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.

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.

Vibration of a thickness-twist mode piezoelectric resonator with asymmetric, nonuniform electrodes.

We studied the effect of electrodes with varying thicknesses on thickness-twist modes in a piezoelectric plate resonator of crystals of 6mm symmetry. The focus is on the effects of asymmetric electrodes, which do not seem to have been examined before. A theoretical analysis is performed using the theory of linear piezoelectricity. A trigonometric series solution is obtained that is relatively rare from the equations of piezoelectricity. Numerical calculations are made based on the series solution. Results show that asymmetric, nonuniform electrodes have a strong effect on vibration mode shapes. This effect offers the possibility of using nonuniform electrodes in design to achieve various goals. The quantitative results in this paper are useful for the purpose.

Nonlinear interface between the piezoelectric harvesting structure and the modulating circuit of an energy harvester with a real storage battery.

This paper studies the performance of an energy harvester with a piezoelectric bimorph (PB) and a real electrochemical battery (ECB), both are connected as an integrated system through a rectified dc-dc converter (DDC). A vibrating PB can scavenge energy from the operating environment by the electromechanical coupling. A DDC can effectively match the optimal output voltage of the harvesting structure to the battery voltage. To raise the output power density of PB, a synchronized switch harvesting inductor (SSHI) is used in parallel with the harvesting structure to reverse the voltage through charge transfer between the output electrodes at the transition moments from closed-to open-circuit. Voltage reversal results in earlier arrival of rectifier conduction because the output voltage phases of any two adjacent closed-circuit states are just opposite each other. In principle, a PB is with a smaller, flexural stiffness under closed-circuit condition than under open-circuit condition. Thus, the PB subjected to longer closed-circuit condition will be easier to be accelerated. A larger flexural velocity makes the PB to deflect with larger amplitude, which implies that more mechanical energy will be converted into an electric one. Nonlinear interface between the vibrating PB and the modulating circuit is analyzed in detail, and the effects of SSHI and DDC on the charging efficiency of the storage battery are researched numerically. It was found that the introduction of a DDC in the modulating circuit and an SSHI in the harvesting structure can raise the charging efficiency by several times.

On the eigenvalue problem for free vibrations of a piezoelectric/piezomagnetic body.

We present a systematic analysis of the eigenvalue problem associated with free, small-amplitude vibrations in an elastic body possessing piezoelectric, piezomagnetic, and magnetoelectric couplings. An abstract formulation is introduced. The operators in the abstract formulation are shown to be self-adjoint, from which a series of fundamental properties of resonant frequencies and vibration modes are proved concisely. A variational formulation and a perturbation analysis of the eigenvalue problem are also given, based on the abstract formulation.

Adjusting the resonant frequency of a PVDF bimorph power harvester through a corrugation-shaped harvesting structure.

We propose a corrugated polyvinylidene fluoride (PVDF) bimorph power harvester with the harvesting structure fixed at the two edges in the corrugation direction and free at the other edges. The resonant frequency of a corrugated PVDF bimorph is readily adjusted through changing either its geometrical configuration or the span length, which can keep the harvester operating at the optimal state in environments with different ambient vibrations. The governing equations of a PVDF bimorph with a corrugation shape are derived from the transfer-matrix technique. Statistical results show that the adaptability of a harvester to the operating environment can be improved greatly by designing the harvesting structure with adjustable resonant frequency.

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.

Analysis of a piezoelectric bimorph plate with a central-attached mass as an energy harvester.

This article analyzes the performance of a piezoelectric energy harvester in the flexural mode for scavenging ambient vibration energy. The energy harvester consists of a piezoelectric bimorph plate with a central-attached mass. The linear piezoelectricity theory is applied to evaluate the performance dependence upon the physical and geometrical parameters of the model bimorph plate. The analytical solution for the flexural motion of the piezoelectric bimorph plate energy harvester shows that the output power density increases initially, reaches a maximum, then decreases monotonically with the increasing load impedance, which is normalized by a parameter that is a simple combination of the physical and geometrical parameters of the scavenging structure, the bimorph plate, and the frequency of the ambient vibration, underscoring the importance for the load circuit to have the impedance desirable by the scavenging structure. The numerical results illustrate the considerably enhanced performances by adjusting the physical and geometrical parameters of the scavenging structure.

A spiral-shaped harvester with an improved harvesting element and an adaptive storage circuit.

A piezoelectric energy harvester consists of a spiral-shaped piezoelectric bimorph to transfer mechanical energy into electric energy, an electrochemical battery to store the scavenged electric energy, and a rectifier together with a step-down dc-dc converter to connect the two components as an integrated system. A spiral-shaped harvesting structure is studied in this paper because it is very useful in the microminiaturization of advanced sensing technology. The aim of employing a step-down dc-dc converter in the storage circuit is to match the optimal output voltage of the piezoelectric bimorph with the battery voltage for efficient charging. In order to raise the output power density of a harvesting element, moreover, we apply a synchronized switch harvesting on inductor (SSHI) in parallel with the piezoelectric bimorph to artificially extend the closed-circuit interval of the rectifier. Numerical results show that the introduction of a dc-dc converter in the storage circuit or a SSHI in the harvesting structure can raise the charging efficiency several times higher than a harvester without a dc-dc converter or an SSHI.

An exact analysis of a rectangular plate piezoelectric generator.

We study thickness-twist vibration of a finite, piezoelectric plate of polarized ceramics or 6-mm crystals driven by surface mechanical loads. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The plate is properly electroded and connected to a circuit such that an electric output is generated. The structure analyzed represents a piezoelectric generator for converting mechanical energy to electrical energy. Analytical expressions for the output voltage, current, power, efficiency, and power density are given. The basic behaviors of the generator are shown by numerical results.

Mass sensitivity of thickness-twist modes in a rectangular piezoelectric plate of hexagonal crystals.

Mass sensitivity of thickness-twist vibration modes in a rectangular plate piezoelectric resonator of 6 mm crystals are obtained from the three-dimensional equations of linear piezoelectricity. The boundary conditions at the finite-plate boundaries all have been taken into consideration. The solutions obtained are exact, which is relatively few for piezoelectric problems over finite domains. The results are fundamental and useful to the understanding and design of piezoelectric resonators and acoustic wave sensors made of polarized ceramics, ZnO and AlN.

Propagation of thickness-twist waves through a joint between two semi-infinite piezoelectric plates.

We study the propagation of thickness-twist waves through a joint between two semi-infinite piezoelectric plates of crystals with 6-mm symmetry or polarized ceramics. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The solution shows the cutoff of certain waves and the presence of localized electromechanical fields near the joint. The results are of fundamental importance to the understanding and design of resonators and other devices made from plates of these materials, in particular thin film resonators of ZnO and AlN.

Theoretical modeling of a thickness-shear mode circular cylinder piezoelectric transformer.

We propose a piezoelectric transformer operating with thickness-shear modes of a circular cylinder and perform a theoretical analysis on the transformer. An exact solution from the three-dimensional equations of piezoelectricity is obtained. The output voltage, input admittance, and efficiency of the transformer are determined. The basic behaviors of the transformer are shown by numerical results.

Analysis of temperature compensation in a plate thickness mode bulk acoustic wave resonator.

We analyze temperature-induced frequency shift in a thickness mode bulk acoustic wave resonator with a layer of another material for temperature compensation. The perturbation integral by Tiersten is used to calculate frequency shifts in the resonator under a temperature change. It is shown that, with a proper design of the compensation layer, temperature sensitivity of the resonator can be reduced or made zero.

Weakly nonlinear behavior of a plate thickness-mode piezoelectric transformer.

We analyzed the weakly nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance. An approximate analytical solution was obtained. Numerical results based on the analytical solution are presented. It is shown that on one side of the resonant frequency the input-output relation becomes nonlinear, and on the other side the output voltage experiences jumps.

Effects of electrodes with varying thickness on energy trapping in thickness-shear quartz resonators.

We study the possibility of using electrodes of varying thickness for strong energy trapping in quartz thickness-shear resonators as an alternative for contoured resonators. A theoretical analysis is performed. Results show that nonuniform electrodes can produce strong trapping of thickness-shear modes.

Oscillatory interaction between bubbles and confining microvessels and its implications on clinical vascular injuries of shock-wave lithotripsy.

This paper presents a detailed study of the oscillation characteristics of a bubble confined inside a deformable microvessel, whose size is comparable with the bubble size. The vessel's compliance is characterized by a nonlinear relation between the intraluminal pressure and the expansion ratio of the vessel radius, which represents the variation of the vessel stiffness with the pressure of the filling liquid. In this analysis, an initially spherical bubble evolves into an ellipsoid, and the asymmetric oscillation appears immediately after the driving pressure is applied and magnifies with oscillation cycles. Compared with the symmetric oscillation in an unconstrained environment, the vessel constraint makes the bubble contract significantly more and subsequently expand in a more violent rebound, inducing substantially larger peaks of the intraluminal pressure exerted on the vessel wall. A larger initial bubble/vessel radius ratio leads to not only a larger peak but also a higher oscillation frequency of the intraluminal pressure, which are the two most dominating parameters in determining the vessel's failure under cyclic loading. The numerical results have further shown that an increase of the vessel wall stiffness strengthens the asymmetric effect, i.e., a larger peak of the intraluminal pressure with a higher oscillation frequency, and so does a larger pre-existing pressure in the liquid filling the vessel. These findings imply that the asymmetric effect is one of the primary mechanisms for clinical injuries of capillary and small blood vessels and for the higher risk of pediatric and hypertension patients in shock wave lithotripsy.

Nonlinear behavior of a piezoelectric power harvester near resonance.

We analyze the behavior of a model piezoelectric power harvester near resonance. Nonlinear effects of large deformations due to resonance are considered using a cubic theory of the displacement gradient. Results on the output current and power are presented, which exhibit multivaluedness and jump phenomena.

A high-sensitivity, dual-plate, thickness-shear mode pressure sensor.

We propose a dual-plate pressure sensor operating with pressure-induced frequency shifts of thickness-shear modes of a crystal plate resonator. Under an applied normal pressure. The dual-plate structure causes flexure in the crystal plate rather than circumferential compression in usual thickness-shear pressure sensors. This suggests higher sensitivity because a plate responds to a normal pressure more than to a circumferential compression, which is shown by a theoretical analysis using the theory for small fields superposed on initial fields.

Thickness-shear vibrations of rotated Y-cut quartz plates with imperfectly bonded surface mass layers.

A solution is obtained from the three-dimensional equations of linear piezoelectricity for the pure thickness-shear vibration of rotated Y-cut quartz or langasite plates with imperfectly bonded surface mass layers. The solution includes a few results in the literature as special cases. It is shown that the mass layers lower the resonant frequencies when they are relatively perfectly bonded to the crystal surface, and that loosely bonded mass layers may raise the frequencies. The results are useful in the analysis of frequency stability of quartz resonators and acoustic wave sensors.