Dynamical scattering and the quantification of electron energy-loss spectra of solids

Abstract

An important application of electron energy-loss spectroscopy (EELS) carried out in the electron microscope is to the elemental analysis of microscopic samples which may be as small as 1 nm in linear dimension, i.e. in samples of only 10^–20 g. This technique is particularly important for the study of the first row elements of the periodic table which are not easily investigated using the alternative technique of X-ray emission spectroscopy (XRE). Until recently it was thought that uncertainties of some 10% were associated with the detection limit for light elements and for the accuracy with which the concentration of light elements present in the sample could be measured. This limit stems in part from the inaccuracies inherent in the random statistics of the counting process and in part from systematic errors in the calculation of the relevant cross-sections and corrections. However, the improved understanding of the various systematic errors and corrections as well as recent developments in parallel detection means that it should now be possible to carry out chemical analyses with an accuracy of the order of 1% or better. We examine the effect of Bragg scattering, which in electron microscopy must be trated in the dynamical scattering limit, on the accuracy of elemental analysis using EELS. Neglect of this effect may lead to errors of up to 20% in the chemical analysis. The theory of such multiple scattering is outlined and three representative samples are studied: boron nitride, nickel oxide and silicon. These examples permit us to examine the effect of Bragg scattering on estimates of the relative amounts of two elements as well as on estimates of the absolute amounts of a single element.