Simplified equations for correction parameters for elastic scattering effects in AES and XPS for Q, β and attenuation lengths

In this work we develop simple equations, suitable for the analyst, based on the Monte Carlo calculations of Jablonski, for the corrections arising from elastic scattering. These concern modification of the angular anisotropy in XPS and the absolute intensities in both Auger electron spectroscopy (AES) and x-ray photoelectron spectroscopy (XPS) as a function of the atomic number Z. We also derive more accurate equations for these parameters and the ratio of the attenuation length, L, to the inelastic mean free path (IMFP) based on a knowledge of omega, where omega is the ratio of the IMFP to the sum of the transport mean free path (TrMFP) and the IMFP. The first equations give the corrections to the anisotropy, beta (eff)(alpha)/beta, and the total emission, Q(alpha), from Jablonski's work in terms of a total of four equations and a total of 19 coefficients to replace Jablonski's two equations with a total of 2376 coefficients. The present equations describe the dependencies of beta (eff)(alpha)/beta and Q(a) on the angle of electron emission a, the electron energy E and the atomic number of the matrix in the ranges 0 degrees < alpha < 70 degrees, 300 < E < 1500 eV and 6 < Z < 83. The standard deviation of the scatter with regard to Jablonski's calculations are 4.6% for beta (eff)(alpha)/beta and 1.35% for Q(alpha), giving an overall uncertainty for quantification, relative to the Monte Carlo calculations, of better than 2%. The equations allow values of beta (eff)(alpha) to be calculated for revised values of beta and for elements other than the 27 studied by Jablonski. They also allow Q(a) to be calculated for other elements and for energies appropriate to Auger electrons within the above ranges. More complex equations, derived from a slight modification to the transport equations, allow beta (eff)(0)/beta, Q(0) and the ratio L/IMFP to be derived from a knowledge of w. These equations exhibit a standard deviation of scatter of 2.8%, 0.3% and 1.1%, respectively, compared with the Monte Carlo calculations of Jablonski and of Cumpson and Seah, leading to uncertainties in quantification of the order of 1%. These equations are more complex for the analyst to use than the simple equations as a function of Z, but have superior accuracies and accuracies that are probably limited by the precision of the Monte Carlo calculations. (C) Crown Copyright 2001. Reproduced by permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd.