Nanoelectromechanics of piezoelectric indentation and applications to scanning probe microscopies of ferroelectric materials

Nanoelectromechanics of piezoelectric indentation, including the structure of coupled electroelastic fields and stiffness relations, is analysed for flat, spherical, and conical indenter geometries. Exact solutions in elementary functions for electroelastic fields inside the material are obtained using the recently established correspondence principle between the elastic and the piezoelectric problems. The stiffness relations fully describe the indentation process and relate indentation depth, indentation force and bias to the relevant material properties and indenter parameters. This extends the results of Hertzian mechanics to piezoelectric materials. The stiffness relations are utilized for quantitative understanding of the electromechanical scanning probe microscopies (SPM) of ferroelectric and piezoelectric materials, including piezoresponse force microscopy, atomic force acoustic microscopy, scanning near-field acoustic microscopy, and heterodyne ultrasonic-electrostatic force microscopy. The structure of the electroelastic field yields a quantitative measure of signal generation volume in electromechanical SPMs and also provides a quantitative basis for the analysis of tip-induced polarisation switching and local hysteresis loop measurements.     

聚丙烯压电驻极体膜的压电和声学性能研究

以多孔聚丙烯(PP)膜为原材料, 通过压缩气体膨化工艺和电晕极化方法成功制备出PP压电驻极体膜, 并研究了该功能膜的压电和声学性能. 结果表明PP压电驻极体膜厚度方向和横向的杨氏模量分别为1.4和480 MPa, 因此压电系数d₃₃比d₃₁和d₃₂高2个量级以上, d₃₃是该类压电膜压电效应的主要性能指标, 而 d₃₁和d₃₂可以忽略不计. PP压电驻极体膜的准静态压电系数d₃₃在15-35 kPa的压强范围内具有良好的线性度. 在2-300 Hz的测试频率范围内, 300 Hz 下的d₃₃是2 Hz下的81%, 这主要是由PP膜的杨氏模量随频率增大而增强引起的. 在100 Hz-100 kHz 的音频和超声波频率范围内, PP压电驻极体膜具有平坦的频响曲线; 在1 kHz下其开路电压灵敏度和压电系数d₃₃分别为0.85 mV/Pa和164 pC/N. 关键词： 聚丙烯压电驻极体 压电效应 声学性能     

压电条SH声辐射场研究

具有一定宽度和厚度的无穷长压电条置于均匀各向同性半空间上, 压电条在电激励下产生机械振动从而在整个空间产生声场. 将压电条取为6mm晶系, 其对称主轴沿长度方向. 针对这 种压电换能器结构, 深入研究了SH波的激发和辐射特性. 首先将压电条中的声场展开为傅里 叶级数, 而将压电条下的无界半空间中的声场展开为傅里叶积分, 然后根据边界条件得到了 整个空间中声场的求解方案, 通过数值模拟计算了声场的分布特性, 并和传统方法进行了定 量的对比和分析. 最后采用最陡下降法(鞍点法)研究并得到了压电条声辐射场的远场近似表 达式, 分析了声场的指向性规律. 结果表明只有当频率f和压电条宽度a的乘积 fa<1 kHz·m 时, 传统方法得到的结果是可靠的，当频率升高时，压电条内应力和位移呈振荡式分布，频率愈高振荡愈激烈，且与传统方法的差异愈大.本文对声学微系统与声传感器件的研究具有 重要意义. 关键词： 压电条 6mm晶系 表面位移 指向性因子     

圆环状复合材料高频宽带水声换能器

研制了一种圆环状高频宽带水声换能器。利用压电复合材料Q值低从而频带宽的特点,采用双环轴向堆叠产生双模态耦合的结构方式拓宽换能器的带宽。通过理论分析与仿真计算,确定敏感元件几何尺寸。用切割-浇注-被覆电极等工艺制备出压电复合材料圆环;再将制备出的外径相同,壁厚不等的压电复合材料圆环轴向叠堆制成叠堆敏感元件,最后灌注防水透声层制成换能器。对制得的换能器进行水下性能测试,测得该换能器谐振频率为410 kHz,最大发射电压响应为150 dB,-3 dB带宽达60 kHz,水平指向性开角(-5 dB)为360°,-3 dB垂直指向性开角约20°。结果表明将复合材料圆环轴向堆叠可显著拓展换能器的带宽,且实现声波的水平全向发射。      

Nonlinear piezoelectricity in epitaxial ferroelectrics at high electric fields

Nonlinear effects in the coupling of polarization with elastic strain have been predicted to occur in ferroelectric materials subjected to high electric fields. Such predictions are tested here for a PbZr0.2Ti0.8O3 ferroelectric thin film at electric fields in the range of several hundred MV/m and strains reaching up to 2.7%. The piezoelectric strain exceeds predictions based on constant piezoelectric coefficients at electric fields from approximately 200 to 400 MV/m, which is consistent with a nonlinear effect predicted to occur at corresponding piezoelectric distortions.     

Frequency-dependent localization length of SH-wave in randomly disordered piezoelectric phononic crystals

In this paper, the localization length that represents the distance of elastic waves propagating along the disordered periodic structures is defined as the reciprocal of the smallest positive Lyapunov exponent, i.e. the localization factor. The algorithm for determining all the Lyapunov exponents in continuous dynamic systems presented by Wolf et al. is employed to calculate those in discrete dynamic systems. Numerical results of the localization lengths of SH-wave are presented and discussed in ordered and disordered piezoelectric phononic crystals to identify the different effect degrees for the decay of electrical potential in the polymers and the randomness on the localization level. For the disordered case, disorder in the thickness of the polymers and disorder in the elastic constant of the piezoelectric ceramics are all considered. The results show that some parameters such as the incident angle of elastic wave, the randomness degree and the piezoelectricity of piezoelectric ceramics and so on have pronounced effects on the frequency-dependent localization length.     

Two new designs of lamp-type piezoelectric metamaterials for active wave propagation control

A major limitation of current metamaterials is that they control the wave propagation depending on their structure. Active metamaterials in this paper are designed whose physical structure is fixed, yet the position where they control the wave propagation can be changed by piezoelectric conditions. Two kinds of lamp-type piezoelectric metamaterials were assembled from an aluminum base, rubber plate and steel column, the piezoelectric patches were attached on both sides of the steel column, which can change the equivalent elastic modulus of the whole structure when the pair of patches are accessed by an LC circuit. The equivalent elastic modulus becomes zero or negative when the frequency of the circuit varies between 29,000 Hz and 30,000 Hz, in this case the two kinds of lamp-type piezoelectric metamaterials behave as a wave localization and a wave guide, respectively. The advantage of the lamp-type piezoelectric metamaterials is that we can control the wave propagation actively, as long as we change the position of the piezoelectric patches or choose the kind of lamp-type piezoelectric metamaterial. This is more flexible than a traditional passive metamaterial and provides a new way for us to design some acoustic equipment, such as acoustic cloaking, an acoustic black hole, filter or wave guide.     

A non-contact technique for evaluation of elastic structures at large stand-off distances: applications to classification of fluids in steel vessels

A novel technique for non-contact evaluation of structures in air at large stand-off distances (on the order of several meters) has been developed. It utilizes a recently constructed air-coupled, parametric acoustic array to excite the resonance vibrations of elastic, fluid-filled vessels. The parametric array is advantageous for NDE applications in that it is capable of producing a much narrower beamwidth and broader bandwidth than typical devices that operate under linear acoustic principles. In the present experiments, the array operates at a carrier frequency of 217 kHz, and the sound field several meters from the source is described spectrally by the envelope of the drive voltage. An operating bandwidth of more than 25 kHz at a center frequency of 15 kHz is demonstrated. For the present application, the array is used to excite vibrations of fluid-filled, steel containers at stand-off distances of greater than 3 m. The vibratory response of a container is detected with a laser vibrometer in a monostatic configuration with the acoustic source. By analyzing the change in the response of the lowest order, antisymmetric Lamb wave as the interior fluid loading conditions of the container are changed, the fluid contained within the steel vessel is classified.     

Characterization of piezoelectric materials with large piezoelectric and electromechanical coupling coefficients

The relaxor based ferroelectric (1-x)Pb(Zn(1/3)Nb(2/3))O(3)-xPbTiO(3) and (1-x)Pb(Mg(1/3)Nb(2/3))O(3)-xPbTiO(3) single crystals provided new challenges in property characterization because their extraordinarily large piezoelectric coefficients and electromechanical coupling coefficients. Large errors may occur in some of the derived material constants using conventional characterization techniques. This paper will analyze the inadequacy of the traditional characterization methods and provide some basic guidelines for properly characterizing piezoelectric materials with extremely high piezoelectric and electromechanical coupling coefficients.     

Nanoscale imaging of surface piezoresponse on GaN epitaxial layers

Surfaces of GaN films were investigated by atomic force microscopy (AFM) with implemented piezoelectric force microscopy technique. A model of PFM based on the surface depletion region in GaN films is discussed. The local piezoelectric effect of the low frequency regime was found to be in phase with the applied voltage on large domains, corresponding to a Ga-face of the GaN layer. Low piezoresponse is obtained within the inter-domain regions. The use of frequencies near a resonance frequency enhances very much the resolution of piezo-imaging, but only for very low scanning speed the piezo-imaging can follow the local piezoelectric effect. An inversion of the PFM image contrast is obtained for frequencies higher than the resonance frequencies. The effect of a chemical surface treatment on the topography and the piezoresponse of the GaN films was also investigated. Textured surfaces with very small domains were observed after the chemical treatment. For this kind of surfaces, piezo-induced torsion rather than bending of the AFM cantilever dominates the contrast of the PFM images. A small memory effect was observed, and explained by surface charging and confinement of the piezoelectric effect within the carrier depletion region at the GaN surface.     

The influence of different doping elements on microstructure, piezoelectric coefficient and resistivity of sputtered ZnO film

ZnO film is attractive for high frequency surface acoustic wave device application when it is coupled with diamond. In order to get good performance and reduce insertion loss of the device, it demands the ZnO film possessing high electrical resistivity and piezoelectric coefficient d₃₃. Doping ZnO film with some elements may be a desirable method. In this paper, the ZnO films undoped and doped with Cu, Ni, Co and Fe, respectively (doping concentration is 2.0 at.%) are prepared by magnetron sputtering. The effect of different dopants on the microstructure, piezoelectric coefficient d₃₃, and electrical resistivity of the film are investigated. The results indicate that Cu dopant can enhance the c-axis orientation and piezoelectric coefficient d₃₃, the Cu and Ni dopant can increase electrical resistivity of the ZnO film up to 10⁹ Ω cm. It is promising to fabricate the ZnO films doped with Cu for SAW device applications.     

Mechanoelectrical transformations upon the elastic impact excitation of composite dielectric materials

The elastic impact excitation of dielectric materials leads to an ac electromagnetic field that is a superposition of the following several fields: the field appearing when a striker approaches a surface with an excess surface charge, a field induced by electrification processes when a striker is in contact with a material surface, the field created by a shift in the acoustic wave of charges at internal inhomogeneities, the field appearing upon acoustic surface-charge oscillations, and the field that is induced in piezoactive heterogeneous materials by the piezoelectric effect.     

Elastic response of an acoustic coating on a rib-stiffened plate

This paper develops a three-dimensional analytical model of a fluid-loaded acoustic coating affixed to a rib-stiffened plate. The system is loaded by a plane wave that is harmonic both spatially and temporally. The model begins with Navier-Cauchy equations of motion for an elastic solid, which produces displacement fields that have unknown wave propagation coefficients. These are inserted into stress equations at the boundaries of the plate and the acoustic coating. These stress fields are coupled to the fluid field and the rib stiffeners with force balances. Manipulation of these equations develops an infinite number of indexed equations that are truncated and incorporated into a global matrix equation. This global matrix equation can be solved to determine the wave propagation coefficients. This produces analytical solutions to the systems’ displacements, stresses, and scattered pressure field. This model, unlike previously developed analytical models, has elastic behavior and thus incorporates higher order wave motion that makes it accurate at higher wavenumbers and frequencies. An example problem is investigated for three specific model results: (1) the dynamic response, (2) a sonar array embedded in the acoustic coating, and (3) the scattered pressure field. An expression for the high frequency limitation of the model is derived. It is shown that the ribs can have a significant impact on the structural acoustic response of the system.     

Relaxor Behaviour and Ferroelectric Properties of （Li0.12Na0.88） （Nb0.9-xWa0.10Sbx）O3 Lead-Free Ceramics

New lead-free ceramics （Lio.12Na0.88） （Nbo.9-x Ta0.10 Sbx） 03 （0.01 × 0.06） are synthesized by solid-state reaction method. The dielectric, piezoelectric and ferroelectric properties of the ceramics are studied. The dielectric constant dependence with temperature and frequency of the ceramic specimen with x = 0.04 shows typical characteristics of relaxor ferroelectrics, and the Vogel-Fulcher relationship is fulfilled. The dielectric behaviour and its relation to the phase transition phenomena are discussed. The polarization hysteresis loops at room temperature are also measured.     

薄膜体声波谐振器的力敏特性研究

薄膜体声波谐振器(FBAR)力传感器作为一种新型的谐振式传感器,力敏特性是其设计原理。以FBAR微加速度计为例研究了工作在纵波模式,采用具有纤锌矿结构的AlN作为压电薄膜的FBAR,施加应力载荷后,其弹性常数改变导致FBAR谐振频率偏移的力敏特性。首先,采用有限元(FEA)静力学仿真,得到惯性力载荷作用下集成在硅微悬臂梁上的压电薄膜的应力分布;选取最大应力值作为载荷,基于第一性原理计算纤锌矿AlN的弹性系数与应力的关系式,预测惯性力载荷作用下AlN弹性系数的最大变化量。其次,采用谐响应分析,对比空载和不同惯性力载荷作用下FBAR微加速度计的谐振频率和偏移特性,预测FBAR微加速度计的加速度-谐振频率偏移特性。最后仿真分析得到:惯性力载荷作用下,FBAR微加速度计的谐振频率向高频偏移,灵敏度约为数kHz/g;其加速度增量-谐振频率偏移特性曲线具有良好的线性度。     

Screen charge transfer by grounded tip on ferroelectric surfaces

We have investigated polarization reversal and charge transfer effects by a grounded tip on 50 nm thick ferroelectric thin films using piezoelectric force microscopy and Kelvin force microscopy. We observed the polarization reversal in the center of written domains, and also identified another mechanism, which is the transfer of screen charges toward the grounded tip. In order to overcome these phenomena, we successfully applied a modified read/write scheme featuring a bias voltage. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dielectric response in ferroelectric BaTiO3

The far-infrared optical and dielectric properties of ferroelectric perovskite titanate powder BaTiO₃ are reported. The terahertz time-domain spectroscopy (THz-TDS) measurement reveals that the low frequency dielectric response of BaTiO₃ is closely related to the lowest pair of transverse optical (TO) and longitudinal optical (LO) modes near at 180 cm⁻¹, which is verified by Raman spectroscopy. This result provides a better understanding of the relation of low-frequency dielectric function with the optical phonon mode for ferroelectric materials. Combining terahertz TDS with Raman spectra, the overall low frequency optical phonon response of BaTiO₃ is presented in an extended spectral range from 6.7 to 1200 cm⁻¹.     

Coherent acoustic phonon oscillations in semiconductor multiple quantum wells with piezoelectric fields

Large coherent acoustic phonon oscillations were demonstrated using InGaN/GaN multiple quantum wells with piezoelectric fields. With UV femtosecond pulse excitation, photogenerated carriers screened the piezoelectric field and initiated the displacive coherent phonon oscillations. The specific phonon frequency was selected by the coupling between the periodic carrier distribution and the corresponding acoustic phonon mode. The induced acoustic phonon oscillation resulted in piezoelectric field modulation and then caused absorption variation through the quantum confined Franz-Keldysh effect. The wave vector uncertainty due to the finite sample width was found to determine the observed dephasing time.     

An improvement of tilted AlN for shear and longitudinal acoustic wave

This study investigates c-axis tilted aluminum nitride (AlN) piezoelectric films for the improvement of both shear and longitudinal acoustic wave resonances. Solidly-mounted resonator (SMR) structure is adopted for the applications of high frequency wireless communications and high sensitivity sensors. As to the piezoelectric layer, c-axis tilted AlN has the capability to excite the dual-mode resonances, namely, the longitudinal and shear mode resonances. In this study, SMR devices made with a seven-layer molybdenum/silicon dioxide (Mo/SiO₂) Bragg reflector and the c-axis tilted AlN are carried out. A conventional off-axis sputtering technique is applied to grow the tilted AlN. The outcome frequency responses show dual resonant characteristics. However, the longitudinal resonance fades away with the AlN c-axis tilted angle, and the quality factor of the longitudinal resonance decreases. Consequently, we make an improvement by tilting the off-center substrates toward the sputtering source and successfully enhance the longitudinal resonance while preserving the shear resonance at the same time. Not only the shear resonance for the liquid-based sensing application, but also an outstanding longitudinal resonance could be obtained. The practicability of the dual-mode resonator is extended.     

Investigation of dielectric, piezoelectric and ferroelectric properties of b-axis grown triglycine sulphate single crystal

Large single crystal of triglycine sulphate (dimension 100 mm along monoclinic b-axis and 15 mm in diameter) was grown using the unidirectional solution growth technique. The X-ray diffraction studies confirmed the growth/long axis to be b-axis (polar axis). The dielectric studies were carried out at various temperatures to establish the phase transition temperature. The frequency response of the dielectric constant, dielectric loss and impedance of the crystal along the growth axis, was monitored. These are typically characterized by strong resonance peaks in the kHz region. The piezoelectric coefficients like stiffness constant (C), elastic coefficient (S), electromechanical coupling coefficient (k) and d ₃₁ were calculated using the resonance-antiresonance method. Polarization (P)-Electric field (E) hysteresis loops were recorded at various temperatures to find the temperature-dependent spontaneous polarization of the grown crystal. The pyroelectric coefficients were determined from the pyroelectric current measurement by the Byer and Roundy method. The ferroelectric domain patterns were recorded on (010) plane using scanning electron microscopy and optical microscopy.