Partial Dislocation In Silicon Research Articles

A new reconstruction core of the 30° partial dislocation in silicon

ABSTRACTThe partial dislocation in silicon is investigated theoretically in the framework of the fully discrete Peierls–Nabarro model and first-principles calculations. A new reconstructed core composed of a periodic arrangement of one tetragon and two heptagons (477-core) is proposed. Similar to the partial dislocation, we find that there are actually two types of reconstructed cores for the partial dislocation, namely, a well-known 558-core and a new 477-core. The energy of the 477-core is 0.137 eV/Å higher than that of the 558-core. However, from the molecular dynamics simulation, we found that the 477-core may have a macroscopic lifetime for temperature below 30 K. The full kinks and the partial kinks due to the appearance of the 477-core are also studied. Remarkably, it is found that formation and migration of the global kinks deeply involve with the partial kinks, and the creation and motion of partial kinks can be attributed to the rotation of a single bond. Our results are helpful in understanding the mechanism of kink nucleation and the plasticity of silicon.

On a Plasticity by Partial Dislocations in Silicon at Very High Stress

Perfect dislocations have been found controlling the plasticity of silicon at high stress. Such evidence has been obtained from a number of experiments and atomistic computations. This is also consistent with the larger Peierls stresses encountered by partial dislocations as compared to perfect dislocations at low temperatures. However at very high stress and in the same temperature range partial dislocation have been reported to occur in a few experiments as well as in some atomistic computations. The aim of this paper is to discuss in what situations partial dislocations can be nucleated, what could be the nuclei responsible for their nucleation and the conditions where partial dislocations could control the plastic deformation in the place of perfect dislocations.

The 90° partial dislocation in semiconductor silicon: An investigation from the lattice P–N theory and the first principle calculation

The 90° partial dislocation in silicon is studied theoretically in the framework of the improved P–N model and the first principle calculation. Instead of the frequently used integro-differential equation, a fully discrete dislocation equation is proposed to determine the core structure (distribution of dislocation density). Furthermore, in order to describe the dislocation structure precisely, the effective interaction γ-surface is generalized to be the γ-potential and the space change induced by the appearance of the dislocation is addressed self-consistently. With the γ-potential calculated from the first-principles, the core structures and the stress field are explicitly obtained through the variational method and the superposition principle. The reconstructions are examined for an isolated dislocation using ab initio combined with the analytical theory. It is found that in the analytical theory there are two types of core structures. One is the stable (ground-state) structure referred to as the B-type dislocation. Another is the unstable structure referred to as the O-type dislocation. The single-period (SP) dislocation originates from the B-type dislocation and the double-period (DP) dislocation originates from the O-type dislocation. The movement of dislocation is realized by transformation from one type to another. The energy difference between different dislocations measures the height of the Peierls barrier. It is observed that the energy difference decreases after the reconstruction and thus the height of the Peierls barrier is reduced by the reconstruction. The results presented are helpful in understanding the effects associated to the details of the dislocation structure such as the brittle–ductile transition and the electronic structure.

Multi-scale simulation of the stability and diffusion of lithium in the presence of a 90° partial dislocation in silicon

The stable positions, binding energies, and dynamic properties of Li impurity in the presence of a 90° partial dislocation in Si have been studied by using the multi-scale simulation method. The corresponding results are compared with the defect-free Si crystal in order to reflect how the dislocation defect affects the performances of Li-ion batteries (LIBs) at the atomic level. It is found that the inserted Li atom in the dislocation core and nearest regions is more stable, since the binding energies are 0.13 eV to 0.52 eV larger than the bulk Si. Moreover, it is easier for Li atom to diffuse into those defect areas and harder to diffuse out. Thus, Li dopant may tend to congregate in the dislocation core and nearest regions. On the other side, the 90° partial dislocation can glide in the {111} plane accompanied by the diffusion of Li impurity along the pentagon ring of core. In addition, the spacious heptagon ring of dislocation core can lower the migration barrier of Li atom from 0.63 eV to 0.34 eV, which will enhance the motion of the dopant. Therefore, the presence of 90° partial dislocations may provide a fast and favorable diffusion path for the congregated Li impurity, which finally facilitates the lithiation of LIBs.

Prediction of the threshold load of dislocation emission in silicon during nanoscratching

This paper establishes an analytical model to predict the normal threshold load that causes the emission of partial dislocations in silicon during nanoscratching. In the modeling, the deformation mechanisms and the sequence of microstructural changes already explored by experiment and molecular dynamics will be exactly followed; that is, with increasing the normal load of nanoscratching, phase transformation first takes place, followed by partial dislocation emission from the interface between the phase transformed zone and the original crystalline silicon when the scratching load reaches its threshold. The model postulates that the emission process represents the generation of a dipole of Shockley partial dislocations. One partial dislocation of the dipole, located at the interface, is considered immobile, while the other partial dislocation moves into the bulk of the crystalline silicon. The mobile partial dislocation slips along a crystallographic plane, and a stacking fault is formed in its wake. Based on the above, the threshold normal scratching load for the emission of a partial dislocation is determined by means of the energy criterion. The influence of the indenter geometry and the location of dislocation nucleation on the threshold normal scratching load is then investigated. Compared with the deformation of silicon under nanoindentation, the present study concludes that the threshold load under scratching is always smaller, and that a sharp indenter leads to a relatively smaller threshold load. The model prediction is well verified by scratching experiments.

Computing transition rates of thermally activated events in dislocation dynamics

We present a numerical method to compute the transition rates of thermally activated events in dislocation dynamics on the atomistic scale, based on the formula from the transition state theory. The method is applied to the migration of kinks in 30° partial dislocations in silicon. To our knowledge, this is the first time that the contribution of entropy to the transition rate of such events has been calculated using reliable atomistic models.

A Theoretical Study of Copper Contaminated Dislocations in Silicon

Recently, the interaction of copper with dislocations in p-type Si/SiGe/Si structures has been investigated experimentally and a new dislocation related DLTS-level at Ev +0.32 eV was detected after intentional contamination with copper. To determine the origin of this newly detected level, in this work we present first density functional calculations of substitutional copper at 90◦ and 30◦ partial dislocations in silicon. Defect–dislocation binding energies are determined and electrical gap levels are calculated and compared with the experimental data. As a result, the observed level at Ev + 0.32 eV is tentatively assigned to the single acceptor level of substitutional copper at the dislocation.

Interaction of dislocations with vacancies in silicon: Electronic effects

The authors report on an ab initio investigation of the interaction of vacancies with the core of 90° partial dislocation in silicon. For the single-period and the double-period core reconstructions, they find the vacancy formation energies at the core sites to be lower than in the crystalline environment. Moreover, they find that the vacancy-dislocation coupling does not change the U-negative nature of a vacancy in silicon, but leads to quantitative changes in the relative stability of different charge states, as the Fermi level sweeps the electronic band gap in this material.

Kinetic Monte Carlo and density functional study of hydrogen enhanced dislocation glide in silicon

We investigate Hydrogen Enhanced Dislocation Glide [HEDG], using n-fold way Kinetic Monte Carlo simulations of the interaction between hydrogen and 90° partial dislocations in silicon, and a range of new density functional calculations. We examine two different hydrogen arrival species, as well as hydrogen recombination at the dislocation. The Monte Carlo simulations use a line-wise description of the dislocation line parameterized using density functional calculations of migration and formation energies of various dislocation line defects and their complexes with hydrogen. From this we suggest that the rate of H2 expulsion from the dislocation core increases as we approach HEDG, but that if the concentration of the hydrogen species goes beyond that required for HEDG it then slows dislocation motion by choking the line with defects comprised of two hydrogen atoms in a reconstruction bond. A `dislocation engine' model is proposed whereby hydrogen enters the dislocation line, catalyses motion, and is expelled along the core as H2.

First principles simulations of antiphase defects on the SP90° partial dislocation in silicon

We study the structure and energies of formation of antiphase defects on the single period (SP)90° partial dislocation in silicon using a first principles density functional method. Weconsider two types of antiphase defect, the type first proposed by Hirsch (1980 J.Microsc. 118 3) wholly inside the dislocation core, and another type that liespartly outside the core. Both types are stable and contain one atom which isthreefold coordinated. Each of these atoms has a dangling hybrid which lies in adirection perpendicular to the dislocation line on the slip plane. We obtain values of1.39 ± 0.03 eVand 1.41 ± 0.03 eV for the average formation energy of single antiphase defects of the inside and outsidetypes, respectively. We have obtained, using a tight binding scheme, bandstructurescorresponding to these two types of defect, and we find both of them to be associated withstates in the gap and each dangling hybrid to contain one electron.

The equilibrium structures of the90° partial dislocation in silicon

We consider the free energies of the single-period (SP) and double-period (DP) core reconstructions of thestraight 90° partial dislocation in silicon. The vibrational contributions are calculated with aharmonic model. It is found that it leads to a diminishing difference between thefree energies of the two core reconstructions with increasing temperature. Thequestion of the relative populations of SP and DP reconstructions in a single straight90° partial dislocation is solved by mapping the problem onto a one-dimensional Ising model ina magnetic field. The model contains only two parameters and is solved analytically. Itleads to the conclusion that for the majority of the published energy differences betweenthe SP and DP reconstructions the equilibrium core structure is dominated by the DPreconstruction at all temperatures up to the melting point. We review whether it is possibleto distinguish between the SP and DP reconstructions experimentally, both in principleand in practice. We conclude that aberration corrected transmission electronmicroscopy should be able to distinguish between these two core reconstructions, butpublished high resolution micrographs do not allow the distinction to be made.

Electronic charge effects on dislocation cores in silicon

Using first-principles calculations, we investigate electronic charge effects on the structural stability of partial dislocations in silicon. For the 30° partial dislocation, we find that the unreconstructed core sustains all possible charge states associated with the dislocation-related electronic bands, as the Fermi level (μe) sweeps the electronic band gap, while the reconstructed core remains neutral for p-type doping and intrinsic regimes. Both core configurations become negatively charged for n-type doping. In the case of the 90° partial dislocation, the three known core configurations (namely, the single-period and double-period reconstructed cores and the unreconstructed one) remain neutral in the p-type and intrinsic regimes, but the negatively charged states become stable in the n-type region, for all three geometries. More important, we find that the relative stability between the three structures is strongly charge-state dependent, with the unreconstructed core becoming energetically favorable in the n-type regime. Our results provide elements for understanding the role of doping on dislocation mobility in semiconductors.

Migration Processes of the 30° Partial Dislocation in Silicon

The migration processes of the 30 degrees partial dislocation in silicon have been investigated using first-principles total-energy calculations. We have presented for the first time a reliable determination of the formation and migration energies of kinks, which are consistent with experiments. The obtained results indicate that the 30 degrees partial dominates the dislocation dynamics in Si and suggest the dislocation glide picture based on the no-collision model. We suggest that the interpretation of experimental studies on the dislocation dynamics should be reexamined in light of these results.

Linewise kinetic Monte Carlo study of silicon dislocation dynamics

We present a number of n-fold way kinetic Monte Carlo simulations of the glide motion of $90\ifmmode^\circ\else\textdegree\fi{}$ partial dislocations in silicon. We undertake a survey of ratios of kink formation energy ${F}_{k}$ to kink migration barrier ${W}_{m},$ over a range of temperatures and applied stresses. These simulations are compared with Hirth-Lothe theory and an extension to the Hirth-Lothe theory of Kawata and Ishiota. The latter is found to give the best description of the system. Using literature first principle values for the kink and soliton formation and migration energies, a model combining both strained bond and soliton mediated motion shows a negligible contribution to dislocation motion from the solitons. The high soliton pair creation barrier was limiting and a soliton mediated mechanism for dislocation motion would have to achieve thermal equilibrium concentration via impurity or point defect interaction to be effective. We also show that if this can be overcome solitons greatly increase the mobility of the dislocation, even without a binding energy between solitons and kinks. The simulation coded here is easily expandable to incorporate further dislocation line effects such as impurities at the line.

Temperature effects on dislocation core energies in silicon and germanium

Temperature effects on the energetics of the $90\ifmmode^\circ\else\textdegree\fi{}$ partial dislocation in silicon and germanium are investigated, using nonequilibrium methods to estimate free energies, coupled with Monte Carlo simulations. Atomic interactions are described by Tersoff and environment-dependent interatomic potentials. Our results indicate that the vibrational entropy has the effect of increasing the difference in free energy between the two possible reconstructions of the $90\ifmmode^\circ\else\textdegree\fi{}$ partial, namely, the single-period and the double-period geometries. This effect further increases the energetic stability of the double-period reconstruction at high temperatures. The results also indicate that anharmonic effects may play an important role in determining the structural properties of these defects in the high-temperature regime.

Arsenic segregation, pairing and mobility on the cores of partial dislocations insilicon

We studied the effects of arsenic on properties of dislocations in silicon. Thetheoretical investigation was carried out using ab initio total energy methods,based on the density functional theory. We find that the interaction ofan arsenic impurity in the crystal with a dislocation results in a chargeexchange, driving the dislocation core to a negative charge state. Thisinteraction is essentially electrostatic and attractive, and leads to arsenicsegregation. Although arsenic segregation to the core is energetically favourable,formation of arsenic pairs inside the core is energetically unfavourable. We alsoinvestigated the role of vacancies in arsenic diffusion inside the dislocation core.

Interaction of As impurities with 30° partial dislocations in Si: An ab initio investigation

We investigated through ab initio total energy calculations the interaction of arsenic impurities with the core of a 30° partial dislocation in silicon. It was found that when an arsenic atom sits in a crystalline position near the dislocation core, there is charge transfer from the arsenic towards the dislocation core. As a result, the arsenic becomes positively charged and the core negatively charged. The results indicate that the structural changes around the impurity are very small in both environments, namely, the crystal and the dislocation core. In this scenario, the interaction between arsenic and the core is essentially electrostatic, which eventually leads to arsenic segregation. The segregation energy was found to be as large as 0.5 eV/atom. Additionally, it was found that arsenic pairing inside the core is not energetically favorable.

Boundary conditions for dislocation core structure studies: application to the 90° partial dislocation in silicon

The effects of boundary conditions on studies of dislocation cores are examined, using the 90° partial dislocation in Si as an illustration. The relative stability of two possible reconstructions of the core are explored using periodic supercell calculations and cylindrical boundary conditions and the results compared. It is argued that the stable core structure depends systematically on the stress field experienced by the dislocation, and that this dependence can be quantified effectively using a combination of periodic supercells and elasticity theory.

Dopant interaction with a dislocation in silicon: local and non-local effects

We performed a theoretical investigation on the interaction of arsenic impurities with a 30° glide partial dislocation in silicon. Our calculations were performed by ab initio total energy methods, based on the density functional theory and the local density approximation. We find that an arsenic atom, in a crystalline position, gives away one electron to the dislocation, becoming positively charged while the dislocation core is negatively charged. The interaction between arsenic and the core is essentially electrostatic, which leads to arsenic segregation.

Reconstruction defects on partial dislocations in semiconductors

Using ab initio total energy calculations, we investigated the structural and electronic properties of reconstruction defects, or antiphase defects, in the core of a 30° partial dislocation in silicon and gallium arsenide. In GaAs, we identified two different reconstruction defects in the dislocation cores, corresponding to a Ga undercoordinated atom, and an As undercoordinated atom. Formation energies of these reconstruction defects were compared to experimental results on the concentration of electrically active centers in deformed semiconducting materials.