Stopping Cross Sections 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.

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.

Elastic scattering cross sections and transport of tin ions in extreme ultraviolet lithography sources

Energetic tin ions are created by laser produced plasmas in extreme-ultraviolet lithography sources where hydrogen must be used as a buffer gas to protect critical optical components. In this study, the quantum chemistry code NWChem is used to calculate the interatomic potential between singly ionized tin and molecular hydrogen. The interatomic potential was fit by an inverse-power potential, a modified universal ZBL potential, and a two-piece-Lennard-Jones potential which were in turn used to calculate the classical distance of closest approach, scattering angle, total elastic scattering cross sections. Furthermore, the universal Ziegler-Biersack-Littmark (ZBL) potential was used in the open-source binary collision approximation codes RustBCA as well as Stopping Range in Matter and Transport of Ion in Matter (SRIM/TRIM) to calculate ion ranges, straggling, and stopping cross sections in a hydrogen gas target.

Modified El-Hoshy−Gibbons model for electronic stopping cross sections in Si and SiC for low-velocity ions with atomic numbers between 5 and 15

The El-Hoshy−Gibbons model, which reduces not only the atomic numbers of projectiles (Z 1) and targets but also the impact parameter for small-angle collisions (R 0) in the Firsov model, was modified based on the relation between R 0 and the Kohn−Sham radii of projectiles (r KS); namely, the reduction factor y of R 0 was chosen to be 10 when R 0 was larger r KS and 5 in the case R 0 ≤ r KS. This modification improved the reproducibility of the periodic dependences of the electronic stopping cross sections in Si, as well as those in SiC, for low-velocity ions with 5 ≤ Z 1 ≤ 15.

Corrigendum to “Contribution of molecular orbital promotion to the electronic stopping cross section at slow atom solid collisions”. [Nucl. Inst. Methods Phys. Res. B (2024) 165217

Corrigendum to “Contribution of molecular orbital promotion to the electronic stopping cross section at slow atom solid collisions”. [Nucl. Inst. Methods Phys. Res. B (2024) 165217

Comparison of electronic stopping cross sections for channeled implantation of Al ions between the 〈0001〉 and 〈11 2¯ 3〉 directions in 4H-SiC

Electronic stopping cross sections (S e) for channeled implantation of Al ions in 4H-SiC were compared between the 〈0001〉 and 〈11 2¯ 3〉 directions. We first modeled S e for random implantation (S e random) by combining the Firsov equation at an Al-ion energy E < 8.6 MeV with the constant (i.e. 4.22 × 10−13 eV cm2/atom) at E > 8.6 MeV. We then assumed S e for channeled implantation being k S e random and fitted k to the reported maximum channeled ranges of 18−20 MeV Al in 4H-SiC. The resultant k 〈112̄3〉 of 0.53 being smaller than k 〈0001〉 of 0.70 was consistent with the difference in the maximum impact parameters.

Contribution of molecular orbital promotion to the electronic stopping cross section at slow atom solid collisions

The autoionization states formation due to MO promotion during collisions of keV-energy ions with solids produces a dominant contribution to inelastic energy losses and, accordingly, to the electronic stopping powers dE/dx. The correlations of emitted electron numbers δ with the values of inelastic energy losses Q are shown. When corresponding distances of closest approach are reached, the MO orbital promotion produces a stepwise increase in values of Q and δ. Based on the measured ionization cross-sections and Q values, electronic stopping powers can be calculated. For the case when such measurements are not available, the scaling for the ionization cross section in the case of K, L and M shell excitation can be used.We have proposed a new model for calculating electronic stopping power in which the formation of autoionization states in atomic collisions makes a dominant contribution to the inelastic energy loss and ionization of colliding atoms. Using data on the values of energy losses and ionization cross sections, it is possible to calculate the values of electronic stopping. The model predicts the threshold character of the dE/dx dependence versus the collision velocity and an increase in inelastic energy losses at the collision energies at which the threshold for the corresponding MO promotion occurs.

Calculation of Nuclear Stopping Power

Fast charged particles interact with matter mainly by interaction with the electron shell of the atoms causing ionization and excitation, i.e. inelastic scattering. However, for lower velocity projectiles an important part of the energy loss is due to elastic scattering on the nuclei, which is called nuclear stopping. In the present paper we calculate the nuclear stopping cross section of protons and antiprotons in different materials. The obtained results are compared with calculations by other groups and with the electronic stopping cross sections. The difference between the results for protons and antiprotons is explained. Keywords: interaction of charged particles with matter, nuclear stopping, Barkas effect.

Contribution of molecular orbital promotion to the electronic stopping cross section at slow atom solid collisions

The autoionization states formation due to MO promotion during collisions of keV-energy ions with solids produces a dominant contribution to inelastic energy losses and, accordingly, to the electronic stopping powers dE/dx. The correlations of emitted electron numbers δ with the values of inelastic energy losses Q are shown. When corresponding distances of closest approach are reached, the MO orbital promotion produces a stepwise increase in values of Q and δ. Based on the measured ionization cross-sections and Q values, electronic stopping powers can be calculated. For the case when such measurements are not available, the scaling for the ionization cross section in the case of K, L and M shell excitation can be used.We have proposed a new model for calculating electronic stopping power in which the formation of autoionization states in atomic collisions makes a dominant contribution to the inelastic energy loss and ionization of colliding atoms. Using data on the values of energy losses and ionization cross sections, it is possible to calculate the values of electronic stopping. The model predicts the threshold character of the dE/dx dependence versus the collision velocity and an increase in inelastic energy losses at the collision energies at which the threshold for the corresponding MO promotion occurs.

Molecular electronic stopping cross section for H and He beams colliding with water: projectile charge state contribution

Abstract When an ion beam impinges on a target material, electron stripping and capture processes involve different charge fraction states in the beam, such that each projectile charge state produces a different energy-loss. In this work, the energy deposition of swift hydrogen and helium ion beams colliding with a water target in the gas phase is studied. The electronic structure of the molecular target is represented in terms of core, bond, and lone pair orbital decomposition within a Harmonic Oscillator representation. In this way, the stopping cross section becomes only a function of the orbital mean excitation energy, I 0i . The ion beam charge fraction compositions colliding on water is determined from the work of Wedlund et al (2019) Astronomy &amp; Astrophysics, 630, A36) by accounting for the electron transfer cross sections. We find that the larger the projectile charge state, the larger the electronic stopping cross section and that the beam charge fraction determines the position of the maximum of the electronic stopping curve. Also, in agreement with the experiment, evidence is given on the dominant role of the largest projectile charge state in defining the stopping cross section for high energy collisions, while for low collision energies it is the lowest charge state together with all possible charge states contributing at the maximum of the electronic stopping cross section curve. Our results are reported and compared to available experimental data showing an excellent agreement to the available literature.

Estimation of electronic stopping cross sections of 4H-SiC for 2–26 MeV Al random-ion implantations

Electronic stopping cross sections of 4H-SiC for 2−26 MeV Al random-ion implantations (S e random) were estimated from the reported dependence of the projected range on the ion-implantation energy (E 0). The estimated S e random was a couple of times larger than the reported electronic stopping cross section along the 〈0001〉 channel and proportional to the square root of the ion energy (E) in the case E < 10 MeV. When E ranged from 10 to 26 MeV, the S e random saturated around 5 × 10−13 eV cm2 atom−1, suggesting that the Bethe-Bloch region, where S e random decreases with E, should exist at E larger than 26 MeV.

Experimental electronic stopping cross-section of tungsten bulk and sputter-deposited thin films for slow protons, deuterons and helium ions

Experimental electronic stopping cross-section of tungsten bulk and sputter-deposited thin films for slow protons, deuterons and helium ions

Comprehensive radiological parameterizations of proton and alpha particle interactions for some selected biomolecules: theoretical computation

Investigation of the interaction of radiations with biomolecules has several applications in the fields of radiation biophysics, radiation protection, medical biology, and medical physics. In this study, a comprehensive radiological parameterization of proton and alpha particles interactions at the energy range of (1 keV–10 GeV) and (1 keV–1 GeV), respectively for nucleotide bases (adenine, guanine, cytosine, uracil, thymine), carbohydrates (glucose, sucrose, raffinose), lipids (cholesterol, retinol, progesterone, cortisone, and phylloquinone), and fatty acids (lauric, myristic, palmitic, stearic, oleic, linoleic, linolenic, arachidonic, and arachidic) biomolecules have been carried out using PAGEX computer software. The radiological parameters calculated are the mass stopping power (S(E)/ρ), mass stopping cross-section (S c), effective atomic number (Z eff), and effective electron density (N eff). The highest values of S(E)/ρ and S c of proton and alpha particle interactions with the biomolecules occurred at the kinetic energy of about 0.1 and 0.5 MeV, respectively while that of the Z eff and N eff occurred at 0.1 MeV and 1 MeV, respectively. The S(E)/ρ and S c similarly vary with the kinetic energy due to their relations. As expected, the dependence of the Z eff and N eff of the biomolecules on the incidence energy was found to be similar. The comparisons of the Z eff and N eff calculated in this study, using PAGEX software with some studies in the literature that used the interpolation method showed variations that account for differences between the two methods.

Obrazovanie i raspad avtoionizatsionnykh sostoyaniy - osnovnoy mekhanizm neuprugikh poter' pri stolknoveniyakh atomov keV-energiy

It has been shown that the formation of autoionization states makes the dominant contribution to inelastic energy loss and to ionization in keV atomic collisions, i.e., at velocities lower than the velocities of atomic electrons. Scaling laws have been proposed to calculate the cross sections for the formation of vacancies in inner K and L electron shells of colliding atoms. A model has been proposed to relate ionization processes and the observed inelastic energy losses. Auger transitions in a short-lived quasimolecule formed by two atoms approaching each other have been studied. The nature of the continuous component in electron spectra emitted in collisions has been determined. It has been shown that the excitation of autoionization states determines the stopping cross sections for keV atoms in matter.

Electronic interaction of slow hydrogen, helium, nitrogen, and neon ions with silicon

We investigate the electronic excitation of silicon by hydrogen, helium, nitrogen, and neon ions for ion energies ranging from several tens to a few hundred kiloelectronvolts. Experiments are carried out in transmission geometry using a time-of-flight medium energy ion scattering system. The targets are self-supporting, single-crystalline Si (100) foils with nominal thicknesses of 50 and 200 nm. Stopping cross-sections (SCSs) are derived and compared with datasets available from the literature and predictions from theory. The results for H projectiles reveal good agreement with literature datasets, within quoted uncertainties. For He projectiles, the results show good agreement with most of the literature data. For N ions, higher values than reported in the literature are measured. For Ne, where literature data are scarce, we extend the velocity regime for which data exist by a factor of two toward higher velocities. The electronic SCS is found to be proportional to ion velocity for all impinging ions, for velocities below the Bohr velocity $(v&lt;{v}_{0})$. Comparison with theoretical predictions for a homogeneous free electron gas indicates strong contributions of local energy loss processes different from those expected for electron-hole pair excitation in binary collisions for all ions different from protons.

The study of the straggling energy loss

Straggling is the broadening of energy distribution of a beam charge particle penetrating through a material medium. The calculationsrepresenta problem of considerable complexity.The theoretical literature on straggling is rather limitedcomparedto the one on stopping cross section. In the present work, the energyloss of straggling has been studied theoretically for interaction of ions in target .&#x0D; The present work is a part of a thesis submitted for the PhD Degree in physics, in 2012 [1]. A program has been written inFORTRAN-90 using Compaq Visual FORTRAN V6.6 for compiling, linking and executing.A copy of the program is Available in [1]. Theagreementis achieved with previous works.

Sub-keV corrections to binary encounter cross section models for electron ionization of liquid water with application to the Geant4-DNA Monte Carlo code

IntroductionThe electron ionization cross section of water is one of the most important input in Monte Carlo studies of cellular radiobiological effects. Analytical cross section models of the binary-encounter type have the potential of reducing simulation time and facilitate application to a variety of biological materials (other than water). The Binary-Encounter-Bethe (BEB) and Binary-Encounter-Dipole (BED) models of NIST are perhaps the most popular of such models giving reliable results for atoms and molecules in the gas-phase over a wide energy range. However, the use of such models to sub-keV electron energies in liquid water raises concerns due to the neglect of condensed phase effects that leads to a significant overestimation when compared to medium-specific dielectric models. PurposeTo modify the BEB and BED models towards better agreement with the recommended low-energy dielectric model of Geant4-DNA (Option 4). To implement the new modifications to the existing BEB model of the Option 6 physics constructor of Geant4-DNA and re-evaluate fundamental transport quantities for sub-keV electrons. MethodsIn analogy to a Yukawa potential a simple, yet physically-motivated, modification of the Burgess correction term is proposed to account for the reduction of the Coulomb interaction due to the polarizability of the target. The magnitude of the correction is guided by the dielectric-based ionization cross section implemented in Option 4. ResultsDifferential, total and stopping ionization cross sections for low-energy electrons in liquid water are presented. When combined with the Vriens correction (which is not included in Option 6), the proposed modification to the BEB and BED models brings the ionization and stopping cross sections in much better agreement against those used in the Option 4 dielectric model of Geant4-DNA, with up to 30% and 10% deviation, respectively. Implementation of the new correction to the Option 6 constructor of Geant4-DNA and re-evaluation of fundamental transport quantities, such as electron penetration ranges and dose-point-kernels, reduced the discrepancies from Option 4 at sub-keV energies from 20 to 100% (or more) to well below 10% in most cases. ConclusionsA simple modification to the BEB and BED analytic models was found to improve their performance for sub-keV electrons in liquid water medium. Implementation of the new modification to the Option 6 constructor of Geant4-DNA significantly improved the agreement with the recommended low-energy Option 4 constructor for a variety of fundamental quantities related to electron transport.

Sensitivity of ion implantation to low-energy electronic stopping cross-sections

Clarifying the sensitivity of ion implantation to low-energy electronic stopping cross-sections (ESCS) is critical to assess different ESCS for simulating radiation damage in the fields like materials science, space exploration and electronic industry. The Monte Carlo code IM3D improved with a users’ ESCS module and a proposed analytical model are used to investigate the sensitivity of ion depth distribution to different ESCS including Stopping and Range of Ions in Matter (SRIM), Binary Theory (BT) and Unitary Convolution Approximation (UCA) at low energies (lower than 75 keV/u). The analytical model is consistent with IM3D well and thus provides a simple way to assess arbitrary ESCS. We found that the larger the ratio of electronic to nuclear energy loss is, the stronger sensitivity of ion depth distribution to ESCS is. Based on the assessment, the upgraded SRIM database and BT with the shell correction for light ions while UCA with the Bloch correction for heavy ions are recommended for simulating ion implantation to agree with experimental results.

Re-evaluation of energy dependence of electronic stopping cross-section for Al ions into 4H-SiC (0001)

To apply channeled-ion implantation to cost-effective multi-epitaxial growth for 4H-SiC superjunction devices, we re-evaluated the Al-ion energy (E) dependence of the electronic stopping cross section (S e) in 4H-SiC based on the recently reported secondary-ion mass spectrometry measured depth profiles. By including the effect of stripping of the ion electrons on the E dependence of S e, we successfully reproduced the reported maximum channeled ranges of Al into 4H-SiC (0001), ranging from 0.6 μm at the implantation-energy (E 0) of 60 keV to 7.2 μm at E 0 of 8 MeV.

Inelastic collisions of fast charged particles with atoms: Bethe asymptotic formulas and shell corrections

The relativistic plane-wave Born approximation is applied to the study of inelastic collisions of charged particles with atoms, by considering atomic wave functions calculated from the independent-electron approximation with the self-consistent Dirac-Hartree-Fock-Slater potential. A database of longitudinal and transverse generalized oscillator strengths (GOSs) has been computed by using accurate numerical methods for all the subshells of the ground-state configurations of the elements with atomic numbers from 1 (hydrogen) to 99 (einsteinium). The calculated GOS do not satisfy the Bethe sum rule; departures from the sum rule are in accordance with previous theoretical estimates. Asymptotic high-energy formulas for the total cross section, the stopping cross section, and the energy-straggling cross section are derived with proper account of the relativistic departure from the Bethe sum rule. The shell correction is calculated as the energy-dependent term that, when added to the asymptotic formula, reproduces the value of the atomic cross section calculated by integrating the energy-loss differential cross section. Shell corrections to the stopping cross section obtained from the present approach are presented and compared with previous estimates.