Strain hardening in nanolayered thin films

Experimental results indicate that metal–ceramic multilayered thin films have unusual properties such as high strength, measurable plasticity and high strain hardening rate when both layers are nanoscale. Furthermore, the strength and strain hardening rate show a pronounced size effect, depending not only on the layer thickness but also on the layer thickness ratio. We analyze the strain hardening behavior of nanoscale multilayers using a three-dimensional crystal elastic–plastic model (3DCEPM) that describes plastic deformation based on the evolution of dislocation density in metal and ceramic layers according to confined layer slip mechanism. These glide dislocations nucleate at interfaces, glide inside layers and are deposited at interfaces that impede slip transmission. The high strain hardening rate is ascribed to the closely spaced dislocation arrays deposited at interfaces and the load transfer that is related to the layer thickness ratio of metal and ceramic layers. The measurable plasticity implies the plastically deformable ceramic layer in which the dislocation activity is facilitated by the interaction force among the deposited dislocations within interface and in turn is strongly related to the ceramic layer thickness.     

纳米尺度圆孔表面薄膜界面失配位错形核机理

研究了无限大基体内纳米尺度圆孔表面薄膜中界面螺型位错形核的临界条件,薄膜考虑了表/界面效应。运用弹性复势方法,获得了两个区域应力场的解析解答,并导出位错形核能公式,由此讨论了表/界面效应对薄膜界面位错形核的影响规律。算例结果表明,表/界面效应在纳米尺度下对位错形核的影响显著,不同表/界面效应下位错形核的临界薄膜厚度有很大差异,当基体与薄膜的相对剪切模量超过某一值后,只有考虑负的表/界面应力时位错才有可能形核;薄膜厚度在小于某一临界尺寸时负的表/界面应力更容易位错形核,薄膜厚度大于某一临界尺寸时正的表/界面应力更容易位错形核。     

Nanometric patterning with ultrathin twist bonded silicon wafers

Ultrathin films of silicon bonded on 4-inch (001) silicon wafers have been obtained by combining a direct hydrophobic silicon bonding technique with a layer transfer. The strain field produced by the dislocation network localized at the bonded interface is a good candidate to induce a long-range order growth of nanostructure. To be able to make this new kind of substrate, knowledge of the dislocation strain field extension is essential. Grazing incidence X-ray diffraction allows us to measure its spatial extension through the diffraction peak satellites due to different dislocation networks. The exponential decay of these peaks were measured and compared. We found that the decrease of the strain field extension is almost two times lower for the screw dislocation network than for the ‘mixed’ dislocations one. The film thickness control is then two times more critical for the screw dislocations.     

Strain and strain relaxation in semiconductors

Single-crystal semiconductor layers can be grown with large coherency strains. This review covers their standard elasticity theory and methods of measuring the strain. High-quality strained layers are thermodynamically stable up to a critical thickness, and both theoretical and experimental determinations of critical thickness are considered. Above critical thickness there is a metastable regime, with thicknesses of a few tens of nanometres for a typical misfit ε0∼1%. A relaxation critical thickness is identified, above which compressive strain produces plastic relaxation so the strain in a layer is less than its misfit (tensile layers commonly experience cracking instead of plastic relaxation). Relaxing layers may have a misfit ε0∼1%, and thicknesses of a few hundred nanometres. In the high-mismatch regime, any strain severely perturbs the crystal growth; this occurs typically for misfits of 2% upwards. The review concludes with some unresolved questions about multilayer structures. This revised version was published online in August 2006 with corrections to the Cover Date.     

Dislocation wall formation during interdiffusion in thin bimetallic films

Transmission electron microscopy observations are described of the diffusion-induced behaviour of misfit dislocations originally present in the interface of thin bimetallic films. Experiments were carried out with specimens consisting of a layer of approximately 500 Å Cu vapour deposited onto an electropolished Ni substrate approximately 1000 Å thick. Diffusion anneals were performed in situ in the electron microscope at annealing temperatures in the range 450–600°C. The dislocation behaviour in Cu/Ni bicrystals with originally a (100) interface was photographed and video-recorded. A cross-grid of misfit dislocations parallel to 〈110〉 directions was present in the original interface. The Burgers vectors were of type $\text{1}\text{2}$a〈110〉 lying in the interface. During diffusion the misfit dislocations became distributed in the diffusion zone. When $\text{2Dt}$ (where D is the diffusion coefficient and t is the annealing time at a given temperature) exceeded a value of 40–50 Å, the dislocations started to align vertically forming dislocation walls along 〈110〉 directions parallel to the original interface. This resulted in a dislocation cell structure. Lengthwise the dislocation walls grew with shocks. The elastic strain energy of a finite edge dislocation array was estimated. Using this result an energy criterion for the formation of dislocation walls was derived. From this criterion it followed that dislocation wall formation may start to occur when $\text{2Dt}$≈ 45 Å, in good correspondence with the experimental results. Some additional observations of recrystallization phenomena during interdiffusion are reported.     

Misfit dislocations in epitaxial films III. Theory

Observations on the growth of Pd on (001)Au and (111)Au substrates have shown that Pd deposits grow pseudomorphically up to a few monolayers thickness, whereupon misfit dislocations nucleate at the Pd surface and grow into the Pd-Au interface to relieve misfit strains. In this paper the critical thicknesses for coherency loss in Pd/(001)Au and Pd/(111)Au films are measured accurately using an X-ray microanalysis technique. The nucleation and growth of the observed misfit dislocation sources, described in previous papers, is examined in detail theoretically, and the results are compared with experiment. It is shown that misfit dislocation sources in Pd/(001)Au and Pd/(111)Au films nucleate at different deposit thicknesses in excellent quantitative agreement with experiment and are the most energetically favourable sources.     

Diffusion induced grain boundary migration in the Ag–Zn system

Diffusion induced grain boundary migration (DIGM) has been studied in the Ag–Zn system by exposing polycrystalline Ag to Zn vapor with a Ag-25 wt.% Zn alloy as the source of Zn. The time and temperature dependence of the migration distance has been studied in the temperature range 660 to 810 K. The composition profile was obtained on the sheet cross-section along a line perpendicular to the edge to determine D_bδ at each temperature. Similarly, the Zn concentration profile was obtained from the region swept by the migrating grain boundary. The coherency strain energy, the total chemical free energy change and the effective free energy change were calculated. The regular solution model was used for calculating the free energy change. It has been observed that a fraction of the total free energy has been used for volume diffusion in front of the migrating grain boundary. The instantaneous rate of migration has been observed to be directly proportional to the chemical free energy change and the coherency strain energy. The instantaneous rate of migration versus the composition graph has indicated that the driving force for DIGM in the Ag–Zn system is the coherency strain energy.The fine-grained layer formed at the surface follows a parabolic growth behavior. The diffusion coefficients calculated from the composition profile as well as from the rate of growth of the fine-grained layer are of the same order of magnitude. The diffusivity values are four to six orders of magnitude higher than the volume diffusion coefficients. From the activation energy and the diffusivities it is clear that DIGM in the Ag–Zn system occurs by the diffusion of Zn along the grain boundaries of polycrystalline Ag.     

Stability of strained thin films with interface misfit dislocations: A multiscale computational study

The stability of thin single-crystal, internal-defect-free Fe films on Mo(110) and W(110) substrates is investigated through calculations of energetics including contributions from the misfit strain, interfacial misfit dislocations, film surface and interface. The misfit dislocation model is developed through the Peierls-Nabarro framework, employing ab initio calculations of the corrugation potential at the film/substrate interface as an input to the model. The surface and interfacial energies for pseudomorphic films are calculated as a function of film thickness from 1 to 10 layers, employing first-principles spin-polarized density-functional theory calculations in the generalized gradient approximation. First-principles calculations are also employed to obtain the Fe surface stress used in the Peierls-Nabarro model to account for the strain dependence of the surface energy. It is found that the competition between the misfit strain, misfit dislocations, film surface and interfacial energies gives rise to a driving force for solid-state dewetting of a single-crystal, internal-defect-free film, i.e., an instability of a flat film that leads to formation of thicker and thinner regions. The details of the energetics are presented to demonstrate the robustness of the mechanism. Our findings indicate that misfit dislocations and their configurations play a significant role in a morphological evolution of metallic thin films.     

Pull-off test for a cracked layer bonded to a rigid foundation

This paper is concerned with the plane strain problem of an elastic incompressible layer bonded to a rigid foundation. An upward tensile force is applied to the top surface of the layer through a rigid strip of finite thickness. The layer contains either a finite central crack or two semiinfinite external cracks. The analysis leads to a system of singular integral equations. These integral equations are solved numerically and the interface stress distributions, stress intensity factors at the crack tips and at the corners of the rigid strip, probable cleavage angle for the finite crack and strain energy release rate are calculated for various geometries.     

On the interpretation of structural and light emitting properties of InGaN/GaN epitaxial layers grown above and below the critical layer thickness

In this contribution, the optical and structural properties of InGaN/GaN layers grown by metal-organic chemical vapour deposition (MOCVD) are studied. The main focus of this investigation is on the difference between microstructural and luminescence characteristics, for layers grown below and above the critical layer thickness (CLT) for elastic strain relaxation. By comparing the photoluminescence properties of samples grown under the same nominal conditions, except the deposition time, it is shown that in InGaN films grown above the CLT (x), an additional lower energy secondary luminescence component emerges. Specifically, for an InGaN layer with x∼0.1, the energy splitting between the two components is about 160 meV. The surface of samples with thicknesses larger than CLT(x), are found to be rough with pronounced islanding occurring, indicating that a Stranski-Krastanow 2D to 3D growth mode transition takes place after the CLT. A detailed structural characterization by high-resolution reciprocal space mapping reveals that the appearance of 3D islands is associated with elastic strain relaxation. Strong lateral and depth variations of the strain field associated to a peculiar 2D/3D growth mode can explain structural and optical properties, which are typically considered “anomalous” and frequently ascribed to phase segregation effects in InGaN. A simple calculation based on elastic strain relaxation, accounts for the observed energy splitting on the photoluminescence.     

Pull-off test for a cracked layer bonded to a rigid foundation

This paper is concerned with the plane strain problem of an elastic incompressible layer bonded to a rigid foundation. An upward tensile force is applied to the top surface of the layer through a rigid strip of finite thickness. The layer contains either a finite central crack or two semi-infinite external cracks. The analysis leads to a system of singular integral equations. These integral equations are solved numerically and the interface stress distributions, stress intensity factors at the crack tips and at the corners of the rigid strip, probable cleavage angle for the finite crack and strain energy release rate are calculated for various geometries.     

Misfit dislocations and stress in In<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Ga<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>As/GaAs heterostructures

We have estimated the elastic properties of In_{1 − x} Ga _x As/GaAs heterostructures and the characteristics of misfit dislocations in such heterostructures: misfit dislocation spacing, Burgers vector length in various interfaces, surface density of dangling bonds, film/substrate interface energy, critical film thickness below which pseudomorphic growth is possible without misfit dislocations, elastic strain energy of the film-substrate system, average elastic strain of a thin-film island as a function of its radius, thermal stresses induced by the thermal-expansion and lattice mismatches between the layers in contact, and crack length in the film.     

Spacing of edge fractures in layered materials

Opening-mode fractures developed from a free surface in a layered material often terminate at the interface that divides the fractured layer and the underlying layer. They also display regular spacing that is of the same order of magnitude as the thickness of the fractured layer. We have investigated the stress distribution between two adjacent edge fractures as a function of the ratio of fracture spacing to thickness of the fractured layer using a two-layer elastic model with a fractured top layer. The results show that when the ratio of fracture spacing to the layer thickness changes from greater than to less than a critical value the normal stress acting perpendicular to the fractures near the free surface changes from tensile to compressive. This stress state transition precludes further infilling of fractures unless they are driven by mechanisms other than a pure extension, or there are flaws that significantly perturb the local stress field between the fractures. Hence, the critical fracture spacing to layer thickness ratio defines a lower limit for fractures driven by extension, which also defines the condition of fracture saturation. The critical value of the fracture spacing to layer thickness ratio is independent of the average strain of the fractured layer, and it increases with increasing ratio of Young's modulus of the fractured layer to that of the underlying layer. The critical value increases with increasing Poisson's ratio of the fractured layer, but it decreases with increasing Poisson's ratio of the underlying layer. For the case with the same elastic constants for the fractured layer and the underlying layer, the critical spacing to layer thickness ratio is about 3.1. Delamination between the fractured layer and the underlying layer makes the critical spacing to layer thickness ratio much greater. Infilling fractures grow more easily from flaws located near the bottom of the fractured layer than from those located near the free surface when the spacing to layer thickness ratio is less than the critical value. The propagation of an edge flaw between adjacent edge fractures is unstable, but for the flaw to propagate to the interface, its height has to be greater than a critical size, that decreases with increasing fracture spacing to layer thickness ratio. The propagation behavior of an internal flaw with its lower tip at the interface depends on the edge fracture spacing to layer thickness ratio. The propagation is unstable, when the fracture spacing to layer thickness ratio is greater than a critical value; stable, when the fracture spacing to layer thickness ratio is less than another critical value; and first unstable, then stable, and/or unstable again, when the fracture spacing to layer thickness ratio is between these two critical values.     

Morphology and interfacial structure of gamma precipitates in the beta phase of a Ti-Al-Nb-Zr alloy

The morphology and interfacial structure of γ precipitates in the β phase of a Ti-44%Al-4%Nb-4%Zr alloy have been studied using transmission electron microscopy. The γ precipitates exhibit an acicular morphology bounded by two principal facets and two minor facets. One of the major facets adopts a commensurate singular interface structure, which forms at an orientation close to the Kurdjumov-Sachs relationship. On an atomic scale these facets adopt a 'step-terrace' configuration, and the coherency strain on the terrace is relieved by the dislocation character of the steps. The other major facet adopts a one-dimensionally incommensurate singular interface structure at the Pitsch orientation relationship. The angular incompatibility between these two singular structures is accommodated by dislocations in the incommensurate interface. The configuration of these dislocations suggests that this is accomplished by nucleation at the facet junctions and subsequent climb along the facets.     

Elastic strain and misfit dislocation density in Si0.92Ge0.08 films on silicon substrates

Thin (less than 1 μm) epitaxial Si_0.92Ge_0.08 films on (100) Si substrates were grown by an UHV evaporation technique at a substrate temperature of 750 °C. The film strain and misfit dislocation density were examined by means of X-ray diffraction and transmission electron microscopy, respectively. The films are shown to be in state of compression, and the misfit dislocation density depends strongly on film thickness. The critical film thickness below which pseudomorphic growth without misfit dislocations occurs is found to be about 0.1 μm. The extrapolation model of van der Merwe's misfit dislocation theory is modified assuming low lattice mismatch and a diamond structure. The misfit dislocation distances thus calculated are compared with the measured distances, and it is found that the former are always smaller than the latter.     

Morphological transformations of thin heteroepitaxial films

The features of two-and three-dimensional growth of thin heteroepitaxial films are analysed with allowance for the energy of misfit dislocation (MD) networks. Criteria for distinguishing between Frank-van der Merwe, Stranski-Krastanov and Volmer-Weber growth modes are suggested. For the Stanski-Krastanov mode the transition from layer to island growth is considered to be associated with an increase in the interface energy owing to MD formation. The critical thickness of the pseudomorphic film in the case of the formation of dislocated islands is much less than that in the case of the introduction of MDs into the continuous film and depends on an average migration length of the adatoms. Some theoretical results are compared with experimental results for germanium films obtained by molecular beam epitaxy on Si(001) and Si(111) substrates.     

Atomistic modeling of plastic deformation in B2-FeAl/Al nanolayered composites

In this work, the deformation response of the B2-FeAl/Al intermetallic composites, as a model material system for nanolayered composites comprised of intermetallic interfaces, has been explored. We use atomistic simulations to study the deformation mechanisms and the interface misfit dislocation structure of B2-FeAl/Al nanolayered composites. It is shown that two sets of dislocations are contained in the interface misfit dislocation network and are correlated with the initial dislocation nucleation from the interfaces. The effects of layer thickness on the uniaxial deformation response of the B2-FeAl/Al multilayers are investigated. We observed that under compressive loading the smaller proportion of the FeAl layers leads to the lower overall flow stress. Under tensile loading, the void formation mechanism is investigated, suggesting the interface structure and the dislocation activities in the FeAl layers playing a significant role to trigger the strain localization which leads to void nucleation commencing at the interface. It is also found that the deformation behavior in the “weak” Fe/Cu interface behaves substantially different than that of the “strong” FeAl/Al interface. The atomistic modeling study of the nanolayered composites here underpinned the mechanical response of “strong” intermetallic interface material systems. There is no void nucleation during the entire plastic deformations in the Fe/Cu simulations, which is attributed to much higher dislocation density, more slip systems activated, and relative uniformly distributed dislocation traces in the Fe phase of the Fe/Cu multilayers.

     

干摩擦应变诱导板条马氏体固态非晶化的能量分析及其模型

使用定点离子束切割制样(FIB)并根据透射电镜(TEM)表征，分析了板条马氏体钢干摩擦层内部板条马氏体协调塑性变形、演变为纳米层片结构并发生非晶化的全过程。结果表明，高密度位错缠结和缺陷集中是纳米层片结构的典型特征，这种结构产生的界面在高应变驱动下发生非晶化。这些非晶产物，为进一步细化磨屑和形成表面自润滑层提供结构条件。基于上述实验结果并结合摩擦学和材料学理论建立了干摩擦过程中的非晶化形核模型，计算了发生非晶化的热力条件和能量壁垒。结果表明，根据经典形核理论和晶体向非晶转变的吉布斯自由能壁垒计算公式所建立的干摩擦非晶化形核能量模型，可用于计算发生非晶化必需的临界位错密度值。根据对应的计算结果，可控制摩擦条件用干摩擦应变诱导板条马氏体的固态非晶化。     

Image force and stability of a screw dislocation inside a coated cylindrical inhomogeneity with interface stresses

The image force and stability of a screw dislocation inside a coated cylindrical inhomogeneity with interface stresses are analyzed. A three-phase composite cylinder model is utilized to study the issues. The stress boundary condition at the interface of the coating layer is modified by incorporating surface/interface stress. The analytical solution of complex functions of the inhomogeneity, the coating layer, and the infinite matrix is derived by means of the complex variable method. With the aid of the obtained stress fields and the Peach–Koehler formula, the explicit expression of the image force acting on the screw dislocation is obtained. The critical radius of the inhomogeneity where the screw dislocation stays is evaluated. The influence of the interface stresses on the image force and the critical radius of the inhomogeneity is derived. The results indicate that the negative interface stresses attract the dislocation, and the positive interface stresses repel the dislocation. The critical radius of inhomogeneity will increase for considering the negative interface stresses and will decrease for considering the positive interface stresses.     

Multiscale Modeling of Deformation in Polycrystalline Thin Metal Films on Substrates

The time‐dependent irreversible deformation of a thin metal film constrained by a substrate is investigated by a mesoscopic discrete dislocation simulation scheme incorporating information from atomistic studies of dislocation nucleation mechanisms. The simulations take into account dislocation climb along the grain boundaries in the film as well as dislocation glide along slip planes inclined and parallel to the film/substrate interface. The calculated flow stress and other features are compared with relevant experimental observations. The work is focused on deformation of a polycrystalline film without a cap layer, for which diffusive processes play an important role. The dislocation‐based simulations reveal information on the prevailing deformation mechanisms under different conditions and for different film thicknesses. Despite of the limitations of the two‐dimensional dislocation model, the simulations exhibit a film thickness dependent transition between creep dominated and dislocation glide dominated deformation, which is in good agreement with experimental observations.