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.     

The deposition of Fe or Co clusters on Cu substrate by molecular dynamic simulation

A molecular dynamic method is used to simulate the film growth process of Fe or Co clusters depositing on Cu substrate with low energy. The tight-binding (TB-SMA) many-body potential is used to simulate the interaction between atoms. The effects of different incident energies and/or substrate temperatures on the surface roughness, layer coverage function, radial distribution function (RDF), and residual stress are investigated. From the simulation results, as the substrate temperature and/or incident energy is increased, the surface roughness of the grown film could be reduced, and the interface intermixing is increased. Also, as compared to Co–Cu system, Fe–Cu system has better surface roughness, less interface intermixing, and similar radial distribution function as well as average stresses.     

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.     

Investigation on periodic cracking of elastic film/substrate system by the extended finite element method

Multiple cracking behavior in a thin elastic film bonded to a thick elastic substrate is investigated by the extended finite element method. Stress and stress intensity factor are obtained using a periodic finite element model for the cracked film/substrate system. The influences of various parameters including crack length, film thickness, periodic crack spacing, and relative stiffness of the substrate on the stress and stress intensity factor are discussed in detail. It is demonstrated that the effects of geometric parameters are more sensitive than that of material property. In particular, the crack spacing has a saturation value due to interactions of neighboring cracks and relief of tensile stress in the film. The film/substrate couple with multiple periodic cracks can exhibit a positive potential in improving the durability of the film/substrate system.     

二氧化钛薄膜表面粗糙度研究

为了探究二氧化钛(TiO₂)薄膜表面粗糙度的影响因素, 利用离子束辅助沉积电子束热蒸发技术对不同基底粗糙度以及相同基底粗糙度的K9玻璃完成二氧化钛(TiO₂)光学薄膜的沉积。采用TalySurf CCI非接触式表面轮廓仪分别对镀制前基底表面粗糙度和镀制后薄膜表面粗糙度进行测量。实验表明, TiO₂薄膜表面粗糙度随着基底表面的增大而增大, 但始终小于基底表面粗糙度, 说明TiO₂薄膜具有平滑基地表面粗糙的作用; 随着沉积速率的增大, 薄膜表面粗糙度先降低后趋于平缓; 对于粗糙度为2 nm的基底, 离子束能量大小的改变影响不大, 薄膜表面粗糙度均在1.5 nm左右; 随着膜层厚度的增大, 薄膜表面粗糙度先下降后升高。     

单层单晶石墨烯与柔性基底界面性能的实验研究

单晶石墨烯具有更优异的力学及电学性能,有望成为新一代柔性电子器件的核心材料.因此,有必要从实验的角度精细分析化学气相沉积法制得的大尺度单晶石墨烯与柔性基底复合结构的界面力学行为.本文通过显微拉曼光谱实验方法测量了不同长度的单层单晶石墨烯/PET(聚对苯二甲酸乙二醇酯)基底的界面力学性能参数及其在长度方向上界面边缘的尺度效应.实验给出了石墨烯在PET基底加载过程中与基底间黏附、滑移、脱黏三个界面状态的演化过程与应力分布规律.实验发现,单晶石墨烯与柔性基底间由范德瓦耳斯力控制的界面应变传递过程存在明显的边缘效应,并且与石墨烯的长度有关.界面的切应力具有尺度效应,其值随石墨烯长度的增加而减小,而石墨烯界面传递最大应变以及界面脱黏极限则不受试件尺度的影响.     

Externally applied stress sign and film elastic properties effects on brittle film fracture

Rectangular stainless steel samples with TiN film deposited on the front lateral surface were loaded in three-point bending to the maximum normal strain of 6%. Scanning electron microscopy showed that vertical cracks appeared in the tension zone when the tensile strain exceeded 1.5%, while horizontal cracks appeared in the compression zone when the compressive strain exceeded –2.9%. Film cracks in the compressive zone originate from the tensile stress imposed by the plastically deformed substrate due to the Poisson’s expansion. Taking plastic deformation and Poisson’s expansion of the substrate in compression into account, theoretical analysis of normal stress distribution along the cracked film segment in compression is presented. Substrate strain and film elastic properties affect film cracking in the compressive zone. At larger compressive strain, some transverse cracks along with buckling cause the film spallation. The presented method is useful for studying brittle film fracture with variable strain levels in a single sample.     

硅基锗薄膜选区外延生长研究

利用超高真空化学气相沉积系统, 基于低温Ge缓冲层和选区外延技术, 在Si/SiO₂图形衬底上选择性外延生长Ge薄膜. 采用X射线衍射、扫描电镜、原子力显微镜、拉曼散射光谱等表征了其晶体质量和应变等参数随图形尺寸的变化规律. 测试结果显示, 位错密度随着图形衬底外延窗口的尺寸减小而减少, Ge层中的张应变随窗口尺寸的增大先增大而后趋于稳定. 其原因是选区外延Ge在图形边界形成了(113)面, 减小了材料系统的应变能, 而单位体积应变能随窗口尺寸的增加而减少; 选区外延厚度为380 nm的Ge薄膜X射线衍射曲线半高宽为678", 表面粗糙度为0.2 nm, 表明选区生长的Ge材料具有良好的晶体质量, 有望应用于Si基光电集成.     

Effect of periodic surface cracks on the interfacial fracture of thermal barrier coating system

Periodic surface cracks and interfacial debonding in thermal barrier coating (TBC) system may be induced during cooling process. The objective of this work is to investigate the effect of periodic surface cracks on the interfacial fracture of TBC system. The finite element method (FEM) incorporating cohesive zone model is used in analysis. It is found that surface crack spacing has significant effect on the initiation and propagation of short interface crack. Three different regions are identified for describing the effect of surface crack spacing. In Region I the interface crack driving force is dramatically reduced due to high surface crack density. In this case, the initiation of interfacial delamination can be delayed. Region II applies as the surface crack spacing is moderate. Analysis of this transition zone brings to the definition of normalized critical surface crack spacing. Region III arises for sufficient large surface crack spacing. In this case, the interface crack driving force reaches a steady state, where the effects of adjacent surface cracks are relatively insignificant and can be ignored. It can be concluded that an appropriately high surface crack density can enhance the durability of TBC system.     

Morphologies of epitaxial islands on a lattice-misfitted substrate

Under certain growth conditions for systems with a film/substrate lattice misfit, the deposited material is known to aggregate into island-like shapes. We have obtained an analytical expression of the total free energy, which consists of strain energy, surface energy and interfacial energy of a coherent island/substrate system, and the change of equilibrium aspect ratio versus the volume of the island and the misfit of lattices in the system, which provides a broad perspective on island behaviour. These then were used to study the equilibrium shapes of the system. The results show that in order to minimize the total free energy, a coherent island will have a particular height-to-width aspect ratio, called equilibrium aspect ratio, that is a function of the island volume and misfit. The aspect ratio is increased with increasing island volume at a fixed misfit, and with increasing misfit strain between the island and substrate at a fixed island volume. Moreover, the effect of misfit dislocation on the equilibrium shape of the island is also examined. The results obtained are in good agreement with experiment of observations and thus can serve as a basis for interpreting the experiments.     

Segregation of silicone acrylate from acrylate mixture at resin-mold interface and its effect on UV embossing

When silicone diacrylate was added in small amount (<5 wt.%) to ultraviolet (UV) curable formulations containing other oligomeric diacrylates, there was segregation of the silicone additive at the solid substrate-formulation interface. The amount was quantified by X-ray photoelectron spectroscopy measurement of the UV cured film surface composition. The effect of silicone diacrylate concentration, resin formulation and substrate polarity on silicone surface excess was systematically studied. Young's-Gibbs adsorption theory was applied to the prediction of the silicone surface excess at the solid substrate interface for these oligomeric mixtures. Further, we proposed a simplified Young's-Gibbs adsorption theory equation to predict the variation of surface excess from only formulation surface tension and substrate critical surface tension. The selective segregation is beneficial to demolding in UV embossing since only small amount of release added can result in large decrease of the mold-resin interfacial energy difference leading to easy demolding and high replication fidelity.     

Investigation of interface roughness cross-correlation properties of optical thin films from total scattering losses

The interface roughness and interface roughness cross-correlation properties affect the scattering losses of high-quality optical thin films. In this paper, the theoretical models of light scattering induced by surface and interface roughness of optical thin films are concisely presented. Furthermore, influence of interface roughness cross-correlation properties to light scattering is analyzed by total scattering losses. Moreover, single-layer TiO₂ thin film thickness, substrate roughness of K9 glass and ion beam assisted deposition (IBAD) technique effect on interface roughness cross-correlation properties are studied by experiments, respectively. A 17-layer dielectric quarter-wave high reflection multilayer is analyzed by total scattering losses. The results show that the interface roughness cross-correlation properties depend on TiO₂ thin film thickness, substrate roughness and deposition technique. The interface roughness cross-correlation properties decrease with the increase of film thickness or the decrease of substrates roughness. Furthermore, ion beam assisted deposition technique can increase the interface roughness cross-correlation properties of optical thin films. The measured total scattering losses of 17-layer dielectric quarter-wave high reflection multilayer deposited with IBAD indicate that completely correlated interface model can be observed, when substrate roughness is about 2.84 nm.     

柔性基周期性厚度梯度薄膜的应变效应

可控的表面微结构在柔性电子、仿生器件和能源材料等方面均具有重要的应用价值.本文采用编织铜网作为掩模板,利用磁控溅射技术在柔性聚二甲基硅氧烷(PDMS)基底上制备具有周期分布的厚度梯度金属银薄膜,研究了薄膜在单轴压缩/拉伸过程中的形貌演化规律.实验发现,在单轴机械载荷作用下,银薄膜表面将形成相互垂直的条纹褶皱和多重裂纹.膜厚的梯度变化调制了薄膜的面内应力分布,导致褶皱在膜厚较小处率先形成,并逐渐扩展到膜厚较大区域,而裂纹则基本限定在膜厚较小区域.基于应力理论和有限元计算,对周期性厚度梯度薄膜的褶皱和裂纹的形貌特征、演化行为和物理机制进行了深入分析.该研究将有助于加深对非均匀薄膜体系的应变效应的理解,并有望通过梯度薄膜的结构设计在柔性电子等领域获得应用.     

Edge effect and interface confinement modulated strain distribution and interface adhesion energy in graphene/Si system

In order to clarify the edge and interface effect on the adhesion energy between graphene(Gr)and its substrate,a theoretical model is proposed to study the interaction and strain distribution of Gr/Si system in terms of continuum medium mechanics and nanothermodynamics.We find that the interface separation and adhesion energy are determined by the thickness of Gr and substrate.The disturbed interaction and redistributed strain in the Gr/Si system induced by the effect of surface and interface can make the interface adhesion energy decrease with increasing thickness of Gr and diminishing thickness of Si.Moreover,our results show that the smaller area of Gr is more likely to adhere to the substrate since the edge effect improves the active energy and strain energy.Our predictions can be expected to be a guide for designing high performance of Grbased electronic devices.     

Be原子在Be基底上的沉积过程研究

利用分子动力学方法模拟了Be原子在Be基底上的沉积过程. 模拟了沉积粒子不同入射动能条件下, 沉积薄膜表面形态的差异. 在一定能量范围内, 增加粒子入射动能可以减小薄膜的表面粗糙度. 但是, 过高的入射动能, 不利于减小薄膜表面粗糙度. 通过沉积薄膜中原子配位数以及单个原子势能沿薄膜厚度的分布, 分析沉积原子入射动能对于薄膜及表面结构的影响. 沉积动能较大时, 薄膜的密度较大; 单个原子势能沿薄膜厚度分布较为连续; 同时薄膜中原子应力沿薄膜厚度分布较为连续. 最后, 分析了沉积粒子能量转化的过程、粒子初始动能对基底表面附近粒子局部动能增加的影响.     

基于Wenzel模型的粗糙界面异质形核分析

异质形核是形核发生的主要形式. 经典形核理论对基底界面作了理想化平面假设,然而实际异质形核体系中理想平直的固体界面是不存在的,这导致了异质形核描述与实际情况的偏差. 考察了固相晶胚在非平整界面上的异质形核过程,基于Wenzel润湿模型,分析了非理想界面的粗糙度因子对固相晶胚形核功的影响规律. 结果表明:当基底与晶核之间的本征润湿角小于90°时,基底界面越粗糙越有利于形核;本征润湿角大于90°时,基底界面越粗糙越不利于形核. 同时,游离晶胚在基底上润湿是球冠晶胚形成的重要途径,粗糙界面润湿过程中界面自由能的 关键词： 异质形核 粗糙界面 Wenzel模型 润湿过程     

Three-dimensional phase field microelasticity theory of a multivoid multicrack system in an elastically anisotropic body: Model and computer simulations

The phase field microelasticity theory of a three-dimensional, elastically anisotropic system of voids and cracks is proposed. The theory is based on the equation for the strain energy of the continuous elastically homogeneous body presented as a functional of the phase field, which is the effective stress-free strain. It is proved that the stress-free strain minimizing the strain energy of this homogeneous modulus body fully determines the elastic strain and displacement of the body with voids and/or cracks. The proposed phase field integral equation describing the elasticity of an arbitrary system of voids and cracks is exact. The geometry and evolution of multiple voids and/or cracks are described by the phase field, which is the solution of the time-dependent Ginzburg-Landau equation. Other defects, such as dislocations and precipitates, are trivially integrated into this theory. The proposed model does not impose a priori constraints on possible void and crack configurations or their evolution paths. Examples of computations of elastic equilibrium of systems with voids and/or cracks and the evolution of cracks under applied stress are considered.     

Stress-Assisted Reaction at a Solid-Fluid Interface

On the interface between a solid and a fluid, a reaction can occur in which atoms either leave the solid to join the fluid, or leave the fluid to join the solid. If the solid is in addition subject to a mechanical load, two outcomes may be expected. The reaction may proceed uniformly, so that the interface remains flat as the solid recedes or extends. Alternatively, the reaction may cause the interface to roughen and develop sharp cracks, leading to fracture. This paper reviews the current understanding of the subject. The solid-fluid is a thermodynamic system: the solid is in elastic equilibrium with the mechanical load, but not in chemical equilibrium with the fluid. Thermodynamic forces that drive the interfacial reaction include chemical energy difference between the solid and the fluid, elastic energy stored in the solid, and interfacial energy. The reaction is taken to be thermally activated. A kinetic law is adopted in which the stress affects both the activation energy and the driving force of the interface reaction. A linear perturbation analysis identifies the stability condition, which differs substantially from the well known stability condition based on the driving force alone. Large perturbations are examined by assuming that the interface varies as a family of cycloids, from slight waviness to sharp cracks. An analytic elasticity solution is used to compute the stress field in the solid, and a variational method to evolve the shape of the interface.     

Effect of the substrate temperature and deposition rate on the initial growth of thin lithium niobate-tantalate films deposited from a thermal plasma

Thin lithium niobate-tantalate (LiNb_0.5Ta_0.5O₃) films are studied at the initial stage of deposition from a thermal plasma. The effect of two deposition parameters (the substrate temperature and the deposition rate) on the film morphology, the film crystallinity, and the density of nuclei growing on a (0001) sapphire substrate are investigated. It is shown that the crystalline structure and roughness of a film are determined, for the most part, in the initial growth stage and therefore depend directly on both parameters. At the optimum temperatures and growth rates for obtaining good characteristics of (0006) texture, crystallinity, and surface roughness of the films, the film nuclei on the substrate have a high density and good epitaxial orientation to it. If the growth conditions are not optimum, the islands are either amorphous or have a low density on the substrate surface. The nucleation activation energy is observed to decrease as the deposition rate increases, which supports the assumption that the species that are active in film deposition are “hot” clusters forming in an oxygen-argon plasma in the immediate vicinity of the substrate.