{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T01:31:35Z","timestamp":1775698295984,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T00:00:00Z","timestamp":1608854400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2018YFB20020301"],"award-info":[{"award-number":["2018YFB20020301"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61901440"],"award-info":[{"award-number":["61901440"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004826","name":"Beijing Municipal Natural Science Foundation","doi-asserted-by":"publisher","award":["4202080"],"award-info":[{"award-number":["4202080"]}],"id":[{"id":"10.13039\/501100004826","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The piezoelectric cantilever resonator is used widely in many fields because of its perfect design, easy-to-control process, easy integration with the integrated circuit. The tip displacement and resonance frequency are two important characters of the piezoelectric cantilever resonator and many models are used to characterize them. However, these models are only suitable for the piezoelectric cantilever with the same width layers. To accurately characterize the piezoelectric cantilever resonators with different width layers, a novel model is proposed for predicting the tip displacement and resonance frequency. The results show that the model is in good agreement with the finite element method (FEM) simulation and experiment measurements, the tip displacement error is no more than 6%, the errors of the first, second, and third-order resonance frequency between theoretical values and measured results are 1.63%, 1.18%, and 0.51%, respectively. Finally, a discussion of the tip displacement of the piezoelectric cantilever resonator when the second layer is null, electrode, or silicon oxide (SiO2) is presented, and the utility of the model as a design tool for specifying the tip displacement and resonance frequency is demonstrated. Furthermore, this model can also be extended to characterize the piezoelectric cantilever with n-layer film or piezoelectric doubly clamped beam.<\/jats:p>","DOI":"10.3390\/s21010087","type":"journal-article","created":{"date-parts":[[2020,12,25]],"date-time":"2020-12-25T09:30:19Z","timestamp":1608888619000},"page":"87","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Modeling the Piezoelectric Cantilever Resonator with Different Width Layers"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5072-5937","authenticated-orcid":false,"given":"Zhenxi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences; Beijing 100049, China"},{"name":"State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0538-5520","authenticated-orcid":false,"given":"Jiamin","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences; Beijing 100049, China"},{"name":"State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5347-0124","authenticated-orcid":false,"given":"Xudong","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences; Beijing 100049, China"},{"name":"State Key Laboratory of Transducer Technology, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100010, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4839","DOI":"10.1063\/1.1633009","article-title":"Microcantilevers integrated with heaters and piezoelectric detectors for nano data-storage application","volume":"83","author":"Lee","year":"2003","journal-title":"Appl. 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