On the phenomenological description of surface absorption of light by metals

Fresnel’s formulas for the coefficients of light reflection from a metal surface are refined to take into account light absorption by conduction electrons during their reflection from the boundary of the metal. The estimates obtained show that the refinement may reveal itself in ellipsometric measurements if their errors do not exceed ∼0.5%.     

The surface relaxation of Al as determined by electron energy loss spectroscopy on plasmons

Electron energy loss spectroscopy (EELS) on plasmons has been applied to determine the thermal expansion coefficient on the surface and to estimate the density of conduction electrons in the surface layer of aluminium. Using the data on the temperature dependence of the surface plasmon energy shift, the value of thermal expansion coefficient on the surface was calculated to be α_s=1.3 × 10^?4K^?1 that is about two times higher than the bulk value. A simple model is proposed which takes account of the influence of electron density non-uniformity in the surface layer on the dispersion of plasma oscillations. An estimation of the density of conduction electrons in the surface layer based on the observed dependence of the surface plasmon energy on the energy of primary electrons gave a value about 5% lower than the bulk value. The thickness of altered surface layer is about 10 Å.     

A study of the orientation dependence of the electron energy loss spectra for single crystal films of copper and silver

Apart from two peaks caused by bulk and surface plasmons, four or five peaks (depending on the crystal type) of electron energy losses due to inter- and intraband electron transitions are observed in the investigation of the electron energy loss spectra for metals (Cu, Ag). A comparative analysis of the spectra for Cu or Ag films reveals a shift of bulk plasmon loss peaks to higher values for polycrystals, as in the case of transition metals and semiconductors. In a study concerning the orientation dependence of the energy loss spectra (ELS) for electrons scattered from the copper and silver surface, the anisotropy of the bulk plasmon peak is found when the incident beam’s polar angle or the sample’s azimuthal angle are altered. The anisotropy of the primary electron energy loss for plasmon excitation is also observed, depending on the sample orientation relative to the direction incident electrons. The energy losses are found to increase with an increasing atomic packing density of planes and crystal transparency relative to the incident beam.     

Coherent inelastic electron reflection from a random medium with a sharp boundary

The weak localization of electrons inelastically scattered in a random medium with a sharp boundary is considered. An inelastic electron collision is accompanied by the excitation of a single bulk plasmon. The coherence of electron scattering results from the interference of electron waves related to two possible realizations of the process in which an electron excites a bulk plasmon and undergoes high-angle elastic scattering by chaotically arranged force centers. The sharpness of the boundary means that the statistically averaged length scale and depth of the surface mocroroughnesses are much smaller than the decay length of the wave field of fast electrons in the medium. The same condition is also imposed on the tail size of the electron density of the medium in vacuum. The theory developed makes it possible to determine the bulk-plasmon generation intensity by measuring the ratio of the electron fluxes inelastically and elastically reflected from the surface of a random medium. For this purpose, one should find the dependence of the ratio of these fluxes on three angles, namely, the polar angle of incidence of electrons, the polar angle of electron exit from the medium, and the azimuth angle between the projections of the velocities of the incident (v) and escaping (v′) electrons on the surface plane. Optimum conditions for the detection of this specific azimuth dependence are theoretically grounded for the case where both electron collisions occur in the near-surface region.     

Angular pattern of electron diffraction by reflection in the plasmon channel of energy losses

We have constructed a theory for the excitation of plasmons by a fast charged particle that undergoes diffraction in a single crystal and then is scattered elastically and incoherently through a large angle. The theory allows the 30-year-old experimental results that have seemed strange to be explained. An increase in the diffraction contrast in the channel of inelastic electron scattering related to the excitation of a bulk plasmon compared to the diffraction contrast of elastically and incoherently reflected electrons was observed in these experiments. Based on this theory, we show that the excitation of a surface plasmon affects only slightly the angular diffraction pattern, leaving it almost the same as that for elastically reflected electrons. These peculiarities of elastic and inelastic diffraction can be used to identify the type of energy plasma loss.     

Quantification of surface effects: Monte Carlo simulation of REELS spectra to obtain surface excitation parameter

The surface excitation effect is investigated by using the quantum mechanical frame work of complex self-energy of electrons which interact with a bounded semi-infinite medium. In the self-energy formalism, differential inverse inelastic mean free path (DIIMFP) has contributions from bulk and surface plasmons. Monte Carlo simulation of the interaction of electrons with a solid medium and surface has been performed. The surface excitation parameter (SEP) is then obtained from the simulated reflection electron energy loss spectroscopy (REELS) spectra. The calculated SEP results by Monte Carlo simulation are compared with the previous calculations of total surface excitation probability, which was estimated by a numerical integration of surface term of DIIMFP. The contribution merely due to surface excitations towards REELS spectra is extracted by subtracting the two Monte Carlo simulated REELS spectra that based on the two models of electron inelastic scattering, i.e. a full surface model (SM) and a pure bulk model (BM). The surface excitations found to be significant at low energy losses and diminish at higher energy losses whereas the bulk plasmon contributions show opposite behavior and are negligible at lower energy losses. The average number of surface excitations is then evaluated by the computation of ratio of the integrated surface contribution to the elastic peak. The calculated results for Ag are found to be reasonably in agreement with our previous results for total probability of surface excitations and other reported experimental data for SEP. Surface correction factor (SCF) is calculated using SEP for several metals and is compared with the reported ratio of SCF with Ni sample as reference.     

Energy loss and plasmon excitation during electron emission in the proximity of a solid surface

We study the interaction with bulk and surface modes of electrons emitted in the proximity of a solid surface. We analyze the modifications in the energy loss, and in bulk and surface plasmon excitations, taking into account the effects due to the sudden creation of the electron and residual atomic hole, and the finite distance to the surface. The process is described using the dielectric function formulation and the specular reflection model. We derive expressions for the electrostatic potential in the medium and in vacuum, which include all the terms due to bulk and surface modes. The effect of each term in the energy loss rate and in the average number of plasmon excitations is discussed. The results illustrate in detail the different spatial dependences of the electron and ion interactions with the bulk and surface perturbations, through the relevant range of distances for studies of electron emission in the proximity of solid surfaces.     

Surface excitation probabilities in surface electron spectroscopies

The phenomenon of surface excitation is competitive in nature for elastic and other inelastic scattering processes in surface electron spectroscopies; the knowledge of influence of surface excitations in electron energy loss spectra is then essential for quantitative surface analysis with these spectroscopies. The inelastic scattering of an electron moving in the vicinity of a surface is considered in a self-energy formalism to estimate the contribution of surface excitation in electron-solid interactions via the total surface excitation probability. The formulation uses the optical bulk dielectric function and provides the spatial and angular dependence of the differential and total inelastic cross-sections. The kinetic energy range of probing electrons considered is 100-5000 eV and the numerical evaluation of total surface excitation probabilities are performed for several metals, Au, Ag, Cu, Ni, Fe and Ti; empirical formulae for the surface excitation probability are given for each of these materials and compared with experimental results for the surface excitation parameter. The total surface excitation probability is higher in Ag as compared to other metals under consideration, for identical conditions of electron-solid interactions.     

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.     

Phonon heat transport in gallium arsenide

The lifetimes of quantum excitations are directly related to the electron and phonon energy linewidths of a particular scattering event. Using the versatile double time thermodynamic Green’s function approach based on many-body theory, an ab-initio formulation of relaxation times of various contributing processes has been investigated with newer understanding in terms of the linewidths of electrons and phonons. The energy linewidth is found to be an extremely sensitive quantity in the transport phenomena of crystalline solids as a collection of large number of scattering processes, namely, boundary scattering, impurity scattering, multiphonon scattering, interference scattering, electron–phonon processes and resonance scattering. The lattice thermal conductivities of three samples of GaAs have been analysed on the basis of modified Callaway model and a fairly good agreement between theory and experimental observations has been reported.     

Focusing of electrons reflected from a crystal with loss of energy

A study is made of the features arising in the spatial distributions of reflected electrons as a result of a focusing effect. Experiments are conducted on single-crystal Mo (100) with primary electron energies of 0.5–2 keV and detection of electrons which lose fixed amounts of energy up to 300 eV. An analysis of the data establishes the dependence of the electron focusing efficiency on the amount of energy loss. It is shown that when electrons are reflected with single losses through plasmon excitation, the magnitude of the effect is determined mainly by the average number of scattering atoms encountered by an electron along its path to the surface. When the energy losses are high, defocusing owing to multiple elastic and inelastic scattering of the electrons is found to predominate. Zh. Tekh. Fiz. 68, 128–133 (June 1998)     

A study of the influence of surface layers’ disordering on the spectrum of energy losses of electrons passed through copper thin single crystal films

Results of the experimental investigation of energy losses of electron passed through thin films Cu (100) with a thickness of d ≈ 420 ? at E _p = 3 keV are presented. It is revealed that the surface plasmon peak disappears at a primary electron energy of ≥6 keV. For the first time, the degree of surface amorphization and area of the disordered layer are estimated by the change of elastic peak intensity during the passage of electrons through thin films of Cu (100). There is an additional energy loss of electrons peak caused by bulk plasmon, its intensity depending on the irradiation dose under ionic bombardment.     

Quasi-static surface modes of plasma layer with anisotropic electron temperature

Quasi-static surface wave propagation in a plasma layer with anisotropic electron temperature is considered. The case is analyzed where the electron temperature in the direction normal to the plasma boundary is considered to be zero, while in the direction along the boundary, electrons are described by the Maxwellian velocity distribution. It is shown that the modes of such a layer are described by equations for bulk plasma waves with renormalization of the electron density affecting the surface wave dispersion and damping.     

Elastic scattering of electrons by helium and neon atoms

Summary  Partial and total cross-sections of electrons scattering by helium and neon atoms are calculated at eleven values of incident energy ranging from 0.1 a.u. to 1.1 a.u. The calculations are carried out via model potential (describing the electron target interaction). The iterative Green’s function partial-wave expansion technique was used. The comparison between our results and those obtained by other authors show significant agreement and supports our simple model scattering process.     

Dyadic Green’s function of a PEMC cylinder

The dyadic Green’s function of a PEMC cylinder is derived with the aid of the principle of scattering superposition and Ohm–Rayleigh method. The PEMC boundary conditions are presented in dyadic form and it shows that how the impedance parameter of PEMC and cross-polarized fields appear in the Green’s function. The asymptotic expansions of the dyadic function is calculated in order to attain a closed form for the electrical field.     

Resonance and composition effects on the Raman scattering from silver-gold alloy clusters

Low-frequency Raman scattering experiments have been performed on thin films consisting of pure gold or gold-silver alloy clusters embedded in alumina matrix. It is clearly shown that the quadrupolar vibrational modes are observed by Raman scattering because of the effect of resonance with the excitation of the electronic surface dipolar plasmon. This is due to the strong coupling between the collective electronic dipolar excitation and the quadrupolar vibrational modes. This effect of resonance does not exist with the core electron excitations. The mixing of the conduction electron dipolar excitation (surface plasmon) with the core electrons leads to the quenching of the resonant Raman scattering. Received 16 November 2000     

Scattering of a surface plasmon polariton beam by chains of dipole nanoparticles

Scattering and splitting of surface plasmon polaritons (SPPs) by a chain of strongly interacting nanoparticles located near a metal surface are numerically studied. The applied numerical model is based on the Green’s function formalism and point–dipole approximation for scattering by nanoparticles. Dependencies of the splitting efficiency on the inter-particle distance in the chain and on the angle of incidence of the SPP Gaussian beam are considered. It is found that the splitting efficiency depends on the inter-particle distances especially when the angle between the SPP beam and the chain is relatively small. The role of multiple scattering in the SPP splitting by the chains of nanoparticles is also discussed.     

Monte Carlo simulation for Multi-Mode Elastic Peak Electron Spectroscopy of crystalline materials: Effects of surface structure and excitation

The Multi-Mode Elastic Peak Electron Spectroscopy (MM-EPES) analysis is confined to incoherent electron elastic scattering and the use of variable primary energy. This experimental method is very sensitive to the surface region of the sample. However, for quantitative interpretation, the MM-EPES method needs jointly a Monte Carlo (MC) computer simulation of electron trajectories in the solid. In the present work, we proposed a new approach to calculate the percentage η_e of elastic reflected electrons by the surface of a sample. This simulation takes into account the surface effects (i.e. surface plasmon), and the atoms arrangement in the substrate. The concept of the surface excitation parameter (SEP) is also presented. Computer simulations were performed on the three low index single crystals of Cu, Au, Si and Ag. The results confirm that the distribution of substrate atoms, according to the crystallographic structure, influences the intensity measured by EPES.A simple prediction formula was proposed to calculate η_e for elastic electrons entering in a Retarding Field Analyzer (RFA) spectrometer which is the apparatus giving experimentally numerical values of the percentage η_e.     

Study of J-T effect on the self-energy of electrons in manganite systems

We present here a theoretical study of the effect of Jahn-Teller(J-T) distortion on the self-energy of electrons in the CMR manganites. The model consists of the itinerant e _g electrons distorted by J-T effect and the localized t _2g core electrons carrying strong ferromagnetism due to Hund’s rule. The phonon interacts with the e _g electrons as well as the J-T distorted e _g band. The electron Green’s functions are calculated by Zubarev’s technique. The electron self-energy which carries all the information of the model is calculated from the Green’s function. The effect of J-T distortion, magnetism on the frequency and temperature dependent dynamic self-energy is presented in this paper. The results are discussed.