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The energy loss function (ELF) is a key parameter for the calculations of energy losses undergone by electrons in matter. It is often the only input in the calculations performed within the models based on the semi-classical dielectric response theory. Its perfect knowledge is thus of primordial importance. To evaluate the ELF, it is usual to consider as a model an expansion in Drude-Lindhard (DL) type oscillators with fixed values of the strength, width, energy and dispersion for the various oscillators. However, for materials that are characterized by a single sharp oscillator as aluminium or indium, it has been shown [Phys. Rev. B 46 (1992) 2486] that the damping parameter that corresponds in the DL model to the width of the oscillator increases for decreasing incident electron energy. To emphasize this effect, we perform in this work systematic calculation of the ELF for an indium target and for incident electron energies between 200 and 2000-eV. The ELF is determined by comparing REELS (reflection electron energy loss spectroscopy) experimental inelastic electron scattering cross sections with cross sections calculated within the semi-classical dielectric response model, which is implemented in the QUEELS-e(k,ω)-REELS software (Quantitative analysis of Electron Energy Losses at Surfaces) [Surf. Interface Anal. 36 (2004) 824]. We also perform measurements and calculations for varying incident and exit angles of the electron, namely for angles to the surface normal between 15o and 75o, to check the validity of our results for all geometries. Our results show that the damping parameter of indium in the DL model for electron energy of 200-eV is three times larger than for energy of 2000-eV. Copyright © 2014 John Wiley & Sons, Ltd.

Hard X-ray photoelectron spectroscopy (HXPS) using X-rays in the 1.5–15 keV energy range generated by synchrotron sources becomes an increasingly important analysis technique due to its potential for bulk sensitive measurements. However, besides their high energy, another characteristic of photons generated by synchrotron sources is their linear polarization while X-rays from Al K α or Mg K α for instance are unpolarized. This difference implies a possible variation in total path travelled by the photoelectrons generated by the X-rays inside the medium and consequently a modification of the resulting spectrum shape. We show the influence of the polarization on the partial intensity distributions, namely the number of electrons escaping after n inelastic scattering events, for photoelectron with energies of 0.5, 1, 2, 3, 4 and 5 keV and originating from Si 1s 1/2 , Cu 1s 1/2 , Cu 2p 3/2 , Au 4d 3/2 and Au 4f 7/2 subshells. Moreover, we point out the influence of the dipole approximation leading to an underestimation of the partial intensity distributions due to the neglect of the forward–backward asymmetry of the angular photoelectron distribution.

Surface excitations significantly influence the measured peak intensities in elastic peak electron spectroscopy. They are characterised by the surface excitation parameter (SEP) defined as the change in excitation probability of an electron caused by the presence of the surface in comparison with an electron moving in an infinite medium. It is thus important to have a large database of SEP values or to have the possibility to determine it with a user-friendly software. Recently, Novak developed the programme Software for Electron Solid Inelastic Interaction Parameter Calculations (SESINIPAC) within the model of Tung, Chen, Kwei and Chou, which allows to determine inelastic mean free path, differential inelastic mean free path, SEP and differential SEP for various energy loss function models and dispersion relations with as only input the energy loss function of the material. Using SESINIPAC, we calculate SEP for 27 different types of materials (metals, semiconductors and insulators) and for various angles and energies. We compare these results with those obtained previously with the software Quantitative Analysis of Electron Energy Losses at Surfaces (QUEELS), which uses the Yubero-Tougaard model. We show that the dependence on angle of emission and energy is quite similar for the two models. However, the absolute values calculated with SESINIPAC are generally larger than those calculated with QUEELS, and the mean relative difference is 20% for metals and semiconductors but exceeds 50% for insulators. Copyright © 2012 John Wiley & Sons, Ltd.

The backward and forward electron emission yields γB and γF have been calculated by Monte Carlo simulations for helium (He++, He+ or He0) ions incident on thin amorphous carbon foils with energies around the electronic stopping power maximum (0.2–2 MeV). Besides the direct excitation of target electrons by the incident projectile, we have taken into account the different charge changing processes (He++ ↔ He+ ↔ He0) undergone by the helium ion in the target. We discuss in particular the connection between the electron emission yield γ and the electronic stopping power (dE/dx)e. We compare our results with previously published experimental results.

Ion induced electron emission (IIEE) is usually described as a three-step process, i.e. electron excitation by the incident projectile, electron transport (and multiplication) and electron escape through the potential barrier at the surface. In many cases, the first step of the process has been carefully described. The second step of the process, i.e. electron transport and multiplication, has often been treated in a very rough way, a simple decreasing exponential law being sometimes used. It is precisely the aim of the present work to show the importance of a correct description of electron transport and multiplication in a theoretical calculation of IIEE. A short overview of the electron transport models developed for IIEE is given in this work. The so-called “Infinite medium slowing-down model” often used in recent works is evaluated by means of Monte Carlo simulations. In particular, the importance of considering correctly the semi-infinite character of the medium and the boundary condition at the vacuum-medium interface is discussed. Quantities like the electron escape depth are also briefly discussed. This evaluation has been performed in the particular case of protons ( 25 keV E H + 3 MeV , without charge exchange) incident on polycrystalline aluminium targets.

7 páginas, 5 figuras.-- et al., Charge changing processes (electron capture and loss) of light ions moving inside metals contribute significantly to the electronemission at intermediate and low impact velocities. An improved method for the description of screening of the moving ion in the electron gas developed by Nagy et al. [Nucl. Instrum. Methods 1996;B115:58.] and Lifshitz et al. [Phys. Rev. A 1998;57:200] will be used to determine the velocity-dependent bound-state wave functions and binding energies related to the moving projectile. These wave functions and binding energies are the basic ingredients for the calculation of the electron capture and loss rates, which determine the equilibrium charge state fractions of the different projectile species, as well as for the calculation of the electron excitation during the charge transfer processes. Explicit calculations were performed for Mg. We compare the contribution of electronemission by decay of plasmons generated during the charge transfer processes with that of plasmon excitation by fast secondary electrons generated by binary ion–electron collisions. The total plasmon-mediated electron yield, obtained by summing the contributions of different mechanisms of each projectile species, weighted with the respective charge state fraction, will be compared with available experimental data.

The forward and backward electron emission yields γ F and γ B have been calculated by Monte Carlo simulation for protons (H + ) and hydrogen atoms (H 0 ) (with energies between 25 keV and 5 MeV) incident on thin amorphous carbon foils. Direct electron excitations by the incident projectiles as well as electron excitations resulting from charge exchange processes undergone by H + or H 0 have been taken into account. For the latter, Auger and Shell processes have been considered. Subsequent electron transport has been considered in order to calculate the forward and backward electron emission yields γ F and γ B .

The forward ( γ F ) and backward ( γ B ) electron emission yields have been measured for protons incident on thin carbon foils for incident energies between 2 and 7 MeV as a function of the target thickness. Comparisons with theoretical results obtained by Monte Carlo simulations are presented. In particular, the Meckbach factor R γ = γ F / γ B is discussed.

It is well known that the charge state of incident ions has an influence on the stopping power as well as on the electron emission characteristics. We have studied here electron emission for protons and hydrogen atoms incident on polycrystalline Al targets for impact velocities up to 2v0 (v0 is the Bohr velocity). Besides the direct excitation of target electrons by the incident projectile, we have considered different charge changing processes that give rise to additional electron excitation, hence contributing to electron emission. These processes are also responsible for the charge state dynamics of the moving projectile. We compare our results with previous results and in particular with the predictions of the simple model proposed by Ghosh and Khare [Phys. Rev. 125 (1962) 1254].

Stopping power d E /d x and electron emission yield γ are known to be strongly influenced by electron capture and loss processes. In this work we consider proton impact on thin Al foils for impact velocities below two atomic units. We investigate the effect of the charge changing processes on the forward/backward electron emission yields, γ F and γ B as well as on the specific yields, Λ F and Λ B ( Λ = γ /(d E /d x )). The dependence of the emission yields and of the specific yields as a function of the target thickness is discussed in terms of the charge changing processes.

For incident protons with velocities around 1 a.u., electron capture and loss processes are known to play an important role. In particular, electron emission as well as electronic stopping power are strongly influenced by the charge changing processes. Several different electron capture and loss processes have been identified [Solid State Phys. 43 (1990) 229], i.e. Auger valence band processes, shell processes and resonant coherent processes. In the latter, the incident projectile undergoes a periodic excitation due to the periodic crystalline potential so that an electron can be lost or captured. In the literature, several different choices have been made for the crystalline potential. It is precisely the aim of the present work to review and compare the various potentials used in the literature and to show the influence of this choice on the resonant coherent electron capture and loss cross sections.

When a monoenergetic electron beam bombards a solid target, some electrons are backscattered without energy loss. This elastic electron backscattering effect plays an important role in many experimental techniques, like low-energy electron diffraction, scanning electron microscopy and others. Recently, the elastic peak has been used for the experimental determination of electron inelastic mean free paths (IMFPs) in the solid. This experimental determination (which is now considered as the most reliable [J. Phys. Chem. Ref. Data 28 (1999) 19] consists in comparing the measurement to a model calculation in which the IMFP is a parameter. In most cases for the model calculation, a simple non-analog Monte Carlo simulation (where the inelastic events are considered as absorptions and taken into account by a weight) is used. In many cases, long computational times are needed, especially when the solid angle of the electron detector is small. In this work, we introduce a new weighted Monte Carlo algorithm, which combines several techniques for variance reduction. Results of extensive numerical tests are presented, demonstrating the increased effectiveness of the new algorithm.

Charge changing processes are known to have a strong influence on ion-induced electron emission characteristics. However, up to now, only a few theoretical models of electron emission incorporate electron capture and loss cross sections. For incident protons with velocities around 1 a.u., a thorough theoretical model of the various charge changing processes undergone by the proton is necessary for a correct description of the electron emission induced by the projectile. Indeed, all the electrons excited in the various processes have to be taken into account. In this work, we consider conduction band Auger capture and loss processes. In particular, we consider plasmon assisted processes, which are not negligible with respect to electron–hole pair assisted Auger processes for electron capture.

A theoretical study of the characteristics of kinetic electron emission induced by He + and He ++ ions (in the MeV-range) incident on polycrystalline aluminium targets is presented in this paper. The models of interactions for the incident projectiles as well as for the excited electrons are described. Especially, the electron excitation induced by incident He + is calculated by taking into account the structure of the composite projectile. Charge exchange processes by the projectiles are also considered. The subsequent electron transport and escape is calculated by means of a Monte Carlo simulation code. The calculated electron emission yield is compared to experimental results. The differences between He + and He ++ are discussed, the role of the electron lost by He + being especially emphasised.

In recent years, there has been an increasing interest in the elastic electron backscattering phenomenon partly due to its use in experimental determination of inelastic electron mean-free-paths. A critical review is presented of the current status of theoretical models to describe this phenomenon. Particular stress is put on determination of the accuracy and range of validity of various analytical models by comparison to extensive Monte Carlo simulations.

Low energy elastic electron backscattering has been used recently as a new tool for surface analysis. The theoretical description of this phenomenon has been mostly made by Monte Carlo simulation. Recently, several analytical approaches have been developed based on the Boltzmann equation for electron transport. However, these approaches do not give a clear image of the elastic electron backscattering phenomenon. It is precisely the aim of this paper to contribute to the study of this phenomenon by Monte Carlo simulation and to propose a very simple expression for the backscattering yield as well as a simple model for the angular distribution of elastically reflected electrons.

International audience; The building up of the space charge induced by electron bombardment in an insulating target is due to the stabilization of self-trapped electrons and holes in polaronic traps. For the energies considered, the target charges positively and the secondary electrons emitted at low energies can be attracted back to the surface. This results in a self-regulation effect where the total secondary yield tends to unity and the surface potential stabilizes at a low positive value. This conclusion is checked for various experimental conditions. The electrons landing on the target form a ring of negative charges that progressively spread out on the surface of the sample.

It is well known that the electron emission yield from insulators is larger than from metals. Most of the previous works on electron emission have been on metals, and very few works have been done on insulators, either experimentally or theoretically. We present in this paper a microscopic description of proton induced electron emission from alumina. Elastic and inelastic interactions for the incident protons and excited electrons are considered as well as the charging-up of the target. The characteristics of proton induced electron emission from alumina (especially the yield γ) are calculated by a Monte Carlo simulation method. A comparison with aluminum targets is done, especially with respect to the influence of the electron inelastic mean free path and of the work function.

Charge state effects are known to be important for particle induced electron emission. Indeed, the charge state of the incident beam has a strong effect on the emission yields. Incident neutral hydrogen atoms can induce secondary electrons after an electron loss process. At high impact energies (above 200 keV) target electrons are excited by both the proton and the electron which can be treated in a first approximation as independent “primary particles”. A more precise description should include different microscopic processes: (i) target electron excitation by the undissociated neutral H0; (ii) excitation of the projectile electron by the loss process accompanied by target electron excitation; (iii) excitation of target electrons by the proton and the electron. At high impact energies it is justified to neglect the capture processes. It is the aim of this paper to calculate the electron emission characteristics of aluminum including all these processes. The various microscopic processes are incorporated in a Monte Carlo simulation code.

It has been evidenced experimentally that, for proton impact on a thick solid target, the ratio Λ of the backward electron yield γB and the electronic stopping power ( d E d x) e is approximately constant over a large energy range (a few keV to several MeV). The macroscopic theoretical models (Sternglass 1957; Schou 1980; …) assume constancy of this ratio. However, from a microscopic point of view, there is no obvious reason for that. We present in this paper a microscopic calculation (microscopic cross sections and Monte Carlo simulation method for the transport) for proton induced electron emission from aluminium and amorphous carbon. The electron yields and the factors Λ from thick and thin (forward and backward emissions) targets are calculated and compared to experimental results.

Many experiments have shown that the backward yield of secondary electrons induced by protons in solid targets is proportional to the electronic stopping power Se: γB = ΛBSe. The parameter λb can be considered as a “material parameter” because it is constant over a wide proton energy range. The forward yield, which can be measured with very thin targets, seems to exhibit the same property. Using a Monte Carlo model for the electron transport in aluminium, we have shown that the anisotropy of the angular distribution of the electrons excited by the proton plays a dominant role together with the number of elastic collisions suffered by an electron before it escapes. When this number is low (forward emission at low proton energy), the yield is approximately proportional to the total excitation cross section and, when it is large (backward emission), the yield is proportional to the stopping power.

Experiments on the secondary emission of electrons from thin carbon foils bombarded with protons have shown that the forward-backward yield ratio increases with energy below 200 keV. Theoretical calculations for an aluminium target, on the contrary, show that this ratio decreases with energy. To explain this discrepancy, we have included in our Monte Carlo simulation model the electron capture and loss process, assuming that a proton-captured electron system does not excite electrons in the solid. We have also taken into account the partial yield due to the lost electrons. This simple model, applied to aluminium, gives results consistent with the carbon experiments. We have also studied the statistics of the number of secondary electrons accompanying an outgoing proton or hydrogen atom.

An electron reaching the detector after being backscattered from a solid surface in a reflection electron energy loss spectroscopy (REELS) experiment follows a so-called $V$-type trajectory if it is reasonable to consider that it has only one large elastic scattering event along its total path length traveled inside the solid. $V$-type trajectories are explicitly assumed in the dielectric model developed by Yubero et al. [Phys. Rev. B 53, 9728 (1996)] for quantification of electron energy losses in REELS experiments. However, the condition under which this approximation is valid has not previously been investigated explicitly quantitatively. Here, we have studied to what extent these REELS electrons can be considered to follow near $V$-type trajectories. To this end, we have made Monte Carlo simulations of trajectories for electrons traveling at different energies in different experimental geometries in solids with different elastic scattering properties. Path lengths up to three to four times the corresponding inelastic mean free paths have been considered to account for 80--90% of the total electrons having one single inelastic scattering event. On this basis, we have made detailed and systematic studies of the correlation between the distribution of path lengths, the maximum depth reached, and the fraction of all electrons that have experienced near $V$-type trajectories. These investigations show that the assumption of $V$-type trajectories for the relevant path lengths is, in general, a good approximation. In the rare cases, when the detection angle corresponds to a scattering angle with a deep minimum in the cross section, very few electrons have experienced true $V$-type trajectories. However, even in these extreme cases, a large fraction of the relevant electrons have near $V$-type trajectories.

A calculation is performed in order to analyze the charge-state dependence of the kinetic electron emission induced by slow ions in metals. All stages of the emission process are included: the excitation of the electrons, the neutralization of the projectile during its passage through the solid, and the transport of the excited electrons from where they are created to the surface. It is shown that the number of excited electrons depends strongly on the ion charge state. Nevertheless, due to the fast neutralization of the ions within the escape depth of the excited electrons, no significant initial charge-state dependence is expected in the kinetic electron yield. This result is consistent with available experimental data., J.I.J. and R.D.M. acknowledge partial support from the Basque Departamento de Educación, Universidades e Investigación, the University of Basque Country UPV/EHU (Grant No. 9/UPV 00206.215-13639/2001), and the Spanish Ministerio de Ciencia y Tecnología (Grant Nos. BSM2001- 0076 and MAT2001-0946). R.D.M. acknowledges partial support by the Gipuzkoako Foru Aldundia.

International audience; It is often assumed that the kinetic electron emission yield γ is proportional to the electronic stopping power dE/dx for ions incident on solid targets. Though these two phenomena are based on the same physical process in which the incident ions lose their energy in the target in electron excitations, there is no reason why the ratio Λ=γ/(dE/dx) should be constant. We present in this paper a comparison between experimental and theoretical results for protons incident on thin carbon foils in a wide energy range (200 keV-9.2 MeV). The ratios ΛB=γB/(dE/dx) and ΛF=γF/(dE/dx) for both the backward (B) and forward (F) emission yields are studied as a function of the incident proton energy as well as the target thickness.

The emission statistics of secondary electrons emitted from solid targets under ion impact has been recently the object of much interest from a theoretical as well as experimental point of view since it provides very useful information about the electron excitation process in the solid. In the case of very thin targets, it is possible to measure simultaneously the number of electrons emitted from both sides of the target and the exit charge state of the projectile. The resulting two variable (number of electrons emitted in the backward and in the forward directions) statistical distribution shows in some cases a clear correlation between the numbers of electrons emitted from both sides of the target. This correlation between backward and forward emission has been studied from Monte Carlo simulations and from experiments for H0 and H+ projectiles incident on thin carbon foils in the MeV energy range. It is shown that the charge exchange processes of the incident projectiles in the target play an important role in the interpretation of the backward–forward correlation of the secondary electron emission.

The secondary electron emission has been measured for 2 MeV H+ and for H0 projectiles passing through very thin carbon foils without charge changing. We have studied the statistics of the emission from both entrance and emergence surfaces. Simultaneously, Monte Carlo calculations have been performed for similar experimental conditions (500 keV

Recently, measurements on the statistics of the number of electrons emitted due to MeV light ion impact on solid targets have been fitted adequately by negative binomial distributions. We present here Monte Carlo simulations for backward and forward emissions induced by protons incident on thin carbon foils in the energy range 250 keV –2 MeV, and compare them with experimental results. A general discussion on the statistical distribution of the number of emitted electrons is given. A transport model giving the general form of the probability generating function (pgf) of the distribution of the number of emitted electrons is also proposed.

Theoretical predictions of three electron transport models are compared for H+ induced secondary electron emission from Al. In particular, the secondary electron energy distribution and the ion energy dependence of the secondary electron yield have been obtained. For thin targets, we have calculated the forward and backward electron yields as well as their dependence upon the angle of incidence of the ions. Our results are in agreement with the presently available experimental data. However, further work is needed to describe adequately the thin foil results.

The improved age-diffusion model for secondary-electron transport is applied to aluminum. Electron cross sections for inelastic collisions with the free-electron gas using the Lindhard dielectric function and for elastic collisions with the randomly distributed ionic cores are used in the calculations. The most important characteristics of backward secondary-electron emission induced by low-energy electrons on polycrystalline Al targets are calculated and compared to experimental results and to Monte Carlo calculations. The model appears to predict the electronic yield, the energy spectra, and the spatial dependence of secondary emission with reasonable accuracy. © 1987 The American Physical Society.

We have developed in this paper a semianalytical electron transport model designed for parametric studies of secondary-electron emission induced by low-energy electrons (keV range) and by fast light ions (100 keV range). The primary-particle transport is assumed to be known and to give rise to an internal electron source. The importance of the nearly isotropic elastic scattering in the secondary-electron energy range (50 eV) and the slowing-down process strongly reduce the influence of the anisotropy of the internal electron source, and the internal electron flux is nearly isotropic as is evidenced by the experimental results. The differential energy behavior of the inelastic scattering kernel is very complicated and the real kernel is replaced by a synthetic scattering kernel of which parameters are obtained by energy and angle moments conservation. Through a P1 approximation and the use of the synthetic scattering kernel, the Boltzmann equation is approximated by a diffusion slowing-down equation for the isotropic part of the internal electron flux. The energy-dependent partial reflection boundary condition reduces to a Neumann-Dirichlet boundary condition. An analytical expression for the Greens function of the diffusion slowing-down equation with the surface boundary condition is obtained by means of approximations close to the age-diffusion theory and the model allows for transient conditions. Independently from the improved age-diffusion model, a correction formula is developed in order to take into account the backscattering of primary electrons for an incident-electron problem. © 1987 The American Physical Society.