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At least 19 records

Enabling attractive-repulsive potentials in binary-collision-approximation monte-carlo codes for ion-surface interactions

Abstract Binary Collision Approximation (BCA) codes for ion-material interactions, such as SRIM, Tridyn, F-TRIDYN, and SDtrimSP, have historically been limited to screened Coulomb potentials even at low energies due to the difficulty in numerically solving the Distance of Closest Approach (DOCA) problem for attractive-repulsive potentials. Techniques such as direct n-body simulation or modifications to Newton’s method are either prohibitively costly or not guaranteed to work for all potentials. Advanced rootfinding techniques, such as companion matrix solvers, offer a solution. For many attractive-repulsive potentials, however, a companion matrix cannot be used directly, because there is no way to put the associated functions into a monomial basis form. A complementary technique is proxy rootfinding—by finding the best-fit polynomial approximant of a function, the zeros of the approximant can be guaranteed to be close to the zeros of the function. Using the Chebyshev basis and grid offers additional guarantees with regards to the quality of the approximation, the speed of convergence, and the avoidance of Runge’s phenomenon. By finding Chebyshev interpolants and using the Chebyshev-Frobenius companion matrix, the zeros of any real function on a bounded domain can be found. Here we show that using an Adaptive Chebyshev Proxy Rootfinder with Automatic Subdivision (ACPRAS) with appropriate scaling functions, numerical issues presented by attractive-repulsive potentials, including those of scale, can be handled. Using these techniques, we show that it is possible to include any physically reasonable interatomic potential in a BCA code, and to guarantee correctness of the resulting scattering angle calculations.

Materials Science↗

Sputtering of Surfaces by Ion Irradiation: A Comparison of Molecular Dynamics and Binary Collision Approximation Models to Laboratory Measurements

We compare various sputtering simulation methods to experimental results in both the low energy (<1 keV) and high energy (≥1 keV) impact regimes for argon ions impacting a pure copper substrate at normal incidence. Our results indicate that for high energy impacts, both binary collision approximation (BCA) and molecular dynamics methods can be used to generate reasonable predictions for the yield and energy distribution of the sputtered atoms. We also find reasonable agreement between the theoretical and experimental results down to impact energies of 600 eV. However, at 200 eV impact energies, significant discrepancies appear between the experimental and theoretical ejecta energy distributions in the peak position, the width of the energy distribution, and the magnitude of the high energy tail. These discrepancies appear to arise from the experimental results being only for atoms sputtered normal to the substrate surface, whereas the theoretical results are integrated over all 2π solid angles above the surface. Using the BCA code SDTrimSP and limiting the results to only atoms emitted within ±15° of the surface normal brings theory and experiment into reasonable agreement. These results suggest that for low energy impacts, the energy distribution of sputtered atoms is highly dependent on the emission angle of the ejecta.

Solar wind↗

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Burnett, K.↗

hPIC2: A hardware-accelerated, hybrid particle-in-cell code for dynamic plasma-material interactions

The exascale era of high performance computing promises to bring the field of computational plasma physics ever closer to the goal of accurate multiscale modeling. Such computers will rely on hardware acceleration to offload work to dedicated components, notably general-purpose graphics processing units (GPUs). However, devices from different manufacturers require software to be written with different parallel programming models, greatly increasing the code maintenance burden of applications designed to perform on more than one such device. hPIC2 is a hybrid plasma simulation code developed with the Kokkos performance portability framework to target the architectures that will drive exascale computing for the foreseeable future. As a hybrid simulation code, hPIC2 investigates the simultaneous use of various plasma models on the same domain, at the same time. hPIC2 also optionally couples to RustBCA, which accurately models ion-material interactions using the binary collision approximation (BCA) method. In conclusion, hPIC2 therefore achieves scalable performance on a variety of computing architectures when simulating complex and diverse plasmas, particularly near plasma-material interfaces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Crystallographic and temperature effects in low-energy collisions for plasma–material interactions

The interaction of plasma with materials is critical for the fundamental understanding of non-equilibrium processes and their wide application. Recent achievements in fusion energy research emphasize the importance of this problem. Because modelling and predicting plasma–material interactions (PMI) require considering a tremendous number of single plasma particle–surface interaction events, this type of modelling was, until recently, possible only within a binary collision approximation (BCA). The BCA approach considers materials as uniform temperature-insensitive media. The research presented here addresses the PMI problem within an atomistic-based approach for the first time at a statistically significant level. Approximately 10 5 molecular dynamics trajectories were generated for 100 eV deuterium ions interacting with a tungsten surface. The research demonstrated the critical importance of incorporating the discrete lattice structure of matter into the model. Deuterium penetration depth and fraction of backscattered deuterium ions strongly depend on the surface orientation, the impact incident ion directions, and the ions’ initial positions. On average, the BCA-based calculations underestimate the penetration depth by a factor of two or more, and the fraction of backscattered atoms is overestimated by a factor of two or more. As a result, increasing the material temperature from 500 to 3000 K reduces penetration depth by about 30% and increases the fraction of backscattered atoms by 250%.

36 MATERIALS SCIENCE↗

A far wing line shape theory and its application to the water continuum absorption in the infrared region. I

The present theory for the continuous absorption that is due to the far-wing contribution of allowed lines is based on the quasistatic approximation for the far wing limit and the binary collision approximation of one absorber molecule and one bath molecule. The validity of the theory is discussed, and numerical results of the water-continuum absorption in the IR region are presented for comparison with experimental data. Good agreement is obtained for both the magnitude and temperature dependence of the absorption coefficients.

Ma, Q.↗

Predicting displacement damage for ion irradiation: Origin of the overestimation of vacancy production in SRIM full-cascade calculations

Ion irradiation and implantation have wide applications that demand accurate determination of displacement damage profile and distribution of implanted ion concentration. The prediction of vacancies is especially important to determine displacements per atom (dpa), the standard parameter of primary radiation damage in materials. However, significant discrepancies exist in estimations of vacancies between full-cascade (F-C) and quick calculation (Q-C) options in the popular computer code SRIM. This study inspected the SRIM code and a relatively new code called Iradina, which uses a similar methodology, to develop an understanding of the origin of vacancy overestimation in the F-C options for SRIM and Iradina. Here, we found that the default values of thresholds (namely final energy in SRIM and replacement energy in Iradina) in displacement production calculations results in excessively large number of calculated vacancies and very few replacements. After conducting multiple calculations using SRIM, Iradina, and MARLOWE (all based on the binary collision approximation), a comparison of the results indicates that there is a shortcoming in the SRIM and Iradina F-C methodology for treating near-threshold collisions. This issue is responsible for the deficiency of replacements and excess of calculated vacancies in the SRIM and Iradina F-C results. Drawing on the principles of collision physics, we propose recommendations for modifying the source codes to address these issues.

36 MATERIALS SCIENCE↗

Multidisciplinary benchmarks of a conservative spectral solver for the nonlinear Boltzmann equation

The Boltzmann equation describes the evolution of the phase-space probability distribution of classical particles under binary collisions. Approximations to it underlie the basis for several scholarly fields, including aerodynamics and plasma physics. While these approximations are appropriate in their respective domains, they can be violated in niche but diverse applications which require direct numerical solution of the original nonlinear Boltzmann equation. An expanded implementation of the Galerkin–Petrov conservative spectral algorithm is employed to study a wide variety of physical problems. Enabled by distributed precomputation, solutions of the spatially homogeneous Boltzmann equation can be achieved in seconds on modern personal hardware, while spatially-inhomogeneous problems are solvable in minutes. Here, several benchmarks are presented focusing on accuracy compared to both analytic theoretical predictions and other Boltzmann solvers. These benchmarks span several physical domains including weakly ionized plasma, gaseous fluids, and atomic-plasma interaction.

97 MATHEMATICS AND COMPUTING↗

A linked-scale coupled model of mass erosion and redistribution in plasma-exposed micro-foam surfaces

Surface evolution due to exposure to harsh environments is of importance in many scientific and technological applications. In plasma-exposed materials, the surface receives charged particles from the plasma, leading to a series of processes that drive the system far from equilibrium and may lead to the severe deterioration of the surface properties. Although surface morphological changes are driven by atomic collisions taking place over picoseconds and nanometers, these processes result in mass loss and redistribution of matter over much larger length and time scales. This necessitates a multi-scale approach capable of capturing the range of processes linking primary atomic collision events with engineering-level surface geometry changes. In this paper, we develop a computational model to simulate the morphological evolution and effective erosion rate of micro-architected tungsten foams during low-energy plasma ion bombardment. Furthermore, the model acts on several length scales, with the energy and angular dependence of the sputtering yield of flat tungsten surfaces determined using the SRIM code based on the binary collision approximation. This information is introduced into a low-fluence, short-term Monte Carlo raytracing model, and further into a high-fluence, long-term particle transport model. In the latter, material particles representing billions of atoms are described in a digitized 3-D representation of the foam structure from X-ray tomography data, and are sputtered off and redeposited using the atomistic information. We show that the redeposition of sputtered atoms leads to partial self-healing in the bottom layers with a sharp reduction in the sputtering coefficient of low density foams, roughly 25% of the solid W value. This is in qualitative agreement with recent experiments on low porosity W structures. At high fluence, the foam structure degrades considerably as there are fewer ligaments available to recapture sputtered atoms and, consequently, the sputtering rate increases again.

36 MATERIALS SCIENCE↗

Radiation induced athermal diffusivity in uranium mononitride

Uranium mononitride (UN) is one of the ceramic nuclear fuel alternatives to oxide fuel considered for light water reactors and advanced reactor designs. Properties like self- and fission gas diffusivity need to be better understood, given that they influence key fuel performance phenomena such as fission gas swelling and release. In particular, the radiation induced athermal (D 3 ) diffusivity remains challenging to accurately predict and has only been sparsely characterized in UN, despite its importance as it likely governs diffusion at the low temperatures this high-thermal-conductivity fuel form may operate. Molecular Dynamics simulations are used to estimate the mean square displacement induced by a primary knock-on atom (PKA) with a given kinetic energy. These results are combined with the PKA energy distributions obtained from binary collision approximation calculations to obtain the displacement due to a particular fission fragment. Finally, this is combined with experimental fission fragment yields to determine the displacement due to an average fission event and, thus, express the athermal diffusivity as a function of the fission rate density. These results are in excellent agreement with available experimental data. In conclusion, a particular importance is given to the understanding and the quantification of the variability of these results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Molecular dynamics simulations of reflection and sputtering behavior of boron under deuterium ion irradiation

Boronization is a commonly used method of wall conditioning in fusion reactors. The application of boron films to the plasma-facing materials results in enhanced plasma performance due to the reduction of intrinsic impurities. This is primarily driven by a reduction in oxygen content that is chemically trapped in the boron film. The reactive nature of these boron films also raises questions concerning interactions with hydrogen isotopes. In this work, boron-deuterium interactions were studied using molecular dynamics (MD). Reactive force field potentials were used to model the chemical interactions between B and D. An amorphous boron substrate was irradiated by D atoms at varying incident energies, 10 eV < E i < 150 eV and angles, 0° < α < 85°. The reflection probability was calculated and compared to results from the commonly-used binary collision approximation (BCA) method. This comparison found that the BCA underestimated the reflection probability at E i < 35 eV and α > 45 ∘ . The source of this discrepancy was found to be the surface binding energy model. The BCA calculation with an isotropic surface binding energy model was more closely aligned to the MD result. This, in combination with a correction function based on the MD results allows for corrections to the reflection probability of deuterium impinging on boron surfaces. The sputtering of the substrate material was also studied. While this study did not contain sufficient events to quantitatively describe the sputtering behavior, some qualitative results emerged: namely, chemical sputtering of B and D-containing molecules (BD, BD 2 , BD 3 ) at low ( < 20 eV) incident deuterium energies. This result suggests that chemical sputtering could be a significant factor in limiting boron coating lifetime when exposed to lower ion energies, such as those in detached plasmas. The results show that chemical interactions should be taken into account when modeling the interactions between D ions and B surfaces.

Boron↗

Quantitative investigation of surface structure and interatomic potential with impact-collision ion scattering spectroscopy

Helium ion beam interactions with materials have important implications for magnetic confinement fusion, material modification, and helium ion microscopy. These interactions depend on the precise physics of how helium ions channel into the materials, which can vary greatly based on the local crystalline orientation. Here, we performed a dedicated experiment to investigate helium ion channeling in a well-characterized tungsten single crystal. Time-of-flight impact-collision ion scattering spectroscopy was used to obtain multi-angle maps of the backscattering intensity for 3 keV He + → W(111). We found that the backscattering intensity profile arising from helium ion channeling could be well described by a shadow cone analysis. This analysis revealed that subsurface W atoms as deep as the ninth monolayer contributed to the backscattering intensity profile. Binary collision approximation simulations were performed with MARLOWE to model the experimental maps with sufficient accuracy to allow for quantitative comparisons using reliability factors. These quantitative comparisons were applied to investigate how the W lattice structure and He–W interatomic potential affect the multi-angle maps.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nanoscale dynamics during self-organized ion beam patterning of Si. II. Kr + bombardment

Understanding the self-organized ion beam nanopatterning of elemental semiconductors, particularly silicon, is of intrinsic scientific and technological interest. This is the second component of a two-part coherent x-ray scattering and x-ray photon correlation spectroscopy (XPCS) investigation of the kinetics and fluctuation dynamics of nanoscale ripple development on silicon during 1 keV Ar + (part I) and Kr + bombardment at 65° polar angle. Here it is found that the ion-enhanced viscous flow relaxation is essentially equal for Kr + -induced patterning as previously found for Ar + patterning despite the difference in ion masses. However, the magnitude of the surface curvature-dependent roughening rate in the early-stage kinetics is larger for Kr + than for Ar + , consistent with expectations that the heavier ion gives an increased mass redistributive contribution to the initial surface instability. As with the Ar + case, fluctuation dynamics in the late stage show a peak in correlation times at the length scale corresponding to the dominant structural feature on the surface—the ripples. Finally, it is shown that speckle motion during the surface evolution can be analyzed to determine spatial inhomogeneities in erosion rate and ripple velocity. This allows the direction and speed of ripple motion to be measured in a real time experiment. In the present case, ripple motion is found to be into the projected direction of the ion source, in contrast to expectations from an existing sputter erosion driven model with parameters derived from binary collision approximation simulations.

36 MATERIALS SCIENCE↗

Machine Learning for Predictive Performance Analysis in Charged Particle Beam Tools

Imaging methods driven by probes, electrons, and ions have played a dominant role in modern science and engineering. Opportunities for machine vision and AI that focus on consumer problems like driving and feature recognition, are now presenting themselves for automating aspects of the scientific processes. This proposal aims to enable and drive discovery in ultra-low energy implantation by taking advantage of faster processing, flexible control and detection methods, and architecture-agnostic workflows that will result in higher efficiency and shorter scientific development cycles. Custom microscope control, collection and analysis hardware will provide a framework for conducting novel in situ experiments revealing unprecedented insight into surface dynamics at the nanoscale. Ion implantation is a key capability for the semiconductor industry. As devices shrink, novel materials enter the manufacturing line, and quantum technologies transition to being more mainstream. Traditional implantation methods fall short in terms of energy, ion species, and positional precision. Here we demonstrate 1 keV focused ion beam Au implantation into Si and validate the results via atom probe tomography. We show the Au implant depth at 1 keV is 0.8 nm and that identical results for low energy ion implants can be achieved by either lowering the column voltage, or decelerating ions using bias – while maintaining a sub-micron beam focus. We compare our experimental results to static calculations using SRIM and dynamic calculations using binary collision approximation codes TRIDYN and IMSIL. A large discrepancy between the static and dynamic simulation is found that is due to lattice enrichment with high stopping power Au and surface sputtering. Additionally, we demonstrate how model details are particularly important to the simulation of these low-energy heavy-ion implantations. Finally, we discuss how our results pave a way to much lower implantation energies, while maintaining high spatial resolution.

47 OTHER INSTRUMENTATION↗

Probability Density Function for the spatial and intensity distribution of neutron-induced defects in Silicon

The ability to model semiconductor device degradation under neutron irradiation depends upon having a robust modeling capability for the neutron-induced collision cascades as well as a means to analytically fit the resulting probability distributions of defect production and ionizing energy deposition for purposes of extrapolation to low-probability, high-consequence scenarios. In this paper, the widely-utilized binary collision approximation codes MARLOWE and SRIM are deployed in conjunction with a critical examination of their parameterizations as benchmarked against higher-fidelity molecular dynamics simulations. A simple 3-parameter form described by the Generalized Logistic Distribution is shown to be a good fit to Frenkel pair and ionization intensity distributions in bulk silicon. The BCA codes are then applied to simulate cascades in 5 nm layers of a representative gate-all-around nanosheet transistor, where joint probability distributions of threshold levels of damage to multiple layers are evaluated.

36 MATERIALS SCIENCE↗

Measurement and Simulation of Ultra-Low-Energy Ion–Solid Interaction Dynamics

Ion implantation is a key capability for the semiconductor industry. As devices shrink, novel materials enter the manufacturing line, and quantum technologies transition to being more mainstream. Traditional implantation methods fall short in terms of energy, ion species, and positional precision. Here, we demonstrate 1 keV focused ion beam Au implantation into Si and validate the results via atom probe tomography. We show the Au implant depth at 1 keV is 0.8 nm and that identical results for low-energy ion implants can be achieved by either lowering the column voltage or decelerating ions using bias while maintaining a sub-micron beam focus. We compare our experimental results to static calculations using SRIM and dynamic calculations using binary collision approximation codes TRIDYN and IMSIL. A large discrepancy between the static and dynamic simulation is found, which is due to lattice enrichment with high-stopping-power Au and surface sputtering. Additionally, we demonstrate how model details are particularly important to the simulation of these low-energy heavy-ion implantations. Finally, we discuss how our results pave a way towards much lower implantation energies while maintaining high spatial resolution.

36 MATERIALS SCIENCE↗

Collisional redistribution of radiation. III - The equation of motion for the correlation function and the scattered spectrum

Computations were made of the scattering of monochromatic radiation by a degenerate atom in the binary-collision approximation for field strengths whose products of the Rabi frequency for atomic transition and the duration of a strong collision are much less than 1. An expression of motion for the correlation function is derived which does not exclude the region where thermal correlations may be neglected; the equation is valid outside the quantum-regression regime, and has a straightforward solution for practical cases. Solutions for the weak-field linear response regime are presented in terms of generalized absorption and emission profiles which depend on the indices of the atomic multipoles.

Burnett, K.↗

Solar Wind Ion Sputtering of Sodium from Silicates Using Molecular Dynamics Calculations of Surface Binding Energies

For nearly 40 yr, studies of exosphere formation on airless bodies have been hindered by uncertainties in our understanding of the underlying ion collisional sputtering by the solar wind (SW). These ion impacts on airless bodies play an important role in altering their surface properties and surrounding environment. Much of the collisional sputtering data needed for exosphere studies come from binary collision approximation (BCA) sputtering models. These depend on the surface binding energy (SBE) for the atoms sputtered from the impacted material. However, the SBE is not reliably known for many materials important for planetary science, such as plagioclase feldspars and sodium pyroxenes. BCA models typically approximate the SBE using the cohesive energy for a monoelemental solid. We use molecular dynamics (MD) to provide the first accurate SBE data we are aware of for Na sputtered from the above silicate minerals, which are expected to be important for exospheric formation at Mercury and the Moon. The MD SBE values are ∼8 times larger than the Na monoelemental cohesive energy. This has a significant effect on the predicted SW ion sputtering yield and energy distribution of Na and the formation of the corresponding Na exosphere. We also find that the SBE is correlated with the coordination number of the Na atoms within the substrate and with the cohesive energy of the Na-bearing silicate. Our MD SBE results will enable more accurate BCA predictions for the SW ion sputtering contribution to the Na exosphere of Mercury and the Moon.

Lunar surface↗