ANALYSIS OF THE PIEZOTRONIC EFFECT OF A PIEZOELETRIC SEMICONDUCTOR FIBER UNDER MUTIPLE LOCAL TEMPERATURE LOADINGS 1)

温度改变产生的极化电势可对压电半导体结构内的物理量进行有效调控, 这在穿戴电子器件及与温度相关的半导体电子器件中有重要工程应用价值. 本文针对在多个局部均匀温度变化作用下的压电半导体杆结构, 采用一维热压电半导体多场耦合方程, 基于线性化的漂移-扩散(drift-diffusion)电流模型导出了问题的解析解. 以两个局部温度载荷情况为例, 数值分析了局部温度改变对压电半导体内位移、电势、电位移、极化强度、载流子分布等物理场的影响. 对于温度改变较大的情况, 在COMSOL软件的PDE模块中, 采用非线性电流模型, 进行数值模拟. 研究结果表明: 由于两个局部区域的温度改变, 在半导体杆内形成了局部势垒和势阱, 不同的温度改变量和作用区域会产生不同高度/深度的势垒/势阱, 为基于压电半导体的热压电电子学器件结构设计提供了理论指导.     

新型厚薄通用的压电层合板三角形CDST-S6E单元

基于压电复合材料层合板一阶剪切变形理论及叠层理论,构造了一种新型三角形三节点压电层合板单元,简记为CDST-S6E单元.该单元采用压电耦合的运动方程求解位移场及电势场,层合板主体结构用一阶剪切变形理论模拟,其剪应变场及单元转角场由结点包含有两个剪切自由度的DST-S6单元理论确定,电势作为附加自由度,应用叠层理论对压电层合板的电势场沿厚度方向进行线性插值.该CDST-S6E单元不需要借助减缩积分、假设应力或应变等辅助数学手段,也不会产生对稳定性带来影响的附加零能模式,可较好避免厚薄板单元的剪切闭锬问题且具有简洁的表达形式.数值算例表明,CDST-S6E单元具有较高的精度,可以较为精确地预测压电层合板的变形及电势场,是一种厚薄通用的优质压电层合板单元.     

热载荷下压电复合板有限元建模与形变控制

热载荷是引起在轨空间结构形变的重要因素之一，采用压电材料对结构热变形进行主动补 偿，需要建立热、电、力场相互耦合的动力学模型. 基于高阶位移场、高阶电势分布和线性 温度模型，推导了压电复合板结构的热、电、力场耦合的高阶有限元模型. 通过对压电双晶 片梁的分析，得到了压电片中电势沿厚度方向的抛物线型分布，而非通常文献中假设的线性 化分布模型的结果. 针对表面粘贴压电片的压电复合板，计算了热载荷作用下压电复合板的变形、 传感器的电压以及主动补偿后的结构变形，与文献给出的结果基本一致，验证了模型的正 确性. 同时还指出热电效应对结构变形和传感器电压具有十分重要的影响.     

层状压电半导体板的稳态弯曲振动分析

本文针对具有极化-变形-载流子耦合的层状压电半导体复合悬臂结构，理论研究了自由端在周期荷载作业下的稳态响应问题，导出了板中位移场、电场、载流子等物理量的解析表达式，并数值分析了周期荷载的幅值、激励频率和初始载流子浓度对结构宏观力学响应的影响。数值结果表明：在一阶固有频率下，结构内部各物理量响应幅值较大；在高阶固有频率下，各物理量响应出现多个局部峰值区域，其幅值相对减小，载流子会朝局部极值区域“聚集”或“离开”局部极值区域。初始载流子浓度在一定范围内对结构的固有频率以及各物理量的稳态响应有显著的调控作用。     

压电空心圆柱中的波特性

基于三维线性压电弹性理论,采用Legendre多项式方法研究了电开路时压电空心圆柱中轴向波的传播特性.给出了结构的频散曲线及其相应的非压电情况,展示了压电的影响.比较了压电对轴对称模态和弯曲模态影响的区别.从电势分布的角度分析了压电对弯曲扭转波的影响.最后讨论了径厚比和极化方向对波传播压电效应的影响.     

功能梯度压电材料圆环位移和电势边值问题的精确解

圆环形的压电材料器件在智能结构中得到了广泛的应用。本文推导了横观各向同性功能梯度压电材料圆环在内、外边界上给定位移和电势情况下的一般解。极化方向在圆环的半径方向，材料常数的梯度方向也设定在半径方向，并可表示为半径r的幂，本构关系为线性。然后推导了压电圆环外壁固定、接地，内壁沿垂向有一微小位移、电势分别为余弦分布和均匀分布的问题的精确解，并计算了该问题在这两种电势情况下产生的无量纲形式的径向和环向位移、电势、应力及电位移沿径向分布的数值结果。计算中考虑了不同的材料梯度，以及内壁的位移与电势的不同比例。     

恒磁场作用下压磁/压电半导体复合圆柱壳的耦合响应分析

本文针对由压磁材料和压电半导体材料组成的无限长复合圆柱壳结构,理论研究了其在径向恒磁场作用下结构内的多场耦合力学响应问题。为解析求解方便,文中分别采用单向耦合法和线性全耦合法,导出复合圆柱壳内位移场、电场、载流子等物理量的解析表达式。利用导出的解析表达式,数值分析了磁场大小和半导体层厚度比对结构内电势、电场和载流子的影响。计算结果表明：磁场和厚度比均可用来有效调控半导体层内的电学量,复合圆柱壳结构的厚度比有一个最优区间。     

恒磁场作用下压磁/压电半导体复合圆柱壳的耦合响应分析

本文针对由压磁材料和压电半导体材料组成的无限长复合圆柱壳结构，理论研究了其在径向恒磁场作用下结构内的多场耦合力学响应问题。为解析求解方便，文中分别采用单向耦合法和线性全耦合法，导出复合圆柱壳内位移场、电场、载流子等物理量的解析表达式。利用导出的解析表达式，数值分析了磁场大小和半导体层厚度比对结构内电势、电场和载流子的影响。计算结果表明：磁场和厚度比均可用来有效调控半导体层内的电学量，复合圆柱壳结构的厚度比有一个最优区间。     

基于Legendre多项式的双压电层合板三维压电谱元法模拟

谱单元作为一种高阶单元具有计算效率高和精度高的特点。本文在基于Legendre正交多项式的三维谱单元基础上提出了三维压电谱单元模型,用于压电层合板静力和动力性能模拟研究。压电层合板结构中的位移和电势自由度均离散到三维压电谱单元Gauss-Lobatto-Legendre(GLL)配置节点上,并且未对电势沿压电层厚度方向上的变化做任何假定。通过提高谱单元中沿压电层合板厚度方向上的形函数阶数的方法,来削弱三维谱单元在模拟薄板结构中出现的剪切闭锁现象。为验证单元的计算精度,取双压电层合板结构进行静力和动力行为模拟验证,并将计算结果与现有文献中的其它单元模型及有限元结果进行对比。结果表明,压电谱单元可有效模拟压电层合板的静力和动力行为,且提高谱单元形函数阶数可提高数值模拟精度。     

压电材料中切口/接头端部平面电弹性场奇异性有限元分析

为了对平面载荷作用下压电材料中切口或接头端部附近电弹性场奇异性问题进行分析，首先以应力平衡方程、Maxwell方程和和边界条件为基础，得到一种求解压电材料特征问题的弱式方程；其次，假定楔形切口或接头端部附近单元内位移和电势沿径向分布为指数形式，而周向方向分布则采用泡函数插值，将其代入弱式方程，建立一种只需对楔形切口或接头端部附近周边进行离散的一维简单有限元方法．压电材料的极化轴可以是任意方向．利用该有限元模型讨论了楔形切口角度、极化轴方向和边界条件对奇性场的影响．通过和其它特定情况下的现有解相比，证实了该文有限元数值方法的有效性，而且精度很高．     

Nonlinear magneto-mechanical-thermo coupling characteristic analysis for transport behaviors of carriers in composite multiferroic piezoelectric semiconductor nanoplates with surface effect

In this paper, to better reveal the surface effect and the screening effect as well as the nonlinear multi-field coupling characteristic of the multifunctional piezoelectric semiconductor (PS) nanodevice, and to further improve its working performance, a magneto-mechanical-thermo coupling theoretical model is theoretically established for the extensional analysis of a three-layered magneto-electro-semiconductor coupling laminated nanoplate with the surface effect. Next, by using the current theoretical model, some numerical analyses and discussion about the surface effect, the corresponding critical thickness of the nanoplate, and the distributions of the physical fields (including the electron concentration perturbation, the electric potential, the electric field, the average electric displacement, the effective polarization charge density, and the total charge density) under different initial state electron concentrations, as well as their active manipulation via some external magnetic field, pre-stress, and temperature stimuli, are performed. Utilizing the nonlinear multi-field coupling effect induced by inevitable external stimuli in the device operating environment, this paper not only provides theoretical support for understanding the size-dependent tuning/controlling of carrier transport as well as its screening effect, but also assists the design of a series of multiferroic PS nanodevices.

     

Effects of an attached functionally graded layer on the electromechanical behaviors of piezoelectric semiconductor fibers

In this paper, we propose a specific two-layer model consisting of a functionally graded (FG) layer and a piezoelectric semiconductor (PS) layer. Based on the macroscopic theory of PS materials, the effects brought about by the attached FG layer on the piezotronic behaviors of homogeneous n-type PS fibers and PN junctions are investigated. The semi-analytical solutions of the electromechanical fields are obtained by expanding the displacement and carrier concentration variation into power series. Results show that the antisymmetry of the potential and electron concentration distributions in homogeneous n-type PS fibers is destroyed due to the material inhomogeneity of the attached FG layer. In addition, by creating jump discontinuities in the material properties of the FG layer, potential barriers/wells can be produced in the middle of the fiber. Similarly, the potential barrier configuration near the interface of a homogeneous PS PN junction can also be manipulated in this way, which offers a new choice for the design of PN junction based devices.

     

Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media

A modified polarization saturation model is proposed and addressed mathematically using a complex variable approach in two-dimensional(2 D) semipermeable piezoelectric media. In this model, an existing polarization saturation(PS) model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displacement(COD), the crack opening potential(COP), and the local stress intensity factors(SIFs) are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.     

考虑挠曲电效应的压电纳米薄板力-电-热耦合特性研究

摘要：挠曲电效应是由应变梯度引起的,与尺度相关的力电耦合效应。基于Kirchhoff板假设和挠曲电理论,本文推导了温度和电压作用下的压电薄板力-电-热耦合微分控制方程,定量分析了微分控制方程中非线性项的影响,并针对四周固支压电薄板采用Ritz法求解,数值计算了压电薄板的弯曲和振动行为。在研究温度和挠曲电效应对薄板耦合特性和力学行为的影响时,本文分别考虑了材料系数不随温度变化和随温度线性变化两种情况。以PZT-5H为例,我们讨论了挠曲电和温度对压电薄板的横向位移和固有频率的影响。研究结果表明挠曲电效应对压电纳米薄板的力学行为影响很大,且具有明显的尺寸效应。此外,薄板对温度变化非常敏感。因此,可通过挠曲电效应和温度来调控压电纳米薄板的多场耦合特性和力学行为,进而优化基于压电薄板的NEMS/MEMS中传感器、作动器等电子器件的性能。     

考虑挠曲电效应的压电纳米薄板力-电-热耦合特性研究

摘要：挠曲电效应是由应变梯度引起的，与尺度相关的力电耦合效应。基于Kirchhoff板假设和挠曲电理论，本文推导了温度和电压作用下的压电薄板力-电-热耦合微分控制方程，定量分析了微分控制方程中非线性项的影响，并针对四周固支压电薄板采用Ritz法求解，数值计算了压电薄板的弯曲和振动行为。在研究温度和挠曲电效应对薄板耦合特性和力学行为的影响时，本文分别考虑了材料系数不随温度变化和随温度线性变化两种情况。以PZT-5H为例，我们讨论了挠曲电和温度对压电薄板的横向位移和固有频率的影响。研究结果表明挠曲电效应对压电纳米薄板的力学行为影响很大，且具有明显的尺寸效应。此外，薄板对温度变化非常敏感。因此，可通过挠曲电效应和温度来调控压电纳米薄板的多场耦合特性和力学行为，进而优化基于压电薄板的NEMS/MEMS中传感器、作动器等电子器件的性能。     

Typical transient effects in a piezoelectric semiconductor nanofiber under a suddenly applied axial time-dependent force

Based on the mechanical motion equation, Gauss' s law, and the current continuity condition, we study a few typical transient effects in a piezoelectric semiconductor(PS) fiber to realize the startup and turning-off functions of common piezotronic devices. In this study, the transient extensional vibration induced by a suddenly applied axial time-dependent force is examined in a cantilevered n-type ZnO nanofiber. Neither the magnitude of the loadings nor the doping concentration significantly affects the propagation caused by disturbance of the axial displacement.However, both of the factors play an important role in the propagation caused by disturbance of the electron concentrations. This indicates that the electromechanical coupling effect can be expected to directly determine the electronic performance of the devices. In addition, the assumption of previous simplified models which neglect the charge carriers in Gauss' s law is discussed, showing that this assumption has a little influence on the startup state when the doping concentration is smaller than 10~(21) m~(-3).This suggests that the screening effect of the carriers on the polarized electric field is much reduced in this situation, and that the state is gradually transforming into a pure piezoelectric state. Nevertheless, the carriers can provide a damping effect, which means that the previous simplified models do not sufficiently describe the turning-off state. The numerical results show that the present study has referential value with respect to the design of newly multifunctional PS devices.     

Stress-induced potential barriers and charge distributions in a piezoelectric semiconductor nano?ber

The performance of a piecewise-stressed ZnO piezoelectric semiconductor nano?ber is studied with the multi-?eld coupling theory. The ?elds produced by equal and opposite forces as well as sinusoidally distributed forces are examined. Speci?c distributions of potential barriers, wells, and regions with effective polarization charges are found. The results are fundamental for the mechanical tuning on piezoelectric semiconductor devices and piezotronics.