Shuffle Set Research Articles

Determination of the discreteness correction in dislocation equations for sphalerite crystals

Abstract The discreteness correction for simple lattices has been determined, however, there is still no detailed and rigorous derivation of the discreteness correction for compound lattices due to the relatively complex structure (simple lattices have only one set per slip system, while complex lattices have at least two sets). A lattice dynamics model which takes into account the energy increments caused by changes in bond length and bond angle is constructed for sphalerite crystals and the relationships between discreteness parameters and elastic constants are determined for the slip system. Compared to glide set, the discreteness correction for shuffle set is much larger due to it is mainly contributed by the interactions between nearest neighbor atoms. Based on the results obtained from the model, the dislocations in ZnS crystal are investigated. The theoretical prediction result of Peierls stress for shuffle dislocation closely matches the experimental critical shear stress. It is inferred that the initial plastic deformation of ZnS is closely related to the movement of shuffle dislocations.

Atomic structure, stability, and dissociation of dislocations in cadmium telluride

Dislocation plays a crucial role in many material properties of semiconductors, ranging from plastic deformation to electronic transport. But the dislocation structures and reactions remain controversial in many semiconductors. Here, we systematically examine the dislocation properties of cadmium telluride (CdTe), a prototype of II-VI compound semiconductors, using molecular statics and molecular dynamics simulations with a machine-learning force field. We find that dislocation cores in CdTe are not reconstructed along the dislocation line due to the significant ionic bonding characteristics. Moreover, the undissociated screw dislocation in the shuffle set is more stable than that in the glide set, and the glide dislocation tends to move to the shuffle set, followed by random movement rather than dissociation, arising from its low Peierls stress. For 60° perfect dislocation, it also prefers to locate in the shuffle set, but the 60° glide dislocation is dissociated into a pair of 30° and 90° partial dislocations connected by a stacking fault with a width of ∼9.03 nm at low temperatures through reconfiguring atomic bonds in the core. This work provides an atomic-level understanding of dislocation core properties in CdTe, laying a basis for interpreting the mechanical and electronic performance of CdTe and other II-VI semiconductors.

Phase field modeling of dislocations and obstacles in InSb

We present a phase-field dislocation dynamics (PFDD) model informed by first-principle calculations to elucidate the competitive dislocation nucleation and propagation between the glide and shuffle sets in InSb diamond cubic crystal. The calculations are directly informed with generalized stacking fault energy curves on the (111) slip plane for both the “glide set,” with the smaller interplanar spacing, and the “shuffle set,” with the larger interplanar spacing. The formulation also includes elastic anisotropy and the gradient term associated with the dislocation core. The PFDD calculations show that under no stress the equilibrium structure of screw glide set dislocations dissociates into Shockley partials, while those of the shuffle set dislocations do not dissociate, remaining compact. The calculated dislocation core widths of these InSb dislocations agree well with the measured values for other semiconductor materials, such as Si and GaN. We find that a shuffle set dislocation emits from a dislocation source at an applied stress about three times smaller than that needed to emit leading and trailing partials successively on the glide set plane. Once the partial dislocations in the glide set are emitted, they propagate faster than the shuffle set perfect dislocation at the same stress level.

Effects of grain size and protrusion height on the surface integrity generation in the nanogrinding of 6H-SiC

The size and protrusion height of abrasive grains of a grinding wheel are not uniform, which can greatly influence the surface integrity generation of a ground component. The purpose of this paper is to explore such effects on the deformation and material removal mechanisms of 6H-SiC subjected to nanogrinding with the aid of molecular dynamics simulations. It was found that a nanogrinding process can fall into one or more of the following regimes with respect to material removal, i.e., no-wear, adhering, ploughing and cutting regimes, depending on both the depth of grain cut and size of abrasive grains. The plastic deformation in 6H-SiC starts with surface amorphization under the grinding stresses, followed by the activation of partial and perfect dislocations in the shuffle set of the material’s basal plane.

Atomic-level calculations and experimental study of dislocations in InSb

Plastic deformation in InSb single crystals is governed by the motion of dislocations. Since InSb has a diamond cubic lattice, it possesses two sets of slip planes: a shuffle set and a glide set. Transmission electron microscopy analysis of deformed bulk single crystals shows that, at low temperatures (<20 °C), dislocations have narrow cores, while at higher temperatures, they have extended cores. However, it remains unclear to which slip plane set these dislocations belong. In this paper, by combining experiments and atomic-level calculations, we show that dislocations with narrow and extended cores, respectively, belong to the shuffle and glide sets. The conclusion is reached by calculating the generalized stacking fault energy curves and ideal shear stresses using density functional theory calculations and the intrinsic stacking fault width associated with dislocations using atomistic simulations. It is also found that while the shuffle set dislocations are easier to activate at lower temperatures, dislocations on the glide set become dominant at higher temperatures.

Propagation of stacking faults from “composite” dislocation cores at low temperature in silicon nanostructures

The unexpected occurrence of extended stacking faults in silicon nanostructures at high stress and low temperature is discussed. It is shown that those stacking faults result from the operation of “composite” dislocation core structures. It is demonstrated that such cores allow for the propagation of partial dislocations in the shuffle set with the benefit of a low Peierls stress. A classical atomistic calculation confirms indeed that shuffle partial dislocations can move under a shear stress of about 3.3 GPa (5.5% shear strain) at room temperature.

Homogeneous and heterogeneous dislocation nucleation in diamond

Dislocation nucleation plays a key role in plastic deformation of diamond crystal. In this paper, homogeneous and heterogeneous nucleation nature for diamond 16112 glide set dislocation and 12110 shuffle set dislocation is studied by combining molecular dynamics method and continuum mechanics models. Our results show that although heterogeneous dislocation nucleation can decrease its activation energy, the activation energy at 0 GPa for diamond heterogeneous nucleation is still in the range of 100 eV. For 16112 glide set and 12110 shuffle set homogeneous nucleation, their critical nucleation shear stress approaches to diamond's ideal shear strength which implies that those dislocations do not nucleate before diamond structural instability only by a purely shearing manner. While for 16112 glide set and 12110 shuffle set heterogeneous nucleation, their critical nucleation shear stresses are 28.9 GPa and 48.2 GPa, these values are less than diamond's ideal shear strength which implies that these dislocations may be nucleated heterogeneously under certain shear stress condition. In addition, our results also indicate there exists a deformation mode transformation for diamond deformation behavior at strain rate of 10−3/s. Our results provide a new insight into diamond dislocation nucleation and deformation.

The Relationship Between Atomic Structure and Strain Distribution of Misfit Dislocation Cores at Cubic Heteroepitaxial Interfaces

The atomic reconstruction of a misfit dislocation (MD) core causes change in the strain distribution around the core. Several MD cores at the AlSb/GaAs (001) cubic zincblende interface, including a symmetrical glide set Lomer dislocation (LD), a left-displaced glide set LD, a glide set LD with an atomic step, a symmetrical shuffle set LD, and a 60° dislocation pair, were studied using simulated projected potential and aberration-corrected transmission electron microscope images. Image deconvolution was also used to restore structure images from nonoptimum-defocus images. The corresponding biaxial strain maps, ε xx (in-plane) and ε yy (out-of-plane), were obtained by geometric phase analysis using the GaAs substrate as the reference lattice. The results show that atomic structure characteristics of MD cores can be revealed by the strain maps. The strain maps should be measured from optimum-defocus images or restored structure images. Furthermore, the ε xx strain map has been found more accurate than the ε yy strain map for MD cores, and the specimen thickness should be below the critical thickness due to the influence of dynamical scattering.

Dislocation glide-controlled room-temperature plasticity in 6H-SiC single crystals

In situ transmission electron microscopy observations of uniaxial compression of sub-300nm diameter, cylindrical, single-crystalline 6H-SiC pillars oriented along 〈0001〉 and at 45° with respect to 〈0001〉 reveal that plastic slip occurs at room-temperature on the basal {0001} planes at stresses above 7.8GPa. Using a combination of aberration-corrected electron microscopy, molecular dynamics simulations and density functional theory calculations, we attribute the observed phenomenon to basal slip on the shuffle set along 〈11¯00〉. By comparing the experimentally measured yield stresses with the calculated values required for dislocation nucleation, we suggest that room-temperature plastic deformation in 6H-SiC crystals is controlled by glide rather than nucleation of dislocations.

Temperature dependence of screw dislocation mobility on shuffle-set of silicon

Large-scale atomistic simulations are performed in order to observe local behaviors of screw dislocations located on the shuffle set of (111) in single crystal silicon, focusing on the propagation process of the screw dislocations. A quadrupolar arrangement of screw dislocations is utilized to impose the periodic boundary conditions along each of the three spatial directions. With the aid of molecular dynamics simulations, the dislocation mobility is investigated in terms of the critical resolved shear stress. Based on the results from the simulations, we discuss effects of the model size and temperature on the critical resolved shear stress. After choosing the proper model size to reduce undesirable interference between the dislocations, we further estimate the Peierls stress by fitting from a set of the critical resolved shear stresses at various temperatures. Meanwhile, we observe a double kink mechanism in the dislocation propagation which is the most energetically favorable dislocation movement in silicon. We investigate the formation and migration of kink pairs on an undissociated screw dislocation in silicon.

Atomistic Simulation on Indented Defects in Silicon

Silicon is known as one of the widely used materials in electronic fields for its excellent semiconductive characteristics. However, these characteristics are vulnerable to internal defects, which randomly exist in any materials. In the present study, defects in single crystalline silicon thin film were investigated by atomistic simulation of nano-indentation at zero temperature. The Tersoff potential and the spherical indenter were applied to the model of silicon. The symmetric axis parameter method is novelly proposed to identify defects in the diamond cubic structure. Under the nanoindentation condition, the ring slip appears close to the indentation region on the free surface and propagates along with [110]/(111). The dislocation is initiated closely to the ring slip and emitted on the (111) plane by the dissociation into two partial dislocations. It was found that the symmetric axis parameter method successfully separated the perfect dislocations, the partial dislocations and the stacking fault from perfect structure, i.e., diamond cubic structure, even though it was not able to distinguish between glide set and shuffle set dislocations.

The 60° basal dislocation in wurtzite GaN: Energetics, electronic and core structures

We have carried out computer atomistic simulations, based on an efficient density functional based tight binding method, to investigate the core configurations of the 60° basal dislocation in GaN wurtzite. Our energetic calculations demonstrate that the glide configuration with N polarity is the most energetically favorable over both the glide and the shuffle sets in nitrogen-rich growth conditions. However, in the case of gallium-rich growth conditions, the shuffle configuration with gallium polarity becomes the most favorable. Otherwise, we found that all the four configurations of the 60° basal dislocation introduces both shallow and deep states but the glide configuration with N polarity, which introduce only shallow states.

Atomistic Simulation of Undissociated 60&deg ; Basal Dislocation in Wurtzite GaN.

We have carried out computer atomistic simulations, based on an efficient density functional based tight binding method, to investigate the core configurations of the 60°basal dislocation in GaN wurtzite. Our energetic calculations, on the undissociated dislocation, demonstrate that the glide configuration with N polarity is the most energetically favorable over both the glide and the shuffle sets.

Dislocations in 4H‐ and 3C‐SiC single crystals in the brittle regime

AbstractNanoindentations at room temperature have been performed on 4H‐ and 3C‐SiC single crystals, and resulting microstructures have been analyzed by Transmission Electron Microscopy. In both structures, dislocations emitted from imprints are perfect dislocations lying in the basal plane for 4H‐ and in the {111} planes for 3C‐SiC. Dislocation segments are not dissociated and they are assumed to be lying in the shuffle set where only one bound per atom has to be cut for dislocation motion. It is deduced that the low stacking fault energy of silicon carbide is not involved in plasticity under high stress as compared to high temperature behaviour. The change in deformation mechanism reported in this study indicates that silicon carbide exhibits the same behaviour under high stress as other semiconducting materials, as silicon or antimonide indium. This could be a general feature for all this family of materials (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Electron microscope study of dislocations introduced by deformation in a Si between 77 and 873 K

Dislocations were introduced into Si by scratching between 77 and 873 K. The nature and configurations of dislocations were determined by the weak-beam method. Dislocations introduced below 703 K were perfect dislocations of the shuffle set, while those introduced above 823 K were dissociated dislocations of the glide set. At 77 K, the shuffle set of dislocations was very straight; between RT and 363 K, the shuffle set of dislocations blunted, but mostly parallel to crystallographic orientations. Above 383 K, the shuffle set of dislocations was heavily zigzagged. The mechanism responsible for the zigzagging of the shuffle set of dislocations was discussed.

Mechanism of formation of the misfit dislocations at the cubic materials interfaces

High-angle annular dark-field scanning transmission electron microscopy and molecular dynamic simulation are applied to study the misfit dislocations at the GaSb/GaAs interface. In the investigated samples, three types of misfit dislocations have been observed: shuffle and glide set Lomer dislocations and 60° dislocation pairs. The dislocation density tensor analysis is next used to quantify the Burgers vector of misfit dislocations and investigate the misfit dislocation formation mechanism. This work demonstrates that, in these hetero-structures, the dominant mechanism underlying the formation of misfit dislocations is the glide and reaction of 60° dislocations. It is shown that the final structure of each misfit dislocation depends on the Burgers vectors of the initial 60° dislocations. Finally, this analysis points out an approach to determine the local rotation at interface due to mixed type dislocations.

Investigation of the anisotropic strain relaxation in GaSb islands on GaP

The strain relaxation at the initial stages of highly mismatched (11.8%) GaSb grown on a GaP substrate following a Ga-rich surface treatment by molecular beam epitaxy has been investigated. High resolution transmission electron microscopy and moiré fringe analysis were used to determine the relaxation state in these GaSb islands in the [110] and [1–10] directions. The measurements revealed an anisotropic strain relaxation in these two directions; there is a higher misfit strain relaxation along the [110] direction where the islands are elongated, which is in agreement with a higher density of misfit dislocations. By combining molecular dynamics simulations and TEM results, the anisotropy in the strain relaxation is shown to be related to the asymmetry in the formation of interface misfit dislocations. The P-core glide set 60° dislocations (α type) and the Ga-core shuffle set Lomer dislocations serve as the primary misfit dislocation which contributes to the strain relaxation in the (1–10) interface, and the Ga-core glide set 60° dislocations (β type) and the P-core shuffle set Lomer dislocations for the (110) interface, respectively. The lower formation energy and higher glide velocity of the P-core glide set 60° dislocations (α type) result in a higher line density and more uniform periodical distribution of the misfit dislocation in the (1–10) interface. The higher fraction of Lomer dislocations, which is related to the dislocation configuration stability and surface treatment, promotes a better strain relief in the (1–10) interface, with a corresponding elongation of islands in the [110] direction.

Reaction pathway analysis for dislocation nucleation from a sharp corner in silicon: Glide set versus shuffle set

Using reaction pathway sampling, we have investigated the shear stress dependences of the activation energies of shuffle-set and glide-set dislocation nucleation from a sharp corner in silicon. The gradient of the glide-set dislocation curve is lower than that of the shuffle-set dislocation, and the athermal stress of glide-set dislocation is largely higher than that of shuffle-set dislocation. As a result, the two curves have a cross point, which means that shuffle-set dislocation is likely nucleated at high stress and low temperature and glide-set dislocation is likely nucleated at low stress and high temperature. Our result clearly explains the mechanism of recent molecular dynamics on these two types of dislocation nucleation at different temperatures and stress regimes. With increased compressive stress on the slip plane, the activation energy of the shuffle-set dislocation nucleation is greatly decreased, while that of glide-set dislocation nucleation is slightly increased. That would explain why shuffle-set dislocations were found under compressive stress fields.

Plasticity of indium antimonide between −176 and 400 °C under hydrostatic pressure. Part I: Macroscopic aspects of the deformation

Indium antimonide (InSb) single crystals have been plastically deformed between −176 and 400 °C, i.e. below and above the brittle-to-ductile transition temperature situated around 150–160 °C, via the use of microindentation below room temperature (RT) and the Paterson press (compression under gaseous pressure) above RT. The evolution of the macroscopic mechanical data (hardness and critical resolved shear stress) with temperature suggests the existence of three deformation regimes with transitions at T tr1 = 150 °C and T tr2 = 20 °C. T tr1 coincides with the brittle-to-ductile temperature, while T tr2 may coincide with a transition in the nature of dislocations with dislocations propagating in the glide set above T tr2 while moving in the shuffle set below T tr2.

Plasticity of indium antimonide between −176 °C and 400 °C under hydrostatic pressure. Part II: Microscopic aspects of the deformation

Indium antimonide (InSb) has been plastically deformed over a wide temperature range, from 400 down to −176 °C (see the companion paper: Kedjar B, Thilly L, Demenet JL, Rabier J. Acta Mater 2009) and transmission electron microscopy was used to characterize the deformation microstructures. In the ductile regime, i.e. T > T tr1 ≈ 150 °C, the crystal deforms via the nucleation and motion of perfect dislocations belonging to the glide set. In the brittle domain, i.e. for T < T tr1 ≈ 150 °C, two regimes are observed: for T tr2 ≈ 20 °C < T < T tr1 ≈ 150 °C, the crystal deformation takes place via the nucleation and glide of dissociated perfect dislocations or only leading partials, while for T < T tr2 ≈ 20 °C, the crystal deformation proceeds via the nucleation and motion of perfect dislocations belonging to the shuffle set. In view of these observations, the brittle-to-ductile transition (at T tr1) is confirmed to correspond to a change in the dislocation nature in the glide set, from partial-mediated plasticity at low temperature to perfect-mediated plasticity at high temperature. Another transition is observed at T tr2 and corresponds to the glide-to-shuffle transition which is observed experimentally for the first time in a III–V compound semiconductor.