Resonant Frequency Analysis of Capacitive Micromachined Ultrasonic Transducers (CMUTs) with Layered Membranes

doi:10.3901/JME.2019.24.011

Abstract

Abstract: Capacitive micromachined ultrasonic transducers (CMUTs) show important applications in fields of 3D ultrasound and underwater imaging. The resonant frequency is one of the important performance parameters of CMUTs, which determines the imaging resolution. For CMUTs with multilayer circular membranes, the calculation methods for the equivalent structure and material property parameters of the multilayer membranes as well as the equivalent electrode distance are proposed. As such, the vibrating equation of the multilayer membranes under both DC bias and AC voltages is established. Both Galerkin method and energy equivalent method are utilized to solve the vibrating equation, and two types of analytical expressions for the resonant frequency are obtained. The numerical results based on finite element method (FEM) are used to validate the analytical expressions, and parametric study for the analytical expressions is further conducted. The results indicate that the analytical expression based on the energy equivalent method has higher accuracy in resonant frequency predication than the one based on the Galerkin method. The theoretical expression is applicable to the cases where the membrane diameter to its thickness ratio is in the range from 20 to 100, and the cavity height is less than or equal to the thickness of CMUTs membranes. The relative error of the theoretical analysis is within 5% with respect to the FEM simulation in almost the whole varying range of the bias voltages, i.e. from 0 V to the voltage closed to the collapse voltage. In addition, CMUTs with three layers of membranes are employed to experimentally validate the analytical expression. The results show that the experimental value of the resonant frequencies of the fabricated CMUTs chips under different bias voltages agree well with the theoretical value by the analytical expression. Therefore, the derived analytical expression for the resonant frequency can be widely used for the design and optimization of CMUTs with multilayer membranes.

Key words: CMUTs, multilayer membranes, vibrating equations, energy equivalent methods, resonant frequencies, analytical expressions

CLC Number:

TH77

LI Zhikang, ZHAO Libo, LI Jie, ZHAO Yihe, XU Tingzhong, LUO Guoxi, LI Xuejiao, GUO Shuaishuai, JIANG Zhuangde. Resonant Frequency Analysis of Capacitive Micromachined Ultrasonic Transducers (CMUTs) with Layered Membranes[J]. Journal of Mechanical Engineering, 2019, 55(24): 11-20.

References

[1] YU Yuanyu, PUN S, MAK P, et al. Design of a collapse-mode CMUT with an embossed membrane for improving output pressure[J]. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2016, 63(6):854-863.
[2] SAUTTO M, SAVOIA A, QUAGLIA F, et al. A comparative analysis of CMUT receiving architectures for the design optimization of integrated transceiver front ends[J]. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2017, 64(5):826-838.
[3] RAMADAN1 K, SAMEOTO D, EVOY S. A review of piezoelectric polymers as functional materials for electromechanical transducers[J]. Smart Materials and Structures, 2014, 23(3):033001.
[4] WANG D, FILOUX E, LEVASSORT F, et al. Fabrication and characterization of annular-array, high-frequency, ultrasonic transducers based on PZT thick film[J]. Sensors and Actuators A-Physical, 2014, 216:207-213.
[5] CHOE J, ORALKAN O, NIKOOZADEH A, et al. Volumetric real-time imaging using a CMUT ring array[J]. Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2012, 59(6):1201-1211.
[6] MATRONE G, SAVOIA A, TERENZI M, et al. A volumetric CMUT-based ultrasound imaging system simulator with integrated reception and μ-beamforming electronics models[J]. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2014, 61(5):792-804.
[7] ZHANG Rui, ZHANG Wendong, HE Changde, et al. Underwater imaging using a 1x16 CMUT linear array[J]. Sensors, 2016, 16(3):312.
[8] LIM J, TEKES C, DEGERTEKIN F, et al. Towards a reduced-wire interface for CMUT-based intravascular ultrasound imaging systems[J]. IEEE Transactions on Biomedical Circuits and Systems, 2017, 11(2):400-410.
[9] ZHAO Yihe, LU Dejiang, ZHAO Libo, et al. Capacitive micromachined ultrasonic transducers for biochemical detection with flexible high sensitivity[C]//Proceedings IEEE Micro Electro Mechanical Systems, JAN 21-25, 2018, Belfast, North Ireland, IEEE, 2018:924-927.
[10] PARK K, LEE H, KUPNIK M, et al. Fabrication of capacitive micromachined ultrasonic transducers via local oxidation and direct wafer bonding[J]. Journal of Microelectromechanical Systems, 2011, 20(1):95-103.
[11] TALEBIAN S, REZAZADEH G, FATHALILOU M, et al. Effect of temperature on pull-in voltage and natural frequency of an electrostatically actuated microplate[J]. Mechatronics, 2010, 20(6):666-673.
[12] VOGL G, NAYFEH A. A reduced-order model for electrically actuated clamped circular plates[J]. Journal of Micromechanics and Microengineering, 2005, 15(4):684-690.
[13] ZHAO Xiaopeng, ABDEL-RAHMAN E, NAYFEH A. A reduced-order model for electrically actuated microplates[J]. Journal of Micromechanics and Microengineering, 2004, 14(7):900-906.
[14] MOHAMMADI V, ANSARI R, SHOJAEI M F, et al. Size-dependent dynamic pull-in instability of hydrostatically and electrostatically actuated circular microplates[J]. Nonlinear Dynamics, 2013, 73:1515-1526.
[15] HU Kaiming, ZHANG Wenming, YAN Han, et al. Nonlinear pull-in instability of suspended graphene-based sensors[J]. Europhysics Letters, 2019, 125:20011.
[16] SAGHIR S, YOUNIS M. An investigation of the static and dynamic behavior of electrically actuated rectangular microplates[J]. International Journal of Non-Linear Mechanics, 2016, 85:81-93.
[17] PORFIRI M. Vibrations of parallel arrays of electrostatically actuated microplates[J]. Journal of Sound and Vibration, 2008, 315(4):1071-1085.
[18] LI Zhikang, ZHAO Libo, YE Zhiying, et al. Resonant frequency analysis on an electrostatically actuated microplate under uniform hydrostatic pressure[J]. Journal of Physics D-Applied Physics, 2013, 46(19):195108.
[19] ZHAO Libo, JIANG Zhuangde, LI Zhikang, et al. "Modeling of electrostatically actuated microplates", micro electro mechanical systems[M]. Singapore:Springer, 2018.
[20] ENGHOLM M, PEDERSEN T, THOMSEN E. Modeling of plates with multiple anisotropic layers and residual stress[J]. Sensors and Actuators A Physical, 2016, 240:70-79.
[21] CERTON D, TESTON F, PATAT F. A finite difference model for CMUT devices[J]. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 2005, 52(12):2199-2210.
[22] VENTSEL E, KRAUTHAMMER T. Thin Plates and shells:Theory, analysis, and applications[M]. New York:Marcel Dekker, Inc., 2001.
[23] LADABAUM I, JIN X, SOH H, et al. Surface micromachined capacitive ultrasonic transducers[J]. IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control, 1998, 45(3):678-689.
[24] LI Zhikang, ZHAO Libo, JIANG Zhuangde, et al. An improved method for the mechanical behavior analysis of electrostatically actuated microplates under uniform hydrostatic pressure[J]. Journal of Microelectromechanical Systems, 2015, 24(2):474-485.
[25] SOEDEL W. Vibrations of shells and plates[M]. New York:Marcel Dekker Inc., 1981.
[26] ZHAO Libo, LI Jie, LI Zhikang, et al. Fabrication of capacitive micromachined ultrasonic transducers with low-temperature direct wafer-bonding technology[J]. Sensors and Actuators A-Physical, 2017, 264:63-75.
[27] HOPCROFT M A, NIX W D AND KENNY T W, What is the Young's modulus of silicon?[J]. Journal of Microelectromechanical Systems, 2010, 19:229-238.