Toward a predictive atomistic model of ion implantation and dopant diffusion in silicon

We review the development and application of kinetic Monte Carlo simulations to investigate defect and dopant diffusion in ion implanted silicon. In these types of Monte Carlo models, defects and dopants are treated at the atomic scale, and move according to reaction rates given as input parameters. These input parameters can be obtained from first principles calculations and/or empirical molecular dynamics (MD) simulations or can be extracted from fits to experimental data. Time and length scales differing several orders of magnitude can be followed with this method, allowing for direct comparison with experiments. The different approaches are explained and some results presented.     

Cutting and controlled modification of graphene with ion beams

Using atomistic computer simulations, we study how ion irradiation can be used to alter the morphology of a graphene monolayer, by introducing defects of specific type, and to cut graphene sheets. Based on the results of our analytical potential molecular dynamics simulations, a kinetic Monte Carlo code is developed for modeling morphological changes in a graphene monolayer under irradiation at macroscopic time scales. Impacts of He, Ne, Ar, Kr, Xe, and Ga ions with kinetic energies ranging from tens of eV to 10?MeV and angles of incidence between 0° and 88° are studied. Our results provide microscopic insights into the response of graphene to ion irradiation and can directly be used for the optimization of graphene cutting and patterning with focused ion beams.     

Monte Carlo simulations in zeolites

In this short review, the applications of Monte Carlo simulations to the study of the adsorption and diffusion of hydrocarbons in zeolites are discussed. We focus on those systems for which the conventional molecular simulation techniques, molecular dynamics and Monte Carlo, are not sufficiently efficient. In particular, to simulate the adsorption and diffusion of long-chain hydrocarbons, novel Monte Carlo techniques have been developed. Here we discuss configurational-bias Monte Carlo (CBMC) and kinetic Monte Carlo (KMC). CBMC was developed to compute the thermodynamic properties. KMC is applied to compute transport properties. The use of these methods is illustrated with examples of technological importance.     

Cascade damage evolution: rate theory versus kinetic Monte Carlo simulations

The thermal evolution of defects produced by ion irradiation is studied by kinetic Monte Carlo and Rate Theory approaches. An isochronal annealing is simulated to evidence the different thermally activated mechanisms that govern defect evolution. KMC simulations show that in the case of ion irradiation, additional recovery peaks should be expected, in comparison to electron irradiation conditions. A comparison between kMC and RT results indicates that some of these peaks are due to spatially – correlated recombinations that occur at low temperature. Therefore kMC and RT approaches differ at low temperature. However, at higher temperature results obtained by both models are in near perfect agreement. In addition, we studied the influence of vacancy cluster mobility on the evolution of damage. KMC simulations show that the mobility of V₂, V₃ and V₄ clusters does not significantly affect the evolution of defects and can be neglected in these conditions.     

Atomic mechanisms of grain boundary diffusion: Low versus high temperatures

We analyze recent results of atomistic computer simulations of grain boundary (GB) diffusion in metals. At temperatures well below the bulk melting point T_m GB diffusion occurs by random walk of individual vacancies and self-interstitials. Both defects are equal participants in the diffusion process and can move by a large variety of diffusion mechanisms, many of which are collective transitions. GB diffusion coefficients can be computed by kinetic Monte Carlo simulations. At high temperatures, the presence of large concentrations of point defects is likely to alter the diffusion mechanisms. Molecular dynamics simulations of GB structure and diffusion in copper reveal a continuous GB premelting in close vicinity of T_m. However, diffusion in high-energy GBs becomes almost independent of the GB structure (“universal”) at temperatures well below T_m. This behavior can be tentatively explained in terms of heterophase fluctuations from the solid to the liquid phase. The exact diffusion mechanisms in the presence of heterophase fluctuations are yet to be established.     

A method for measuring tissue-equivalent dose using a pin diode and activation foil in epithermal neutron beams with EN < 100 keV

Silicon (Si) pin diodes can be used for neutron dosimetry by observing the change in forward bias voltage caused by neutron induced displacement damage in the diode junction. Pin diode energy response depends on Si displacement damage KERMA (K(Si)). It is hypothesised that tissue-equivalent (TE) neutron dose could be expressed as a linear combination of K(Si) and foil activation terms. Monte Carlo simulations (MCNP) of parallel monoenergetic neutron beams incident on a cylindrical TE phantom were used to calculate TE dose, K(Si) and Au, Cu and Mn foil activations along the central axis of the phantom. For spectra with neutron energies <100 keV, it is possible to estimate the TE kerma based on silicon damage kerma and Cu or Mn foil measurements. More accurate estimates are possible for spectra where the maximum neutron energy does not exceed 30 keV.     

Energy deposition control during cluster bombardment: a molecular dynamics view

Molecular dynamics simulations are performed to model C60 and Au3 bombardment of a molecular solid, benzene, in order to understand the energy deposition placement as a function of incident kinetic energy and incident angle. Full simulations are performed for 5 keV projectiles, and the yields are calculated. For higher energies, 20 and 40 keV, the mesoscale energy deposition footprint model is employed to predict trends in yield. The damage accumulation is discussed in relationship to the region where energy is deposited to the sample. The simulations show that the most favorable conditions for increasing the ejection yield and decreasing the damage accumulation are when most of the projectile energy is deposited in the near-surface region. For molecular organic solids, grazing angles are the best choice for achieving these conditions.     

Embedded atom potentials in fcc and bcc metals

A new embedded atom potential has been proposed in this paper. The potential is expressed by simple functions and is applicable to the molecular dynamics simulations of large atomic systems. The potential parameters are determined from the experimental data using the cohesive energy, Born stability, elastic constants, C₁₁,C₁₂ and C₄₄, the formation energy of a vacancy. In case of fcc the stacking fault energy is also used to fit parameters. The potential functions for copper, silver and gold for fcc metals and for bcc metals Nb, Ta and Va are presented.     

Thermodynamic properties of amorphous silicon via tight binding simulations

An atomic-scale structure of amorphous silicon, generated by reverse Monte Carlo, has been used as a starting configuration for finite temperature molecular dynamics simulations performed by an orthogonal tight binding Hamiltonian. Structural, dynamic, elastic and electronic structure properties have been investigated in the range of temperatures up to and above the melting transition. The amorphous silicon structure undergoes a melting transition at a temperature sensibly smaller than that of the crystalline structure. Above this temperature, the structure has the same properties of an under-cooled liquid and it has a metallic behavior.     

Detection of nuclear recoils in prototype dark matter detectors, made from Al, Sn and Zn superheated superconducting granules

This work is part of an ongoing project to develop a superheated superconducting granule (SSG) detector for cold dark matter and neutrinos. The response of SSG devices to nuclear recoils has been explored irradiating SSG detectors with a 70 MeV neutron beam. The aim of the experiment was to test the sensitivity of Sn, Al and Zn SSG detectors to nuclear recoil energies down to a few keV. The detector consisted of a hollow teflon cylinder (0.1 cm³ inner volume) filled with tiny superconducting metastable granules embedded in a dielectric medium. The nuclear recoil energies deposited in the SSG were determined measuring the neutron scattering angles with a neutron hodoscope. Coincidences in time between the SSG and the hodoscope signals have been clearly established. In this paper the results of the neutron irradiation experiments at different SSG intrinsic thresholds are discussed and compared to Monte Carlo simulations. The results show that SSG are sensitive to recoil energies down to 1 keV. The limited angular resolution of the neutron hodoscope prevented us from measuring the SSG sensitivity to even lower recoil energies.     

Effect of energy nonequipartition on the transport properties in a granular mixture

The Boltzmann kinetic theory is used to analyze the effect of energy nonequipartition on the pressure and the shear viscosity of a granular binary mixture under simple shear flow. Theory and Monte Carlo simulations show that both quantities exhibit a non–monotonic behaviour with the mass ratio in contrast to the predictions made from previous theories based on the equipartition assumption. Our results agree qualitatively well with recent molecular dynamics simulations performed by Alam and Luding [Granular Matter 4, 139 (2002)]. The authors acknowledge partial support from the MCYT (Spain) through Grants No. BFM2001-0718 and ESP2003-02859.     

Estimating Errors in the Inspection of Complex Products

It has been experimentally determined that human inspectors visually examining a complex product for defects may be expected to miss 15 percent of the defects present. Under the conditions of this experiment (30 percent lot fraction defective), this level of performance would result in a type II error of 10 percent and a type I error of 3 percent. A combination of iconic and Monte Carlo simulation was used in performing the experiment.     

The multiple scattering profile in gamma ray Compton studies

The spectrum of 662 keV gamma radiation, multiply scattered by a nickel sample, has been measured directly in a Compton scattering experiment at a scattering angle of 104°. Under these conditions the multiple profile extends well beyond the single and this affords an opportunity to check the Monte Carlo simulation commonly used to correct the single line shapes (Compton profiles). Measurements in reflection and transmission geometries on thin samples produced markedly different multiple profiles which were found to agree with the simulations within the statistical accuracy of the comparison. This provides the first direct validation of the multiple scattering correction procedure in Compton profile analysis.     

Atomic-scale computer simulation of primary irradiation damage effects in metals

Molecular dynamics (MD) has been used extensively to simulate displacement cascades in metals; and this paper contains a summary of the progress made to date. It includes results dealing with the effect of primary knock-on atom energy and irradiation temperature on defect formation in a variety of metals. It is shown that in addition to data on the number of defects produced, quantitative information is available on the distribution of defects created in clusters. Thus, the nature of the primary damage state is now clear. The successful development of multiscale models to describe the evolution of radiation damage microstructure and its impact on material performance requires detailed atomic-level information about the stability, motion and interaction of defects. This is starting to be obtained by MD and some recent results are discussed. The place of atomic-scale modelling in the multiscale problem of radiation damage is shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modelling materials driven far from equilibrium

Materials driven from equilibrium offer a challenging field for both time and space multiscale modelling. In materials under irradiation the elementary damaging process, that is, the nuclear collision leading to the displacement cascade, is modelled by molecular dynamics (≈ 10 ps, 10³ nm³), whereas the later stage recovery process is modelled by kinetic Monte Carlo (≈ years, 10⁴ nm³); at still a coarser scale, grain boundary segregations are modelled by a meanfield approximation of the very same atomistic model as used in kinetic Monte Carlo modelling. Connecting this broad range of time scales helps to elucidate basic issues on the criteria for alloy stability under irradiation. Irradiation effects on plasticity are beginning to be modelled in the same spirit; a first molecular dynamics study of the interaction of cascade debris with gliding dislocations has been reported together with the first results of mesoscale modelling of dislocation dynamics in the course of a nanoindentation test. Such studies can be extended to materials processed by ball milling.     

Monte Carlo simulations of the photon calibration fields at the underground laboratory of PTB

A unique photon calibration facility operated by Physikalisch-Technische Bundesanstalt (PTB) provides photon fields with area dose rates in the order of the natural environmental radiation and even below. This facility is located in an underground laboratory in the Asse salt mine at a depth of 490 m below ground, where the ambient dose equivalent rate is only 2 nSv h(-1). Radioactive sources of the nuclides (241)Am, (57)Co, (137)Cs, (60)Co and (226)Ra are used to generate photon fields with different characteristics. In the past, the basic properties of the photon field, especially the area dose rate at the reference point and the mean energy of the photon spectra, were calculated by using analytic methods. However, information about scattered photons is only accessible through an investigation of spectra by performing Monte Carlos simulations. Therefore, the photon spectra at the reference point of the calibration facility were calculated using the Monte Carlo transport code MCNP. The results obtained by using this method are of relevance for the traceability of the reference dose rate values to PTB's primary standards, as well as for the determination of the mean photon energy of the spectra. The latter was calculated with respect to the different quantities 'photon fluence', 'air kerma' and 'ambient dose equivalent'. The origin of the scattered component in the photon spectrum is investigated in detail by studying the photon field produced by the quasi-monoenergetic gamma emitter (137)Cs (E(γ) = 662 keV) under various geometrical conditions. Implications of the Monte Carlo simulations on the traceability of the dose rate reference values as well as on the assessment of uncertainties will be described.     

Critical Temperatures of Random Iron–Cobalt Overlayers on the fcc-Cu(001) Substrate

We have theoretically investigated thermodynamic properties of random iron–cobalt monolayer deposited on the fcc(001) face of copper. The effective two-dimensional Heisenberg Hamiltonian was constructed from first principles and used to estimate the Curie temperature. The random-phase approximation as well as Monte Carlo approach are used and critically compared. Calculations indicate a weak maximum of the Curie temperature for Fe-rich composition of the overlayer.     

Molecular dynamics simulations of energetic aluminum cluster deposition

We investigated energetic aluminum cluster deposition using a classical molecular dynamics (MD) simulation and the Metropolis Monte Carlo (MC) simulation. When local area reached melting state on the surface around impact point of an energetic aluminum cluster during a few ps, intermixing was easily achieved and a good epitaxial film with optimum bulk density was formed. For excellent film growth using cluster impact, it is necessary to make local area temperature higher than melting temperature on the surface around the impact point of an energetic cluster.