Mario M. Jakas

Spike models for sputtering: Effect of the surface and the material stiffness

Abstract Bombarding a solid with fast ions can give atoms within a localized region enough kinetic energy to escape from the material. Thermal spike models have been used to explain this process for metals, insulators and condensed gas solids. Here we use molecular dynamics (MD) simulations of a cylindrical spike to examine the effect of material stiffness and surface boundary conditions on the spike calculations of the yield. When loss from the surface of the material is suppressed, the dependence of the yield on the effective stopping power, (d E /d x ) eff , is roughly quadratic at high (d E /d x ) eff as in most spike calculations. If escape is allowed, rather than reducing the surface temperature and the yield, both the temperature and the yield increase dramatically and the yield exhibits the roughly linear dependence reported earlier for full MD calculations at high (d E /d x ) eff and constant track radius. This change in dependence is determined by the radial pressure pulse and the energy flow to the surface. By changing a parameter in the interaction potential the stiffness of the material in the MD simulations is varied which changes the effect of the pressure pulse. Not surprisingly, for very stiff materials the yield cannot be related to the spike model but more closely resembles spallation.

Transport theories of sputtering

The use of linear transport theory to calculate several observable quantities in the sputtering process is reviewed. The basic equations previously solved in the literature to obtain the sputtering yield and the energy spectra of sputtered atoms are re–derived and briefly analysed. Comparison with experiments and comments on limitations of theoretical models are included.

The production of high-energy electrons during low energy atomic collisions in solids

Abstract The acceleration of electrons during low-energy atomic collisions in solids is studied. It is shown that a classical, high energy electron can be “trapped” in a sequence of head-on collisions with the ion and the target atom. Then, due to the Fermi acceleration mechanism the trapped electron may absorb energy from the center-of-mass motion up to a maximum value, above which such a sequence becomes unstable. A quantum study of the same process indicates that virtual states appear higher in the continuum of the quasi-molecule formed by the nuclei in the colliding pair, which can be used by the electron to increase its energy during the incoming part of the collision.

Fluid dynamics calculation of sputtering

Abstract The sputtering yields from hot, cylindrical spikes are calculated. To this end, the evolution with time of the energy deposited in a Lennard–Jones target is assumed to be described by the fluid dynamics equations. Furthermore, a crystal pressure is introduced that provides the forces which keep the target around normal density at low temperature. The results of these calculations show that, contrary to predictions of the standard thermal spike theory, the sputtering yield increases with excitation energy in a less-than-quadratic manner. The origin of such a discrepancy relates to the elastic wave resulting from the high-pressure built up in the hot spike. This wave appears to be more efficient than thermal conduction in carrying energy away from the hot core of the spike. The sensitivity of the sputtering yield upon viscosity, the speed of sound and other thermodynamics properties of the target are investigated.

Calculation of energetic H2+-transmission yield using an efficient Monte Carlo algorithm

The transmission yield of 0.1–1.0 MeV/amu H2+ molecular ions as a function of dwell-time (τ) in thin carbon foils have been calculated by Monte Carlo (MC) simulations. As transmission yields drop rapidly with increasing dwell-time, the simulations are speeded up by using a technique known as killing-and-splitting (KS). This technique enables us to simulate, for the first time, the transmission of molecules over the entire range of dwell-time where experimental results are available, i.e., 0 < τ < 30 fs. A detailed description of the KS-method and comparisons of calculations with previous experiments are offered.

The influence of multiple scattering and Coulomb repulsion on the transmission of H2+ through solid targets

Abstract The transmission yield of H2+ ions through solid targets decreases rapidly with dwell time in the foil. This is basically due to the occurrence of three mechanisms: screened Coulomb repulsion, multiple scattering and the wake forces. Using Monte Carlo simulations, we studied the relative importance of these processes in the transmission yield by switching them “on” and “off” alternatively. It was found that for small dwell times the yield drops mainly as a result of the Coulomb repulsion between the nuclei. At larger dwell times multiple scattering by target atoms becomes the dominant mechanism; whereas the wake forces become important at bombarding energies smaller than 150 keV/amu.

Classical-trajectory Monte-Carlo calculations of the electronic stopping cross-section for proton, antiproton and hydrogen projectiles impinging on hydrogen atoms

Although classical mechanics cannot account for the electronic structure of atoms and molecules, the present study shows that the stopping cross-section can be calculated, to a high degree of accuracy, by assuming that electrons are classical particles. In fact, using such an approach, the electronic stopping cross-section (S e) for protons, antiprotons and hydrogen (H0) projectiles bombarding hydrogen atoms has been calculated and the results are found to compare remarkably well with both experiments and previous quantum-mechanics calculations. The dependence of S e on the initial state of the electron is analyzed. It turned out that S e is particularly sensitive to the initial eccentricity of the electron orbit. Similarly, an analysis of the electron trajectory during projectile–target scattering reveals interesting aspects of the stopping process which may help one to understand the way electrons absorb energy from the incoming projectile.

The particle spectra in multicomponent collision cascades

The origin of an apparent difficulty found in recent analytical calculations of the flux of particles within a multicomponent collision cascade was investigated. According to the results in this paper, such an inaccuracy stems from the fact that the assumptions used to solve the transport equation do not hold. Both exact numerical calculations of the transport equation as well as computer simulations show this to be the case, and a number of cases appear to exist for which approximate analytical solutions previously obtained by Vicanek et al fail to produce the right results.

Computer simulations of the interaction between a heavy charge and a classical harmonic oscillator

The interaction of a heavy, point-like charge with a classical electron harmonically bound to a positive, heavy nucleus was simulated. Attention was focused on the stopping of the moving charge. Although most results in this paper can be explained within the framework of Bohrs and more recent theoretical studies, discrepancies do appear. The stopping number ( L ) does not seem to be a universal function of \xi = mv_{0}^{3}/(Z_{1}e^{2}\omega) as was previously proposed. Actually, L seems to be also a function of the amplitude A , the oscillator frequency \omega and the sign of the ion charge. For \xi \ll 1 , and provided the ion is positively charged, simulations yield L s which are greater than theoretical predictions. This seems to be caused by the fact that, during the collision, the electron is first virtually captured by the ion and released later in a higher energy state. In the high velocity regime, a partition rule similar to that which holds for a quantum harmonic oscillator seems to also hold for the classical counterpart. However, instead of the quantum equipartition a two-third partition rule appears to hold in the classical case.

The angular dependence of the energy loss for high energy H+-ions transmitted through thin Al films

Using both classical Monte Carlo simulations and analytical calculations we have investigated the angular dependence of the energy loss (ADEL) for 200 keV protons traversing thin Al films. Our results indicate that the variation of the energy loss with ejection angle may not be as sensitive to the functional form of the energy loss in a single collision as previously assumed. According to present calculations the ADEL is to a great extent determined by multiple scattering and the energy loss in a single, head-on collision.