本文是利用一四道光罩之微機電壓電製程，成功設計且製造一應用於測距儀之包含多埠的鋯鈦酸鉛微機電壓電超聲波傳感器。包括機械、電氣和聲學領域在內的理論建模已得到充分研究，並整合為設計的等效電路模型。為了產生較大的輸出聲壓，微機電壓電超聲波傳感器必需操作在較大的驅動電壓下，而元件的非線性行為可能會影響聲壓的輸出效率，因此元件的非線性問題不容忽視。
在非線性的研究中，本文提出了同時結合電訊號量測以及光學機械位移訊號的量測的方法，進行了一系列的非線性現象的驗證與探討。其中包含了透過參量效應產生的非線性能量轉移，進而激發在全頻譜上的機械共振模態；除此之外，在驅動訊號的大電壓操作下，我們也透過光學量測儀器觀測到了在特定的頻率範圍內，會因為非線性的模態耦合產生特殊的非線性機械旋轉運動；而在持續增加電壓使元件操作在更不穩定區域時，我們甚至能夠透過閉迴路起振的方式，在特定的起振範圍中，觀測到自我產生頻率梳的非線性特性。而這些非線性的響應皆限制了驅動訊號的操作範圍，進而導致聲壓的輸出效率變低。
為了克服這些缺點，本文提供了一個非線性行為模型來模擬微機電壓電超聲波傳感器的非線性暫態響應。除此之外，為了抑制非線性暫態響應並減少量測距離時的衰盪時間，本文提出了一個方法，透過針對驅動波形進行了優化結合窗形函數，藉此提升最小感測距離的範圍。此項技術顯示了一種簡單有效的方法，可以減少元件的衰盪時間並抑制由非線性引起的輸出干擾，從而有利於微機電壓電超聲波傳感器的軸向分辨率以及訊號分辨率，其效果特別顯著於短距離的量測驗證中。
最後通過同樣的製程方法，本文也成功設計且製造了用於接收端的氮化鋁微機電壓電超聲波傳感器來提升測距儀之感測度，結合了商用測試電路開發版實現了中長距離的量測驗證以及類比訊號解調，藉此降低量測產生的誤差。不僅是通過優化驅動波形改善了短距離量測的瓶頸，而且通過脈衝回波的操作方式，驗證了中長距離的量測。透過此系統與本文所開發的技術，成功設計與實現了測距儀之應用。

In the future topology of AIoT, physical transducers play an important role to combine the analog signal from environment with interface circuits. Therefore, high-performance transducers are required to be explored in recent years. The piezoelectric transducer has a significant seat on market share and is predicted to keep continuously growing. Based on these demands, piezoelectric transducers for ultrasound applications become the most attractive and promising target.
In this work, a multi-port PZT-based PMUT has been successfully demonstrated in a 4-mask piezoelectric fabrication process. The theoretical modeling including mechanical, electrical, and acoustic domains has been fully studied and integrated as an equivalent circuit model for design. Since the PMUT needs to operate under a large driving force, it leads to the nonlinearity of MEMS devices that cannot be ignored. The strong nonlinearity might affect acoustic radiation efficiency. For nonlinearity characterization, we present the details of the energy transfer path during parametric resonance over a wide frequency span. Apart from this phenomenon, a time-dependent nonlinear rotating nodal line of the piezoelectric resonant transducer caused by the nonlinear mode coupling is also observed in LDV. Moreover, if we pump more energy into the nonlinear resonant transducer, the frequency combs can be generated before the device goes into a chaotic state.
The nonlinear effects limit the performance of PMUT both in the transmitting and receiving nodes. To overcome these drawbacks, we provide a nonlinear behavior model to mimic the nonlinear transient response in this work. We also provide a modification of the driving waveform to suppress the nonlinear transient response and reduce the ring-down time during distance characterization. This technique shows a simple and effective method for reducing the membrane ring-down time and suppressing the output interferences caused by nonlinearity to benefit axial resolution for piezoelectric micromachined ultrasonic transducers, especially in short-distance characterization. In this work, a prototype of the rangefinder realized by the proposed PMUTs and the evaluation board has been demonstrated. Not only the short distance has been verified through the modification of the driving waveform, but also the long distance has been characterized through the pulse-echo system. Therefore, the technology developed in this work is expected to pave a way for range-finding applications.

[1] Yole Développement, “Piezoelectric Devices: From Bulk to Thin-Film 2019 report,” http://www.yole.fr, July 2019.
[2] R. C. Ruby, P. Bradley, Y. Oshmyansky, A. Chien and J. D. Larson, “Thin film bulk wave acoustic resonators (FBAR) for wireless applications,” Proc. IEEE Ultrason. Symp., pp. 813-821, 2001.
[3] H. Yu, W. Pang, H. Zhang, and E. S. Kim, “Film bulk acoustic resonator at 4.4 GHz with ultra low temperature coefficient of resonant frequency,” Tech. Dig. 18th IEEE Int. MEMS Conf., pp. 28-31, 2005.
[4] P. V. Wright, “A review of SAW resonator filter technology,” Proc. IEEE Ultrason. Symp., pp. 29-38, 1992.
[5] E. Berkenpas, S. Bitla, P. Millard and M. P. da Cunha, “Pure shear horizontal SAW biosensor on langasite,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 51, no. 11, pp. 1404-1411, 2004.
[6] M. Moriyama, K. Totsu and S. Tanaka, “Sol-gel deposition and characterization of lead zirconate titanate thin film using different commercial sols,” Sensors and Materials, vol. 31, no. 8, pp. 2497-2509, 2019.
[7] I. O. Wygant, X. Zhuang, D. T. Yeh, O. Oralkan, A. S. Ergun, M. Karaman, et al., “Integration of 2D CMUT arrays with front-end electronics for volumetric ultrasound imaging,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 55, no. 2, pp. 327-342, 2008.
[8] D. M. Mills, “Medical imaging with capacitive micromachined ultrasound transducer (cMUT) arrays,” IEEE Ultrasonics Symp., vol. 1, pp. 384-390, 2004.
[9] T. Holscher et al., “Effects of varying duty cycle and pulse width on high-intensity focused ultrasound (HIFU)-induced transcranial thrombolysis,” J. Ther. Ultrasound, vol. 1, no. 1, pp. 18, 2013.
[10] S.H. Wong et al., “Advantages of capacitive micromachined ultrasonics transducers (CMUTs) for high intensity focused ultrasound (HIFU),” IEEE Ultrasonics Symposium, pp. 1313-1316, 2007.
[11] H.-Y. Tang et al., “3-D ultrasonic fingerprint sensor-on-a-chip,” IEEE J. Solid-State Circuits, vol. 51, no. 11, pp. 2522-2533, 2016.
[12] X. Jiang, B. E. Boser, and D. A. Horsley et al., “Monolithic ultrasound fingerprint sensor,” Microsystems & Nanoengineering, vol.3, no.17059, 2017.
[13] Yole Développement, “Ultrasound Sensing Technologies 2020 report,” http://www.yole.fr, Nov. 2020.
[14] Y. Lu, A. Heidari, S. Shelton, A. Guedes and D. A. Horsley, "High frequency piezoelectric micromachined ultrasonic transducer array for intravascular ultrasound imaging", Proc. IEEE 27th Int. Conf. MEMS, pp. 745-748, 2014.
[15] J. Wang, Z. Zheng, J. Chan and J. T. W. Yeow, “Capacitive micromachined ultrasound transducers for intravascular ultrasound imaging,” Microsyst. Nanoeng., vol. 6, no. 1, pp. 73, 2020.
[16] B. W. Drinkwater and P.D. Wilcox, “Ultrasonic arrays for non-destructive evaluation: A review,” NDT&E Int., vol. 39, pp. 525-541, 2006.
[17] K. K. Shung and M. Zipparo, “Ultrasonic transducers and arrays,” IEEE Eng. Med. Biol. Mag., vol. 15, pp. 20-30, 1996.
[18] D. E. Dausch et al., “In vivo real-time 3-D intracardiac echo using PMUT arrays,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr., vol. 61, pp.1754-1764, 2014.
[19] Y. Qiu, et al., “Piezoelectric micromachined ultrasound transducer (PMUT) arrays for integrated sensing, actuation and imaging,” Sensors, vol. 15, no.4, pp. 8020-8041, 2015.
[20] F. Sammoura, et al., “A two-port piezoelectric micromachined ultrasonic transducer,” 2014 Joint IEEE International Symposium on the Applications of Ferroelectric, International Workshop on Acoustic Transduction Materials and Devices & Workshop on Piezoresponse Force Microscopy, pp. 1-4, 2014.
[21] S. Akhbari, et al., “Bimorph Piezoelectric Micromachined Ultrasonic Transducers,” IEEE/ASME J. Microelectromech. Syst., vol. 25, no. 2, pp. 326-336, 2016.
[22] S. Shelton et al., “CMOS-compatible AlN piezoelectric micromachined ultrasonic transducers,” Proceedings, IEEE International Ultrasonics Symposium, pp. 402-405, 2009.
[23] R. Przybyla, et al., “A micromechanical ultrasonic distance sensor with >1 meter range,” Tech. Dig., 16th International Solid-State Sensors, Actuators and Microsystems Conference, pp.2070-2073, 2011.
[24] G. Perçin, et al., “Micromachined two-dimensional array piezoelectrically actuated transducers,” Applied physics letters, Vol. 72, no. 11, pp. 1397-1399, 1998.
[25] P. Muralt, et al., “Piezoelectric micromachined ultrasonic transducers based on PZT thin films,” IEEE Trans. Ultrason. Ferroelect. Freq. Contr., vol. 52, no. 12, pp. 2276-2288, 2005.
[26] G.-H. Feng and G.-Y. Chu, “A curvature self-detectable 3D arc-shaped IPMC/PVDF transducer with acoustic beam generation and tunable focal range abilities,” Tech. Dig., 17th Int. Conf. on Solid-State Sensors & Actuators (Transducers’13), 16-20, pp. 790-793, 2015.
[27] Q. Nguyen, et al., “Paper-based ZnO nanogenerator using contact electrification and piezoelectric effects,” IEEE/ASME J. Microelectromech. Syst., vol. 24, no. 3 pp. 519-521, 2015.
[28] M. F. M. Sabri, et al., “Fabrication and Characterization of Microstacked PZT Actuator for MEMS Applications,” IEEE/ASME J. Microelectromech. Syst., vol. 24, no. 1 pp. 80-90, 2015.
[29] S. Senturia, Microsystem Design. Springer, 2000.
[30] J. N. Reddy, Theory and Analysis of Elastic Plates and Shells. vol. 1, Taylor and Francis, 2007.
[31] D. T. Blackstock, Fundamentals of Physical Acoustics. Wiley, 2000.
[32] S. E. Shelton, “Piezoelectric Micromachined Ultrasound Transducers for Air-coupled Applications,” Ph.D. Dissertation, University of California, Davis, 2014.
[33] C.-S. Li, et al., “Multimode characteristics of high-frequency CMOS-MEMS resonators,” Proceedings, 2014 Joint Conf. of the IEEE Int. Frequency Control Symp., pp. 478-480, 2014.
[34] A. A. Trusov, et al., “The effect of high order non-linearities on sub-harmonic excitation with parallel plate capacitive actuators,” ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 923-931, 2007.
[35] M. Mathieu, “Memoire sur le mouvement vibratoire d’une membrane de forme elliptique,” J. Math. Pures Appl. Vol. 13, pp.137–203, 1868.
[36] Y. Kusano, et al., “Effects of DC bias tuning on air-coupled PZT piezoelectric micromachined ultrasonic transducers,” IEEE/ASME J. Microelectromech. Syst., vol. 27, no. 2, pp. 296-304, 2018.
[37] Y. Kusano, et al., “Wideband air-coupled PZT piezoelectric micromachined ultrasonic transducer through DC bias tuning,” Proc. IEEE 30th Int. Conf. MEMS, pp. 950-953, 2017.
[38] M.-G. Suh, et al., “Microresonator soliton dual-comb spectroscopy,” Science, vol. 354, pp. 600–603, 2016.
[39] G. Pillai and S.-S. Li, “Controllable multichannel acousto-optic modulator and frequency synthesizer enabled by nonlinear MEMS resonator,” Sci. Rep., vol. 11, 10898, 2021.
[40] C. Acar, et al., “Environmentally robust MEMS vibratory gyroscopes for automotive application,” IEEE Sensors Journal, vol. 9, pp. 1895-1906, 2009.
[41] K. Lien, et al., “Microfluidic systems integrated with a sample pretreatment device for fast nucleic-acid amplification,” IEEE/ASME J. Microelectromech. Syst., vol. 17, no. 2, pp. 288-301, 2008.
[42] R. d. A. P. Andrade, et al., “A nanometer resolution wearable wireless medical device for non invasive intracranial pressure monitoring,” IEEE Sensors Journal, vol. 21, pp. 22270-22284, 2021.
[43] T. J. Kippenberg, et al., “Microresonator-based optical frequency combs,” Science, vol. 332, pp. 555–559, 2011.
[44] B. K. McFarland, et al., “High harmonic generation from multiple orbitals in N2,” Science, vol. 322, pp. 1232–1235, 2008.
[45] P. Parra-Rivas, et al., “Frequency comb generation through the locking of domain walls in doubly resonant dispersive optical parametric oscillators.” Opt. Lett., vol. 44, pp. 2004–2007, 2019.
[46] G. Sobreviela et al., “Parametric noise reduction in a high-order nonlinear MEMS resonator utilizing its bifurcation points,” IEEE/ASME J. Microelectromech. Syst., vol. 26, no. 26, pp. 1189-1195, 2017.
[47] Junhui Hu and A. K. Santoso, “A pi-shaped ultrasonic tweezers concept for manipulation of small particles,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control. Vol. 51, no. 11, pp. 1499-1507, 2004.
[48] M. A. Rahman, et al., “Cooperative micromanipulation using the independent actuation of fifty microrobots in parallel,” Sci Rep., vol. 7, 3278, 2017.
[49] P. M. Polunin, et al., “Characterization of MEMS resonator nonlinearities using the ringdown response,” IEEE/ASME J. Microelectromech. Syst., vol. 25, no.2, pp. 297-303, 2016.
[50] C.-Y. Liu, G. Pillai, and S.-S. Li, “Exploring the parametric energy transfer in a multi-mode piezoelectric resonator with nonlinear harmonic,” Proc. IEEE 33th Int. Conf. MEMS, pp. 1187-1190, 2020.
[51] A. Sarrafan, et al., “A nonlinear rate microsensor utilising internal resonance,” Sci Rep., vol. 9, 8648, 2019.
[52] S. Perisanu, et al., “Beyond the linear and Duffing regimes in nanomechanics: circularly polarized mechanical resonances of nanocantilevers,” Phy. Rev. B, vol. 81, 165440, 2010.
[53] P. L. Yu, and S. A. Bhave, “Circularly polarized mechanical resonances,” 2018 Solid State Sensor, Actuator and Microsystems Workshop (Hilton Head), 2018.
[54] S. Tin, et al., “Experimental verification and characterization of sub-harmonic traveling wave on an ultrasonic micromotor,” Proceedings, IEEE International Ultrasonics Symposium, pp. 1841-1844, 2010.
[55] D. A. Stepanenko, andV. T. Minchenya, “Development and study of novel non-contact ultrasonic motor based on principle of structural asymmetry,” Ultrasonics vol. 52, no. 7, pp. 866-872, 2012.
[56] YASUDA, et al., “Multi-mode response of a square membrane: vibration, control engineering, engineering for industry,” JSME international journal, vol. 30, pp. 963-969, 1987.
[57] T. A. Nayfeh, et al., “Subharmonic travelling waves in a geometrically non-linear circular plate,” International journal of non-linear mechanics, vol. 29, pp. 233-245, 1994.
[58] A. F. Vakakis, “Dynamics of a nonlinear periodic structure with cyclic symmetry,” Acta Mech., vol. 95, pp. 197-226, 1992.
[59] T. A. Nayfeh, et al., Linear and nonlinear structural mechanics. John Wiley & Sons (2008).
[60] R. Wang, et al., “Effect of Zn content on corrosion resistance of as-cast Al-6Si-3Cu alloy,” Mater. Lett., vol. 312, 131658, 2022.
[61] S. Kocer, et al., “Resonant varifocal mems mirror,” Proc. IEEE 33th Int. Conf. MEMS, pp. 963-966, 2022.
[62] Q. Shi, et al., “Investigation of geometric design in piezoelectric microelectromechanical systems diaphragms for ultrasonic energy harvesting,” Appl. Phys. Lett., vol. 108, 193902, 2016.
[63] E. Cuche, et al., “One-shot analysis,” Nature Photon, vol. 3, pp. 633–635, 2009.
[64] Li, J., Crivoi, et al., “Three dimensional acoustic tweezers with vortex streaming,” Commun. Phys., vol. 4, no.1, 113, 2021.
[65] A. Marzo, et al., Holographic acoustic elements for manipulation of levitated objects. Nat. Commun., vol. 6, 8661, 2015.
[66] T. Fortier et al., “20 years of developments in optical frequency comb technology and applications,” Commun. Phys., vol. 2, no. 1, pp. 1-16, 2019.
[67] M. Park et al., “Formation, evolution, and tuning of frequency combs in microelectromechanical resonators,” IEEE/ASME J Microelectromech Syst., vol. 28, no. 3, pp. 429-431, 2019.
[68] Z. Qi et al., “Existence conditions for phononic frequency combs,” Appl. Phys. Lett., vol. 117, no. 18, 2020.
[69] X. Wang et al., “Frequency comb in 1:3 internal resonance of coupled micromechanical resonators,” Appl. Phys. Lett., vol. 120, no. 17, 2022.