Binary Collision Approximation Code Research Articles

Coupling Nuclear Predictions into Damage Simulations with SPECTRA-PKA

Modern nuclear physics software is well validated, providing advanced capabilities to support the engineering of the future generations of fission and fusion reactors. Transport simulators can model the transport of neutrons through reactor geometries, and inventory codes can accurately predict transmutation and activation. Meanwhile, material modeling applies a variety of techniques to understand how structural damage and composition changes will alter the properties of materials, ultimately limiting their usable lifetime in a reactor. Bridging the gap between nuclear simulation tools and materials modeling is a necessary step if these lifetimes are to be accurately predicted, which, for fusion, is critical to provide the necessary assurance of commercial viability. SPECTRA-PKA is a tool developed to compute the rates of structural damage source events, i.e. the primary knock-on atoms (PKAs), using the same nuclear data as used by transport and inventory simulations. Now, it has been interfaced with the binary collision approximation code SDTrimSP, allowing those PKA events, distributed spatially and temporally in an atomic system, to be converted into damage cascades. This computational infrastructure provides insight into the variation in damage distributions between different materials under the same nuclear environment. Example simulations for materials under fusion reactor conditions demonstrate how the rich detail of the nuclear environment can be applied directly to modeling, without the need for integral-average measures that omit those details.

Ion–surface interactions in plasma-facing material design

A multi-scale simulation framework for ion–solid interactions in plasma-exposed materials provides crucial insight into advancing fusion energy and space electric propulsion. Leveraging binary-collision approximation (BCA) simulations, the framework uniquely predicts sputter yields and analyzes material transport within volumetrically complex materials. This approach, grounded in the validated BCA code TRI3DYN, addresses key limitations in existing models by accurately capturing ion–solid interaction physics. A case study is presented, highlighting the framework’s ability to replicate experimental sputter yield results, underscoring its reliability and potential for designing durable materials in harsh plasma environments. Insights into sputtering transport phenomenology mark a significant advancement in material optimization for improved resilience in plasma-facing applications.

Assessing trajectory-dependent electronic energy loss of keV ions by a binary collision approximation code

The inelastic energy deposition of energetic ions is a decisive quantity for numerous industrial-scale applications, such as sputtering and ion implantation, yet the underlying physics being governed by dynamic many-particle processes is commonly only qualitatively understood. Recently, transmission experiments on single-crystalline targets (Phys. Rev. Lett. 124, 096601 & Phys. Rev. A 102, 062803) revealed a complex energy scaling of the inelastic energy loss of low-energy ions heavier than protons along different trajectories. We use a Monte Carlo like binary collision approximation code equipped with an impact-parameter-dependent modeling of the inelastic energy losses to assess the role of local contributions to electronic excitations in these cases. We compare angular intensity distributions of calculated trajectories with experimental results for 50-keV 4He and 100-keV 29Si ions transmitted in a time-of-flight setup through single-crystalline silicon (001) foils with nominal thicknesses of 200 and 50 nm, respectively. In these calculations, we employ different models of electronic energy loss, i.e., local and nonlocal forms for light and heavy projectiles. We find that the vast number of projectiles are eventually channeled along their trajectories, regardless of the alignment of the crystal with respect to the incident beam. It is, however, only when local electronic energy loss is considered that the simulated two-dimensional maps and energy distributions show excellent agreement with the experimental results, where channeling leads to significantly reduced stopping, especially for heavier projectiles. We demonstrate the relevance of these effects for ion implantations by assessing the nonlinear and nonmonotonic scaling of the ion range with the thickness of a random surface layer. Published by the American Physical Society 2024

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

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.

On the missing single collision peak in low energy heavy ion scattering

We present experimental and simulation data on the oblique angle scattering of heavy Sn ions at 14keV energy from a Mo surface. The simulations are performed with the binary collision approximation codes TRIM, TRIDYN, TRI3DYN, SDTrimSP, and IMSIL. Additional simulations were performed in the molecular dynamics framework with LAMMPS. Our key finding is the absence of an expected peak in the experimental energy spectrum of backscattered Sn ions associated with the pure single collision regime. In sharp contrast to this, however, all simulation codes we applied do show a prominent single collision signature both in the energy spectrum and in the angular scatter pattern. We discuss the possible origin of this important discrepancy and show in the process, that widely used binary collision approximation codes may contain hidden parameters important to know and to understand.

Modeling experimental low energy ion scattering multi-angle maps with molecular dynamics FAN

Multi-angle maps obtained with low energy ion scattering (LEIS) are not only a convenient way to visualize the atomic-level surface structure of single crystals, but also provide a comprehensive data set that is useful for quantitative fitting with models. However, modeling these maps is often difficult due to the complexity of the scattering process, as well as the number of simulations needed to accurately reproduce a single experimental map. For example, traditional molecular dynamics (MD) and binary collision approximation (BCA) simulations typically require on the order of one billion simulated ion trajectories to obtain sufficient statistics. This problem is exacerbated when modeling impact-collision ion scattering spectroscopy (ICISS) maps, as backscattering cross sections are much smaller than forward-scattering cross sections. A workaround to this problem was given by Neihus and Spitzl in the form of FAN (Niehus and Spitzl, 1991), a simulation that approximates the angular dependence of the backscattering signal by only simulating ion trajectories that reach and emanate from lattice atoms, using a BCA code. This greatly reduces the number of trajectories that must be calculated, though it can oversimplify some of the more complex collision sequences. In this work, we develop a fully three-dimensional FAN code that uses MD to simulate trajectories rather than the BCA. Our approach exploits the improved speed of FAN, while retaining the more accurate ion trajectory calculations of MD. We apply the MD-FAN simulation to model LEIS measurements on two surfaces. First, we benchmark our MD-FAN simulation in a comparison to a BCA simulation for 3 keV He+ incident on W(111) that has been previously reported in Wong et al. (2020). The MD-FAN map had stronger agreement with the experimental ICISS measurements than did the BCA map, despite containing nearly 100-fold fewer ion trajectories. Second, to obtain experimental data sets for a more complex surface, we perform experimental ICISS measurements using a 3 keV He+ beam on a magnetite single crystal, Fe3O4(001) to generate a multi-angle map. The simulated MD-FAN map for the Fe3O4(001) surface once again agreed well with the experimental map, allowing for quantitative comparisons. The MD-FAN simulation also provided insight into the scattering processes, revealing that some of the observed pattern arises from 3 keV He+ that have backscattered into the detector from Fe atoms more than 2 nm below the surface.

Influence from the electronic shell structure on the range distribution during channeling of 40–300 keV ions in 4H-SiC

Ion implantation is performed in 4H-SiC with 11B, 27Al, 31P, 51V, 71Ga, and 75As ions using energies between 40 and 300 keV at various fluences along the [000-1] or the ⟨11-2-3⟩ axes. Secondary ion mass spectrometry is utilized to determine the depth distribution of the implanted elements. A Monte Carlo binary collision approximation (MC-BCA) code for crystalline targets is then applied to explain the influence of the electronic shell structure on electronic stopping and the obtained channeled ion depth distributions. The results show that, as the atomic number increases in a row of the periodic table, i.e., as the ionic radius decreases and the electron clouds densify, the interaction with the target electrons increases and the range is reduced. The decreased range is particularly pronounced going from 27Al to 31P. The reduction in channeling depth is discussed in terms of electronic shells and can be related to the ionic radii, as defined by Kohn–Sham. It is shown that these shell effects in channeled implantations can easily be included in MC-BCA simulations simply by modifying the screening length used in the local treatment of electronic stopping in channels. However, it is also shown that, for vanadium ions with an unfilled d-shell, this simple model is insufficient to predict the electronic stopping in the channels.

Sputtering of nanostructured tungsten and comparison to modelling with TRI3DYN

He-induced nanostructured tungsten (so-called W-fuzz) was bombarded with Ar ions under 60° and the dynamic erosion behaviour was experimentally investigated. By using a highly sensitive quartz-crystal-microbalance technique in a particle catcher configuration, the sputtered particles distribution of W-fuzz could be evaluated. In contrast to a flat sample, where sputtered particles are emitted primarily in forward direction, we find that W-fuzz samples emit sputtered particles preferably in backward direction (i.e. in the direction of the incident ion beam). After continuous Ar irradiation of a W-fuzz sample the distribution approaches that of a flat sample. In addition to experimental data we also show modelling results obtained with a state-of-the-art Monte-Carlo (MC) binary collision approximation (BCA) code TRI3DYN in full 3D. Surface morphology changes as monitored by SEM as well as the dynamic sputtering behaviour can be well reproduced by the full 3D MC-BCA code.

Influence of a thin amorphous surface layer on de-channeling during aluminum implantation at different temperatures into 4H-SiC

Ion implantation is an important technique in semiconductor processing and has become a key technology for 4H-SiC devices. Today, aluminum (Al) implantations are routinely used for p-type contacts, p+-emitters, terminations and many other applications. However, in all crystalline materials, quite a few ions find a path along a crystal channel, so-called channeling, and these ions travel deep into the crystal. This paper reports on the channeling phenomenon during Al implantation into 4H-SiC, and in particular, the influence of a thin native oxide will be discussed in detail. The effects of thermal lattice vibrations for implantations performed at elevated temperatures will also be elucidated. 100 keV Al ions have been implanted along the [000-1] direction employing samples with 4° miscut. Before implantation, the samples have been aligned using the blocking pattern of backscattered protons. Secondary ion mass spectrometry has been used to record the Al depth distribution. To predict implantation profiles and improve understanding of the role of crystal structure, simulations were performed using the Monte-Carlo binary collision approximation code SIIMPL. Our results show that a thin surface layer of native oxide, less than 1 nm, has a decisive role for de-channeling of aligned implantations. Further, as expected, for implantations at elevated temperatures, a larger degree of de-channeling from major axes is present due to increased thermal vibrations and the penetration depth of channeled aluminum ions is reduced. The values for the mean-square atomic displacements at elevated temperatures have been extracted from experimental depth profiles in combination with simulations.

BCA simulations of ion irradiation of tungsten fuzz

A model based on the Binary Collision Approximation (BCA) approach is developed to study the penetrative and sputtering properties of tungsten “fuzz” under low-energy ion bombardment. In the model, tungsten fuzz structures are created with building blocks and then are processed to generate finite element meshes, which are used as input in the BCA code IM3D. Fuzz structures of different densities and textures are created by changing the parameters of the building blocks. Helium and argon ions with different energies are applied to bombard the fuzz structures. Simulation results confirm that low-energy helium ions can penetrate several hundred nanometers into tungsten fuzz just by going through the open channels or by bouncing between the fuzz tendrils. The penetrative properties depend on the fuzz density, the orientation and length of the building blocks, and do not depend on the energy of helium ions. These results provide an adequate explanation on how helium atoms transport through thick fuzz layers and offer new insights to fuzz growth mechanisms. Sputtering properties of W fuzz are also studied. Results show that the sputtering yield of W fuzz is significantly lower than flat tungsten surfaces, which is in good consistence with experimental findings.

Large current ion beam polishing and characterization of mechanically finished titanium alloy (Ti6Al4V) surface

Ti6Al4V samples with a surface roughness of about 0.2 μm were polished by a high fluence ion beam source, and influences of the ion current, energy and incident angle on the surface roughness of Ti6Al4V were studied. The as-polished surfaces were characterized by laser scanning confocal microscopy (LSCM), atomic force microscopy (AFM), grazing incidence X-ray diffraction (GIXRD) and X-ray photoelectron spectroscopy (XPS). The LSCM images revealed that the density of pits in the original surface decreased greatly after the ion polishing process. In addition, the surface roughness calculated from these images proved that the mean value reduced to 53 nm with an ion energy, current and incident angle of 600 eV, 130 mA and 75°, respectively. The smoothing effect was also confirmed by the power spectral density (PSD) functions calculated from the AFM data. GIXRD patterns indicated that the Ti6Al4V samples mainly contain the hexagonal close packed (HCP) α-Ti, no recognizable peaks corresponding to the body centered cubic (BCC) β-Ti were observed. Furthermore, after the ion beam polishing process, the phase of all the as-polished samples kept steady. The XPS results revealed that C, O, Ti, Al and V were present in both the original as well as the polished samples. In addition, due to the highly reactive characteristics of Ti, Al and V elements, a higher signal for oxygen can also be observed on the outermost surface of the ion beam polished samples. The polishing process of Ti6Al4V surface bombarded by Ar ion beam is also simulated by binary collision approximation (BCA) code SDTrimSP, the effects of ion beam energy and incident angle on the sputtering yield were investigated. The results showed that the sputtering yield of Ti, Al and V atoms increased almost linearly with the ion energy. However, as for the influence of ion incident angle, the sputtering yield first increased gradually from 0° and peaked at about 65°, then decreased rapidly because the incident angle is too large for Ar ion to penetrate into the surface of Ti6Al4V sample.

F-TRIDYN simulations of tungsten self-sputtering and applications to coupling plasma and material codes

Fractal-TRIDYN (F-TRIDYN) is an upgraded version of the Monte Carlo, Binary Collision Approximation code TRIDYN for simulating ion-surface interactions. F-TRIDYN adds an explicit model of surface roughness and additional output modes for coupling to both plasma and material codes. Code-coupling represents a compelling path toward whole-device modeling, especially for future fusion reactors. Whole device models need to span length and time scales of many orders of magnitude. Atomic processes in materials that occur on the order of picoseconds, such as changes to surface morphology, will have an effect on fusion plasma performance over many hours of operational time. Conversely, interactions with the plasma will drive chemical, thermal, and morphological processes in the material. Simulating this complex interaction between the plasma and the plasma-facing material demands fast interfaces between material and plasma codes. F-TRIDYN is a flexible code for simulating atomic-scale ion-surface interactions, which are responsible for interactions between plasma and surface such as sputtering and implantation. F-TRIDYNs surface roughness model allows the effect of surface roughness on ion-surface interactions to be simulated. Surface roughness can significantly alter sputtering yields and other ion-surface interaction quantities. Understanding the role surface roughness plays in Plasma-Material Interactions will be crucial to modeling the performance of future fusion reactors such as ITER. F-TRIDYN is also suited for the simulation of a wider range of plasma-surface interactions where surface morphology may play a role, including those utilized for sputter-coating and plasma treating applications.

Study of Defects Produced by Displacement Cascades in Tantalum Monocarbide

We used the binary collision approximation code Marlowe to simulate displacement cascades in tantalum monocarbide. We investigated the damage production, the spatial configurations of the resulting defects, and the vacancy clustering. Statistics over 5000 cascades were accumulated, and primaries with kinetic energies up to 20 keV were launched from lattice sites. Elastic collisions between atoms were modeled by the universal Ziegler–Biersack–Littmark, Moliere, and Born–Mayer potentials. The Lindhard–Scharff–Schiott theory was used to account for the inelastic energy losses. Principal components analysis was utilized to evaluate the volume of the damaged zone. Analysis of the simulation results shows that no more than 40% of the displaced Ta and C atoms constitute permanent damage. The number of surviving tantalum Frenkel pairs is about twice the carbon one. The cascade volume distributions deviate from a Gaussian distribution showing high degree of dispersion. Only small vacancy clusters are observed within the investigated range of the primary energies, and 33% of the produced vacancies are considered as isolated point defects in 20 keV cascade.

Stochastic Gain Degradation in III–V Heterojunction Bipolar Transistors Due to Single Particle Displacement Damage

As device dimensions decrease, single displacement effects become more important. We measured the gain degradation in III–V heterojunction bipolar transistors due to single particles using a heavy ion microbeam. Two devices with different sizes were irradiated with various ion species ranging from oxygen to gold to study the effect of the irradiation ion mass on gain change. From the single steps in the inverse gain (which is proportional to the number of defects), we calculated cumulative distribution functions to help determine design margins. The displacement process was modeled using the MARLOWE binary collision approximation code. The entire structure of the device was modeled and the defects in the base–emitter junction were counted to be compared with the experimental results. While we found good agreement for the large device, we had to modify our model to reach reasonable agreement for the small device.

F-TRIDYN: A Binary Collision Approximation code for simulating ion interactions with rough surfaces

Fractal TRIDYN (F-TRIDYN) is a modified version of the widely used Monte Carlo, Binary Collision Approximation code TRIDYN that includes an explicit model of surface roughness and additional output modes for coupling to plasma edge and material codes. Surface roughness plays an important role in ion irradiation processes such as sputtering; roughness can significantly increase the angle of maximum sputtering and change the maximum observed sputtering yield by a factor of 2 or more. The complete effect of surface roughness on sputtering and other ion irradiation phenomena is not completely understood. Many rough surfaces can be consistently and realistically modeled by fractals, using the fractal dimension and fractal length scale as the sole input parameters. F-TRIDYN includes a robust fractal surface algorithm that is more computationally efficient than those in previous fractal codes and which reproduces available experimental sputtering data from rough surfaces. Fractals provide a compelling path toward a complete and concise understanding of the effect that surface geometry plays on the behavior of plasma-facing materials. F-TRIDYN is a flexible code for simulating ion-solid interactions and coupling to plasma and material codes for multiscale modeling.

Dynamic Coupling of Boltzmann Plasma Model to Surface Erosion Model for Kinetic Treatment of Plasma-Material Interactions

We present an innovative coupled Boltzmann–binary collision approximation (BCA) method for the simulation of the near-wall plasma in the presence of a material-releasing wall. The method is based on a full-f multispecies Boltzmann solver for the plasma (charged and neutral species) coupled to a modification of the classical BCA code TRIDYN. Both the plasma ions and the impurities are treated as Boltzmann kinetic species, allowing high resolution even at very disparate densities, particle fluxes, drift velocities, and energy fluxes. From the distribution functions, all the fluid moments (density, heat flux, etc.) and the net and gross erosion rates are derived. An example of calculation of a helium plasma facing a beryllium wall is reported, showing the evolution of the phase-spaces of ions, neutrals, and material impurities in the near-wall region at nominal ITER conditions.

Determination of recombination radius in Si for binary collision approximation codes

Displacement damage caused by ions or neutrons in microelectronic devices can have significant effect on the performance of these devices. Therefore, it is important to predict not only the displacement damage profile, but also its magnitude precisely. Analytical methods and binary collision approximation codes working with amorphous targets use the concept of displacement energy, the energy that a lattice atom has to receive to create a permanent replacement. It was found that this “displacement energy” is direction dependent; it can range from 12 to 32eV in silicon. Obviously, this model fails in BCA codes that work with crystalline targets, such as Marlowe. Marlowe does not use displacement energy; instead, it uses lattice binding energy only and then pairs the interstitial atoms with vacancies. Then based on the configuration of the Frenkel pairs it classifies them as close, near, or distant pairs, and considers the distant pairs the permanent replacements. Unfortunately, this separation is an ad hoc assumption, and the results do not agree with molecular dynamics calculations. After irradiation, there is a prompt recombination of interstitials and vacancies if they are nearby, within a recombination radius. In order to implement this recombination radius in Marlowe, we used the comparison of MD and Marlowe calculation in a range of ion energies in single crystal silicon target. The calculations showed that a single recombination radius of ∼7.4Å in Marlowe for a range of ion energies gives an excellent agreement with MD.

Simulation of the Neutral Particle Converter of the ARIES-L Device

This paper presents the concept of Lunar regolith surface layer composition analysis using solar wind bombardment and registration of the sputtered and knocked out atoms converted into ions with solid-state converters and subsequent registration of ions by high-aperture electrostatic analyzer. Monte Carlo binary collision approximation code is used to calculate angular and energy distributions of scattered and sputtered atoms. Literature data are used for evaluation of charged fractions of scattered and sputtered components and SIMION code is used for calculation of charged particles trajectories in electrostatic deflector. The total sensitivity of the proposed scheme is evaluated.

Radiation re-solution of fission gas in non-oxide nuclear fuel

Renewed interest in fast nuclear reactors is creating a need for better understanding of fission gas bubble behavior in non-oxide fuels to support very long fuel lifetimes. Collisions between fission fragments and their subsequent cascades can knock fission gas atoms out of bubbles and back into the fuel lattice. We showed that these collisions can be treated as using the so-called “homogenous” atom-by-atom re-solution theory and calculated using the Binary Collision Approximation code 3DOT. The calculations showed that there is a decrease in the re-solution parameter as bubble radius increases until about 50nm, at which the re-solution parameter stays nearly constant. Furthermore, our model shows ion cascades created in the fuel result in many more implanted fission gas atoms than collisions directly with fission fragments. This calculated re-solution parameter can be used to find a re-solution rate for future bubble simulations.

Modelling of target effects in reactive HIPIMS

In reactive High Power Impulse Magnetron Sputtering (HIPIMS) of oxides, target effects such as reduced surface oxidation during pulse off time, increased implantation of reactive gas due to the higher discharge voltage as compared to normal DC sputtering, and enhanced target cleaning during on time are considered to be responsible for the differences compared to reactive DC sputtering. These effects are assumed to cause changes in the target oxide coverage and hence lead to the hysteresis shifts observed in experimental studies. In this contribution, the target processes are simulated using the binary collision approximation code TRIDYN. Using an Al target sputtered in Ar+O2 mixture as a model system, a range of pulse configurations is simulated for different oxygen partial pressures. The results indicate that the target effects alone are not sufficient to explain the observed shift of hysteresis and its frequency dependence.