Impact Parameter Dependent Energy Loss Research Articles

Impact of the experimental approach on the observed electronic energy loss for light keV ions in thin self-supporting films

Energy spectra of keV ions interacting with self-supporting foils of Au and W were recorded with a Time-of-Flight Medium-Energy Ion Scattering system in different backscattering and transmission geometries in an otherwise identical experimental setup. For He ions transmitted through Au spectra of detected particles depending on geometry show two distinct components, i.e. different energy loss distributions in the film, whereas for protons no such phenomenon was observed. The two components in the spectrum of transmitted He could be attributed to impact parameter dependent energy loss, being more prominent for He than for protons. The main origin of the necessary impact parameter selection along different trajectories is expected to be texture in the Au-foils. Electronic stopping powers obtained from both, most probable energy loss in transmission and best fits to spectrum width in backscattering are in agreement within experimental uncertainties. This observation applied for all investigated combinations of projectile and target material.

Contrast modes in a 3D ion transmission approach at keV energies

We present options for visualizing contrast maps in 3D ion transmission experiments. Simultaneous measurement of angular distributions and flight time of ions transmitted through self-supporting, single-crystalline silicon foils allows for mapping of intensity and different energy loss moments. The transmitted projectiles were detected mainly for random beam-sample orientation using pulsed beams of He ions and protons with incident energies 50 and 200 keV. Differences in contrast, observed when varying the projectile type and energy, can be attributed to sample nuclear and electronic structure and bear witness to impact parameter dependent energy loss processes. Our results provide a base for interpretation of data obtained in prospective transmission studies when for example using a helium ion microscope.

Dependence of secondary electron emission on the emergent angle of 1 MeV/u H+, He2+ and Li3+ penetrating a thin carbon foil

With 1MeV/u H+, He2+ and Li3+ beams incident on a carbon foil of 2.2μg/cm2 in thickness, the statistical distributions of the number of simultaneously emitted secondary electrons (SE’s) have been measured as a function of the emergent angle of foil-transmitted ions in the range from 0.0mrad to 4.0mrad for every 0.5mrad step. The measurement of SE’s was carried out in the forward and backward directions of the incident beam independently. The SE yields, that is, the mean number of emitted electrons per incident ion, increase with increasing the emergent angle and saturate at larger angles. This trend is common to the projectiles used and also to the forward and backward directions. As a result of a Monte Carlo simulation taking account of the impact parameter dependent energy loss in a single collision of a proton with a carbon atom, it is found that the calculated energy losses exhibit an emergent angular dependence quite similar to that of the measured SE yields. However the measured SE yields divided by the square of the projectile atomic number, ZP, becomes smaller with increasing ZP, especially for the backward emission. A similar observation has been reported by other authors and this trend seems to originate from the preferencial fast internal SE production by heavier projectiles followed by their escape from a thin target foil.

Dependence of secondary electron emission on the emergent angle of 2.5-MeV protons penetrating a thin carbon foil

With 2.5-MeV proton beams incident on a carbon foil of $1.8\ensuremath{\mu}{\mathrm{g}/\mathrm{c}\mathrm{m}}^{2}$ in thickness, the statistical distributions of the number of simultaneously emitted secondary electrons (SEs) have been measured as a function of the emergent angle of ions penetrating the foil in the range from 0.0 mrad to 2.0 mrad for every 0.5-mrad step. The measurement of SEs was carried out at the forward and backward directions of the incident beam separately. For all of the measured angles, the probability of simultaneous n electron emission per projectile, ${W}_{n},$ exhibits roughly an exponential decrease with increasing n. Up to $\ensuremath{\sim}1\mathrm{mrad},$ however, the decreasing rate becomes smaller with an increase in the emergent angle. On the other hand, ${W}_{n}$ reaches saturation at larger angles. This behavior is common to the forward and backward SE emission. In terms of this angular dependence, the average SE yields per projectile at the forward direction, ${\ensuremath{\gamma}}_{\mathrm{F}},$ and at the backward direction, ${\ensuremath{\gamma}}_{\mathrm{B}},$ increase as high as about 50% at 1.0 mrad compared with corresponding ones at 0.0 mrad and saturate at larger angles. As a result of a Monte Carlo simulation taking account of the impact parameter dependent energy loss in a single collision of a proton with a carbon atom, it is found that the calculated energy losses exhibit a quite similar emergent angle dependence to that of the measured SE yields.

The unitary convolution approximation for heavy ions

The convolution approximation for the impact-parameter dependent energy loss is reviewed with emphasis on the determination of the stopping force for heavy projectiles. In this method, the energy loss in different impact-parameter regions is well determined and interpolated smoothly. The physical inputs of the model are the projectile-screening function (in the case of dressed ions), the electron density and oscillators strengths of the target atoms. Moreover, the convolution approximation, in the perturbative mode (called PCA), yields remarkable agreement with full semi-classical-approximation (SCA) results for bare as well as for screened ions at all impact parameters. In the unitary mode (called UCA), the method contains some higher-order effects (yielding in some cases rather good agreement with full coupled-channel calculations) and approaches the classical regime similar as the Bohr model for large perturbations ( Z/ v≫1). The results are then used to compare with experimental values of the non-equilibrium stopping force as a function of the projectile charge as well as with the equilibrium energy loss under non-aligned and channeling conditions.

Limitations to depth resolution in ion scattering experiments

The energy spectra of scattered ions in Rutherford backscattering and elastic recoil scattering experiments are commonly described using stopping power and straggling data. These, in turn, are based on statistical approximations and thus neglect the characteristics of individual ion–atom collisions. This simplified analysis is not justified when considering experiments with high-energy resolution. We have performed theoretical and experimental studies to understand the shape of high-energy resolution ion scattering spectra. The impact parameter dependent energy loss in single ion–atom collisions has been calculated using the semi-classical approximation (SCA). We show that limitations for extracting monolayer depth resolution become obvious from this non-statistical approach. Experiments were performed using a medium energy ion scattering (MEIS) system. For the case of 100 keV protons scattered on sulfur atoms, good agreement between the theoretical description and experimental data was found. The influence of thermal vibrations of the sample atoms on the backscattering spectra is discussed.

Angular dependence of the electronic stopping power of Li ions channeled around the Si 〈1 0 0〉 direction

In the present work we report on measurements of the electronic stopping power of 1.2 MeV 7Li + ions channeled through the Si 〈1 0 0〉 axis as a function of the incident angle between −1.2° and 1.2°. The experiments were done using the Rutherford backscattering technique with a SIMOX sample. The measured ratio α between the channeling and random stopping powers as a function of the angle show an upside down Gaussian-like angular dependence with a minimum of α=0.84±0.04 and a FWHM of 0.67°±0.10°. From the experimental data the impact parameter dependent energy loss is estimated and compared with first order calculations.

The Z14-term in electronic stopping: impact parameter dependence and stopping cross section for a quantal harmonic oscillator

The Z 1 4-correction to the electronic stopping cross section of a quantal harmonic oscillator has been evaluated accurately. The calculation is performed within the impact parameter description, where the projectile is assumed to follow a straight line trajectory during the collision. By applying the third Born approximation the impact parameter dependent energy loss to the oscillator is determined to the fourth order in the interaction. The corresponding Z 1 4-correction to the stopping cross section is found by integrating over all impact parameters, and the results are compared with the Bloch estimate. For large impact parameters the classical limit of the Z 1 4-correction is evaluated and simple estimates of the overall stopping cross section are derived from this limit. Comparison with experiments is made on the basis of an oscillator model of atomic stopping, and the agreement is found to be good.

Stopping power of fast channeled protons in Hartree-Fock approximation

The electronic energy loss of MeV-protons in crystals is investigated in the Hartree-Fock approximation for the core electrons of the target. It turns out that each core electron can be regarded as stopping the proton independent of all other electrons without restriction by the Pauli principle. For the channeling stopping power the impact parameter dependent energy loss of a proton moving rectilinearly past a crystal ion is calculated in first Born approximation. Low excitations of the core electrons lead to a long range impact parameter dependence, whereas high excitations contribute to the energy loss proportional to the electron density sampled along the proton trajectory. The results are applied to 4 MeV proton channeling along the main channels of Si using Clementi wave functions for the core electrons and a free electron approximation for the valence electrons. The comparison with the experimental results of Clarket al. yields good agreement. In the high velocity limit a reduction of the channeling stopping power to 0.64(0.83) of the random value is predicted for Si(C).