1. Introduction {#s0005}
===============

Low energy ion scattering (LEIS) is well established as a standard method suitable for quantification of composition and structure of surfaces. The field of recent applications ranges from research on catalysts [@bb0005] via in-situ growth monitoring [@bb0010] or surface structure analysis [@bb0015] to investigations of organic field-effect transistors [@bb0020]. The supreme surface sensitivity of LEIS is based on the fact that the backscattered ion yield is extremely surface sensitive, since at the energies typically employed (0.5--4 keV) primary ions, e.g. He, are very efficiently neutralised. Although qualitative understanding of the different charge exchange processes is available, a quantitative prediction of the ion yield for fixed geometry and a specific combination of projectile and target element is not yet possible [@bb0025]. Thus, whenever LEIS is used for quantitative analysis, careful calibration is required, usually by elemental standards.

Ongoing research by different groups aims on a thorough understanding of the relevant charge exchange processes. A recent finding is, that the neutralization efficiency for He^+^ scattered from single crystals with different surface orientations may differ significantly [@bb0030; @bb0035; @bb0040; @bb0045; @bb0050; @bb0055]. Experiments performed in grazing incidence can be accurately described by a theoretical model [@bb0060]. This model has been recently modified to describe also experiments in large angle backscattering [@bb0065] where no significant surface orientation dependence of the ion signal was expected [@bb0025]. Note, that in large angle backscattering some evidence for influence of the chemical environment and the trajectory can be found in literature, which are, however, much smaller in magnitude than the recently discovered crystal effects [@bb0070; @bb0075; @bb0080; @bb0085; @bb0090].

For charge exchange of He^+^ ions on metallic surfaces two types of processes have to be distinguished: (i) Auger processes, which depend on the available interaction time, and (ii) resonant charge exchange processes, which are only active below a certain distance of projectile and target atom.

*Auger neutralization* (AN) along the trajectory is possible at any primary projectile energy [@bb0095]. The neutralization rate -- *dP*^+^/*dt* depends on the Auger transition rate Γ~A~ via -- *dP*^+^/*dt* = *P*^+^∙ Γ~A~. Accordingly, surviving probabilities *P*^+^~in~ and *P*^+^~out~ for incoming and outgoing trajectories follow$$P_{\text{j}}^{+} = \exp\left\lbrack {-_{0}{\int{}^{\Delta t_{\text{j}}}\Gamma}_{\text{A}}\left( {z\left( t \right)} \right)dt} \right\rbrack = \exp\left\lbrack {- \left\langle \Gamma_{\text{A}} \right\rangle\Delta t_{\text{j}}} \right\rbrack \approx \exp\left\lbrack {- \left\langle \Gamma_{\text{A}} \right\rangle\Delta z_{\text{j}}/v_{\bot\text{j}}} \right\rbrack \equiv \exp\left\lbrack {- v_{\text{cj}}/v_{\bot\text{j}}} \right\rbrack\text{,}$$where j stands for *in* or *out*, 〈Γ~A~〉 denotes the transition rate averaged over the trajectory and Δ*t* is the time spent by the projectile in the region Δ*z*, where neutralization processes occur. The characteristic velocity *v*~*c*~, defined in Eq. [(1)](#fo0005){ref-type="disp-formula"}, is a measure for neutralization efficiency. From Eq. [(1)](#fo0005){ref-type="disp-formula"} it is clear that AN scales with Δ*t*, which is approximately equivalent to scaling with the velocity component *v*~⊥~ of the projectile normal to the surface. *P*~AN~^+^ describes the fraction of projectiles that have survived surface scattering without being neutralized by AN and is given by *P*~AN~^+^ = *P*~in~^+^·*P*~out~^+^ = exp\[−〈Γ~A~〉(Δ*t*~in~ + Δ*t*~out~)\] ≈ exp(− *v*~*c*~/*v*~⊥~), with the abbreviation 1/*v*~⊥~ ≡ 1/*v*~⊥ in~ + 1/*v*~⊥ out~.

Resonant charge exchange processes in a close collision, i.e. *resonant neutralization* (RN) and *resonant reionization* (RI) [@bb0100], become possible for a minimum distance between projectile and scattering centre smaller than a critical value *R*~min~(*E*, *θ*) [@bb0105; @bb0110]. These resonant processes are enabled by a shift of the He 1 s-level to higher binding energies, due to interaction with the electronic system of the target atoms [@bb0115]. In the collision between the projectile and a target atom, a minimum distance smaller than *R*~min~ is reached if -- for a fixed scattering angle *θ* -- the projectile energy *E* exceeds a certain threshold *E*~th~. The specific value of *E*~th~ depends on the atomic species of the collision partners and on the scattering angle *θ*. For instance, for He^+^ scattered from Cu and *θ*= 129°, *E*~th~ = 2100 eV [@bb0025]. Thus, the probabilities for the resonant processes in the collision, *P*~RN~ and *P*~RI~, depend on *E* and *θ* instead of *v*~⊥~. Note, that at typical conditions in the reionization regime (*P*~AN~^+^ \> 0.25) *P*~RN~ \> *P*~RI~ holds, so that *P*^+^ \< *P*~AN~^+^. In the case of backscattering by a single close collision the *P*^+^ is thus described by$$P^{+} = \left( {P_{\text{in}}{}^{+}\cdot\left( {1 - P_{\text{RN}}} \right) + \left( {1 - P_{\text{in}}{}^{+}} \right)\cdot P_{\text{RI}}} \right)\cdot P_{\text{out}}{}^{+}$$

Additionally a non-local ionization process is possible for neutral He atoms: in an *Auger ionization* (AI) process two electrons are excited simultaneously, one from the projectile atomic level and one from the conduction band of the metal [@bb0120]. In contrast to AN, AI requires a minimum kinetic energy of the projectile [@bb0060]. Therefore, this process will contribute considerably only at high projectile energies and is expected to be of minor relevance in the present study.

In LEIS applications it is an important issue that the majority of elements feature a very low reionization threshold E~th~[@bb0025]. In consequence, the majority of experiments are performed in the reionization energy regime. This may significantly increase the information depth and lead to an additional dependence of the ion fraction on the sample orientation, as indicated by recent results [@bb0045; @bb0050]. In this context it is clear, that the probabilities *P*~RN~ and *P*~RI~ for resonant charge exchange are a key quantity to predict the ion spectrum in an experiment. However, a theoretical treatment of these processes is difficult, due to the strong perturbation of the electronic states caused by the backscattered ion at short interaction distances [@bb0115]. Experiments on single crystals permit to simplify interpretation of experimental results, since the information depth can -- in double alignment geometries [@bb0125] -- be limited to the outermost atomic layer also in large angle backscattering experiments at *E* \> *E*~th~. Furthermore, they can serve as a calibration standard for experiments on polycrystals in order to deduce information on the ion fraction by relative measurements [@bb0130].

In the present study probabilities for resonant charge exchange in close collisions of He^+^ with Au and Cu atoms were determined in a wide energy range. Based on these results, an interpretation of the ion spectrum obtained from polycrystalline surfaces is presented. This yields information on the information depth probed in LEIS experiments at *E* \> *E*~th~.

2. Experimental setup {#s0010}
=====================

The experiments were performed using the Time-Of-Flight -- (TOF-) LEIS setup ACOLISSA [@bb0135] with a scattering angle θ of 129° and a detector acceptance angle of 0.92°. The system is typically operated at a time resolution set from 10 to 25 ns corresponding to an energy resolution of 1 to 5% for He^+^ ions at 3 keV. A post acceleration voltage can be applied along part of the flight path between sample and detector to separate backscattered ions from neutrals. The primary beam current is set between 25 and 100 nA in full beam mode, yielding 5 to 20 pA in the chopped beam mode, which makes TOF-LEIS virtually non-destructive. The beam current remains constant to within 10% after thermal equilibration (\~ 2 h). At normal incidence, the beam spot on the sample was found to be smaller than 1 mm in diameter. From this the "safe" range of incident angles follows (angle of incidence *α* \< 65°, with respect to the surface normal) ensuring that the whole irradiated spot is visible for the detector. The angular precision of the manipulator is ± 0.1° and ± 0.2° for polar and azimuth scans, respectively.

The samples were prepared by repetitive sputtering--annealing cycles, performed with 3 keV Ar^+^ ions and subsequent heating, typically to \~ 650 K, depending on the sample. Surface purity was checked by Auger electron spectroscopy (AES) and crystal structure of single crystals by low-energy electron diffraction (LEED).

Measurements were performed for Cu(100) and Cu~0.5~Au~0.5~(100) single crystal surfaces and polycrystalline Cu. ^4^He^+^ ions with primary energies ranging from 0.6 to 9 keV were used as projectiles. For single crystals spectra were recorded in double alignment geometries, which suppress contributions from deeper layers due to channeling and blocking [@bb0125]. This allows determination of the ion fraction P^+^ from the areas of the surface peaks of neutrals and ions [@bb0140; @bb0045]. Ion fractions for polycrystalline samples were deduced in relative measurements by comparison to single crystals [@bb0145].

3. Results {#s0015}
==========

Experiments were performed in 2 distinct double alignment geometries for a Cu(100) and a Cu~0.5~Au~0.5~(100) single crystal. The latter surface is employed because the outermost atomic layer is composed by Au atoms exclusively [@bb0150; @bb0155], without any reconstructions as typically observed for the low-index surfaces of elemental Au single crystals [@bb0160]. Thus, for both surfaces it is possible to limit the obtained signal to the outermost atomic layer [@bb0055]. Ion fractions of ^4^He^+^ atoms scattered from surface atoms were deduced. Auger neutralization rates for the investigated surfaces are known from previous experiments [@bb0045; @bb0055]. Thus, it is possible to extract information on the probabilities for resonant charge transfer in close collisions via Eq. [(2)](#fo0010){ref-type="disp-formula"} by measurements of *P*^+^ in two distinct geometries and calculation of the corresponding Auger survival probabilities *P*~in~^+^ and *P*~out~^+^.

[Fig. 1](#f0005){ref-type="fig"}a shows *P*~RN~ and *P*~RI~ for scattering from Cu atoms and He energies in the range from 1.8 to 10 keV. The statistical uncertainties are indicated by the error bars in [Fig. 1](#f0005){ref-type="fig"}a and b. Possible systematic errors are expected to arise mainly from uncertainties in the angle of incidence, which however leads to a scaling factor for all probabilities derived, and thus does not change qualitatively their energy dependence. In [Fig. 1](#f0005){ref-type="fig"}a both probabilities increase monotonically with the primary energy. At energies below E~th~ the probabilities are expected to vanish; this is observed for *P*~RI~, while for *P*~RN~ a small, but finite positive value is obtained. This is not consistent with *P*~RN~ = 0 within statistical uncertainty and thus has to be attributed to the limited precision in adjustment of the angle of incidence. In the whole range of energies investigated, *P*~RN~ is found to be larger than *P*~RI~. This is in concordance with the observation that in the reionization regime the experimental ion fraction *P*^+^ is found lower than predicted from extrapolation of low energy AN data. Qualitative agreement with data from [@bb0165] is found with respect to the energy scaling of the data, except for *P*~RI~ at the highest energy. Note, that the experiments in [@bb0165] were not performed using a single crystal. Evaluation was thus performed in a different way: a single scattering model was employed to deduce *P*^+^. In comparison, evaluation of data deduced from experiments on single crystals is expected to be significantly less sensitive to systematic errors.

In [Fig. 1](#f0005){ref-type="fig"}b results obtained for scattering from Au surface atoms are presented. For Au, an even faster increase of *P*~RN~ with the primary energy is observed. In contrast to Cu, *P*~RI~ is found below 10% in the whole range of energies investigated. These findings are remarkable since Cu and Au feature very similar properties of the conduction electrons, from which one might expect similar energy dependencies of the charge exchange probabilities.

When in experiments in the reionization regime double alignment conditions are abandoned, strong subsurface contributions add to the detected ion yield and alter the yield of backscattered neutrals even more strongly [@bb0045; @bb0050]. From this, it can be expected, that for experiments performed with polycrystalline samples the ion yield contains subsurface contributions in any geometry.

The most obvious evidence for subsurface contributions to the ion yield is found in the low energy tail in the energy spectrum of backscattered ions. [Fig. 2](#f0010){ref-type="fig"} shows energy converted TOF-spectra [@bb0170] for backscattered ^4^He^+^ ions with a primary energy of 8 keV; Cu(100) in double alignment geometry and a polycrystalline copper surface served as samples. Spectra were recorded for identical scattering angle, angle of incidence and incident charge. The spectrum recorded for the single crystal shows only a very small low energy background. From this, it can be concluded, that in double alignment geometry, almost no subsurface scattered particles are detected in an ionic charge state. The shape of the surface peak can be fitted very well by a Gaussian distribution, applying a single scattering model [@bb0175].

The spectrum recorded for the polycrystalline sample exhibits a pronounced low-energy background. In order to be detected in the low energy background a particle must have undergone multiple collisions and significant electronic energy loss along a longer trajectory.

To fit the low-energy contribution, a step-function with similar width as the surface peak was employed. This results in a very good fit of the ion spectrum in the energy range under consideration. Note that this procedure is not expected to realistically describe the shape of the low energy background in a wider energy range -- the background is known to diminish at lower energies. Nevertheless, this approach yields an effective background height, which can be compared to the height of the neutral spectrum (see [Fig. 3](#f0015){ref-type="fig"}). This comparison permits to extract neutralization information from the spectrum, i.e. whether the ions have survived Auger neutralization or have been reionized.

At higher energies, Auger neutralization gets less effective due to shorter interaction time. Nevertheless, it is still effective enough to prevent projectiles from surviving without being neutralized, when they are backscattered in sufficiently large depth to be part of the background, i.e. for trajectories necessary to account for the observed energy loss due to electronic and nuclear stopping [@bb0180; @bb0185]. It is possible to model the ion fractions for different trajectory length, when assuming, that Eq. [(2)](#fo0010){ref-type="disp-formula"} is valid for scattering from the individual layers. Note, that for simplicity of calculations only a single large angle scattering event is employed in the calculation. Two distinct Auger neutralization rates are assumed, with a lower AN rate along the straight line segment of the trajectory and a higher rate for the layer in which the backscattering collision takes place. AN-rates are obtained from [@bb0045] and from a comparison of the ion yields for first and second layer scattering from Cu(100) (see also [@bb0175]). The ion fractions deduced by this method are shown in [Table 1](#t0005){ref-type="table"}. Thus, it is clear, that the majority of ions detected at these energies have been reionized in a close collision. In a next step, it is of interest, where reionizing collisions take place. If reionization in the outermost layer is assumed to be responsible for the observed ion yield, the spectrum intensity can be modeled from the neutral spectrum in the following way: firstly, particles with equal final energies are expected to have experienced similar path lengths irrespective of their final charge state. Secondly, in the experimental spectrum presented, the ratio of neutral and ion yields is found to be \~ 100 at energies a few hundred eV below *k*·*E*~0~. Thirdly, employing an effective cross section for reionization (*P*~RI,eff~·*R*~min~^2^π) [@bb0190] and *P*~out~^+^, this calculation yields a ratio of neutral to ionized projectiles of about 1500, which is far from experimental facts. Thus, reionization in the outermost atomic layer cannot be the major contribution to the reionization background.

In an alternative scenario, reionization in the backscattering collision is considered to be important, accounts -- together with the decreasing efficiency of Auger neutralization -- for the observed ion yield. [Table 1](#t0005){ref-type="table"} indicates that by inclusion of reionization (*P*~RI~ = 0.5) ion fractions from layers 5 to 7 are sufficiently high to account for the observed reionization background.

[Fig. 4](#f0020){ref-type="fig"}a) visualizes the calculated ion fractions (red circles) obtained for 8 keV He^+^ projectiles scattered from the first seven monolayers of polycrystalline Cu (compare also [Table 1](#t0005){ref-type="table"}). The figure presents the contributions from projectiles that have neither been neutralized by AN nor by RN in a close collision ("survivals" -- black squares) and projectiles that have been reionized in a close collision with *P*~RI~ = 0.5 (see [Fig. 1](#f0005){ref-type="fig"}a) (reionized projectiles -- green triangles). The contribution of survivals to the ion yield is rapidly decaying and almost exclusively limited to the first two to three monolayers. In contrast, the ion fraction of reionized projectiles decays more slowly with the number of monolayers, i.e. with increasing trajectory length. It is possible to determine the decay length *d* where the ion signal has decreased to a fraction 1/e of the first monolayer contribution: This calculation results for the total ion fraction in *d*~tot~ = 2.6 monolayers, for the ion fraction of survivals in *d*~surv~ = 1.7 and for the ion fraction of reionized projectiles in *d*~reion~ = 3.3 (see [Fig. 4](#f0020){ref-type="fig"}a). For comparison the same calculation was performed for 3 keV He^+^, which is typical for LEIS applications (see [Fig. 4](#f0020){ref-type="fig"}b)). Due to the lower probabilities for resonant charge transfer in a close collision and more effective Auger neutralization, the ion signal is more surface sensitive at lower energies. The corresponding decay lengths are found to be *d*~tot~ = 1.45 monolayers, *d*~surv~ = 1.43 monolayers and *d*~reion~ = 2.1 monolayers. The inset shows the data with logarithmic scaling of the ordinate, to visualize that for deeper layers reionized particles will always dominate the ion yield, even if the overall probability for reionization is low.

These data confirm that high surface sensitivity can be expected for LEIS experiments on polycrystalline surfaces also at energies where probabilities for resonant charge transfer are high. When the corresponding energy loss is considered (see [Table 1](#t0005){ref-type="table"}), it becomes clear that proper evaluation of the ion spectra and separation of the background will limit the signal to at most 2.5 monolayers in a typical application. Only in unfavourable cases artefacts due to an increased information depth have to be expected. Typical examples might be bad sample alignment for single crystals, or a sample composition with a few monolayers of low-Z elements on top of a high-Z material with high probabilities for resonant charge transfer.

Based on the previous findings, it is justified to model the ion peak by the contributions from the first and second monolayers. Assuming single scattering from these two layers the ion peak will be described within two different approaches. In both, the most important assumption is that the polycrystalline surface can be reasonably approximated by randomly oriented (111)-facets, which is expected due to the low surface energy of the (111) surface [@bb0195]. The first approach is based on the ion yield from the outermost atomic layer of a (100) surface (see [Fig. 2](#f0010){ref-type="fig"}). From this, one can calculate the ion yield expected for the first two layers of a polycrystalline surface, by making use of known Auger rates [@bb0050] and the ion trajectories obtained from molecular dynamics simulations [@bb0200]. [Fig. 2](#f0010){ref-type="fig"} presents the results from this calculation for the contribution from first and second monolayer as dashed and dotted lines respectively, as well as their sum (full green line). The full black line shows the sum of these contributions and the fit to the low energy background. Very good agreement is found between calculations and experiment.

Alternatively, it is possible to calculate the number of projectiles scattered from one and two atomic layers, by means of Monte-Carlo simulations [@bb0205]. The incident charge is obtained from normalization to the height of the neutral spectrum. The yield of projectiles scattered from the surface -- together with Auger rates for first and second layer deduced from single crystalline references -- yields the backscattered ion contribution from the surface. [Fig. 5](#f0025){ref-type="fig"} shows the contribution from the first and second monolayer as dashed and dotted lines respectively, and their sum (full blue line). Again, very good agreement between calculations and experiment is found.

4. Summary and conclusions {#s0020}
==========================

In the present investigation it has been shown, that the probabilities for resonant charge transfer of He ions in close collisions may exhibit very different behaviors for different materials, i.e. for Au and Cu. Since the electronic configuration of the conduction band of these materials is very similar, this indicates, that details in the electronic structure of the sample atoms strongly influence the dynamics of the projectile\'s atomic levels in a close collision. The presented results indicate that in the reionization regime the ion yield is due survivals that never have changed charge state and reionized projectiles; In the surface peak of the ion spectrum, considerable contributions of both have to be expected, the relative importance depending on the energy dependent probabilities of the resonant processes and on the Auger neutralization rate. In the background of the ion spectrum at lower ion energies, reionized projectiles represent the major contribution, since reionization takes place in the backscattering collision well below the surface, and AN is relevant only along the outgoing path. Since for the survivals, *P*~in~^+^·(1 − *P*~RN~)·*P*~out~^+^ governs the contribution to the ion yield, while for the projectiles that are reionized well below the surface, *P*~RI~·*P*~out~^+^ holds, the latter contribution dominates for sufficiently large depth.

Based on the insights discussed above and making use of the knowledge of the probabilities of resonant processes and of Auger neutralization efficiency it is possible to model the ion spectrum for backscattering from polycrystalline surfaces.

Analytic models are not available to quantitatively permit precise composition analysis of multi-element samples. Therefore, in a next step it would be desirable to include charge exchange processes into Monte-Carlo simulations. This includes a thorough study of Auger rates in the solid in order to calculate neutralization along the trajectory. Additionally, it is important to determine probabilities for resonant charge transfer in close collisions for the elements of interest and subsequently to compute distance dependent charge transfer rates.

This work was supported by the Austrian Science Fund (FWF) under Contract No. P20831.

![Probabilities for resonant charge transfer in close collisions deduced from experiments on Cu(100) and Cu~0.5~Au~0.5~(100) (full symbols): black squares show probabilities for resonant neutralization, red circles for resonant reionization in a 129° scattering event. Open symbols show data deduced from polycrystalline Cu [@bb0170]. Error bars shown indicate statistical errors. The maximum influence of a possible systematic error is discussed in the text.](gr1){#f0005}

![Experimental ion spectra for 8 keV He^+^ ions scattered from polycrystalline Cu (black open circles) and a Cu(100) single crystal in double alignment geometry (red open triangles). Also shown is a fit to the low energy background for the polycrystal (dashed black line) and calculations for the expected ion yield from scattering from the first two monolayers (dashed and dotted green (grey) lines respectively) based on the single crystal data. The sum of the fitting models (black full line) shows very good agreement with the experiment. For details see text.](gr2){#f0010}

![Experimental spectra of detected backscattered ions (black open circles) and neutrals (red open circles) at energies around the kinematic limit kE~0~ for 8 keV He^+^ scattered from polycrystalline Cu. The full and dashed lines are to guide the eye (see also [Fig. 2](#f0010){ref-type="fig"}).](gr3){#f0015}

![Calculated ion fractions for a) 8 keV He^+^ projectiles scattered from the first seven monolayers in polycrystalline Cu. b) 3 keV He^+^ projectiles scattered from the first seven monolayers in polycrystalline Cu. The total ion fraction (red circles), the fraction of projectiles reionized in a close collision (green triangles), and the fraction of projectiles, which survived AN and RN in a close collision (black squares) is shown. The inset in b) shows the same data with logarithmic ordinate. For details see text.](gr4){#f0020}

![Experimental ion spectra for 8 keV He^+^ ions scattered from polycrystalline Cu (black open circles). Also shown is a fit to the low energy background for the polycrystal (dashed black line) and calculations for the expected ion yield from scattering from the first two monolayers (dashed and dotted green (grey) lines respectively) based on Monte-Carlo simulations (TRBS \[42\]) and the neutral scattering yield. The sum of the fitting models (black full line) shows very good agreement with the experiment. For details see text.](gr5){#f0025}

###### 

Ion fractions for scattering from individual monolayers in a polycrystal, modeled by a (111) single crystal. It can be seen from the ion fraction with P~RI~ equal zero, that Auger neutralization very efficiently decreases contributions from ions that survived Auger neutralization along their entire trajectory. P^+^ for P~RI~ = 0.5 is found to be sufficiently large for monolayers 5--7 to account for the observed ion yield in the low energy background.

  Monolayer, \#   P^+^ (P~RI~ = 0)   P^+^ (P~RI~ = 0.5)   Energy loss, eV
  --------------- ------------------ -------------------- -----------------
  1               0.074              0.16                 16.5
  2               0.019              0.085                49.5
  3               0.005              0.041                83
  4               0.0013             0.019                115
  5               0.00033            0.0082               149
  6               8.62E−05           0.0036               182
  7               3.21E−05           0.0015               215
