A. S. Gryazev

Photoelectron spectra of finite-thickness layers

A method of computing x-ray photoemission spectra in the wide range of energy losses and different sighting angles is presented. Photoemission spectra for layers of finite thickness are investigated. Angular and energy spectra are analyzed using the invariant imbedding principle. They are computed using small-angle approximation and the exact numerical solution of the multiple photoelectron scattering events in solids. The presented methods of x-ray photoemission spectra analysis are compared regarding their efficiencies. Comparison of the exact numerical solution to those based on straight line approximation and small-angle approximation reveals an error in straight line approximation of about 50%. Numerical solutions are compared with the experimental data and Monte-Carlo simulations.

Interpretation of X-ray photoelectron spectra with regard to multiple elastic and inelastic scattering

X-ray photoelectron spectroscopy data are analyzed by solving the problem of the photoemission-current density function using the invariant immersion method. X-ray photoelectron spectra in a wide energy loss range are described on the basis of exact solution of the problem of elastic photoelectron scattering in solids using the discrete ordinate technique. The X-ray photoelectron spectrum is recorded in the form of a series of inelastic scattering orders. Comparison of the results of the exact solution with the data of transport and small-angle approximations reveals significant errors in the approximate solutions in X-ray photoelectron spectroscopy. The spectra calculated using different approximations are presented and compared with the experiment. The errors of the traditional background subtraction procedures are considered.

Intrinsic excitation effect for the Al and Mg samples XPS analysis

DIIMFP extraction method based on the numerical solution of electron scattering is presented. DIIMFP data extracted from Reflected Electron Energy Loss Spectra (REELS) is used for Photoelectron spectroscopy (PES) calculations. Experimental data can be described accurately without any intrinsic excitation effect. Authors propose that intrinsic energy losses were introduced to face inaccuracies due to inadequate description of electron energy loss process.

Determination of atomic hydrogen in hydrocarbons by means of the reflected electron energy loss spectroscopy and the X-ray photoelectron spectroscopy

Elastic peaks electron spectroscopy (EPES) is a perspective tool for measuring the hydrogen atomic density in hydrocarbons. It is known that hydrogen elastic peaks overlap inelastic energy loss spectra. This fact complicates the quantitative interpretation of EPES spectra. In this paper, a novel technique based on the joint use of EPES and X-ray photoelectron spectroscopy (PES) is proposed. A key part of the method is the inelastic scattering background subtraction which is performed in two steps. At the first step, differential inelastic scattering cross-sections are retrieved from PES spectra, while at the second step, the retrieved cross-sections are used to remove the inelastic scattering signal from EPES spectra. Both REELS and PES spectra are described on the base of the invariant imbedding method forming a consistent framework for the surface state analysis. A good agreement is obtained between calculated spectra and experimental data.

Angle-resolved photoelectron spectra of layers of finite thickness

The procedure for calculating X-ray photoelectron spectra in wide ranges of energy losses and viewing angles is developed. The spectra of semi-infinite samples and finite-thickness layers are studied. The angular and energy spectra are analyzed via a solution to the problem for the function of photoelectron emission flux density by means of the invariant embedding method. The energy spectrum is represented in the form of a number of inelastic collisions. The results of exact numerical solution of the problem of multiple photoelectron scattering in solids using the straight-line and small-angle approximations, experimental data, and results of Monte Carlo simulation are compared. Errors in calculations using the straight-line approximation and the advantages of models for describing the spectra in the framework of the small-angle approximation are revealed.

Differential inverse inelastic mean free paths and differential surface excitation probability in aluminium in the energy range of 0.5–120 keV

Electron energy loss and photoelectron spectra are obtained on the basis of transfer equation solution. The boundary problem is solved using invariant imbedding approach. The partial intensity method is used to calculate electron energy loss and photoelectron spectra. Differential inelastic electron scattering cross sections in bulk aluminium and in a surface layer are extracted by fitting procedure in an energy range 0.5–120 keV. The method of spectra computation is tested by comparison of results with the experimental data of five foreign scientific laboratories. The physical meaning of the surface-excitation parameter is discussed.

Extracting the differential inverse inelastic mean free path and differential surface excitation probability of Tungsten from X-ray photoelectron spectra and electron energy loss spectra

Precise knowledge of the differential inverse inelastic mean free path (DIIMFP) and differential surface excitation probability (DSEP) of Tungsten is essential for many fields of material science. In this paper, a fitting algorithm is applied for extracting DIIMFP and DSEP from X-ray photoelectron spectra and electron energy loss spectra. The algorithm uses the partial intensity approach as a forward model, in which a spectrum is given as a weighted sum of cross-convolved DIIMFPs and DSEPs. The weights are obtained as solutions of the Riccati and Lyapunov equations derived from the invariant imbedding principle. The inversion algorithm utilizes the parametrization of DIIMFPs and DSEPs on the base of a classical Lorentz oscillator. Unknown parameters of the model are found by using the fitting procedure, which minimizes the residual between measured spectra and forward simulations. It is found that the surface layer of Tungsten contains several sublayers with corresponding Langmuir resonances. The thicknesses of these sublayers are proportional to the periods of corresponding Langmuir oscillations, as predicted by the theory of R.H. Ritchie.

Differential inverse inelastic mean free path determination on the base of X-ray photoelectron emission spectra

The photoelectron spectroscopy model is based on the solution of the radiative transfer equation with inner sources. The exact numerical solutions using BDF method are presented. PES, XAES and EELS spectra are described as series by the number of inelastic scatterings. Differential inverse inelastic mean free path for Be and W are obtained from the experimental data by the fitting procedure.

Reflected electron-energy-loss spectra, differential inverse inelastic mean free paths, and angular resolved X-ray photoelectron spectra of a niobium sample

A technique for recovering the differential inverse inelastic mean free paths (DIIMFP) of electrons in Nb from the reflected electron energy loss spectra (REELS) at initial energies of 5 to 40 keV using a threelayer model of the sample surface is presented. The recovered DIIMFP are used for analyzing X-ray photoelectron spectra measured at different viewing angles. Comparison with experimental data is carried out.

Software tools for profile analysis of multi-layered systems by using the Elastic Peak Electron Spectroscopy

The new generation of spectrometers with high energy resolution can resolve elastic peaks of electrons reflected by atoms in solids. In this regard, there is an increasing interest in the applications of the so-called Elastic Peak Electron Spectroscopy (EPES) for measuring composition-versus-depth profiles since it is non-destructive and sensible to the presence of hydrogen in solids. This study presents numerical tools for quantitative interpretation of the EPES signal. They include modules for peak detecting, estimating the elastic peak intensities and retrieving composition-versus-depth profiles. The latter is based on the transport theory and invokes the straight line approximation (SLA). The examples of profile retrieval using the SLA are given. The accuracy of the proposed model is analyzed.