Casimir Effect on the Pull-in Parameters of Nanometer Switches

Casimir effect on the critical pull-in gap and pull-in voltage of nanoelectromechanical switches is studied. An approximate analytical expression of the critical pull-in gap with Casimir force is presented by the perturbation theory. The corresponding pull-in parameters are computed numerically, from which one can notice the nonlinear effect of Casimir force on the pull-in parameters. The detachment length has been presented, which increases with increasing thickness of the beam.

Molecular Dynamics And Density Functional Studies Of A Body-Centered-Tetragonal Polymorph Of Zno

We report a previously unknown body-centered-tetragonal structure for ZnO. This structure results from a phase transformation from wurtzite in [0001]-oriented nanorods during uniaxial tensile loading and is the most stable phase for ZnO when stress is above 7 GPa. The stress-induced phase transformation has important implications for the electronic, piezoelectric, mechanical, and thermal responses of ZnO. The discovery of this polymorph brings about a more complete understanding of the extent and nature of polymorphism in ZnO. A crystalline structure-load triaxiality map is developed to summarize the relationship between structure and loading.

Piezoelectricity Of Zno Films Prepared By Sol-Gel Method

ZnO piezoelectric thin films were prepared on crystal substrate Si(111) by sol-gel technology, then characterized by scanning electron microscopy, X-ray diffraction and atomic force microscopy (AFM). The ZnO films characterized by X-ray diffraction are highly oriented in (002) direction with the growing of the film thickness. The morphologies, roughness and grain size of ZnO film investigated by AFM show that roughness and grain size of ZnO piezoelectric films decrease with the increase of the film thickness. The roughness dimension is 2.188-0.914 nm. The piezoelectric coefficient d(33) was investigated with a piezo-response force microscope (PFM). The results show that the piezoelectric coefficient increases with the increase of thickness and (002) orientation. When the force reference is close to surface roughness of the films, the piezoelectric coefficient measured is inaccurate and fluctuates in a large range, but when the force reference is big, the piezoelectric coefficient d(33) changes little and ultimately keeps constant at a low frequency.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.

Snap-through and pull-in instabilities of an arch-shaped beam under an electrostatic loading

The snap-through and pull-in instabilities of the micromachined arch-shaped beams under an electrostatic loading are studied both theoretically and experimentally. The pull-in instability that results in a system collision with an electrode substrate may lead to a system failure and, thus, limits the system maximum displacement. The beam/plate structure with a flat initial configuration under an electrostatic loading can only experience the pull-in instability. With the different arch configurations, the structure may experience either only the pull-in instability or the snap-through and pull-in instabilities together. As shown in our computation and experiment, those arch-shaped beams with the snap-through instability have the larger maximum displacement compared with the arch-shaped beams with only the pull-in stability and those with the flat initial configuration. The snap-through occurs by exerting a fixed load, and the structure experiences a discontinuous displacement jump without consuming power. Furthermore, after the snap-through jump, the structures are demonstrated to have the capacity to withstand further electrostatic loading without pull-in. Those properties of consuming no power and increasing the structure deflection range without pull-in is very useful in microelectromechanical systems design, which can offer better sensitivity and tuning range.

Stability and bifurcation behaviour of electrostatic torsional NEMS varactor influenced by dispersion forces

The influences of Casimir and van der Waals forces on the nano-electromechanical systems (NEMS) electrostatic torsional varactor are studied. A one degree of freedom, the torsional angle, is adopted, and the bifurcation behaviour of the NEMS torsional varactor is investigated. There are two bifurcation points, one of which is a Hopf bifurcation point and the other is an unstable saddle point. The phase portraits are also drawn, in which periodic orbits are around the Hopf bifurcation point, but the periodic orbit will break into a homoclinic orbit when meeting the unstable saddle point.

压电材料椭圆切口的力学分析

在线性压电本构方程框架下，用复势函数方法对椭圆切口模型进行了精确的数值计算。完整地考虑了各向异性力电耦合效应以及切口内不同电介质的介电性质。给出了切口内部不同介电性质对压电材料内部应力的影响。指出了Sosa文章里的一些计算错误。由于现在文献中很小有关于电导通边界条件政府解的数值结果，所以本文同时提供了不同电边界条件下的理论解的数值结果。最后通过最小势能原理建立了8结点有限元模型，对椭圆切口问题进行了计算并与理论解进行了仔细比较。

Piezoelectricity of ZnO films prepared by sol-gel method

ZnO piezoelectric thin films were prepared on crystal substrate Si(111) by sol-gel technology, then characterized by scanning electron microscopy, X-ray diffraction and atomic force microscopy (AFM). The ZnO films characterized by X-ray diffraction are highly oriented in (002) direction with the growing of the film thickness. The morphologies, roughness and grain size of ZnO film investigated by AFM show that roughness and grain size of ZnO piezoelectric films decrease with the increase of the film thickness. The roughness dimension is 2.188-0.914 nm. The piezoelectric coefficient d(33) was investigated with a piezo-response force microscope (PFM). The results show that the piezoelectric coefficient increases with the increase of thickness and (002) orientation. When the force reference is close to surface roughness of the films, the piezoelectric coefficient measured is inaccurate and fluctuates in a large range, but when the force reference is big, the piezoelectric coefficient d(33) changes little and ultimately keeps constant at a low frequency.

线性压电材料的有限元分析

本文利用线性压电学理论，编制了线性压电材料四结点等参有限元程序，进行了校核，并对PZT-5A材料压电智能元件和压电材料标准断裂试进行了计算，计算包括：①采用实际工程应用的压电智能元件尺寸，计算了元件的压电响应；并针对元件内部电极尖端区域容易引起破坏的现象，计算了该区域的奇异应力、应变场及电场。②计算了加力和加电两种情况下压电材料标准断裂试件应力强度因子影响系数F_I和电位移强度因子影响系数F_D。裂纹面边界条件采用D-P条件，试件包括紧凑拉伸标准试件和三点弯曲标准试件。③应用Lagrange乘子法将Parton裂纹边界条件加于有限元程序中，计算了上述两种标准断裂试件的F_I和F_D，计算结果与采用D-P裂纹边界条件的计算结果有很大差异。

带压电陶瓷片梁的力学分析和二类变量广义变分原理

对于采用贴有压电陶瓷片作为作动元件的智能结构，在进行自适应控制时，往往要分析压电陶瓷片所引起的结构中的应力、应变和位移。对于带有压电陶瓷片梁的力学分析，文献中大多采用Euler-Bernoulli模型，即不考虑梁中的剪力，且假定梁沿厚度方向满足直法线假定。考虑到压电陶瓷片对梁的作用主要是通过粘贴层以剪力的形式传递到梁上，梁截面上的剪应力和剪应变一般很大，其影响不能忽略。本文采用Hellinger-Reissner二类变分广义余能原理，导出考虑梁截面上剪应力和剪应变影响的方程式，其中采用吉尔法求解非齐次常微分方程组。并将求得的解与相同条件的有限元解进行比较。结果证明该方法很有效。本文还对二类广义变分法进行了一般的讨论，发现，在使用二类广义变分法求解时，随着应力和位移所取项数的增加，结果有时反而变坏。并对二类广义变分法的使用提出了一些建议。

Energy Functions And Basic Equations For Ferroelectrics

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.

Near-diffraction-limited, 35.4 W laser-diode end-pumped Nd:YVO4 slab laser operating at 1342 nm

A diode stack end-pumped Nd:YVO4 slab laser at 1342 nm with near-diffraction-limited beam quality by using a hybrid resonator was presented. At a pump power of 139.5 W, laser power of 35.4 W was obtained with a conversion efficiency of 25.4% of the laser diode to laser output. The beam quality M-2 factors were measured to be 1.2 in the unstable direction and 1.3 in the stable direction at the output power of 29 W. (C) 2009 Optical Society of America

A laser-diode-pumped acoustic-optic Q-switched Nd:YVO4 slab laser with a hybrid resonator

A 32.1 W laser-diode-stack pumped acoustic-optic Q-switched Nd:YVO4 slab laser with hybrid resonator at 1064 nm was demonstrated with the pumping power of 112 W and repetition rate of 40 kHz, the pulse duration was 32.47 ns. The slope efficiency and optical-to-optical efficiency were 37 and 28.7%, respectively. At the repetition rate of 20 kHz and pumping power of 90 W, the average output power and pulse duration were 20.4 W and 20.43 ns, respectively. With the pumping power of 112 W, the beam quality M-2 factors in CW operation were measured to be 1.3 in stable direction and 1.6 in unstable direction.

Application of sample-and-hold circuits in the laser frequency-shifting

A new method of frequency-shifting for a diode laser is realized. Using a sample-and-hold circuit, the error signal can be held by the circuit during frequency shifting. It can avoid the restraint of locking or even lock-losing caused by the servo circuit when we input a step-up voltage into piezoelectric transition (PZT) to achieve laser frequency-shifting.