Effect of energy loss in the simulation of slow ion scattering by a solid surface

As previously shown [B. Arezki, Y. Boudouma, P. Benoit-Cattin, A.C. Chami, C. Benazeth, K. Khalal, M. Boudjema, J. Phys.: Condens. Mat. 10 (1998) 741, K. Khalal-Kouache, A.C. Chami, M. Boudjema, P. Benoit-Cattin, C. Benazeth, Y. Boudouma, Nucl. Instr. and Meth. B 183 (2001) 279], energy spectra of scattered particles from amorphous solid surface can be deduced from angular distributions of the total path length of the projectiles. In preceding papers [K. Khalal-Kouache, A.C. Chami, M. Boudjema, P. Benoit-Cattin, C. Benazeth, Y. Boudouma, Nucl. Instr. and Meth. B 183 (2001) 279, K. Khalal-Kouache, A. Mekhtiche, A.C. Chami, M. Boudjema, Surf. Coat. Technol. 201 (2007) 8420], a model based on the transport theory was used to simulate the scattering of slow ions by a solid target. Angular distributions of the total path length were computed and compared, in absolute value, to those simulated using a Monte Carlo code. A good agreement was obtained except for the highest values of the total path length L. In the transport theory, the variation of the scattering cross section versus energy during the slowing down of the particle was not taken into account. The purpose of this contribution is to take into account this effect within the model. The obtained results are found to be in agreement with Monte Carlo computation for angular distributions of the total path length and for energy spectra of the scattered ions.     

Algorithm for forcing scattered radiation to arbitrary convex regions in neutral particle Monte Carlo simulation

A new algorithm is presented to improve the efficiency of neutral particle Monte Carlo radiation transport. When a radiation quantum is produced from a source or undergoes a scattering event, it is divided into two parts. One continues to undergo the normal analogue transport process. The other is deterministically transported to a randomly selected point on the surface of an arbitrary convex region, from where it continues normal transport. Application of this approach substantially improves efficiency in cases where particles must reach small geometric regions in order to make tally contributions. The algorithm is demonstrated in a simulation of X-ray scattering in a radiographic imaging application.     

Energy loss and straggling of Li ions in the polymer foils

Energy loss and straggling of 0.18-0.78 MeV/amu ⁷Li ions in polycarbonate, polyethylene terephthalate and polypropylene foils were measured by means of a transmission technique with a half-covered detector. The stopping force measurements are compared with the SRIM 2006 calculation and the database of the ICRU report 73. The measured energy loss straggling are in satisfactory agreement with the results yielded using the empirical formula at the higher energy region. The obtained data also demonstrated that the validity of Bragg’s rule applied to stopping force and energy loss straggling for ⁷Li ions in polymer foils.     

The simulation of implantation of heavy charged particles in a crystalline material

We have studied the channeling effect in the ion implantation by simulating the collision of heavy charged particles with a crystalline material. In order to determine the penetration depth of fast heavy ions in crystalline material, we modified a model from pervious work and studied a situation where heavy As and P ions impinging on a crystal Si〈1 0 0〉 surface. A new stopping power calculation method is combined to the transport theory based ion range calculation equation for the fast and accurate numerical calculation of ion ranges. We simulated penetration event by dividing the surface of crystal in to three different region based on the distance from atomic centers in crystal structure. We solved differential equation numerically for each ions simulated. The results have been compared with similar models and the experimental data from literature. We found a good agreement with experiment for the behavior of distribution of ions in the crystalline substance. The model proposed here can be used successfully to predict channeling implantation profiles of heavy ions.     

Measurement of the energy deposition profile for U ions with specific energy 500 and 950 MeV/u in stainless steel and copper targets

The paper presents the results of precision measurements of the total stopping range and energy deposition function of ²³⁸U ions with specific energies E = 500 and 950 MeV/u in stainless steel and copper targets. The experiment was performed at the SIS-18 facility (GSI Darmstadt) in the experimental area Cave A in September 2004-May 2005.The measured energy deposition profiles are compared with calculations using the codes ATIMA, PHITS, SHIELD and SRIM.     

Stopping of 0.3-1.2 MeV/u protons and alpha particles in Si

The stopping cross sections ε(E) of silicon for protons and alpha particles have been measured over the velocity range 0.3-1.2 MeV/u from a Si//SiO₂//Si (SIMOX) target using the Rutherford backscattering spectrometry (RBS) with special emphasis put on experimental aspects. A detection geometry coupling simultaneously two solid-state Si detectors placed at 165° and 150° relative to each side of the incident beam direction was used to measure the energies of the scattered ions and determine their energy losses within the stopping medium. In this way, the basic energy parameter, E_x, at the Si/SiO₂ interface for a given incident energy E₀ is the same for ions backscattered in the two directions off both the Si and O target elements, and systematic uncertainties in the ε(E) data mainly originating from the target thickness are significantly minimized. A powerful computer code has been elaborated for extracting the relevant ε(E) experimental data and the associated overall uncertainty that amounts to less than 3%. The measured ε(E) data sets were found to be in fair agreement with Paul’s compilation and with values calculated by the SRIM 06 computer code. In the case of ⁴He⁺ ions, experimental data for the γ effective charge parameter have been deduced by scaling the measured stopping cross sections to those of protons crossing the same target with the same velocity, and compared to the predictions of the SRIM 06 computer code. It is found that the γ-parameter values generated by the latter code slightly deviate from experiment over the velocity region around the stopping cross section maximum where strong charge exchanges usually occur.     

Erratum to “On the gas-solid difference in stopping power for low energy ions” [Nucl. Instr. and Meth. B 262 (2007) 13]

Recently, we claimed that the gas-solid difference in stopping powers persists from high down to low ion energies. This claim was based on a comparison between experimental data and the table of ICRU Report 73. We reconsider this claim in view of a recent article by Sigmund and Schinner where the claim was rejected. We find that the apparent gas-solid difference shown in our calculations is an artifact: it really points to an inadequacy of the table of ICRU 73 for low energy ions.     

Total bremsstrahlung spectral photon distributions in metallic targets in the photon energy range of 5-10 keV by Tl beta particles

Total bremsstrahlung spectral photon distributions produced by beta particles of the ²⁰⁴Tl beta emitter in thick targets of Al, Ti, Sn and Pb targets were evaluated at photon energies from 5 keV to 10 keV. Experimental measurements were compared with the theoretical total bremsstrahlung spectral photon distributions obtained from Elwert corrected (non-relativistic) Bethe-Heitler theory and modified Elwert factor (relativistic) Bethe-Heitler theories for ordinary bremsstrahlung, and the modified Elwert factor (relativistic) Bethe-Heitler theory which includes polarization bremsstrahlung in the stripped atom approximation. The experimental results show better agreement with the modified Elwert factor (relativistic) Bethe-Heitler theory which includes the contribution of polarization bremsstrahlung. The contributions of polarization bremsstrahlung decrease with increased photon energy, particularly for medium and high Z elements. Hence its contribution cannot be neglected while studying the total bremsstrahlung spectral photon distributions in thick targets, produced by continuous beta particles in the studied energy region.     

The solid-gas difference in stopping powers, and statistical analysis of stopping power data

For the purpose of treating the difference in stopping power between condensed and gaseous substances, we first discuss our method of statistical analysis of published experimental data. We distinguish between a positive effect where the difference between mass stopping powers S_solid − S_gas is positive and a negative effect where the opposite holds true. Experimentally, the positive effect has been found so far with heavy ions at high energy, and the negative effect with light ions at low energy. The positive effect is due to the difference in ionic charges and can be described by the CasP program by Grande and Schiwietz. An apparent persistence of the positive effect down to low energy is found to be mainly an artifact inherent in the stopping table of ICRU Report 73. The negative effect can be described by a difference in mean ionization potentials between gases and condensed matter. It is large for metals, much smaller for compounds. It should be possible to see both effects in one projectile - target combination.     

Application of the Monte Carlo method to the analysis of measurement geometries for the calibration of a HP Ge detector in an environmental radioactivity laboratory

A gamma spectrometer including an HP Ge detector is commonly used for environmental radioactivity measurements. The efficiency of the detector should be calibrated for each geometry considered. Simulation of the calibration procedure with a validated computer program is an important auxiliary tool for environmental radioactivity laboratories. The MCNP code based on the Monte Carlo method has been applied to simulate the detection process in order to obtain spectrum peaks and determine the efficiency curve for each modelled geometry. The source used for measurements was a calibration mixed radionuclide gamma reference solution, covering a wide energy range (50-2000 keV). Two measurement geometries - Marinelli beaker and Petri boxes - as well as different materials - water, charcoal, sand - containing the source have been considered. Results obtained from the Monte Carlo model have been compared with experimental measurements in the laboratory in order to validate the model.     

Summary of “IAEA intercomparison of IBA software”

The International Atomic Energy Agency has sponsored a formal intercomparison exercise for the seven depth profiling ion beam analysis codes, which are: GISA, RUMP, RBX, DEPTH, DataFurnace, SIMNRA and MCERD. This intercomparison is published in Nucl. Instr. and Meth. B [N.P. Barradas, K. Arstila, G. Battistig, M. Bianconi, N. Dytlewski, C. Jeynes, E. Kótai, G. Lulli, M. Mayer, E. Rauhala, E. Szilágyi, M. Thompson, Nucl. Instr. and Meth. B 262 (2007) 281-303] and summarised here. The codes implement all known physical effects and they are all evaluated. We demonstrate that there is agreement between codes often better than 0.1%; and also detailed agreement with real spectra, showing in particular that the SRIM 2003 stopping powers for Si are correct to 0.6% for 1.5 MeV He. For the case of heavy ion elastic recoil detection (HI-ERD) the single scattering codes performed poorly for scattered particles, although recoiled particles were calculated correctly.     

International Atomic Energy Agency intercomparison of ion beam analysis software

Ion beam analysis (IBA) includes a group of techniques for the determination of elemental concentration depth profiles of thin film materials. Often the final results rely on simulations, fits and calculations, made by dedicated codes written for specific techniques. Here we evaluate numerical codes dedicated to the analysis of Rutherford backscattering spectrometry, non-Rutherford elastic backscattering spectrometry, elastic recoil detection analysis and non-resonant nuclear reaction analysis data. Several software packages have been presented and made available to the community. New codes regularly appear, and old codes continue to be used and occasionally updated and expanded. However, those codes have to date not been validated, or even compared to each other. Consequently, IBA practitioners use codes whose validity, correctness and accuracy have never been validated beyond the authors’ efforts. In this work, we present the results of an IBA software intercomparison exercise, where seven different packages participated. These were DEPTH, GISA, DataFurnace (NDF), RBX, RUMP, SIMNRA (all analytical codes) and MCERD (a Monte Carlo code). In a first step, a series of simulations were defined, testing different capabilities of the codes, for fixed conditions. In a second step, a set of real experimental data were analysed. The main conclusion is that the codes perform well within the limits of their design, and that the largest differences in the results obtained are due to differences in the fundamental databases used (stopping power and scattering cross section). In particular, spectra can be calculated including Rutherford cross sections with screening, energy resolution convolutions including energy straggling, and pileup effects, with agreement between the codes available at the 0.1% level. This same agreement is also available for the non-RBS techniques. This agreement is not limited to calculation of spectra from particular structures with predetermined parameters, but also extends to extracting information from real data. In particular, we have shown data from an Sb implanted sample where the Sb fluence was certified with an uncertainty of 0.6%. For this sample, and using SRIM03 stopping powers for 1.5 MeV ⁴He in Si, the codes were able to extract the Sb fluence with an average 0.18% deviation from the certified value and a 0.11% agreement between the codes. Thus IBA is a suitable technique for accurate analysis where traceability is critical. These results confirm that available IBA software packages are, within their design limitations, consistent and reliable. The protocol established may be readily applied to validate future IBA software as well.     

Stopping power and energy straggling of protons in graphite and amorphous carbon obtained from a resonance in BS spectra

Backscattering (BS) spectra with a sharp 4.8-MeV resonance for carbon targets have been measured using proton beams in an energy range 4.85-6.1 MeV per 100-keV step. By systematic analyses of the resonance peak profiles, values of stopping power and energy straggling have been deduced for proton energies from 0.8 to 3.4 MeV which corresponds to a penetration depth of 88 μm. In particular, to investigate the difference in stopping power and straggling caused by target inhomogeneity, we used two target materials which were highly oriented pyrolytic graphite (HOPG, 2.26 g/cm³) as a homogeneous material and amorphous carbon (1.73 g/cm³) as an inhomogeneous material. We describe a method of measuring stopping power and straggling using a resonance in the BS spectra. The stopping powers obtained are compared with the values determined by SRIM-2006. Moreover, collision straggling and a density straggling due to the inhomogeneity of the target materials are evaluated from the width broadening of resonance peaks.     

Channeling of protons in double-walled carbon nanotubes in kinetic model

A kinetic model combined with the dielectric response theory is employed to study the electronic excitation on the nanotube walls during the channeling of protons through double-walled carbon nanotubes. Analytical expressions of the self-energy and stopping power are obtained with protons moving along the axis of the double-walled nanotubes. Calculation results show us interesting double-peak curves of the self-energy and stopping power, under strong influence of the damping factor and the special double-walled nanotube geometry. Relatively increasing the damping factor and the chiral parameter of the outer wall can reduce the interference effects between the two walls and weaken the double-peak to one-peak shapes.     

Electronic stopping power for proton in amino acids and protein in 0.05-10 MeV range

The stopping powers for 0.05-10 MeV protons in a group of 15 amino acids and a protein have been systematically calculated. The calculations are based on Ashley’s dielectric model. An approach of evaluating the optical energy loss function is incorporated into the Ashley’s model because no experimental optical data are available for these bioorganic compounds. The Barkas-effect correction and Bloch correction are included and an empirical minimum impact parameter a is used for the Barkas-effect correction. The proton stopping powers for the 15 amino acids and the protein in the energy range from 0.05 to 10 MeV are presented here for the first time and might be useful for studies of various radiation effects in these materials.     

Current status of kinematically complete studies of basic fragmentation processes in atomic systems

Recent developments on kinematically complete experiments on basic atomic fragmentation processes are reviewed. Comparisons between theoretical and experimental fully differential cross sections for single ionization of light atoms by charged particle impact are analyzed. Furthermore, a method developed very recently, four-particle Dalitz plots, is discussed in context of double ionization. The extraordinary power of these plots is their capability to provide a comprehensive picture of the momentum exchange between all four final-state particles in a single spectrum.     

Z2 structure of the stopping power for electron beams

The target atomic number (Z₂) dependence of the collision stopping power for electron beams have been investigated for the purpose of determining primary mechanisms in stopping of electrons in elemental matter. The stopping powers of target elements with atomic numbers Z₂ = 1-92 for the electrons have been evaluated on the basis of Gümü? method. The variation of the stopping power depending on energy of electrons and type of target has been studied to obtain the elements with the strongest stopping force property for electron beams. A strong Z₂ oscillation in the collision stopping power has been observed whereas the mass collision stopping powers are found to be decreasing with increasing atomic number of the target. It is also found that the electron slowing down in matter mainly depends on the atomic density of target and initial energy of electrons.     

A Time of Flight-Energy spectrometer for stopping power measurements in Heavy Ion-ERD analysis at iThemba LABS

The quantitative analysis of thin layers using Heavy Ion-Elastic Recoil Detection (HI-ERD) can be reliably performed if the stopping powers of the probing ions and recoils in a given target matrix are known accurately. Unfortunately for many projectile/target combinations experimental data is limited and where available, deviations of up to 50% between experiment and theory have been reported. This presentation describes the assembly of a Time of Flight-Energy (ToF-E) detector system developed for HI-ERD analysis and adapted for stopping power measurements at iThemba LABS. First results from energy loss measurements of 0.1-0.5 MeV/nucleon ²⁸Si and ⁸⁴Kr ions in ZrO₂ are presented and compared with predictions of the widely used SRIM2003 (Stopping Range of Ions in Matter).     

A Monte Carlo investigation of secondary electron emission from solid targets: Spherical symmetry versus momentum conservation within the classical binary collision model

A Monte Carlo scheme is described where the secondary electron generation has been incorporated. The initial position of a secondary electron due to Fermi sea excitation is assumed to be where the inelastic collision took place, while the polar and azimuth angles of secondary electrons can be calculated in two different ways. The first one assumes a random direction of the secondary electrons, corresponding to the idea that slow secondary electrons should be generated with spherical symmetry. Such an approach violates momentum conservation. The second way of calculating the polar and azimuth angles of the secondary electrons takes into account the momentum conservation rules within the classical binary collision model. The aim of this paper is to compare the results of these two different approaches for the determination of the energy distribution of the secondary electrons emitted by solid targets.     

Computer simulation of sputtering at the low index (1 0 0), (1 1 0) and (1 1 1) surfaces of Ni3Al in a STEM

The present study is relevant to the preferential Al sputtering and/or enhancement of the Ni/Al ratio in Ni₃Al observed by the scanning transmission electron microscopy fitted with a field emission gun (FEG STEM). Atomic recoil events at the low index (1 0 0), (1 1 0) and (1 1 1) surfaces of Ni₃Al through elastic collisions between electrons and atoms are simulated using molecular dynamics (MD) methods. The threshold energy for sputtering, E_sp, and adatom creation, E_ad, are determined as a function of recoil direction. Based on the MD determined E_sp, the sputtering cross-sections for Ni and Al atoms in these surfaces are calculated with the previous proposed model. It is found that the sputtering cross-section for Al atoms is about 7-8 times higher than that for Ni, indicating the preferential sputtering of Al in Ni₃Al, in good agreement with experiments. It is also found that the sputtering cross-sections for Ni atoms are almost the same in these three surfaces, suggesting that they are independent of surface orientation. Thus, the sputtering process is almost independent of the surface orientation in Ni₃Al, as it is controlled by the sputtering of Ni atoms with a lower sputtering rate.