A Comprehensive Theory of Electron Probe Microanalysis

Abstract

An ideal theory for the electron probe microanalyzer would enable the analyst to obtain corrected concentrations that were precise and accurate for essentially any combination of elements and operating conditions. First consider the fundamental assumption of microprobe analysis, i.e., that the characteristic x-ray intensities generated by the electron beam in the specimen are proportional to the mass fraction of each emitting element present and that to determine these quantities entails correcting the observed data for x-ray absorption, backscatter losses and fluorescence effects. To do this requires that the depth distribution of x-ray production be known for the material in question. Therefore a logical starting point in the search would be to devise a theoretical model that would be able to predict the relative number and depth distribution of x-ray production, or φ(ρz) as it is called, as a function of the relevant physical parameters: namely the accelerating potential, E ₀, the critical excitation potential of the x rays of interest, E _c, the mean atomic number and atomic weight of the specimen, Z and A, and the orientation of the specimen’s surface with respect to the electron beam. If this can be accomplished then immediately a number of other benefits accrue, not the least of which would be an equation for the electron range, valuable information when analyzing specimens that are thought to be nonuniform. That in turn brings up the next requirement: the theory should be able to predict the x-ray signal from various configurations of nonuniform specimens such as thin deposits or layered samples and thin film specimens such as are used in the TEM/STEM. Additional features such as the ability to predict backscattered and transmitted or absorbed electron fluxes from these various types of specimens would also be useful in particular circumstances. To predict the x-ray generation in specimens with two or even three dimensions smaller than the electron range would be the ultimate quest.