Measurements of Electron Inelastic Mean Free Paths in Materials

Abstract

We present a method for determining inelastic mean free paths (IMFPs) in materials using high-accuracy measurements of x-ray absorption fine structure (XAFS). For electron energies below 100 eV, theoretical predictions have large variability and alternate measurement techniques exhibit significant uncertainties. In this regime, the short IMFP makes photoelectrons ideal for structural determination of surfaces and nanostructures, and measurements are valuable for studies of diverse fields such as low-energy electron diffraction and ballistic electron emission microscopy. Our approach, here applied to solid copper, is unique and exhibits enhanced sensitivity at electron energies below 100 eV. Furthermore, it is readily applicable to any material for which sufficiently high accuracy XAFS data can be obtained.

Theoretical and experimental developments in the determination of electron energy loss functions and inelastic mean free paths in elemental solids and binary compounds

“…Results are compared with recent high profile x-ray measurements of the inelastic mean free path in copper [7] and molybdenum [8]. Agreement with experiment is found to significantly increase below 50 eV, and be consistent with previous treatments at higher energies.…”

“…This scheme uniquely satisfies optical sum rules, avoids common plasmon fitting routines, and is independent of experimental optical data. Significant corrections to previous derivations are demonstrated, particularly in the highly uncertain loss region below 100 eV [6].…”

Electron Mobility Sensor Scheme-Based on a Mach–Zehnder Interferometer Approach

“…The other simulation parameters used are given in the related figure captions. This Matlab program was used to simulate the parameters of a device which were selected to be as close to those of devices reported in the recent literature [31][32][33]. From Figure 1, it can be seen that the operation assumes the light from a monochromatic source is input into an MZI and split equally into two arms, following which the signals are combined at the output 50:50 coupler, for which the output intensity is determined, using Equation (1).…”

“…From the results obtained, a device sensitivity of~2x10 −14 −1 −1 is obtained. Such device parameters are realistic given the materials and fabrication parameters [35][36][37][38][39], while the approach using the stacked layers of silicon-graphene material were tested and experimentally verified in the literature [40]. Gold forms the basis of the mobility sensor, and other materials can also be applied, with the optimum fabrication parameters to be found the references [34].…”

Photoemission simulation for photocathode design: theory and application to copper and silver surfaces

“…It was chosen to be 5.54Å for copper and 6.13Å for silver. These values are calculated as the average of those reported in the literature [22][23][24][25][26]. The heaviside step function H(p ⊥ > 0) ensures that only final state electrons characterised by a positive momentum along the direction perpendicular to the surface (p ⊥ ) contribute to the QE.…”