Differential phase contrast from electrons that cause inner shell ionization

TL;DR

This paper explores differential phase contrast imaging using core-loss electrons caused by inner shell ionization, revealing how inelastic scattering influences contrast and its potential for thicker, element-specific imaging.

Contribution

It introduces a transition potential approach for modeling inelastic DPC and analyzes the effects of delocalization and incoherence on image contrast and interpretability.

Findings

Inelastic DPC contrast depends on ionization interaction range.

Inelastic DPC images are more robust at larger sample thicknesses.

Signal-to-noise ratio improves with thickness, aiding thicker sample imaging.

Abstract

Differential Phase Contrast (DPC) imaging, in which deviations in the bright field beam are in proportion to the electric field, has been extensively studied in the context of pure elastic scattering. Here we discuss differential phase contrast formed from core-loss scattered electrons, i.e. those that have caused inner shell ionization of atoms in the specimen, using a transition potential approach for which we study the number of final states needed for a converged calculation. In the phase object approximation, we show formally that differential phase contrast formed from core-loss scattered electrons is mainly a result of preservation of elastic contrast. Through simulation we demonstrate that whether the inelastic DPC images show element selective contrast depends on the spatial range of the ionization interaction, and specifically that when the energy loss is low the delocalisation can lead to contributions to the contrast from atoms other than that ionized. We further show that inelastic DPC images remain robustly interpretable to larger thicknesses than is the case for elastic DPC images, owing to the incoherence of the inelastic wavefields, though subtleties due to channelling remain. Lastly, we show that while a very high dose will be needed for sufficient counting statistics to discern differential phase contrast from core-loss scattered electrons, there is some enhancement of signal-to-noise ratio with thickness that makes inelastic DPC imaging more achievable for thicker samples.