Surface Effects on the Piezoelectricity of ZnO Nanowires

S. Dai and H.S. Park
Journal of the Mechanics and Physics of Solids 2013; 61:385-397

Abstract

We utilize classical molecular dynamics to study surface effects on the piezoelectric properties of ZnO nanowires as calculated under uniaxial loading. An important point to our work is that we have utilized two types of surface treatments, those of charge compensation and surface passivation, to eliminate the polarization divergence that otherwise occurs due to the polar (0001) surfaces of ZnO. In doing so, we find that if appropriate surface treatments are utilized, the elastic modulus and the piezoelectric properties for ZnO nanowires having a variety of axial and surface orientations are all reduced as compared to the bulk value as a result of polarization-reduction in the polar [0001] direction. The reduction in effective piezoelectric constant is found to be independent of the expansion or contraction of the polar (0001) surface in response to surface stresses. Instead, the surface polarization and thus effective piezoelectric constant is substantially reduced due to a reduction in the bond length of the Zn-O dimer closest to the polar (0001) surface. Furthermore, depending on the nanowire axial orientation, we find in the absence of surface treatment that the piezoelectric properties of ZnO are either effectively lost due to unphysical transformations from the wurtzite to non-piezoelectric d-BCT phases, or also become smaller with decreasing nanowire size. The overall implication of this study is that if enhancement of the piezoelectric properties of ZnO is desired, then continued miniaturization of square or nearly square cross section ZnO wires to the nanometer scale is not likely to achieve this result.

This paper is available in PDF form .


Surface Piezoelectricity, Size-effects in Nanostructures and the Emergence of Piezoelectricity in Non-piezoelectric Materials

S. Dai, M. Gharbi, P. Sharma and H.S. Park
Journal of Applied Physics 2011; 110:104305

Abstract

In this work, using a combination of a theoretical framework and atomistic calculations, we highlight the concept of surface piezoelectricity that can be used to interpret the piezoelectricity of nanostructures. Focusing on three specific material systems (ZnO, SrTiO3 and BaTiO3), we discuss the renormalization of apparent piezoelectric behavior at small scales. In a rather interesting interplay of symmetry and surface effects, we show that nanostructures of certain non-piezoelectric materials may also exhibit piezoelectric behavior. Finally, for the case of ZnO, using a comparison with first principles calculations, we also comment on the fidelity of the widely-used core-shell interatomic potentials to capture non-bulk electro-mechanical response.

This paper is available in PDF form .


A New Multiscale Formulation for the Electromechanical Behavior of Nanomaterials

H.S. Park, M. Devel and Z. Wang
Computer Methods in Applied Mechanics and Engineering 2011; 200:2447-2457

Abstract

We present a new multiscale, finite deformation, electromechanical formulation to capture the response of surface-dominated nanomaterials to externally applied electric fields. To do so, we develop and discretize a total energy that combines both mechanical and electrostatic terms, where the mechanical potential energy is derived from any standard interatomic atomistic potential, and where the electrostatic potential energy is derived using a Gaussian-dipole approach. By utilizing Cauchy-Born kinematics, we derive both the bulk and surface electrostatic Piola-Kirchoff stresses that are required to evaluate the resulting electromechanical finite element equilibrium equations, where the surface Piola-Kirchoff stress enables us to capture the non-bulk electric field-driven polarization of atoms near the surfaces of nanomaterials. Because we minimize a total energy, the present formulation has distinct advantages as compared to previous approaches, where in particular, only one governing equation is required to be solved. This is in contrast to previous approaches which require either the staggered or monolithic solution of both the mechanical and electrostatic equations, along with coupling terms that link the two domains. The present approach thus leads to a significant reduction in computational expense both in terms of fewer equations to solve and also in eliminating the need to remesh either the mechanical or electrostatic domains due to being based on a total Lagrangian formulation. Though the approach can apply to three-dimensional cases, we concentrate in this paper on the one-dimensional case. We first derive the necessary formulas, then give numerical examples to validate the proposed approach in comparison to fully atomistic electromechanical calculations.

This paper is available in PDF form .


Piezoelectric Constants for ZnO Calculated Using Classical Polarizable Core-Shell Potentials

S. Dai, M.L. Dunn and H.S. Park
Nanotechnology 2010; 21:445707

Abstract

We demonstrate the feasibility of using classical atomistic simulations, i.e. molecular dynamics and molecular statics, to study the piezoelectric properties of ZnO using core-shell interatomic potentials. We accomplish this by reporting piezoelectric constants for ZnO as calculated using two different classical interatomic core-shell potentials, that originally proposed by Binks et al., and that proposed by Nyberg et al. We demonstrate that the classical core-shell potentials are able to qualitatively reproduce the piezoelectric constants as compared to benchmark \emph{ab initio} calculations. We further demonstrate that while the presence of the shell is required to capture the electron polarization effects that control the clamped ion part of the piezoelectric constant, the major shortcoming of the classical potentials is a significant underprediction of the clamped ion term as compared to previous ab initio results. However, the present results suggest that overall, these classical core-shell potentials are sufficiently accurate to be utilized for large scale atomistic simulations of the piezoelectric response of ZnO nanostructures.

This paper is available in PDF form .