Finite width effect of thin-films buckling on compliant substrate: Experimental and theoretical studies

Buckling of stiff thin films on compliant substrates has many important applications ranging from stretchable electronics to precision metrology and sensors. Mechanics plays an indispensable role in the fundamental understanding of such systems. Some existing mechanics models assume plane-strain deformation, which do not agree with experimental observations for narrow thin films. Systematic experimental and analytical studies are presented in this paper for finite-width stiff thin films buckling on compliant substrates. Both experiments and analytical solution show that the buckling amplitude and wavelength increase with the film width. The analytical solution agrees very well with experiments and therefore provides valuable guide to the precise design and control of the buckling profile in many applications. The effect of film spacing is studied via the analytical solutions for two thin films and for periodic thin films.     

磁电复合材料中拓扑磁结构的力学调控

磁性斯格明子是在一些铁磁材料中存在的一种重要拓扑磁结构，由于其具有独特的磁-电-力-热多场耦合特性，在未来新型自旋电子器件中有着广泛的应用前景。然而，磁性斯格明子一般需要在外加磁场下才能稳定存在，极大地限制了其在自旋电子器件中的实际应用。本文基于实空间下磁电材料的相场模拟，发现铁电和铁磁复合薄膜中铁电斯格明子可以通过界面变形来稳定铁磁斯格明子。由于力电耦合效应，铁电层中铁电斯格明子的非均匀分布极化在界面产生周期性的非均匀界面变形。界面变形通过力磁耦合效应，使铁磁层中的磁性斯格明子在没有外加磁场的条件下能够稳定存在。本文的研究结果表明，基于磁电复合材料中的力-电-磁耦合效应，通过优化设计复合材料中不同组元的结构，可以实现拓扑磁结构的力学调控，从而为设计基于拓扑磁结构的新型自旋电子器件提供了新思路。     

压电薄板屈曲有限元分析及DKQ单元

在机电耦合本构方程基础上,利用Hamilton原理推导了压电薄板屈曲分析的有限元特征方程和机电耦合的内力计算公式,在有限元实现中选择了基于Kirchhoff薄板假定的四边形薄板单元（DKQ单元）,并给出该单元的几何刚度阵及其数值积分方法。在大型通用有限元分析和优化设计软件系统JIFEX中实现了该方法。给出的数值验证了DKQ单元在屈曲分析和压电薄板静力分析中具有较高精度和收敛性,通过机械荷载和电荷载联合作用下的临界荷载计算,表明压电耦合效应能够影响结构的稳定性,可以通过改变外加电压对结构稳定性进行控制。     

铅基压电薄膜材料的制备、微结构与性能

随着微电子技术的发展和高度集成化的趋势,压电薄膜材料愈来愈受到人们的重视.本文对铅基类压电薄膜材料的研究进展进行了评述,主要讨论了:(1) 两种主要制备方法:脉冲激光熔融法(PLD)和溶胶凝胶法(Sol-Gel); (2) 压电薄膜微观结构的表征,如畴结构,薄膜材料与大块材料的差别等;(3) 压电薄膜材料力学、电学及相互耦合性能的评价参数,薄膜处理过程的相变和残余应力和破坏特征.最后提出了人们可能关注的一些问题.      

Stress and Moisture Effects on Thin Film Buckling Delamination

Deposition processes control the properties of thin films; they can also introduce high residual stresses, which can be relieved by delamination and fracture. Tungsten films with high 1–2 GPa compressive residual stresses were sputter deposited on top of thin (below 100 nm) copper and diamond-like carbon (DLC) films. Highly stressed films store large amounts of strain energy. When the strain energy release rate exceeds the films' interfacial toughness, delamination occurs. Compressive residual stresses cause film buckling and debonding, forming open channels. Profiles of the buckling delaminations were used to calculate the films' interfacial toughness and then were compared to the adhesion results obtained from the superlayer indentation test. Tests were conducted in both dry and wet environments and a significant drop in film adhesion, up to 100 times was noticed due to the presence of moisture at the film/substrate interface.     

A Force Domain Analog-to-Digital Converter Applied to Microscale Tensile Test

Mechanical characterization of sub-micron thin films or similar small scale structures have been a continuous challenge to the mechanics community due to the difficulty in accurately quantizing the applied load and the resulted deformation. In this paper, a new force-domain analog-to-digital converter (F-D ADC) created from the concept of Flash ADC in electronics is developed to perform thin film tensile tests. The key component of the F-D ADC is a quantizer-array of microfabricated buckling beams of varying lengths. During testing, the tensile force applied in the test specimen is converted to the compressive force in the quantizer beam array and digitized by using the critical buckling load of the beams as they progressively buckle with increasing force amplitude. The deformation of the specimen is controlled by the piezoelectric actuator. Successful testing of (110) single crystal silicon and titanium/nickel (Ti/Ni) multilayer thin film specimens demonstrated the feasibility of this novel F-D ADC concept.     

压电板屈曲和后屈曲的有限元分析

采用板的一附剪切理论,并考虑结构的几何非线性,基于Ｔｏｔａｌ Ｌａｇｒａｎｇｅ方法,建立了在弱非线性耦合假设下压电智能的有限元控制方法,分析了没边界条件下压电板的屈曲和后屈曲,计算结果表明,在单向压力作用下,材料的压电效应和外加电压对板的屈曲载荷及后屈曲影响很小;而电场对位移加载简支板的屈曲影响较显著。该文为压电材料的工程应用提供了理论指导,同时提供了一种有效的有限元分析方法。     

Strain tunability of dielectric and ferroelectric properties in epitaxial lead titanate thin films

Many distinguished properties of epitaxial ferroelectric thin films can be tunable through the misfit strain. The strain tunability of ferroelectric and dielectric properties in epitaxial lead titanate ultrathin films is numerically investigated by using a phase field model, in which the surface effect of polarization is taken into account. The response of polarization to the applied electric field in the thickness direction is examined with different misfit strains at room temperature. It is found that a compressive misfit strain increases the coercive field and the remanent polarization while a tensile misfit strain decreases both of them. The nonlinear dielectric constants of the thin films with tensile misfit strains are much larger than those of the thin films without misfit strains, which are attributed to the existence of the a/c/a/c multiple domains in the thin films under tensile misfit strains.     

Localized ridge wrinkling of stiff films on compliant substrates

Wrinkling of thin stiff films on thick compliant elastomeric substrates subject to plane strain compression is considered for cases in which the substrate is pre-stretched prior to film attachment. Advanced wrinkling modes are investigated that evolve as the systems are compressed beyond the onset of the primary sinusoidal wrinkling mode. If the substrate pre-stretch is greater than about 40%, an advanced mode in the form of a series of well-spaced ridges separated by relatively flat film is observed in the simulations. Our experiments reveal a localization mode in the form of alternating packets of large and small amplitude wrinkles, but not ridges, while ridge formation has been observed in other recent experiments. Measurements of undulation amplitudes have been made for wrinkle fields of stiff films formed by oxidation of the surface of pre-stretched PDMS substrates. Simulations have been performed with a finite element model and an analytical film/substrate model. The formation of the ridge mode is a consequence of the altered nonlinearity of the substrate produced by the pre-stretch. The role of the tangential substrate stiffness in suppressing localization at the ridges is also highlighted. If there is no substrate pre-stretch, or if the substrate is pre-compressed, the primary sinusoidal mode gives way to an entirely different sequence of advanced modes usually entailing period doubling followed by folding. The nature of substrate nonlinearity that leads to ridges or folds is discussed.     

Highly reliable bipolar resistive switching in sol-gel derived lanthanum-doped PbTiO3 thin film： Coupling with ferroelectricity？

Nanoscale PbxLa1-,Ti1-x/4O3 （PLT） thin film has been fabricated on Pt／Ti／SiO2／Si substrates by chemical solution deposition （CSD） method. Ferroelectricity of the fresh-made PLT thin film has been clearly detected through piezoelectric force microscopy （PFM） by writing reversible ferroelectric domains. However, PLT thin film also shows off-standard ferroelectric hysteresis loops highly dependent on frequency, indicating large amount of mobile space charges in the film. Subsequent current-voltage （C-V） studies show that sandwich-like Pt／PLT／Pt structure exhibits notable bipolar resistive switching （BRS） characteristics with high stability （〉 103 switching cycles）. It is found that the C-V curves of both high- and low-resistance states have the feature of space-charge-limited current （SCLC） conduction, indicating important roles of defects in the conduction. X-ray photoelectron spectroscopy measurement further verifies that oxygen vacancies based conductive filament mechanism is likely responsible for the observed RS effect. Our demonstration of stable RS effect in the PLT thin film and its possible coupling with ferroelectricity is promising in device development and applications, such as development of ferroelectric-tunable RS memories.     

Size-dependent response of ultra-thin films with surface effects

A modified continuum model of elastic films with nano-scale thickness is proposed by incorporating surface elasticity into the conventional nonlinear Von Karman plate theory. By using Hamilton’s principle, the governing equations and boundary conditions of the ultra-thin film including surface effects are derived within the Kirchhoff’s assumption, where the effects of non-zero normal stress and large deflection are taken into account simultaneously. The present model is then applied to studying the bending, buckling and free vibration of simply supported micro/nano-scale thin films in-plane strains and explicit exact solutions can be obtained for these three cases. The size-dependent mechanical behavior of the thin film due to surface effects is well elucidated in the obtained solutions.     

MINIMUM SIZE OF 180 DEGREE DOMAINS IN FERROELECTRIC THIN FILMS COVERED BY ELECTRODES

Ferroelectric domain switching under low voltage or short pulses is of interest for the development of high-density random access memory (FRAM) devices. Being necessarily very small in size, instability and back switching often occur when the external voltage is removed, which creates serious problems. In this investigation, a general approach to determine the minimum size of ferroelectric domain to avoid back switching was developed, and as an example, a 180°domain in a ferroelectric thin film covered by the upper and lower electrodes was considered in detail. We note that our approach is generally applicable to many other fields, including phase transformation, nucleation and expansion of dislocation loops in thin films, etc.     

具有压电材料弹性环形板的屈曲

对在不同位置粘有任意多对压电片的弹性环形板在电压和径向压力作用下的轴对称屈曲进行了研究．根据压电效应的等效作用量，初参数法以及传递矩阵方法得到了环板屈曲的特征方程．对不同位置及不同宽度的压电片，计算了结构的屈曲载荷．并得到了稳定性边界曲线．     

Deformation and buckling of a pre-stretched soft elastic film induced by spatially modulated electric fields

We study mechanical response of a uniaxially pre-stretched soft elastic film to spatially modulated electric fields. The film is adhered onto a rigid, conductive substrate, and the electric field is generated through a periodically patterned electrode over the film. Our work shows that at low applied voltages the deformation of the film follows the pattern of the electrode, allowing for the transfer of the surface morphology of the electrode onto the film surface in opposite sign. However, when the voltage reaches a threshold, the film buckles to form stripped pattern parallel to the tensile direction. This newly resulting deformation is superposed on that before onset of buckling, leading to complicated and ordered topography of the film. The phenomenon may provide a new clue for creating ordered surface structures with the aid of elastic buckling.     

Buckling of a stiff thin film on a pre-strained bi-layer substrate

Controlled buckling can impart stretchable mechanics to brittle materials when integrated as thin films on soft, elastomeric substrates. Typical elastomers are permeable to fluids, however, and therefor unable to provide robust barriers to entry of water, for instance, into devices built with the supported thin films. In addition, the mechanical strength of a system dominated by a soft substrate is often unsatisfactory for realistic applications. We show that introduction of a bi-layer substrate yields a robust, high strength system that maintains stretchable characteristics, with a soft layer on top of a relatively stiff layer in the substrate. As a mechanical protection, a soft encapsulation layer can be used on top of the device and the stretchability of the encapsulated system is smaller than that of the system without encapsulation. A simple, analytic model, validated by numerical analysis and FEA, is established for stiff thin films on a bi-layer substrate, and is useful to the design of stretchable systems.     

温度场下岛-桥结构屈曲薄膜的动力学分析

基于岛-桥结构的柔性电子器件已被用于健康监测和皮肤电子等领域。但是柔性电子器件在工作中极易受工作温度变化等激励产生振动,进而影响器件的灵敏度与可靠性。因此本文研究在温度场作用下岛-桥结构屈曲薄膜的动力学问题。首先,基于Euler-Bernoulli梁理论,建立温度场作用下岛-桥结构屈曲薄膜的动力学控制方程。其次,通过引入新变量,将原动力学方程引入Hamilton体系中,得到相应的Hamilton正则方程。随后,采用辛Runge-Kutta方法求解该Hamilton正则方程,并与经典Runge-Kutta方法对比,数值结果显示了辛算法在求解非线性动力学方程时高精度、高数值稳定性的优势,进一步讨论了温度变化量、预应变、阻尼系数等对屈曲薄膜动力学响应的影响。本文研究为柔性电子器件动力学设计提供了理论参考。     

Two-dimensional equations for thin-films of ionic conductors

A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck (PNP) theory, the two-dimensional (2D) equations for thin ionic conductor films are obtained from the three-dimensional (3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.     

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。