Ion-target Combinations Research Articles

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.

Predicting electronic stopping powers using stacking ensemble machine learning method

PurposeAccurate electronic stopping power data is crucial for calculations of radiation-induced effects in a wide range of applications, from dosimetry and radiotherapy to particle physics. The data is dependent on the parameters of both the incident charged particle and the stopping medium. The existent Bethe theory can be used to calculate the stopping power of high-energy ions, but fails at lower energies, leaving incomplete and even contradictory experimental data, often expanded through extrapolations with fitting formula, as the only accessible resource. Moreover, the majority of the experimental data is available for elements only, further limiting the validity of fitting approaches for complex material compositions. A relatively novel machine learning methodology has been proven to be effective for exactly these types of problems. In this study, Stacking Ensemble Machine Learning (EML) algorithm was developedto predict electronic stopping power for any incident ion and target combination over a wide range of ion energies. For this purpose, five ML models, namely Bagging Regressor (BR), eXtreme Gradient Boosting (XGB), Adaptive Boosting (AdB), Gradient Boosting (GB), and Random Forest (RF), were selected as base and meta learners to construct the final Stacking EML. Methods40,044 experimental measurements, from 1928 to the present, available on the International Atomic Energy Agency (IAEA) website were used to train machine learning (ML) algorithms. This database consists of 593 various ion-target combinations across the energy range of 0.037 to 985 MeV. For model training, the eleven most important features were selected. The model evaluation was performed using several error metrics, including R-squared (R2), root-mean-squared-error (RMSE), mean-absolute-error (MAE), and mean-absolute-percentage-error (MAPE), on both the training and test datasets. ResultsBased on model performance evaluation tests, a stack of XGB and RF via BR meta-learner had the lowest error margin. The value of R2 = 0.9985 indicated a near-ideal fit to all samples in the training data across the entire range of stopping powers. R2 = 0.9955 for predictions made by the model on the unseen test data suggested that the model accurately predicted the test data. ConclusionsThe developed model can serve as a universal tool to generate the eSP data in a wide range of cases, regardless of the availability of experimental data or reliable theoretical equations. Overall, the results of the developed tool testified to the power of machine learning approaches, and the suitability of the chosen models for solutions to practically important physics problems.

Estimation of erosion phenomena within helicon plasma sources through a steady-state explicit analytical model

Helicon plasma sources produce high-density discharges without the need of electrodes in direct contact with the plasma, which is thought to provide them with long operational lifetimes. An explicit steady-state analytical model is described with the capability of depicting the 2D plasma density distribution, the sheath potentials and the estimated sputtering and etch rates along the plasma-facing components of the source. The individual constituting submodels are fitted against available experimental data, and the model is used to predict erosion rates within the VX-CR research helicon plasma source. Erosion within these components is dependent on the value of plasma density along the boundaries, the electron temperature and the particular ion-target material combination. The highest erosion rates are found along the upstream system boundary, followed by the regions near the helicon antenna straps where a capacitive RF sheath is formed. The assumptions and limitations of the model are discussed, and future improvements are proposed.

On the use of SRIM for calculating vacancy production: Quick calculation and full-cascade options

The vacancy production behavior for a broad range of incident ion-target combinations were examined by using both the full cascade (F-C) and quick calculation of damage (Q-C) options of Stopping and Range of Ions in Matter (SRIM-2013) code. Vacancy production for each option was evaluated using both the convenient vacancy text file in SRIM, and by manual manipulation of the energy transfer, ionization, and phonon text file data to calculate the depth-dependent damage energy for the Norgett-Robinson-Torrens (NRT) defect production model. The F-C vacancy text file method was observed to overpredict vacancy production by a factor of ~1.1 to 4 times when compared to values calculated using the F-C damage energy method or either of the SRIM Q-C methods. Based on our extensive data set obtained for 142 unique bombarding ion-target combinations, we show that the SRIM F-C vacancy text file method should not be used for vacancy production calculations. This error appears to be due to mischaracterization within the SRIM F-C option of some near-threshold replacement events as vacancies instead of replacements. Use of the latest SRIM stopping powers in the SRIM F-C approach provides a better calculation of electronic and nuclear stopping compared to the Lindhard stopping power analytical approximation used to calculate the damage energy of recoil atoms in the SRIM Q-C option, and therefore SRIM F-C approach is deemed to provide the best accuracy for vacancy production (within the binary collision approximation) as long as the damage energy method is used. Alternately, the SRIM Q-C option using either the vacancy.txt or damage energy method provides relatively fast calculation speeds with moderate quantitative differences from the F-C damage energy results (~0 to ~ 30% for the investigated ion-target cases).

Machine learning for the prediction of stopping powers

The stopping power of a material upon interaction with an energetic ion is the key measure of how far that ion will travel. The implications of accurate particle range calculations are tremendous, affecting every single application in which particle radiation is involved, from nuclear power to medicine. An approach is presented which attempts to overcome current shortcomings in the theoretical understanding of stopping power, as well as the methods used to interpret and exploit measured data. This is a considerable challenge, however the use of a novel machine learning methodology is shown to hold great promise in this endeavour: the ultimate aim being the ability to correctly predict the stopping value for any energy, ion and target combination, having no pre-existing experimental data.A random forest regression algorithm is trained using over 34,000 experimental measurements, representing stopping power values for 522 ion-target combinations across the energy range 10-3 to 102 MeV/amu, and ion and target atomic masses 1 to >240. Evaluation is carried out using several fundamental error metrics, over the whole dataset as well as for individual combinations, to provide the most comprehensive understanding of performance when tested under strict cross-validation criteria. The resulting model is shown to yield predicted stopping power curves corresponding closely to those of the true experimental values, with an ability to generalise across target elements, compounds, mixtures, alloys and polymers, irrespective of phase, and for a wide range of ion masses.

Near-threshold, steady state interaction of oxygen ions with transition metals: Sputtering and radiation enhanced diffusion

Transition metals used in semiconductor, photolithography and fusion applications interact with low energy oxygen ions. Understanding erosion, the nature of the formed oxide and depth of oxygen transport is necessary in mitigating unexpected performance of sensors, optics or plasma facing components. Oxide formation is governed by both the ion–target combination and the incident ion energy. We study the interaction of the transition metals molybdenum, ruthenium, palladium and tungsten, with oxygen ions in the energy region of 50–500 eV. Near-threshold sputtering of metals was experimentally measured and compared to predictions by the Monte Carlo code TRIDYN. Compositional changes and oxide thicknesses following sputtering were measured using Angle resolved X-ray photoelectron spectroscopy and subsequently compared to limiting oxide formed by atomic oxygen exposures. Sputter yields in some cases (ruthenium) were found to be sensitive to ion beam impurities such as ozone (<1% of background gas) leading to chemical sputtering. Ion induced oxide thicknesses (for molybdenum and tungsten) were found to be larger than those predicted by ballistic transport where sputtering is balanced by implantation. It is hypothesized that radiation enhanced diffusion of free oxygen leads to thicker oxide films at low ion energies.

Effect of impact-parameter-dependent electronic energy loss on reflected-ion spectra

Conventional theory and computation of the slowing-down of ions and associated radiation effects relies on a scheme proposed by Lindhard and Scharff, in which electronic energy losses enter as a friction force. We study limitations of this scheme, when the dependence of electronic losses on the impact parameter in individual atomic collisions is taken into account. We study this feature on the projected range – where it is found to be insignificant – and on reflected-ion spectra – where major changes are observed, dependent on ion energy and ion-target combination. Most sensitive are the position of the peak in the reflected-energy spectrum as well as the behavior near the maximum energy loss. Systems studied include He-Ag, Ne-Ag, B-Si and D-Pt.

Calculation of Ion Reflection from Solids: Computer Simulation and Theory

A computer program is developed to study ion reflection from solid surfaces. The program uses the cutoff Coulomb potential, the binary collision approximation, and the model of local inelastic energy losses. For a fixed ion-target combination, the reflection coefficient is calculated as a function of the ion energy and incidence angle. A reflection theory for the scattering cross section which depends on the transferred energy in accordance with the power law is constructed. Good agreement of the simulation results with the experiment and the theory is obtained.

Prediction of ion-induced nanopattern formation using Monte Carlo simulations and comparison to experiments

Ion induced nanopattern formation has been experimentally investigated for many different ion-target combinations and different ion irradiation conditions. Several theories and models have been developed throughout the past few years to explain the observed boundary conditions for pattern formation as well as features of the patterns like wavelengths, growth rates, shapes, and amplitudes. To compare specific experiments with the predictions of analytical theories, it is necessary to calculate the linear and non-linear coefficients of the respective equation of motion of a surface profile. Monte Carlo simulations of ion–solid interactions based on the binary collision approximation provide a very fast, rather universal, and accurate way to calculate these coefficients. The universality expresses the broad range of ion species, ion energies, and target compositions accessible by the simulations. The coefficients are obtained from the moments of calculated crater functions, describing ion erosion, mass redistribution, and ion implantation. In this contribution, we describe how most linear, non-linear, and higher order coefficients can be determined from crater function moments. We use the obtained data to compare the results of selected experimental studies with the predictions of theoretical models. We find good quantitative agreement, e.g., for irradiation of Si with Ar and Kr ions, Al2O3 with Ar and Xe ions, and amorphous carbon with Ne ions.

Expanded PASS stopping code

The first version of the PASS code was developed in 2000 on the basis of binary theory of electronic stopping, a generalization of Niels Bohr’s 1913 theory of the stopping of alpha particles in matter. The code has been applied in a number of fundamental studies of energy-loss problems, including Barkas-Andersen effect and straggling as well as channeling and electron emission, and it underlies the ICRU tabulation of stopping data for ions with atomic numbers 3–16 in 25 elementary and 32 compound materials over an energy range from 25 keV/u to 1 GeV/u.We report about a major expansion of the code, so that mean energy losses can be computed for 92 ions in 92 elemental targets. Comparisons with measurements have been made over the entire energy range for which experimental data are listed in the IAEA database.The code allows to compute energy losses for arbitrary compound target materials by assuming Bragg additivity. Predictions beyond the Bragg rule are available for selected materials.In this paper we specify the underlying physics and improvements of the code during the period since its first implementation. Strengths and weaknesses are demonstrated graphically for a number of ion-target combinations. Tables for 92 × 92 ion-target combinations over an energy range from 1 keV/u to 1 GeV/u are freely accessible on the internet in the DPASS (Dataset PASS) code.

Heavy ion PIXE cross sections in Ti, Zn, Nb, Ru and Ta for 4.8–30.0 MeV oxygen and 3.0–12.0 MeV lithium beams

Heavy ion Particle Induced X-ray Emission (PIXE) spectroscopy offers a number of advantages over standard proton PIXE, such as higher yields and therefore higher sensitivity. However, in order to be able to use heavy ion PIXE more detailed measurements of the ionisation and X-ray cross sections for heavy ions are required. This issue was recognised by one of the Coordinated Research Projects (CRP) of the IAEA on MeV Secondary Ion Mass Spectrometry (SIMS). ANSTO took part in this CRP and we measured X-ray production cross sections on a range of samples for oxygen and lithium beam in the energy range of 4.8–30 MeV and 3–12 MeV, respectively. Here we report on these X-ray production cross section measurements and compare the results with theoretical models. Further energy shifts of the characteristic X-ray lines for the different ion-target combinations are presented and discussed.

Angle-dependent sputter yield of rippled surfaces

Atomistic (binary-collision) simulation is used to study the sputter yield of rippled C and Si surfaces bombarded with Ar and Ga ions in a wide range of incidence angles and energies. This study was motivated by conflicting theoretical predictions of results when the ion energy is varied. Most simulations refer to a sinusoidal ripple topography with h/λ = 0.05–0.15, where h and λ are the amplitude and wavelength of ripples, respectively. Results are compared with Monte Carlo simulation based on Sigmund’s continuum model of ion sputtering and not tied to a specific ion-target combination. Both types of simulation do not confirm a strong suppression of the angular variation in the sputter yield from rippled surfaces with increasing ion energy, predicted theoretically (Makeev and Barabási, 2004).

Cross sections of X-ray production induced on Ti, Fe, Zn, Nb and Ta by O, Cl, Cu and Br ions with energies between 4 MeV and 40 MeV

Differential cross section of X-ray production induced by O, Cl, Cu and Br ions with energies between 4 MeV and 40 MeV have been measured for thin targets of Ti, Fe, Zn, Nb and Ta in a direct way. A fully characterized silicon drift diode was used as X-rays detector. Beam currents have been measured by a system of two Faraday cups. Corrections for target thickness effects have been applied to the raw data. Experimental cross sections are compared both with theory and with previously published results. Experimental results from other authors are in reasonable agreement with ours over a wide energy range. Theory produces consistent results in the case of oxygen ions but gives cross sections even orders of magnitude below the experimental ones for heavier ions (ECPSSR-UA) or contrasting results (PWBA) depending on the ion-target combination.

Systematics of heavy-ion charge-exchange straggling

The dependence of heavy-ion charge-exchange straggling on the beam energy has been studied theoretically for several ion-target combinations. Our previous work addressed ions up to krypton, while the present study focuses on heavier ions, especially uranium. Particular attention has been paid to a multiple-peak structure which has been predicted theoretically in our previous work.For high-Z1 and high-Z2 systems, exemplified by U in Au, we identify three maxima in the energy dependence of charge-exchange straggling, while the overall magnitude is comparable with that of collisional straggling. Conversely, for U in C, charge-exchange straggling dominates, but only two peaks lie in the energy range where we presently are able to produce credible predictions. For U–Al we find good agreement with experiment in the energy range around the high-energy maximum.The position of the high-energy peak – which is related to processes in the projectile K shell – is found to scale as Z12, in contrast to the semi-empirical Z13/2 dependence proposed by Yang et al.Measurements for heavy ions in heavy targets are suggested in order to reconcile a major discrepancy between the present calculations and the frequently-used formula by Yang et al.

Anatomy of charge-exchange straggling

We have studied charge-exchange straggling theoretically for swift krypton and silicon ions and five target gases in the MeV/u energy regime. We find a pronounced two-peak structure for all ion-target combinations. The peak at the highest energy appears around the velocity where the bare ion and the one-electron ion are equally abundant in the equilibrium charge distribution. Correspondingly, the low-energy peak appears near the cross-over between the charge fractions of the two- and the three-electron ion. The possibility of further peaks at lower energies is discussed. Our findings are compared with recent experimental results on straggling of krypton beams.

Model to estimate fractal dimension for ion-bombarded materials

Comprehensive fractal Monte Carlo model ITMC-F (Hu and Hassanein, 2012 [1]) is developed based on the Monte Carlo ion bombardment simulation code, i.e., Ion Transport in Materials and Compounds (ITMC) code (Hassanein, 1985 [2]). The ITMC-F studies the impact of surface roughness on the angular dependence of sputtering yield. Instead of assuming material surfaces to be flat or composed of exact self-similar fractals in simulation, we developed a new method to describe the surface shapes. Random fractal surfaces which are generated by midpoint displacement algorithm and support vector machine algorithm are combined with ITMC. With this new fractal version of ITMC-F, we successfully simulated the angular dependence of sputtering yield for various ion-target combinations, with the input surface roughness exponent directly depicted from experimental data (Hu and Hassanein, 2012 [1]). The ITMC-F code showed good agreement with the experimental data. In advanced, we compare other experimental sputtering yield with the results from ITMC-F to estimate the surface roughness exponent for ion-bombarded material in this research.

Effects of Accumulation of Impurities into Target Materials for Sputtering

Sputtering yields have been measured for many ion-target combinations so far [1][2]. Monte Carlo simulation codes [3][4] have been developed to estimate ion-solid interactions, and are in good agreement with experimental data on sputtering yields [1][2]. Several empirical formulae which predict the energy dependence of sputtering yields for any ion-target combinations were proposed [2][5]. The Yamamura-Tawara semi-empirical formula [2], hereafter we abbreviate to Y-T formula, are applied to estimate sputtering yields in the present work. Experimental works on the sputtering yields of carbon due to xenon ions have shown significant yields below the threshold energy predicted by the empirical formula at normal incidence [6-12]. The predicted threshold energy is 160.84 eV for the xenon–carbon combination in the Y-T formula [2]. In this paper we report the results of sputtering yields of carbon under the xenon ion bombardment calculated with a Monte Carlo code ACAT [4] to find the reason to explain the discrepancy between the experimental results and the predictions from the Y-T formula. Atoms of Xe are retained in graphite to make atomic xenon fraction as high as 14% after the low energy Xe plasma sputtering experiment [10]. We will correlate the amount of the incident particles retained into a target material and the resultant sputtering yields from graphite materials, under a continuous bombardment of Xe ions.

How surface roughness affects the angular dependence of the sputtering yield

Comprehensive model is developed to study the impact of surface roughness on the angular dependence of sputtering yield. Instead of assuming surfaces to be flat or composed of exact self-similar fractals, we developed a new method to describe the surfaces. Random fractal surfaces generated by midpoint displacement algorithm in computer graphics area and Support vector machine algorithm in pattern recognition area are combined with the Monte Carlo ion bombardment simulation code, i.e., Ion Transport in Materials and Compounds (ITMC) code [1]. With this new fractal version of ITMC-F, we successfully simulated the angular dependence of sputtering yield for various ion-target combinations. Examples are given for 5keV Ar ions bombarding iron, graphite, and silicon surfaces, with the input surface roughness exponent directly depicted from experimental data. Comparison is made with previous models to account for surface roughness and recent experimental data. The ITMC-F code showed good agreement with the experimental data.

Generation of shielding data for neutron radiation produced by heavy ions

The operation of heavy ion accelerators is unavoidably associated with the production of ionizing radiation. Neutron and gamma radiation is released when the impinging ions interact with nuclei of target materials. Consequently the architectural shielding design has to meet the requirements for a sufficient shielding design. The aim of this work is the provision of attenuation data for normal concrete on the basis of double differential source distributions (solid angle, energy) of released neutron radiation, the dominating radiation component for ions in the energy range to be considered here. For this purpose attenuation data for mono-energetic neutron radiation in a spherical geometry were computed using the radiation transport code FLUKA in an energy range from 100 keV to 3 GeV for a depth in the spherical concrete shielding from 1.5 m to 8 m. Measured or calculated double differential neutron yields serve as source terms. The mono-energetic attenuation curves can then be multiplied with the source strength of the corresponding energy bin. A superposition of all neutron energy specific attenuation curves delivers the total dose as a function of the shielding thickness for each angular range provided by the source data. Examples will be given for resulting attenuation curves with the input of measured and calculated double differential neutron yields. This arithmetical procedure can be a useful tool for example for facilities operating heavy ion accelerators with a large variety of ion-target combinations in a wide energy range. Comprehensive data bases for sources distributions are now available which make the shielding planning of these kinds of facilities easier.

Ion induced high energy electron emission from copper

We present measurements of secondary electron emission from Cu induced by low energy bombardment (1–5 keV) of noble gas (He +, Ne + and Ar +) and Li + ions. We identify different potential and kinetic mechanisms and find the presence of high energetic secondary electrons for a couple of ion-target combinations. In order to understand the presence of these fast electrons we need to consider the Fermi shuttle mechanism and the different ion neutralization efficiencies.