Effect of flexoelectricity on electrostatic potential in a bent piezoelectric nanowire

Flexoelectricity presents a strong size effect, and should not be ignored for nanodevices. By taking the flexoelectricity into account, an analytical solution is deduced for the piezoelectric potential generated in a bent ZnO nanowire (NW) cantilever. It is shown that the electric potential in the NW is not independent of z-coordinate, which is different from the results based on the classical piezoelectric theory. The results also show that the effect of flexoelectricity on the voltage is significant in a bent ZnO NW even though the flexoelectric coefficients are set to be the minimum. Moreover, we find that the flexoelectricity plays an important role in filling the gap between the results from the classical piezoelectric theory and experimental results. It is indicated that one can use the flexoelectricity to modify the transfer efficiency from mechanical energy to electrical energy through strain engineering.

[1]  L. Eric Cross,et al.  Flexoelectric effects: Charge separation in insulating solids subjected to elastic strain gradients , 2006 .

[2]  Zhong Lin Wang,et al.  Direct-Current Nanogenerator Driven by Ultrasonic Waves , 2007, Science.

[3]  Zhong Lin Wang,et al.  Piezoelectric Nanogenerators Based on Zinc Oxide Nanowire Arrays , 2006, Science.

[4]  R. D. Mindlin Continuum and lattice theories of influence of electromechanical coupling on capacitance of thin dielectric films , 1969 .

[5]  E. Artacho,et al.  The flexoelectricity of barium and strontium titanates from first principles , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[6]  Daining Fang,et al.  Size-dependent ferroelectric behaviors of BaTiO3 nanowires , 2008 .

[7]  A. Tagantsev,et al.  Piezoelectricity and flexoelectricity in crystalline dielectrics. , 1986, Physical review. B, Condensed matter.

[8]  L. Eric Cross,et al.  Strain-gradient-induced electric polarization in lead zirconate titanate ceramics , 2003 .

[9]  D. Vanderbilt,et al.  First-principles theory of frozen-ion flexoelectricity , 2011, 1108.4997.

[10]  Xiaoyong Wei,et al.  Symmetry of flexoelectric coefficients in crystalline medium , 2011 .

[11]  D. Fang,et al.  Molecular dynamics investigations on the size-dependent ferroelectric behavior of BaTiO3 nanowires , 2009, Nanotechnology.

[12]  Q. He,et al.  The number and types of all possible rotational symmetries for flexoelectric tensors , 2011, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[13]  Shuling Hu,et al.  A theory of flexoelectricity with surface effect for elastic dielectrics , 2010 .

[14]  Zhengzheng Shao,et al.  A continuum model of piezoelectric potential generated in a bent ZnO nanorod , 2010 .

[15]  Zhong Lin Wang,et al.  Electrostatic potential in a bent piezoelectric nanowire. The fundamental theory of nanogenerator and nanopiezotronics. , 2007, Nano letters.

[16]  A. Petri,et al.  Acoustic investigation of the elastic properties of ZnO films , 1987 .

[17]  G. Odegard,et al.  Nanocomposite electrical generator based on piezoelectric zinc oxide nanowires , 2010 .

[18]  Tahir Cagin,et al.  Enhanced size-dependent piezoelectricity and elasticity in nanostructures due to the flexoelectric effect , 2008 .

[19]  Neha Sharma,et al.  Electromechanical coupling in nonpiezoelectric materials due to nanoscale nonlocal size effects: Green's function solutions and embedded inclusions , 2006 .

[20]  A. Gruverman,et al.  Supplementary Materials for Mechanical Writing of Ferroelectric Polarization , 2012 .

[21]  M. Schubert,et al.  Infrared dielectric functions and phonon modes of high-quality ZnO films , 2003 .

[22]  L. Eric Cross,et al.  Flexoelectricity of barium titanate , 2006 .

[23]  Pcy Lee,et al.  Lattice-Dynamics Approach to the Theory of Elastic Dielectrics with Polarization Gradient , 1970 .

[24]  Neha Sharma,et al.  On the possibility of piezoelectric nanocomposites without using piezoelectric materials , 2007 .

[25]  Leslie E. Cross,et al.  Possible piezoelectric composites based on the flexoelectric effect , 1999 .

[26]  S. Shen,et al.  Variational principles and governing equations in nano-dielectrics with the flexoelectric effect , 2010 .

[27]  A Lubk,et al.  Flexoelectric rotation of polarization in ferroelectric thin films. , 2011, Nature materials.

[28]  Hongkun Park,et al.  Ferroelectric phase transition in individual single-crystalline BaTiO3 nanowires. , 2006, Nano letters.

[29]  L. Eric Cross,et al.  Flexoelectric polarization of barium strontium titanate in the paraelectric state , 2002 .

[30]  Tahir Cagin,et al.  Dramatic enhancement in energy harvesting for a narrow range of dimensions in piezoelectric nanostructures , 2008 .

[31]  D. Fang,et al.  Strain effect on ferroelectric behaviors of BaTiO3 nanowires: a molecular dynamics study , 2010, Nanotechnology.

[32]  L. Eric Cross,et al.  Large flexoelectric polarization in ceramic lead magnesium niobate , 2001 .

[33]  J. Nye Physical Properties of Crystals: Their Representation by Tensors and Matrices , 1957 .

[34]  Zhong Lin Wang,et al.  Piezoelectric and semiconducting coupled power generating process of a single ZnO belt/wire. A technology for harvesting electricity from the environment. , 2006, Nano letters.

[35]  D. Fang,et al.  Systematic study of the ferroelectric properties of Pb(Zr0.5Ti0.5)O3 nanowires , 2008 .