Modeling elasticity in crystal growth

A new model of crystal growth is presented that describes the phenomena on atomic length and diffusive time scales. The former incorporates elastic and plastic deformation in a natural manner, and the latter enables access to time scales much larger than conventional atomic methods. The model is shown to be consistent with the predictions of Read and Shockley for grain boundary energy, and Matthews and Blakeslee for misfit dislocations in epitaxial growth.     

晶体相场法模拟异质外延过程中界面形态演化与晶向倾侧

采用晶体相场模型研究了异质外延过程中失配应变与应力弛豫对外延层界面形态演化的影响, 并对由衬底倾角引起的外延层晶向倾侧进行了分析.研究结果表明: 在有一定倾角的衬底晶体上进行外延生长时,若衬底和外延层之间失配度较大 (ε>0.08),外延层中弹性畸变能会以失配位错的形式释放, 最终薄膜以稳定的流动台阶形式生长且外延层的晶向倾角与衬底倾角呈近似线性关系. 而当衬底和外延层之间失配度较小(ε<0.04)不足以形成失配位错时, 外延层中弹性畸变能会以表面能的形式释放,最终使薄膜以岛状形态生长. 在高过冷度条件下,衬底倾角和失配度较大时,衬底和外延层之间会形成由大量位错规则排列而成的小角度晶界从而显著改变外延层的生长位向.     

采用纳米晶柱阵列衬底抑制失配位错形成的分子动力学模拟研究

运用分子动力学方法对纳米晶柱阵列衬底上铝簿膜的外延生长进行了模拟研究.所采用的原子间相互作用势为嵌入原子法(EAM)多体势.模拟结果表明：采用纳米晶柱阵列衬底可以在不形成失配位错的条件下释放其上生长的外延薄膜晶体中的失配应变,有效地抑制其中失配位错的形成,获得高质量的外延薄膜晶体;这种纳米晶柱阵列的几何设计应满足两个基本条件：1) 晶柱的横截面尺寸应大于对应温度下的晶柱热失稳临界尺寸,以克服纳米结构的热失稳,模拟显示700K下铝的热失稳临界尺寸为19nm;2) 晶柱的高度与间距之比应大于076,以保证 关键词： 失配位错 分子动力学 纳米晶柱 铝     

Structure of epitaxial crystal interfaces

Theoretical work on the structural influences of misfit, bonding and crystal dimension in epitaxial bicrystals is reviewed. The main contents relate to the model in which the inter-action between the crystal halves is represented by a periodic force acting at the interface, the crystals are approximated by elastic continua and the structure is assumed to be governed by lowest energy principles. In this model the misfit is accommodated by sequences of misfit dislocations located at the interface and/or overall lattice strains. The degree to which one or the other mechanism dominates depends on the size and shape of the crystal in addition to the elastic and bonding properties. Realistic approximations for various special cases, e.g. monolayers, thick crystals and intermediate thicknesses, are considered. An exact solution covering the entire spectrum of interest does not exist.     

Misfit disclinations at crystal/crystal and crystal/glass interfaces

Theoretical concepts have been developed for a new type of misfit defects, misfit disclinations, at crystal/crystal and crystal/glass interfaces. It is shown, in particular, that the formation of misfit disclinations is an efficient physical micromechanism of misfit stress relaxation at crystal/crystal interfaces. A model describing misfit disclinations at crystal/glass interfaces has been constructed. The energy characteristics of phase boundaries with misfit disclination ensembles are estimated. Fiz. Tverd. Tela (St. Petersburg) 41, 1637–1643 (September 1999)     

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.     

Ordered step arrays on evaporated As (0001) vicinal surfaces

A computational procedure dealing with a one-dimensional epitaxial monolayer model was developed in part I. In this part it is extended and applied to the two-dimensional case, allowing for misfit along two perpendicular interfacial directions. The model employed differs slightly from that used by van der Merwe in that the overgrowth film is simulated by a plane of atoms linked to each other by elastic springs. This allows for an exact determination of the equilibrium boundary conditions. The results show (i) that the rectangular boundary edge is slightly deformed, lateral contractions occurring where the misfit dislocations intersect the boundary edge, (ii) that the dependence of stable structures on misfit is in good agreement with the analytical results of van der Merwe, (iii) that misfit dislocations are introduced alternately at the mutually perpendicular edges of a system having quadratic symmetry, (iv) that a segmented dependence of lowest energy on crystal size is obtained, one segment for each additional dislocation, (v) that a saw-toothed dependence of average strain on crystal size, in qualitative agreement with the experimental work of Vincent, results and (vi) that a fine structure in the energy curves results from discrete adatom peripheral growth.     

Characterization of crystal growth using a spiral nucleation model

Classical concepts of two-dimensional nucleation and spiral growth are used together with recent findings on the dynamics of dislocation spirals to derive a new crystal growth model. Initial growth nuclei result from the organization of adsorbed molecules in spirals around surface dislocations. The energetic barrier for the activation of the spiral nuclei is considerably lower than the admitted by classical two dimensional nucleation models. Stable nuclei evolve into bigger growth hillocks in supersaturated media through the incorporation of adsorbed units into their steps. The displacement velocity of steps during solution and vapour growth is calculated by different kinetic approaches, taking into consideration the distinct role of surface diffusion in each process, and avoiding known limitations of conventional theories. A generalized expression is obtained relating the crystal growth rate with main variables such as supersaturation, temperature, crystal size, surface topology and interfacial properties. At the end of the paper, the crystallization kinetics of sucrose measured at 40 °C is interpreted in the light of the new perspectives resulting from the proposed model. The application example illustrates how to estimate interfacial and topological properties from the experimental crystal growth results.     

GaAs/AlGaAs分子束外延材料的X射线双晶形貌观察

本文介绍了用非平行非对称(+、-)双晶X射线形貌术研究Ⅲ—Ⅴ族化合物外延晶体的设置和原理。分析了外延后形成的弯曲样品造成的衍射效应。对分子束外延(MBE)法生长的GaAs/AlGaAs衬底和外延层分别进行了X射线形貌术观察。讨论了外延层中存在的失配位错、生长小丘、沾污和局部微差取向等缺陷。对位错的组态和来源进行了初步分析。本实验结果也表明,有应变超晶格过渡层的MBE法对生长优质的GaAs/AlGaAs外延片是有利的。     

初始压入位置对Ni基单晶合金纳米压痕影响研究

针对Ni基单晶合金建立初始压入γ 相的γ /γ' 模型和初始压入γ'相的γ'/γ 模型, 采用分子动力学方法模拟金刚石压头压入两种模型的纳米压痕过程, 计算两种模型[001]晶向硬度. 采用中心对称参数分析两种模型(001)相界面错配位错对纳米压痕过程的影响. 结果显示: 弛豫后, 两种模型(001)相界面错配位错形式不同, 其中γ'/γ 模型(001)相界面错配位错以面角位错形式存在; 压入深度在0.930 nm 之前, 两种模型(001)相界面错配位错变化不大, 压入载荷-压入深度及硬度-压入深度曲线较符合; 压入深度在0.930 nm之后, γ'/γ 模型(001)相界面错配位错长大很多, 导致相同压入深度时γ'/γ 模型比γ /γ'模型压入载荷和硬度计算结果小; 压入深度在2.055 nm之后, γ /γ'模型(001)相界面错配位错对γ 相中位错进入γ'相有阻碍作用, 但仍有部分位错越过(001) 相界面进入γ' 相中, γ'/γ 模型(001)相界面处面角位错对γ' 相中位错进入γ 相有更明显的阻碍作用, 几乎无位错越过(001) 相界面进入γ 相中, 面角位错的强化作用更明显, 所以γ'/γ 模型比γ /γ'模型压入载荷上升速度快.     

Bridging the phase-field and phase-field crystal approaches for anisotropic material systems

In this paper the amplitude representation of the anisotropic phase-field crystal (APFC) model recently proposed as a generalized model for isotropic as well as anisotropic crystal lattice systems is developed. The relationship between the amplitude equations and the standard phase-field model for solidification of pure substances with elasticity effects is derived which provide an explicit connection between the phase-field and APFC models. On the one hand we present a computationally more efficient model and highlight its potential as a bridge between the PFC and phase-field models with anisotropic interface energies and kinetics on the other hand.     

Influences of misfit strains on liquid phase heteroepitaxial growth

Influences of misfit strains with different signs on liquid phase heteroepitaxial growth are studied by binary phase field crystal model. It is amazing to find that double islands are formed because of lateral and vertical separation. The morphological evolution of epitaxial layer depends on signs of misfit strains. The maximum atomic layer thickness of double islands under negative misfit strain is larger than that of under positive misfit strain at the same evolutional time, and size differences between light and dark islands is much smaller under negative misfit strain than that of under positive misfit strain. In addition, concentration field and density field approximately have similar variational law along x direction under the same misfit strain but show opposite variational trend under misfit strains with different signs. Generally, free energy of epitaxial growth systems keeps similar variational trend under misfit strains with different signs.     

Delocalized dislocations in quantum dots

A theoretical model describing nucleation of the misfit dislocations with delocalized cores in island films is proposed. The parameters of nanoislands (quantum dots) with such delocalized misfit dislocations in the Ge/Si system are estimated. Within the framework of the proposed model, nucleation of the delocalized misfit dislocations at the quantum dots in a broad range of parameters is energetically more favorable than nucleation of the perfect misfit dislocations usually considered in the models of dislocated quantum dots.     

Positron annihilation in alpha- and beta-cyclodextrin

A new type of misfit dislocation multiplication is deduced from high-voltage electron micrographs of thin Ge layers on GaAs substrates. Two misfit dislocations with the same Burgers vectors on different glide planes cross and annihilate at the intersection point resulting in the formation of two angular dislocations. The tip of one of these dislocations may reach the growth surface by glide breaking into two separate dislocation segments. These segments may glide to form additional misfit dislocations, which may undergo the same multiplication process.     

Misfit dislocation locking and rotation during gallium nitride growth on SiC/Si substrates

The effect of changing the misfit dislocation propagation direction during GaN layer growth on the AlN/SiC/Si(111) structure surface is detected. The effect is as follows. As the GaN layer growing on AlN/SiC/Si(111) reaches a certain thickness of ~300 nm, misfit dislocations initially along the layer growth axis stop and begin to move in the direction perpendicular to the growth axis. A theoretical model of AlN and GaN nucleation on the (111) SiC/Si face, explaining the effect of changing the misfit dislocation motion direction, is constructed. The effect of changing the nucleation mechanism from the island one for AlN on SiC/Si(111) to the layer one for the GaN layer on AlN/SiC/Si is experimentally detected and theoretically explained.     

相场晶体法模拟过冷熔体中的晶体生长

利用相场晶体(phase-field crystal)模型,采用有限差分法,模拟了过冷熔体中晶体生长过程,研究了不同相区、不同过冷度对晶体生长过程的影响.结果表明,在共存区中,随着演化的进行,晶体生长被抑制,液-晶边界层逐渐变厚;在单相区中,随着过冷度的增大,晶态区面积显著增加,液-晶边界层逐渐变薄.晶体生长速度和过冷度成近似线性的关系. 关键词： 相场晶体 自由能函数 过冷熔体 晶体生长     

Strain relief and growth optimization of GaSb on GaP by molecular beam epitaxy

In this paper, the impact of growth parameters on the strain relaxation of highly lattice mismatched (11.8%) GaSb grown on GaP substrate by molecular beam epitaxy has been investigated. The surface morphology, misfit dislocation and strain relaxation of the GaSb islands are shown to be highly related to the initial surface treatment, growth rate and temperature. More specifically, Sb-rich surface treatment is shown to promote the formation of Lomer misfit dislocations. Analysis of the misfit dislocation and strain relaxation as functions of the growth temperature and rate led to an optimal growth window for a high quality GaSb epitaxial layer on (001) GaP. With this demonstrated optimized growth, a high mobility (25?500?cm(2)?V (-1)?s(-1) at room temperature) AlSb/InAs heterostructure on a semi-insulating (001) GaP substrate has been achieved.     

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.     

Investigation on dislocation-based mechanisms of void growth and coalescence in single crystal and nanotwinned nickels by molecular dynamics simulation

Abstract

Molecular dynamics simulations were conducted to elucidate dislocation mechanisms of the void growth and coalescence in single crystal and nanotwinned nickels subjected to uniaxial tension. The simulation results reveal that twin boundary is capable of decreasing the critical stress, suppressing the emission of dislocations and reducing the overall stiffness of the crystal. A size-scale dependence of critical stress is definitely illustrated through stress–strain response, where the larger void size leads to the lower critical stress and strain. It is the successive emissions of leading partials and the subsequent trailing partials that cause the atoms on the void surfaces to escape from the void surfaces continually, and consequently the voids grow to be larger and larger with increasing strain. The voids in the nanotwinned nickel coalesce earlier than those in the single crystal nickel even though the initiation of dislocations in the former is later than that in the latter. Void fraction remains a constant during elastic deformation, while it presents a linear increase with increasing strain during plastic deformation. Evolution of void fraction during void growth and coalescence is independent on void size.     

Misfit dislocations in gold/Permalloy multilayers

Several groups have reported the misfit dislocation structures in Au/Ni_0.8Fe_0.2 multilayers where the lattice parameter misfit is very large. To explore the factors controlling such structures, molecular dynamics simulations have been used to simulate the vapour-phase growth of (111)-oriented Au/Ni_0.8Fe_0.2 multilayers. The simulations revealed the formation of misfit dislocations at both the gold-on-Ni_0.8Fe_0.2 and the Ni_0.8Fe_0.2-on-gold interfaces. The dislocation configuration and density were found to be in good agreement with previously reported high-resolution transmission electron microscopy observations. Additional atomic-scale simulations of a model nickel–gold system indicated that dislocations are nucleated as the first nickel layer is deposited on gold. These dislocations have an (a/6)?112? Burgers vector, typical of a Shockley partial dislocation. Each dislocation creates an extra {220} plane in the smaller lattice parameter nickel layer. These misfit-type dislocations effectively relieve misfit strain. The results also indicated that the dislocation structure is insensitive to the energy of the depositing atoms. Manipulation of the deposition processes is therefore unlikely to reduce this component of the defect population.