Binary Elastic Collisions Research Articles

Properties of secondary particles for ion beam sputtering of silicon using low-energy oxygen ions

The properties of secondary particles for sputtering silicon with primary low-energy oxygen ions were investigated with dependence on the primary ion energy Eion and geometric parameters (ion incidence angle, polar emission angle, and scattering angle). The mass and energy distributions of the secondary particles were measured by energy-selective mass spectrometry. The experimental results were compared with simulations using the Monte Carlo code sdtrimsp and with calculations based on a simple elastic binary collision model. The main secondary ion species were found to be O+, O2+, Si+, and SiO+. Their energy distribution functions depend on the primary ion energy Eion and the scattering angle γ. For O+, Si+, and SiO+ ions, a decreasing scattering angle γ or an increasing primary ion energy Eion leads to a pronounced feature in the high-energy part of the distributions. The energy distributions of the secondary O2+ ions show hardly any changes with regard to the primary ion energy or the scattering angle γ. In the case of the O+ ions, the energy distribution appears to reflect several direct scattering channels, which could be associated with the primary ion energy Eion, and half of the ion energy Eion/2. The present experimental results are compared with previous investigations for the sputtering of Si with the noble gas ions, such as Ne+, Ar+, and Xe+.

Ion beam sputtering of silicon: Energy distributions of sputtered and scattered ions

The properties of sputtered and scattered ions are studied for ion beam sputtering of Si by bombardment with noble gas ions. The energy distributions in dependence on ion beam parameters (ion energy: 0.5–1 keV; ion species: Ne, Ar, Xe) and geometrical parameters (ion incidence angle, polar emission angle, and scattering angle) are measured by means of energy-selective mass spectrometry. The presence of anisotropic effects due to direct sputtering and scattering is discussed and correlated with process parameters. The experimental results are compared to calculations based on a simple elastic binary collision model and to simulations using the Monte-Carlo code sdtrimsp. The influence of the contribution of implanted primary ions on energy distributions of sputtered and scattered particles is studied in simulations. It is found that a 10% variation of the target composition leads to detectable but small differences in the energy distributions of scattered ions. Comparison with previously reported data for other ion/target configurations confirms the presence of similar trends and anisotropic effects: the number of high-energy sputtered ions increases with increasing energy of incident ions and decreasing scattering angle. The effect of the ion/target mass ratio is additionally investigated. Small differences are observed with the change of the primary ion species: the closer the mass ratio to unity, the higher the average energy of sputtered ions. The presence of peaks, assigned to different mechanisms of direct scattering, strongly depends on the ion/target mass ratio.

Derivation of the zeroth retardation order Boltzmann equation from nonstandard space–time Wigner quantum kinetics

A derivation of the equation of motion satisfied by a prototype of the forward space–time Wigner distribution, that incorporates a Fourier transformation of truncated time shifts as compared with the standard Wigner distribution, is carried out in the case of a many-body system within the formalism of nonequilibrium Green’s functions of quantum field theory. In particular, the single-particle equation found in López and Soler (2016) is recovered when the self-energy interaction effects are neglected. Then, a sinc-corrected quantum kinetic Boltzmann equation is derived that rules the evolution of the standard Wigner transform, which is shown to be reduced to the usual Boltzmann equation when only binary elastic collisions are considered.

Proof of quantum mechanical H-theorem beyond binary collisions in quantum gases

We have proved the quantum mechanical H-theorem for dilute Bose and Fermi gases by generalizing the quantum statistical Boltzmann equation for all possible many-body elastic collisions among the particles in the quantum gases within the Lippmann–Schwinger formalism. Previous study by Pauli did almost the same only for binary elastic collisions. We are considering all possible many-body elastic collisions for the current study. Our proof offers a better understanding of the foundation of the second law of thermodynamics for quantum gases.

Electron irradiation effects on the nucleation and growth of Au nanoparticles in silicon nitride membranes

The formation of Au nanoparticles (NPs) in Au+ ion-implanted silicon nitride thin films and membranes was investigated as a function of post-implantation thermal treatments or room temperature electron irradiation at energies of 80, 120, 160, and 200 keV. The samples were characterized by Rutherford Backscattering Spectrometry and Transmission Electron Microscopy. High-temperature thermal annealing (1100 °C, 1 h) resulted in the formation of Au particles with a mean diameter of ≈1.3 nm. In comparison, room-temperature electron irradiation at energies from 80 to 200 keV caused the formation of larger Au particles according to two growth regimes. The first regime is characterized by a slow growth rate and occurs inside the silicon nitride membrane. The second regime presents a fast growth rate and starts when Au atoms become exposed to the back free surface of the membrane. Realistic binary electron-atom elastic collision cross-sections were used to analyze the observed nanoparticle growth and membrane sputtering phenomena. The results obtained demonstrate that binary electron-atom elastic collisions can account for the microstructure modifications if the critical displacement energies for the sputtering of N and Si atoms are around 14 ± 3 eV, and the displacement energy for surface located Au atoms is approximately 1.25 ± 0.2 eV. Irradiation experiments using focused electron probes demonstrate that the process provides fine control of nanoparticle formation, resulting in well-defined sizes and locations.

Rate of energy change of proton traversing in hot high-Z plasmas due to nuclear collision

The rate of change of the energy of the projectile proton moving in hot Au plasmas due to the elastic binary collision between the projectile and the target ion at different density and temperature is studied based on the potential from ionic sphere model. It is found that the proton may obtain energy when its kinetic energy is less than the plasma temperature, which means that the proton and the target ion are in thermal equilibrium when the kinetic energy of the proton is around the plasma temperature. The well known model (Phys. Rev. 126, 1 (1962)) is found not to work in hot high-Z plasmas. The reason for this is explored and found relevant to the very small thermal velocity of the high-Z ion compared with the projectile. This leads to the failure to ignore the dependence of the Coulomb logarithm upon the relative velocity between the projectile and the target ion. A revised model is proposed by us and found to work well while the revised model (Phys. Rev. A 29, 2145 (1984)) is unsatisfactory in this case.

Emergence of distinguishability of patterns of collisions of particles in a non-equilibrium chaotic system

We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. This is characterized by counting how many times different pairs collided at a given time. It was shown using plausible assumption of decay of correlations that on coarse-grained time-scale the determination of the particle with which the given particle collides next is like tossing a coin. We demonstrate that this implies that for a typical trajectory in the phase space each particle has stable “preferences” during indefinitely long periods of time whose average is infinite. During these periods the particle persistently collides more with certain particles and less with others. This effect generalizes and can be tested on small gaseous systems with arbitrary short-range interactions.

Single Ion as a Three-Body Reaction Center in an Ultracold Atomic Gas

We report on three-body recombination of a single trapped Rb(+) ion and two neutral Rb atoms in an ultracold atom cloud. We observe that the corresponding rate coefficient K(3) depends on collision energy and is about a factor of 1000 larger than for three colliding neutral Rb atoms. In the three-body recombination process large energies up to several 0.1 eV are released leading to an ejection of the ion from the atom cloud. It is sympathetically recooled back into the cloud via elastic binary collisions with cold atoms. Further, we find that the final ionic product of the three-body processes is again an atomic Rb(+) ion suggesting that the ion merely acts as a catalyzer, possibly in the formation of deeply bound Rb(2) molecules.

On a peculiarity of low-energy ion scattering from a well-ordered bcc W(211) surface

Abstract A peculiarity in the backscattering of keV He+ ions by a well-ordered high-purity W(2 1 1) surface is reported. Besides the normal elastic binary collision peak and the low-energy tail due to backscattering in deeper layers, an extra peak is observed for an inelastic loss of about 95 eV. This unusually large loss has a constant value over a wide range of primary energies (1.5–4.5 keV). An extra peculiarity is that the peak is only observed for the scattering in normal incidence towards the (2 1 1) plane. It is also not seen for polycrystalline W. The energy loss may be due to a quasi-double or -triple collisions of He particles with the row-trough structure of W(2 1 1) involving electronic excitation of both He and W atoms. Alternatively it may be due to a special channeling/dechanneling process for the incident ions.

Transverse momentum diffusion and collisional jet energy loss in non-Abelian plasmas

We consider momentum broadening and energy loss of high momentum partons in a hot non-Abelian plasma due to collisions. We solve the coupled system of Wong-Yang-Mills equations on a lattice in real time, including binary hard elastic collisions among the partons. The collision kernel is constructed such that the total collisional energy loss and momentum broadening are lattice spacing independent. We find that the transport coefficient $\hat{q}$ corresponding to transverse momentum broadening receives sizable contributions from a power-law tail in the $p_\perp$-distribution of high-momentum partons. We establish the scaling of $\hat{q}$ and of $dE/dx$ with density, temperature and energy in the weak-coupling regime. We also estimate the nuclear modification factor $R_{AA}$ due to elastic energy loss of a jet in a classical Yang-Mills field.

Universal extremal statistics in a freely expanding Jepsen gas

We study the extremal dynamics emerging in an out-of-equilibrium one-dimensional Jepsen gas of (N+1) hard-point particles. The particles undergo binary elastic collisions, but move ballistically in between collisions. The gas is initially uniformly distributed in a box [-L,0] with the "leader" (or the rightmost particle) at X=0 , and a random positive velocity, independently drawn from a distribution phi(V) , is assigned to each particle. The gas expands freely at subsequent times. We compute analytically the distribution of the leader's velocity at time t , and also the mean and the variance of the number of collisions that are undergone by the leader up to time t . We show that in the thermodynamic limit and at fixed time t>>1 (the so-called "growing regime"), when interactions are strongly manifest, the velocity distribution exhibits universal scaling behavior of only three possible varieties, depending on the tail of phi(V) . The associated scaling functions are entirely different from the usual extreme-value distributions of uncorrelated random variables. In this growing regime the mean and the variance of the number of collisions of the leader up to time t increase logarithmically with t , with universal prefactors that are computed exactly. The implications of our results in the context of biological evolution modeling are pointed out.

Uniqueness for a Class of Spatially Homogeneous Boltzmann Equations Without Angular Cutoff

We consider the 3-dimensional spatially homogeneous Boltzmann equation, which describes the evolution in time of the velocity distribution in a gas, where particles are assumed to undergo binary elastic collisions. We consider a cross section bounded in the relative velocity variable, without angular cutoff, but with a moderate angular singularity. We show that there exists at most one weak solution with finite mass and momentum. We use a Wasserstein distance. Although our result is far from applying to physical cross sections, it seems to be the first one which deals with cross sections without cutoff for non Maxwellian molecules.

Ion fractions in the scattering of hydrogen on different reconstructed silicon surfaces

A theoretical calculation that accounts for a fairly complete description of the resonant charge-exchange process occurring in H 0 scattering by Si surfaces is presented. Two reconstructed surfaces for the target: Si(1 0 0)2 × 1 and Si(1 1 1)7 × 7, are analyzed in this work. The interacting system is described by an extended spin-less Anderson Hamiltonian where valence as well as core states of the surface atoms are included. The interaction terms are calculated by taking into account the extended features of the surface and the localized atom–atom interactions within a mean-field approximation. The study is focused mainly in the description of the collision process in terms of short range interactions. The density of states for the surface and subsurface atoms are obtained in each case, from a molecular dynamic-density functional theory in the local density approximation. A binary elastic collision is assumed to fix the projectile trajectory, while the inelastic processes are determined by the interaction of the projectile atom with all the surface atoms ‘seen’ along its trajectory. The ion fractions are calculated by using the Keldysh–Green’s function formalism to solve the time dependent process. We analyze the negative ion fractions of hydrogen measured by Maazouz et al. By including the interaction of the ion projectile with the target atoms seen during its trajectory and averaging over a variety of scattering centers as it may occur in the experimental situation, we obtained a smooth dependence with the exit angle that does not reflect the specific details of the local density of states and the surface topography while reproducing very well the general trends of the experiment. The ion fraction is found to be almost independent on the incoming energy for large values of the exit angles, while in the opposite cases where the projectile spends longer times in contact with the surface, the effect of the parallel component of the velocity has an increasing importance. Thus, the fine details of the surface are ‘better captured’ as the parallel velocity component becomes smaller.

Determination of target mass from ISS data in the presence of inelastic losses

Ion scattering spectroscopy (ISS) is often used to identify the masses of surface atoms through measurement of scattered-ion energies. Mass analysis is straightforward when the scattering events can be described by binary elastic collision kinematics. However, inelastic and multiple scattering effects can alter the final energy of the detected particles, complicating the analysis. Here we present a method that uses ISS data collected at two or more observation angles to identify both the mass of the scattering center and any inelastic energy loss. Use of this technique can also allow detection and quantification of certain systematic errors, such as uncertainties in the initial beam energy, detected ion energy and scattering angle. While ion scattering is stressed here, the presented technique works equally well for the analysis of direct recoil ion energies. An example using He+ ISS data recorded on an Al–Ag alloy illustrates the abilities of this method.

Low-energy ion beamline scattering apparatus for surface science investigations

We report on the design, construction, and performance of a high current (monolayers∕s), mass-filtered ion beamline system for surface scattering studies using inert and reactive species at collision energies below 1500 eV. The system combines a high-density inductively coupled plasma ion source, high-voltage floating beam transport line with magnet mass-filter and neutral stripping, decelerator, and broad based detection capabilities (ions and neutrals in both mass and energy) for products leaving the target surface. The entire system was designed from the ground up to be a robust platform to study ion-surface interactions from a more global perspective, i.e., high fluxes (>100μA∕cm2) of a single ion species at low, tunable energy (50–1400±5eV full width half maximum) can be delivered to a grounded target under ultrahigh vacuum conditions. The high current at low energy problem is solved using an accel-decel transport scheme where ions are created at the desired collision energy in the plasma source, extracted and accelerated to high transport energy (20 keV to fight space charge repulsion), and then decelerated back down to their original creation potential right before impacting the grounded target. Scattered species and those originating from the surface are directly analyzed in energy and mass using a triply pumped, hybrid detector composed of an electron impact ionizer, hemispherical electrostatic sector, and rf/dc quadrupole in series. With such a system, the collision kinematics, charge exchange, and chemistry occurring on the target surface can be separated by fully analyzing the scattered product flux. Key design aspects of the plasma source, beamline, and detection system are emphasized here to highlight how to work around physical limitations associated with high beam flux at low energy, pumping requirements, beam focusing, and scattered product analysis. Operational details of the beamline are discussed from the perspective of available beam current, mass resolution, projectile energy spread, and energy tunability. As well, performance of the overall system is demonstrated through three proof-of-concept examples: (1) elastic binary collisions at low energy, (2) core-level charge exchange reactions involving Ne+20 with Mg∕Al∕Si∕P targets, and (3) reactive scattering of CF2+∕CF3+ off Si. These studies clearly demonstrate why low, tunable incident energy, as well as mass and energy filtering of products leaving the target surface is advantageous and often essential for studies of inelastic energy losses, hard-collision charge exchange, and chemical reactions that occur during ion-surface scattering.

Ion fractions in the scattering of hydrogen on silicon surfaces

We present a theoretical calculation of the resonant charge-exchange process occurring in H0 scattering by Si(100)2 × 1 surfaces. In the atom-surface interacting system the core states of the surface atoms are included and the parameters of the Hamiltonian are calculated in an ab initio basis taking into account the extended features of the surface and the localized atom-atom interactions within a mean-field approximation. The density of states of the surface and sub-surface atoms are obtained from a molecular dynamic-density functional theory in the local density approximation. An elastic binary collision is assumed to fix the projectile trajectory, while the inelastic processes are determined by the interaction of the projectile atom with all the surface atoms ‘seen’ along its trajectory. The ion fractions are calculated by using the Green-Keldysh formalism to solve the time dependent process. The results, obtained as an average over different possibilities for the scattering center, reproduce the general trends of the experiment. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Quantum dynamics of H2 formation on a graphite surface through the Langmuir Hinshelwood mechanism.

We have studied the formation of the H2 molecule on a graphite surface, when both H atoms are initially physisorbed. The graphite surface is assumed to be planar, and a model potential is obtained in a semiempirical way to reproduce the experimental properties of H physisorption on graphite. The reaction probability has been computed in the case when the angular momentum of the relative H-H motion lies parallel to the surface plane. Three-dimensional wave packet calculations have been performed for collision energies ranging from 2 to 50 meV. It is shown that the reaction occurs with a significant probability and produces the H2 molecule with a considerable amount of vibrationnal energy. A simple mechanical model is presented, where desorption of the nascent H2 molecule results from two successive binary elastic collisions.

Viscosity of meson matter

We report a calculation of the shear viscosity in a relativistic multicomponent meson gas as a function of temperature and chemical potentials. We approximately solve the Uehling-Uhlenbeck transport equation of kinetic theory, appropriate for a boson gas, with relativistic kinematics. Since at low temperatures the gas can be taken as mostly composed of pions, with a fraction of kaons and etas, we explore the region where binary elastic collisions with at least one pion are the dominant scattering processes. Our input meson scattering phase shifts are fits to the experimental data obtained from chiral perturbation theory and the inverse amplitude method. Our results take the correct nonrelativistic limit (viscosity proportional to the square root of the temperature), show a viscosity of the order of the cube of the pion mass up to temperatures somewhat below that mass, and then a large increase due to kaons and etas. Our approximation may break down at even higher temperatures, where the viscosity follows a temperature power law with an exponent near 3.

Large-angle back-scattering of Ar q+ ( q=1–13) during quasi-binary collisions with CsI(1 0 0) in the energy range 10 eV/ q –2.8 keV/ q: Energy loss analysis and scattered charge state distributions

We report on measurements of absolute scattered projectile charge fractions for Ar 11+ ions with incident energies in the range 3–30 keV, that have been 120° back-scattered from CsI(1 0 0) in quasi-binary collisions. Use of a time-of-flight technique that incorporates a biased drift region permitted full separation of all scattered charged states, including neutrals. In contrast to our Ar 11+ results for Au(1 1 0), the scattered neutral fraction is smaller, and relatively independent of incident projectile energy over the entire investigated range. In addition, we have measured, at a fixed energy of ∼5 keV, scattered charged state distributions as function of incident charge states in the range 1+ to 13+. In a separate measurement utilizing electrostatic instead of TOF analysis of the scattered charge states, we attempted to evaluate the effect of surface charging on energy loss of low energy scattered projectiles by absolute measurements of the scattered 1+ energies of incident Ar 11+ ions incident on CsI(1 0 0) at energies down to 10 eV/ q. Apart from small deviations from the elastic binary collision energy loss expected for large angle scattering, ascribable to the image charge interaction, no measurable effect due to surface charging was found down to the lowest investigated energies.

Implantation of Pt3- and Ag3- clusters into graphite: an STM study

We have investigated the impact of small platinum clusters, Pt3-, on the surface of graphite for incident cluster energies in the range 50-1500 eV. The density of features observed in the STM rises markedly with increasing impact energy. Results for Pt3- clusters and the lighter Ag3- clusters can be overlaid, i.e. the feature density is independent of the cluster mass. This behaviour violates the binary elastic collision model for energy transfer to the substrate, but is consistent with recent simulations of the implantation of large clusters into the graphite surface.