Static and dynamic interactions with spatially dispersive media

Electrostatic image force energy for charges in three-layer structures: exact formulas and their approximations

The problem of image force energyW(Z) in three-layer plane structures, whereZis the coordinate perpendicular to the layers, has been reconsidered. In the classical electrostatic limit, where the dielectric permittivitiesɛ_iof all structure components (i= 1, 2, 3) are constants, the exact general dependencesW(Z) were obtained for each layer and anyɛ_i-combination in terms of the Lerch transcendent function. For certain combinations ofɛ_i, an ion adsorption minimum was found to arise in one of the covers far from the interlayer. Some other combinations ofɛ_ican lead to the appearance of a potential barrier, which does not permit a free charge existing in the cover to approach the interlayer, although it will be attracted to the interlayer in the close vicinity of the latter. For symmetric structures (ɛ₁=ɛ₃), the asymptotic behavior ofW(Z→∞)was shown to beZ-2rather thanZ-1, as it takes place in the two-layer case. Simple approximate analytical formulas that describeW(Z) and possess high accuracy for arbitrary relationships among theɛ_i-constants were proposed.

Surface excitations in the modelling of electron transport for electron-beam-induced deposition experiments

The aim of the present overview article is to raise awareness of an essential aspect that is usually not accounted for in the modelling of electron transport for focused-electron-beam-induced deposition (FEBID) of nanostructures: Surface excitations are on the one hand responsible for a sizeable fraction of the intensity in reflection-electron-energy-loss spectra for primary electron energies of up to a few kiloelectronvolts and, on the other hand, they play a key role in the emission of secondary electrons from solids, regardless of the primary energy. In this overview work we present a general perspective of recent works on the subject of surface excitations and on low-energy electron transport, highlighting the most relevant aspects for the modelling of electron transport in FEBID simulations.

Surface excitations in electron spectroscopy. Part I: dielectric formalism and Monte Carlo algorithm

The theory describing energy losses of charged non-relativistic projectiles crossing a planar interface is derived on the basis of the Maxwell equations, outlining the physical assumptions of the model in great detail. The employed approach is very general in that various common models for surface excitations (such as the specular reflection model) can be obtained by an appropriate choice of parameter values. The dynamics of charged projectiles near surfaces is examined by calculations of the induced surface charge and the depth- and direction-dependent differential inelastic inverse mean free path (DIIMFP) and stopping power. The effect of several simplifications frequently encountered in the literature is investigated: differences of up to 100% are found in heights, widths, and positions of peaks in the DIIMFP. The presented model is implemented in a Monte Carlo algorithm for the simulation of the electron transport relevant for surface electron spectroscopy. Simulated reflection electron energy loss spectra are in good agreement with experiment on an absolute scale. Copyright © 2012 John Wiley & Sons, Ltd.

Validity of the semi-classical approach for calculation of the surface excitation parameter

The problem of surface plasmon excitation by moving charges has been elaborated by several different approaches, mainly based on dielectric response theory within either semi-classical or quantum mechanical frameworks. In this work, a comparison of the surface excitation effect between two different frameworks is made by calculation of the differential inverse inelastic mean free path (DIIMFP) and a Monte Carlo simulation of reflection electron energy loss spectroscopy (REELS) spectra. A semi-classical modeling of the interaction between electrons and a solid surface is based on analyzing the work done by moving electrons; the stopping power and inelastic cross section are derived with the induced potential. On the other hand, a quantum mechanical approach is based on derivation of the complex inhomogeneous self-energy of the electrons. The numerical calculation shows that the semi-classical model presents almost the same values of DIIMFP as by the quantum model except at the glancing condition. The simulation of REELS spectra for Ag and SiO(2) as well as a comparison with experimental spectra also confirms that a good agreement with the spectral shape is found among the two simulation results and the experimental data.

Heterocoagulation of chalcopyrite and pyrite minerals in flotation separation

Heterocoagulation between various fine mineral particles contained within a mineral suspension with different structural and surface chemistry can interfere with the ability of the flotation processes to selectively separate the minerals involved. This paper examines the interactions between chalcopyrite (a copper mineral) and pyrite (an iron mineral often bearing gold) as they approach each other in suspensions with added chemicals, and relates the results to the experimental data for the flotation recovery and selectivity. The heterocoagulation was experimentally studied using the electrophoretic light scattering (ELS) technique and was modelled by incorporating colloidal forces, including the van der Waals, electrostatic double layer and hydrophobic forces. The ELS results indicated that pyrite has a positive zeta potential (zeta) up to its isoelectric point (IEP) at approximately pH 2.2, while chalcopyrite has a positive zeta up to its IEP at approximately pH 5.5. This produces heterocoagulation of chalcopyrite with pyrite between pH 2.2 and pH 5.5. The heterocoagulation was confirmed by the ELS spectra measured with a ZetaPlus instrument from Brookhaven and by small-scale flotation experiments.