×

Effects of surface impedance on current density in a piezoelectric resonator for impedance distribution sensing. (English) Zbl 1480.74152

Summary: We study the relationship between the surface mechanical load represented by distributed acoustic impedance and the current density distribution in a shear mode piezoelectric plate acoustic wave resonator. A theoretical analysis based on the theory of piezoelectricity and trigonometric series is performed. In the specific and basic case when the surface load is due to a local mass layer, numerical results show that the current density concentrates under the mass layer and is sensitive to the physical as well as geometric parameters of the mass layer such as its location and size. This provides the theoretical foundation for predicting the surface impedance pattern from the current density distribution, which is fundamental to the relevant acoustic wave sensors.

MSC:

74J05 Linear waves in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
78A55 Technical applications of optics and electromagnetic theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bottom, V. E., Introduction to Quartz Crystal Unit Design (1982), New York: Van Nostrand Reinhold, New York
[2] Salt, D., Hy-Q Handbook of Quartz Crystal Devices (1987), Berkshire: Van Nostrand Reinhold, Berkshire
[3] Lakin, K. M., A review of thin-film resonator technology, IEEE Microwave Magazine, 4, 2, 61-67 (2003)
[4] Tiersten, H. F., Linear Piezoelectric Plate Vibrations (1969), New York: Plenum, New York
[5] Campbell, C. K., Surface Acoustic Wave Devices for Mobile and Wireless Communications (1998), Orlando: Academic Press, Orlando
[6] Hashimoto, K. Y., Surface Acoustic Wave Devices in Telecommunications (2000), Berlin: Springer, Berlin · Zbl 0952.76001
[7] Sauerbrey, G., Verwendung von schwingquarzen zur wägung dünner schichten und zur mikrowägung, Ztschrift Für Physik, 155, 2, 206-222 (1959)
[8] Kanazawa, K. K.; Gordon Ii, J. G., The oscillation frequency of a quartz resonator in contact with a fluid, Analytica Chimica Acta, 175, 99-105 (1985)
[9] Reed, C. E.; Kanazawa, K. K.; Kaufman, J. H., Physical description of a viscoelastically loaded AT-cut quartz resonator, Journal of Applied Physics, 68, 5, 1993-2001 (1990)
[10] Martin, S. J.; Granstaff, V. E.; Frye, G. C., Characterization of a quartz crystal microbalance with simultaneous mass and liquid loading, Analytical Chemistry, 63, 20, 2272-2281 (1991)
[11] Duncan-Hewitt, W. C.; Thompson, M., Four-layer theory for the acoustic shear wave sensor in liquids incorporating interface slip and liquid structure, Analytical Chemistry, 64, 1, 94-105 (1992)
[12] Jing, Y.; Chen, J.; Chen, X.; Gong, X., Frequency shift of thickness-shear vibrations of AT-cut quartz resonators due to a liquid layer with the electrode stiffness considered, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 54, 7, 1290-1292 (2007)
[13] Link, M.; Schreiter, M.; Weber, J.; Primig, R.; Pitzer, D.; Gabl, R., Solidly mounted ZnO shear mode film bulk acoustic wave resonators for sensing applications in liquids, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 53, 2, 492-496 (2006)
[14] Fu, Y. Q.; Luo, J. K.; Du, X. Y.; Flewitt, A. J.; Li, Y.; Markx, G. H.; Walton, A. J.; Milne, W. I., Recent developments on ZnO films for acoustic wave based bio-sensing and microfluidic applications: a review, Sensors & Actuators B: Chemical, 143, 2, 606-619 (2010)
[15] Zhang, Y.; Bao, Y., Sensitivity analysis of multi-layered C-axis inclined zigzag zinc oxide thin-film resonators as viscosity sensors, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 61, 3, 525-534 (2014)
[16] Liu, J.; Du, J. K.; Wang, J.; Yang, J. S., Thin film bulk acoustic wave piezoelectric resonators with circular ring driving electrodes for mass sensing, Integrated Ferroelectrics, 192, 1, 57-66 (2018)
[17] Cumpson, P. J.; Seah, M. P., The quartz crystal microbalances; radial/polar dependence of mass sensitivity both on and off the electrodes, Measurement Science & Technology, 1, 7, 544-555 (1990)
[18] Tatsuma, T.; Watanabe, Y.; Oyama, N., Multichannel quartz crystal microbalances, Analytical Chemistry, 71, 17, 3632-3636 (1999)
[19] Shen, F.; Lu, P., Influence of interchannel spacing on the dynamical properties of multichannel quartz crystal microbalance, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 50, 6, 668-675 (2003)
[20] Liu, N.; Yang, J. S.; Wang, J.; Kosinski, J. A., Analysis of a monolithic, nonperiodic array of quartz crystal microbalances, Japanese Journal of Applied Physics, 52, 7, 77301 (2013)
[21] Tiersten, H. F., Perturbation theory for linear electroelastic equations for small fields superposed on a bias, The Journal of the Acoustical Society of America, 64, 3, 832-837 (1978) · Zbl 0383.73086
[22] Lu, Y. P.; Tang, H. Y.; Fang, S.; Wang, Q., Ultrasonic fingerprint sensor using a piezoelectric micromachined ultrasonic transducer array integrated with complementary metal oxide semiconductor electronics, Applied Physics Letters, 106, 263503 (2015)
[23] Park, H.; Roh, Y., Design of ultrasonic fingerprint sensor made of 1-3 piezocomposites by finite element method, Japanese Journal of Applied Physics, 56, 1, 07JD06 (2017)
[24] Bicz, W.; Gumienny, Z.; Pluta, M., Ultrasonic sensor for fingerprints recognition, Proceedings of SPIE — The International Society for Optics and Photonics, 2634, 104-111 (1995)
[25] Choi, W. Y.; Kang, K. C.; Park, K. K., Ultrasonic fingerprint sensor in underglass prototype using impedance mismatching, Journal of Mechanical Science and Technology, 34, 2, 1-9 (2020)
[26] Fung, S.; Lu, Y.; Tang, H. Y.; Tsai, J. M.; Daneman, M.; Boser, B. E.; Horsley, D. A., Theory and experimental analysis of scratch resistant coating for ultrasonic fingerprint sensors, 2015 IEEE International Ultrasonics Symposium (2015), Taipei: IEEE, Taipei
[27] Jiang, X. Y.; Tang, H. Y.; Lu, Y.; Ng, E. J.; Tsai, J. M.; Boser, B. E.; Horsley, D. A., Ultrasonic fingerprint sensor with transmit beam forming based on a PMUT array bonded to CMOS circuitry, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 64, 9, 1401-1408 (2017)
[28] Schmitt, R. M.; Zeichman, J.; Casanova, A. C.; Delong, D., Model based development of a commercial, acoustic fingerprint sensor, 2012 IEEE International Ultrasonics Symposium (2012), Dresden: IEEE, Dresden
[29] Tang, H. Y.; Lu, Y.; Jiang, X.; Ng, E. J.; Tsai, J. M.; Horsley, D. A.; Boser, B. E., 3-D ultrasonic fingerprint sensor-on-a-chip, IEEE Journal of Solid-State Circuits, 51, 11, 2522-2533 (2016)
[30] Bleustein, J. L., A new surface wave in piezoelectric materials, Applied Physics Letters, 13, 12, 412-413 (1968)
[31] Yang, J. S.; Chen, Z. G.; Hu, Y. T., Vibration of a thickness-twist mode piezoelectric resonator with asymmetric, non-uniform electrodes, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 55, 4, 841-848 (2008)
[32] Yang, J. S., Antiplane Motions of Piezoceramics and Acoustic Wave Devices (2010), Singapore: World Scientific, Singapore · Zbl 1194.74001
[33] Tiersten, H. F., Wave propagation in an infinite piezoelectric plate, Journal of the Acoustical Society of America, 35, 234-239 (1963)
[34] Yang, J. S., Vibration of Piezoelectric Crystal Plates (2013), Singapore: World Scientific, Singapore
[35] Tiersten, H. F.; Stevens, D. S., An analysis of thickness-extensional trapped energy resonant device structures with rectangular electrodes in the piezoelectric thin film on silicon configuration, Journal of Applied Physics, 54, 10, 5893-5910 (1983)
[36] Zhao, Z. N.; Qian, Z. H.; Wang, B.; Yang, J. S., Energy trapping of thickness-extensional modes in thin film bulk acoustic wave resonators, Journal of Mechanical Science and Technology, 29, 7, 2767-2673 (2015)
[37] Zhao, Z. N.; Qian, Z. H.; Wang, B., Energy trapping of thickness-extensional modes in thin film bulk acoustic wave filters, AIP Advances, 6, 1, 993-995 (2016)
[38] Zhao, Z. N.; Qian, Z. H.; Wang, B., Vibration optimization of ZnO thin film bulk acoustic resonator with ring electrodes, AIP Advances, 6, 4, 1735-1739 (2016)
[39] Yang, J. S.; Zhou, H. G.; Zhang, W. P., Thickness-shear vibration of rotated Y-cut quartz plates with relatively thick electrodes of unequal thickness, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 52, 5, 918-922 (2005)
[40] Du, J. K.; Xian, K.; Wang, J.; Yang, J. S., Thickness vibration of piezoelectric plates of 6 mm crystals with tilted six-fold axis and two-layered thick electrodes, Ultrasonics, 49, 2, 149-152 (2009)
[41] Auld, B. A., Acoustic Fields and Waves in Solids (1973), New York: John Wiley and Sons, New York
[42] Kumar, Y.; Rangra, K.; Agarwal, R., Design and simulation of FBAR for quality factor enhancement, MAPAN-Journal of Metrology Society of India, 32, 113-119 (2017)
[43] Khine, L.; Wong, L. Y L.; Soon, J. B W.; Tsai, J. M., FBAR resonators with sufficient high Q for RF filter implementation, Advanced Materials Research, 254, 70-73 (2011)
[44] Tay, K. W.; Huang, C. L.; Wu, L., Highly c-axis oriented thin AlN films deposited on gold seed layer for FBAR devices, Journal of Vacuum Science & Technology B, 23, 4, 1474-1479 (2005)
[45] Yang, C. M.; Uehara, K.; Kim, S. K.; Kameda, S., Highly c-axis-oriented AlN film using Mocvd for 5 Ghz-band Fbar filter, 2003 IEEE Ultrasonics Symposium Proceedings, 171-173 (2003), New York: IEEE, New York
[46] Wingqvist, G.; Yantchev, V.; Katardjiev, I., Mass sensitivity of multilayer thin film resonant BAW sensors, Sensors & Actuators A: Physical, 148, 1, 88-95 (2008)
[47] Zhou, C. J.; Yang, Y.; Shy, Y.; Cai, H. L.; Ren, T. L.; Chan, M.; Zhou, J.; Jin, H.; Dong, S. R.; Yang, C. Y., Visible-light photoresponse of AlN-based film bulk acoustic wave resonator, Applied Physics Letters, 102, 19, 1-3 (2013)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.