Simulation of electron spectra for surface analysis using the partial‐intensity approach (PIA)

Abstract

The partial-intensity approach for simulating electron scattering is outlined, and relevant algorithms that were introduced in the past decade are presented. This is important for understanding the signal generation and surface sensitivity for a wide variety of techniques such as X-ray photoelectron spectroscopy (XPS), Auger electron spectroscopy (AES), Auger-photoelectron coincidence spectroscopy (APECS), elastic peak electron spectroscopy (EPES), reflection electron energy loss spectroscopy (REELS), electron probe microanalysis (EPMA), total electron yield (TEY) and the like. In particular, the so-called trajectory-reversal algorithm is discussed, both for emission problems (relevant for XPS, AES, and APECS) as well as for reflection problems (relevant for EPES and REELS), as this algorithm allows one to achieve enhanced efficiencies in simulations of many orders of magnitude compared to a conventional simulation. It is then shown that the simulation of the partial intensities (i.e. the number of n-fold inelastically scattered electrons) is not only useful for simulation of model spectra but is also essential for truly quantitative interpretation of experimental spectra. Finally, the stochastic process for multiple scattering beyond the constant cross-section approximation is treated. Using the generalized stochastic process, the above approaches can be extended to techniques such as EPMA, TEY and the like in a straightforward way. Illustrative examples are given for the topics mentioned above.

Analysis of reflection electron energy loss spectra (REELS) for determination of the dielectric function of solids: Fe, Co, Ni

“…The bulk partial intensities can be obtained most conveniently by means of a Monte Carlo calculation, by calculating the distribution of pathlengths Q(s) the electrons travel in the solid and using the formula [16]:…”

“…Reasonably accurate knowledge of the shape and magnitude of the elastic scattering cross section is important, however, since the shape of the pathlength distribution depends on it. Near a deep minimum of the cross section this dependence may even be critical [16], giving rise to qualitatively different sequences of partial intensities.…”

High-resolution KLM Auger spectra of Ni metal excited by X-rays

“…In the present work, the background correction was done using the Partial Intensity Analysis method 12 in combination with the Monte Carlo simulation of electron trajectories. This is a sophisticated and much more appropriate approach to take into account the effects of multiple elastic and inelastic electron scattering processes along the path of the signal electron within the solid sample 22 . Despite of the difficulties mentioned above, the measured relative intensities of the KLM Auger diagram lines of metallic Ni are in a good agreement with the results of the calculations obtained for free atoms in the intermediate coupling scheme (see Table 3 …”

Algorithm for evaluating layer thickness based on electron average energy shift analysis

“…Extensive work was carried out over the years to eliminate these disturbances from the electron spectra measurements and to evaluate the electron IMFP [15][16][17][18][19][20][21]. However, there are still many assumptions in the field of electron transport.…”