Dipole of edge misfit dislocations and critical radius conditions for buried strained cylindrical inhomogeneity

A theoretical model is proposed for elastic stress relaxation of a buried strained cylindrical inhomogeneity, which assumes the edge misfit dislocation dipole formation in the soft matrix at some distance from the interface. The critical radius of the inhomogeneity for the formation of the edge misfit dislocation dipole is given and the influence of various parameters on the critical radius is evaluated. The result indicates that the critical radius decreases with increasing misfit strain and core radius of the misfit dislocation. It is also found that, compared to the edge misfit dislocation dipole formation in the interface, the critical radius of the inhomogeneity decreases when the location of an edge misfit dislocation dipole formation is in the soft matrix at some distance from the interface.     

Surface/interface effects on the formation of misfit dislocation in a core–shell nanowire

The misfit strain within the core of a two-phase free-standing core–shell nanowire resulting in the generation of an edge misfit dislocation or an edge misfit dislocation dipole at the core–shell interface is considered theoretically within both the classical and surface/interface elasticity approaches. The critical conditions for the misfit dislocation generation are studied and discussed in detail with special attention to the non-classical surface/interface effect. It is shown that this effect is significant for fine cores of radius smaller than roughly 20 interatomic distances. The positive and negative surface/interface Lamé constants mostly make the generation of the misfit dislocation easier and harder, respectively. Moreover, the positive (negative) residual surface/interface tensions mostly make the generation of the misfit dislocation harder (easier). The formation of individual misfit dislocation is energetically more preferential in finer two-phase nanowires, while the formation of misfit dislocation dipole is more expectable in the coarser ones.     

外延生长薄膜中失配位错形成条件的分子动力学模拟研究

运用分子动力学方法对负失配条件下的外延铝簿膜中失配位错的形成进行了模拟研究.所采 用的原子间相互作用势为嵌入原子法(EAM)多体势.模拟结果显示：在500K下长时间静态弛豫 ，表面和内部结构完整的外延膜在9—80原子层厚度范围内(约为其热力学临界厚度的3—40 倍)均不形成失配位错，而在薄膜表面预置一个单原子层厚、三个原子直径大小的凸台或凹 坑时，失配位错则能够在15个原子层厚的外延膜上迅速形成：在动态沉积生长条件下，表面 自然形成凹凸，初始厚度为9个原子层厚的外延膜在沉积生长中迅速形成失配位错.在三种条 件下，所形成的位错均为伯格斯矢量与失配方向平行的全刃位错.分析发现：在压应力作用 下，表面微凸台诱发了其侧薄膜内部原子的挤出，造成位错形核；而表面微凹坑则直接因压 应力作用形成了一个表面半位错环核. 关键词： 外延薄膜 失配位错 分子动力学 铝     

Role of edge dislocations in plastic relaxation of GeSi/Si(001) heterostructures: Dependence of introduction mechanisms on film thickness

It has been shown that, in the GeSi/Si(001) heterosystem at lattice parameter mismatches of ～2% and more, a small critical thickness of the introduction of dislocations leads to the implementation of the mechanism of induced nucleation of misfit dislocations. This mechanism consists in that the stress field of an already existing 60° dislocation provokes introduction of a secondary 60° dislocation with an opposite-sign screw component. As a result of the interaction of such dislocation pairs, edge misfit dislocations are formed, which do control the plastic relaxation process. This mechanism is most efficient when dislocations are introduced at the GeSi film thickness only slightly exceeding the critical thickness of the introduction of 60° dislocations, and there are threading dislocations. The dominant type of misfit dislocations (60° or edge) in the Ge-on-Si(001) system can be controlled by varying the mismatch parameter in the heteropair.     

Nucleation of misfit dislocations and plastic deformation in core/shell nanowires

During fabrication of metal nanowires, an oxide layer (shell) that surrounds the metal (core) may form. Such an oxide-covered nanowire can be viewed as a cylindrical core/shell nanostructure, possessing a crystal lattice mismatch between the core and shell. Experimental evidence has shown that, in response to this mismatch, mechanical stresses induce plastic deformation in the shell and misfit dislocations nucleate at the core/shell interface. As a result, the mechanical, electrical and optoelectronic properties of the nanowire are affected. It is therefore essential to be able to predict the critical conditions at which misfit dislocation nucleation at the nanowire interface takes place and the critical applied load at which the interface begins deforming plastically. Two approaches are explored in order to analyze the stress relaxation processes in these oxide-covered nanowires: (i) energy considerations are carried out within a classical elasticity framework to predict the critical radii (of the core and shell) at which dislocation nucleation takes place at the nanowire interface; (ii) a strain gradient plasticity approach is applied to estimate the flow stress at which the interface will begin deforming plastically (this stress is termed “interfacial-yield” stress). The interfacial-yield stress, predicted by gradient plasticity, depends, among other material parameters, on the radii of the core and shell. Both approaches demonstrate how the geometric parameters of nanowires can be calibrated so as to avoid undesirable plastic deformation; in particular, method (i) can give the radii values that prevent misfit dislocation formation, whereas method (ii) can provide, for particular radii values, the critical stress at which interface deformation initiates.     

外延PbZr0.4Ti0.6O3薄膜厚度对其铁电性能的影响

从Landau-Devonshire唯象理论出发，考虑到晶格失配导致的NFDA3位错应力场与极化场的耦合，研究了在SrTiO₃衬底上外延生长的PbZr_0.4Ti_0.6O₃薄膜厚度对其自发极化强度、电滞回线的影响. 结果表明，产生刃位错的PbZr_0.4Ti_0.6O₃薄膜临界厚度为～1.27nm，当薄膜厚度大于临界厚度时，在所形成的位错附近，极化强度出现急剧变化，形成自发极化强度明显减弱的“死层”；随着薄膜厚度的减小，位错间距增大，“死层”厚度与薄膜总厚度之比增加. 由薄膜电滞回线的变化情况可知，其剩余极化强度随着薄膜厚度的减小而逐渐减小. 关键词： 铁电薄膜 自发极化强度 电滞回线 位错     

Initial stages of misfit stress relaxation through the formation of prismatic dislocation loops in GaN–Ga<Subscript>2</Subscript>O<Subscript>3</Subscript> composite nanostructures

The initial stages of misfit stress relaxation through the formation of rectangular prismatic dislocation loops in model composite nanostructures have been considered. The nanostructures are either spherical or cylindrical GaN shells grown on solid or hollow β-Ga²O₃ cores or planar thin GaN films on β-Ga²O₃ substrates. Three characteristic configurations of prismatic dislocation loops, namely, square loops, loops elongated along the GaN/Ga²O₃ interface, and loops elongated along the normal to the GaN/Ga²O₃ interface, have been analyzed. The generation of prismatic dislocation loops from the interface into the bulk of the GaN shell (film), from the free surface into the GaN shell (film), and from the interface into the β-Ga²O₃ core (substrate) has been investigated. It has been shown that, for the minimum known estimate of the lattice misfit (2.6%) in some of the considered nanostructures, no any prismatic dislocation loops can be generated. If the generation of prismatic dislocation loops is possible, then in all the considered nanostructures, the energetically more favorable case corresponds to prismatic dislocation loops elongated along the GaN/Ga²O₃ interfaces, and the more preferred generation of prismatic dislocation loops occurs from the GaN free surface. The GaN/Ga²O₃ nanostructures that are the most and least resistant to the formation of prismatic dislocation loops have been determined. It has been found that, among the considered nanostructures, the planar two-layer GaN/Ga²O₃ plate is the most resistant to the generation of prismatic dislocation loops, which is explained by the action of an alternative mechanism for the relaxation of misfit stresses due to the bending of the plate. The least resistant nanostructure is the planar three-layer GaN/Ga²O₃/GaN plate, in which GaN films have an identical thickness and which itself as a whole does not undergo bending. The critical thicknesses of the GaN shells (films), which must be exceeded to ensure the growth of these shells (films) so as to avoid the formation of prismatic dislocation loops, have been calculated for all the studied nanostructures and three known estimates of the lattice misfits (2.6, 4.7, and 10.1%).     

Combined effects of substrate compliance and film compositional grading on strain relaxation in layer-by-layer semiconductor heteroepitaxy: the case of InAs/In0.50Ga0.50As/GaAs(1 1 1)A

A systematic theoretical analysis is presented of the combined effects of substrate compliance and film compositional grading on the relaxation of strain due to lattice mismatch in layer-by-layer semiconductor heteroepitaxy. The analysis is based on a combination of continuum elasticity theory and a novel atomistic simulation approach for modeling structural and compositional relaxation in layer-by-layer heteroepitaxial systems. Results are presented for InAs epitaxy on GaAs(1 1 1)A compliant substrates with some marginal film compositional grading that consists of one monolayer of In_0.50Ga_0.50As grown on the substrate surface prior to InAs growth. A parametric study is carried out over a wide range of substrate thicknesses. Interfacial stability with respect to misfit dislocation formation, the dependence on substrate thickness of a thermodynamic critical film thickness, and the completion of the coherent-to-semicoherent interfacial transition are examined in detail. In addition, the structural characteristics and compositional distribution of the corresponding semicoherent interfaces, the associated strain fields, as well as the film surface morphological characteristics are analyzed. Most importantly, the role of segregation at defects of a semicoherent interface in the thermodynamics of layer-by-layer heteroepitaxial growth is demonstrated. Our study shows that systematic combination of the mechanical behavior of thin compliant substrates with grading of the epitaxial film composition provides a very promising engineering strategy for strain relaxation in heteroepitaxy.     

Analysis of the dislocation structure at the Ge/Si(111) heterointerface

We demonstrate the formation of a modified triangular network of Shockley edge partial misfit dislocations at a plastic-relaxation level of ρ = 0.72 of 3D Ge(111) islands grown on a wetting layer. The network forms due to the offset of one dislocation family by 40% of the interdislocation spacing. We report ultra-high-vacuum scanning tunnel microscopy and high-resolution transmission electron microscopy data and the results of theoretical calculation of the stress fields induced in the film volume by the introduction of misfit dislocations. We establish the Ge-film-thickness range acceptable for observing elastic undulation of the surface by scanning tunneling microscopy.     

Generation of rectangular prismatic dislocation loops in shells and cores of composite nanoparticles

A theoretical model has been proposed for describing the relaxation of misfit stresses in a spherically symmetric composite core-shell nanoparticle due to the generation and expansion of rectangular prismatic dislocation loops at the internal and external interfaces. The critical conditions of the formation of these loops have been calculated for nanoparticles consisting of a relatively massive core and a thin shell. It has been shown that the generation of dislocation loops is possible when the misfit of the lattice parameters of the core and shell of the nanoparticle exceeds a critical value that depends on the nanoparticle radius, the shell thickness, the loop formation position, and the shape of loops. This condition holds for a loop in the shell when the shell thickness either lies in a specific range of small values or (for a larger misfit) is less than a critical value. For the generation of loops in the core, the shell thickness should exceed a critical value. The dislocation loops elongated along the core-shell interface are formed more readily. As the shell thickness increases at a fixed nanoparticle radius, the energetically more favorable generation of a dislocation loop occurs first from the free surface into the bulk of the shell, then from the interface into the shell, and finally from the interface into the core of the nanoparticle.     

考虑相界效应的Ni基单晶合金纳米压痕模拟

利用分子动力学方法分别模拟金刚石压头压入Ni模型和Ni基单晶合金γ/γ′模型的纳米压痕过程,通过计算得到两种模型[001]晶向的弹性模量及硬度.采用中心对称参数分析不同压入深度时两种模型内部位错形核、长大过程以及Ni基单晶合金γ/γ′(001)相界面错配位错对纳米压痕过程的影响.结果显示:压入深度0.641 nm之前,两种模型的压入载荷-压入深度曲线相似,说明此时相界面处的错配位错对纳米压痕过程的影响很小;压入深度0.995 nm时,在错配位错处发生位错形核,晶体在γ相中沿着{111}面滑移,随即导致Ni基单晶合金γ/γ′模型压入载荷的下降,并在压入深度达到1.487 nm之前低于Ni模型相同压入深度时的压入载荷;压入深度从1.307 nm开始,由于相界面错配位错的阻碍作用,Ni基单晶合金γ/γ′模型压入载荷上升速度较快.     

Self-organized growth of nanoparticles on a surface patterned by a buried dislocation network

The self-organized growth of Co nanoparticles is achieved at room temperature on an inhomogenously strained Ag(001) surface arising from an underlying square misfit dislocation network of 10 nm periodicity buried at the interface between a 5 nm-thick Ag film and a MgO(001) substrate. This is revealed by in situ grazing-incidence small-angle x-ray scattering. Simulations of the data performed in the distorted wave Born approximation framework demonstrate that the Co clusters grow above the dislocation crossing lines. This is confirmed by molecular dynamic simulations indicating preferential Co adsorption on tensile sites.     

Misfit dislocations in nanocomposites with quantum dots,nanowires and their ensembles

We review theoretical concepts and experimental results on the physics of misfit dislocations in nanocomposite solids with quantum dots (QDs) and nanowires (quantum wires). Special attention is paid to thermodynamic theoretical models of formation of misfit dislocations in QDs and nanowires, including composite core–shell nanowires. The effects of misfit dislocations on the film growth mode during heteroepitaxy and phase transitions in QD systems are analysed. Experimental results and theoretical models of the ordered spatial arrangement of QDs growing on composite substrates with misfit dislocation networks are discussed. The influence of subsurface dislocations in composite substrates on the nucleation of QDs and nanowires on the substrate surface is considered. Models of misfit strain relaxation and dislocation formation in nanofilms on compliant substrates are also reviewed.     

Nano-islands on a composite substrate with misfit dislocations

Spatial arrangements of nano-islands (quantum dots) on the free surface of a composite two-layer substrate containing misfit dislocations of edge type are theoretically examined. It is shown that the elastic interaction between misfit dislocations and nano-islands is capable of causing coagulation of nano-islands. The coagulation of nano-islands is shown to be favourable when the upper-layer thickness is smaller than a critical thickness, H₀. An analytical form of H₀ is presented for the partial case with four-to-one correspondence between nano-islands and cells of the misfit dislocation network. Received: 5 December 2000 / Accepted: 29 March 2001 / Published online: 20 June 2001     

Elastic-energy relaxation in heterostructures with strained nanoinclusions

Elastic-energy relaxation in systems with nanoinclusions is considered. The relaxation is related to the formation of the following dislocation loops: a single misfit dislocation loop or a group of such loops on the matrix-nanoinclusion interface and/or a satellite dislocation loop near the inclusion. The critical inclusion sizes beginning from which misfit dislocation loops and satellite dislocation loops can nucleate are determined for various models of relaxation processes. The dependences of the satellite-dislocation-loop diameter on the inclusion size are calculated and compared with experimental data.     

界面结构对Cu/Ni多层膜纳米压痕特性影响的分子动力学模拟

金属多层膜调制周期下降到纳米级时,其力学性质会发生显著改变. Cu-Ni晶格失配度约为2.7%,可以形成共格界面和半共格界面,实验中实现沿[111]方向生长的调制周期为几纳米且具有异孪晶界面结构的Cu/Ni多层膜,其力学性质发生显著改变.本文采用分子动力学方法对共格界面、共格孪晶界面、半共格界面、半共格孪晶界面等四种不同界面结构的Cu/Ni多层膜进行纳米压痕模拟,研究压痕过程中不同界面结构类型的形变演化规律以及位错与界面的相互作用,获取Cu/Ni多层膜不同界面结构对其力学性能的影响特征.计算结果表明,不同界面结构的样品在不同压痕深度时表现出的强化或软化作用机理不同,软化机制主要是由于形成了平行于界面的分位错以及孪晶界面的迁移,强化机制主要是由于界面对位错的限定作用以及失配位错网状结构与孪晶界面迁移时所形成的弓形位错之间的相互作用.     

Inhomogeneity of misfit stresses in nickel-base superalloys: Effect on propagation of matrix dislocation loops

It is shown experimentally that, during annealing and creep under low applied stresses, matrix dislocation loops frequently cross-glide. The periodic length of the zigzag dislocations deposited in the interfaces is equal to that of the γ/γ′-microstructure. Initially, the zigzag dislocations move in the (001) interface by a combination of glide and climb but then they stop near the γ′-edges and align along ?100?. Reactions of such dislocations lead to the formation of square interfacial networks consisting of ?100? oriented edge dislocations. The complex dislocation movement is explained by the inhomogeneity of the misfit stresses between γ- and γ′-lattices. The tensile components of the stress tensor drive the dislocations through the channel, whereas the shear components near the γ′-edges cause the zigzag movement and the ?100? alignment. The total effect is the most efficient relaxation of the misfit stresses. The results are relevant, especially for single-crystal superalloys of the newest generations, which have an increased γ/γ′-misfit due to the high level of refractory elements.     

Prediction of dislocation formation in epitaxial multilayers subject to in-plane loading

A theoretical model is described to predict equilibrium distributions of misfit dislocations in one or more anisotropic epitaxial layers of a multilayered system deposited on a thick substrate. Each layer is regarded as having differing elastic and lattice constants, and the system is subject to biaxial in-plane mechanical loading. A stress transfer methodology is developed enabling both the stress and displacement distributions in the system to be estimated for cases where the interacting dislocations are of a pure edge configuration. Energy methods are used to determine equilibrium distributions of the dislocations for given external applied stress states. It is shown that the new model accurately reproduces known exact analytical solutions for the special case of just one isotropic epitaxial layer applied to an isotropic semi-infinite substrate having the elastic constants of the substrate but differing lattice constants. The model is used to consider equilibrium dislocation distributions in capped epitaxial systems with misfit dislocations. It is shown that the simplifying assumptions often made in the literature, regarding the uniformity of elastic properties and the neglect of anisotropy, can lead to critical thicknesses being underestimated by 15–18%. The application of uniaxial tensile stresses increases the value of critical thicknesses. The model can be used to analyse dislocations in various non-neighbouring layers provided the dislocation density has the same value in all layers in which dislocations have formed. This type of analysis enables the prediction of the deformation of metallic multilayers subject to mechanical and thermal loading.     

The surface and interface nucleation of misfit dislocations as a possible source of asymmetric strain relaxation in vicinal heterostructures

The surface nucleation of misfit dislocations in vicinal (001) oriented heterostructures with compressive and tensile stresses is discussed. It is shown that beside the asymmetrical stressing of opposite dislocation slip planes due to the vicinal substrate, the surface steps have a similar effect. The effect of the steps has the same-sign asymmetry for a compressive stressed epilayer, but opposite for the tensile case. The effect on dislocation nucleation energy is calculated. For miscut angles used normally, the step energy contribution exceeds that of due to the vicinal substrate. The extension to interface nucleation is treated qualitatively.     

温度对镍基单晶高温合金γ/γ'相界面上错配位错运动影响的分子动力学研究

用分子动力学方法研究了温度对镍基单晶高温合金γ/γ'相界面上错配位错运动的影响.研究结果表明:无论是在低温还是在高温下,错配位错的运动都是通过扭折的形核及扭折沿位错线的迁移来实现;在低温时错配位错的相互作用有利于错配位错的运动;然而在高温时错配位错的相互作用可以阻碍错配位错的运动,从而阻碍γ和γ'相界面的相对滑动,有利于提高镍基单晶高温合金的高温力学性能. 关键词： 镍基单晶高温合金 相界面 错配位错 分子动力学模拟