Inverse Modeling of Heterogeneous Structures in Electron Probe Microanalysis

Abstract

Electron probe microanalysis (EPMA) is a powerful tool for chemical characterization of materials on a microscopic scale. However, EPMA has the drawback that its information volume has a spatial extent of some 100 nm to a few µm. With the introduction of new electron sources, i.e., Schottky Thermal Field and Cold Field Emitter, where the electron beam is focused down to a few nm, measurements can be nowadays performed on the sub-micrometer scale. The goal of the work is to reveal the chemical composition of structures smaller than the excitation volume. New strategies are presented where the acquisition is performed at different positions on the sample and as a scan across a fine structure by using one or more single beam energies. Besides the well-known Monte-Carlo simulation, a deterministic model is also used. The deterministic model is based on moment equations of the Boltzmann equation. Inverse modeling is presented for several case studies. Due to the highly complex nonlinearity of the inverse model, an ill-posed and well-posed problem is shown as well. Finally, the method is extended to reconstruct 2D structures, i.e., rectangular shaped particles, with heterogeneous composition on lateral and depth scale.