{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T11:18:09Z","timestamp":1768735089082,"version":"3.49.0"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2015,12,3]],"date-time":"2015-12-03T00:00:00Z","timestamp":1449100800000},"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>This paper describes the design and experimental evaluation of a silicon micro-machined resonant accelerometer (SMRA). This type of accelerometer works on the principle that a proof mass under acceleration applies force to two double-ended tuning fork (DETF) resonators, and the frequency output of two DETFs exhibits a differential shift. The dies of an SMRA are fabricated using silicon-on-insulator (SOI) processing and wafer-level vacuum packaging. This research aims to design a high-sensitivity SMRA because a high sensitivity allows for the acceleration signal to be easily demodulated by frequency counting techniques and decreases the noise level. This study applies the energy-consumed concept and the Nelder-Mead algorithm in the SMRA to address the design issues and further increase its sensitivity. Using this novel method, the sensitivity of the SMRA has been increased by 66.1%, which attributes to both the re-designed DETF and the reduced energy loss on the micro-lever. The results of both the closed-form and finite-element analyses are described and are in agreement with one another. A resonant frequency of approximately 22 kHz, a frequency sensitivity of over 250 Hz per g, a one-hour bias stability of 55 \u03bcg, a bias repeatability (1\u03c3) of 48 \u03bcg and the bias-instability of 4.8 \u03bcg have been achieved.<\/jats:p>","DOI":"10.3390\/s151229803","type":"journal-article","created":{"date-parts":[[2015,12,3]],"date-time":"2015-12-03T11:12:09Z","timestamp":1449141129000},"page":"30293-30310","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["Microelectromechanical Resonant Accelerometer Designed with a High Sensitivity"],"prefix":"10.3390","volume":"15","author":[{"given":"Jing","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Yan","family":"Su","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"Qin","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]},{"given":"An-Ping","family":"Qiu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China"}]}],"member":"1968","published-online":{"date-parts":[[2015,12,3]]},"reference":[{"key":"ref_1","unstructured":"Marek, J., and G\u00f3mez, U.M. (2012). Chips A Guide to the Future of Nanoelectronics the Frontiers Collection, Springer-Verlag."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1109\/JMEMS.2002.805207","article-title":"A vacuum packaged surface micromachined resonant accelerometer","volume":"11","author":"Seshia","year":"2002","journal-title":"J. Microelectromech. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1140","DOI":"10.1109\/JMEMS.2010.2067437","article-title":"A resonant microaccelerometer with high sensitivity operating in an oscillating circuit","volume":"19","author":"Comi","year":"2010","journal-title":"J. Microelectromech. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.proche.2009.07.134","article-title":"A small and high sensitivity resonant accelerometer","volume":"1","author":"Pinto","year":"2009","journal-title":"Procedia Chem."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/j.sna.2013.03.031","article-title":"Phase noise analysis of micromechanical silicon resonant accelerometer","volume":"197","author":"Shi","year":"2013","journal-title":"Sens. Actuators A Phys."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1088\/0960-1317\/15\/2\/013","article-title":"A cmos-compatible high aspect ratio silicon-on-glass in-plane micro-accelerometer","volume":"15","author":"Chae","year":"2005","journal-title":"J. Micromech. Microeng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1088\/0960-1317\/17\/6\/015","article-title":"A silicon micromachined high-shock accelerometer with a bonded hinge structure","volume":"17","author":"Fan","year":"2007","journal-title":"J. Micromech. Microeng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1016\/j.sna.2008.03.017","article-title":"In-plane mems-based nano-g accelerometer with sub-wavelength optical resonant sensor","volume":"145","author":"Krishnamoorthy","year":"2008","journal-title":"Sens. Actuators A Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"768","DOI":"10.1109\/JMEMS.2014.2319196","article-title":"A seismic-grade resonant mems accelerometer","volume":"23","author":"Zou","year":"2014","journal-title":"J. Microelectromech. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zou, X., Thiruvenkatanathan, P., and Seshia, A.A. (2012, January 21\u201324). Micro-electro-mechanical resonant tilt sensor. Proceedings of the 2012 IEEE International Frequency Control Symposium (FCS), Baltimore, MD, USA.","DOI":"10.1109\/FCS.2012.6243702"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.1109\/JSEN.2005.857876","article-title":"A resonant accelerometer with two-stage microleverage mechanisms fabricated by soi-mems technology","volume":"5","author":"Su","year":"2005","journal-title":"IEEE Sens. J."},{"key":"ref_12","unstructured":"Xia, G.-M., Qiu, A.-P., Shi, Q., and Su, Y. (2013, January 3\u20136). Test and evaluation of a silicon resonant accelerometer implemented in soi technology. Proceedings of the 2013 IEEE Sensors, Baltimore, MD, USA."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Dong, J.-H., Qiu, A.-P., and Shi, R. (2011, January 8\u20139). Temperature influence mechanism of micromechanical silicon oscillating accelerometer. Proceedings of the 2011 IEEE Power Engineering And Automation Conference (PEAM), Wuhan, China.","DOI":"10.1109\/PEAM.2011.6135118"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"805","DOI":"10.3788\/OPE.20111904.0805","article-title":"Application of microlever to micromechanical silicon resonant accelerometers","volume":"19","author":"Shi","year":"2011","journal-title":"Opt. Precis. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1137\/S1052623496303470","article-title":"Convergence properties of the Nelder-Mead simplex method in low dimensions","volume":"9","author":"Lagarias","year":"1998","journal-title":"SIAM J. Optim."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1093\/comjnl\/7.4.308","article-title":"A simplex method for function minimization","volume":"7","author":"Nelder","year":"1965","journal-title":"Comput. J."},{"key":"ref_17","unstructured":"Brosnihan, T.J., Bustillo, J.M., Pisano, A.P., and Howe, R.T. (1997, January 16\u201319). Embedded interconnect and electrical isolation for high-aspect-ratio, soi inertial instruments. Proceedings of the 1977 Internatonal Conference Solid State Sensors and Actuators, Transducers \u201997, Chicago, IL, USA."},{"key":"ref_18","unstructured":"Torunbalci, M.M., Alper, S.E., and Akin, T. (2014, January 25\u201326). Wafer level hermetic encapsulation of mems inertial sensors using soi cap wafers with vertical feedthroughs. Proceedings of the 2014 International Symposium on Inertial Sensors and Systems (ISISS), Laguna Beach, CA, USA."},{"key":"ref_19","unstructured":"Renard, S. (2000). Micromachining and Microfabrication, International Society for Optics and Photonics."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Lin, C.-W., Hsu, C.-P., Yang, H.-A., Wang, W.C., and Fang, W. (2008). Implementation of silicon-on-glass mems devices with embedded through-wafer silicon vias using the glass reflow process for wafer-level packaging and 3D chip integration. J. Micromech. Microeng., 18.","DOI":"10.1088\/0960-1317\/18\/2\/025018"},{"key":"ref_21","unstructured":"Harris, C.M., Piersol, A.G., and Paez, T.L. (2002). Harris\u2019 Shock and Vibration Handbook, McGraw-Hill New York."},{"key":"ref_22","unstructured":"Roessig, T.-A.W. (1998). Integrated Mems Tuning Fork Oscillators for Sensor Applications, University of California."},{"key":"ref_23","unstructured":"IEEE (1999). IEEE Standards Association."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1109\/T-UFFC.1987.26997","article-title":"Time and frequency (time-domain) characterization, estimation, and prediction of precision clocks and oscillators","volume":"34","author":"Allan","year":"1987","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_25","unstructured":"Lefort, O., Jaud, S., Quer, R., and Milesi, A. (2012, January 18\u201319). Inertial grade silicon vibrating beam accelerometer. Proceedings of Inertial Sensors and Systems 2012, Karlsruhe, Germany."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1480","DOI":"10.1109\/JSSC.2008.923616","article-title":"A cmos readout circuit for soi resonant accelerometer with 4-bias stability and 20-resolution","volume":"43","author":"He","year":"2008","journal-title":"Solid-State Circuits, IEEE J."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Argyris, J.H., and Kelsey, S. (1960). Energy Theorems and Structural Analysis, Springer.","DOI":"10.1007\/978-1-4899-5850-1"},{"key":"ref_28","unstructured":"Iyer, S.V. (2003). Modeling and Simulation of Non-Idealities in a Z-Axis Cmos-Mems Gyroscope. [Ph.D. Thesis, Carnegie Mellon University]."},{"key":"ref_29","unstructured":"Timoshenko, S., Woinowsky-Krieger, S., and Woinowsky-Krieger, S. (1959). Theory of Plates and Shells, McGraw-hill New York."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/12\/29803\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:53:20Z","timestamp":1760216000000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/12\/29803"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,3]]},"references-count":29,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2015,12]]}},"alternative-id":["s151229803"],"URL":"https:\/\/doi.org\/10.3390\/s151229803","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12,3]]}}}