Electronic Stopping Research Articles

Molecular Dynamic Simulation of Primary Damage with Electronic Stopping in Indium Phosphide.

Indium phosphide (InP) is an excellent material used in space electronic devices due to its direct band gap, high electron mobility, and high radiation resistance. Displacement damage in InP, such as vacancies, interstitials, and clusters, induced by cosmic particles can lead to the serious degradation of InP devices. In this work, the analytical bond order potential of InP is modified with the short-range repulsive potential, and the hybrid potential is verified for its reliability to simulate the atomic cascade collisions. By using molecular dynamics simulations with the modified potential, the primary damage defects evolution of InP caused by 1-10 keV primary knock-on atoms (PKAs) are studied. The effects of electronic energy loss are also considered in our research. The results show that the addition of electronic stopping loss reduces the number of point defects and weakens the damage regions. The reduction rates of point defects caused by electronic energy loss at the stable state are 32.2% and 27.4% for 10 keV In-PKA and P-PKA, respectively. In addition, the effects of electronic energy loss can lead to an extreme decline in the number of medium clusters, cause large clusters to vanish, and make the small clusters dominant damage products in InP. These findings are helpful to explain the radiation-induced damage mechanism of InP and expand the application of InP devices.

Potential for suprathermal chain reactions in degenerate deuterium plasmas at high densities

Abstract It is argued that fusion chain reactions in the D-D system are feasible with
supra-thermal deuterons in the MeV regime, with new generations of deuterons being
generated either via neutron-deuteron and proton-deuteron collisions, provided that fuel
densities in excess of 1000 gcm −3 are reached. The propagation of supra-thermal deuterons
in an infinite, dense deuterium target was studied using a Monte Carlo method that includes
multiple nuclear reactions, electron and ion stopping, along with neutron and proton
knock-ons. Prior studies into this system are extended and it is shown that : (a)dense
pure deuterium may be more supportive of chain reactions via refinements to the ion-ion
stopping number, (b) such chain reactions can be supported even when the target is electron
degenerate, and (c) the D-T reaction plays a critical role in sustaining these chain reactions.

Prediction of electron-solid interaction parameters using machine learning.

Electron backscattering coefficient and electron-stopping power are essential concepts in many disciplines, from radiation to materials science, semiconductor manufacturing, and space exploration. They enable precise calculations, measurements, and simulations of electron interactions with matter, which contribute to advancing science, technology, and safety in a variety of applications. The availability of these data is fundamental to scientific research to validate hypotheses, conduct experiments, and explore new theories. A relatively novel machine learning approach has demonstrated notable success in enhancing data quality and completeness, significantly contributing to the facilitation of data discovery. Using fundamental material property data, the stacking ensemble machine learning (EML) technique was established in this study to generate electron-solid interaction parameters for any target material over a wide range of energies. The final stacking EML was built using the base and meta learners bagging regressor (BR), K-nearest neighbors (k-NN), random forest (RF), support vector regression (SVR), and eXtreme Gradient Boosting (XGB). In this study, two publicly available databases with a total of 4030 data points were used. Training datasets have 785 and 525 data points for electron backscattering coefficient and stopping power, respectively, whereas testing datasets contain 262 and 175 data points. Fivefeatures were used as input variables to train different individual algorithms and their combinations. On both the training and test datasets, the model was evaluated using different error metrics, including R-squared (R2), mean-absolute-error (MAE), root-mean-squared-error (RMSE), and mean-absolute-percentage-error (MAPE). Our model evaluation tests revealed that combining RF and XGB with a k-NN meta-learner outperformed other algorithms. The analysis of error metrics demonstrated a very close fit to all samples in each training dataset. Furthermore, predictions made by the model on unseen test data indicated accurate estimations of new backscattering and stopping power data. The developed model achieved high prediction accuracy for various target materials across the broad electron energy spectrum. The outcomes demonstrate the effectiveness of machine learning methodology and the chosen models' suitability for addressing substantial physics challenges.

Effect of stress and irradiation fluence on latent track formation in swift heavy ion irradiation: A case study on TiO2

Swift Heavy Ions (SHI) irradiation, characterized by high kinetic energy ions, induces significant material/structural modification, e.g., latent track. However, the intricate interaction among various physics, i.e., mechanical stress, phase transition, and heat transfer, has been ignored in the continuum-based approaches in favor of simplicity. Here, we developed a two-dimensional coupled phase-field inelastic-thermal spike (PF-iTS) model to investigate the effect of thermal cross-talk, elastic energy, and irradiation fluence on latent track formation and size. The results reveal a shift in the critical electronic stopping energy and a reduced track radius under mechanical stress. Additionally, the study demonstrates the impact of thermal cross-talk between incidents, i.e., simultaneous and delayed double ion impacts, showing potential track merging and variations in track morphology.

Bulk, overlap and surface effects of swift heavy ions in CeO2

Formation of tracks of swift heavy ions decelerating in the electronic stopping regime in CeO2 was studied, combining the Monte Carlo code TREKIS with molecular dynamics. We show that strong lattice disordering (melting) followed by structure recovery form finally a damaged ion track consisting of a discontinuous crystalline region in CeO2. Normal ion impacts result in appearance of spherical crystalline hillocks on CeO2 surface. The solid-vacuum interface strongly suppresses the recrystallization of the near-surface layers, forming conically shaped tracks with several tens of nanometers lengths. Grazing ion irradiation induces intensive material expulsion from the surface forming finally grooves surrounded by nanohillocks. The processes of surface nanostructures formation is similar to those observed previously in CaF2 which has the similar crystalline structure, however requires much longer recrystallization time. Recent experimental data confirm the simulation results.

Machine learning study of universal electronic stopping cross-sections of ions in matter

Accurate electronic stopping cross-section (ESCS) database of ions in matter is crucial for precise simulation of radiation damage. Based on the experimental-cleaned database of SRIM, binary theory and unitary convolution approximation as well as the descriptor pool extracted from these models, we developed a universal machine learning ESCS database using the least absolute shrinkage and selection operator (LASSO) algorithm. This method allows for predictions for ion-target combinations with atomic numbers from 1 to 92, within the energy range from 1 keV/u to 1 GeV/u, addressing the limitations of machine learning on training dataset. The database exhibits remarkable accuracy in predicting ESCS and ion depth distribution/range, along with robust reciprocity performance. Key descriptors are also determined, which closely mimic the Lindhard-Scharff-Schiott and Bohr-Bethe-Bloch formulations, achieved through precise adjustments of the exponent of individual elements. The proposed universal ESCS database surpasses the accuracy of existing databases, supporting related applications across a wide range of energies and systems.

Experimental and calculated electronic stopping force determination of 24Cr, 28Ni and 22Ti ions crossing PVC and Mylar foils in the ion energy domain of LSS theory

Energy loss measurements for heavy ions (28Ni,24Cr and 22Ti) crossing thin polymeric foil such as PVC and Mylar in the energy range 0.1–0.3 MeV/n have been carried out utilizing the 6MV Tandem accelerator facility at iThemba-labs in Johannesburg (South Africa). These measurements deduced experimental stopping force data have been compared with those calculated using Lindhard, Scharff and Schiott formulation (LSS) and SRIM-2013 predictions. A large significant deviation has been observed between experimental values and those calculated by LSS formula. Based on physical postulate, we have developed a reasonably simple semi-empirical formula that takes in to account a mean residual projectile charge Z1¯ and suitable ξe factor which depend on Z1 and Z2. This new modified LSS formula has been tested and the calculated stopping force values generated by this formula are in close agreement with the measured ones.

Accelerating multiscale electronic stopping power predictions with time-dependent density functional theory and machine learning

Knowing the rate at which particle radiation releases energy in a material, the “stopping power,” is key to designing nuclear reactors, medical treatments, semiconductor and quantum materials, and many other technologies. While the nuclear contribution to stopping power, i.e., elastic scattering between atoms, is well understood in the literature, the route for gathering data on the electronic contribution has for decades remained costly and reliant on many simplifying assumptions, including that materials are isotropic. We establish a method that combines time-dependent density functional theory (TDDFT) and machine learning to reduce the time to assess new materials to hours on a supercomputer and provide valuable data on how atomic details influence electronic stopping. Our approach uses TDDFT to compute the electronic stopping from first principles in several directions and then machine learning to interpolate to other directions at a cost of 10 million times fewer core-hours. We demonstrate the combined approach in a study of proton irradiation in aluminum and employ it to predict how the depth of maximum energy deposition, the “Bragg Peak,” varies depending on the incident angle—a quantity otherwise inaccessible to modelers and far outside the scales of quantum mechanical simulations. The lack of any experimental information requirement makes our method applicable to most materials, and its speed makes it a prime candidate for enabling quantum-to-continuum models of radiation damage. The prospect of reusing valuable TDDFT data for training the model makes our approach appealing for applications in the age of materials data science.

Comparison of electronic stopping powers of 4H-SiC and 2H-GaN for low-velocity 〈0001〉 channeled ions with atomic numbers of 12 to 15

Measured electronic stopping powers along the 〈0001〉 direction (S e) of 4H-SiC and 2H-GaN for low-velocity 12Mg, 13Al, and 15P ions were reproduced with the modified El-Hoshy−Gibbons model that reduced not only the atomic numbers of projectiles and targets but also the impact parameter for small-angle collisions (based on the Kohn−Sham radii of projectiles) in the Firsov model. Unreported S e of 2H-GaN for low-velocity 14Si ions was then predicted to be between S e of 2H-GaN for 12Mg ions and S e of 4H-SiC for 13Al ions, indicating not only Al and Mg but also Si channeling being usable for fabricating cost-effective superjunctions.

SRIM simulation of hydrogen ions interaction with bismuth oxide nanoparticles doped with rare earth elements

Simulation methods have received much attention across various fields in recent years. The rare-earth lutetium tantalate (LuTaO4) doped “Bismuth Oxide (Bi2O3) thin films were deposited onto polymer substrates using a SRIM program.” The SRIM program was used to calculate some physical characteristics of Bi2O3 films at energies between 1.0 MeV and 20 MeV. The “electronic and nuclear stopping powers” of LuTaO4, Bi2O3, C10H8O4, and LuTaO4/ Bi2O3/C10H8O4 samples were investigated. These findings show that rare earth doping may improve the performance of composite materials. The interaction of ion beams with matter can result in a wide variety of phenomena. The deposition of Bi2O3 films doped with LuTaO4 on C10H8O4 led to changes in the “electronic and nuclear stopping powers” and range in the materials. Published data were compared with the results obtained and the calculations parameters were provided.

Deeper-band electron contributions to stopping power of silicon for low-energy ions.

This study provides accurate results for the electronic stopping cross sections of H, He, N, and Ne in silicon in low to intermediate energy ranges using various non-perturbative theoretical methods, including real-time time-dependent density functional theory, transport cross section, and induced-density approach. Recent experimental findings [Ntemou et al., Phys. Rev. B 107, 155145 (2023)] revealed discrepancies between the estimates of density functional theory and the observed values. We show that these discrepancies vanish by considering the nonuniform electron density of the deeper silicon bands for ion velocities approaching zero (v → 0). This indicates that mechanisms such as "elevator" and "promotion," which can dynamically excite deeper-band electrons, are active, enabling a localized free-electron gas to emulate ion energy loss, as pointed out by Lim et al. [Phys. Rev. Lett. 116, 043201 (2016)]. The observation and the description of a velocity-proportionality breakdown in electronic stopping cross sections at very low velocities are considered to be a signature of the contributions of deeper-band electrons.

Determining the stopping power of low kinetic energy Ne+ projectiles in self-Assembled monolayers

Neutral impact collision ion scattering spectroscopy (NICISS) is used to measure the energy loss in organic self-assembled monolayers (SAMs) on Au using Ne+ with low kinetic energies from 3 to 5 keV. With increasing film thickness, the energy loss of the projectiles increases because the projectile experiences more collisions with target atoms.Through comparing Monte-Carlo simulations with the NICISS experiments, it was found that contributions from nuclear stopping for Ne+ were significantly larger than for He+ mainly due to the stronger contribution of small-angle scattering of Ne+ making Ne NICISS unsuitable for depth profiling at energies of 5 keV or lower. The measured Ne+ electronic stopping in SAMs is small despite the large atomic number of Ne. Comparing experiments and DFT calculations shows that the latter accurately reproduce stopping powers for Ne+, while SRIM overestimates the stopping power. This contrasts He+ ions, where DFT and SRIM align closely with experiments.

Modeling swift heavy ion irradiation of substrate-supported two-dimensional material via two-temperature molecular dynamics simulations

This study employs two-temperature molecular dynamics simulations to investigate swift heavy ion irradiation of SiO2 substrate-supported two-dimensional material graphene. Material-dependent electronic and thermal properties are integrated into each region to model the energy transfer between the electronic and atomic subsystems of the studied materials. Simulations of interactions with Xe heavy ions are performed with ion kinetic energies ranging from 0.5 to 25 GeV with electronic stopping powers from ∼2.6 to 17.7 keV/nm. With the studied ion energy range, nanopores with a diameter of up to 5 nm can be formed in graphene due to the thermally driven sputtering effect, while amorphization occurs along the ion track in the SiO2 substrate. The coupling between the substrate and two-dimensional material significantly impacts the structural change due to heat transfer and atomic interactions among different layers of materials. The method applied in this work provides a valuable tool for modeling and understanding the structural modifications induced by ion irradiation in layered structures.

The electronic stopping power of self-irradiated molybdenum in different charge states

Molybdenum is not only an excellent photovoltaic material but also a crucial component in semiconductors. However, its high bandgap restricts its application in optoelectronic devices. This limitation arises primarily because the energy barrier between photogenerated electron-hole pairs cannot be directly overcome by sunlight. Self-irradiation can overcome these barriers, allowing efficient separation of photogenerated electrons and holes, making molybdenum an excellent light-absorbing material. By altering the charge state of molybdenum-based materials, their light absorption can be adjusted. This project aims to systematically study the optical properties and electronic stopping power of molybdenum-based materials in different charge states through theoretical calculations and experiments.

High-energy heavy ions as a tool for production of nanoporous graphene

Single-layered supported graphene sheets were irradiated by iodine, copper, silicon, and oxygen ions in the MeV energy range. The selected ion beams cover a wide range of nuclear and electronic stopping powers. Raman spectroscopy used for the analysis of irradiated graphene samples reveals similar, nanometer-sized, pores due to the ion impacts, but with varying probability of their formation. We observed an inverse relationship between ion velocity and the size of the nanopores. Also, we observed damage accumulation is influenced by electronic stopping in all cases when electronic stopping is greater than nuclear stopping by two orders of magnitude. The systematic investigation presented in this work enables custom-made production of nanoporous graphene using high-energy heavy ion beams.

Highly accurate ab initio electronic stopping power results for protons in Al material: a Lindhard stopping theory investigation

The main goal of this work is to enhance theoretical precision evaluations for the random electronic stopping power (RESP) of protons in solid targets across a wide range of energies, including low, intermediate, and high energies. The RESP of protons is investigated in different crystalline forms of Al material: FCC and two theoretical build structures (hexagonal and tetragonal). Initially, we divide the RESP calculations of protons in Al material into two individual contributions: one for the valence electrons and the other for the core electrons. Using this approach, we introduce a combination method that defines the total RESP as the sum of these contributions. We estimate the core electrons’ contribution to the RESP results within the local density approximation (LDA) based on the Lindhard stopping theory, where we calculate the density of Al material within the density functional theory (DFT) framework. We employ the RESP contribution of valence electrons as determined in our previous study within the linear response time-dependent density functional theory. We produce high-quality RESP results with the assistance of the combination method with low computational cost compared to other theoretical works. We test the accuracy of using the LDA based on Lindhard’s stopping model in calculating the RESP of protons in the Al target. In addition, within this approach, we investigate the influence of the crystal structure on core electrons’ contribution to the RESP.

Temperature Effects of Nuclear and Electronic Stopping Power on Si and C Radiation Damage in 3C-SiC.

Silicon carbide has been considered a material for use in the construction of advanced high-temperature nuclear reactors. However, one of the most important design issues for future reactors is the development of structural defects in SiC under a strong irradiation field at high temperatures. To understand how high temperatures affect radiation damage, SiC single crystals were irradiated at room temperature and after being heated to 800 °C with carbon and silicon ions of energies ranging between 0.5 and 21 MeV. The number of displaced atoms and the disorder parameters have been estimated by using the channeling Rutherford backscattering spectrometry. The experimentally determined depth profiles of induced defects at room temperature agree very well with theoretical calculations assuming its proportionality to the electronic and nuclear-stopping power values. On the other hand, a significant reduction in the number of crystal defects was observed for irradiations performed at high temperatures or for samples annealed after irradiation. Additionally, indications of saturation of the crystal defect concentration were observed for higher fluences and the irradiation of previously defected samples.

Time-dependent density-functional theory study on nonlocal electron stopping for inertial confinement fusion

Understanding laser–target coupling is of the utmost importance for achieving high performance in laser-direct-drive (LDD) inertial confinement fusion (ICF) experiments. Thus, accurate modeling of electron transport and deposition through ICF-relevant materials and conditions is necessary to quantify the total thermal conduction and ablation. The stopping range is a key transport quantity used in thermal conduction models; in this work, we review the overall role that the electron mean free path (MFP) plays in thermal conduction and hydrodynamic simulations. The currently used modified Lee–More model employs various physics approximations. We discuss a recent model that uses time-dependent density functional theory (TD-DFT) to eliminate these approximations in both the calculation of the electron stopping power and corresponding MFP in conduction zone polystyrene (CH) plasma. In general, the TD-DFT calculations showed a larger MFP (lower stopping power) than the standard modified Lee–More model. Using the TD-DFT results, an analytical model for the electron deposition range, λTD−DFT(ρ,T,K), was devised for CH plasmas between ρ=[0.05−1.05] g/cm3, kBT=[100−1000] eV. We implemented this model into LILAC, for simulations of a National Ignition Facility-scale LDD implosion and compared key physics quantities to ones obtained by simulations using the standard model. The implications of the obtained results and the path moving forward to calculate this same quantity in conduction-zone deuterium–tritium plasmas are further discussed, to hopefully close the understanding gap for laser target coupling in LDD-ICF simulations.

Suprathermal-ion-driven fusion chain reactions in the pure deuterium system

It is argued that fusion chain reactions in the D-D system is feasible with supra-thermal deuterons in the MeV regime, with new generations of deuterons being generated either via neutron–deuteron or proton–deuteron collisions. The propagation of supra-thermal deuterons in an infinite, hot, dense deuterium target was studied using a Monte Carlo method that includes multiple nuclear reactions, electron and ion stopping, along with neutron and proton knock-ons. Over a wide range of densities we observed significant, albeit sub-critical chain reactions in the multi-keV temperature regime. At very high densities (over 1000 gcm−3) and temperatures (over 40 keV) we observed chain reactions that reached criticality. These results suggest that there is a case to re-assess the potential of inertial confinement fusion based on deuterium-heavy targets.

BEB-based models for ionisation cross sections of electron and positron impact with diatomic molecules

The ionising interactions of high-energy particles with molecules have applications in many areas. Despite this, some areas, including positron scattering, lack experimental data due to difficulties in performing experiments. Here, quick and simple methods for computing direct electron and positron impact ionisation cross sections are presented. These calculations, performed using the open-source software RAPID-CS, can provide a complete data set as a first approximation for when experimental, or more detailed computational work is not available. The cross-sectional data set includes the total, partial/fragment-specific, single-differential, average secondary electron energy and stopping power cross sections. The molecules N2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}, O2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} and CO were chosen to study due to the availability of positron scattering data. An overall good agreement with experimental and other computational results is presented.Graphical abstractDirect electron (left) and positron right) impact partial ionisation cross sections for N2. Total cross section: red, N2+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N^{+}_{2}$$\\end{document} partial cross section: blue, N+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{+}$$\\end{document} partial cross section: green.electron: solid lines: BEB, experimental measurements by Lindsay and Mangan [36]:Ürosses, Straub et al. [37]: stars, Opel et al. [39]: squares. Positron: solid lines: BEB0, Dashed lines: BEBA, Marler and Surko [23]: red crosses, Bluhme et al. [24]: stars