{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:36:42Z","timestamp":1760243802827,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2012,12,12]],"date-time":"2012-12-12T00:00:00Z","timestamp":1355270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper develops the technologies of mechanical characterization of CMOS-MEMS devices, and presents a robust algorithm for extracting mechanical properties, such as Young\u2019s modulus, and mean stress, through the external electrical circuit behavior of the micro test-key. An approximate analytical solution for the pull-in voltage of bridge-type test-key subjected to electrostatic load and initial stress is derived based on Euler\u2019s beam model and the minimum energy method. Then one can use the aforesaid closed form solution of the pull-in voltage to extract the Young\u2019s modulus and mean stress of the test structures. The test cases include the test-key fabricated by a TSMC 0.18 \u03bcm standard CMOS process, and the experimental results refer to Osterberg\u2019s work on the pull-in voltage of single crystal silicone microbridges. The extracted material properties calculated by the present algorithm are valid. Besides, this paper also analyzes the robustness of this algorithm regarding the dimension effects of test-keys. This mechanical properties extracting method is expected to be applicable to the wafer-level testing in micro-device manufacture and compatible with the wafer-level testing in IC industry since the test process is non-destructive.<\/jats:p>","DOI":"10.3390\/s121217094","type":"journal-article","created":{"date-parts":[[2012,12,12]],"date-time":"2012-12-12T11:02:13Z","timestamp":1355310133000},"page":"17094-17111","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["CMOS-MEMS Test-Key for Extracting Wafer-Level Mechanical Properties"],"prefix":"10.3390","volume":"12","author":[{"given":"Wan-Chun","family":"Chuang","sequence":"first","affiliation":[{"name":"Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University, Kaohsiung 80424, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuh-Chung","family":"Hu","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Electro-Mechanical Engineering, Center of Green Technology, National ILan University, ILan 260, 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":[[2012,12,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/S0924-4247(01)00740-3","article-title":"Vertical comb-finger capacitive actuation and sensing for CMOS-MEMS","volume":"95","author":"Xie","year":"2002","journal-title":"Sens. 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