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Research Papers

Modeling of Piezoelectric Bimorph Nano-Actuators With Surface Effects

[+] Author and Article Information
Chunli Zhang

Department of Civil Engineering,
University of Siegen,
Siegen 57068,
Germany
Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China

Chuanzeng Zhang

Department of Civil Engineering,
University of Siegen,
Siegen 57068, Germany
e-mail: c.zhang@uni-siegen.de

Weiqiu Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou 310027, China

1Corresponding author.

Manuscript received December 12, 2012; final manuscript received December 31, 2012; accepted manuscript posted February 19, 2013; published online August 21, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(6), 061015 (Aug 21, 2013) (7 pages) Paper No: JAM-12-1552; doi: 10.1115/1.4023693 History: Received December 12, 2012; Revised December 31, 2012; Accepted February 19, 2013

Two-dimensional (2D) equations of piezoelectric bimorph nano-actuators are presented which take account of the surface effect. The surface effect of the bimorph structure is treated as a surface layer with zero thickness. The influence on the plate's overall properties resulted from the surface elasticity and piezoelectricity is modeled by a spring force exerting on the boundary of the bulk core. Using the derived 2D equations, the anti-parallel piezoelectric bimorph nano-actuators of both cantilever and simply supported plate type are investigated theoretically. Numerical results show that the effective properties and the deflections of the antiparallel bimorph nano-actuators are size-dependent. The deflection at the resonant frequency achieves nearly 50 times as that under the static driving voltage.

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References

Fan, Z. Y., and Lu, J. G., 2005, “Zinc Oxide Nanostructures: Synthesis and Properties,” J. Nanosci. Nanotechnol., 5, pp. 1561–1573. [CrossRef] [PubMed]
Tagantsev, A. K., Meunier, V., and Sharma, P., 2009, “Novel Electromechanical Phenomena at the Nanoscale: Phenomenological Theory and Atomistic Modeling,” MRS Bull., 34, pp. 643–647. [CrossRef]
Dai, S. X., Gharbi, M., Sharma, P., and Park, H. S., 2011, “Surface Piezoelectricity: Size Effects in Nanostructures and the Emergence of Piezoelectricity in Non-Piezoelectric Materials,” J. Appl. Phys., 110, p. 104305. [CrossRef]
Wang, Z. L., and Song, J. H., 2006, “Piezoelectric Nanogenerators Based on Zinc Oxide Nanowire Arrays,” Science, 312, pp. 242–246. [CrossRef] [PubMed]
Wang, X. D., 2001, “Piezoelectric Nanogenerators-Harvesting Ambient Mechanical Energy at the Nanometer Scale,” Nano Energy, 1, pp. 13–24. [CrossRef]
Wang, Z. L., 2004, “Zinc Oxide Nanostructures: Growth, Properties and Applications,” J. Phys.: Condens. Matter, 16, pp. R829–R858. [CrossRef]
Gao, P. X., Song, J., Zhou, J., and Wang, Z. L., 2007, “Nanowire Piezoelectric Nanogenerators on Plastic Substrates as Flexible Power Sources for Nanodevices,” Adv. Mater.19, pp. 67–72. [CrossRef]
Song, J. H., Zhou, J., and Wang, Z. L., 2006, “Piezoelectric and Semiconducting Coupled Power Generating Process of a Single ZnO Belt/Wire: A Technology for Harvesting Electricity From the Environment,” Nano Lett., 6, pp. 1656–1662. [CrossRef] [PubMed]
Feng, X., Yang, B. D., Liu, Y. M., Wang, Y., Dagdeviren, C., Liu, Z. J., Carlson, A., Li, J. Y., Huang, Y. G., and Rogers, J. A., 2011, “Stretchable Ferroelectric Nanoribbons With Wavy Configurations on Elastomeric Substrates,” ACS Nano., 5, pp. 3326–3332. [CrossRef] [PubMed]
Sinha, N., Wabiszewski, G. E., Mahameed, R., Felmetsger, V. V., Tanner, S. M., Carpick, R. W., and Piazza, G., 2009, “Piezoelectric Aluminum Nitride Nanoelectromechanical Actuators,” Appl. Phys. Lett., 95, p. 053106. [CrossRef]
Chang, J. Y., Min, B-K, Kim, J. B., and Lin, L. W., 2009, “Bimorph Nano Actuators Synthesized by Focused Ion Beam Chemical Vapor,” Microelectron. Eng., 86, pp. 2364–2368. [CrossRef]
Chen, Q. C., Shi, Y., Zhang, Y. S., Zhu, J., and Yan, Y. J., 2006, “Size Dependence of Young's Modulus in ZnO Nanowires,” Phys. Rev. Lett., 96, p. 075505. [CrossRef] [PubMed]
Agrawal, R., Peng, B., Gdoutos, E. E., and Espinosa, H. D., 2008, “Elasticity Size Effects in ZnO Nanowires—A Combined Experimental-Computational Approach,” Nano Lett.8, pp. 3368–3674. [CrossRef]
Agrawal, R., and Espinosa, H. D., 2011, “Giant Piezoelectric Size Effects in Zinc Oxide and Gallium Nitride Nanowires: A First Principles Investigation,” Nano Lett., 11, pp. 786–790. [CrossRef] [PubMed]
Gurtin, M. E., and Murdoch, A. I., 1975, “A Continuum Theory of Elastic Material Surfaces,” Arch. Ration. Mech. Anal., 57, pp. 291–323. [CrossRef]
Gurtin, M. E., and Murdoch, A. I., 1978, “Surface Stress in Solids,” Int. J. Solids Struct., 14, pp. 431–440. [CrossRef]
He, L. H., Lim, C. W., and Wu, B. S., 2004, “A Continuum Model for Size-Dependent Deformation of Elastic Films of Nano-Scale Thickness,” Int. J. Solids Struct., 41, pp. 847–857. [CrossRef]
Lu, P., He, L. H., Lee, H. P., and Lu, C., 2006, “Thin Plate Theory Including Surface Effects,” Int. J. Solids Struct.43, pp. 4631–4647. [CrossRef]
Lim, C. W., and He, L. H., 2004, “Size-Dependent Nonlinear Response of Thin Elastic Films With Nano-Scale Thickness,” Int. J. Mech. Sci., 46, pp. 1715–1726. [CrossRef]
Sheng, H. Y., Li, H. P., Lu, P., and Xu, H. Y., 2010, “Free Vibration Analysis for Micro-Structures Used in MEMS Considering Surface Effects,” J. Sound Vib., 329, pp. 236–246. [CrossRef]
Lü, C. F., Lim, C. W., and Chen, W. Q., 2009, “Size-Dependent Elastic Behavior of FGM Ultra-Thin Films Based on Generalized Refined Theory,” Int. J. Solids Struct., 46, pp. 1176–1185. [CrossRef]
Lü, C. F., Lim, C. W., and Chen, W. Q., 2009, “Elastic Mechanical Behavior of Nano-Scaled FGM Films Incorporating Surface Energies,” Compos. Sci. Technol.69, pp. 1124–1130. [CrossRef]
Wang, Y., and Feng, X., 2009, “Dynamic Behaviors of Controllably Buckled Thin Films,” Appl. Phys. Lett., 95, p. 231915. [CrossRef]
Wang, Y., Feng, X., Lu, B. W., and Wang, G. F., 2012, “Surface Effect on the Bulked Thin Film,” ASME J. Appl. Mech., 80, p. 021002. [CrossRef]
Chen, W. Q., and Zhang, Ch., 2010, “Anti-Plane Shear Green's Functions for an Isotropic Elastic Half-Space With a Material Surface,” Int. J. Solids Struct., 41, pp. 1641–1650. [CrossRef]
Koguchi, H., 2007, “Effects of Surface Stresses on Elastic Fields Near Surface and Interface,” J. Solid Mech. Mater. Eng.1, pp. 152–168. [CrossRef]
He, L. H., and Lim, C. W., 2006, “Surface Green Function for a Soft Elastic Half-Space: Influence of Surface Stress,” Int. J. Solids Struct.43, pp. 132–143. [CrossRef]
Huang, G. Y., and Yu, S. W., 2006, “Effect of Surface Piezoelectricity on the Electromechanical Behavior of a Piezoelectric Ring,” Phys. Status Solidi B, 243, pp. R22–R24. [CrossRef]
Pan, X. H., Yu, S. W., and Feng, X. Q., 2011, “A Continuum Theory of Surface Piezoelectricity for Nanodielectrics,” Sci. China: Phys. Mech. Astron., 54, pp. 564–573. [CrossRef]
Yan, Z., and Jiang, L. Y., 2011, “Surface Effects on the Electromechanical Coupling and Bending Behaviours of Piezoelectric Nanowires,” J. Phys. D: Appl. Phys., 44, p. 075404. [CrossRef]
Yan, Z., and Jiang, L. Y., 2011, “The Vibrational and Buckling Behaviors of Piezoelectric Nanobeams With Surface Effects,” Nanotechnology, 22, p. 245703. [CrossRef] [PubMed]
Yan, Z., and Jiang, L. Y., 2011, “Electromechanical Response of a Curved Piezoelectric Nanobeam With the Consideration of Surface Effects,” J. Phys. D: Appl. Phys., 44, p. 365301. [CrossRef]
Zhang, C. L., Chen, W. Q., and Zhang, Ch., 2012, “On Propagation of Anti-Plane Shear Waves in Piezoelectric Plates With Surface Effects,” Phys. Lett. A, 376, pp. 3281–3286. [CrossRef]
Chen, W. Q., 2011, “Surface Effect on Bleustein-Gulyaev Wave in a Piezoelectric Half-Space,” Theor. Appl. Mech. Lett., 1, p. 041001. [CrossRef]
Chen, W. Q., 2012, “Wave Propagation in Piezoelectric Plate With Surface Effect,” Analysis of Piezoelectric Structures and Devices, D. N.Fang, J.Wang, and W. Q.Chen, eds., Higher Education Press, Beijing (to be published).
Zhang, C. L., Chen, W. Q., Li, J. Y., and Yang, J. S., 2009, “Two-Dimensional Equations for Laminated Piezoelectro-Magnetic Plates,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 56, pp. 1046–1053. [CrossRef] [PubMed]
Ding, H. J., and Chen, W. Q., 2001, Three Dimensional Problems of Piezoelasticity, Nova Science Publishers, New York.
Smits, J. G., and Choi, W. S., 1991, “The Constituent Equations of Piezoelectric Heterogeneous Bimorphs,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 56, pp. 256–270. [CrossRef]
Mitrushchenkov, A., Chambaud, G., Yvonnet, J., and He, Q. C., 2010, “Towards an Elastic Model of Wurtzite AlN Nanowires,” Nanotechnology, 21, p. 255702. [CrossRef] [PubMed]
Miller, R. E., and Shenoy, V. B., 2000, “Size-Dependent Elastic Properties of Nanosized Structural Elements,” Nanotechnology, 11, pp. 139–147. [CrossRef]

Figures

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Fig. 1

Schematic sketch of the piezoelectric bimorph with surface effect

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Fig. 2

Schematic sketch of antiparallel bimorph (a), cantilever plate antiparallel bimorph (b), and simply supported plate antiparallel bimorph (c)

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Fig. 4

The maximum deflection of AlN nanobimorph actuators (Case 1: at x1 = b, Case 2: at x1 = 0)

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Fig. 5

The deflection versus the bimorph's thickness (the ratio of length-to-thickness is 80)

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Fig. 6

The normalized deflection at x1 = b for Case 1

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Fig. 3

Miller–Shenoy coefficient

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Fig. 7

The deflection versus the driving frequency for Case 1 and Case 2 with 300 nm thickness

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Fig. 8

The deflection versus the driving frequency for Case 1 with 200 nm and 300 nm thickness (lr=80)

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Fig. 9

The deflection versus the driving frequency for Case 1 with 200 nm and 300 nm thickness (2b=16μm)

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Fig. 10

The deflection with and without surface effect versus the driving frequency for Case 1 with 200 nm thickness (lr=80)

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