P. S. Kaplya

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.

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.

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.

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.

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.

Influence of the processes of elastic scattering on the X-ray photoelectron spectroscopy spectra of nonuniform layered targets

The spectra of X-ray electrons emitted by a nonuniform layered target are calculated in the small-angle approximation using the discrete-coordinate method. The errors in the calculations based on the small-angle and transport approximations are determined.