{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T05:45:22Z","timestamp":1775454322716,"version":"3.50.1"},"reference-count":13,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2015,10,28]],"date-time":"2015-10-28T00:00:00Z","timestamp":1445990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Micromachines"],"abstract":"<jats:p>Movable suspended microstructures are the common feature of sensors or devices in the fields of Complementary-Metal-Oxide-Semiconductors and Micro-Electro-Mechanical Systems which are usually abbreviated as CMOS-MEMS. To suspend the microstructures, it is commonly to etch the sacrificial layer under the microstructure layer. For large-area microstructures, it is necessary to design a large number of etching holes on the microstructure to enhance the etchant uniformly and rapidly permeate into the sacrificial layer. This paper aims at evaluating the fringe capacitance caused by etching holes on microstructures and developing empirical formulas. The formula of capacitance compensation term is derived by curve-fitting on the simulation results by the commercial software ANSYS. Compared with the ANSYS simulation, the deviation of the present formula is within \u00b15%. The application to determine the capacitance of an electrostatic micro-beam with etching holes is demonstrated in a microstructure experiment, which agrees very well with the experimental data, and the maximum deviation is within \u00b18%. The present formula is with simple form, wide application range, high accuracy, and easy to use. It is expected to provide the micro-device designers to estimate the capacitance of microstructures with etching holes and predominate in the device characteristics.<\/jats:p>","DOI":"10.3390\/mi6111445","type":"journal-article","created":{"date-parts":[[2015,10,28]],"date-time":"2015-10-28T13:43:01Z","timestamp":1446039781000},"page":"1617-1628","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["The Fringe-Capacitance of Etching Holes for CMOS-MEMS"],"prefix":"10.3390","volume":"6","author":[{"given":"Yi-Ta","family":"Wang","sequence":"first","affiliation":[{"name":"Department of Mechanical and Electromechanical Engineering, National ILan University, ILan 26041, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuh-Chung","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Electromechanical Engineering, National ILan University, ILan 26041, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen-Chang","family":"Chu","sequence":"additional","affiliation":[{"name":"Institute of Applied Mechanics, National Taiwan University, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pei-Zen","family":"Chang","sequence":"additional","affiliation":[{"name":"Institute of Applied Mechanics, National Taiwan University, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,10,28]]},"reference":[{"key":"ref_1","unstructured":"Rabinovich, V.L., Gupta, R.K., and Senturia, S.D. (1997, January 16\u201319). The effect of release-etch holes on the electromechanical behaviour of MEMS structures. Proceedings of the International Conference on Solid State Sensors and Actuators, Chicago, IL, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2637","DOI":"10.1109\/20.951259","article-title":"Modeling the effect of etch holes on ferromagnetic MEMS","volume":"37","author":"Fang","year":"2001","journal-title":"IEEE Trans. Magn."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Elshurafa, A.M., and El-Masry, E.I. (2006, January 27\u201329). Effects of etching holes on capacitance and tuning range in MEMS parallel plate variable capacitors. Proceedings of the 6th International Workshop on System-on-Chip for Real-Time Applications, Cairo, Egypt.","DOI":"10.1109\/IWSOC.2006.348240"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Elshurafa, A.M., and El-Masry, E.I. (2007, January 5\u20138). Design considerations in MEMS parallel plate variable capacitors. Proceedings of the 50th Midwest Symposium on Circuits and Systems, Montreal, QC, Canada.","DOI":"10.1109\/MWSCAS.2007.4488764"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bendali, A., Labedan, R., Domingue, F., and Nerguizian, V. (2006, January 7\u201310). Holes effects on RF MEMS parallel membranes capacitors. Proceedings of the Canadian Conference on Electrical and Computer Engineering, Ottawa, ON, Canada.","DOI":"10.1109\/CCECE.2006.277600"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1080\/00207217.2010.488911","article-title":"Effect of etch holes on the capacitance and pull-in voltage in MEMS tunable capacitors","volume":"97","author":"Fang","year":"2010","journal-title":"Int. J. 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Proceedings of the 13th International Congress on Mesomechanics, Vicenza, Italy."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1177\/1045389X12449917","article-title":"Effects of etching holes on complementary metal oxide semiconductor-microelectromechanical systems capacitive structure","volume":"24","author":"Tu","year":"2012","journal-title":"J. Intell. Mater. Syst. Struct."}],"container-title":["Micromachines"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-666X\/6\/11\/1445\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:51:05Z","timestamp":1760215865000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-666X\/6\/11\/1445"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,28]]},"references-count":13,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2015,11]]}},"alternative-id":["mi6111445"],"URL":"https:\/\/doi.org\/10.3390\/mi6111445","relation":{},"ISSN":["2072-666X"],"issn-type":[{"value":"2072-666X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,28]]}}}