Modeling and Measurements of CMUTs with Square Anisotropic Plates

Mette Funding la Cour; Thomas Lehrmann Christiansen; Christian Dahl-Petersen; Kasper Reck; Ole Hansen; Jørgen Arendt Jensen; Erik Vilain Thomsen

doi:10.1109/ULTSYM.2013.0559

Modeling and Measurements of CMUTs with Square Anisotropic Plates

Mette Funding la Cour, Thomas Lehrmann Christiansen, Christian Dahl-Petersen, Kasper Reck, Ole Hansen, Jørgen Arendt Jensen, Erik Vilain Thomsen

Technical University of Denmark

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Abstract

The conventional method of modeling CMUTs use the isotropic plate equation to calculate the deflection, leading to deviations from FEM simulations including anisotropic effects of around 10% in center deflection. In this paper, the deflection is found for square plates using the full anisotropic plate equation and the Galerkin method. Utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is <0.1%. The deflection was measured on fabricated CMUTs using a white light interferometer. Fitting the anisotropic calculated deflection to the measurement a deviation of 0.5-1.5% is seen for the fitted values. Finally it was also measured how the device behaved under increasing bias voltage and it is observed that the model including anisotropic effects is within the uncertainty interval of the measurements.

Original language	English
Title of host publication	Proceedings of the 2013 IEEE International Ultrasonics Symposium
Publisher	IEEE
Publication date	2013
Pages	2187-2190
ISBN (Print)	9781467356862
DOIs	https://doi.org/10.1109/ULTSYM.2013.0559
Publication status	Published - 2013
Event	2013 IEEE International Ultrasonics Symposium - Prague Convention Center , Prague, Czech Republic Duration: 21 Jul 2013 → 25 Jul 2013 http://ewh.ieee.org/conf/uffc/2013/

Conference

Conference	2013 IEEE International Ultrasonics Symposium
Location	Prague Convention Center
Country/Territory	Czech Republic
City	Prague
Period	21/07/2013 → 25/07/2013
Internet address	http://ewh.ieee.org/conf/uffc/2013/

Keywords

Fields, Waves and Electromagnetics
Anisotropic magnetoresistance
Equations
Finite element analyses
Mathematical model
Silicon
Voltage measurement
Substrates

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@inproceedings{589e0024189a440abcdd37793d79c91f,

title = "Modeling and Measurements of CMUTs with Square Anisotropic Plates",

abstract = "The conventional method of modeling CMUTs use the isotropic plate equation to calculate the deflection, leading to deviations from FEM simulations including anisotropic effects of around 10% in center deflection. In this paper, the deflection is found for square plates using the full anisotropic plate equation and the Galerkin method. Utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is <0.1%. The deflection was measured on fabricated CMUTs using a white light interferometer. Fitting the anisotropic calculated deflection to the measurement a deviation of 0.5-1.5% is seen for the fitted values. Finally it was also measured how the device behaved under increasing bias voltage and it is observed that the model including anisotropic effects is within the uncertainty interval of the measurements.",

keywords = "Fields, Waves and Electromagnetics, Anisotropic magnetoresistance, Equations, Finite element analyses, Mathematical model, Silicon, Voltage measurement, Substrates",

author = "{la Cour}, {Mette Funding} and Christiansen, {Thomas Lehrmann} and Christian Dahl-Petersen and Kasper Reck and Ole Hansen and Jensen, {J{\o}rgen Arendt} and Thomsen, {Erik Vilain}",

year = "2013",

doi = "10.1109/ULTSYM.2013.0559",

language = "English",

isbn = "9781467356862",

pages = "2187--2190",

booktitle = "Proceedings of the 2013 IEEE International Ultrasonics Symposium",

publisher = "IEEE",

address = "United States",

note = "2013 IEEE International Ultrasonics Symposium, IUS 2013 ; Conference date: 21-07-2013 Through 25-07-2013",

url = "http://ewh.ieee.org/conf/uffc/2013/",

}

la Cour, MF, Christiansen, TL, Dahl-Petersen, C, Reck, K, Hansen, O , Jensen, JA & Thomsen, EV 2013, Modeling and Measurements of CMUTs with Square Anisotropic Plates. in Proceedings of the 2013 IEEE International Ultrasonics Symposium . IEEE, pp. 2187-2190, 2013 IEEE International Ultrasonics Symposium, Prague, Czech Republic, 21/07/2013. https://doi.org/10.1109/ULTSYM.2013.0559

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T1 - Modeling and Measurements of CMUTs with Square Anisotropic Plates

AU - la Cour, Mette Funding

AU - Christiansen, Thomas Lehrmann

AU - Dahl-Petersen, Christian

AU - Reck, Kasper

AU - Hansen, Ole

AU - Jensen, Jørgen Arendt

AU - Thomsen, Erik Vilain

PY - 2013

Y1 - 2013

N2 - The conventional method of modeling CMUTs use the isotropic plate equation to calculate the deflection, leading to deviations from FEM simulations including anisotropic effects of around 10% in center deflection. In this paper, the deflection is found for square plates using the full anisotropic plate equation and the Galerkin method. Utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is <0.1%. The deflection was measured on fabricated CMUTs using a white light interferometer. Fitting the anisotropic calculated deflection to the measurement a deviation of 0.5-1.5% is seen for the fitted values. Finally it was also measured how the device behaved under increasing bias voltage and it is observed that the model including anisotropic effects is within the uncertainty interval of the measurements.

AB - The conventional method of modeling CMUTs use the isotropic plate equation to calculate the deflection, leading to deviations from FEM simulations including anisotropic effects of around 10% in center deflection. In this paper, the deflection is found for square plates using the full anisotropic plate equation and the Galerkin method. Utilizing the symmetry of the silicon crystal, a compact and accurate expression for the deflection can be obtained. The deviation from FEM in center deflection is <0.1%. The deflection was measured on fabricated CMUTs using a white light interferometer. Fitting the anisotropic calculated deflection to the measurement a deviation of 0.5-1.5% is seen for the fitted values. Finally it was also measured how the device behaved under increasing bias voltage and it is observed that the model including anisotropic effects is within the uncertainty interval of the measurements.

KW - Fields, Waves and Electromagnetics

KW - Anisotropic magnetoresistance

KW - Equations

KW - Finite element analyses

KW - Mathematical model

KW - Silicon

KW - Voltage measurement

KW - Substrates

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DO - 10.1109/ULTSYM.2013.0559

M3 - Article in proceedings

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BT - Proceedings of the 2013 IEEE International Ultrasonics Symposium

PB - IEEE

T2 - 2013 IEEE International Ultrasonics Symposium

Y2 - 21 July 2013 through 25 July 2013

ER -

Modeling and Measurements of CMUTs with Square Anisotropic Plates

Abstract

Conference

Keywords

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