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Continuum modeling of charging process and piezoelectricity of ferroelectrets

Xu, Bai-Xiang and von Seggern, Heinz and Zhukov, Sergey and Gross, Dietmar (2013):
Continuum modeling of charging process and piezoelectricity of ferroelectrets.
In: Journal of Applied Physics, pp. 094103(1-12), 114, (9), ISSN 00218979, [Online-Edition: http://dx.doi.org/10.1063/1.4819441],
[Article]

Abstract

Ferroelectrets in the form of electrically charged micro-porous foams exhibit a very large longitudinal piezoelectric coefficient d33. The structure has hence received wide application interests as sensors particularly in acoustic devices. During charging process, electrical breakdown (Paschen breakdown) takes place in the air pores of the foam and introduces free charge pairs. These charges are separated by electrostatic forces and relocated at the interfaces between the polymer and the electrically broken-down medium, where they are trapped quasistatically. The development of this trapped charge density along the interfaces is key for enabling the piezoelectricity of ferroelectrets. In this article, an internal variable based continuum model is proposed to calculate the charge density development at the interfaces, whereas a Maxwell stress based electromechanical model is used for the bulk behavior, i.e., of the polymer and of the medium where the Paschen breakdown takes place. In the modeling, the electrostatic forces between the separated charge pairs are included, as well as the influence of deformation of the solid layers. The material models are implemented in a nonlinear finite element scheme, which allows a detailed analysis of different geometries. A ferroelectret unit with porous expanded polytetrafluoroethylene (ePTFE) surrounded by fluorinated ethylene propylene is studied first. The simulated hysteresis curves of charge density at the surfaces and the calculated longitudinal piezoelectric constant are in good agreement with experimental results. Simulations show a strong dependency of the interface charge development and thus the remnant charges on the thicknesses of the layers and the permittivity of the materials. According to the calculated relation between d33 and the Young's modulus of ePTFE, the value of the Young's modulus of ePTFE is identified to be around 0.75 MPa, which lies well in the predicted range of 0.45 to 0.80 MPa, determined from the dielectric resonance spectra in the work of Zhang et al. [X. Q. Zhang et al., J. Appl. Phys. 108, 064113 (2010)]. To show the potential of the models, it is also applied to simulation of ferroelectrets with a lens shape. The results indicate that the electrical breakdown happens in a sequential manner, and the local piezoelectric coefficient varies with position. Thereby, the middle point on the surface exhibits the maximum d33. The simulation results obtained by the proposed models will provide insight for device optimization.

Item Type: Article
Erschienen: 2013
Creators: Xu, Bai-Xiang and von Seggern, Heinz and Zhukov, Sergey and Gross, Dietmar
Title: Continuum modeling of charging process and piezoelectricity of ferroelectrets
Language: English
Abstract:

Ferroelectrets in the form of electrically charged micro-porous foams exhibit a very large longitudinal piezoelectric coefficient d33. The structure has hence received wide application interests as sensors particularly in acoustic devices. During charging process, electrical breakdown (Paschen breakdown) takes place in the air pores of the foam and introduces free charge pairs. These charges are separated by electrostatic forces and relocated at the interfaces between the polymer and the electrically broken-down medium, where they are trapped quasistatically. The development of this trapped charge density along the interfaces is key for enabling the piezoelectricity of ferroelectrets. In this article, an internal variable based continuum model is proposed to calculate the charge density development at the interfaces, whereas a Maxwell stress based electromechanical model is used for the bulk behavior, i.e., of the polymer and of the medium where the Paschen breakdown takes place. In the modeling, the electrostatic forces between the separated charge pairs are included, as well as the influence of deformation of the solid layers. The material models are implemented in a nonlinear finite element scheme, which allows a detailed analysis of different geometries. A ferroelectret unit with porous expanded polytetrafluoroethylene (ePTFE) surrounded by fluorinated ethylene propylene is studied first. The simulated hysteresis curves of charge density at the surfaces and the calculated longitudinal piezoelectric constant are in good agreement with experimental results. Simulations show a strong dependency of the interface charge development and thus the remnant charges on the thicknesses of the layers and the permittivity of the materials. According to the calculated relation between d33 and the Young's modulus of ePTFE, the value of the Young's modulus of ePTFE is identified to be around 0.75 MPa, which lies well in the predicted range of 0.45 to 0.80 MPa, determined from the dielectric resonance spectra in the work of Zhang et al. [X. Q. Zhang et al., J. Appl. Phys. 108, 064113 (2010)]. To show the potential of the models, it is also applied to simulation of ferroelectrets with a lens shape. The results indicate that the electrical breakdown happens in a sequential manner, and the local piezoelectric coefficient varies with position. Thereby, the middle point on the surface exhibits the maximum d33. The simulation results obtained by the proposed models will provide insight for device optimization.

Journal or Publication Title: Journal of Applied Physics
Volume: 114
Number: 9
Uncontrolled Keywords: electrets, electric breakdown, ferroelectric materials, finite element analysis, permittivity, piezoelectricity, polymer foams, Young's modulus
Divisions: 11 Department of Materials and Earth Sciences > Material Science
11 Department of Materials and Earth Sciences > Material Science > Electronic Materials
11 Department of Materials and Earth Sciences > Material Science > Mechanics of functional Materials
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue > B - Characterisation > Subproject B7: Polarisation and charging in electrical fatigue ferroelectrics
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue > C - Modelling > Subproject C6: Micromechanical Simulation on Interaction of Point Defects with Domain Structure in Ferroelectrics
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue > B - Characterisation
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue > C - Modelling
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres > CRC 595: Electrical fatigue
11 Department of Materials and Earth Sciences
Zentrale Einrichtungen
Exzellenzinitiative
DFG-Collaborative Research Centres (incl. Transregio) > Collaborative Research Centres
DFG-Collaborative Research Centres (incl. Transregio)
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Exzellenzinitiative > Graduate Schools
Date Deposited: 09 Oct 2013 14:12
Official URL: http://dx.doi.org/10.1063/1.4819441
Additional Information:

SFB 595 Cooporation B7, C6

Identification Number: doi:10.1063/1.4819441
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