Abstract
The dispersion curves of bulk waves propagating in both AlN and ZnO film bulk acoustic resonators (FBARs) are presented to illustrate the mode flip of the thickness-extensional (TE) and 2nd thickness-shear (TSh2) modes. The frequency spectrum quantitative prediction (FSQP) method is used to solve the frequency spectra for predicting the coupling strength among the eigen-modes in AlN and ZnO FBARs. The results elaborate that the flip of the TE and TSh2 branches results in novel self-coupling vibration between the small-wavenumber TE and large-wavenumber TE modes, which has never been observed in the ZnO FBAR. Besides, the mode flip leads to the change in the relative positions of the frequency spectral curves about the TE cut-off frequency. The obtained frequency spectra can be used to predict the mode-coupling behaviors of the vibration modes in the AlN FBAR. The conclusions drawn from the results can help to distinguish the desirable operation modes of the AlN FBAR with very weak coupling strength from all vibration modes.
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GRUDKOWSKI, T., BLACK, J., REEDER, T., CULLEN, D., and WAGNER, R. Fundamental-mode VHF/UHF minature acoustic resonators and filters on silicon. Applied Physics Letters, 37(11), 993–995 (1980)
LAKIN, K. and WANG, J. Acoustic bulk wave composite resonators. Applied Physics Letter, 38(3), 125–127 (1981)
NAKAMURA, K., SASAKI, H., and SHIMIZU, H. ZnO/SiO2-diaphragm composite resonator on a silicon wafer. Electronics Letters, 17(14), 507–509 (1981)
GILL, G. S. and PRASAD, M. Development of film bulk acoustic wave resonator: a review. Sensor Letters, 14(4), 346–361 (2016)
NAN, T. X., LIN, H., GAO, Y., MATYUSHOV, A., YU, G. L., CHEN, H. H., SUN, N., WEI, S. J., WANG, Z. G., LI, M. H., WANG, X. J., BELKESSAM, A., GUO, R. D., CHEN, B., ZHOU, J., QIAN, Z. Y., HUI, Y., RINALDI, M., MCCONNEY, M. E., HOWE, B. M., HU, Z. Q., JONES, J. G., BROWN, G. J., and SUN, N. X. Acoustically actuated ultra-compact NEMS magnetoelectric antennas. Nature Communications, 8, 296 (2017)
GAO, J. N., LIU, G. R., LI, J., and LI, G. Q. Recent developments of film bulk acoustic resonators. Functional Materials Letters, 9(3), 1630002 (2016)
MUJAHID, A., AFZAL, A., and DICKERT, F. L. An overview of high frequency acoustic sensors-QCMs, SAWs and FBARs-chemical and biochemical applications. Sensors, 19(20), 4395 (2019)
ZHANG, Y. and CHEN, D. Multilayer Integrated Film Bulk Acoustic Resonators, Springer Science & Business Media, Heidelberg, 5–12 (2012)
GONG, X., HAN, M., SHANG, X., XIONG, J., DUAN, J., and SEKIMOTO, H. Two-dimensional analysis of spurious modes in aluminum nitride film resonators. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 54(6), 1171–1176 (2007)
ZHU, F., QIAN, Z., and WANG, B. Wave propagation in piezoelectric layered structures of film bulk acoustic resonators. Ultrasonics, 67, 105–111 (2016)
LI, N., QIAN, Z., and YANG, J. Two-dimensional equations for piezoelectric thin-film acoustic wave resonators. International Journal of Solids and Structures, 110, 170–177 (2017)
HE, H., YANG, J., ZHANG, W., and WANG, J. Effects of mode coupling on the admittance of an at-cut quartz thickness-shear resonator. Chinese Physics B, 22(4), 047702 (2013)
LIU, B., JIANG, Q., HU, Y., and YANG, J. High-frequency vibrations of piezoelectric plates driven by lateral electric fields. International Journal of Engineering Science, 49(12), 1435–1442 (2011)
ZHAO, Z., PANG, X., QIAN, Z., KUZNETSOVA, I., MA, T., and YONG, Y. K. Lateral size-dependence in UHF mode-coupled ZnO FBARs to suppress undesirable eigenmodes and weaken mounting effect. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 67(8), 1647–1655 (2020)
LI, N., QIAN, Z., and YANG, J. Effects of aspect ratio on the mode couplings of thin-film bulk acoustic wave resonators. AIP Advances, 7(5), 055113 (2017)
LI, N., WANG, B., and QIAN, Z. Effects of mode couplings on the vibration characteristics of partially electroded thin-film bulk acoustic wave resonators. AIP Advances, 9(6), 065203 (2019)
LI, N., WANG, B., and QIAN, Z. Suppression of spurious lateral modes and undesired coupling modes in frame-like FBARs by 2-D theory. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 67(1), 180–190 (2019)
HUANG, H., LI, N., WANG, B., QIAN, Z., HUANG, B., MA, T., and KUZNETSOVA, I. Two-dimensional coupling vibration analysis of laterally acoustically coupled two-port thin-film bulk acoustic resonators. Acta Mechanica Solida Sinica, 33(4), 464–478 (2020)
ZHAO, Z., WANG, B., QIAN, Z., and YONG, Y. K. A novel approach to quantitative predictions of high-frequency coupled vibrations in layered piezoelectric plates. International Journal of Engineering Science, 157, 103407 (2020)
ZHAO, Z., WANG, B., ZHU, J., and QIAN, Z. Mode couplings in high-frequency thickness-extensional vibrations of ZnO thin film resonator based on weak boundary condition. International Journal of Mechanical Sciences, 148, 223–230 (2018)
ZHAO, Z. and CHEN, W. Investigation on high-frequency and mode-coupling vibrations in thickness-extensional piezoelectric thin-film resonators with initial stress. Applied Mathematical Modelling, 112, 78–90 (2022)
ZHAO, Z., WANG, B., QIAN, Z., KUZNETSOVA, I., MA, T., and YONG, Y. K. Design considerations for frequency shifts in a laterally finite FBAR sensor in contact with the newtonian liquid. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 67(11), 2402–2412 (2020)
RUBY, R. A snapshot in time: the future in filters for cell phones. IEEE Microwave Magazine, 16(7), 46–59 (2015)
LIU, Y., CAI, Y., ZHANG, Y., TOVSTOPYAT, A., LIU, S., and SUN, C. Materials, design, and characteristics of bulk acoustic wave resonator: a review. Micromachines, 11(7), 630 (2020)
ZHANG, Z., LIANG, J., ZHANG, D., PANG, W., and ZHANG, H. A novel bulk acoustic wave resonator for filters and sensors applications. Micromachines, 6(9), 1306–1316 (2015)
FATTINGER, G. G., MARKSTEINER, S., KAITILA, J., and AIGNER, R. Optimization of acoustic dispersion for high performance thin film BAW resonators. 2005 IEEE Ultrasonics Symposium, IEEE, Netherlands, 1175–1178 (2005)
HASHIMOTO, K. Y. RF Bulk Acoustic Wave Filters for Communications, Artech House, Boston, 67–70 (2009)
JOSE, S., HUETING, R., and JANSMAN, A. On the rule of thumb for flipping the dispersion relation in baw devices. 2011 IEEE International Ultrasonics Symposium, IEEE, Orlando, 1712–1715 (2011)
ZHU, F., WANG, B., and QIAN, Z. A numerical algorithm to solve multivariate transcendental equation sets in complex domain and its application in wave dispersion curve characterization. Acta Mechanica, 230, 1303–1321 (2019)
ZHU, F., QU, Y., and PAN, E. A new model for acoustic attenuation of GHz waveguide induced by metal electrodes in piezoelectric composites. International Journal of Mechanical Sciences, 231, 107564 (2022)
QIN, L., CHEN, Q., CHENG, H., CHEN, Q., LI, J. F., and WANG, Q. M. Viscosity sensor using ZnO and AlN thin film bulk acoustic resonators with tilted polar c-axis orientations. Journal of Applied Physics, 110, 094511 (2011)
AULD B. A. Acoustic Fields and Waves in Solids, John Wiley & Sons, New York, 357–382 (1973)
ZHAO, Z. and CHEN, W. Predictions of dynamic multimode-coupling and high-frequency vibrations in magneto-electro-elastic heterostructures. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 69(5), 1804–1814 (2022)
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This work was also partly supported by the specialized research projects of Huanjiang Laboratory, Zhuji, Zhejiang Province.
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Conflict of interest Weiqiu CHEN is an editorial board member for Applied Mathematics and Mechanics (English Edition) and was not involved in the editorial review or the decision to publish this article. The authors declare no conflict of interest.
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Project supported by the National Natural Science Foundation of China (Nos. 11872329, 12192211, and 12072315), the Natural Science Foundation of Zhejiang Province of China (No. LD21A020001), the National Postdoctoral Program for Innovation Talents of China (No. BX2021261), and the China Postdoctoral Science Foundation Funded Project (No. 2022M722745)
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Zhao, Z., Li, N., Qu, Y. et al. Novel mode-coupling vibrations of AlN thin film bulk acoustic resonator operating with thickness-extensional mode. Appl. Math. Mech.-Engl. Ed. 44, 2187–2206 (2023). https://doi.org/10.1007/s10483-023-3056-6
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DOI: https://doi.org/10.1007/s10483-023-3056-6
Key words
- AlN film
- mode flip
- frequency spectrum quantitative prediction (FSQP)
- dispersion curve
- mode-coupling vibration