{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T16:17:40Z","timestamp":1781194660306,"version":"3.54.1"},"reference-count":27,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2019,10,14]],"date-time":"2019-10-14T00:00:00Z","timestamp":1571011200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61674043"],"award-info":[{"award-number":["61674043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper presents three-dimensional (3D) models of high-frequency piezoelectric micromachined ultrasonic transducers (PMUTs) based on the finite element method (FEM). These models are verified with fabricated aluminum nitride (AlN)-based PMUT arrays. The 3D numerical model consists of a sandwiched piezoelectric structure, a silicon passive layer, and a silicon substrate with a cavity. Two types of parameters are simulated with periodic boundary conditions: (1) the resonant frequencies and mode shapes of PMUT, and (2) the electrical impedance and acoustic field of PMUT loaded with air and water. The resonant frequencies and mode shapes of an electrically connected PMUT array are obtained with a laser Doppler vibrometer (LDV). The first resonant frequency difference between 3D FEM simulation and the measurement for a 16-MHz PMUT is reasonably within 6%, which is just one-third of that between the analytical method and the measurement. The electrical impedance of the PMUT array measured in air and water is consistent with the simulation results. The 3D model is suitable for predicting electrical and acoustic performance and, thus, optimizing the structure of high-frequency PMUTs. It also has good potential to analyze the transmission and reception performances of a PMUT array for future compact ultrasonic systems.<\/jats:p>","DOI":"10.3390\/s19204450","type":"journal-article","created":{"date-parts":[[2019,10,14]],"date-time":"2019-10-14T12:14:05Z","timestamp":1571055245000},"page":"4450","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":37,"title":["3D FEM Analysis of High-Frequency AlN-Based PMUT Arrays on Cavity SOI"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3820-4570","authenticated-orcid":false,"given":"Wenjuan","family":"Liu","sequence":"first","affiliation":[{"name":"State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 201203, China"},{"name":"Universit\u00e9 Polytechnique Hauts-de-France, CNRS, Universit\u00e9 Lille, ISEN. Centrale Lille, UMR 8520\u2013IEMN\u2014Institut d\u2019\u00c9lectronique de Micro\u00e9lectronique et de Nanotechnologie, DOAE\u2014D\u00e9partement d\u2019Opto-Acousto- \u00c9lectronique, F-59313 Valenciennes CEDEX 9, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4131-3508","authenticated-orcid":false,"given":"Leming","family":"He","sequence":"additional","affiliation":[{"name":"State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 201203, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xubo","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 201203, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jia","family":"Zhou","sequence":"additional","affiliation":[{"name":"State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 201203, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7309-2343","authenticated-orcid":false,"given":"Weijiang","family":"Xu","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Polytechnique Hauts-de-France, CNRS, Universit\u00e9 Lille, ISEN. Centrale Lille, UMR 8520\u2013IEMN\u2014Institut d\u2019\u00c9lectronique de Micro\u00e9lectronique et de Nanotechnologie, DOAE\u2014D\u00e9partement d\u2019Opto-Acousto- \u00c9lectronique, F-59313 Valenciennes CEDEX 9, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nikolay","family":"Smagin","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Polytechnique Hauts-de-France, CNRS, Universit\u00e9 Lille, ISEN. Centrale Lille, UMR 8520\u2013IEMN\u2014Institut d\u2019\u00c9lectronique de Micro\u00e9lectronique et de Nanotechnologie, DOAE\u2014D\u00e9partement d\u2019Opto-Acousto- \u00c9lectronique, F-59313 Valenciennes CEDEX 9, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Malika","family":"Toubal","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Polytechnique Hauts-de-France, CNRS, Universit\u00e9 Lille, ISEN. Centrale Lille, UMR 8520\u2013IEMN\u2014Institut d\u2019\u00c9lectronique de Micro\u00e9lectronique et de Nanotechnologie, DOAE\u2014D\u00e9partement d\u2019Opto-Acousto- \u00c9lectronique, F-59313 Valenciennes CEDEX 9, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hao","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuandong","family":"Gu","sequence":"additional","affiliation":[{"name":"Institute of Microelectronics, Agency for Science, Technology and Research (A*STAR), Singapore 138634, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinghui","family":"Xu","sequence":"additional","affiliation":[{"name":"Institute of Microelectronics, Agency for Science, Technology and Research (A*STAR), Singapore 138634, Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Denis","family":"Remiens","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Polytechnique Hauts-de-France, CNRS, Universit\u00e9 Lille, ISEN. Centrale Lille, UMR 8520\u2013IEMN\u2014Institut d\u2019\u00c9lectronique de Micro\u00e9lectronique et de Nanotechnologie, DOAE\u2014D\u00e9partement d\u2019Opto-Acousto- \u00c9lectronique, F-59313 Valenciennes CEDEX 9, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Junyan","family":"Ren","sequence":"additional","affiliation":[{"name":"State Key Laboratory of ASIC and System, School of Microelectronics, Fudan University, Shanghai 201203, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1109\/TBME.1983.325150","article-title":"Ultrasound Transducers for Pulse-Echo Medical Imaging","volume":"BME-30","author":"Hunt","year":"1983","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_2","unstructured":"Silk, M.G. (1984). 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