General oscillation strength of core-shell electron excitation by fast electrons based on Dirac solutions

Abstract text (incl. figure legends and references)

STEM-EELS is widely used for probing the local structure, composition and electronic states of materials at the atomic scale. The rich information of EELS comes from the complex inelastic scattering process where fast electrons transfer their energy and momentum to the atoms by exciting the associated atomic electrons to higher unoccupied states, which is elemental specific and local density of states sensitive. To quantify EELS, a common practice is to fit the observed spectrum [1] with the scattering cross-sections calculated from the experimental parameters and general oscillation strength (GOS) database. The current GOS is based on the Hartree-Fock solution of atomic orbitals [2], which does not include the full relativistic effects but can apply the first order correction through (1) the relativistic mass correction for the kinetic energy (2) spin-orbital coupling and (3) the Darwin term -- the inherent error can be significant for heavy elements where the electron relativistic effect is significant. Also, the relativistic electrodynamics during the scattering is not considered in the transition matrix equation, which has been shown to be critical for the correct prediction of magic angle and orientation anisotropy [3] of EELS and energy-filtered CBED [4]. In addition, due to the limited computing resources at that time, the GOS database has limited energy-momentum ranges with coarse sampling.

For better quantification of EELS, here we developed an inelastic scattering physics code for the database generation of GOS based on Dirac solutions with relativistic electrodynamics. In this treatment, the spin-orbital splitting is naturally included, for instance for Ti L23 shown in Fig.1. The sampling is finely chosen for a much wider energy-momentum space than before. We hope the newly developed GOS database can benefit the EELS community for both academic use and industry integration. For future development, we will follow the same inelastic scattering physics for simulating EELS and EDX in the multislice algorithm under channeling conditions.

Reference:

[1]Verbeeck, J., and S. Van Aert. "Model based quantification of EELS spectra." Ultramicroscopy 101.2-4 (2004): 207-224.

[2]Leapman, R. D., P. Rez, and D. F. Mayers. "K, L, and M shell generalized oscillator strengths and ionization cross sections for fast electron collisions." The Journal of Chemical Physics 72.2 (1980): 1232-1243.

[3]Schattschneider, P., Hébert, C., Franco, H., & Jouffrey. "Anisotropic relativistic cross sections for inelastic electron scattering, and the magic angle." Physical Review B 72.4 (2005): 045142.

[4]Dwyer, C. "Relativistic effects in atomic inner-shell ionization by a focused electron probe." Physical Review B 72.14 (2005): 144102.

Fig.1 Plots of GOS as a function of momentum and energy losses for Ti L23 edges. The difference due to spin-orbital splitting is also included.