Thickness vibration of piezoelectric plates of 6mm crystals with tilted six-fold axis and two-layered thick electrodes

We perform a theoretical analysis of thickness vibrations in piezoelectric plates of crystals with 6 mm symmetry. The six-fold axis is tilted with respect to the plate surfaces. The major surfaces of the plate are covered with two layers of electrodes of different metals. The equations of linear piezoelectricity are used for the crystal plate. The electrodes are modeled by the equations of elasticity. Thickness vibrations frequencies and modes as well as impedance are calculated and examined.     

Energy trapping in power transmission through a circular cylindrical elastic shell by finite piezoelectric transducers

We study the transmission of electric energy through a circular cylindrical elastic shell by acoustic wave propagation and piezoelectric transducers. Our mechanics model consists of a circular cylindrical elastic shell with finite piezoelectric patches on both sides of the shell. A theoretical analysis using the equations of elasticity and piezoelectricity is performed. A trigonometric series solution is obtained. Output voltage and transmitted power are calculated. Confinement and localization of the vibration energy (energy trapping) is studied which can only be understood from analyzing finite transducers. It is shown that when thickness-twist mode is used the structure shows energy trapping with which the vibration can be confined to the transducer region. It is also shown that energy trapping is sensitive to the geometric and physical parameters of the structure.     

Thickness-shear vibration of a quartz plate connected to piezoelectric plates and electric field sensing

We study thickness-shear vibration of a quartz plate connected to two piezoelectric ceramic plates with initial deformations caused by a biasing electric field. The theory for small deformations superposed on finite biasing deformations in an electroelastic body is used. It is shown that the resonant frequencies of the incremental thickness-shear vibration of the quartz plate vary with the biasing electric field. The biasing electric field induced frequency shift depends linearly on the field. Therefore this effect may be used for electric field sensing. The dependence of the electric field induced frequency shift on various material and geometric parameters is examined. When the electric field is of the order of 100 V/mm, the relative frequency shift is of the order of 10⁻⁵. The case when the piezoelectric plates are replaced by piezomagnetic plates is also investigated for magnetic field sensing, and similar results are obtained.     

Further studies on thickness vibrations of piezoelectric plate excited by parallel field

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On the propagation of long thickness-stretch waves in piezoelectric plates

We study the propagation of thickness-stretch waves in a piezoelectric plate of polarized ceramics with thickness poling or crystals of class 6 mm whose sixfold axis is along the plate thickness. For device applications we consider long waves with wavelengths much longer than the plate thickness. A system of two-dimensional equations in the literature governing thickness-stretch, extensional, and symmetric thickness-shear motions of the plate is further simplified. The equations obtained can be used to analyze piezoelectric plate acoustic wave devices operating with thickness-stretch modes.     

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

We study the effects of electrodes of nonuniform thickness on thickness-shear vibration frequencies and mode shapes of quartz resonators. This paper extends a previous paper from electrodes of stepped thickness to continuously varying thickness. Numerical results for electrodes of linearly varying thickness are presented. The results show that strong energy trapping can be achieved and adjusted using electrodes with variable thickness.     

Exact second order formalism for the study of electro-acoustic properties in piezoelectric structures under an initial mechanical stress

In this study we develop the exact second order formalism of piezoelectric structures under an external mechanical stress. Indeed, previous models are approximated since they consist in deriving all the equations in the natural coordinate system (corresponding to the pre-stress free case). Hence, our exact formalism proposes to obtain the whole of equations in the current coordinate system (which is the coordinate system after the pre-deformation). Then, this exact formalism is used to derive the modified Christoffel equations and the modified KLM model. Finally, we quantify the correction with the approximate formalism on several transfer functions and electro-mechanical parameters for a non hysteretic material (lithium niobate). In conclusion, we show that for this material, significant corrections are obtained when studying the plane wave velocities and the electrical input impedance (about 4%), whereas other parameters such as coupling coefficient and impulse response are less influenced by the choice of coordinate systems (corrections less than 0.5%).     

Impurity-related intraband absorption in coupled quantum dot-ring structure under lateral electric field

The effects of a lateral electric field on intraband absorption in GaAs/GaAlAs two-dimensional coupled quantum dot-ring structure with an on-center hydrogenic donor impurity are investigated. The confining potential of the system consists of two parabolas with various confinement energies. The calculations are made using the exact diagonalization technique. A selection rule for intraband transitions was found for x-polarized incident light. The absorption spectrum mainly exhibits a redshift with the increment of electric field strength. On the other hand, the absorption spectrum can exhibit either a blue- or redshift depending on the values of confinement energies of dot and ring. Additionally, electric field changes the energetic shift direction influenced by the variation of barrier thickness of the structure.     

High intensity of interband transitions in double-barrier structures with a high-frequency electric field

A solution of a two-band analogue of the time-dependent Schrödinger equation describing resonance coherent electron interaction with a high-frequency field was found for a symmetric double-barrier structure, and an analytic expression was obtained for the small-signal conductivity proportional to the electron transition intensity. It was found that the high-frequency conductivity of double-barrier structures in the case of interband transitions could be significantly higher than in the case of intersubband transitions.     

Relation between the electric response and the characteristics of elastic waves under shock excitation of heterogeneous dielectric materials with piezoelectric inclusions

A physicomathematical model is proposed for the electric response to elastic shock excitation of piezo-containing heterogeneous materials. The parameters of the electric signal under a pulsed action on a dielectric sample containing a piezoelectric inclusion are calculated theoretically using the apparatus of the mechanics of continuous media, and the conformity to experimental results is observed.     

Defect detection in semiconductor layers with built-in electric field with the use of cathodoluminescence

Cathodoluminescence (CL) in scanning electron microscopy (SEM) is commonly accepted as revealing local properties of a specimen region illuminated by an electron beam. CL is widely used to visualize defects in semiconductor structures. However, the presence of a strong electric field in, for example, heterojunctions or p–n junctions causes a separation of generated electron–hole (e–h) pairs and suppresses recombination in the specimen region excited by the beam. As a result CL – a radiative recombination – becomes quenched. At the same time, electron beam-induced current (EBIC) flows throughout the structure, which may produce secondary electroluminescence that is registered by the CL detector. Consequently, the CL measurement is distorted and if there are defects in the structure, they remain unrevealed. The current study shows that registration of the CL signal for different values of electron beam current (including high ones) enables true defect detection in semiconductor layers with built-in electric field. Results for a special test structure prepared with focused ion beam on AlGaAs/GaAs laser heterostructures with an 8 nm InGaAs quantum well are presented.     

Nonlinear absorption and refractive index of Brillouin scattered mode in piezoelectric semiconductor plasmas by an applied magnetic field

With the aid of hydrodynamic model, a detailed analytical investigation is made of the stimulated Brillouin scattering (SBS) of the Stokes component of the scattered wave in piezoelectric-doped semiconductor plasma subjected to a magnetostatic field. The origin of the SBS process lies in the third-order nonlinear optical susceptibility arising due to the induced nonlinear current density and acoustic perturbations internally generated due to crystal properties such as piezoelectricity and electrostriction. Using the coupled mode theory of plasmas the effective refractive index and absorption coefficient are determined via the effective susceptibility. The influence of piezoelectricity, magnetostatic field and doping concentration has been explored. The analysis has been applied to both noncentrosymmetric and centrosymmetric crystals. Numerical estimates are made for n-type InSb crystal duly irradiated by a frequency doubled 10.6 μm CO₂ lasers. Results are found to be well in agreement with available literature. The analysis establishes that a large nonlinear refractive index and small absorption coefficient can easily be obtained under moderate excitation intensity in piezoelectric doped magnetized semiconducting crystal, which proves its potential as candidate material for the fabrication of cubic nonlinear devices.     

Propagation of thickness-twist waves in elastic plates with periodically varying thickness and phononic crystals

We study the propagation of thickness-twist (TT) waves in a crystal plate of AT-cut quartz with periodically varying, piecewise constant thickness. The scalar differential equation by Tiersten and Smythe is employed. The problem is found to be mathematically equivalent to the motion of an electron in a periodic potential field governed by Schrodinger’s equation. An analytical solution is obtained. Numerical results show that the eigenvalue (frequency) spectrum of the waves has a band structure with allowed and forbidden bands. Therefore, for TT waves, plates with periodically varying thickness can be considered as phononic crystals. The effects of various parameters on the frequency spectrum are examined.     

Anisotropy of Lamb and SH waves propagation in langasite single crystal plates under the influence of dc electric field

Paper is presented the results of computer simulation. Effect of the homogeneous dc electric field influence on the propagation of zero and first order Lamb and SH waves in piezoelectric langasite single crystal plates for a lot of cuts and directions have been calculated. Crystalline directions and cuts with maximal and minimal influence of dc electric field have indicated. Effect of hybridization of plate modes has been discussed.     

Internal electric fields due to piezoelectric and spontaneous polarizations in CdZnO/MgZnO quantum well with various applied electric field effects

The strain-induced piezoelectric polarization and the spontaneous polarization can be reduced effectively using the applied electric field in the CdZnO/ZnMgO quantum well (QW) structure with high Cd composition. That is, optical properties as a function of internal and external fields in the CdZnO/ZnMgO QW with various applied electric field result in the increased optical gain due to the fact that the QW potential profile is flattened as a result of the compensation of the internal field by the reverse field as confirmed. These results demonstrate that a high-performance optical device operation can be realized in CdZnO/MgZnO QW structures by reducing the droop phenomenon.     

Optical property and collective excitation of plasmon in a multiple-quantum-well superlattice in electric field

A finite type-I superlattice with different dielectric media on either side of the surfaces is considered under a perturbing electric fields parallel to the superlattice axis on the basis of an infinite square potential well. Using the random-phase approximation, the density–density correlation function including intra- and inter-level transitions in a multiple-quantum-well (MQW) is calculated. The dispersion relations for the surface and the bulk states are obtained as functions of the momentum wave vector and the averaged electric field strength over the quantum well. The Raman intensities due to the bulk and the surface plasmons for the intra- and the inter-level transitions are also obtained for incoming light energy.     

Stability of cylindrical conducting fluids with heat and mass transfer in longitudinal periodic electric field

A novel system to study the effect of an axial periodic electric field on the stability of a system of cylinders of conducting fluids in the presence of heat and mass transfer is investigated. The stability of a cylindrical interface between the vapor and liquid phases of a fluid is studied when the vapor is hotter than the liquid and the two phases are enclosed between two cylindrical surfaces coaxial with the interface. The linear dispersion relation is found to be of damped Mathieu-type equation with real coefficients. The method of multiple time scales is used to obtain approximate solution and analyze the stability criteria for both the nonresonant and resonant cases. The stability of the system is also discussed analytically and numerically for such cases. It is found that both the heat and mass transfer coefficient and the dimensions of the system have destabilizing influences on the considered system, while azimuthal wavenumber is found to have a stabilizing effect. The dual role of the electric field frequency is also observed on the stability of the system depending on the electrical conductivities values. Finally the behaviour of the resonance points corresponding to the effects of each of the above physical parameters are determined, and a comparison between the obtained results with the corresponding results in the case of a constant applied electric field is achieved.     

Growth of crystalline quartz films with AT-cut plane by means of catalyst-enhanced vapor-phase epitaxy under atmospheric pressure

Crystalline quartz films with an AT-cut plane have been grown by catalyst-enhanced vapor-phase epitaxy, at atmospheric pressure, using two quartz buffer layers on a sapphire (110) substrate. In this method, the first quartz buffer layer was deposited on the sapphire (110) substrate at 773 K. After annealing at 823 K, the second buffer layer was deposited at 723 K. The crystal quartz epitaxial layer was then grown at 843 K. The X-ray full-width-at-half-maximum (FWHM) value of the crystalline quartz film obtained was smaller than that of crystalline quartz prepared using a hydrothermal process. The crystalline quality of the quartz films was dependent on the thickness of the buffer layers. Furthermore, it was found that angle control of the cut plane depended on the film thickness of the second buffer layer. The quartz films grown by vapor phase epitaxy show good oscillation characteristics at room temperature.     

Photoluminescence of Er3+ ions in amorphous silicon layers under intensive laser excitation

Transients of the photoluminescence (1.54 μm) of Er³⁺ ions embedded in an amorphous silicon matrix excited with intensive laser pulses are simulated using a phenomenological model which takes into account both the defect-related excitation mechanism and stimulated optical transitions in the ions. The simulated transients are compared with the experimental ones observed in Er-doped amorphous silicon layers under pulsed laser excitation. The modeling and the experimental results demonstrate a possibility to realize a regime of superradiance in the system of Er³⁺ ions pumped via an electronic excitation of the amorphous matrix. Received: 7 August 2001 / Revised version: 1 November 2001 / Published online: 17 January 2002