C.M. Kwei

Surface excitation parameters of low-energy electrons crossing solid surfaces

The surface excitation parameter, which describes the influence of surface excitations by electrons for the vacuum side in electron spectroscopies, has been calculated for electrons of 200-2000 eV energies crossing surfaces of Cu, Ag, Au, Fe, Pd, Ni, MgO and SiO 2 , These calculations were performed for both incident and escaping electrons by the use of dielectric response theory. Spatially varying differential inverse mean free paths for surface excitations as a function of electron distance from the surface were found. The results showed that small differences existed in the surface excitation parameter among different metals but large differences occurred between metals and semiconductors or insulators, Calculated surface excitation parameters were fitted very well to a simple formula, i.e. P. = aE -b , where P. is the surface excitation parameter and E is the electron energy.

ELECTRON INELASTIC MEAN FREE PATHS FOR PLASMON EXCITATIONS AND INTERBAND-TRANSITIONS

Abstract Both plasmon excitations and interband transitions are important in the response of valence bands to fast electrons. An extended Drude dielectric function was established to describe such a response in solids of complex band structures. Parameters in this function were determined by a fit of the imaginary part of the function to experimental optical data. The real part of the dielectric function and the energy-loss function were also checked with experimental data to confirm critical-point energies in the interband transitions and plasmon energies in the collective excitations. In addition, sum-rules about the imaginary part of the dielectric function and the energy-loss function, respectively, were applied to assure the accuracy of these functions. Electron inelastic mean free paths in several solids were calculated and compared to available experimental and theoretical data.

ELECTRON INELASTIC MEAN FREE PATHS VERSUS ATTENUATION LENGTHS IN SOLIDS

The electron inelastic mean free path is of basic importance in theoretical and applied radiation physics and surface physics. It can be calculated using the dielectric function for the valence band and atomic generalized oscillator strengths for inner shells of a solid. Although the experimentally determined attenuation length is conceptually different from the theoretically calculated mean free path, they are frequently used interchangeably in a loosely defined manner. For electrons with energies below a few keV, elastic scattering plays an important role in connecting these two quantities. This work employed elastic scattering cross sections derived using the partial wave expansion method with a solid potential to evaluate the path length distribution of an electron transmitted through a solid film. Both the analytical multiple-scattering formulation and the numerical Monte Carlo simulation have been applied in this investigation. A comparison between electron inelastic mean free paths and attenuation lengths was made.

Electron inelastic interactions with overlayer systems

An overlayer system composed of a thin film on the top of a semi-infinite substrate was studied in this work for electron inelastic interactions. Analytical expressions for the depth-dependent inelastic differential and integral inverse mean free paths were derived for both incident and escaping electrons. The interface (film-substrate) effect and the surface (vacuum-film) effect were analyzed by comparing the results of an overlayer system and a semi-infinite system. It was found that the interface effect extended to several angstroms on both sides of the interface for a 500 eV electron incident into or escaping from the vacuum–SiO2–Si and the vacuum–Au–Ni systems. An application of the spatial-varying inelastic differential inverse mean free paths was made by Monte Carlo simulations of the electron elastic backscattering from an overlayer system. Good agreement was found between results calculated presently and data measured experimentally on the elastic reflection coefficient.

Monte Carlo calculations of the reflection electron energy loss spectra in gold

The reflection electron energy loss spectra in gold have been calculated using a Monte Carlo approach. A description of Monte Carlo simulations based on the dielectric response theory for inelastic volume and surface excitations and the partial wave expansion method for elastic scattering was presented. The influence of surface excitations on the angular and energy spectra of reflected electrons was analysed. These excitations contributed to the energy spectra by single and plural inelastic loss peaks and by the multiple inelastic loss background. Surface plasmons were particularly important for glancing incident or escape electrons. The contribution from surface excitations to the angular spectra was significant for energy losses of a few tenths of an electronvolt but less significant for lower and higher energy losses. The angular spectra revealed single elastic scattering peaks for zero energy loss but flatter multiple elastic scattering curves for large energy losses. In all cases, Monte Carlo simulation results, including surface excitations, agreed very well with experimental data.

Energy losses of charged particles moving parallel to the surface of an overlayer system

An energetic charged particle moving parallel to the surface of an overlayer system was studied. This system was composed of a thin film on the top of a semi-infinite substrate. Based on the dielectric response theory, the induced potential was formulated by solving the Poisson equation and matching the boundary conditions. The stopping force was built-up using the energy-momentum conservation relations and the extended Drude dielectric functions with spatial dispersion. Surface (vacuum–film) and interface (film–substrate) excitations were included in the formulations of the interaction between charged particles and the overlayer system. Results of the wake potential were presented for protons moving parallel to a vacuum–copper–silicon system. Dependences of the induced potential and the stopping force on film thickness, distance of the proton from surface, and proton velocity were investigated.

Angular distribution of electrons elastically backscattered from amorphous overlayer systems

Abstract Monte Carlo calculations have been performed of the angular distribution of electrons elastically backscattered from amorphous overlayer systems composed of thin copper films and semi-infinite silicon substrates. These calculations showed that the angular distribution of the elastically reflected intensity was dependent on film thickness and electron energy. They also showed that elastically backscattered electrons were due substantially to one, two and three scatterings with single-scattering events contributing about half of the intensity. Based on these findings, we have derived a formula for the contribution from single-scattering events to the angular distribution of the elastically reflected intensity. Combining this formula and the P 1 -approximation for multiple scattering, we were able to construct an analytic formula for the angular distribution of electrons elastically backscattered from overlayer systems. Results from this approach were in good agreement with those computed using Monte Carlo simulations.

Stopping power of semiconducting III-V compounds for low-energy electrons

The stopping power of III-V compounds for incident electrons has been studied. An extended Drude-type dielectric function has been employed for the response of valence band. The local plasma approximation has been applied for the response of inner shells. Stopping powers of GaAs, GaSb, GaP, InSb and InAs were computed and compared to the limited data.

The surface effect on Au 4f X-ray photoelectron spectra

Abstract An investigation of the surface effect on Au 4f X-ray photoelectron spectra was made for different emission angles. It was found that surface plasmon excitations made significant contributions to the spectra in single and plural energy-loss peaks and in the multiple loss background. Our approach involved Monte Carlo simulations of photoelectrons in the interior region of the solid and Poisson stochastic processes in the surface region. The partial-wave expansion method with the Hartree-Fock-Wigner-Seitz potential for the solid was used to calculate differential electron elastic scattering cross sections. An extended Drude dielectric function model was employed to compute electron differential inverse mean free paths for volume excitations. The inelastic mean free paths in the surface region became spatially-varying and were calculated. Differential probabilities for surface excitations were determined using the same model dielectric function. The computed X-ray photoelectron spectra including surface excitations agreed quite well with experimental data.

Angular distribution of electrons elastically backscattered from non-crystalline solid surfaces

In the energy range 100 eV-2 keV, we applied the Monte Carlo method to analyse the elastic reflection coefficient and the angular distribution of electrons elastically backscattered from the solid surface of an isotropic and homogeneous medium. Results indicated that elastically backscattered electrons arose substantially from only a few scatterings with a single scattering event contributing to approximately half of these electrons. Thus, neither the multiple scattering model nor the single scattering model is sufficient to describe the angular distribution. To improve these models, we evaluated the contribution from one, two and three scatterings exactly and higher scatterings by the P1-approximation, an approximate method to solve the Boltzmann transport equation assuming multiple elastic scattering of electrons in the solid. This approach allowed us to derive analytical formulations for the elastic reflection coefficient and the angular distribution of elastically backscattered electrons. Results calculated based on these formulations were in good agreement with those using Monte Carlo simulations and experimental data.