Synthesis surface effects on the stress and deformation of film/substrate system

The closed-form solutions of bending curvature and stress distribution in film/substrate system with the synthesis surface effect are proposed by minimizing the total potential energy. Effects of the roughness and the residual surface stress on stress in film are addressed. Results reveal that, at a given thickness of the substrate, effects of roughness and residual surface stress on the bending curvature become significant with decreasing the film thickness. The roughing surface will enlarge the magnitudes of bending curvature and film stress. The direction change of residual surface stresses can lead to a reversed bending of film/substrate system.     

Edge misfit dislocation formation at the interface of a nanopore and infinite substrate with surface/interface effects

The model of an edge misfit dislocation at the interface of the hollow nanopore and the infinite substrate with surface/interface stress is investigated. Using the complex variable method, analytical solutions for complex potentials of a film due to an edge misfit dislocation located in the film with surface/interface effect are derived, and the stress fields of the film and the edge misfit dislocation formation energy can be obtained. The critical conditions for edge misfit dislocation formation are given at which the generation of an edge misfit dislocation is energetically favourable. The influence of the ratio of the shear modulus between the film and the infinite substrate, the misfit strain, the radius of the nanopore and the surface/interface stress on the critical thickness of the film is discussed.     

Buckling of a stiff thin film on a compliant substrate under anisotropic biaxial prestrain

The structure of stretchable electronics is based on the buckling of a thin film on a compliant substrate. Under anisotropic biaxial prestrains, this structure may buckle into several patterns, including cylindrical, checkerboard, and undulating patterns. The displacement and energy of each pattern are deduced analytically. By comparing their minimum potential energies, the critical buckling condition of each pattern is determined. After secondary bifurcation, the checkerboard pattern occurs just above the critical prestrains, but the undulating pattern dominates other regions. The buckling amplitude and wavenumber of the undulating pattern are shown under biaxial prestrains. Even if the structure is under equi-biaxial prestrains, it may buckle into an asymmetric undulating pattern.     

Physics perspectives of heavy-ion collisions at very high energy

The structure of stretchable electronics is based on the buckling of a thin film on a compliant substrate. Under anisotropic biaxial prestrains, this structure may buckle into several patterns, including cylindrical, checkerboard, and undulating patterns. The displacement and energy of each pattern are deduced analytically. By comparing their minimum potential energies, the critical buckling condition of each pattern is determined. After secondary bifurcation, the checkerboard pattern occurs just above the critical prestrains, but the undulating pattern dominates other regions. The buckling amplitude and wavenumber of the undulating pattern are shown under biaxial prestrains. Even if the structure is under equi-biaxial prestrains, it may buckle into an asymmetric undulating pattern.     

Thickness of the helium film on a curved substrate

It is estimated that, on a substrate with radius of curvature 500Å, a helium film is approximately 1/8 as thick at it would be on a flat substrate.     

考虑介质膨胀速率的锂离子电池管状电极中扩散诱导应力及轴向支反力分析

硅作为锂离子电池阴极材料相对于传统负极材料具有高比容量,价格低廉等优势.本文针对充电过程中锂离子电池中电极建立力学模型和扩散模型,并在扩散模型引入考虑介质膨胀速率的影响.以硅空心柱形电极为例,分析了恒流充电下介质膨胀速率对电极中扩散诱导应力分布的影响,并研究了不同内外半径比、充电速率、材料参数以及锂化诱导软化系数(lithiation induced softening factor,LISF)对轴向的支反力达到临界欧拉屈曲力所需时间的影响.结果表明,随着电极中锂浓度上升,介质膨胀速率对应力分布的影响增大,对轴向的支反力影响较小.弹性模量和应力成正比,但其与轴向的支反力达到临界欧拉屈曲力所需时间无关;扩散系数与所需时间成反比;偏摩尔体积增大时,达到临界屈曲力所需时间减少;随着LISF绝对值增大,完全锂化时轴向力降低.     

Hydrogen-induced buckling of Pd films studied by positron annihilation

Hydrogen loading of thin films introduces very high compressive stresses which grow in magnitude with increasing hydrogen concentration. When the hydrogen-induced stresses exceed a certain critical in-plane stress value, the loaded film starts to detach from the substrate. This results in the formation of buckles of various morphologies in the film layer. Defect studies of a hydrogen loaded Pd film which undergoes a buckling process are presented, using slow positron implantation spectroscopy, in situ acoustic emission, and direct observations of the film structure by transmission electron and optical microscopies. It is found that buckling of the film occurs at hydrogen concentrations x_H ≥ 0.1 and causes a significant increase of the dislocation density in the film.     

Kink instability of a highly deformable elastic cylinder

When a soft elastic cylinder is bent beyond a critical radius of curvature, a sharp fold in the form of a kink appears catastrophically at its compressed side while the tensile side remains smooth. The critical radius increases linearly with the diameter of the cylinder but remains independent of its material properties such as modulus; the maximum deflection at the location of the kink depends on both the material and geometric properties of the cylinder. The catastrophic dynamics of evolution of the kink depicts propagation of a shear wave from the location of the kink towards the edges signifying that kinking is an elastic response of the material which results in extreme localization of curvature. We have rationalized this phenomenon in the light of the classical Euler's buckling instability in slender elastic rods.     

离子束溅射制备低应力深紫外光学薄膜

采用离子束溅射制备了Al F3、Gd F3单层膜及193 nm减反和高反膜系,分别使用分光光度计、原子力显微镜和应力仪研究了薄膜的光学特性、微观结构以及残余应力。在优选的沉积参数下制备出消光系数分别为1.1×10~(-4)和3.0×10~(-4)的低损耗AlF_3和GdF_3薄膜,对应的折射率分别为1.43和1.67,193 nm减反膜系的透过率为99.6%,剩余反射几乎为零,而高反膜系的反射率为99.2%,透过率为0.1%。应力测量结果表明,AlF_3薄膜表现为张应力而GdF_3薄膜具有压应力,与沉积条件相关的低生长应力是AlF_3和GdF_3薄膜残余应力较小的主要原因,采用这两种材料制备的减反及高反膜系应力均低于50 MPa。针对平面和曲率半径为240 mm的凸面元件,通过设计修正挡板,250 mm口径膜厚均匀性均优于97%。为亚纳米精度的平面元件镀制193 nm减反膜系,镀膜后RMS由0.177 nm变为0.219 nm。     

The definition and calculation of interfacial energies for thin films

We provide a new definition of the interfacial energy which eliminates three physically extraneous contributions from the conventional definition: (1) the strain or stress energy due to lattice mismatch between film and substrate; (2) the surface energy of the film-vacuum interface; and, (3) the substrate surface energy contribution from substrate layers below the film layers. This new interface energy then quantifies the variation in interactions among film/substrate, film/film and substrate/substrate bonding. Using this new definition, we derive the equations for evaluation of the interfacial energy in terms of the interaction energy for any atom in each layer of the film/substrate, film/film and substrate/substrate systems. With this formulation, it is simple to determine the dependence of the interfacial energy on the film thickness using virtually any interaction potential. Using a corrected effective medium theory, we present results for a few pseudomorphic film systems containing Ni/Cu, Ni/Ag, Cu/Ag and Rh/Ag on (111) and (100) surfaces. These systems cover a wide range of lattice mismatch and alloy formation energies. The results demonstrate that the new definition of interfacial energy converges after only 3–4 film layers, regardless of the degree of lattice mismatch. We also show that the interfacial energies at (100) and (111) interfaces differ and that the interfacial energy for a given pair of materials depends on which of the materials is the film.     

柔性液晶微透镜阵列的制备与性能研究

针对集成成像视场角狭小的问题,设计并制备了一种柔性圆孔驱动电极控制液晶分子偏转的可弯曲和焦距可调的柔性液晶微透镜阵列。利用光刻技术在柔性ITO基板表面刻蚀并形成规则的圆孔阵列电极,旋涂工艺制备柔性聚酰亚胺(PI)膜层,PI膜层经60℃加热5 min后,再利用等离子体在功率630 W条件下处理5 min固化成PI取向层。利用液晶盒成盒工艺将上、下基板组装成液晶透镜,研究未弯曲和弯曲曲率半径7.5 cm条件下液晶微透镜阵列的光学性能。实验结果表明,所制备的液晶透镜在未弯曲和曲率半径为7.5 cm的情况下均可实现聚焦功能,且液晶微透镜阵列的干涉圆环均匀,聚焦光斑小。在驱动电压3~5.3 Vrms下,弯曲曲率半径为7.5 cm的液晶微透镜阵列焦距可调的范围为0.43~1.05 mm。     

GaSb基PECVD法制备SiO2薄膜的应力研究

为了实现在GaSb衬底上获得低应力的SiO₂薄膜,研究了等离子体增强化学气相沉积法（PECVD）在晶格失配较大的GaSb衬底上沉积SiO₂薄膜的应力情况。通过改变薄膜沉积时的工艺条件,如反应温度、射频功率、反应压强、气体流量比,并基于曲率法模型,对镀膜前后的曲率半径进行了实验测量,利用Stoney公式计算相关应力值并绘制应力变化曲线。详细讨论了PECVD工艺条件的改变对SiO₂薄膜应力所产生的影响。同时通过在Si衬底上沉积SiO₂薄膜,对比分析了导致薄膜应力产生的因素及变化过程。实验结果表明,在沉积温度为300℃、射频功率为20 W、腔体压强为90 Pa、气体流量比SiH₄/N₂O为125/70 cm³·min^-1的工艺参数下,PECVD法在GaSb衬底上沉积的SiO₂薄膜应力相对较小。     

ZnO外延膜与蓝宝石衬底的取向偏差及其弯曲变形

采用常压MOCVD方法在Al2O3(00．1)衬底上生长出了高质量ZnO单晶薄膜。由ZnO(00．2)面和Al2O3(00．6)面及ZnO(10．2)面和Al2O3(11．6)面X射线双晶(w／2θ衍射曲线的相对峰位,得到ZnO外延膜的晶格常数及外延层和衬底间的取向差异角。结果表明外延层和衬底在应力作用下产生了取向差和晶格畸变,并且取向倾斜方向与衬底的切割倾角方向一致;高温直接生长的样品的取向差比有低温缓冲层样品更大,晶格畸变也更严重。高温直接生长的样品弯曲半径小而应力更大;实验测量的应力值和理论计算的热应力值之间存在差异,原因主要是晶格失配应力的存在。有缓冲层的样品由于能更好地弛豫晶格失配引入的应力,热应力所占整个残余应力的比例相对更大。     

Thin film stress measurement by instrumented optical fibre displacement sensor

Residual stress can adversely affect the mechanical, electronic, optical and magnetic properties of thin films. This work describes a simple stress measurement instrument based on the bending beam method together with a sensitive non-contact fibre optical displacement sensor. The fibre optical displacement sensor is interfaced to a computer and a Labview programme enables film stress to be determined from changes in the radius of curvature of the film-substrate system. The stress measurement instrument was tested for two different kinds of thin film, hard amorphous carbon nitride (CN) and soft copper (Cu) films on silicon substrates deposited by RF magnetron sputtering. Residual stress developed in 500 nm thick CN thin films deposited at substrate temperatures in the range 50-550 °C was examined and it was found that stress in CN films decreased from 0.83 to 0.44 GPa compressive with increase of substrate temperature. Residual stress was found to be tensile (121 MPa) for Cu films of thickness 1500 nm deposited at room temperature.     

Improving metal-enhanced photoluminescence by micro-pattern of metal nanoparticles: a case study of Ag–ZnCdO system

Micro-pattern of Ag nanoparticles and Ag film is inserted between ZnCdO film and the substrate to enhance the photoluminescence (PL) of ZnCdO films, achieving enhancement ratio of 21.2 and 7.1, respectively. Time-resolved photoluminescence shows that the PL lifetime of Ag/ZnCdO films is longer than that of bare ZnCdO, which is attributed to surface modification and surface plasmons coupling. The improved enhancement in the sample with Ag pattern is attributed to the fact that periodic Ag structure offers additional scattering mediums and thus increases the light extraction efficiency.     

Controlling the surface buckling wrinkles by patterning the material system of hard-nano-film/soft-matter-substrate

Wrinkling and buckling of nano-films on the compliant substrate are always induced due to thermal deformation mismatch.This paper proposes effective means to control the surface wrinkling of thin film on the compliant substrate,which exploits the curvatures of the curve cracks designed on the stiff film.The procedures of the method are summarized as:1)curve patterns are fabricated on the surface of PDMS(Polydimethylsiloxane)substrate and then the aluminum film with the thickness of several hundred nano-meters is deposited on the substrate;2)the curve patterns are transferred onto the aluminum film and lead to cracking of the film along the curves.The cracking redistributes the stress in the compressed film on the substrate;3)on the concave side of the curve,the wrinkling of the film surface is suppressed to be identified as shielding effect and on the convex side the wrinkling of the film surface is induced to be identified as inductive effect.The shielding and inductive effects make the dis-ordered wrinkling and buckling controllable.This phenomenon provides a potential application in the fabrication of flexible electronic devices.     

Application of optical 3D measurement on thin film buckling to estimate interfacial toughness

The shape-from-focus (SFF) method has been widely studied as a passive depth recovery and 3D reconstruction method for digital images. An important step in SFF is the calculation of the focus level for different points in an image by using a focus measure. In this work, an image entropy-based focus measure is introduced into the SFF method to measure the 3D buckling morphology of an aluminum film on a polymethylmethacrylate (PMMA) substrate at a micro scale. Spontaneous film wrinkles and telephone-cord wrinkles are investigated after the deposition of a 300 nm thick aluminum film onto the PMMA substrate. Spontaneous buckling is driven by the highly compressive stress generated in the Al film during the deposition process. The interfacial toughness between metal films and substrates is an important parameter for the reliability of the film/substrate system. The height profiles of different sections across the telephone-cord wrinkle can be considered a straight-sided model with uniform width and height or a pinned circular model that has a delamination region characterized by a sequence of connected sectors. Furthermore, the telephone-cord geometry of the thin film can be used to calculate interfacial toughness. The instability of the finite element model is introduced to fit the buckling morphology obtained by SFF. The interfacial toughness is determined to be 0.203 J/m² at a 70.4° phase angle from the straight-sided model and 0.105 J/m² at 76.9° from the pinned circular model.     

附着铜膜的内应力及屈服强度

用X-射线衍射和热循环基片弯曲方法测量了附着在基体上纯铜膜的内应力和屈服强度。内应力为张应力且随工作气体（氩气）压强的增加而减小但随膜厚的增加而增加。钢基体上铜膜的张屈服强度与膜厚的倒数成反比。压屈服强度也同样依赖于膜厚，即膜越薄，压屈服强度越高。     

Buckle morphologies of wedge-shaped Fe films quenched by silicone oil during deposition

A characteristic wedge-shaped iron (Fe) film system, deposited on glass substrates by a DC-magnetron sputtering method and quenched by silicone oil during deposition, has been successfully fabricated. Telephone cord buckles induced by residual compressive stress can be widely observed in the samples. They are shown to nucleate and grow slowly in the atmosphere, but propagate rapidly after disturbance of the film by an external force. Various buckling phenomena, such as generation of disordered telephone cord networks on a isotropic substrate, formation of parallel wavy buckle and circular blister lines on a patterned substrate, partial healing of buckling by pushing the film back to the substrate during the propagation process, occurrence of straight-sided blisters near a step edge, are present in this paper.     

Enhancing accuracy to Stoney equation

This paper proposes a three-dimensional system for modelling stress in thin films deposited on plane substrates much thicker than the film itself. The approach is the minimization of the deformation energy of the sample (substrate + film), considering the deformed substrate as a small spherical surface with large curvature radius. Results of the model show the validity limits of the well-established Stoney equation that satisfy the upper theoretical limit of Poisson ratio (ν) for isotropic materials. Our main result is that the stress values obtained in general literature using Stoney equation are underestimated when considering a typical Poisson ratio for substrates in the range of 0.25 ≤ ν_s ≤ 0.4.