指導教授：翁宗賢臺灣大學：應用力學研究所林柏甫Lin, Po-FuPo-FuLin2014-11-302018-06-292014-11-302018-06-292014http://ntur.lib.ntu.edu.tw//handle/246246/264129加速度感測晶片應用廣泛，包括生活中常見的交通載具、行動裝置、體感設備，到航太產業、軍用飛彈等領域。其中，在軍用武器的應用領域裡，整個飛行載具系統必須能承受相當程度的衝擊力道，故需使用高 G 值加速感測晶片來量測加速度變化。隨著近年微機電(MEMS)製程的發展，加速度感測晶片的可靠度及量測範圍已有效提升，各種能量測到數十萬G值的加速度感測晶片陸續開發出來。然而，在設計加速度感測晶片的過程中，考量到製程設備、機台精度、成本考量等因素，不同的製造方法、不同的裝置都會有不同結構設計上的需求及限制。但目前並無一簡便方法能較準確預測機械構型改變對於加速度感測晶片輸出訊號的影響，只能將數個不同設計輸入數值計算模擬軟體分析，透過分析結果找出相對合適的設計，但這樣的做法通常需要花費不少的時間與成本。 因此，本文探討一高線性度高G 值微型壓阻式加速度感測晶片的幾何設計，經由數值模擬結果，迴歸加速度感測晶片輸出訊號與其幾何參數間的關係方程式，並將不同設計之自然頻率、訊號解析度等因素加入考量，建立一套預測輸出訊號的設計方法。本文依據Kuells等人一文中的一壓阻式加速度感測晶片[8]設計做為參考，該結構由一平板狀的懸臂樑與四根位於懸臂樑上側的長軸方向、以垂直於板面對稱配置的四根長方柱狀壓阻器構成，此結構受衝擊時會產生形變與振動，可以以彈簧與質量系統分析之，然而該晶片所設定三邊之邊界條件會造成微機電製程研製上的困難，提高生產成本。本文期望研究結果能適用於更多的微機電製程，故調整其部分的邊界條件，使該機械構型能更容易製作。因此，本文改變數個幾何參數並建立數位模型，所探討模型的懸臂樑長度變化從350μm到600μm、深度130μm到500μm、寬度12.5μm到25μm，壓阻器長度變化從10μm到30μm、截面積3μm2到24μm2，接著運用數值模擬軟體分析這些機械構型在受到半正弦波的高G值衝擊加速度條件下，各個壓阻器應力響應狀態，衝擊半正弦波的峰值變化範圍從5000G到100000G。為便於後續簡易設計，本文從計算結果中推導出各設計參數與壓阻器應力間的關係，再從應力推算晶片輸出訊號。 將結果進行適當之分析與迴歸處理後，成功得出所有設計參數與壓阻器應力、輸出訊號的關係方程式。此結果可供後人在實際研製類似結構之加速感測晶片之前，先根據製程機台與成本等因素，訂定各幾何參數尺寸及衝擊範圍，並代入各關係式中，由最大應力關係式得出的數值，可判斷該尺寸設計於衝擊歷程中是否發生破壞；輸出訊號關係式可用於預測輸出訊號數值，可根據此數值判斷輸出訊號強度是否適用於量測儀器的敏感度；若所得數值不適用，可用別的尺寸數值再代入重新求得新預測值，直到得到較適用的結果。本文將這些設計與研判過程以互動式畫面呈現，可迅速計算出設計構型的良窳，十分簡便。Nowadays, micro-accelerometer is widely integrated, in the devices used in our daily life, such as vehicles, mobile devices and smartosensory devices, as well as in some high-tech applications, such as aerospace technology and military weapons. Especially in the application of military aspects, the warhead of projectile must be sustainable to high impact so that it needs to install a high-G accelerometer to detect severe environment. With the development of the micro-electro-mechanical system (MEMS) in recent years, the reliability and measurement range of accelerometer has been improved. Various types of accelerometers, which could be operated up to 10,000 G or higher impacts, were developed successively. However, in the process of design an accelerometer chip, the sizes of devices, accuracy of manufacturing and cost must take into consideration. Different configurations of devices or manufacturing processes may lead to different requirements and restrictions in the design. As such, there is no simple and accurate way to predict the influence of the mechanical sizes of the device to the output signal of the sensor. We can only construct various models by computer aided design (CAD) software, then relay into computer aided engineering (CAE) software for simulation to find out the better design from the computational results. Nevertheless, it cost a lot of time. Consequently, this thesis exploited the geometry design of a high linearity and high-G microaccelerometer by correlating the CAE computational results of various geometrical sizes of the accelerometer structure and the output signals. Besides, this thesis also put the natural frequency of the structure and sensitivity of the sensor into consideration to establish a new design guideline for forecasting the output signal. This thesis referred to a piezoresistive accelerometer chip designed by Kuells, which composed of a flat-plate cantilever beam and four piezoresistors placed symmetrically on the central upside of the cantilever beam and perpendicularly to the beam. This structure deformed and vibrated in response to the applied impact. It could be modeled as a spring-mass system. However, the configuration of the beam had three fixed edges with suspended piezoresistors which had some difficulties to manufacture by MEMS processes. This thesis relaxed this restriction by releasing the lower longitudinal edge of the beam which could be realized by etching the trenches through the wafer. To investigate the influence of geometry on the performance of the accelerometer, this thesis implemented several models in different geometrical sizes. The cantilever beam had a length ranged from 350μm to 600μm, its depth ranged from 130μm to 500μm, and its width ranged from 12.5μm to 25μm; the piezoresistors had the length ranged from 10μm to 30μm, and the cross-sectional area ranged from 3μm2 to 24μm2. The stress responses of these models were numerically simulated subjected to a half-sine wave impact with various amplitudes and durations by the CAE software. The peak values of half-sine waves ranged from 5,000G to 100,000G with specific durations. To make the design process more simple and efficient, this thesis correlated the regression equations for the design parameters and the respondent average stresses of the piezoresistors firstly, and then converted the stresses into the output voltage signals based on the piezoresistive effect. After properly analyzing and regressing of the resultant data, this thesis successfully concluded two correlation equations for the rapid design of the flat-plate microaccelerometer. The first one describes the relationship between all size parameters and the output voltage signals; and the second one describes the relationship between the size parameters and the maximum respondent stress of the microstructure. Before manufacturing a similar structure of the accelerometer chip, one can put the requirements of sensing device, accuracy, cost into consideration; and then sketch primitive geometry sizes of the device and plug into these two equations. The maximum stress equation can be forecasted which dictates the safety of the structure during the impact. Subsequently, the magnitude of the output signal for sensing can be predicted by the output signal equation. If the forecasting value of the output signal is not fit for the sensitivity of the sensing device, one should change the design parameters and recalculate for a new design, until a satisfactory device is resulted. The design process is programmed in an interactive interface which facilitates the user to design an accelerometer quickly and easily.中文摘要 I Abstract III 目錄 V 表目錄 IX 圖目錄 XIII 符號表 XVII 第一章 緒論 1 1-1 前言 1 1-2 文獻回顧 2 1-3 研究動機與目的 4 1-4 本文架構 4 第二章 加速度感測晶片理論與衝擊規範 10 2-1 加速度感測器種類 10 2-1-1 壓電式(Piezoelectric) 10 2-1-2 壓阻式(Piezoresistive) 11 2-1-3 電容式(Capacitive) 11 2-1-4 本文採用之加速度感測晶片設計 11 2-2 壓阻式加速度感測晶片原理 12 2-2-1 彈簧與質量塊系統 12 2-2-3 惠斯通電橋感測原理 17 2-3 壓阻式加速度感測晶片設計方法 19 2-3-1 壓阻式加速感測晶片設計主要考量因素 19 2-3-2 壓阻器位置設計 19 2-3-3 質量塊系統設計 20 2-3-4 幾何常數計算 20 2-3-5 壓阻式加速感測晶片優值計算 21 2-4 MIL-STD 883E美軍衝擊規範簡介 22 2-5 決定係數(Coefficient of determination)R2簡介 22 第三章 數值模型建立與設定流程 28 3-1單位選定 28 3-2 建立數值模型 28 3-3 定義元素類型 29 3-4 材料參數設定 29 3-5 劃分網格 30 3-6 設定邊界條件 31 3-7 設定負載 31 3-8 數值分析求解 31 3-9 後處理器 32 3-10 失效判定 32 第四章 加速感測晶片設計參數方程式推導 41 4-1 設計參數定義與設計範圍 41 4-2 分析數值模擬計算結果之方法 43 4-2-1 輸出訊號推算 43 4-2-2 材料破壞判定 45 4-3 推導關係方程式 46 4-3-1 G值與壓阻器應力關係式 47 4-3-2 懸臂樑長度、厚度與壓阻器應力關係式 49 4-3-2-1 多項式近似 50 4-3-2-2非整數次方近似 53 4-3-3懸臂樑長度、深度與壓阻器應力關係式 57 4-3-4懸臂樑厚度、深度與壓阻器應力關係式 58 4-3-5懸臂樑各幾何參數與壓阻器應力關係式 60 4-3-6 壓阻器幾何參數與壓阻器應力關係式 64 4-3-7 各關係式合併 69 4-3-8 壓阻器平均應力關係式轉換為輸出訊號關係式 70 4-4 關係方程式討論 72 4-5 隨機抽樣驗證 74 4-6 互動界面設計 74 第五章 結論與未來展望 129 5-1結論 129 5-2 未來展望 130 參考文獻 1322230641 bytesapplication/pdf論文公開時間：2014/09/23論文使用權限：同意有償授權(權利金給回饋學校)加速感測晶片動態響應高G衝擊模擬互動設計thesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/264129/1/ntu-103-R01543017-1.pdf