Electronic Stopping Cross Section Research Articles

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.

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

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.

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.

Electronic energy loss assessment in theoretical modeling of primary radiation damage in tungsten

Reliable electronic energy loss needs to be accounted for to accurately estimate primary radiation damage of materials in theory. By introducing four types of electronic stopping cross-sections ([Formula: see text]) into the Monte Carlo (MC) code (IM3D) of collision cascade, and using an object kinetic MC model of short-term defect evolution, we studied the complete process of production and annealing of primary defects in tungsten (W) under high-energy ([Formula: see text] MeV) self-ion and low-energy ([Formula: see text] keV - hundreds keV) neutron-primary knock-on atom (PKA) irradiation. Different [Formula: see text] and their effects were evaluated to accurately estimate primary radiation damage. The difference in electronic energy loss changes the fraction of damage energy, affecting the number of primary defects and their spatial/size distributions. This effect is even pronounced with increasing initial energy, with deviations up to 40% and 60% for damage range and defect number, respectively. The simulation results with [Formula: see text] calculated by time-dependent density functional theory (TDDFT) are quantitatively consistent with experimental damage peaks in self-ion irradiated W and molecular dynamics simulated number of survival defects in neutron-PKA irradiated W. Thus, we recommend using [Formula: see text] calculated by TDDFT to estimate primary radiation damage in W with relative accuracy. It helps understand primary damage behaviors, further accurately simulate long-term defect evolution and predict properties of materials under irradiation.

Assessing electronic energy loss of heavy ions detected in reflection geometry

We study energy loss spectra of bromine ions scattered from silver thin films in the energy range of 4 to 36 MeV in forward reflection geometry. The different contributions to the energy loss are analyzed by complementary Monte Carlo simulations. We assess the dependence of the scattering yield and nuclear and electronic losses on the penetration depth of detected ions. For scattering from larger depth, we observe decreased elastic losses and increased trajectory length in comparison with predictions from single scattering, with increasing effects for lower energies. To investigate the entanglement of energy loss and depth information, electronic stopping cross sections are deduced from the experimental spectra by two different approaches: (a) assuming a single scattering model and (b) making use of Monte Carlo simulations. The data obtained from the two approaches are compared, and we assess the relative contributions from nuclear stopping and from the effect of multiple scattering on trajectory length. Results of both methods are discussed in the context of composition depth profiling and compared with data from literature and with Stopping and Range of Ions in Matter (SRIM) predictions resulting in good agreement.

Experimental electronic stopping cross section of tungsten for light ions in a large energy interval

Electronic stopping cross section of tungsten for light ions was experimentally measured in a wide energy interval (20 to 6000 keV for protons and 50 to 9000 keV for helium) in backscattering and transmission geometries. The measurements were carried out in three laboratories (Austria, Germany and Sweden) using five different set-ups, the stopping data deduced from different data sets showed excellent agreement amongst each other, with total uncertainty varying within 1.5–3.8% for protons and 2.2–5.5% for helium, averaged over the respective energy range of each data set. The final data is compared to available data and to widely adopted semi-empirical and theoretical approaches, and found to be in good agreement with most adopted models at energies around and above the stopping maximum. Most importantly, our results extend the energy regime towards lower energies, and are thus of high technological relevance, e.g., in fusion research. At these low energies, our findings also revealed that tungsten – featured with fully and partially occupied f- and d-subshells, respectively – can be modeled as an electron gas for the energy loss process.

Dipole and generalized oscillator strengths-dependent electronic properties of helium atoms immersed in a plasma

Atoms subjected to extreme environmental conditions are of fundamental importance due to the modification of their electronic properties. In this work, we study the helium atom when immersed in a plasma environment. In order to describe the plasma medium, we use two models when solving the Schrodinger equation in a restricted Hartree–Fock approach: the Debye–Huckel screened (DHS) potential and a more general exponential-cosine screened Coulomb (ECSC) potential. The plasma length parameter, $$\lambda $$ , in both model potentials characterizes the plasma screening effects which cause an increase or decrease in the electronic properties of the helium atom. We report results for the total electronic ground state energy, orbital energy, dipole oscillator strengths, generalized oscillator strengths (GOS), mean excitation energy, electrostatic dipole polarizability, and electronic stopping cross section. We find that the ECSC plasma model produces a less bound system than the DHS plasma model at the same value of the screening length, $$\lambda $$ . However, the ECSC model potential has a stronger dipole transition from the 1s to the 2p and 3p states than the DHS model potential. Also, the ECSC potential predicts a higher static dipole polarizability than the DHS model potential, with a consequent lower mean excitation energy. We also find a larger GOS for the ECSC than for the DHS for the same momentum transfer at the same value of the screening length, $$\lambda $$ . Consequently, the ECSC mode potential produces a larger electronic stopping cross section than the DHS for the same $$\lambda $$ and projectile velocity. In the limit of $$\lambda \rightarrow \infty $$ , we have excellent agreement with the free helium properties. These quantitative values for the electronic properties would be useful for the investigations of the atomic structure and collisions of helium atoms immersed in plasmas.

Analytical expression for the electronic stopping cross section of atomic gas targets for hydrogen projectiles

The author derives an analytical expression for the electronic stopping cross section of atomic gas targets at nonrelativistic velocities for hydrogen ions. The expression is based on an ab initio approach to account for the electronic excitations and charge exchange processes at low collision energies and the correct Bethe approach at high collision energies.

Contribution of Autoionization Processes to the Electronic Stopping Power

It is shown that the excitation of autoionization states during the collisions of keV-energy ions with a solid plays a determining role in the formation of inelastic energy losses and, accordingly, the electronic-stopping cross section Se. It is proposed to estimate the Se values using the relationship between the cross section for autoionization-state excitation and the ionization cross section. For cases where the ionization cross sections are unknown, scaling is used to calculate the ionization cross sections when the L and M shells are excited. The threshold dependence of Se versus the energy of bombarding ions is predicted.

Experimental electronic stopping cross section of transition metals for light ions: Systematics around the stopping maximum

Electronic stopping cross sections of different transition metals (Nb, Pd, Ta, and Pt) for light ions have been experimentally determined in a wide energy range. We performed relative measurements using different backscattering geometries for protons (from 50 to 5000 keV) and helium (from 80 to 10 000 keV). Data are compared to values from the literature, as well as to the widely used semiempirical (srim) and modeling (dpass) approaches. The magnitude and energy dependence of the deduced stopping power at energies around the Bragg peak, as well as the different trends observed within individual periods, are analyzed with respect to target atomic number and electronic structure. We also compare the observed magnitude of electronic stopping to several different theoretical approaches.

Electronic excitation of transition metal nitrides by light ions with keV energies

We investigated the specific electronic energy deposition by protons and He ions with keV energies in different transition metal nitrides of technological interest. Data were obtained from two different time-of-flight ion scattering setups and show excellent agreement. For protons interacting with light nitrides, i.e. TiN, VN and CrN, very similar stopping cross sections per atom were found, which coincide with literature data of N2 gas for primary energies ⩽25 keV. In case of the chemically rather similar nitrides with metal constituents from the 5th and 6th period, i.e. ZrN and HfN, the electronic stopping cross sections were measured to exceed what has been observed for molecular N2 gas. For He ions, electronic energy loss in all nitrides was found to be significantly higher compared to the equivalent data of N2 gas. Additionally, deviations from velocity proportionality of the observed specific electronic energy loss are observed. A comparison with predictions from density functional theory for protons and He ions yields a high apparent efficiency of electronic excitations of the target for the latter projectile. These findings are considered to indicate the contributions of additional mechanisms besides electron hole pair excitations, such as electron capture and loss processes of the projectile or promotion of target electrons in atomic collisions.

Calculation of the electronic, nuclear, rotational, and vibrational stopping cross sections for H atoms irradiation on H2, N2 and O2 gas targets at low collision energies

In this work, we present a study of hydrogen atoms interacting with hydrogen, nitrogen, and oxygen molecules in the gas phase in order to determine the projectile energy loss, the stopping cross section, and energy deposition with implication in hydrogen and proton dosimetry and radiotherapy. Our calculations are performed with a density-functional tight-binding (DFTB) as well as by an ab initio electron-nuclear dynamic (END). The H atoms have a low collision energy in the range of 1–100 eV for the DFTB and 1–1000 eV for the END. We decompose the projectile energy deposition into its electronic, nuclear, rotational, and vibrational energy target contributions. We find that for low collisions energy, DFTB and END are in fair agreement when comparing the nuclear and rotational contributions. However, we find discrepancies for the vibrational and electronic energy loss between both approaches. The largest discrepancy is found in the electronic energy loss as DFTB carries the electronic dynamics in the ground state. We confirm that the electronic stopping cross section is proportional to the projectile velocity as obtained by END showing a threshold effect and that it is underestimated by codes like SRIM. Our study shows that at low collision energies a quantum-classical molecular dynamics approach as DFTB can be used to determine the energy-loss process of a projectile penetrating a material target. Finally, we compare our results to available experimental data finding good agreement when extrapolated to high collision energies.