Equilibrium surface roughness of a strained epitaxial film due to surface diffusion induced by interface misfit dislocations

In recent years, developments in the microelectronics industry have led to extensive studies of the growth and characterization of thin solid films and their implementation in electronic and opto-electronic devices. A goal is to produce thin films with minimal bulk and surface defects. For those systems produced by epitaxial growth of a film on a substrate that has a slightly different lattice parameter, the stress associated with the elastic mismatch strain needed to satisfy the constraint of epitaxy provides a driving force for nucleation and growth of undesirable defects in the film material or on its surface. Among the most common defects are interface misfit dislocations, arranged more or less periodically on the film-substrate interface, which partially relax the elastic mismatch strain in the film. It has been observed that, for some material systems, surface roughness or waviness arises which correlates spatially with the positions of interface misfit dislocations. It is suggested here that the waviness along the surface may be a result of surface diffusion which is driven by a gradient in the chemical potential of the material along the surface. The chemical potential gradient arises from the nonuniform strain field of the interface misfit dislocations, as well as from the unrelaxed elastic mismatch strain. The focus here is on the development of a relatively simple model of this system which leads to an estimate of the magnitude and profile of surface waviness under conditions of thermodynamic equilibrium, i.e., after the material responds to the chemical potential gradient by seeking out a new configuration for which stresses are redistributed and the chemical potential is again uniform. The condition of uniform chemical potential for the final shape leads to an integro-differential equation for the equilibrium surface shape which is solved numerically. For representative values of system parameters, estimates of equilibrium surface roughness are obtained which can vary from less than one percent of film thickness to a significant fraction of film thickness. Although transient aspects of the process are not studied here, the characteristic time for achieving an equilibrium configuration is estimated.     

Disappearance of stress singularity at interface edge due to nanostructured thin film

The purpose of this study is to examine the stress distribution near the interface between a nanostructured thin film and a solid body. We focus on a nanostructured thin film that consists of Ta₂O₅ helical nanosprings fabricated on a Si substrate by dynamic oblique deposition. The mechanical properties of the thin film are obtained by vertical and lateral loading tests using a diamond tip built into an atomic force microscope. The apparent shear and Young’s moduli, G′ and E′, of the thin film are 2-3 orders of magnitude lower than those of a conventional solid Ta₂O₅ film. Moreover, the thin film shows strong anisotropy. A finite element analysis for two types of components with different interface edges between the thin film and an elastic solid body is conducted under uniform displacement. One has a free edge where the surface-interface angle is 90°-90°, and the other has a short interface crack. These analyses indicate the absence of not only stress singularity but also high stress concentration near the free edge and the interface crack tip. The characteristic stress distributions near the interface are due to the nanoscopically discrete structure of the thin film.     

Reverse polarity effect and cross-solder interaction in Cu/Sn–9Zn/Ni interconnect during liquid–solid electromigration

The diffusion behavior of Zn atoms and Cu–Ni cross-solder interaction in Cu/Sn–9Zn/Ni interconnects during liquid–solid electromigration were investigated under a current density of 5.0 × 10³ A/cm² at 230 °C. Under the combined effect of chemical potential gradient and electron wind, Zn atoms with positive effective charge number would directionally diffuse toward the Cu interface under both flowing directions of electrons. When electrons flowed from Cu substrate to Ni substrate, EM significantly enhanced the diffusion of Cu atoms to the opposite Ni interface, resulting in the formation of interfacial Cu₅Zn₈; while no Ni atoms diffused to the opposite Cu interface. When electrons flowed from Ni substrate to Cu substrate, only a small amount of Cu atoms diffused to the opposite Ni interface, resulting in the formation of a thin interfacial (NiCu)₃(SnZn)₄ (containing 3 wt% Cu); EM significantly accelerated the diffusion of Ni atoms to the Cu interface, resulting in the formation of a large amount of (NiCu)₃(SnZn)₄ at the Cu interface. Even under downwind diffusion, no apparent consumption of Cu substrate was observed due to the formation of a thick and dense Cu₅Zn₈ layer at the Cu interface. It is more damaging with electrons flowing from Ni to Cu than that from Cu to Ni.     

Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments

Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for a simply supported stiff thin film resting on a two-parameter elastic foundation in thermal environments. The stiff thin film is modeled as a nonlocal orthotropic plate which contains small scale effects. The elastomeric substrate with finite depth is modeled as a two-parameter elastic foundation. The thermal effects are included and the material properties of the substrate are assumed to be temperature-dependent. The governing equation that includes plate-foundation interaction is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e₀a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies, but increases the nonlinear to linear frequency ratios of the thin film slightly. The results also reveal that the effect of the small scale parameter is significant for compressive buckling, but less pronounced for static bending and marginal for free vibration of the thin film resting on an elastic foundation.     

Structural Distortion and Compositional Gradients Adjacent to Epitaxial LiMn2O4 Thin Film Interfaces

Thin film electrode materials are key components in the development of high rate, high capacity solid‐state Li‐ion batteries. Detailed knowledge of the epitaxial film/substrate(current‐collector) interface structures, which provides insights into epitaxial growth mechanisms and the effects of microstructure on electrochemical properties, is essential for efficient materials and device design. Here we report the epitaxial growth mechanism of a typical cathodic LiMn₂O₄ thin film by exploring the detailed structural and compositional variations in the vicinity of a film/substrate interface using state‐of‐the‐art scanning transmission electron microscopy. Direct observation of atom columns shows the epitaxial film forms an atomically flat and coherent heterointerface with the substrate, but that the crystal lattice is tetragonally distorted with a measurable compositional gradient from the interface to the crystal bulk. The growth mechanism is interpreted in terms of a combination of chemical and physicomechanical effects, namely a complex interplay between the internal Jahn‐Teller distortions induced by oxygen non‐stoichiometry and the lattice misfit strain.     

联合载荷下无裂纹DLC薄膜的内应力有限元分析

本文用有限元分析的方法,对受法向和切向联合载荷作用下的无裂纹类金刚石(DLC)薄膜系统内部应力进行了模拟计算,分析了不同摩擦系数和膜厚比对于内部应力的影响,数值模拟结果表明:较大的摩擦系数可以使得界面处剪切应力和Mises等效应力以及y轴Mises等效应力显著增大,而对于界面处的y向压应力影响不是很大。在一定的范围内(0相似文献   

Surface Electron Transport over a Liquid-Helium Film Covering a Smooth Solid Substrate

No Heading The mobility of surface electrons localized over a superfluid helium film covering a solid substrate is calculated by taking into account the essential scattering processes of electrons by helium atoms, by ripplons and by the helium-substrate interface roughness. The last scattering process dominates for thin helium films with thickness with d 10–6 cm. A new scattering Hamiltonian, recently derived by the method of image forces, is employed. The calculated results for the mobility are compared with experimental data by fitting the two characteristic sizes of the Gaussian correlation model for surface defects. The agreement is rather good in the case of a glass substrate.PACS numbers: 73.20 Dx; 73.90.+f     

用于Si基片上外延BST薄膜的缓冲层的研究进展

由于界面之间的扩散,很难取得在Si基片上BST薄膜的外延.在这种异质结之间,稳定的缓冲层起着良好的阻挡作用以及结构上的延伸功能.综述了用于外延BST薄膜的缓冲层材料的意义和要求,及国内外通过缓冲层来控制界面以及薄膜的外延取向而获得高质量薄膜的最新研究动态,展望了今后用于外延BST薄膜的缓冲层材料发展的趋势.     

Investigation of reactively sputtered TiN films for diffusion barriers

Two groups of reactively sputtered TiN films, gold-yellow films (G films) with low resistivity and high compressive internal stress and brown-black films (B films) with high resistivity, which are formed with and without a negative substrate bias, were examined as potential diffusion barriers.The microstructures and compositions were investigated by Auger electron spectroscopy, electron probe microanalysis and X-ray diffraction. The G films and the B films have a fine-grained and a columnar-arranged morphological structure respectively. Both films exhibit the cubic NaCl-type crystallographic structure strongly oriented towards the (111) plane which is parallel to the substrate surface. They also exhibit a superstoichiometric composition having excess nitrogen atoms. In addition, the B films contain a large number of oxygen atoms.The compressive internal stress in the G film originates from lattice expansion which is probably due to the incorporation of the excess nitrogen atoms. Using the experimental value of the Young's modulus, the expanded lattice parameter in this film was calculated from the corrected interplanar spacing after the silicon substrate had been removed.The superior diffusion barrier capability of the B film is demonstrated through the application of the TiN films to an Au/Pt/TiN/Ti metal system on thick polysilicon. It is assumed that the higher diffusion barrier capability of the B film is due to the reduction of grain boundary diffusion by the oxygen atoms located in the intercolumnar layers. This is supported by film analysis, the peculiar etching behaviour and hardness studies.     

TiO2薄膜与玻璃基板横断截面的TEM及TEM—EDX分析

对玻璃基板上ＴｉＯ２薄膜与基板横断截面进行了ＴＥＭ形貌及ＴＥＭ－ＥＤＸ成分分析．结果表明,薄膜与基板结合致密,Ｎａ＋从基板向ＴｉＯ２薄膜的扩散为负扩散     

Morphological evolution driven by strain induced surface diffusion

We have developed a three-dimensional finite element method to simulate the morphological evolution of a strained surface via surface diffusion, with a view to understanding the self-assembly, shape transitions and stability of low-dimensional quantum structures. We model deposition of an elastic film on a large lattice mismatched substrate. The film surface evolves by surface diffusion, driven by a gradient of the surface chemical potential, which includes the elastic strain energy, elastic anisotropy, surface energy, surface energy anisotropy and the interaction between the film and the substrate. Our simulations reveal that surface energy anisotropy and elastic anisotropy have a strong effect on the morphological evolution and shape transitions of the self-assembled islands. Our simulation results show a good qualitative agreement with experimental results.     

Stretched polymer nanohairs by nanodrawing

A simple, yet innovative, method is presented for fabricating high-aspect-ratio polymer nanohairs (aspect ratio >20) on a solid substrate by sequential application of molding and drawing of a thin polymer film. The polymer film was prepared by spin coating on a rigid or flexible substrate, and the temperature was raised above the polymer's glass transition while in conformal contact with a poly(urethane acrylate) mold having nanocavities. Consequently, capillary forces induced deformation of the polymer melt into the void spaces of the mold and the filled nanostructure was further elongated upon removal of the mold due to tailored adhesive force at the mold/polymer interface. The optimum value of the work of adhesion at the mold/polymer interface ranged from 0.9 to 1.1 times that at the substrate/polymer interface.     

Grain boundary interdiffusion and stresses in thin polycrystalline films

We consider the kinetics of tensile stress relaxation in thin metal film attached to inert substrate, controlled by chemical interdiffusion along the grain boundaries. We assume that the source of diffusing atoms is located at the surface of the film. We show that the kinetics of stress relaxation in the film can be either accelerated or slowed down if compared with the same kinetics in a single-component film, depending on the difference of intrinsic GB diffusion coefficients of the two components. In the case of faster matrix atoms, the tensile stress in the film significantly increases beyond its initial value at the beginning of interdiffusion process, while in the case of faster diffuser atoms, the compressive stresses develop in the film at the intermediate stages of stress evolution.     

Diffusion of a fluid through a spherical elastic solid undergoing large deformations

The diffusion of a fluid through a spherical elastic solid undergoing large deformation is described in this paper. The constitutive model used is the single-constituent model for diffusion of fluids in nonlinear elastic solids, originally presented by Baek and Srinivasa [S. Baek, A.R. Srinivasa, Int. J. Nonlinear Mech. 39 (2004) 201-218] and based on a variational method and on the assumption of continuity of chemical potential across the solid-fluid interface. The balance laws for a single continuum with mass diffusion are cast in spherical coordinates, and suitable boundary conditions are posed to describe the radial diffusion of fluid through an elastic spherical shell with finite thickness. Its inner surface is adjacent to a rigid wall, either impermeable or permeable, while the outside surface is in contact with the fluid that swells the solid, diffuses through it, and exerts a hydrostatic pressure on its surface.     

Kinetics of the formation of nickel aluminide coatings on pure nickel by chemical vapour deposition

A chemical vapour deposition process was used to deposit aluminium onto a pure nickel substrate which was not in contact with the powder mixture. After deposition for about 1 h the aluminium content at the surface reached a high value and then remained almost constant with time. The kinetics of the process is governed by a combination of solid and gas diffusion rates, and a qausi-steady-state appears to exist at the gas-coating interface. The experimental results can be explained satisfactorily by a combination of a stagnant film model for gaseous diffusion and solid diffusion rates.     

Structural and optical properties of high quality ZnO thin film on Si with SiC buffer layer

ZnO thin films are grown on Si substrates with SiC buffer layer using ion plasma high frequency magnetron sputtering. These substrates are fabricated using a technique of solid phase epitaxy. With this technique SiC layer of thickness 20-200 nm had been grown on Si substrates consisting pores of sizes 0.5-5 μm at SiC and Si interface. Due to mismatching in lattice constants as well as thermal expansion coefficients, elastic stresses have been developed in ZnO film. Pores at the interface of SiC and Si are acting as the elastic stress reliever of the ZnO films making them strain free epitaxial. ZnO film grown on this especially fabricated Si substrate with SiC buffer layer exhibits excellent crystalline quality as characterized using X-ray diffraction. Surface topography of the film has been characterized using Atomic Force Microscopy as well as Scanning Electron Microscopy. Chemical compositions of the films have been analyzed using Energy Dispersive X-ray Spectroscopy. Optical properties of the films are investigated using Photoluminescence Spectroscopy which also shows good optical quality.     

Characterizing the Lateral Friction of Nanoparticles on On‐Chip Integrated Black Lipid Membranes

The use of nanoparticles (NPs) in biomedical applications creates a need for appropriate model systems to systematically investigate NP–membrane interactions under well‐defined conditions. Black lipid membranes (BLMs) are free‐floating membranes with defined composition that are ideally suited for characterizing NP–membrane interactions free of any potential perturbation through a supporting substrate. Herein, arrays of microfabricated BLMs are integrated into a chip‐based platform that is compatible with high‐speed optical NP tracking. This system is used to investigate the lateral diffusion of 40 nm gold spheres tethered to biotinylated lipids through antibody‐functionalized ligands (single‐stranded DNA or polyethylene glycol). Although the NPs show an almost free and ergodic diffusion, their lateral motion is subject to substantial drag at the membrane surface, which leads to systematically smaller diffusion coefficients than those obtained for lipids in the membrane through fluorescence recovery after photobleaching. The lateral mobility of the NPs is influenced by the chemical composition and salt concentration at the NP‐membrane interface, but is independent of the ligand density in the membrane. Together with the observation that nanoprisms, which have a larger relative contact area with the membrane than spherical NPs, show an even slower diffusion, these findings indicate that the lateral mobility of NPs tethered in close vicinity to a membrane is significantly reduced by the friction at the NP‐membrane interface.     

Titanium oxide film for the bottom antireflective layer in deep ultraviolet lithography

Titanium oxide thin film, fabricated with tetraisopropyltitanate and oxygen by electron cyclotron resonance-plasma-enhanced chemical vapor deposition, is investigated as a potential candidate for the antireflective layer in KrF excimer laser (248-nm) lithography. The oxygen flow-rate dependence of the optical properties such as the refractive index (n) and the extinction coefficient (k) of the film at the 248-nm wavelength has been characterized, and the films with the expected combinations of n and k values for the antireflective layer have been deposited. Simulation results indicate that reflectance values of less than 4% and as low as 1.2% can be reached at the interface between the photoresist and the film postulating the structures of the photoresist/300-A TiO(x) film/c-Si substrate and the W-Si substrate, respectively, by selected proper combinations of n and k values. Moreover the reflectance can be further reduced to almost zero by changing the film thickness. Thus it is found that titanium oxide thin films can be used as the bottom antireflective layer in KrF excimer laser lithography.     

Delaminating buckling model based on nonlocal Timoshenko beam theory for microwedge indentation of a film/substrate system

A novel model built on the basis of nonlocal Timoshenko beam theory is presented for delaminating buckling in the microwedge indentation test of a thin film on an elastic substrate. Two size effects are accounted for in the proposed model. One is the delamination size effect, and the other is the film thickness effect. The influence of the elastic deformation in the substrate and the indentation-induced impression or notch on the buckling behaviors are taken into consideration by employing coupled line springs as the boundary conditions of the buckled film. The critical stress for buckling, the energy release rate and the phase angle of the interface delamination crack are calculated and compared with those by classical beam theories. Sensitivity of the two size effects is observed.