Monte Carlo simulations of measured electron energy-loss spectra of diamond and graphite: Role of dielectric-response models

Abstract

In this work we compare Monte Carlo (MC) simulations of electron transport properties with reflection electron energy loss measurements in diamond and graphite films. We assess the impact of different approximations of the dielectric response on the observables of interest for the characterization of carbon-based materials. We calculate the frequency-dependent dielectric response and energy loss function of these materials in two ways: a full ab initio approach, in which we carry out time-dependent density functional simulations in linear response for different momentum transfers, and a semi-classical model, based on the Drude-Lorentz extension to finite momenta of the optical dielectric function. Ab initio calculated dielectric functions lead to a better agreement with electron energy loss measured spectra with respect the widely used Drude-Lorentz model. This discrepancy is particularly evident for insulators and semiconductors beyond the optical limit (q = 0), where single particle excitations become relevant. Furthermore, we show that the behaviour of the energy loss function at different accuracy levels has a dramatic effect on other physical observables, such as the inelastic mean free path and the stopping power in the low energy regime (< 100 eV) and thus on the accuracy of MC simulations. * Corresponding authors Email addresses: taioli@ectstar.eu (Simone Taioli), dapor@ectstar.eu (Maurizio Dapor)

Ab initio dielectric response function of diamond and other relevant high pressure phases of carbon

“…This means a much more stable quasi-particle is predicted within BSE. The plasmon peaks shown in the inset of [72], electron-energy loss spectroscopy data by Sato et al [88] and Waidmann et al [89], BSE calculations for ambient conditions by Gao [73], TDDFT calculations at ambient conditions by Azzolini et al [90]. KG, BSE, and TDDFT results of this work.…”

“…Only for the highest densities where we reach pressures of up to 900 GPa, close to the proposed diamond to BC8 transition, differences between KG and TDDFT appear. The observed differences between theories at ambient diamond density are due to the implementation of scissor corrections in our TDDFT results to incorporate the correct band gap vs. an omission of scissor corrections in Azzolini et al [90]. Next we study the dispersion of the plasmon subject to a change in wavenumber.…”

Anisotropic Approach for Simulating Electron Transport in Layered Materials: Computational and Experimental Study of Highly Oriented Pyrolitic Graphite

“…Details on our Monte Carlo approach can be found in Ref. 21 . On the one hand, in the case of inelastic collisions the primary electrons lose their kinetic energy according to the cumulative probability distribution:…”

A comparison between Monte Carlo method and the numerical solution of the Ambartsumian-Chandrasekhar equations to unravel the dielectric response of metals

“…The ELF, which is only a property of the target material, is thus a fundamental quantity directly related to the energy deposited by charged particles [6,7,8]. Typically, the ELF can be computed by using three different approaches [9,10]: i) from ab initio simulations [11,12]; ii) semi-empirically [13], by using experimental measurements of optical or electron energy loss spectra (EELS); iii) from model calculations within the electron gas theory [14].…”

“…The latter are all sources of error in the assessment of the ELF via the DL and MELF models, which must be carefully evaluated. At variance, the ab-initio approaches, while computationally more expensive than the DL and MELF semi-empirical methods, can in principle deliver the most accurate results concerning the ELF [13].…”