Charge-transfer and electron emission in the slow (v < v0) multicharged-ion-surface interaction

Charge transfer and electron emission in the slow (v < v₀) multicharged-ion surface interaction is examined. We discuss the form of the total electronic potential, the influence of image and screening interactions on the projectile state energies, and calculate Auger transition rates and Auger electron emission yields for KVV transitions for the oxygen-copper and oxygen-gold interactions. It is shown that efficient transfer of charge from the valence band of metals occurs within projectile-surface separations of order 2q+7 a.u., where q is the projectile charge.     

Z2 structure and gas-solid effect in the stopping of slow ions

A recent claim by Paul of a systematic gas-solid difference in stopping cross sections for ions such as nitrogen and oxygen in the velocity range v ? v₀ is studied on the basis of existing experimental data. We find that all existing data support the commonly known Z₂ structure which, by and large, follows the valence structure of the target material. Existing experimental evidence is not found to support a specific gas-solid difference in the velocity range under consideration. The possibility of such an effect due to a gas-solid difference in charge state is rejected on theoretical grounds. Data for compound gases and solids are found to be well described by the Bragg additivity rule.We have also studied nitrogen/helium and oxygen/helium stopping ratios which determine the so-called effective-charge ratio. Taking into account the scatter of experimental data, we do not find clear evidence against Northcliffe’s assumption of a stopping ratio independent of Z₂ and common for gases and solids in the considered velocity range, although the absolute value appears too high.     

Higher moments of the energy loss spectrum of swift charged particles penetrating a thin layer of material

Higher moments n(≥ 3) over the electronic energy loss spectrum of swift charged particles penetrating a thin layer of random matter have been evaluated. The calculations have been based on the dielectric as well as the kinetic theory of particle stopping. The aim has been to determine the leading terms in an expansion in inverse powers of the particle velocity in any moment of order n ≥ 3. The leading term in this expansion is identical with the familiar result for free Coulomb scattering on target electrons at rest. The leading correction for all n ≥ 5 is a kinematic term of relative order $\text{〈v}{}^2{}_2\text{〉}\text{v}{}^2$, v₂ being the velocit order n = 3 and 4, the leading corrections turn out to be αv^?4 and may therefore often by ignored. Just as the straggling corrections (n = 2), they turn out to split into kinematic and resonant terms of comparable magnitude. Interference of kinematic and resonant corrections gives rise to terms of higher order in v^?2. Our results have been compared with numerical results of Bichsel who employed hydrogenic wave functions. The agreement is very good for n ≤ 6 For 7 ≤n ≤ 10, pronounced differences occur at low projectile velocities. This difference is consistent with an increasing importance of higher moments over the atomic velocity distribution, v^2₂α, α ≥ 2, and therefore, considerable caution is advised toward the use of hydrogenic wave functions in the evaluation of shell corrections to higher moments. Remarks concerning the validity of the Blunck-Leisegang correction to theoretically evaluated energy loss profiles conclude the paper.     

Charge state of low energy reflected particles

Low energetic noble gas particles, scattered from a metal surface, have only a small probability to leave this surface in the charged state. Even particles scattered from target atoms in the outermost surface layer are nearly all neutralised. Consequently analysis of the charged fraction of the scattered beam guarantees that information is obtained of only this layer. To quantify these low energy ion scattering (LEIS) measurements data on the ion fractions must be known, especially because these fractions have such small values. Besides this practical aspect there is the fundamental question: how does it work, this neutralization mechanism, does the transition rate for electron capture of the scattered particle depend upon its distance from the surface, or are it distant binary collisions with individual metal atoms along its trajectory which give rise to interatomic Auger transitions.Already for many years Hagstrum's theory has been applied to correct for the neutralization effect. This theory is developed to study the ejection of Auger electrons as a result of the interaction of low energetic noble gas ions with a metal surface. Due to the low ion energies used in those experiments, namely the tens eV-region, Hagstrum assumed a structureless metal surface. This means that the normal velocity of the scattered particle, v₁, takes part in determining the ion fraction and not v, the velocity of the scattered particle in its trajectory. It is a question, however, whether this theory may be applied for keV-ions. The distance between scattered particle and metal surface is for these energies namely much smaller than for tens eV's and the surface can no longer be regarded as a plane; this may result in dominating interatomic Auger transitions. But then the trajectory of the scattered particle with its velocity v plays a part in determining the occurrence of neutralization.Another mechanism that may determine the charge state of the scattered particle occurs in the violent collision; neutralization as well as (re)ionization of this particle may take place and influence its charge state. These models are treated in this review and discussed with the help of recent measurements and results of computer simulations of reflected particles.     

Valence structure effects in the stopping of swift ions

The valence structure of a material may affect the stopping of swift charged particles primarily via Z₂ structure, atom–molecule differences, gas–solid differences and metal–insulator differences. These material effects have a common physical origin and can therefore be considered from a unified point of view. Theoretical arguments focus on the effect of binding and orbital motion of the target electrons as well as projectile screening and Barkas–Andersen effect. Generally, valence effects depend on the atomic number, charge state and velocity of the projectile. Reference is made to recent calculations on the basis of binary stopping theory as well as experimental findings.     

Dependence of cluster ranges on target cohesive energy: Molecular-dynamics study of energetic Au402 cluster impacts

It has long been known that the stopping and ranges of atoms and clusters depends on the projectile-target atom mass ratio. Recently, Carroll et al. [S.J. Carroll, P.D. Nellist, R.E. Palmer, S. Hobday, R. Smith, Phys. Rev. Lett. 84 (2000) 2654] proposed that the stopping of clusters also depends on the cohesive energy of the target. We investigate this dependence using a series of molecular-dynamics simulations, in which we systematically change the target cohesive energy, while keeping all other parameters fixed. We focus on the specific case of Au₄₀₂ cluster impact on van-der-Waals bonded targets. As target, we employ Lennard-Jones materials based on the parameters of Ar, but for which we vary the cohesive energy artificially up to a factor of 20. We show that for small impact energies, E₀ ? 100 eV/atom, the range D depends on the target cohesive energy U, D ∝ U^−β. The exponent β increases with decreasing projectile energy and assumes values up to β = 0.25 for E₀ = 10 eV/atom. For higher impact energies, the cluster range becomes independent of the target cohesive energy. These results have their origin in the so-called ‘clearing-the way’ effect of the heavy Au₄₀₂ cluster; this effect is strongly reduced for E₀ ? 100 eV/atom when projectile fragmentation sets in, and the fragments are stopped independently of each other. These results are relevant for studies of cluster stopping and ranges in soft matter.     

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.     

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.     

Measurements of fixed-charge and charge-changing contributions to stopping for 3 MeV/u C and O ions in C foils

A fundamental problem in studies of stopping power near to its maximum is the complexity of the physical processes involved. The projectile-related physics involves higher-order Z₁-dependent effects, charge-state distributions within the target, projectile self-screening, and charge-changing energy loss. Measurements of total dE/dx are not capable of probing this basic physics decisively, even when data on charge state distributions are available. We have therefore devised experiments to reduce the stopping power into its component parts. We describe measurements close to the dE/dx maximum, in which fixed-charge stopping cross sections are determined for the bare ion and the one-electron ion. The energy lost in the capture and loss cycle between these charge states is also determined. The results highlight the important role of charge-changing processes, and show the need for a fresh look at higher-order Z₁ corrections to the Bethe theory.     

Wake effects in the stopping power of molecular ions

The stopping power of diatomic molecular ions is calculated in the framework of the dielectric theory using a Monte Carlo procedure. Vicinage effects are included by application of wake-potential interference and Coulomb repulsion of both molecular fragments. Multiple scattering and energy straggling of the projectile ions are considered and are found to be significant for the stopping power values. The results are compared with stopping power measurements of N₂⁺ ions in carbon.     

Thermal spike analysis of ion-induced tracks in semiconductors

Track data reported in InP and GaAs are analyzed according to the analytical thermal spike model (ATSM) and good agreement with the predictions is found. The Gaussian width of the thermal spike is a(0) ≈ 11 nm compared to a(0) = 4.5 nm in insulators. When the ion velocity v_p is high (E > 8 MeV/nucleon), a similar fraction of the electronic stopping power S_e is transformed into thermal energy of the spike in insulators and semiconductors. The results show that - compared to insulators - v_p affects only slightly the track sizes in semiconductors, which is explained qualitatively by the Coulomb explosion mechanism. The reported correlation between the bandgap energy E_g and a(0) is completed with new data. The results of previous analyses of ion-induced tracks in InP by ATSM are discussed.     

The influence of different experimental methods on the measured energy dependence of stopping powers

The stopping cross section data measured by foil transmission often show an energy dependence different from that of RBS measurements. This cannot be due to problems connected with foil thickness-determination. Therefore, we investigate in this contribution, how the energy loss data in these types of measurements are influenced by the different projectile paths due to impact-parameter selection, plural and multiple scattering, by target properties such as bulk and surface impurities, texture and desity differences and by the use of different energy analyzers. Experiments have been performed which prove the reliability of our target preparation, stopping cross section measurements and data evaluation with respect to these influences.     

Energy-angle distribution measurements for 0.8v020Ne and 209Bi ions penetrating thin carbon foils

Energy-angle distributions have been measured for 0.8v₀, (v₀ = Bohr velocity) Ne and Bi ions penetrating through carbon foils. Comparing the results with a Monte Carlo computer simulation that included an angle dependence only for the elastic collisions, we have observed for Ne projectiles an angle-dependent inelastic loss which, for small angles, is much larger than the elastic contribution in the case of thin foils. In the case of Bi, the energy loss distribution is dominated by elastic collisions. The calculations of Meyer, Klein and Wedell, and Ellmer and Wedell cannot describe the experimental results. The multiple scattering distributions are in agreement with both analytical and Monte Carlo calculations.     

Separation of potential and kinetic electron emission from Si and W induced by multiply charged neon and argon ions

The total secondary electron emission yields, γ_T, induced by impact of the fast ions Ne^q+ (q = 2-8) and Ar^q+ (q = 3-12) on Si and Ne^q+ (q = 2-8) on W targets have been measured. It was observed that for a given impact energy, γ_T increases with the charge of projectile ion. By plotting γ_T as a function of the total potential energy of the respective ion, true kinetic and potential electron yields have been obtained. Potential electron yield was proportional to the total potential energy of the projectile ion. However, decrease in potential electron yield with increasing kinetic energy of Ne^q+ impact on Si and W was observed. This decrease in potential electron yield with kinetic energy of the ion was more pronounced for the projectile ions having higher charge states. Moreover, kinetic electron yield to energy-loss ratio for various ion-target combinations was calculated and results were in good agreement with semi-empirical model for kinetic electron emission.     

The energy distribution of sputtered particles at low bombarding energies

The transport equations for the ion sputtering of metal targets are solved in the P_L-approximation. After a Laplace transform in the logarithmic energy variable, analytical solutions for the flux at the surface can be obtained. These are numerically Laplace inverted for the case of equal masses of projectile and target atoms and hard sphere interaction; the case of a power law scattering cross section dσ(T) = CT^?1dT is covered in P₁-approximation, too. At high bombarding ion energies, the solution recovers the asymptot for the distribution in energy E of sputtered particles; at low bombarding energies, however, the solution displays — for normally incident ions and perpendicularly emitted target atoms — a steeper spectrum. This is in accordance with measurement. Boundary conditions for a semi-infinite medium as well as for an infinite medium are applied; these show only negligible influence on the solution. Furthermore, a solution by way of B_L-approximation is obtained, which confirms the above results.     

Damage creation in α-Al2O3 by MeV fullerene impacts

Single crystals of α-Al₂O₃ were irradiated at room temperature with C₆₀ clusters at normal and grazing incidences. The extent of the induced damage was determined using Rutherford backscattering spectrometry in channeling geometry (RBS-C). A damage cross-section of 3.1 × 10⁻¹² cm² was obtained for the highest electronic stopping power (76.2 keV nm⁻¹). From electron microscopy observations continuous amorphous tracks were evidenced around the projectile trajectory and an electronic stopping power threshold for damage creation of 18 keV nm⁻¹ was also determined. The spatial correlation in depth of the cluster components were deduced from both direct track length measurements and the damage profiles extracted from RBS-C analysis. The maximal correlation length represents about one-third of the projected range (R_p) of a free carbon. Using atomic force microscopy (AFM), conically shaped hillocks corresponding to the out of plane expansion of the latent tracks were observed. These structures characterize nanometric changes of the plastic properties of sapphire induced by high electronic excitations.     

The co-precipitation of vacancies and carbon atoms in quenched platinum

The geometry of secondary defect structures observed in quenched platinum containing various amounts of carbon is shown to be consistent with a simple model based on the premise of a strong impurity (carbon) atom/vacancy binding energy. When the ratio of carbon atoms to vacancies (C_c/C_v) is large, co-precipitation as platelets on {100} planes occurs; whereas when C_c/C_v is small, the effects of carbon are still manifest; the defect geometry is dominated by the vacancy behavior, and loops on {111} planes form. Consideration of the mechanism of defect formation on {100} planes leads to conclusions about the structure of the carbon atom/vacancy complex, its migration and stability. An electron microscopy analysis of the {100} defects is in excellent accord with the proposed model. Implications concerning the likely behavior of carbon atoms in a radiation environment are considered, and an interstitial impurity solute segregation effect to vacancy sinks is predicted.     

Convolution approximation for the energy loss, ionization probability and straggling of fast ions

In this work we describe an extension of the convolution approximation for the ionization probability and energy-loss straggling as a function of the impact parameter for swift ions. Analytical formulas for these quantities are derived and compared to full first-order Born calculations. The physical inputs of the model are the electron density and oscillators strengths of the target as well as the screening function of the projectile (in the case of dressed ions). A very good agreement is obtained for all impact parameters. In addition, we propose a general schema to add contributions from distant and close collisions. In this way physical processes arising from large and small impact parameters can be easily included into a single expression valid for all impact parameters. This model is then used to investigate the projectile-charge q dependence of ionization, stopping and straggling cross-sections.     

Single- and multiple-electron loss cross-sections for fast heavy ions colliding with neutrals: Semi-classical calculations

Extensive calculations of single, multiple and total electron-loss cross-sections of fast heavy ions in collisions with neutral atoms are performed in the semi-classical approximation using the DEPOSIT code based on the energy deposition model and statistical distributions for ionization probabilities. The results are presented for Ar¹⁺, Ar²⁺, Kr⁷⁺, Xe³⁺, Xe¹⁸⁺, Pb²⁵⁺ and U^q+ (q = 10, 28, 39, 62) ions colliding with H, N, Ne, Ar, Kr, Xe and U atoms at energies E > 1 MeV/u and compared with available experimental data and the n-particle classical-trajectory Monte Carlo (nCTMC) calculations. The results show that the present semi-classical model can be applied for estimation of multiple and total electron-loss cross-sections within accuracies of a factor of 2.From calculated data for the total electron-loss cross-sections σ_tot, their dependencies on relative velocity v, the first ionization potential I₁ of the projectile and the target atomic number Z_A are found and a semi-empirical formula for σ_tot is suggested. The velocity range, where the semi-classical approximation can be used, is discussed.     

Monte Carlo study of ion-induced backward and forward secondary electron emission from thin Al foil

A direct Monte Carlo program has been developed to calculate the backward (γ_b) and forward (γ_f) electron emission yields from 20 nm thick Al foil for impact of C⁺, Al⁺, Ar⁺, Cu⁺ and Kr⁺ ions having energies in the range of 0.1-10 keV/amu. The program incorporates the excitation of target electrons by projectile ions, recoiling target atoms and fast primary electrons. The program can be used to calculate the electron yields, distribution of electron excitation points in the target and other physical parameters of the emitted electrons. The calculated backward electron emission yield and the Meckbach factor R = γ_f/γ_b are compared with the available experimental data, and a good agreement is found. In addition, the effect of projectile energy and mass on the longitudinal and lateral distribution of the excitation points of the electrons emitted from front and back of Al target has been investigated.