Low-Energy Electron Inelastic Mean Free Path of Graphene Measured by a Time-of-Flight Spectrometer

Abstract

The detailed examination of electron scattering in solids is of crucial importance for the theory of solid-state physics, as well as for the development and diagnostics of novel materials, particularly those for micro- and nanoelectronics. Among others, an important parameter of electron scattering is the inelastic mean free path (IMFP) of electrons both in bulk materials and in thin films, including 2D crystals. The amount of IMFP data available is still not sufficient, especially for very slow electrons and for 2D crystals. This situation motivated the present study, which summarizes pilot experiments for graphene on a new device intended to acquire electron energy-loss spectra (EELS) for low landing energies. Thanks to its unique properties, such as electrical conductivity and transparency, graphene is an ideal candidate for study at very low energies in the transmission mode of an electron microscope. The EELS are acquired by means of the very low-energy electron microspectroscopy of 2D crystals, using a dedicated ultra-high vacuum scanning low-energy electron microscope equipped with a time-of-flight (ToF) velocity analyzer. In order to verify our pilot results, we also simulate the EELS by means of density functional theory (DFT) and the many-body perturbation theory. Additional DFT calculations, providing both the total density of states and the band structure, illustrate the graphene loss features. We utilize the experimental EELS data to derive IMFP values using the so-called log-ratio method.

Study of Graphene and Thin Foils by a Time-of-Flight Spectrometer for Low Landing Energies

“…The EELS of free-standing monolayer graphene (Figure 1) obtained from very slow transmitted electrons agree well with theoretical simulations and existing literature, thus confirming the functionality of the UHV SLEEM/ToF device [3].…”

“…Second, they are in good agreement with our theoretical results, EELS and band structure, obtained using density functional theory (DFT) and the many-body perturbation theory. We use experimental EELS data to derive effective IMFP [3]. Theoretical approaches to acquire IMFP involve predictive formulas such as TPP-2M [4] or Bethe formula [5] (valid for amorphous materials) and they may also include DFT.…”

“…In the following analysis, we focus on the low landing energy interval (200, 800) eV and energy losses up to approximately 40 eV (which covers both π and π+σ graphene plasmon peaks). The former ensures an overlap with existing IMFP data for comparison purposes (see related references in [3]). Another advantage is that the effect of secondary electrons is reduced in the plasmon part of graphene EELS.…”

“…Applying the log-ratio method (for details see [3]) on the straight-line segment baseline-corrected energy-loss spectra, we arrived at the effective IMFP values shown in Figure 2. We used theoretical "monolayer thickness" of graphene (i.e.…”

Quantification of STEM Images in High Resolution SEM for Segmented and Pixelated Detectors

“…Since the discrete diffraction spots arise from coherent scattering of the incident beam, see reference [ 56 ], and e.g., inelastic mean free path (IMFP) at 15 keV is approximately a half of the value at 30 keV, it does not come as a surprise that the diffraction is suppressed at the lower value of the landing energy. We compare the angles corresponding to the Debye–Scherrer diffraction rings of data displayed in Figure 8 with graphene (i.e., a “single layer graphite”) diffractogram [ 57 ] ( Figure 6 ) and simple calculations using the Bragg formula (lattice constant a = 2.461 Å, interlayer distance c = 6.708 Å), see Table 1 . We estimate the diffraction angle by using a single pair of opposite diffraction spots for each diffraction order, except for the lowest one, in the case of graphene.…”