V. P. Afanas’ev

Photoelectron Emission for Layers of Finite Thickness

Basic tools that describe the energy and angular distributions of photoelectrons emitted by inhomogeneous targets are presented. These are the functions of reflection and transmission, the function of photoelectron emission, the equation for photoelectron flow, and the equation for the transmission function, which describes the dynamics of the angular and energy spectra of photoelectrons when they move in the tar-get. The determining influence of the effects of multiple elastic scattering on the angular distribution of photoelectrons is shown. It is demonstrated in which way and by how much the effect of brightness body rotation, well known in optics, influences the X-ray photoelectron spectroscopy signal. Along with analytical solutions, the results of simulation of the X-ray photoelectron spectroscopy signals are presented.

Direct numerical reconstruction of inelastic cross sections from REELS and ISS spectra

The reconstruction of inelastic scattering cross sections faces two problems: the measured signal (energy spectrum) is a multiple scattering signal; the inelastic energy loss is nonuniform over the target depth. In this paper, we present a method for numerical reconstruction of cross sections from characteristic energy loss spectra, which efficiently solves both problems within a multilayer model. It is shown that the inverse problem of cross section extraction in the three-layer model is ill-conditioned, and the method is practically inapplicable to the three-layer model. The direct numerical reconstruction method yields a strongly “noised” result and can be applied only to obtain a priori information on the inelastic cross section form for further fitting. Using a combination of two methods, inelastic scattering cross sections were reconstructed for aluminum from characteristic energy loss spectra at probe beam energies of 5 and 40 keV. It is shown that ionization in solids should be described as a local process and as a collective one using the dispersion formula similarly to the case of excitation plasmons.

Theory of the formation of the energy spectra of reflected charged particles

The theory of the formation of the energy spectra of electrons and light ions reflected form a solid surface is constructed. It is shown that methods based on the numerical solution of boundary-value problems for the transport equation are the most effective. The boundary-value problem is solved based on the invariant embedding method. Equations for the reflection coefficients Rk(x, n, n0), describing the flux of atomic particles reflected in the direction n and having experienced k events of elastic scattering are obtained. The obtained results are compared with experimental data, the results of simulation using the Monte Carlo method, and the calculations of other authors.

Small-angle approximation and Oswald–Kasper–Gaukler theory of electron reflection from solids

It is shown that the description of the process of electron ref lection from the surface of a solid in the small-angle approximation using the invariant embedding method is completely equivalent to Oswald–Kasper–Gaukler theory. The small-angle approximation is generalized to problems of the determination of the contributions of k-fold inelastic scattering to the energy spectrum of ref lected electrons. The theory is tested by comparing it with the results of other authors and with the data of exact calculations.

Influence of the processes of multiple elastic scattering on the angular distributions of X-ray photoelectrons

Based on the boundary-value problem for the transport equation, the angular distributions of photoelectrons are analyzed using the method of invariant immersion. Monte Carlo (MC) simulation of the process of photoelectron emission is carried out. The determining influence of the process of multiple elastic scattering on the photoelectron spectra is shown. Simple analytical formulas for the angular distributions of photoelectrons are obtained in the small-angle approximation. The results of MC simulation and those of other authors are compared.

Scattering of electrons by vacuum fluctuations of plasma waves

Interaction between a probe electron beam and longitudinal electromagnetic oscillations of the Fermi plasma in metals (plasmons) is investigated by the methods of quantum electrodynamics. The quantum description of plasmons allows one to construct a consistent theory of the scattering process and point out the applicability limits of the existing semiclassical theories. The quantum description of plasmons leads to the concept of electromagnetic vacuum of longitudinal waves, which is the subject of the present study. The vacuum of longitudinal waves significantly deforms the shape of plasma dielectric permittivity, thus leading to the broadening of Langmuir peaks of scattered electrons, which has so far resisted theoretical analysis. The presence of the electromagnetic vacuum of longitudinal plasma waves has a considerable effect on the integral scattering probability of electrons by plasmons.

Effect of multiple elastic scattering on X-ray photoelectron spectroscopy signals over a wide range of energy loss

Spectra from X-ray photoelectron spectroscopy (XPS) measured over a wide range of energy loss are analyzed. The analytic description of XPS spectra over a wide range of energy loss is based on a precise solution to the problem of elastic scattering of photoelectrons in solids. A precise numerical solution is obtained by means of discrete ordinates method. The XPS spectrum is represented as a series by quantity of inelastic scattering. The inconsistency of ignoring multiple elastic processes by using straight line approximations (SLAs) in describing XPS energy spectra is demonstrated.

X-ray photoelectron spectroscopy: Exact solution to the problem with internal sources

A fundamentally new model of multiple photoelectron scattering in solids is described in this paper. It takes into account the nonuniform depth distribution of photoelectron sources and the anisotropic character of single scattering and yields an exact solution to the problem of multiple elastic scattering. Highly accurate and fast algorithms for calculating X-ray photoelectron spectroscopy signals can be developed on the basis of this model.

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.

Quantitative interpretation of energy X-ray photoemission spectra

An analytical description of X-ray photoemission spectra is constructed on the basis of solution of the boundary-value problem for the transport equation taking internal sources into account by invariant embedding methods. Solutions in the small-angle approximation and exact solutions obtained as a result of the numerical procedure. The photoelectron path lengths distributions in a target and coefficients of expansion of the photoemission flux density in a series of inelastic scattering multiplicities are determined. The invalidity of approaches neglecting processes of multiple elastic scattering when describing energy X-ray photoemission spectra is shown. Errors appearing in the case where approximations are used are estimated.