層合壓電板的高頻振動(dòng)分析
High frequency vibrations analysis of layered piezoelectric plates
薄膜體聲波諧振器(FBAR)具有工作頻率高、工藝簡(jiǎn)單、尺寸小、易于集成
等優(yōu)點(diǎn)，成為目前應(yīng)用與高頻通信前置濾波器的首選。典型的壓電頻控器件如石英晶
體諧振器和較為新穎的薄膜體聲波諧振器(FBAR)等都是典型的多層結(jié)構(gòu)，其頻率計(jì)
算方法在這些器件設(shè)計(jì)中有著重要意義。除了基于層狀結(jié)構(gòu)精確分析的頻率計(jì)算方法
外，在附加層厚度如電極等遠(yuǎn)小于基體時(shí)，我們也可以用近似方法。這方面我們已經(jīng)
作過(guò)研究，取得了較好的結(jié)果。現(xiàn)在將把早期在表面波方面的結(jié)果擴(kuò)展到在厚度拉伸
模態(tài)振動(dòng)的層合結(jié)構(gòu)。首先假設(shè)出無(wú)薄膜時(shí)基體的振動(dòng)位移模式，算得振動(dòng)頻率，再
算出不同薄膜厚度對(duì)于振動(dòng)頻率的影響，得出多層結(jié)構(gòu)在厚度拉伸模態(tài)時(shí)振動(dòng)頻率計(jì)
算的精確方法。
關(guān)鍵詞：壓電;石英晶體;諧振器; FBAR;薄膜;電極
Abstract: Film bulk acoustic resonators (FBAR) having the merits of high operating
frequency, simple craft, small size, easy to integrate, become the first choice of filters for high frequency communications. The typical piezoelectric components for frequency control like quartz crystal resonators and the more novel film bulk acoustic resonators are typical layered plates. The method of predicting the vibration frequency has the vital significance in the design of these components. Based on the frequency computational method of layered plates, we may also use the approximate method when the thin film thickness like electrode is smaller than that of substrates. In this case, we already have obtained good results. Now we will expand early results in the surface acoustic waves to the layered plates vibrating in the thickness-stretch mode. First we assume the vibration pattern of substrate when there is no thin film attached and calculate the vibration frequency. Then we study the influence of different film thickness on vibration frequency. Finally we obtain the precise computational solutions of layered plates’ vibration frequency when it is in the thickness-stretch mode. .
Keywords: piezoelectricity; quartz crystal; resonator; FBAR; film; electrode
第一章 序論 ６
1.1 畢業(yè)論文的背景、意義.. ６
1.2 畢業(yè)論文所作的工作 ６
第二章 彈性板的基本理論.. ８
2.1 基本理論介紹 ８
2.1.1 彈性力學(xué)理論.. ８
2.1.2 位移模式 ９
第三章 無(wú)薄膜時(shí)基體的自由振動(dòng).. １１
3.1 無(wú)限大板的自由振動(dòng)的解.. １１
第四章 基體上覆蓋有一層薄膜時(shí)的自由振動(dòng). １３
4.1 基體上覆蓋有一層薄膜時(shí)自由振動(dòng)的解.. １３
4.2 算例.... １７
第五章 基體上覆蓋有兩層薄膜時(shí)的自由振動(dòng) ２０
5.1 基體上覆蓋有兩層薄膜時(shí)自由振動(dòng)的解.. ２０
5.2 算例.. ２５
5.2.1 固定第二層薄膜厚度. .... ２５
5.2.2 固定第一層薄膜厚度. .... ２８
第六章 基體上覆蓋有三層薄膜時(shí)的自由振動(dòng).. ３１
6.1 基體上覆蓋有三層薄膜時(shí)自由振動(dòng)的解.... ３１
第七章 基體上覆蓋有多層薄膜時(shí)的自由振動(dòng) ３９
7.1 基體上覆蓋有多層薄膜時(shí)自由振動(dòng)的解.... ３９
第八章 結(jié)論與展望. ４１
8.1 結(jié)論.... ４１
8.2 展望.... ４３
參考文獻(xiàn). ４４
致 謝. ４５
附 錄 ４６
附錄1：畢業(yè)論文電子材料刻錄光盤(pán).. ４６
附錄2：彈性薄板振動(dòng)數(shù)學(xué)理論介紹.. ４６