Elastic Scattering Corrections in AES and XPS. II. Estimating Attenuation Lengths and Conditions Required for their Valid Use in Overlayer/Substrate Experiments

Abstract

We examine substrate/overlayer experiments and the equations commonly used to quantify overlayer thicknesses. Comparisons with accurate Monte-Carlo simulations show that using attenuation lengths (rather than inelastic mean free paths) eliminates most of the error due to elastic scattering without increasing the complexity of the quantification. We give attenutation lengths for 27 elements, calculated by the criterion that systematic errors in such quantifications should be minimized. These are therefore the best attenuation length values to use in layerwise quantification. We show that, provided these attenuation length values are used, the error in estimation of the thickness of an overlayer due to elastic scattering can be limited to +(5% +1 A) for an emission angle ≤58° from the surface normal, and +(10%a + 1 A) for an emission angle ≤63° from the surface normal. This accuracy is acceptable for most analytical work. Other methods (such as analytical transport theory) are much more complicated, and achieve a high precision that is often unnecessary in view of other uncertainties typically present in these experiments (such as errors due to surface morphology and diffraction effects). The results presented here, using the full theory, show that the analyst's simple straight-line approximation is in fact of adequate accuracy, provided that the correct values of attenuation length are used. Simple semi-empirical equations are presented, which allow the analyst to estimate the attenuation length for electrons of kinetic energy between 50 and 2000 eV, to a standard uncertainty of 6%.