Prestress-loading effect on the current-voltage characteristics of a piezoelectric p-n junction together with the corresponding mechanical tuning laws.

A model is proposed to study the diffusion of non-equilibrium minority carriers under the influence of a piezo potential and to calculate the corresponding current-voltage (I-V) characteristics of a piezoelectric p-n junction exposed to mechanical loading. An effective solution to describe this non-equilibrium process has been put forward including two concepts: the influence of prestress loading on p-n junctions in a quasi-electrostatic thermal equilibrium and the perturbation of small fields superposed on the obtained quasi-electrostatic solutions. A few useful results are obtained through this loaded p-n junction model. Under a forward-bias voltage, a tensile (compressive) loading raises (reduces) the potential barrier of the space charge zone (SCZ), i.e., produces an equivalent reverse- (forward-) electric voltage on the SCZ. When a piezoelectric p-n junction is exposed to a reverse-bias voltage, the current density monotonically decreases with increasing reverse voltage and gradually approaches saturation. A bigger tensile (compressive) loading produces a smaller (larger) saturation current density. The appearance of an equivalent voltage on the SCZ induced by prestress indicates that the performance of a p-n junction with the piezo effect can be effectively tuned and controlled by mechanical loadings. Meanwhile, numerical results show that a loading location closer to the SCZ produces a stronger effect on the I-V characteristics of a piezoelectric p-n junction, implying that the tuning effect of mechanical loadings depends on how much influence of the deformation-induced electric field can reach the SCZ. Furthermore, it is also found that the deformation-induced electric field becomes weak with increasing doping because the higher doping is corresponding to the stronger electric leakage. Thus, the higher mechanical tuning performance on higher doped piezoelectric p-n junctions requires the prestress loadings to be applied closer to the interface of p- and n-zone. This study on a non-equilibrium process of piezoelectric p-n junctions has significance for piezotronics.

Influence of Doping Concentration on the Outputs of a Bent ZnO Nanowire.

In this article, the governing equation on electric potential is established by coupling both the semiconducting characteristics and the piezo-effect property of a ZnO nanowire (ZNW). Carrier redistributions are solved for different doping concentrations while considering the effect of both types of charge carriers. The reason for the semiconducting characteristics of a ZNW to induce electric leakage in energy-harvesting is illustrated in detail and a proper initial carrier concentration, n0 or p0 , is obtained as follows: for a n-type ZnO fiber and for a p-type one under the intrinsic carrier concentration ni = 1.0×1016(1/m3) , which is of significance in both the design and the practical applications of piezotronics and piezo-phototropic devices.

Nonlinear effect of carrier drift on the performance of an n-type ZnO nanowire nanogenerator by coupling piezoelectric effect and semiconduction.

In piezoelectric semiconductors, electric fields drive carriers into motion/redistribution, and in turn the carrier motion/redistribution has an opposite effect on the electric field itself. Thus, carrier drift in a piezoelectric semiconducting structure is essentially nonlinear unless the induced fluctuation of carrier concentration is very small. In this paper, the nonlinear governing equation of carrier concentration was established by coupling both piezoelectric effect and semiconduction. A nonlinear carrier-drift effect on the performance of a ZnO nanogenerator was investigated in detail and it was elucidated that carrier motion/redistribution occurs in the ZnO nanowire (ZNW) cross section while there is no carrier motion in the axial direction. At the same time, we noted that the amplitude of boundary electric charge grows with increasing deformation, but the peaks of boundary electric charge do not appear at the cross-section endpoints. Thus, in order to effectively improve the performance of the ZNW nanogenerator, the effect of electrode configuration on the piezoelectric potential difference and output power was analyzed in detail. The electrode size for the optimal performance of a ZnO nanowire generator was proposed. This analysis that couples electromechanical fields and carrier concentration as a whole has some referential significance to piezotronics.

A two-dimensional model on the coupling thickness-shear vibrations of a quartz crystal resonator loaded by an array spherical-cap viscoelastic material units.

We establish a two-dimensional model on the coupling thickness-shear mode (TSM) vibrations of a quartz crystal resonator (QCR) carrying an array of spherical-cap (SC) viscoelastic material units. The electrical admittance of the compound QCR system is described directly in terms of the physical properties of the surface material units. The admittance spectra about the tendon stem cells (TSCs) acquired from our calculation are compared with the existing experiment data and found to be consistent with each other, indicating our model has good veracity and reliability in analyzing the mechanical properties of covered loadings. Furthermore, we calculate admittance spectra of surface Epoxy Resin (SU-8) units with different geometrical configurations and bulk effect. It is found that both geometrical configuration and bulk effect produce influence on the resonant frequency and admittance of the compound QCR system.

On the nonlinear behavior of a multilayer circular piezoelectric plate-like transformer operating near resonance.

We studied the weakly nonlinear behaviors of a simply-supported multilayer circular piezoelectric plate-like transformer (MCPPT) operating near resonance, where the MCPPT consists of a multilayer circular piezoelectric compound plate with four piezoelectric layers polarized in different directions. Nonlinear effects of large deformations near resonance are considered; it is shown that on one side of the resonant frequency, the output-input relation becomes nonlinear, and the other side, the output voltage becomes multivalued.

An analysis of nonlinear vibrations of coupled thickness-shear and flexural modes of quartz crystal plates with the homotopy analysis method.

We investigated the nonlinear vibrations of the coupled thickness-shear and flexural modes of quartz crystal plates with the nonlinear Mindlin plate equations, taking into consideration the kinematic and material nonlinearities. The nonlinear Mindlin plate equations for strongly coupled thickness- shear and flexural modes have been established by following Mindlin with the nonlinear constitutive relations and approximation procedures. Based on the long thickness-shear wave approximation and aided by corresponding linear solutions, the nonlinear equation of thickness-shear vibrations of quartz crystal plate has been solved by the combination of the Galerkin and homotopy analysis methods. The amplitude frequency relation we obtained showed that the nonlinear frequency of thickness-shear vibrations depends on the vibration amplitude, thickness, and length of plate, which is significantly different from the linear case. Numerical results from this study also indicated that neither kinematic nor material nonlinearities are the main factors in frequency shifts and performance fluctuation of the quartz crystal resonators we have observed. These efforts will result in applicable solution techniques for further studies of nonlinear effects of quartz plates under bias fields for the precise analysis and design of quartz crystal resonators.

The effects of first-order strain gradient in micro piezoelectric-bimorph power harvesters.

The effects of first-order strain gradient in micro piezoelectric-bimorph (PB) power harvesters are investigated by including the first-order gradient terms in the energy density functions. For a PB, the gradient effects can be focused on the analysis of the strain gradient effect in the thickness direction through choosing the strains and the electric displacements as the independent constitutive variables. It is shown theoretically that the first-order gradient effects have raised the natural frequency of the PB and effectively enhanced the output power density of the harvester.

The calculation of electrical parameters of AT-cut quartz crystal resonators with the consideration of material viscosity.

Electrical parameters like resistance and quality factor of a quartz crystal resonator cannot be determined through vibration analysis without considering the presence of material dissipation. In this study, we use the first-order Mindlin plate equations of piezoelectric plates for thickness-shear vibrations of a simple resonator model with partial electrodes. We derive the expressions of electrical parameters with emphasis on the resistance that is related to the imaginary part of complex elastic constants, or the viscosity, of quartz crystal. Since all electrical parameters are frequency dependent, this procedure provides the chance to study the frequency behavior of crystal resonators with a direct formulation. We understand that the electrical parameters are strongly affected by the manufacturing process, with the plating techniques in particular, but the theoretical approach we presented here will be the first step for the precise estimation of such parameters and their further applications in the analysis of nonlinear behavior of resonators. We calculated the parameters from our simple resonator model of AT-cut quartz crystal with the first-order Mindlin plate theory to demonstrate the procedure and show that the numerical results are consistent with earlier measurements.

Frequency shifts in plate crystal resonators induced by electric, magnetic, or mechanical fields in surface films.

We study frequency shifts in plate crystal resonators with surface films. The films are multiphysical, including the effects of inertia, stiffness, intrinsic stress, piezoelectric coupling, and piezomagnetic coupling. Mindlin's two-dimensional equations for a crystal plate with two elastic surface films are generalized to include the multiphysical effects of the films. They are used to study thickness-shear vibrations of a rotated Y-cut quartz plate with initial fields resulting from the mechanical, electric, and magnetic fields in the surface films. Frequency shifts caused by the initial fields are calculated and examined. Results show that plate crystal resonators with multiphysical surface films may be used for electric/magnetic field sensing.

Study on the vibration characteristics of a finite-width corrugated cylindrical shell piezoelectric transducer.

Coupled extensional and flexural vibrations of an ultrasonic piezoelectric transducer are studied in the paper. The ultrasonic piezoelectric transducer is made of piezoelectric polymer PVDF films and modeled as a corrugated cylindrical shell with a finite width in the ridge direction, which consists of multiple pieces of circular cylindrical surfaces smoothly connected along their ridges. The classical shell theory is used to obtain the theoretical solution. Effects of the edge constraints on vibrational characteristics of the resonant frequencies, mode shapes, and internal forces are investigated for a corrugated ultrasonic piezoelectric transducer consisting of a few circular pieces each with a thickness of about 40 microm, radius of 5 mm, and span angle of 120 degrees.

Frequency spectra of AT-cut quartz plates with electrodes of unequal thickness.

We study vibrations of an AT-cut quartz plate with electrodes of unequal thickness. Mindlin's first-order plate theory is used. Dispersion relations for straight-crested waves in an unbounded plate and frequency spectra of modes in a finite plate are obtained. Results show that, because of the unequal thickness of the electrodes, the two originally uncoupled groups of modes are now coupled. One group consists of thickness-shear, flexure, and face-shear. The other has thickness-twist and extension. This coupling by asymmetric electrodes changes the frequency spectra and affects resonator performance. To avoid the effects of this coupling, a series of discrete values of the length/thickness ratio of the crystal plate need to be excluded.

Analysis of multilayered thin-film piezoelectric transducer arrays.

We study coupled extensional and flexural vibrations of a 1-D array of partially electroded, multilayered piezoelectric transducers. The classical theory for laminated plates is used. A theoretical solution is obtained. Based on the solution, basic vibration characteristics of resonant frequencies, mode shapes, and admittance are calculated. Their dependence on geometric parameters is examined. The present analysis represents a significant progress of existing analyses on a single cell of a transducer array.

Vibration characteristics of a circular cylindrical ceramic tube piezoelectric transducer with helical electrodes.

We develop a 1-D mechanics model for coupled extensional and torsional vibrations of a circular cylindrical ceramic tube piezoelectric transducer with helical electrodes. A theoretical analysis of the electrically forced vibration of the tube is performed. Basic vibration characteristics of resonant frequencies, modes, and admittance are calculated and examined. The optimal orientation of the electrodes for exciting torsional modes is determined.

Shear-horizontal vibration of an elastic circular cylindrical shell with two piezoelectric transducers.

We analyze the excitation and detection of shear-horizontal vibrations in a circular cylindrical elastic shell with 2 piezoelectric actuators, one for excitation and the other for detection. The equations of linear elasticity and linear piezoelectricity are used. The mathematical problem is solved using trigonometric series. Basic vibration characteristics including resonant frequencies, mode shapes, and electric output are calculated. It is found that significant responses occur near resonances. The displacement distribution in the elastic shell is particularly strong under and close to the exciting transducer.

Optimization of a circular thin-film piezoelectric actuator lying on a clamped multilayered elastic plate.

A system consisting of a circular multilayered thin-film elastic plate and a piezoelectric actuator, which is generally used for ultrasound generation in air, is studied in this paper. Effects of the electrode dimension of a circular thin-film piezoelectric actuator lying on a clamped multilayered elastic plate are discussed theoretically, while the first-order theory of asymmetrically laminated piezoelectric plates with consideration of coupled extension and flexure of the reference plane is used. Numerical results show that the deflection of the elastic plate can be optimized by adjusting the radius of the top electrode.

Thickness-shear vibration of an AT-cut quartz plate with elliptical electrodes and implications in optimal blank geometry.

We analyze thickness-shear vibration of an AT-cut quartz plate with elliptical electrodes. The electrodes are essentially optimal in the sense of Mindlin in that they approximately satisfy the criterion for Bechmann's number in every direction. The results of our analysis suggest that optimal crystal blank geometry is essentially elliptical. We also suggest a way of machining elliptical crystal blanks.

On the inaccuracy of using Mindlin's first-order plate theory for calculating the motional capacitance of a thickness-shear resonator.

We show that when using Mindlin's first-order theory of piezoelectric plates to analyze a thickness-shear mode resonator, while the frequency can be predicted accurately, the charge, the current, and hence the motional capacitance have significant inaccuracy.

Nonlinear coupling between thickness- shear and thickness-stretch modes in a rotated Y-cut quartz resonator.

We point out an implication of the Poynting effect in nonlinear elasticity. It is shown that, due to the Poynting effect, thickness-stretch vibration can be induced in a plate thickness-shear mode resonator of rotated Y-cut quartz when the thickness-shear deformation is no longer infinitesimal. This nonlinear coupling is particularly strong when the frequency of the thickness-stretch mode is twice the frequency of the thickness-shear mode. The induced thickness-stretch vibration affects the operating thickness-shear mode through Mathieu's equation.

Effect of mass layer stiffness on propagation of thickness-twist waves in rotated Y-cut quartz crystal plates.

We analyze the effect of mass layer stiffness on thickness-twist waves propagating in a rotated Y-cut quartz crystal plate with thin mass layers on its surfaces. An equation that determines the dispersion relation of the waves is given and is solved numerically. Quantitative results of the effect of the mass layer stiffness on wave frequencies are presented. These results are important to the understanding and design of resonators and mass sensors.

Energy trapping in power transmission through an elastic plate by finite piezoelectric transducers.

We study transmission of electric energy through an elastic plate by acoustic wave propagation and piezoelectric transducers. Our mechanics model consists of an elastic plate with finite piezoelectric patches on both sides of the plate. A theoretical analysis using the equations of elasticity and piezoelectricity is performed. Energy trapping that describes the confinement and localization of the vibration energy is examined.