS / NEMS的能量耗散影響的問題還鮮少被討論，本研究認為調節係數將對MEMS / NEMS會有相當程度的影響，將特別討論。因此，本研究將分為四個部分來探討，分別為：
一. 尺寸效應。
二. 高模態效應。
三. 稀薄氣體效應。
四. 調節係數效應。
本研究將採用數值分析的方法來探討以上四個主題，將從以上四個部分的數值解析結果，討論各效應對於SFD、TED、SFD+TED的影響，提出幾點的建議能使MEMS / NEMS能擁有高的品質因數。並討論SFD與TED的相互影響性，將嘗試找出在何種情況下，是必須特別注意SFD及TED是不可分開討論的。

Mechanism of energy dissipation is an important issue in MEMS / NEMS. The energy loss is so much that the efficiency is low and the performance is bad. Therefore, we discussed the mechanisms of energy dissipation for the resonator that is formed by a beam that two ends are fixed. The resonator is one of parts of RF MEMS. Both of the high operating frequency and the high quality factor are important parameters for resonator. For quality factor respect, there are two kinds of mechanisms - extrinsic damping and intrinsic damping in the MEMS / NEMS. The extrinsic damping is squeeze film damping (SFD) and the intrinsic damping is thermoelastic damping (TED). It is easy to be found and important in MEMS / NEMS.
In general, the total quality is calculated by (1.2) to estimate the total energy dissipation in the system. It is valid when the ways of energy dissipation did not interact. However, we believe that could be disobeyed when the SFD and the TED existed simultaneously in the system. Because we know the SFD lead the resonant frequency to be changed from the research about SFD(Bao and Yang 2007), and know the TED will be affected by resonant frequency(Zener 1938). This is a kind of interaction between the SFD and the TED so we doubt the validity of formula. We research the interaction between the SFD and the TED, and try to find out where are invalid for the formula (1.2).
There are many parameters that can affect both of the SFD and the TED -- dimension of object, ambient pressure, thickness of gas film, and resonant mode for example. The gas rarefaction is occurred when the ambient pressure is in the condition of vacuum or the thickness of gas film is smaller than the mean path of free molecular. The value of SFD closes to the value of TED when the gas is attenuated, so the interactive effect is significant for the total quality factor. It would be discussed in this research. Few studies about the effects of accommodation coefficient for the quality factor in MEMS / NEMS. Therefore, we study these subjects in four parts.
1. Effects of dimension.
2. Effects of higher resonant mode.
3. Effects of gas rarefaction.
4. Effects of accommodation coefficient.
We applied numerical analysis in this research. First, we studied the SFD and the TED individually and recommended some advices how to get the high quality factor. Second, we discussed the interactive effects for quality factor when both of the SFD and the TED exist simultaneously in the system.

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