Screw Dislocation In Silicon Research Articles

Locking of Screw Dislocations in Silicon due to Core Structure Transformation

Locking of Screw Dislocations in Silicon due to Core Structure Transformation

Structure and energy of the 〈11¯〉 screw dislocation in silicon using generalized Peierls theory

For the ⟨11¯0⟩ screw dislocation (nondissociated) in silicon, there are three types of core structures that are, respectively, referred to as the shuffle-set dislocation (A-core), glide-set dislocation (C-core), and mix-set dislocation (B-core). Each type of core further displays a planar or nonplanar (fourfold) configuration. In this paper, in the context of the generalized Peierls theory, the energy functional and equation of equilibrium of a screw dislocation with a nonorthogonal fourfold structure is derived and is used to investigate the structure and energy of the ⟨11¯0⟩ screw dislocation in silicon. We find that the energy of the shuffle-set dislocation with a fourfold core is considerably lower than that of the other types of cores. Thus, the shuffle-set dislocation with the fourfold core is the most stable. The glide-set dislocation with a planar core has the highest energy and is the most unstable. As the most stable structure, the shuffle-set screw dislocation with the fourfold core was responsible for wavy slip traces observed at low temperature.

Slip of shuffle screw dislocations through tilt grain boundaries in silicon

In this paper, molecular dynamics (MD) simulations of the interaction between tilt grain boundaries (GBs) and a shuffle screw dislocation in silicon are performed. Results show that dislocations transmit into the neighboring grain for all GBs in silicon. For Σ3,Σ9 and Σ19 GBs, when a dislocation interacts with a heptagon site, it transmits the GB directly. In contrast, when interacting with a pentagon site, it first cross slips to a plane on the heptagon site and then transmits the GB. The energy barrier is also quantified using the climbing image nudged elastic band (CINEB) method. Results show that Σ3 GB provides a barrier for dislocation at the same level of the Peierls barrier. For both Σ9 and Σ19 GBs, the barrier from the heptagon sites is much larger than the pentagon sites. Since the energy barrier for crossing all the GBs at the heptagon sites is only slightly larger than the Peierls barrier, perfect screw dislocations cannot pile up against these GBs. Furthermore, the critical shear stress averaged over the whole sample for the transmission through the Σ9 and Σ19 GBs is almost twice on heptagon site for initially equilibrium dislocation comparing with dislocations moving at a constant velocity.

Atomistic modeling of the dissociation of a screw dislocation in silicon

The nature of dislocations involved in the plastic deformation of semiconductors is different in high- and low-temperature domains. Experimental investigations have not allowed to discriminate between dissociation and nucleation as the main reason behind this transition. In this work, the mechanisms leading to the dissociation of a screw dislocation in silicon, determined by means of atomistic calculations, are described. It is shown that kink pair formation, followed by successive kink migrations, leads to the formation of two 30° partial dislocations from the screw dislocation core. These mechanisms are structurally very similar to those involved in the formation and migration of kinks in the case of a single 30° partial dislocation, because of the close resemblance between the screw and 30° dislocation cores. The calculated activation energy of the whole process is 2.14 eV, thus quite comparable to the energies involved in the propagation of partial dislocations. This shows that dissociation and nucleation processes are likely to be activated at similar temperature ranges.

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.

Molecular dynamics studies of the dissociated screw dislocation in silicon

Characterizing the motion of dislocations through covalent, high Peierls barriermaterials is a key problem in materials science, while despite the progress inexperimental studies the actual observation of the atomistic behaviour involved incore migration remains limited. We have applied a hybrid embedding schemeto investigate the dissociated screw dislocation in silicon, consisting of two30° partials separated by a stacking fault ribbon, under the influence of a constant externalstrain. Our ‘learn on the fly’ hybrid technique allows us to calculate the forces on atoms inthe vicinity of the core region using the tight binding Kwon potential, whilst the remainderof the bulk matrix is treated within a classical approximation. Applying a 5% strain to thedissociated screw dislocation, for a simulation time of 100 ps at a temperature of 600 K, weobserve movement of the partials through two different mechanisms: double kink formationand square ring diffusion at the core. Our results suggest that in these conditions, therole of solitons or anti-phase defects in seeding kink formation and subsequentmigration is an important one, which should be taken into account in future studies.

Theoretical study of kinks on screw dislocation in silicon

Theoretical calculations of the structure, formation, and migration of kinks on a nondissociated screw dislocation in silicon have been carried out using density functional theory calculations as well as calculations based on interatomic potential functions. The results show that the structure of a single kink is characterized by a narrow core and highly stretched bonds between some of the atoms. The formation energy of a single kink ranges from $0.9\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1.36\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, and is of the same order as that for kinks on partial dislocations. However, the kinks migrate almost freely along the line of an undissociated dislocation unlike what is found for partial dislocations. The effect of stress has also been investigated in order to compare with previous silicon deformation experiments which have been carried out at low temperature and high stress. The energy barrier associated with the formation of a stable kink pair becomes as low as $0.65\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for an applied stress on the order of $1\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, indicating that displacements of screw dislocations likely occur via thermally activated formation of kink pairs at room temperature.

Calculations of dislocation mobility using Nudged Elastic Band method and first principles DFT calculations

We present a new technique which makes it possible to determine mobility properties of dislocations with first principles accuracy without having to apply corrections for the influence of boundary conditions. The Nudged Elastic Band method is used together with periodic boundary conditions and all dislocations included in the simulated cell are coherently displaced during the calculations. The method is applied to the displacement of a non-dissociated shuffle screw dislocation in silicon along two different directions. Peierls energies as well as dislocation structure as a function of the dislocation position in the lattice have been obtained. We have determined the Peierls stresses for both directions, in excellent agreement with previous determinations. Finally, we discuss the advantages of the technique over other methods.

Plastic strain field caused by dislocations

Although dislocations have been investigated for almost a 100 years, plastic strains caused by them are not known. Because of that the dislocation energy and the strain field around a dislocation are described using a very simple model e.g. Volterra approach. On the other hand methods of atomistic calculations like ab initio and molecular dynamics allow for relatively precise mechanical description of highly distorted region of dislocation core. Their disadvantages are that the boundary conditions have to be applied periodically. Until now, the discrepancy between results of atomistic calculation and continuum mechanics simulations in a dislocation core region was ascribed to a strong nonlocal interaction. The present article shows a method that allows for a proper energetic description of dislocation cores using the continuum mechanics. A very good correspondence between the dislocation core's energy obtained here and those resulting from atomistic simulations reveals that the proposed methodology may establish new possibilities for the continuum description. The approach is validated by considering a screw dislocation in silicon. Full anisotropy is taken into account. The most important information originated from this paper is that a reliable energetic description of dislocations using continuum methods at the nanoscale is possible.

First principles determination of the Peierls stress of the shuffle screw dislocation in silicon

The Peierls stress of the a/2⟨110⟩ screw dislocation belonging to the shuffle set is calculated for silicon using density functional theory. We have checked the effect of boundary conditions by using two models, the supercell method where one considers a periodic array of dislocations, and the cluster method where a single dislocation is embedded in a small cluster. The Peierls stress is underestimated with the supercell and overestimated with the cluster. These contributions have been calculated and the Peierls stress is determined in the range between 2.4 × 10−2 and 2.8 × 10−2 eV Å−3. When moving, the dislocation follows the {111} plane going through a low energy metastable configuration and never follows the 100 plane, which includes a higher energy metastable core configuration.

Undissociated screw dislocations in silicon: Calculations of core structure and energy

The stability of the perfect screw dislocation in silicon has been investigated using both classical potentials and first-principles calculations. Although a recent study by Koizumi et al. stated that the stable screw dislocation was located in both the 'shuffle' and the 'glide' sets of {111} planes, it is shown that this result depends on the classical potential used, and that the most stable configuration belongs to the 'shuffle' set only, in the centre of one (amp;1tilde;01) hexagon. We also investigated the stability of an sp2 hybridization in the core of the dislocation, obtained for one metastable configuration in the 'glide' set. The core structures are characterized in several ways, with a description of the three-dimensional structure, differential displacement maps and derivatives of the disregistry.

Atomic structures of dislocation intersections at (001) low-angle twist and shear boundaries in silicon

The first atomistic simulations of orthogonal networks of screw dislocations in silicon have been performed to investigate the core structures of dislocation intersections. Structural models for the dislocation intersections are proposed and examined by the classical molecular dynamics method with the empirical interatomic potential of Tersoff. The screw dislocations (b=(a/2)(110)) are assumed to be undissociated, according to experimental data on atomic structures of the synthetic low-angle Si/Si(001) twist boundaries. It is found that cores of the dislocation intersections are formed by closed characteristic groups of atoms (extended point defects). The structure of these defects depends on the fact whether the screw dislocation arrays generate a twist or a shear boundary. The former has a well-defined energy minimum, with the characteristic groups having the point-group symmetry 222 (D2). The latter is found to exhibit a degeneracy in the number of local energy minima, corresponding to non-symmetrical characteristic groups with a different coordination of atoms.

SCATTERING OF ELECTRONS BY SCREW DISLOCATIONS IN SILICON CRYSTALS

In this paper, the scattering of electrons by 〈110〉-screw dislocations insilicon crystals is discussed. We use the tight-binding approximation, only electrons in the s and p state are taken into account. With the long wave length approximation, only scattering of electrons near Г in the first BZ is considered. A scattering theoretical approach yields an integral equation of Kirchh off-Huygens type. The scatlering equation has been solved by means of gauge transformation and Green's function. It is confirmed that, as in the ease of single band in the case of many bands the shadow, which is the region that can not be affected by electron flux, appears in the down stream side of dislocations as well.

Cross slip of single dissociated screw dislocations in silicon and germanium

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