高階AT石英板與高頻壓電薄膜振盪器之設計模擬及實驗

A Theoretical and Experimental Study of Advanced AT-cut Quartz and Piezoelectric Thin Film Resonator

鮑世勇(Shih-Yung Pao)

指導教授 ： 張培仁

國立臺灣大學/工學院/應用力學研究所/博士(2009年)

https://doi.org/10.6342/NTU.2009.00800

摘要

頻率控制元件在各種電子電路中幾乎無所不在，從與個人生活息息相關的手錶、電腦、電視及近年迅速普及的手機、衛星定位系統(GPS)，到飛機、太空、武器系統等，振盪器所提供的精準訊號源均扮演極為重要的角色。在眾多種類的頻控元件中，由於AT石英的穩定度高，使得它成為在數百萬赫茲到數十百萬赫茲頻率範圍內，最重要的一種振盪器；但隨著各類電子產品小型化及功能日新月異的趨勢，對於更高穩定度與更高頻訊號源的需求十分迫切。本論文目的在建立一個創新、有效率並且夠準確的AT石英板振動理論與模擬方法，用於設計AT石英振盪器，以滿足高穩定度頻率源的應用。此外，本文亦研究高泛音體聲波壓電振盪器(High Over Tone Bulk Acoustic Resonators, HBARs) 的重要參數與設計準則，以提供高頻應用的一種解決方案。
本論文首先以R.D. Mindlin的二維石英板振動理論及P.C.Y. Lee建構的有限元素模型為基礎，利用石英弱機電耦合的特性，提出機械振動與壓電響應分離的理論與計算，發展具電極構造的小尺寸石英板理論及有限元素分析方法。此方法可有效率的對石英板振動進行計算與模擬，將原本以一般泛用有限元素軟體模擬需數週甚至數月的計算時間，縮短到數小時至數天即可完成，並且證明其有足夠的準確度可供高階AT石英振盪器開發之用。
在第二部分，利用所提出的理論與自行撰寫的有限元素程式，對AT石英振盪器進行設計開發與實驗。在此部份中，第一個實驗說明如何設計最佳的石英板及電極面尺寸避開模態耦合，進而解決振盪器溫度特性跳動的不穩定問題；第二個實驗則是驗證低頻圓邊晶片(beveled quartz plate)之圓邊量設計；第三個實驗是對石英振盪器的等效模型參數(包括串聯電阻、電容、電感及並聯電容)萃取；第四個實驗為以雙層階梯式電極達到能陷(energy trapping)效果，以解決小型化晶片圓邊製程不易的問題；第五個實驗則是計算晶片研磨加工之路徑，希望獲得更平坦的石英板表面，並探討製程中機械研磨之表面破壞層深度。
第三部份是以Z. Wang建立的共振頻譜法(resonant spectrum method)為基礎，研究高泛音薄膜體聲波壓電振盪器的電極效應及基材對振盪特性的影響。壓電薄膜振盪器的振盪頻率雖高，但受限於製程條件，壓電薄膜無法像單晶結構一樣有很高的Q值，若將壓電薄膜與兩層電極的三明治構造附著於高Q值的基材上，壓電薄膜以基頻，而基材(厚於壓電膜)以泛音模態振盪，如此可得到Q值遠高於僅單獨有壓電薄膜的振盪器，但是基材卻同時會對其他參數造成影響。在此部份中，我們模擬電極效應對各泛音頻率，以及基材對振盪器的Q值、機電耦合係數、電容比與等效電阻等的影響，適當的選擇基材厚度，進而設計適合應用端需求的。
綜言之，本論文提出一個新的、有效率並且夠準確的AT石英板設計模擬方法，可大幅縮短開發高精度AT石英振盪器的時程，此外亦對於石英振盪器的圓邊、研磨等重要製程進行相關的研究；另一方面，模擬高泛音薄膜體聲波壓電振盪器的重要特性參數，並且建立初步的設計準則，為高頻應用提供一可能的解決方案。

關鍵字

AT切割 ； 石英 ； 振盪器 ； 二維理論 ； 有限元素法 ； 薄膜振盪器

並列摘要

From watch, computer, television, cell phone and GPS(Global Positioning System) to automobile, aircraft and weapon system, quartz resonators are key components to provide a pure frequency source to the circuit. Because of the high stability of quartz, it becomes the most important resonator for a few MHz to tens of MHz frequency range. This dissertation addresses a new, efficient and accurate enough theory and simulation method to shorten the development time of high stable AT-cut quartz resonator. The second topic is the study on High over tone Bulk Acoustic Resonator (HBAR). The important parameters of HBAR are simulated as a design guide to provide a solution of high frequency application.
In the first part of this dissertation, based on Mindlin’s 2-D plate vibration theory and the finite element analysis built by Lee, a new theory and simulation model of quartz resonator is presented. This model covers the finite dimension, electrode, beveling, and mounting effects of AT-cut quartz chip plate, and electrical response under the excitation of upper and lower electrodes. On the other hands, using the weak coupling characteristic of quartz, the model deals with the mechanical vibration and electrical response separately that makes the calculation more efficient. To obtain the similar simulation results, it spends a few weeks to months by common commercial finite element analysis software, but only a few hours to days by the program of this research. It substantially shortens the development time of high-end AT-cut quartz resonator to meet the market requirement.
In the second part of this dissertation, there are five designs and experiments verified examples. The first one shows how to design the dimensions of quartz plate and electrodes to avoid the modes coupling and solve the frequency jump problem. The second example is about the beveling process design. The third example extracts the parameters (motional capacitance, resistance, inductance, and stationary capacitance) of the resonator. The forth one is using double layer electrodes (with different dimension) instead of beveled shape to trap the vibration energy. The final example is a study on the lapping process and micro-crack on the quartz chip surface.
In the third part of this dissertation, based on Wang’s direct method, the substrate and electrodes effects in HBAR are studied. Because of the process limitation, the Q-factor of piezoelectric film is hard as high as that of single crystal plate, like quartz. If we mount the sandwich structure (a piezoelectric film with two electrodes) on a high Q substrate, we can get a high Q HBAR. However, the substrate will lower coupling factor of the piezoelectric film and change the capacitance, and resistance, etc. In this part, several HBAR’s resonant characteristics with different kinds of piezoelectric film, electrodes and substrates are calculated. By these simulation results, a design guide of HBAR, e.g. the substrate thickness choosing, is presented.

並列關鍵字

AT-cut ； Quartz ； Resonator ； 2D theory ； FEM ； HBAR

參考文獻

[2] J.N. Reddy, An Introduction to the Finite Element Method, 2nd ed., McGraw-Hill, 1993, pp. 439–445.

[3] M.M. Driscoll, R.A. Jelen and N. Matthews, “Extremely low phase noise UHF oscillators utilizing high-overtone, Bulk acoustic resonators,” Proc. 1990 IEEE Ultrasonics Symposium, 1990, pp. 513-518.

[4] D.S. Balley, M.M. Driscoll, and R.A. Jelen, “Frequency stability of high-overtone Bulk acoustic resonators,” Proc. 1990 IEEE Ultrasonics Symposium, 1990, pp. 509-512

[5] J. Rosenbaum, H.L. Salvo, Jr., and S.V. Krishnaswamy, “Overtone Response of Composite Bulk Acoustic Resonators,” Proc. 40th (1986) Annual Frequency Control Symposium, 1986, pp. 206-210.

[6] H.L. Salvo, Jr. M. Gottlieb and B.R. McAvoy, “Shear Mode Transducers for High Overtone Bulk Resonators,” Proc. 41st (1987) Frequency Control Symposium, 1987, pp. 388-390.