Cracking mechanisms in lithiated silicon thin film electrodes

The massive cracking of silicon thin film electrodes in lithium ion batteries is associated with the colossal volume changes that occur during lithiation and delithiation cycles. However, the underlying cracking mechanism or even whether fracture initiates during lithiation or delithiation is still unknown. Here, we model the stress generation in amorphous silicon thin films during lithium insertion, fully accounting for the effects of finite strains, plastic flow, and pressure-gradients on the diffusion of lithium. Our finite element analyses demonstrate that the fracture of lithiated silicon films occurs by a sequential cracking mechanism which is distinct from fracture induced by residual tension in conventional thin films. During early-stage lithiation, the expansion of the lithium-silicon subsurface layer bends the film near the edges, and generates a high tensile stress zone at a critical distance away within the lithium-free silicon. Fracture initiates at this high tension zone and creates new film edges, which in turn bend and generate high tensile stresses a further critical distance away. Under repeated lithiation and delithiation cycles, this sequential cracking mechanism creates silicon islands of uniform diameter, which scales with the film thickness. The predicted island sizes, as well as the abrupt mitigation of fracture below a critical film thickness due to the diminishing tensile stress zone, is quantitatively in good agreement with experiments.     

A generalized thermal boundary condition for the hyperbolic heat conduction model

 A generalized thermal boundary condition is derived for the hyperbolic heat conduction equation to include all thermal effects of a thin layer, whether solid-skin or fluid film, moving or stationary, in perfect or imperfect thermal contact with an adjacent domain. The thin layer thermal effects include, among others, thermal capacity of the layer, thermal diffusion, enthalpy flow, viscous dissipation within the layer and convective losses from the layer. Six different kinds of thermal boundary conditions can be obtained as special cases of the generalized boundary condition. The importance of the generalized boundary condition is demonstrated comprehensively in an example. The effects of different geometrical and thermophysical properties on the validity of the generalized thermal boundary condition are investigated. Received on 23 May 2001 / Published online: 29 November 2001     

Problem of Low-frequency Localized Oscillations in a Thin Film with Growing Islands

Influence of localization waves to islands growing on a thin film is investigated. The film is modelled as a fluid layer covered by an inertial surface with the variable density of mass and surface tension. Mathematically, the problem is reduces to analysis of a system of non-linear equations describing the growth of island nuclei and wave propagation in the films. The existence of trapped modes for the corresponding frequency-domain problem is established. We show that for large time wave localization near islands gives some contribution in the increase of the velocity of island growth.     

Buckling and postbuckling of a compressed thin film bonded on a soft elastic layer: a three-dimensional analysis

The wrinkling of a stiff thin film bonded on a soft elastic layer and subjected to an applied or residual compressive stress is investigated in the present paper. A three-dimensional theoretical model is presented to predict the buckling and postbuckling behavior of the film. We obtained the analytical solutions for the critical buckling condition and the postbuckling morphology of the film. The effects of the thicknesses and elastic properties of the film and the soft layer on the characteristic wrinkling wavelength are examined. It is found that the critical wrinkling condition of the thin film is sensitive to the compressibility and thickness of the soft layer, and its wrinkling amplitude depends on the magnitude of the applied or residual in-plane stress. The bonding condition between the soft layer and the rigid substrate has a considerable influence on the buckling of the thin film, and the relative sliding at the interface tends to destabilize the system.     

TA2表面磁控溅射CNx/SiC薄膜的纳米压痕与摩擦磨损性能

采用室温磁控溅射技术在工业纯钛(TA2)表面制备出氮化碳/碳化硅(CNx/SiC)双层薄膜,SiC为中间层.研究了CNx薄膜的纳米压痕行为和摩擦磨损性能.试验结果表明:CNx薄膜的纳米硬度(H)为15.80 GPa,杨氏弹性模量(E)为130.88 GPa,硬度与弹性模量比值(H/E)为0.121;与φ4mm的氮化硅球对摩,在载荷1.96 N、室温Kokubo人体模拟体液条件下,CNx薄膜的磨损速率为10-6mm3/(m·N)级,摩擦系数约为0.124,磨损后薄膜未出现裂纹和剥落.分析表明,薄膜具有的良好抗磨性能与其H/E高、抗腐蚀性强以及摩擦系统摩擦系数低相一致.     

Numerical studies for flow and heat transfer of the Powell-Eyring fluid thin film over an unsteady stretching sheet with internal heat generation using the chebyshev finite difference method

An analysis is carried out to study the unsteady two-dimensional Powell-Eyring flow and heat transfer to a laminar liquid film from a horizontal stretching surface in the presence of internal heat generation. The flow of a thin fluid film and subsequent heat transfer from the stretching surface is investigated with the aid of a similarity transformation. The transformation enables to reduce the unsteady boundary layer equations to a system of nonlinear ordinary differential equations. A numerical solution of the resulting nonlinear differential equations is found by using an efficient Chebyshev finite difference method. A comparison of numerical results is made with the earlier published results for limiting cases. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.     

LOCAL BENDING OF THIN FILM ON VISCOUS LAYER

Effects of deposition layer position film are systematically investigated. Because the and number/density on local bending of a thin deposition layer interacts with the thin film at the interface and there is an offset between the thin film neutral surface and the interface, the deposition layer generates not only axial stress but also bending moment. The bending moment induces an instant out-of-plane deflection of the thin film, which may or may not cause the socalled local bending. The deposition layer is modeled as a local stressor, whose location and density are demonstrated to be vital to the occurrence of local bending. The thin film rests on a viscous layer, which is governed by the Navier-Stokes equation and behaves like an elastic foundation to exert transverse forces on the thin film. The unknown feature of the axial constraint force makes the governing equation highly nonlinear even for the small deflection chse. The constraint force and film transverse deflection are solved iteratively through the governing equation and the displacement constraint equation of immovable edges. This research shows that in some special cases, the deposition density increase does not necessarily reduce the local bending. By comparing the thin film deflections of different deposition numbers and positions, we also present the guideline of strengthening or suppressing the local bending.     

纳米压痕法测磁控溅射铝薄膜屈服应力

为了在考虑残余应力下测量出磁控溅射铝薄膜的屈服应力,提出了一种实验测量方法,通过曲率测试法和球形压头纳米压痕法测出磁控溅射铝薄膜的屈服应力．建立球形压痕力学模型,并用ANSYS对球形压痕进行力学有限元仿真,利用直流磁控溅射技术在硅基上淀积一层1 μm厚的铝薄膜,首先通过曲率测试法测量膜内等双轴残余应力,再利用最小二乘曲线拟合法从薄膜/基底系统的球形压头纳米压痕实验数据中提取出铝薄膜的屈服应力,测得磁控溅射铝薄膜的屈服应力为371 MPa．该方法也可以用来研究其他材料的薄膜和小体积材料的力学特性．     

Thermal characteristics of a high heat flux micro-evaporator

Our purpose is to design a high heat flux micro-evaporator that can remove more than 100 W/cm². For this purpose a thin liquid film is evaporized. The liquid film is stabilized in micro-channels by capillary forces. The micro-channels are fabricated by chemical etching on silicon to reduce thermal resistance. For the experiments, the channel plate is heated by an ITO thin film heater deposited on the opposite side of the channel plate. Influence of heat flux, coolant flow rate, and inlet temperature on the temperature of the heater element are investigated. Water is used as working fluid. A maximal heat flux of 125 W/cm² could be achieved for water inlet temperature of 90 °C and flow rate of 1.0 mL/min. The temperature of the heater element is kept constant at about 120 °C with fluctuations within 8 °C. The measured pressure drop is less than 1000 Pa.     

The effect of thermal dispersion on free convection film condensation on a vertical plate with a thin porous layer

An analytical solution to the problem of condensation by natural convection over a thin porous substrate attached to a cooled impermeable surface has been conducted to determine the velocity and temperature profiles within the porous layer, the dimensionless thickness film and the local Nusselt number. In the porous region, the Darcy–Brinkman–Forchheimer (DBF) model describes the flow and the thermal dispersion is taken into account in the energy equation. The classical boundary layer equations without inertia and enthalpyterms are used in the condensate region. It is found that due to the thermal dispersion effect, the increasing of heat transfer is significant. The comparison of the DBF model and the Darcy–Brinkman (DB) one is carried out.     

Mixed-mode interfacial adhesive strength of a thin film on an anisotropic substrate

The mixed-mode interfacial adhesion strength between a gold (Au) thin film and an anisotropic passivated silicon (Si) substrate is measured using laser-induced stress wave loading. Test specimens are prepared by bonding a fused silica (FS) prism to the back side of a 〈1 0 0〉 Si substrate with a thin silicon nitride (Si_xN_y) passivation layer deposited on the top surface. A high-amplitude stress wave is developed by pulsed laser ablation of a sacrificial absorbing layer on one of the lateral surfaces of the FS prism. Due to the negative non-linear elastic properties of the FS, the compressive stress wave evolves into a decompression shock with fast fall time. Careful selection of the incident angle between the pulse and the FS/Si interface generates a mode-converted shear wave in refraction, subjecting the Si_xN_y/Au thin film interface to dynamic mixed-mode loading, sufficient to cause interfacial fracture. A detailed analysis of the anisotropic wave propagation combined with interferometric measurements of surface displacements enables calculation of the interfacial stresses developed under mixed-mode loading. The mixed-mode interfacial strength is compared to the interfacial strength measured under purely tensile loading.     

Multi-layer thin films/substrate system subjected to non-uniform misfit strains

Current methodologies used for the inference of thin film stress through curvature measurement are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to a single layer of thin film deposited on a substrate subjected to the non-uniform misfit strain in the thin film. Such methodologies are further extended to multi-layer thin films deposited on a substrate in the present study. Each thin film may have its own non-uniform misfit strain. We derive relations between the stresses in each thin film and the change of system curvatures due to the deposition of each thin film. The interface shear stresses between the adjacent films and between the thin film and the substrate are also obtained from the system curvatures. This provides the basis for the experimental determination of thin film stresses in multi-layer thin films on a substrate.     

A generalized thermal boundary condition

 A generalized thermal boundary condition is derived to include all thermal effects of a thin layer which is in thermal contact with an adjacent domain. The thin layer may be a stationary or moving solid-skin or fluid-film. The included thermal effects of the thin layer are the thermal capacity of the layer, thermal diffusion, enthalpy flow, viscous dissipation within the layer, convective losses from the layer, and other effects. Six different kinds of thermal boundary conditions can be obtained as special cases of the generalized boundary condition. The generalized boundary condition is given for perfect and imperfect thermal contact between the thin layer and its adjacent domain. The importance of the generalized boundary condition is demonstrated in an example. Received on 23 December 1996     

Formation of a secondary droplet over the crown upon the liquid film rupture under the action of a laser beam

The free surface of a liquid film exposed to a laser beam is deformed and suffers a rupture. Depending on the thermal load intensity and the thermal properties of the liquid the rupture can be accompanied by the formation of secondary droplets over the film crown. This process is investigated using a mathematical model describing the motion of the thin layer of a viscous nonisothermal liquid. The model is based on the two-dimensional Navier–Stokes equations. The boundary conditions at the film-gas and film-liquid interfaces necessary for the solution of these equations are derived in the explicit form. The results of the solution of model problems are presented.     

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。     

A microbeam bending method for studying stress-strain relations for metal thin films on silicon substrates

We have developed a microbeam bending technique for determining elastic-plastic, stress-strain relations for thin metal films on silicon substrates. The method is similar to previous microbeam bending techniques, except that triangular silicon microbeams are used in place of rectangular beams. The triangular beam has the advantage that the entire film on the top surface of the beam is subjected to a uniform state of plane strain as the beam is deflected, unlike the standard rectangular geometry where the bending is concentrated at the support. To extract the average stress-strain relations for the film, we present a method of analysis that requires computation of the neutral plane for bending, which changes as the film deforms plastically. This method can be used to determine the elastic-plastic properties of thin metal films on silicon substrates up to strains of about 1%.Utilizing this technique, both yielding and strain hardening of Cu thin films on silicon substrates have been investigated. Copper films with dual crystallographic textures and different grain sizes, as well as others with strong 〈1 1 1〉 textures have been studied. Three strongly textured 〈1 1 1〉 films were studied to examine the effect of film thickness on the deformation properties of the film. These films show very high rates of work hardening, and an increase in the yield stress and work hardening rate with decreasing film thickness, consistent with current dislocation models.     

Thermal conductivity and its anisotropy research of germanium thin film

Germanium is an important element in semiconductor and microelectronics industries. Its thermal conductivity is an invariable and isotropic parameter in germanium crystal in the same temperature and its thermal conductivity is difficult to be measured in thin film. In the present paper, using the non-equilibrium molecular dynamics simulation method and Stillinger–Weber potential model, the normal and tangential thermal conductivity of germanium thin film are studied. There are remarkable anisotropy and size effect of thermal conductivity in normal and tangential direction of germanium thin film. In the theoretical analysis, Boltzmann transport theory is used to analyze the phonon transport in germanium thin film. Theoretical results further demonstrate the anisotropy and size effect of thermal conductivity in thin film, which indicate the significant decrease of phonon mean free path and predominant boundary phonon scattering in germanium thin film.     

硅基薄膜电极充放电过程应力演化解析解研究

为了研究硅电极在充放电过程中的应力演化,在忽略弹性变形的情况下提出了一个考虑粘塑性的简化力学模型,分别导出了出现相分离和不出现相分离时薄膜电极内应力场的解析解,该模型的计算结果与现有的实验结果相吻合.计算结果表明,当存在相分离时,电极中的应力取决于薄膜电极的厚度和充电速率的乘积;在未出现相分离现象时,应力仅取决于充电速...     

薄膜润滑中双电层效应的理论分析与实验研究

建立了考虑双电层效应的有限宽组合滑块薄膜润滑数学模型,并利用组合滑块与圆盘的滑动摩擦试验对双电层效应进行研究,利用实验结果修正了润滑过程中双电层效应的计算,给出电粘度的计算公式并进行数值分析.结果表明:在薄膜厚度较薄的情况下,双电层效应使得流体的等效粘度随膜厚减小而迅速增加;随着膜厚增加,双电层的电粘度效应逐渐减弱;随着电场强度增加,双电层的电粘度效应增加,当电场强度达到一定程度时,双电层的电粘度效应开始减弱.     

Creation, transportation, and coalescence of liquid drops by means of a light beam

A novel principle of manipulation of discrete drops using concentration-capillary forces controlled by the thermal action of a light beam is proposed. The drops are created by the light beam in a thin layer of absorbing solution and in a film of that solution beneath an air bubble in the cell. The possibility of transporting both a single drop and a drop in an air bubble by means of a light beam is demonstrated. For the first time two drops are made to coalesce on a solid substrate by bringing them into contact by means of a light beam.