本研究旨在將FBAR元件的設計過程加速，以節省時間和成本。目前設計FBAR的過程需要不斷調整參數並進行實作，而缺乏充分的理論計算支持使得這個過程非常耗時耗成本。為了解決這個問題，本研究結合聲波傳播方程式以及壓電方程式，推導出Mason model，然後將Mason模型使用程式語言C++進行程式化，利用電腦運算數學表達式並代入材料參數，快速計算FBAR的特性結果，並比對ADS模擬軟體的模擬結果，驗證出本研究之程式碼可精準模擬FBAR特性。首先，只考慮壓電層所帶來的影響，接著，增加上下電極並更改上下電極厚度，發現當厚度增加時諧振頻率下降，品質因數也隨之下降，最終，增加支撐層並更改支撐層厚度，同樣地，當支撐層厚度增加時諧振頻率以及品質因數下降。且本研究考慮了聲波損耗的影響，諧振頻率並不會因為黏滯係數逐漸增加而受影響，但諧振特性和品質因數會因為黏滯係數的增加而下降。本研究中還包括探討聲波在其他因素影響下可能產生的垂直C軸方向行進的雜散模態。透過整理相關的理論和公式，建立橫向模態分析的Mason模型，用以研究在縱向模態下所產產生的橫向剪切波對FBAR的影響，一般將其視為雜散模態，其結果顯示雜散模態之高次諧波可能出現在靠近縱向模態中的諧振頻率點附近，而雜散模態會在縱向模態的頻率響應中產生的雜散不規則性可能導致設備性能的惡化。本研究的成果將為FBAR技術的發展提供理論支持，並為實驗和實際應用提供更多的協助。

This research aims to expedite FBAR design, saving time and costs. It combines acoustic and piezoelectric equations to derive the Mason model, implemented in C++. Material parameters are used for rapid FBAR characteristic calculations, validated against ADS simulations. Thickness variations of the piezoelectric layer, top/bottom electrodes, and supporting layer impact resonance frequency and quality factor. Acoustic wave losses affect resonance characteristics and quality factor. The study investigates spurious modes, revealing their potential impact on longitudinal mode responses. The research provides theoretical support for FBAR technology advancement and practical applications.

[1] Wikipedia. "5G." https://en.wikipedia.org/w/index.php?title=5G&oldid=1158495464 (accessed 8 June 2023
[2] Y. Liu, Y. Cai, Y. Zhang, A. Tovstopyat, S. Liu, and C. Sun, "Materials, design, and characteristics of bulk acoustic wave resonator: A review," Micromachines, vol. 11, no. 7, p. 630, 2020.
[3] S. Mahon, "The 5G effect on RF filter technologies," IEEE Transactions on Semiconductor Manufacturing, vol. 30, no. 4, pp. 494-499, 2017.
[4] R. Aigner, "SAW and BAW technologies for RF filter applications: A review of the relative strengths and weaknesses," in 2008 IEEE Ultrasonics Symposium, 2008: IEEE, pp. 582-589.
[5] Y. Satoh, T. Nishihara, T. Yokoyama, M. Ueda, and T. Miyashita, "Development of piezoelectric thin film resonator and its impact on future wireless communication systems," Japanese journal of applied physics, vol. 44, no. 5R, p. 2883, 2005.
[6] S.-H. Lee, K. H. Yoon, and J.-K. Lee, "Influence of electrode configurations on the quality factor and piezoelectric coupling constant of solidly mounted bulk acoustic wave resonators," Journal of Applied Physics, vol. 92, no. 7, pp. 4062-4069, 2002.
[7] R. Ruby, "11E-2 review and comparison of bulk acoustic wave FBAR, SMR technology," in 2007 IEEE Ultrasonics Symposium Proceedings, 2007: IEEE, pp. 1029-1040.
[8] K. Leong and J. Mazierska, "Precise measurements of the Q factor of dielectric resonators in the transmission mode-accounting for noise, crosstalk, delay of uncalibrated lines, coupling loss, and coupling reactance," IEEE transactions on microwave theory and techniques, vol. 50, no. 9, pp. 2115-2127, 2002.
[9] R. Ruby, J. Larson, C. Feng, and S. Fazzio, "The effect of perimeter geometry on FBAR resonator electrical performance," in IEEE MTT-S International Microwave Symposium Digest, 2005., 2005: IEEE, pp. 217-220.
[10] K.-W. Tay, C.-L. Huang, and L. Wu, "Influence of piezoelectric film and electrode materials on film bulk acoustic-wave resonator characteristics," Japanese journal of applied physics, vol. 43, no. 3R, p. 1122, 2004.
[11] M. Link, "Study and realization of shear wave mode solidly mounted film bulk acoustic resonators (FBAR) made of c-axis inclined zinc oxide (ZnO) thin films: application as gravimetric sensors in liquid environments," Université Henri Poincaré-Nancy I, 2006.
[12] 張亞非 and 陳達, 薄膜體聲波諧振器的原理、設計與應用. 上海交通大學出版社, 2011.
[13] L. Xu, X. Wu, and Y. Zeng, "Simulation and Research of Piezoelectric Film Bulk Acoustic Resonator Based on Mason Model," presented at the The 6th International Conference on Integrated Circuits and Microsystems, 2021.
[14] K. M. Lakin, "Thin film resonators and filters," in 1999 IEEE Ultrasonics Symposium. Proceedings. International Symposium (Cat. No. 99CH37027), 1999, vol. 2: IEEE, pp. 895-906.
[15] Q.-X. Su, P. Kirby, E. Komuro, M. Imura, Q. Zhang, and R. Whatmore, "Thin-film bulk acoustic resonators and filters using ZnO and lead-zirconium-titanate thin films," IEEE Transactions on Microwave Theory and Techniques, vol. 49, no. 4, pp. 769-778, 2001.
[16] H. Campanella, "Tunable FBARs: Frequency tuning mechanisms," in The 40th European Microwave Conference, 2010: IEEE, pp. 795-798.
[17] S. Krishnaswamy, J. Rosenbaum, S. Horwitz, C. Vale, and R. Moore, "Film bulk acoustic wave resonator technology," in IEEE Symposium on Ultrasonics, 1990: IEEE, pp. 529-536.
[18] Y. Kumar, J. Singh, G. Kumari, R. Singh, and J. Akhtar, "Effect of shapes and electrode material on figure of merit (FOM) of BAW resonator," in AIP Conference Proceedings, 2016, vol. 1724, no. 1: AIP Publishing LLC, p. 020045.
[19] J. F. Rosenbaum, Bulk Acoustic Wave Theory and Devices. 685 Canton Street Norwood, MA 02062: ARTECH HOUSE, INC, 1988, p. 459.
[20] "Acoustic impedance," Lippincott Williams & Wilkins, 2009.
[21] Y. Kobayashi, N. Tanaka, H. Okano, K. Takeuchi, T. Usuki, and K. S. K. Shibata, "Characteristics of surface acoustic wave on AlN thin films," Japanese journal of applied physics, vol. 34, no. 5S, p. 2668, 1995.
[22] J. Sunday, "Systems Theory: An Approach to Mass-Damper-Spring and Mass-Nondamper-Spring Systems," General Letters in Mathematics (GLM), vol. 3, no. 3, 2017.
[23] W. P. Mason, "Phonon viscosity and its effect on acoustic wave attenuation and dislocation motion," The Journal of the Acoustical Society of America, vol. 32, no. 4, pp. 458-472, 1960.
[24] H. Zhang and E. S. Kim, "Micromachined acoustic resonant mass sensor," Journal of Microelectromechanical Systems, vol. 14, no. 4, pp. 699-706, 2005.
[25] W. Pang, H. Zhang, H. Yu, and E. S. Kim, "Analytical and experimental study on second harmonic response of FBAR for oscillator applications above 2GHz," in IEEE Ultrasonics Symposium, 2005., 2005, vol. 4: IEEE, pp. 2136-2139.
[26] P. Dineva et al., Piezoelectric materials. Springer, 2014.
[27] R. G. Polcawich and J. S. Pulskamp, "Additive processes for piezoelectric materials: Piezoelectric MEMS," MEMS materials and Processes Handbook, pp. 273-353, 2011.
[28] L. Qin, Q. Chen, H. Cheng, and Q.-M. Wang, "Analytical study of dual-mode thin film bulk acoustic resonators (FBARs) based on ZnO and AlN films with tilted c-axis orientation," IEEE transactions on ultrasonics, ferroelectrics, and frequency control, vol. 57, no. 8, pp. 1840-1853, 2010.
[29] Microwaves101. "Aluminum Nitride." https://www.microwaves101.com/encyclopedias/aluminum-nitride (accessed 7/7, 2023).
[30] D. A. Feld, R. Parker, R. Ruby, P. Bradley, and S. Dong, "After 60 years: A new formula for computing quality factor is warranted," in 2008 IEEE Ultrasonics Symposium, 2008: IEEE, pp. 431-436.
[31] D. Rosén, J. Bjurstrom, and I. Katardjiev, "Suppression of spurious lateral modes in thickness-excited FBAR resonators," IEEE transactions on ultrasonics, ferroelectrics, and frequency control, vol. 52, no. 7, pp. 1189-1192, 2005.