Quantum-trajectory Monte Carlo method for study of electron–crystal interaction in STEM

Abstract

In this paper, a novel quantum-trajectory Monte Carlo simulation method is developed to study electron beam interaction with a crystalline solid for application to electron microscopy and spectroscopy. The method combines the Bohmian quantum trajectory method, which treats electron elastic scattering and diffraction in a crystal, with a Monte Carlo sampling of electron inelastic scattering events along quantum trajectory paths. We study in this work the electron scattering and secondary electron generation process in crystals for a focused incident electron beam, leading to understanding of the imaging mechanism behind the atomic resolution secondary electron image that has been recently achieved in experiment with a scanning transmission electron microscope. According to this method, the Bohmian quantum trajectories have been calculated at first through a wave function obtained via a numerical solution of the time-dependent Schrödinger equation with a multislice method. The impact parameter-dependent inner-shell excitation cross section then enables the Monte Carlo sampling of ionization events produced by incident electron trajectories travelling along atom columns for excitation of high energy knock-on secondary electrons. Following cascade production, transportation and emission processes of true secondary electrons of very low energies are traced by a conventional Monte Carlo simulation method to present image signals. Comparison of the simulated image for a Si(110) crystal with the experimental image indicates that the dominant mechanism of atomic resolution of secondary electron image is the inner-shell ionization events generated by a high-energy electron beam.

Calculation of Bohmian quantum trajectories for STEM

“…This will make it possible to study the entire electron signal generation process including both elastic and inelastic scattering of electron interaction with a crystalline solid and SE cascade production process. Actually, we have employed this novel approach successfully in the simulation of atomic resolution SE imaging in STEM (Ruan et al, 2014;2015). Considering that SE emission follows an exponential decay law in depth with a typical emission depth about 1 nm (Reimer, 1998); in present calculation the Bohmian quantum trajectories are traced up to a depth of 1 nm, which is considered appropriate for the study of SE imaging.…”

Charging effect induced by electron beam irradiation: a review

“…secondary electrons [57][58][59][60][61][62], Auger electrons [63][64][65][66], and X-rays [67,68] into the simulation. Furthermore, the Monte Carlo method has been proven reliable in investigating electron transport or electron-solid interactions even when the electron energy is as low as several eV [69] or as high as hundreds of keV [70].…”

Novel Quantum Trajectory Approaches to Simulation of Electron Backscatter Diffraction

“…where R and S are the amplitude and the phase of wave function, respectively. By separating the real and imaginary parts of the Schrödinger equation, we can get the following formulas [12,13],…”