Quantitative Agreement between Electron-Optical Phase Images of WSe_{2} and Simulations Based on Electrostatic Potentials that Include Bonding Effects.

Abstract

The quantitative analysis of electron-optical phase images recorded using off-axis electron holography often relies on the use of computer simulations of electron propagation through a sample. However, simulations that make use of the independent atom approximation are known to overestimate experimental phase shifts by approximately 10%, as they neglect bonding effects. Here, we compare experimental and simulated phase images for few-layer WSe_{2}. We show that a combination of pseudopotentials and all-electron density functional theory calculations can be used to obtain accurate mean electron phases, as well as improved atomic-resolution spatial distribution of the electron phase. The comparison demonstrates a perfect contrast match between experimental and simulated atomic-resolution phase images for a sample of precisely known thickness. The low computational cost of this approach makes it suitable for the analysis of large electronic systems, including defects, substitutional atoms, and material interfaces.