Login Register Cart 0
Generic placeholder image

Recent Patents on Engineering

Editor-in-Chief

ISSN (Print): 1872-2121
ISSN (Online): 2212-4047

Back
Journal Home About Journal Editorial Board Journal Insight Current Issue Volumes/Issues
Subscribe
Letter Article

Boundary Conditions Analysis of Circular Capacitive Micromachined Ultrasonic Transducer (CMUT) Devices

Author(s): Jiujiang Wang, Yuanyu Yu*, Jiangming Kuang, Shuang Zhang, Jing Xu and Xin Liu

Volume 15, Issue 3, 2021

Published on: 01 January, 2021

Page: [287 - 293] Pages: 7

DOI: 10.2174/1872212115999210101124611

Price: $65

Abstract

Background: Capacitive Micromachined Ultrasonic Transducer (CMUT) is a new type of ultrasound transducer that has gained much research interest in ultrasound imaging because of its wider bandwidth, higher receiving sensitivity, and is more likely to be integrated with an integrated circuit (IC). The analytical solution is intuitive, fast, and convergent among simulation methods. The membrane deflection is important to the CMUT performance. The deformation of a circular CMUT under an external force can be described by von Kármán equations.

Objective: To find suitable boundary conditions that are crucial for the governing equations to be properly solved to get the analytical solutions for membrane deformation.

Methods: Features of two commonly used CMUT fabrication methods, Sacrificial Release method (SR) and Wafer Bonding (WB) method, are introduced. The force and moment equilibrium conditions of the supporting post are analyzed to get the boundary condition equations.

Results: The analytical results match well with the Finite Element Method (FEM) results for the fixed boundary condition while there are still some differences for the elastic boundary condition.

Conclusion: The boundary conditions for SR fabricated devices are elastic support while the boundary conditions for WB fabricated devices are fixed.

Keywords: CMUT, analytical solution, elastic support boundary condition (BC), fixed BC, governing equations, fabrication method.

Graphical Abstract

[1]
I. Ladabaum, X. Jin, H.T. Soh, A. Atalar, and B.T. Khuri-Yakub, "Surface micromachined capacitive ultrasonic transducers", IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 45, no. 3, pp. 678-690, 1998.
[http://dx.doi.org/10.1109/58.677612] [PMID: 18244219]
[2]
Z. Zheng, S. Na, A.I-H. Chen, Z. Li, L.L.P. Wong, Z. Sun, Y. Yao, P. Liu, and J.T.W. Yeow, "Development of a Novel CMUT-Based Concentric Dual-Element Ultrasonic Transducer: Design, Fabrication, and Characterization", J. Microelectromech. Syst., vol. 27, no. 3, pp. 538-546, 2018.
[http://dx.doi.org/10.1109/JMEMS.2018.2828423]
[3]
Y. Yu, J. Wang, S.H. Pun, C-H. Cheng, K.F. Lei, M.I. Vai, S. Zhang, and P.U. Mak, "Fabrication of embossed capacitive micromachined ultrasonic transducers using sacrificial release process", IEICE Electron. Express, vol. 16, no. 2, pp. 1-11, 2018.
[4]
J. Wang, S.H. Pun, P.U. Mak, C-H. Cheng, Y. Yu, P-I. Mak, and M.I. Vai, "Improved Analytical Modeling of Membrane Large Deflection With Lateral Force for the Underwater CMUT Based on Von Kármán Equations", IEEE Sens. J., vol. 16, no. 17, pp. 6633-6640, 2016.
[http://dx.doi.org/10.1109/JSEN.2016.2586969]
[5]
A. Ergun, G. Yaralioglu, and B. Khuri-Yakub, "Capacitive Micromachined Ultrasonic Transducers: Theory and Technology", J. Aerosp. Eng., vol. 16, no. 2, pp. 76-84, 2003.
[http://dx.doi.org/10.1061/(ASCE)0893-1321(2003)16:2(76)]
[6]
E. Ventsel, and T. Krauthammer, Thin Plates and Shells: Theory: Analysis, and Applications., CRC Press: Boca Raton, FL, USA, 2001.
[http://dx.doi.org/10.1201/9780203908723]
[7]
W. Zhang, H. Zhang, S. Jin, and Z. Zeng, "An Analytical Model for CMUTs with Square Multilayer Membranes Using the Ritz Method", Micromachines (Basel), vol. 7, no. 4, pp. 1-20, 2016.
[http://dx.doi.org/10.3390/mi7040055] [PMID: 30407428]
[8]
B. Bayram, E. Haeggström, G.G. Yaralioglu, and B.T. Khuri-Yakub, "A new regime for operating capacitive micromachined ultrasonic transducers", IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 50, no. 9, pp. 1184-1190, 2003.
[http://dx.doi.org/10.1109/TUFFC.2003.1235329] [PMID: 14561034]
[9]
S. Olcum, F.Y. Yamaner, A. Bozkurt, and A. Atalar, "Deep-collapse operation of capacitive micromachined ultrasonic transducers", IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 58, no. 11, pp. 2475-2483, 2011.
[http://dx.doi.org/10.1109/TUFFC.2011.2104] [PMID: 22083780]
[10]
R. Mukhiya, K. Aditi, M. Prabakar, J. Raghuramaiah, R. Jayapandian, V.K. Khanna Gopal, and Shekhar C., "Fabrication of Capacitive Micromachined Ultrasonic Transducer Arrays With Isolation Trenches Using AnodicWafer Bonding", IEEE Sens. J., vol. 15, no. 9, pp. 5177-5184, 2015.
[http://dx.doi.org/10.1109/JSEN.2015.2437394]
[11]
M. Engholm, A. Tweedie, J. Jensen, G. Harvey, D. Gerald, S.E. Diederichsen, J.A. Jensen, and E.V. Thomsen, “Simulating CMUT Arrays Using Time Domain FEA”, 2017 IEEE INTERNATIONAL ULTRASONICS SYMPOSIUM., (IUS), 2017.
[12]
M. Maadi, and R.J. Zemp, "A Nonlinear Lumped Equivalent Circuit Model for a Single Uncollapsed Square CMUT Cell", IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 66, no. 8, pp. 1340-1351, 2019.
[http://dx.doi.org/10.1109/TUFFC.2019.2914608] [PMID: 31059436]
[13]
S.H. Wong, M. Kupnik, X. Zhuang, D.S. Lin, K. Butts-Pauly, and B.T. Khuri-Yakub, "Evaluation of wafer bonded CMUTs with rectangular membranes featuring high fill factor", IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 55, no. 9, pp. 2053-2065, 2008.
[http://dx.doi.org/10.1109/TUFFC.897] [PMID: 18986902]
[14]
A. Bozkurt, I. Ladabaum, A. Atalar, and B.T. Khuri-Yakub, "Theory and analysis of electrode size optimization for capacitive microfabricated ultrasonic transducers", IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 46, no. 6, pp. 1364-1374, 1999.
[http://dx.doi.org/10.1109/58.808859] [PMID: 18244332]
[15]
B.A. Greenlay, and R.J. Zemp, "Fabrication of Linear Array and Top-Orthogonal-to-Bottom Electrode CMUT Arrays With a Sacrificial Release Process", IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 64, no. 1, pp. 93-107, 2017.
[http://dx.doi.org/10.1109/TUFFC.2016.2620425] [PMID: 28092505]
[16]
M.J.G. Mølgaard, J.M.F. Hansen, M.H. Jakobsen, and E.V. Thomsen, "Sensitivity Optimization of Wafer Bonded Gravimetric CMUT Sensors", J. Microelectromech. Syst., vol. 27, no. 6, pp. 1089-1096, 2018.
[http://dx.doi.org/10.1109/JMEMS.2018.2868864]
[17]
S-l. Chen, and J-c. Kuang, "The Perturbation Parameter in the Problem of Large Deflection of Clamped Circular Plates", Appl. Math. Mech., vol. 2, no. 1, pp. 137-154, 1981.
[http://dx.doi.org/10.1007/BF02432056]
[18]
T-Y. Huang, "On the large deflection of a circular plate with a circular hole at the center under uniform load (in Chinese)", Wuli Xuebao, vol. 13, no. 4, pp. 294-312, 1957.
[19]
S. Timoshenko, and S. Woinowsky-krieger, Theory of plates and shells., McGraw-Hill: New York, 1959.
[20]
X. Zheng, Theory and Applications of Large Deflections of Thin Circular Membranes., Jilin Science and Technology Press: Changchun, China, 1990, pp. 18-19.
[21]
R.C. Hibbeler, Mechanics of materials., Pearson Prentice Hall, 2014.

Rights & Permissions Print Cite
Article Metrics
7
1
© 2024 Bentham Science Publishers | Privacy Policy