{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:14:17Z","timestamp":1760235257478,"version":"build-2065373602"},"reference-count":68,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2021,8,2]],"date-time":"2021-08-02T00:00:00Z","timestamp":1627862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this study, an accurate analytic semi-linear elliptic differential model for a circular membrane MEMS device, which considers the effect of the fringing field on the membrane curvature recovering, is presented. A novel algebraic condition, related to the membrane electromechanical properties, able to govern the uniqueness of the solution, is also demonstrated. Numerical results for the membrane profile, obtained by using the Shooting techniques, the Keller\u2013Box scheme, and the III\/IV Stage Lobatto IIIa formulas, have been carried out, and their performances have been compared. The convergence conditions, and the possible presence of ghost solutions, have been evaluated and discussed. Finally, a practical criterion for choosing the membrane material as a function of the MEMS specific application is presented.<\/jats:p>","DOI":"10.3390\/s21155237","type":"journal-article","created":{"date-parts":[[2021,8,4]],"date-time":"2021-08-04T02:16:07Z","timestamp":1628043367000},"page":"5237","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["A Semi-Linear Elliptic Model for a Circular Membrane MEMS Device Considering the Effect of the Fringing Field"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3837-6671","authenticated-orcid":false,"given":"Mario","family":"Versaci","sequence":"first","affiliation":[{"name":"DICEAM Department, \u201cMediterranea\u201d University, I-89122 Reggio Calabria, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6469-9517","authenticated-orcid":false,"given":"Alessandra","family":"Jannelli","sequence":"additional","affiliation":[{"name":"MIFT Department, University of Messina, I-98166 Messina, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0734-9136","authenticated-orcid":false,"given":"Francesco Carlo","family":"Morabito","sequence":"additional","affiliation":[{"name":"DICEAM Department, \u201cMediterranea\u201d University, I-89122 Reggio Calabria, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3153-9338","authenticated-orcid":false,"given":"Giovanni","family":"Angiulli","sequence":"additional","affiliation":[{"name":"DIIES Department, \u201cMediterranea\u201d University, I-89122 Reggio Calabria, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Pelesko, J.A., and Bernstein, D.H. 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