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CMOS-MEMS Test-Key for Extracting Wafer-Level Mechanical Properties
Department of Mechanical and Electro-Mechanical Engineering, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
Department of Mechanical and Electro-Mechanical Engineering, Center of Green Technology, National ILan University, ILan 260, Taiwan
Institute of Applied Mechanics, National Taiwan University, Taipei 10617, Taiwan
* Author to whom correspondence should be addressed.
Received: 25 October 2012; in revised form: 28 November 2012 / Accepted: 6 December 2012 / Published: 12 December 2012
Abstract: This paper develops the technologies of mechanical characterization of CMOS-MEMS devices, and presents a robust algorithm for extracting mechanical properties, such as Young’s 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’s 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’s modulus and mean stress of the test structures. The test cases include the test-key fabricated by a TSMC 0.18 μm standard CMOS process, and the experimental results refer to Osterberg’s 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.
Keywords: pull-in voltage; Young’s modulus; mean stress; CMOS-MEMS
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Chuang, W.-C.; Hu, Y.-C.; Chang, P.-Z. CMOS-MEMS Test-Key for Extracting Wafer-Level Mechanical Properties. Sensors 2012, 12, 17094-17111.
Chuang W-C, Hu Y-C, Chang P-Z. CMOS-MEMS Test-Key for Extracting Wafer-Level Mechanical Properties. Sensors. 2012; 12(12):17094-17111.
Chuang, Wan-Chun; Hu, Yuh-Chung; Chang, Pei-Zen. 2012. "CMOS-MEMS Test-Key for Extracting Wafer-Level Mechanical Properties." Sensors 12, no. 12: 17094-17111.