Misfit dislocation loops in composite nanowires

A new mechanism for relaxation of misfit stresses in composite nanowires (quantum wires) is suggested and theoretically examined, namely the formation of misfit dislocation loops. The stress field of a prismatic dislocation loop in a cylinder (nanowire) is calculated. The parameters of two-phase composite nanowires at which the formation of misfit dislocation loops is energetically favourable are estimated. The effect of stress fields of dislocation loops on the formation of compositionally modulated nanowires is discussed.     

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.     

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.     

Elastic interaction of dislocation loops and point defects

The elastic interaction energy of a circular dislocation loop with interstitial atoms and vacancies characterized as dilatation or relaxation centres is calculated. Further, the forces which the dislocation loops exert on point defects through elastic interaction are discussed.     

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%).     

Interaction of dislocations with ordered cylindrical precipitates

The size and antiphase boundary effects of a cylindrical inclusion with zero axial misfit in f.c.c. alloys are calculated using the linear isotropic elasticity.The plane strain gives rise to nonzero elastic interaction even inside inclusions with zero misfit direction inclined to the Burgers vector. The extreme value of the total force on a straight dislocation cutting the inclusion axis is determined for different dislocation and inclusion orientations.     

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.     

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.     

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.     

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.     

Role of the dislocation screw component in the formation of the dislocation structure in Ge- and Si-based semiconductor heterosystems

The possibility of solving the problem of propagating dislocations in heterosystems by means of decreasing the number of dislocation families participating in the process of misfit stress relief has been investigated. The system of Γ-shaped misfit dislocations, which is proposed in the literature as the optimal type of plastic relaxation, has been analyzed. Taking into account the effect of the screw dislocation component, this suggestion is valid only for the initial stage of relaxation. The results of simulation of the process of plastic relaxation and experimental investigations of structures containing L-shaped dislocations are presented. Misfit stress relief in heterostructures grown on vicinal substrates has been theoretically and experimentally investigated.     

Homogeneous nucleation of glide dislocation loops in nanoceramics

A theoretical model is proposed for the homogeneous nucleation of glide dislocation loops in nanocrystalline ceramics under deformation at low and high temperatures. The nucleation of a dislocation loop in a crystalline grain is considered an ideal nanoscopic shear whose magnitude (the Burgers vector of the dislocation) increases gradually as the loop is nucleating. The characteristics of the homogeneous nucleation of glide dislocation loops in nanocrystalline ceramics based on cubic silicon carbide are calculated. It is shown that, in general, the homogeneous nucleation of a dislocation loop in nanocrystalline ceramics at high temperatures proceeds in two stages, namely, the athermal nucleation of a loop of a “noncrystallographic” partial dislocation and its thermally activated transformation into an ordinary partial lattice dislocation loop.     

Experimental and theoretical investigation of formation of the oxygen-containing precipitate-dislocation loop system in silicon

A model of coherent and incoherent oxygen-containing precipitates formed in an anisotropic silicon crystal due to the decomposition of a supersaturated oxygen solid solution has been considered. The stresses acting inside and outside the precipitate have been determined in the framework of the classical Eshelby’s approach. A criterion has been proposed for the generation of the misfit dislocation and the onset of motion of the perfect interstitial dislocation loop lying in the precipitate plane. The proposed precipitate model and criterion have been used for determining the dependence of the precipitate radius that corresponds to the formation of the misfit dislocation and the onset of motion of the perfect interstitial dislocation loop when an external load is applied to the sample. The results obtained are compared with the available experimental data.     

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     

A model for the dynamics of loop drag by a gliding dislocation

Clusters of self-interstitial atoms are formed in metals by high-energy displacement cascades, often in the form of small dislocation loops with a perfect Burgers vector. In isolation, they are able to undergo fast, thermally activated glide in the direction of their Burgers vector, but do not move in response to a uniform stress field. The present work considers their ability to glide under the influence of the stress of a gliding dislocation. If loops can be dragged by a dislocation, it would have consequences for the effective cross-section for dislocation interaction with other defects near its glide plane. The lattice resistance to loop drag cannot be simulated accurately by the elasticity theory of dislocations, so here it is investigated in iron and copper by atomic-scale computer simulation. It is shown that a row of loops lying within a few nanometres of the dislocation slip plane can be dragged at very high speed. The drag coefficient associated with this process has been determined as a function of metal, temperature and loop size and spacing. A model for loop drag, based on the diffusivity of interstitial loops, is presented. It is tested against data obtained for the effects of drag on the stress to move a dislocation and the conditions under which a dislocation breaks away from a row of loops.     

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.     

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.     

Instability of interstitial dislocation loops in electron-irradiated dielectrics

The experiments on electron irradiation of yttrium-stabilized zirconium oxide samples show the formation of strong elastic fields near interstitial dislocation loops. The fields increase with an increase in the loop radius and, when the loop radius reaches a certain critical value, the loops became unstable due to the beginning of plastic deformation and the formation of a dislocation network. The mechanism of the occurrence of this instability is suggested. It is based on the accumulation of charges at dislocation loops due to ionization processes in an electron-irradiated dielectric. It is shown that the accumulation of the electric charge at growing dislocation loops in dielectrics may be responsible for an increase in elastic stresses near dislocation loops and for their instability because of the beginning of plastic deformation near the loops when stresses at growing loops become close to the theoretical yield stress of the material.     

Less strain energy despite fewer misfit dislocations: the impact of ordering

The average strain state of Ge films grown on Si(111) by surfactant mediated epitaxy has been compared to the ordering of the interfacial misfit dislocation network. Surprisingly, a smaller degree of average lattice relaxation was found in films grown at higher temperature. On the other hand, these films exhibit a better ordered dislocation network. This effect energetically compensates the higher strain at higher growth temperature, leading to the conclusion that, apart from the formation of misfit dislocations, their ordering represents an important channel for lattice-strain energy relaxation.     

Equilibrium critical thickness for a wurtzite InGaN/GaN heterostructure

We present a finite element model to simulate a combined strained In_xGa_1−xN/GaN heterostructure and an edge misfit dislocation on the basal {0001} slip plane, taking the anisotropic elasticity into account. The introduction of a misfit dislocation partially relaxes the misfit strain. The model directly gives the residual strain, which is the exact strain field stored in the system after relaxation. The critical thickness is then determined based on an overall energy minimization approach including the dislocation core contribution. Compared with the results from other methods and available experimental data, our approach is appropriate for describing the critical thickness of the wurtzite InGaN/GaN material system.