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.     

Effect of internal strain fields on the controllability of nanodimensional ferroelectric films in a plane capacitor

Nanodimensional ferroelectric heteroepitaxial Ba_0.8Sr_0.2TiO₃ films grown by the layer-by-layer mechanism on MgO(100) substrates are examined by the X-ray diffraction and transmission electron microscopy methods. It is established that, when the thickness of the film changes, the stress relaxation proceeds via generation of misfit dislocations at the film-substrate interface. There exists a critical thickness (≈40 nm) of the film below and above which the film possesses tensile and compression stresses, respectively. Examples of how the stresses influence the insulating properties of the films are given.     

Misfit dislocation loops in composite core-shell nanoparticles

The critical conditions have been calculated for the generation of circular prismatic loops of misfit dislocations at the interfaces in spherically symmetric composite core-shell nanoparticles. It has been shown that the formation of these loops becomes energetically favorable if the misfit parameter exceeds a critical value, which is determined by the geometry of the system. The most preferred position of the dislocation loop is in the equatorial plane of the nanoparticle. For a given radius of the nanoparticle, there is a minimum value of the critical misfit parameter below which the generation of a misfit dislocation is energetically unfavorable for any ratio of the core and shell radii. For a misfit parameter exceeding the minimum critical value, there are two critical values of the reduced radius of the particle core in the interval between which the generation of a dislocation loop is energetically favorable. This interval increases with increasing misfit parameter for a fixed particle size and decreases with decreasing particle size for a fixed misfit parameter.     

Generation of dislocation loops in strained quantum dots embedded in a heterolayer

The generation of prismatic dislocation loops in strained quantum dots is investigated. The quantum dots are embedded in a film-substrate heterostructure with mechanical stresses caused by the difference between the lattice parameters of the film (heterolayer) and the substrate. The intrinsic plastic strain ?_m of a quantum dot arises from the misfit between the lattice parameters of the materials of the quantum dot and the surrounding matrix. The interface between the heterolayer and the substrate is characterized by a misfit parameter f. The critical radius of a quantum dot R _c at which the generation of a dislocation loop in the quantum dot becomes energetically favorable is analyzed as a function of the intrinsic plastic strain ?_m and the misfit parameter f.     

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     

Generation and evolution of partial misfit dislocations and stacking faults in thin-film heterostructures

An analysis is made of the specific features in the generation and evolution of partial misfit dislocations at the vertices of V-shaped configurations of stacking fault bands, which terminate in the bulk of the growing film at 90° partial Shockley dislocations. The critical thicknesses h _c of an epitaxial film, at which generation of such defect configurations becomes energetically favorable, are calculated. It is shown that at small misfits, the first to be generated are perfect misfit dislocations and at large misfits, partial ones, which are located at the vertices of V-shaped stacking-fault band configurations emerging onto the film surface. Possible further evolution of stacking-fault band configurations with increasing film thickness are studied.     

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     

Two groups of misfit dislocations in GaAs on Si

High-resolution cross-sectional and conventional plan-view transmission electron microscope observations have been carried out for molecular beam epitaxially grown GaAs films on vicinal Si (001) before and after annealing as a function of film thicknesses and observation directions between two orthogonal 110 directions. Two groups of misfit dislocations are characterized at the interface regions between GaAs and Si by analyzing whether their extra half planes exist in the film or the substrate side. Group I misfit dislocations due to stress caused by a lattice misfit between GaAs and Si consist of partial dislocations and 60° and 90° complete dislocations in an as-grown state. With an increase in the film thickness, partial dislocations decrease and complete dislocations increase. After annealing, partial dislocations almost completely disappear and 90° perfect dislocations are predominantly observed. Group II misfit dislocations due to thermal-expansion misfit-induced stress are all 60°-type complete dislocations regardless of film thicknesses and annealing treatment.On leave from Central Research Laboratory, Hitachi, Ltd., Tokyo 185, Japan     

Misfit dislocations in thin films on plastically deformed substrates

A theoretical model describing the nucleation of misfit dislocations (MD) in interfaces between films and plastically deformed substrates with disclinations is proposed. The ranges of the parameters (disclination strength, density of the disclination ensemble, film thickness, and degree of misfit) within which MD nucleation is energetically favorable are found. It is shown that at certain strengths of disclinations and densities of their ensemble the critical thickness of the film on a plastically deformed substrate with disclinations can exceed that on an undeformed defect-free substrate by a few times.     

Edge misfit dislocation formation at the interface of a nanopore and infinite substrate with surface/interface effects

The model of an edge misfit dislocation at the interface of the hollow nanopore and the infinite substrate with surface/interface stress is investigated. Using the complex variable method, analytical solutions for complex potentials of a film due to an edge misfit dislocation located in the film with surface/interface effect are derived, and the stress fields of the film and the edge misfit dislocation formation energy can be obtained. The critical conditions for edge misfit dislocation formation are given at which the generation of an edge misfit dislocation is energetically favourable. The influence of the ratio of the shear modulus between the film and the infinite substrate, the misfit strain, the radius of the nanopore and the surface/interface stress on the critical thickness of the film is discussed.     

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.     

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.     

Interplay of surface morphology, strain relief, and surface stress during surfactant mediated epitaxy of Ge on Si

Lattice-mismatch-induced surface or film stress has significant influence on the morphology of heteroepitaxial films. This is demonstrated using Sb surfactant-mediated epitaxy of Ge on Si(111). The surfactant forces a two-dimensional growth of a continous Ge film instead of islanding. Two qualitatively different growth regimes are observed. Elastic relaxation: Prior to the generation of strain-relieving defects the Ge film grows pseudomorphically with the Si lattice constant and is under strong compressive stress. The Ge film relieves strain by forming a rough surface on a nm scale which allows partial elastic relaxation towards the Ge bulk lattice constant. The unfavorable increase of surface area is outbalanced by the large decrease of strain energy. The change of film stress and surface morphology is monitored in situ during deposition at elevated temperature with surface stress-induced optical deflection and high-resolution spot profile analysis low-energy electron diffraction. Plastic relaxation: After a critical thickness the generation of dislocations is initiated. The rough phase acts as a nucleation center for dislocations. On Si(111) those misfit dislocations are arranged in a threefold quasi periodic array at the interface that accommodate exactly the different lattice constants of Ge and Si. Received: 1 April 1999 / Accepted: 17 August 1999 / Published online: 6 October 1999     

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.     

A theoretical investigation of glide dislocations in BN/AlN heterojunctions

Glide dislocations with periodic pentagon-heptagon pairs are investigated within the theory of one-dimensional misfit dislocations in the framework of an improved Peierls-Nabarro (P-N) equation in which the lattice discreteness is fully considered. We find an approximate solution to handle misfit dislocations, where the second-order derivative appears in the improved P-N equation. This result is practical for periodic glide dislocations with narrow width, and those in the BN/AlN heterojunction are studied. The structure of the misfit dislocations and adhesion work are obtained explicitly and verified by first-principles calculations. Compared with shuffle dislocations, the compression force in the tangential direction of glide dislocations has a greater impact on the normal direction, and the contributions of the normal displacement to the interfacial energy cannot simply be ignored.     

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.     

Au/Cu(001)异质外延岛演化的分子动力学研究

利用分子动力学弛豫方法模拟了Au/Cu(001)异质外延生长初期Au异质外延岛的形貌演化，分析了Au外延岛演化过程中的局域应力及与基体结合能随表面岛尺寸的变化. 研究结果表明：当异质外延岛小于7×7时，外延岛原子分布呈现赝Cu点阵形貌；当外延岛达到8×8后，外延岛内开始出现失配位错，失配位错数量随外延岛尺寸的增加而增加. 局域压力分析指出，外延岛上原子之间的近邻环境不同导致了所受应力的差异，而外延岛的形变则是由外延岛原子的应力分布所决定. 研究还发现，失配位错的产生导致错位原子与基体原子之间的结合强度减弱，但相对增加了非错位原子与基体原子之间的结合强度. 关键词： 异质外延 表面形貌 局域压力 分子动力学模拟     

Defects and separation of amorphous nanofilms from crystalline substrates

The conditions of separation of an amorphous nanofilm from a crystalline substrate are theoretically studied in terms of a disclination-dislocation model for a crystal-glass interface. In this model, such an interface is characterized by a high density of disclinations and dislocations. A criterion for the separation of an amorphous nanofilm from a crystalline substrate is obtained. The critical nanofilm thickness above which a film begins to separate is calculated as a function of the characteristics of the disclination-dislocation system and the dilatation misfit.     

Nano-structuration of CoO film by misfit dislocations

We have studied the nano-patterning of CoO film induced by misfit dislocation network at the interface with the Ag(0 0 1) substrate. Grazing incidence diffraction (GIXD), X-ray photoemission spectroscopy (XPS) and low energy electron diffraction (LEED) have been used to characterize chemistry and structure of the CoO layers. The XPS spectrum of the Co 2p core level permitted to establish the stoichiometric growth of CoO. The structure of the CoO film together with the absorption sites of cobalt and oxygen atoms was determined, thanks to GIXD measurements. Moreover we have followed the evolution of the in-plane lattice constant of the CoO as a function of the film thickness. It turns out that the CoO film growth starts with the same in-plane lattice constant of the Ag(0 0 1) substrate up to 3-4 ML; afterwards the in-plane parameter of CoO steadily increases before reaching a stable value of 2.98 Å at 23 ML. During the relaxation process, at about 8 ML of film thickness, we observe the formation of a buried misfit dislocation network. These dislocations, that have a period of 9.2 nm for a film thickness of 23 ML, induce mosaicity in the CoO film which then appears as a regular distribution of tilted domains.     

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.