Abstract
The analytical solution for the displacements of an anisotropic piezoelectric material in the uniform electric field is presented for practical use in the “global excitation mode” of piezoresponse force microscopy. The solution is given in the Wolfram Mathematica interactive program code, allowing the derivation of the expression of the piezoresponse both in cases of the anisotropic and isotropic elastic properties. The piezoresponse’s angular dependencies are analyzed using model lithium niobate and barium titanate single crystals as examples. The validity of the isotropic approximation is verified in comparison to the fully anisotropic solution. The approach developed in the paper is important for the quantitative measurements of the piezoelectric response in nanomaterials as well as for the development of novel piezoelectric materials for the sensors/actuators applications.
Highlights
Piezoelectric materials are an important class of materials with applications as sensors, actuators, resonators [1,2,3], electric energy harvesters [4,5], in various microelectronic devices [6,7,8], and in the piezoelectric catalysis for wastewater treatment [9]
The most straightforward Piezoresponse force microscopy (PFM) implementation is in the so-called “global excitation mode”, where an electric field is applied through micro- or nano-sized electrodes, while signal registration is performed utilizing scanning probe microscopy (SPM) probe rastering across the surface [16,29,30,31,32,33,34,35]
Piezoelectric response in the uniform electric field created by the top electrode was analyzed for the case of the arbitrarily oriented piezoelectric material bonded to the rigid substrate, which presents “global excitation mode” PFM measurements
Summary
Piezoelectric materials are an important class of materials with applications as sensors, actuators, resonators [1,2,3], electric energy harvesters [4,5], in various microelectronic devices [6,7,8], and in the piezoelectric catalysis for wastewater treatment [9]. Global excitation can be realized via an electric field applied to the conductive tip across the tip-electrode interface and by the excitation of the electrode with probe acting as a mechanical sensor. In both cases, the solution of the problem of electromechanical response quantification in the applied electric field is close to the conventional laser interferometry problem of the response under the action of the uniform or close-to-the uniform electric field. The solutions are represented in the Wolfram Mathematica interactive code, allowing the visualization and study of the equations in the crystals with arbitrary elastic/piezoelectric matrices and orientation
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