Fully nonlocal inelastic scattering computations for spectroscopical transmission electron microscopy methods

TL;DR

This paper compares two computational approaches for inelastic scattering in TEM spectroscopy, demonstrating that the reciprocal wave method with full nonlocality inclusion offers accurate results without extra costs, highlighting potential pitfalls of local approximations.

Contribution

It introduces a method to include full nonlocality in inelastic scattering calculations within the reciprocal wave approach, improving accuracy over traditional local approximations.

Findings

Reciprocal wave method is computationally competitive with forward propagation.

Including full nonlocality reduces significant errors in TEM spectroscopical analysis.

Locality approximation can lead to misinterpretation of spectroscopic data.

Abstract

The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major approaches to calculate inelastic scattering cross sections of fast electrons on crystals-Yoshioka-equations-based forward propagation and the reciprocal wave method-are founded in two conceptually differing schemes-a numerical forward integration of each inelastically scattered wave function, yielding the exit density matrix, and a computation of inelastic scattering matrix elements using elastically scattered initial and final states (double channeling). Here, we compare both approaches and show that the latter is computationally competitive to the former by exploiting analytical integration schemes over multiple excited states. Moreover, we show how to include full nonlocality of the inelastic scattering event, neglected in the forward propagation approaches, at no additional computing costs in the reciprocal wave method. Detailed simulations show in some cases significant errors due to the z-locality approximation and hence pitfalls in the interpretation of spectroscopical TEM results.