In this work we model the evolution of strain energy during different growth stages of heterostructure nanowires. We find that the minimum energy configuration changes abruptly from fully elastically strained to partially relaxed due to collective formation of a misfit dislocation network. The transition at the critical thickness is associated with a characteristic density of misfits. These insights are gained from a technique developed to simulate misfit dislocations in a finite element framework, incorporating both elastic and plastic relaxation in a stationary heterostructure. We argue that these results have general relevance for mismatched heterostructures.
The experimental x-ray diffraction patterns of a Si$_{0.4}$Ge$_{0.6}$/Si(001) epitaxial film with a low density of misfit dislocations are modeled by the Monte Carlo method. It is shown that an inhomogeneous distribution of 60$^\circ$ dislocations with dislocations arranged in bunches is needed to explain the experiment correctly. As a result of the dislocation bunching, the positions of the x-ray diffraction peaks do not correspond to the average dislocation density but reveal less than a half of the actual relaxation.
Misfit-dislocation hierarchy governs sliding of asymmetric non-CSL grain boundaries
Woodruff School of Mechanical Engineering, Georgia Institute of Technology（佐治亚理工学院机械工程学院）；School of Mechanics and Engineering Science, Peking University（北京大学力学与工程科学学院）；Institute of Microstructure and Property of Advanced Materials, Beijing Key Lab of Microstructure and Property of Advanced Materials, Beijing University of Technology（北京工业大学先进材料微结构及性能研究所）
The high lattice mismatched SiC/Si(001) interface was investigated by means of combined classical and ab initio molecular dynamics. Among the several configurations analyzed, a dislocation network pinned at the interface was found to be the most efficient mechanism for strain relief. A detailed description of the dislocation core is given, and the related electronic properties are discussed for the most stable geometry: we found interface states localized in the gap that may be a source of failure of electronic devices.
Scanning tunneling microscopy combined with molecular dynamics simulations reveal a dislocation-mediated island diffusion mechanism for Cu on Ag(111), a highly mismatched system. Cluster motion is tracked with atomic precision at multiple temperatures and diffusion barriers and prefactors are determined from direct measurements of hop rates. The non-monotonic size dependence of the diffusion barrier is in good agreement with simulations and can lead to enhanced mass transport upon coarsening, in surprising contrast to the traditional island diffusion models where diffusivity reduces with clust…
Superlattice (SL) thin films composed of refractory ceramics unite extremely high hardness and enhanced fracture toughness; a material combination often being mutually exclusive. While the hardness enhancement obtained whentwo materials form a superlattice is well described by existing models based on dislocation mobility, the underlying mechanisms behind the increase in fracture toughness are yet to be unraveled. Here we provide a model based on linear elasticity theory to predict the fracture toughness enhancement in (semi-)epitaxial nanolayers due to coherency stresses and formation of misf…
A possible mechanism for the formation of a 90° misfit dislocation at the Ge/Si(001) interface through homogeneous nucleation is identified from atomic scale calculations where a minimum energy path connecting the coherent epitaxial state and a final state with a 90° misfit dislocation is found using the nudged elastic band method. The initial path is generated using a repulsive bias activation procedure in a model system including 75000 atoms. The energy along the path exhibits two maxima in the energy. The first maximum occurs as a 60° dislocation nucleates. The intermediate minimum correspo…
A study of the STEM probe channeling in a heterostructures crystalline specimen is presented here with a goal to guide appropriate STEM-based characterization for complex structures. STEM analysis of perovskite BaSnO3/LaAlO3 bilayers is performed and the dominating effects of beam channeling on HAADF- and LAADF-STEM are illustrated. To study the electron beam propagating through BaSnO3/LaAlO3 bilayers, probe intensity depth profiles are calculated, and the effects of probe defocus and atomic column alignment are discussed. Characteristics of the beam channeling are correlated to resulting ADF-…
We study numerically the energetics and atomic mechanisms of misfit dislocation nucleation and stress relaxation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Relaxation processes from coherent to incoherent states for different transition paths are studied using interatomic potentials of Lennard-Jones type and a systematic saddle point and transition path search method. The method is based on a combination of repulsive potential minimization and the Nudged Elastic Band method. For a final state with a single misfit dislocation, the minim…
Epitaxially integrated III-V semiconductor lasers for silicon photonics have the potential to dramatically transform information networks, but currently, dislocations limit performance and reliability even in defect tolerant InAs quantum dot (QD) based lasers. Despite being below critical thickness, QD layers in these devices contain previously unexplained misfit dislocations, which facilitate non-radiative recombination. We demonstrate here that these misfit dislocations form during post-growth cooldown due to the combined effects of (1) thermal-expansion mismatch between the III-V layers and…
We determine the critical layer thickness for the appearance of misfit dislocations as a function of the misfit between the lattice constants of the substrate and the adsorbate from Kinetic Monte Carlo (KMC) simulations of heteroepitaxial growth. To this end, an algorithm is introduced which allows the off-lattice simulation of various phenomena observed in heteroepitaxial growth including critical layer thickness for the appearance of misfit dislocations, or self-assembled island formation. The only parameters of the model are deposition flux, temperature and a pairwise interaction potential …
Although the pearlitic steel is one of the most extensively studied materials, there are still questions unanswered about the interface in the lamellar structure. In particular, to deepen the understanding of the mechanical behavior of pearlitic steel with fine lamellar structure, it is essential to reveal the structure-property relationship of the ferrite/cementite interface (FCI). In this study, we analyzed the in-plane shear deformation of the FCI using atomistic simulation combined with extended atomically informed Frank-Bilby (xAIFB) method and disregistry analyses. In the atomistic simul…
Plastic relaxation of the misfit stress in core-shell semi-conducting nanowires can lead to structural defects, detrimental to applications. Core-shell Zn{0.7}Mg{0.3}O/ZnO quantum well heterostructures were deposited on ZnO nanowires. Strain along the a and c axes of the wurtzite structure is relaxed through the glide of dislocation half-loops from the free surfaces, within pyramidal and prismatic planes. Some half-loops are closed up in the barriers to accommodate the misfit at two consecutive interfaces of the quantum well stack. Dislocations are also observed within the nanowire core: contr…
Global optimization of transition paths in complex atomic scale systems is addressed in the context of misfit dislocation formation in a strained Ge film on Si(001). Such paths contain multiple intermediate minima connected by minimum energy paths on the energy surface emerging from the atomic interactions in the system. The challenge is to find which intermediate states to include and to construct a path going through these intermediates in such a way that the overall activation energy for the transition is minimal. In the numerical approach presented here, intermediate minima are constructed…
Heterostructures consisting of PbZr0.2Ti0.8O3 and PbZr0.4Ti0.6O3 films grown on a SrTiO3 (100) substrate with a SrRuO3 bottom electrode were prepared by pulsed laser deposition. Using the additional interface provided by the ferroelectric bilayer structure and changing the sequence of the layers, the dislocation content and domain patterns were varied. The resulting microstructure was investigated by transmission electron microscopy. Macroscopic ferroelectric measurements have shown a large impact of the formation of dislocations and the a/c domain structure on the ferroelectric polarization a…
We study numerically the equilibrium shapes, shape transitions and dislocation nucleation of small strained epitaxial islands with a two-dimensional atomistic model, using simple interatomic pair potentials. We first map out the phase diagram for the equilibrium island shapes as a function of island size (up to N = 105 atoms) and lattice misfit with the substrate and show that nanoscopic islands have four generic equilibrium shapes, in contrast with predictions from the continuum theory of elasticity. For increasing substrate-adsorbate attraction, we find islands that form on top of a finite w…
We report on the growth of axial InAs-on-GaAs nanowire heterostructures on silicon by molecular beam epitaxy using 20 nm diameter Au catalysts. First, the growth parameters of the GaAs nanowire segment were optimized to achieve a pure wurtzite crystal structure. Then, we developed a two-step growth procedure to enhance the yield of vertical InAs-on-GaAs nanowires. We achieved 90% of straight InAs-on-GaAs nanowires by further optimizing the growth parameters. We investigated the composition change at the interface by energy dispersive X-ray spectroscopy and the nanowire crystal structure by tra…
Molecular dynamics simulations revealed significant difference in deformation behaviour of $<$100$>$ BCC Fe nanowires with and without twist boundary. The plastic deformation in perfect $<$100$>$ BCC Fe nanowire was dominated by twinning and reorientation to $<$110$>$ followed by further deformation by slip mode. On the contrary, $<$100$>$ BCC Fe nanowire with a twist boundary deformed by slip at low plastic strains followed by twinning at high strains and absence of full reorientation. The results suggest that the deformation in $<$100$>$ BCC Fe nanowire by dislocation slip is preferred over …
We report on thermal transport properties of wurtzite GaN in the presence of dislocations, by using molecular dynamics simulations. A variety of isolated dislocations in a nanowire configuration were analyzed and found to reduce considerably the thermal conductivity while impacting its temperature dependence in a different manner. We demonstrate that isolated screw dislocations reduce the thermal conductivity by a factor of two, while the influence of edge dislocations is less pronounced. The relative reduction of thermal conductivity is correlated with the strain energy of each of the five st…
An in-situ neutron diffraction investigation of the annealing and healing of dislocations in the bulk Pd-D2 system was carried out. Lattice misfit between the alpha and beta hydride phases produces dislocations during the phase transition in either direction, relieving elastic strain, which is reflected in reduced pressure hysteresis compared to the spinodal hysteresis. The effects on the dislocation density of annealing the metal under vacuum, of annealing in the beta hydride phase, and of the phase transformation itself were investigated by measuring diffraction peak breadths during annealin…
Both continuous and discontinuous precipitation is known to occur in CuAg alloys. The precipitation of Ag-rich phase has been experimentally investigated by atom probe tomography and transmission electron microscopy after ageing treatment of Cu-5%wtAg at 440$^\circ$C during 30'. Both continuously and discontinuously formed precipitates have been observed. The precipitates located inside the grains exhibit two different faceted shapes: tetrahedral and platelet-shaped precipitates. Dislocations accommodating the high misfit at the interface between the two phases have also been evidenced. Based …
Twin boundaries (TBs) are assumed to be obstacles to dislocation motion and increase the strength of metals. Here, we report the abnormal phenomenon that TBs reduce the strength of body-centered cubic (BCC) tungsten (W). [1-11]-oriented W nanowires with (121) twin planes and free of dislocations were fabricated by chemical vapor deposition. In situ tensile tests within the transmission electron microscope were performed on single-crystal and twinned W nanowires. The fracture strength of the twinned W nanowire was 13.7 GPa, 16% lower than that of the single-crystal W nanowire (16.3 GPa). The we…
In the present study, molecular dynamics (MD) simulations have been performed to understand the effect of nanowire size, temperature and strain rate on the variations in dislocation density and deformation mechanisms in $<$100$>$ Cu nanowires. The nanowire size has been varied in the range 1.446-43.38 nm with a constant length of 21.69 nm. Different temperatures varying from 10 K to 700 K and strain rates in the range of $5 \times 10^7$ - $1 \times 10^9$ s$^{-1}$ have been considered. For all the conditions, the variations in dislocation density $(ρ)$ has been calculated as a function of strai…
We study numerically the minimum energy path and energy barriers for dislocation nucleation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Stress relaxation processes from coherent to incoherent states for different transition paths are determined using saddle point search based on a combination of repulsive potential minimization and the Nudged Elastic Band method. The minimum energy barrier leading to a final state with a single misfit dislocation nucleation is determined. A strong tensile-compressive asymmetry is observed. This asymmetr…
Molecular Dynamics (MD) simulations have been carried out to investigate the deformation behaviour of <110>/{111} body centered cubic (BCC) Fe nanowires under tensile and compressive loading. An embedded atom method (EAM) potential was used to describe the interatomic interactions. The simulations were carried out at 10 K with a constant strain rate of $1\times10^{8}$ $s^{-1}$. The results indicate a significant differences in deformation mechanisms under tensile and compressive loading. Under tensile loading, the deformation occurs by the slip of full dislocations, While under compressive loa…
We reexamine two essential issues within the Peierls-Nabarro model which are critical in obtaining accurate values for the Peierls stress. The first issue is related to the sampling scheme of the misfit energy across the glide plane and the second one is the effect of relaxation on the Peierls stress. It is shown that most of the current applications of the Peierls-Nabarro model do not treat properly the two issues and therefore are not able to predict reliable values for the Peierls stress. We argue that the double counting scheme for the misfit energy at both sides of the glide plane is phys…
Due to the large free surface and strong anisotropy, the mechanical property of nanowire differs from its bulk counterpart. In this paper, the strong dependence of NW's strength on its surface orientation is revealed, and two modes of dislocation nucleation have been identified: the corner nucleation and the surface nucleation. The activation energy and activation volume of surface nucleation are much larger than those of the corner nucleation. The intersection line between lateral surface and {111}-type slip plane causes the discrepancy of the nucleation modes for the first dislocation.
The trigonal/bcc orientation relationships (ORs) and their likelihood of occurrence are extensively studied using dispersed Y4Zr3O12nano-precipitates in bcc Fe matrix by means of transmission electron microscopy, image simulations, and a crystallographic model. Two orientation relationships related by a rotation:[1-20]||[111] with (21-2)||(-110) and [1-20]||[111] with (00-3)||(-110), are established and periodic arrays of misfit dislocation doublets are identified at the strained interface in (110) for both ORs. Further eighteen energetically feasible ORs in Y4Zr3O12/bcc system are deduced by …
Strain relief in lattice mismatched heteroepitaxy is mediated by formation and/or propagation of dislocations. Due to their technological significance, the process of strain relief in materials with face-centred cubic (fcc) lattices has been analyzed by several researchers1,2 following the work by Matthews and co-workers in the late 1960s to early 1970s3-6. In the Matthews model, it is assumed that the strain relieved by any misfit dislocation is equal to the edge component of the dislocation burgers vector in the interface plane. This assumption has been used in all subsequent analyses of str…
InAs nanowires with Al$_x$In$_{1-x}$P or Al$x$In$_{1-x}$As shells were grown on GaAs substrates by the Au-assisted vapour-liquid-solid (VLS) method in a gas source molecular beam epitaxy (GS-MBE) system. Core diameters and shell thicknesses were measured by transmission electron microscopy (TEM). These measurements were then related to selected area diffraction (SAD) patterns to verify either interface coherency or relaxation through misfit dislocations. A theoretical strain model is presented to determine the critical shell thickness for given core diameters. Zincblende stiffness parameters a…
We have performed a detailed study of the lattice distortions of InP wurtzite nanowires containing an axial screw dislocation. Eshelby predicted that this kind of system should show a crystal rotation due to the dislocation induced torque. We have measured the twisting rate and the dislocation Burgers vector on individual wires, revealing that nanowires with a 10-nm radius have a twist up to 100% larger than estimated from elasticity theory. The strain induced by the deformation has a Mexican-hat-like geometry, which may create a tube-like potential well for carriers.
High entropy alloys (HEAs) are single phase crystals that consist of random solid solutions of multiple elements in approximately equal proportions. This class of novel materials have exhibited superb mechanical properties, such as high strength combined with other desired features. The strength of crystalline materials is associated with the motion of dislocations. In this paper, we derive a stochastic continuum model based on the Peierls-Nabarro framework for inter-layer dislocations in a bilayer HEA from an atomistic model that incorporates the atomic level randomness. We use asymptotic ana…
When a material is subjected to an applied stress, the material will experience recoverable elastic deformation followed by permanent plastic deformation at the point when the applied stress exceeds the yield stress of the material. Microscopically, the onset of the plasticity usually indicates the activation of dislocation motion, which is considered to be the primary mechanism of plastic deformation. Once plastic deformation is initiated, further elastic deformation is negligible owing to the limited increase in the flow stress caused by work hardening. Here we present experimental evidence …
Moire based strain analysis in wurtzite GaAs -- rock-salt (Pb,Sn)Te core-shell nanowires grown by molecular beam epitaxy
Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Faculty of Physics, University of Warsaw（华沙大学物理学院）；Ensemble3 Centre of Excellence（Ensemble3卓越中心）；International Research Center MagTop, Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所国际研究中心MagTop）
We investigate theoretically the effects of elastic and plastic deformations on heterogeneous nucleation and nanowire formation. In the first case, the influence of the confinement of the critical nucleus between two parallel misfitting substrates is investigated using scaling arguments. We present phase diagrams giving the nature of the nucleation regime as a function of the driving force and the degree of confinement. We complement this analytical study by amplitude equations simulations. In the second case, the influence of a screw dislocation inside a nanowire on the development of the mor…
At vertical edges, thin films of silicon oxide (SiO_{2-x}) contain semiconductive c-Si layered nanocrystals (Si NC) embedded in and supported by an insulating g-SiO2 matrix. Tour et al. have shown that a trenched thin film geometry enables the NC to form switchable nanowires (SNW) when trained by an applied field. The field required to form SNW decreases rapidly within a few cycles, or by annealing at 600 C in even fewer cycles, and is stable to 700C. Here we describe the intrinsic evolution of Si NC and SNW in terms of the competition between internal stresses and electro-osmosis. The analysi…
A long-standing discrepancy exists between experiments and atomistic models concerning the critical strain needed for surface nucleation of dislocations in silicon-germanium systems. While dislocation nucleation is readily observed in hetero-epitaxial thin films with misfit strains less than 4%, existing atomistic models predict that a critical strain over 7.8% is needed to overcome the kinetic barrier for dislocation nucleation. Using zero-temperature energy barrier calculations and finite-temperature Molecular Dynamics simulations, we show that 3-dimensional surface features such as a sharpl…
The coalescence in dense arrays of spontaneously formed GaN nanowires proceeds by bundling: adjacent nanowires bend and merge at their top, thus reducing their surface energy at the expense of the elastic energy of bending. We give a theoretical description of the energetics of this bundling process. The bending energy is shown to be substantially reduced by the creation of dislocations at the coalescence joints. A comparison of experimental and calculated x-ray diffraction profiles from ensembles of bundled nanowires demonstrates that a large part of the bending energy is indeed relaxed by pl…
Molecular dynamics simulations have been performed to understand the influence of temperature on the tensile deformation and fracture behavior of $<$111$>$ BCC Fe nanowires. The simulations have been carried out at different temperatures in the range 10-1000 K employing a constant strain rate of $1\times$ $10^8$ $s^{-1}$. The results indicate that at low temperatures (10-375 K), the nanowires yield through the nucleation of a sharp crack and fails in brittle manner. On the other hand, nucleation of multiple 1/2$<$111$>$ dislocations at yielding followed by significant plastic deformation leadi…
Bottom up nanowires are attractive for realizing semiconductor devices with extreme heterostructures because strain relaxation through the nanowire sidewalls allows the combination of highly lattice mismatched materials without creating dislocations. The resulting nanowires are used to fabricate light emitting diodes (LEDs), lasers, solar cells and sensors. However, expensive single crystalline substrates are commonly used as substrates for nanowire heterostructures as well as for epitaxial devices, which limits the manufacturability of nanowire devices. Here, we demonstrate nanowire LEDs dire…
Density functional theory calculations have been performed to study the structures and energetics of coherent and semicoherent TiC/Fe interfaces. A systematic method for determining the interfacial energy for the semicoherent interface with misfit dislocation network has been developed. The obtained interfacial energies are used to calculate the aspect ratios for the disc-like precipitates and a quantitative agreement with the experimental results is reached. Based on the obtained interfacial energies and atomic structure details, we propose models for describing the evolution of the interfaci…
Accounting for the anharmonicity of the real interatomic potentials in a model in 1+1 dimensions shows that coherent 3D islands can be formed on the wetting layer in a Stranski-Krastanov growth mode predominantly in compressed overlayers. Coherent 3D islanding in expanded overlayers could be expected as an exception rather than as a rule. The thermodynamic driving force of formation of coherent 3D islands on the wetting layer of the same material is the weaker adhesion of the atoms near the islands edges. The average adhesion gets weaker with increasing island's thickness but reaches a saturat…
Nanowire-based light-emitting devices require multi-quantum well heterostructures with high room temperature optical efficiencies. We demonstrate that such efficiencies can be attained through the use of ZnO/Zn(1-x)MgxO core shell quantum well heterostructures grown by metal organic vapour phase epitaxy. Varying the barrier Mg concentration from x=0.15 to x=0.3 leads to the formation of misfit induced dislocations in the multi quantum wells. Correlatively, temperature dependant photoluminescence reveals that the radial well luminescence intensity decreases much less rapidly with increasing tem…
We present a surface stacking fault (SSF) energy approach to predicting defect nucleation from the surfaces of surface-dominated nanostructure such as FCC metal nanowires. The approach leads to a criteria that predicts the initial yield mechanism via either slip or twinning depending on whether the unstable twinning energy or unstable slip energy is smaller as determined from the resulting SSF energy curve. The approach is validated through a comparison between the SSF energy calculation and low-temperature classical molecular dynamics simulations of copper nanowires with different axial and t…
We explore the Bi-surfactant-directed self-assembly and structure of InAs quantum dots grown on GaAs(110) by molecular beam epitaxy. The addition of a Bi flux during InAs deposition changes the InAs growth mode from two-dimensional (2D) Frank-van der Merwe to Stranski-Krastanov, resulting in the formation of three-dimensional (3D) InAs islands on the surface. Furthermore, exposing static InAs 2D layers to Bi induces a rearrangement of the strained layer into 3D islands. We explore the effect of varying the InAs thickness and Bi flux for these two growth approaches, observing a critical thickne…
An off-lattice, continuous space Kinetic Monte Carlo (KMC) algorithm is discussed and applied in the investigation of strained heteroepitaxial crystal growth. As a starting point, we study a simplifying (1+1)-dimensional situation with inter-atomic interactions given by simple pair-potentials. The model exhibits the appearance of strain-induced misfit dislocations at a characteristic film thickness. In our simulations we observe a power law dependence of this critical thickness on the lattice misfit, which is in agreement with experimental results for semiconductor compounds. We furthermore in…
We introduce an off-lattice model with continuous particle distances and pair-potential interactions which allows for the efficient simulation of strained heteroepitaxial growth by means of kinetic Monte Carlo (KMC) simulations. We discuss in detail the application of our model to the simulation of three important strain relaxation mechanisms: First, the formation of misfit dislocations in strained adsorbate films is investigated. We find a power-law misfit dependence of the critical layer thickness, in agreement with various experimental studies. Second, we study the self-assembled island for…
The aim of this comment is to show that anisotropic effects and image fields should not be omitted as they are in the publication of A. Leonardi, S. Ryu, N. M. Pugno, and P. Scardi (LRPS) [J. Appl. Phys. 117, 164304 (2015)] on Pd <011> cylindrical nanowires containing an axial screw dislocation. Indeed, according to our previous study [Phys. Rev. B 88, 224101 (2013)], the axial displacement field along the nanowire exhibits both a radial and an azimuthal dependence with a twofold symmetry due the <011> orientation. As a consequence, the deviatoric strain term used by LRPS is not suitable to an…
