Self-interstitial Diffusion Research Articles

分子動力学法による BCC 鉄中の自己格子間拡散の研究

Self-interstitial diffusion in alpha-iron is investigated using an embedded-atom-method potential and molecular dynamics simulations. Curved Arrhenius plot is obtained for the temperature dependence of diffusion coefficients, which is well explained by the superposition of two transition processes among the two allotropic states of self-interstitial defects, the reformation of <110> dumbbell into another <110> configuration and one-dimensional solitonic propagation of a crowdion on <111> axis.

Effect of Hydrostatic Pressure on Self-Interstitial Diffusion in Si, Ge, Si&amp;lt;Ge&amp;gt; Crystals: Quantum-Chemical Simulations

A theoretical modeling of the diffusion of self-interstitials in silicon and germanium crystals both at normal and high hydrostatic pressure has been carried out using molecular mechanics, semiempirical (PM3, PM5) and ab-initio (SIESTA) methods. According to the simulation for the Si and Ge neutral interstitials (I0) both in silicon and germanium crystals more stable configuration is &lt;110&gt; split interstitial. T is the stable configuration for the double positive interstitial I++, but the interstitial is displaced from the high-symmetry site. Stability of &lt;110&gt; splitinterstitial is not changed under hydrostatic pressure. The activation barriers for the diffusion of interstitials were determined and equal to ΔEa(Si)(&lt;110&gt; -&gt; T1)=0.69 eV; ΔEa (Ge)(&lt;110&gt; -&gt; T1)=1.1 eV. For mixed interstitials the calculated activation barriers equal Si Emix = 1.06 eV, Ge Emix = 0.86 eV. Hydrostatic pressure decreases the activation barriers ΔEa(Si), ΔEa (Ge).

Dynamic prediction of point defects in Czochralski silicon growth. An attempt to reconcile experimental defect diffusion coefficients with the [formula omitted] criterion

Using the FEMAG software, fully time-dependent and global simulations are conducted to predict the distribution of point defects in a growing silicon crystal. Furthermore, the defect governing model is adapted in order to better agree with available measurements of self-interstitial and vacancy diffusion coefficients while respecting the V / G criterion. It is shown that introducing a thermal drift effect can facilitate the construction of a relevant model satisfying both conditions.

Mechanism and energetics of self-interstitial formation and diffusion in silicon

Recent work has suggested that prior determinations of diffusion mechanism and point defect thermodynamics in silicon have been affected by nonequilibrium effects stemming from uncontrolled adsorption-induced suppression of a pathway for defect creation at the surface. Through silicon self-diffusion measurements in ultrahigh vacuum in a short-time kinetic limit, the present work shows unambiguously that interstitials are the primary mediators of self-diffusion over the range $650--1000\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$, moving over distances of $5--9\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ before exchanging into the lattice. The Frank-Turnbull mechanism of interstitial formation does not play a significant role.

Molecular-Dynamics Study of Self-Interstitial Diffusion in bcc-Iron

Self-interstitial diffusion in α-iron is investigated using an embedded-atom-method potential and molecular-dynamics simulations. Curved Arrhenius plot is obtained for the temperature dependence of diffusion coefficients, which is well explained by the superposition of two transition processes among the two allotropic states of self-interstitial defects, the reformation of 〈110〉 dumbbell into another 〈110〉 configuration and one-dimensional solitonic propagation of a crowdion on 〈111〉 axis.

On the correlation between self-interstitial cluster diffusivity and irradiation-induced swelling in Fe–Cr alloys

It is shown that the dependence of self-interstitial cluster diffusivity in Fe–Cr alloys on Cr concentration correlates with that of swelling in these alloys under neutron irradiation; namely, with increasing chromium concentration the cluster diffusivity first decreases and then increases. The origin of such behaviour lies in a relatively long-ranged, ∼1 nm, attractive interaction between Cr atoms and crowdions. The minimum diffusivity is realized for ∼11 at.% Cr, where all crowdions constituting the cluster interact with Cr atoms, but the interaction fields of different Cr atoms do not overlap.

Effect of self-interstitial diffusion anisotropy in electron-irradiated zirconium: A cluster dynamics modeling

A model based on the cluster dynamics approach was proposed in [A. Hardouin Duparc, C. Moingeon, N. Smetniansky-de-Grande, A. Barbu, J. Nucl. Mater. 302 (2002) 143] to describe point defect agglomeration in metals under irradiation. This model is restricted to materials where point defect diffusion is isotropic and is thus not applicable to anisotropic metals such as zirconium. Following the approach proposed by Woo [C.H. Woo, J. Nucl. Mater. 159 (1988) 237], we extended in this work the model to the case where self-interstitial atoms (SIA) diffusion is anisotropic. The model was then applied to the loop microstructure evolution of a zirconium thin foil irradiated with electrons in a high-voltage microscope. First, the inputs were validated by comparing the numerical results with Hellio et al. experimental results [C. Hellio, C.H. de Novion, L. Boulanger, J. Nucl. Mater. 159 (1988) 368]. Further calculations were made to evidence the effect of the thin foil orientation on the dislocation loop microstructure under irradiation. The result is that it is possible to reproduce for certain orientations the ‘unexpected’ vacancy loop growth experimentally observed in electron-irradiated zirconium [M. Griffiths, M.H. Loretto, R.E. Sallmann, J. Nucl. Mater. 115 (1983) 313; J. Nucl. Mater. 115 (1983) 323; Philos. Mag. A 49 (1984) 613]. This effect is directly linked to SIA diffusion anisotropy.

Quantum diffusion: effect of defect-localized phonon dynamics

The quantum diffusion of lattice defects is considered on the basis of the non-perturbative description of the quadratic defect-lattice coupling. This allows to take explicitly into account the effect of defect-localized phonon dynamics. This effect is especially important in the case of diffusion of vacancies and self-interstitials while a defect displacement to a nearest site is accompanied by a breaking and reconstitution of bonds of nearest atoms. It is shown that the local softening of the lattice by a vacancy due to the breaking of bonds produces an enhancement of the contribution of the low frequency phonons while the local hardening of the lattice by an interstitial atom leads to the opposite effect. As a consequence, at low temperatures the diffusion coefficient of vacancies is much smaller than that of interstitial atoms; the temperature dependences of these coefficients are also different. The obtained results are compared with experimental data for diffusion of vacancies in solid helium.

Determination of Diffusivities of Si Self-Diffusion and Si Self-Interstitials using Isotopically Enriched Single-or Multi-30Si Epitaxial Layers

AbstractSelf-diffusivity of Si has been obtained over a wide temperature range (867°C-1300°C) using highly isotopically enriched 30Si epi-layers (99.88%) as a diffusion source into natural Si substrates. 30Si epi-layers were grown on both CZ-Si substrates and non-doped epi-layers grown on CZ-Si substrates using low pressure CVD with 30SiH4. Diffusion was performed in resistance-heated furnaces under a pure Ar atmosphere. After annealing, the concentrations of the respective Si isotopes were measured with secondary ion mass spectroscopy (SIMS). Diffusivity of 30Si (called Si self-diffusivity, DSD) was determined using a numerical fitting process with 30Si SIMS profiles. We found no major differences in self-diffusivity between bulk Si and epi-Si. Within the 867°C -1300°C range investigated, DSD can be described by an Arrhenius equation with one single activation enthalpy: DSD =14 exp (—4.37 eV/kT) cm2/s. The present result is in good agreement with that of Bracht et. al.Diffusivity and thermal equilibrium concentration of Si self-interstitials have been determined using multi-30Si epi-layers consisting of alternative layers with isotopically pure 30Si and natural Si. The sample surface was oxidized and the Si self-interstitials were introduced from the surface. Spreading of 30Si spikes of each layer due to the diffusion of Si self-interstitials generated at the surface was measured with SIMS analysis. The diffusivity of Si self-interstitials, DI, is obtained by fitting with experimental results. In the temperature range between 820 -920°C, DI and thermal equilibrium concentration of Si self-interstitials, CIi, are described by the Arrhenius equations DI3.48×104 exp (—3.82eV/KT) cm2/s and CIi= 9.62×1018 exp (—0.475eV/KT) cm-3, respectively.

Characterization of bulk microdefects in Ge single crystals

The work reported here concerns the characterization of bulk microdefects in germanium single-crystal wafers. From comparison with the case of silicon, it is expected that bulk microdefects are formed due to diffusion and interaction of self-interstitials and vacancies during Czochralski growth, solely dependent on the growth parameters. Unfortunately, several of the defect characterization methods, which can be used for silicon, fail in the case of germanium due to its lower band gap. Therefore, the possibilities of two alternative techniques, x-ray topography and small-angle x-ray scattering, respectively, were investigated. The results, combined with a characterization of the material surface using scanning laser reflectometry, indicate that in Ge, the same kind of intrinsic growth-related defects exist, as in Si.

Determination of Silicon self-interstitial diffusivity using isotopically pure 30Silicon multi-layer

Si self-diffusion under oxygen ambient has been studied using multi-layer structures consisting of alternative layers with isotopically enriched 30Si and natural Si in order to determine the diffusivities of Si self-interstitials. Spreading of 30Si spikes of each layer due to the diffusion of Si self-interstitials generated at the surface was measured with SIMS analysis. The diffusivity of Si self-interstitials, DI, is obtained from the fitting with experimental results. In the temperature range between 820 and 920 °C, DI and thermal equilibrium concentration of Si self-interstitials, CIi, are described by the Arrhenius equations, D I = 3.48 × 10 4 exp ( − 3.82 eV / K T ) (cm 2/s) and C Ii = 9.62 × 10 18 exp ( − 0.475 eV / K T ) (cm −3), respectively.

Strongly non-Arrhenius self-interstitial diffusion in vanadium

We study diffusion of self-interstitial atoms (SIAs) in vanadium via molecular dynamics simulations. The <111>-split interstitials are observed to diffuse one-dimensionally at low temperature, but rotate into other <111> directions as the temperature is increased. The SIA diffusion is highly non-Arrhenius. At T<600 K, this behavior arises from temperature-dependent correlations. At T>600 K, the Arrhenius expression for thermally activated diffusion breaks down when the migration barriers become small compared to the thermal energy. This leads to Arrhenius diffusion kinetics at low T and diffusivity proportional to temperature at high T.

Investigation of two-dimensional diffusion of the self-interstitials in crystalline silicon at 800 °C and at room temperature

The two-dimensional (2D) diffusion of self-interstitials (I) in crystalline Si, both at room temperature and at 800 °C, has been studied by quantitative scanning capacitance microscopy measurements. The 2D I emission from an I source laterally confined down to submicrometer dimensions, obtained by low-energy implantation through a patterned oxide mask, has been observed. At room temperature, I diffusion was monitored by measuring the electrical deactivation of B corresponding to the diffusing interstitial tail and it was demonstrated that this deactivation is due to compensating levels introduced by defects in the Si band gap. At 800 °C I diffusion was monitored by measuring the transient enhanced diffusion of B spikes due to interstitial supersaturation produced during the annealing. In both cases, a dependence of the I depth-penetration on the original source size has been shown.

Self-interstitial diffusion and clustering with impurities in crystalline silicon

In this work the diffusion of ion-beam-injected self-interstitials (Is) and their interaction with impurities in crystalline Si are presented. In particular, the I penetration into a molecular beam epitaxy grown Si structure was studied by means of diffusion effects induced on B spikes, analyzed by a developed simulation code. Trapping effects at sample-surface and bulk are evidenced and modeled. The B marker approach was extended to the two-dimensional (2D) I-diffusion occurring as a consequence of ion implantation through a sub-micron dimension patterned oxide mask. I-source size effects on the I penetration have been found and modeled, quantitatively describing the 2D I-diffusion. The I-substitutional carbon interactions have been also studied, showing the C ability to effectively retain Is. The I-trapping mechanism was quantitatively studied by the simulation code, showing that one I is able to deactivate about two C traps by means of I-trapping and C-clustering reactions. This C property was used to control the ion-implantation induced damage and, consequently, to completely suppress B transient enhanced diffusion. Finally, the interaction between I and B leading to the B agglomeration into small B–I clusters (BICs) has been experimentally investigated. BICs dissolution kinetics was studied at different temperatures, directly using experimental concentration profiles and an opportunely developed B-diffusion simulation code. The activation energy for BICs dissolution and the BICs stoichiometry are extracted and given.

Diffusion of ion beam injected self-interstitial defects in silicon layers grown by molecular beam epitaxy

In this work the silicon self-interstitial (I) diffusion in trap-containing molecular beam epitaxy Si layers is investigated. The I’s are produced by Si ion implantation, and the I supersaturation is reported as a function of the depth and the annealing time. These data are discussed on the basis of two alternative models proposed in literature (“effective diffusivity” model and “filling trap” model). This analysis demonstrates that the second model is more appropriate to describe the proposed phenomenology, since it explains both the increase of the I penetration depth as a function of the implant dose and the very rapid change of the supersaturation versus time. Moreover, the proposed model takes account for the I recombination at the surface.

A Tight-binding Molecular Dynamics Study of the Dissociation of Boron Clusters in c-Si

Boron clusters with silicon self-interstitials have been implicated in the phenomenon of transient enhanced diffusion (TED) following ion implantation of boron and subsequent annealing steps. This paper explores possible dissolution mechanisms for boron-interstitial clusters during the simulation of a typical annealing process. Using tight-binding molecular dynamics (TBMD) and employing a Goodwin-Skinner-Pettifor sp-based TB model, we have been able to observe the complete dissolution of a B 4 I 4 cluster into the surrounding crystalline silicon matrix. Many unsuccessful attempts to observe dissolution are also presented, highlighting the effect of cluster stability, temperature and the role of vacancies in cluster dissolution. Though we can make no unambiguous statements on the definitive dissolution mechanism of boron-defect clusters based on one successful dissolution event, we can hint at key events that appear to be important, such as the diffusion of self-interstitials (presciently predicted by Pelaz et al. ), the "stranding" of boron atoms in their wake, and the importance of mobile boron-self-interstitial (B-I) pairs. The intrinsic diffusivity of boron in a c-Si lattice and its retardation of the diffusivity of Si self-interstitials is also discussed.

Low-dimension self-interstitial diffusion in α-Zr

The mobility of self-interstitials in α-zirconium (α-Zr) is studied with molecular dynamic (MD) and molecular static (MS) simulations, using Ackland’s many-body inter-atomic potential. The basal crowdion configuration is found to be the ground state. Four types of diffusion jumps can be identified via MS, in-plane in-line, in-plane off-line, out-of-plane in-line and out-of-plane off-line. The in-plane migration is dominated by one-dimensional crowdion motion along the [11\(\bar\Box2\Box\)0] directions, interrupted from time to time by off-line or out-of-plane jumps. Based on the MS results, the activation energies and pre-exponentials for the diffusion processes are determined by fits to the Arrhenius plots of Dc and Da. The diffusional anisotropy factor Dc/Da is also obtained, and compares well with experimental results. The mean frequency of each type of jumps is then found using Monte Carlo simulation, and is reported as a function of temperature. The mean lifetime and mean free path of the one-dimensional mobility are then obtained. The 1-D mean free path is found to be unimportant for sink separations involved under the usual irradiation damage conditions.

Direct observation of two-dimensional diffusion of the self-interstitials in crystalline Si

The two-dimensional (2D) diffusion of Si self-interstitials (I) from a submicron laterally confined source has been investigated in detail. High-resolution scanning capacitance microscopy was used for quantitative measurements of the B transient enhanced diffusion induced by the I flux generated by a low-energy Si implantation through a submicron dimension oxide mask. We show that the I depth penetration strongly depends on the original lateral size of the source. The 2D I diffusion has been well described by a 2D rate equations model, using the same physical parameters valid for one-dimensional diffusion.

Dynamics of self-interstitial cluster migration in pure α-Fe and Fe-Cu alloys

We report the results of molecular dynamics simulations of self-interstitial cluster diffusion in pure \ensuremath{\alpha}-Fe and in a dilute Fe--1.0 at. % Cu alloy for a number of cluster sizes, $nl~20.$ We find that the effect of this oversized substitutional solute is to enhance the three-dimensional character of small-cluster diffusion and to impact the general cluster diffusion properties. We explain this through a mechanism directly based on the interactions between the atomic displacement field of the Cu atoms and the self-interstitial clusters. Based on these results, we derive simple power laws for the extrapolation of migration energies and diffusion prefactors to larger sizes, required for longer-range microstructural evolution models. These laws represent an improvement over current parametrizations used in previous calculations.

Dynamics of self-interstitial migration in Fe-Cu alloys

We have performed molecular dynamics simulations of self-interstitial atom diffusion in pure \ensuremath{\alpha}-Fe and in a dilute Fe--1.0-at. % Cu alloy. We find that the presence of this oversized substitutional solute significantly alters the self-interstitial diffusion properties. We explain this through a mechanism directly based on the atomic strain field interactions between the Cu and the self-interstitial atom.