{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T14:11:53Z","timestamp":1766067113956,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T00:00:00Z","timestamp":1582243200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Basic Research Program of China (973 Program)","award":["2017YFC0601603","2018YFC0603301"],"award-info":[{"award-number":["2017YFC0601603","2018YFC0603301"]}]},{"name":"Please fill out both funder and grant number.","award":["41874089"],"award-info":[{"award-number":["41874089"]}]},{"name":"the Natural Science Foundation of China","award":["61871439","41904157"],"award-info":[{"award-number":["61871439","41904157"]}]},{"name":"the China Postdoctoral Science Foundation Funded Project","award":["2019T120652"],"award-info":[{"award-number":["2019T120652"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Capacitive MEMS accelerometers with area-variable periodic-electrode displacement transducers found wide applications in disaster monitoring, resource exploration and inertial navigation. The bonding-induced warpage, due to the difference in the coefficients of thermal expansion of the bonded slices, has a negative influence on the precise control of the interelectrode spacing that is essential to the sensitivity of accelerometers. In this work, we propose the theory, simulation and experiment of a method that can alleviate both the stress and the warpage by applying different bonding temperature on the bonded slices. A quasi-zero warpage is achieved experimentally, proving the feasibility of the method. As a benefit of the flat surface, the spacing of the capacitive displacement transducer can be precisely controlled, improving the self-noise of the accelerometer to 6 ng\/\u221aHz @0.07 Hz, which is about two times lower than that of the accelerometer using a uniform-temperature bonding process.<\/jats:p>","DOI":"10.3390\/s20041186","type":"journal-article","created":{"date-parts":[[2020,2,21]],"date-time":"2020-02-21T10:49:16Z","timestamp":1582282156000},"page":"1186","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Temperature Gradient Method for Alleviating Bonding-Induced Warpage in a High-Precision Capacitive MEMS Accelerometer"],"prefix":"10.3390","volume":"20","author":[{"given":"Dandan","family":"Liu","sequence":"first","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physic, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0757-2362","authenticated-orcid":false,"given":"Huafeng","family":"Liu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physic, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Jinquan","family":"Liu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physic, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3804-0740","authenticated-orcid":false,"given":"Fangjing","family":"Hu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physic, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"given":"Ji","family":"Fan","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physic, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Institute of Geophysics and PGMF, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5079-3641","authenticated-orcid":false,"given":"Wenjie","family":"Wu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physic, Huazhong University of Science and Technology, Wuhan 430074, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1014-9784","authenticated-orcid":false,"given":"Liangcheng","family":"Tu","sequence":"additional","affiliation":[{"name":"MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physic, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Institute of Geophysics and PGMF, Huazhong University of Science and Technology, Wuhan 430074, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1038\/nature17397","article-title":"Measurement of the Earth tides with a MEMS gravimeter","volume":"531","author":"Middlemiss","year":"2016","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wu, W.J., Li, Z., Liu, J.Q., Fan, J., and Tu, L.C. 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