Momentum-Dependent Lifetime Broadening of Electron Energy Loss Spectra: A Self-Consistent Coupled-Plasmon Model

Establishment and validation of an electron inelastic mean free path database for narrow bandgap inorganic compounds with a machine learning approach

Narrow bandgap inorganic compounds are extremely important in many areas of physics. However, their basic parameter database for surface analysis is incomplete. Electron inelastic mean free paths (IMFPs) are important parameters in surface analysis methods, such as electron spectroscopy and electron microscopy. Our previous research has presented a machine learning (ML) method to describe and predict IMFPs from calculated IMFPs for 41 elemental solids. This paper extends the use of the same machine learning method to 42 inorganic compounds based on the experience in predicting elemental electron IMFPs. The in-depth discussion extends to including material dependence discussion and parameter value selections. After robust validation of the ML method, we have produced an extensive IMFP database for 12 039 narrow bandgap inorganic compounds. Our findings suggest that ML is very efficient and powerful for IMFP description and database completion for various materials and has many advantages, including stability and convenience, over traditional methods.

First-Principle Calculation on Inelastic Electron Scattering in Diamond and Graphite

In this work, we consider the inelastic scattering of incident electrons as a key process for analyzing the significant differences in secondary electron (SE) emission between diamond and graphite. Dielectric functions and energy- and momentum-dependent energy loss functions were obtained by first-principle calculations. These were then used to calculate the inelastic mean free path (IMFP) and stopping power in different directions. The results show that the properties of diamond are very close in different directions, and its IMFP is lower than that of graphite when the electron energy is higher than 30 eV. In graphite, the incident electrons may exhibit directional preferences in their motion. These results indicate that, in graphite, SEs are excited in deeper positions than in diamond, and more SEs move in a horizontal direction than in a vertical direction, which leads to the difference in secondary electron yield (SEY).

Unveiling the principle descriptor for predicting the electron inelastic mean free path based on a machine learning framework

The TPP-2M formula is the most popular empirical formula for the estimation of the electron inelastic mean free paths (IMFPs) in solids from several simple material parameters. The TPP-2M formula, however, poorly describes several materials because it relies heavily on the traditional least-squares analysis. Herein, we propose a new framework based on machine learning to overcome the weakness. This framework allows a selection from an enormous number of combined terms (descriptors) to build a new formula that describes the electron IMFPs. The resulting framework not only provides higher average accuracy and stability but also reveals the physics meanings of several newly found descriptors. Using the identified principle descriptors, a complete physics picture of electron IMFPs is obtained, including both single and collective electron behaviors of inelastic scattering. Our findings suggest that machine learning is robust and efficient to predict the IMFP and has great potential in building a regression framework for data-driven problems. Furthermore, this method could be applicable to find empirical formula for given experimental data using a series of parameters given a priori, holds potential to find a deeper connection between experimental data and a priori parameters.

Electron elastic backscattering probability and inelastic mean free path

We study the angular distribution of electron elastic backscattering probability, using the Oswald-Kasper-Gaukler (OKG) model and Monte Carlo simulation. The present results are consistent with experimental data and other theoretical calculations. We also propose an approach that makes the OKG model applicable to determine electron inelastic mean free paths for compounds. We apply the OKG model with the proposed approach to zinc oxide (ZnO) and cerium dioxide (CeO₂).

Low-energy electron properties: Electron inelastic mean free path, energy loss function and the dielectric function. Recent measurements, applications, and the plasmon-coupling theory

We review new self-consistent models of inelastic electron scattering in condensed matter systems for accurate calculations of low-energy electron inelastic mean free paths (IMFPs) for XAFS and low energy diffraction. The accuracy of theoretical determinations of the electron IMFP at low energies is one of the key limiting factors in current XAFS modeling and Monte Carlo transport. Recent breakthroughs in XAFS analysis show that there exist significant discrepancies between theoretical and experimental IMFP values, and that this can significantly impact upon extraction of other key structural parameters from both XANES and XAFS. Resolution of these discrepancies is required to validate experimental studies of material structures, and is particularly relevant to the characterization of small molecules and organometallic systems for which tabulated electron scattering data is often sparse or highly uncertain. Novel models implement plasmon coupling mechanisms for the first time, in addition to causally-constrained lifetime broadening and high-precision density functional theory, and enables dramatic improvements in the agreement with recent high profile IMFP measurements. We discuss a theoretical approach for IMFP determination linking the optical dielectric function and energy loss spectrum of a material with its electron scattering properties and characteristic plasmon excitations. We review models inclusive of plasmon coupling, allowing us to move beyond the longstanding statistical approximation and explicitly demonstrate the effects of band structure on the detailed behaviour of bulk electron excitations in a solid or small molecule. This interrogates the optical response of the material, which we obtain using density functional theory. We find that new developments dramatically improve agreement with experimental electron scattering results in the low-energy region (30 eV  → 200 eV) where plasmon excitations are dominant. Corresponding improvements are therefore made in Low Energy Electron Transport, LEEM, theoretical XAFS spectra and detector modelling.

Hot phonon and carrier relaxation in Si(100) determined by transient extreme ultraviolet spectroscopy

The thermalization of hot carriers and phonons gives direct insight into the scattering processes that mediate electrical and thermal transport. Obtaining the scattering rates for both hot carriers and phonons currently requires multiple measurements with incommensurate timescales. Here, transient extreme-ultraviolet (XUV) spectroscopy on the silicon 2p core level at 100 eV is used to measure hot carrier and phonon thermalization in Si(100) from tens of femtoseconds to 200 ps, following photoexcitation of the indirect transition to the Δ valley at 800 nm. The ground state XUV spectrum is first theoretically predicted using a combination of a single plasmon pole model and the Bethe-Salpeter equation with density functional theory. The excited state spectrum is predicted by incorporating the electronic effects of photo-induced state-filling, broadening, and band-gap renormalization into the ground state XUV spectrum. A time-dependent lattice deformation and expansion is also required to describe the excited state spectrum. The kinetics of these structural components match the kinetics of phonons excited from the electron-phonon and phonon-phonon scattering processes following photoexcitation. Separating the contributions of electronic and structural effects on the transient XUV spectra allows the carrier population, the population of phonons involved in inter- and intra-valley electron-phonon scattering, and the population of phonons involved in phonon-phonon scattering to be quantified as a function of delay time.

Low-energy electron inelastic mean free paths for liquid water

We improve the Mermin-Penn algorithm (MPA) for determining the energy loss function (ELF) within the dielectric formalism. The present algorithm is applicable not only to real metals, but also to materials that have an energy gap in the excitation spectrum. Applying the improved MPA to liquid water, we show that the present algorithm is able to address the ELF overestimation at the energy gap, and the calculated results are in good agreement with experimental data.

Electron beam-based metrology after CMOS

The magnitudes of the challenges facing electron-based metrology for post-CMOS technology are reviewed. Directed selfassembly, nanophotonics/plasmonics, and resistive switches and selectors, are examined as exemplars of important post-CMOS technologies. Materials, devices, and architectures emerging from these technologies pose new metrology requirements: defect detection, possibly subsurface, in soft materials, accurate measurement of size, shape, and roughness of structures for nanophotonic devices, contamination-free measurement of surface-sensitive structures, and identification of subtle structural, chemical, or electronic changes of state associated with switching in non-volatile memory elements. Electron-beam techniques are examined in the light of these emerging requirements. The strong electron-matter interaction provides measurable signal from small sample features, rendering electron-beam methods more suitable than most for nanometer-scale metrology, but as is to be expected, solutions to many of the measurement challenges are yet to be demonstrated. The seeds of possible solutions are identified when they are available.

Electron inelastic mean free path at energies below 100 eV

Knowledge of electron inelastic mean free paths (IMFPs) is important for electron spectroscopy and microscopy studies. Here, we determine the IMFPs at energies below 100 eV for 10 elemental solids (V, Fe, Ni, Mo, Pd, Ag, Ta, W, Pt, and Au) within the dielectric formalism, using the energy-loss function calculated in the adiabatic local-density approximation of time-dependent density-functional theory. The resulting IMFPs at a few eV above the Fermi energy are comparable to those from ab initio calculations in the GW approximation of many-body theory. The present approach provides an alternative to evaluate hot-electron inelastic lifetimes.

Calculations of Electron Inelastic Mean Free Paths. XI. Data for Liquid Water for Energies from 50 eV to 30 keV

We calculated electron inelastic mean free paths (IMFPs) for liquid water from its optical energy-loss function (ELF) for electron energies from 50 eV to 30 keV. These calculations were made with the relativistic full Penn algorithm (FPA) that has been used for previous IMFP and electron stopping-power calculations for many elemental solids. We also calculated IMFPs of water with three additional algorithms: the relativistic single-pole approximation (SPA), the relativistic simplified SPA, and the relativistic extended Mermin method. These calculations were made using the same optical ELF in order to assess any differences of the IMFPs arising from choice of the algorithm. We found good agreement among the IMFPs from the four algorithms for energies over 300 eV. For energies less than 100 eV, however, large differences became apparent. IMFPs from the relativistic TPP-2M equation for predicting IMFPs were in good agreement with IMFPs from the four algorithms for energies between 300 eV and 30 keV but there was poorer agreement for lower energies. We calculated values of the static structure factor as a function of momentum transfer from the FPA. The resulting values were in good agreement with results from first-principles calculations and with inelastic X-ray scattering spectroscopy experiments. We made comparisons of our IMFPs with earlier calculations from authors who had used different algorithms and different ELF data sets. IMFP differences could then be analyzed in terms of the algorithms and the data sets. Finally, we compared our IMFPs with measurements of IMFPs and of a related quantity, the effective attenuation length (EAL). There were large variations in the measured IMFPs and EALs (as well as their dependence on electron energy). Further measurements are therefore required to establish consistent data sets and for more detailed comparisons with calculated IMFPs.

FDMX: extended X-ray absorption fine structure calculations using the finite difference method

A new theoretical approach and computational package, FDMX, for general calculations of X-ray absorption fine structure (XAFS) over an extended energy range within a full-potential model is presented. The final-state photoelectron wavefunction is calculated over an energy-dependent spatial mesh, allowing for a complete representation of all scattering paths. The electronic potentials and corresponding wavefunctions are subject to constraints based on physicality and self-consistency, allowing for accurate absorption cross sections in the near-edge region, while higher-energy results are enabled by the implementation of effective Debye-Waller damping and new implementations of second-order lifetime broadening. These include inelastic photoelectron scattering and, for the first time, plasmon excitation coupling. This is the first full-potential package available that can calculate accurate XAFS spectra across a complete energy range within a single framework and without fitted parameters. Example spectra are provided for elemental Sn, rutile TiO2 and the FeO6 octahedron.

New constraints for low-momentum electronic excitations in condensed matter: fundamental consequences from classical and quantum dielectric theory

We present new constraints for the transportation behaviour of low-momentum electronic excitations in condensed matter systems, and demonstrate that these have both a fundamental physical interpretation and a significant impact on the description of low-energy inelastic electron scattering. The dispersion behaviour and characteristic lifetime properties of plasmon and single-electron excitations are investigated using popular classical, semi-classical and quantum dielectric models. We find that, irrespective of constrained agreement to the well known high-momentum and high-energy Bethe ridge limit, standard descriptions of low-momentum electron excitations are inconsistent and unphysical. These observations have direct impact on calculations of transport properties such as inelastic mean free paths, stopping powers and escape depths of charged particles in condensed matter systems.