Calculation of Bohmian quantum trajectories for STEM

A comparative study on Monte Carlo simulations of electron emission from liquid water

PURPOSE

Liquid water being the major constituent of the human body, is of fundamental importance in radiobiological research. Hence, the knowledge of electron-water interaction physics and particularly the secondary electron yield is essential. However, to date, only very little is known experimentally on the low energy electron interaction with liquid water because of certain practical limitations. The purpose of this study was to gain some useful information about electron emission from water using a Monte Carlo (MC) simulation technique that can numerically model electron transport trajectories in water.

METHODS

In this study, we have performed MC simulations of electron emission from liquid water in the primary energy range of 50 eV-30 keV by using two different codes, i.e., a classical trajectory MC (CMC) code developed in our laboratory and the Geant4-DNA (G4DNA) code. The calculated secondary electron yield and electron backscattering coefficient are compared with experimental results wherever applicable to verify the validity of physical models for the electron-water interaction.

RESULTS

The secondary electron yield vs. primary energy curves calculated using the two codes present the same generic curve shape as that of metals but in rather different absolute values. G4DNA underestimates the secondary electron yield due to the application of one step thermalization model by setting a cutoff energy at 10 eV so that the low energy losses due to phonon excitations are omitted. Our CMC code, using a full energy loss spectrum to model electron inelastic scattering, allows the simulation of individual phonon scattering events for very low energy losses down to 10 meV, which then enables the calculated secondary electron yields much closer to the experimental data and also gives quite reasonable energy distribution curve of secondary electrons.

CONCLUSIONS

It is concluded that full dielectric function data at low energy loss values below 10 eV are recommended for modeling of low energy electrons in liquid water.

A novel quantum dynamical approach in electron microscopy combining wave-packet propagation with Bohmian trajectories

The numerical analysis of the diffraction features rendered by transmission electron microscopy typically relies either on classical approximations (Monte Carlo simulations) or quantum paraxial tomography (the multislice method and any of its variants). Although numerically advantageous (relatively simple implementations and low computational costs), they involve important approximations and thus their range of applicability is limited. To overcome such limitations, an alternative, more general approach is proposed, based on an optimal combination of wave-packet propagation with the on-the-fly computation of associated Bohmian trajectories. For the sake of clarity, but without a loss of generality, the approach is used to analyze the diffraction of an electron beam by a thin aluminum slab as a function of three different incidence (working) conditions which are of interest in electron microscopy: the probe width, the tilting angle, and the beam energy. Specifically, it is shown that, because there is a dependence on particular thresholds of the beam energy, this approach provides a clear description of the diffraction process at any energy, revealing at the same time any diversion of the beam inside the material towards directions that cannot be accounted for by other conventional methods, which is of much interest when dealing with relatively low energies and/or relatively large tilting angles.