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.

Conformation Analysis of Ferrocene and Decamethylferrocene via Full-Potential Modeling of XANES and XAFS Spectra.

Recent high-accuracy X-ray absorption measurements of the sandwich organometallics ferrocene (Fc) and decamethylferrocene (DmFc) at temperatures close to liquid helium are compared with new full-potential modeling of X-ray absorption fine structure (XAFS) covering the near-edge region (XANES) and above up to k = 7 Å(-1). The implementation of optimized calculations of the oscillatory part of the spectrum from the package FDMX allows detailed study of the spectra in regions of the photoelectron momentum most sensitive to differences in the molecular stereochemistry. For Fc and DmFc, this corresponds to the relative rotation of the cyclopentadienyl rings. When applied to high-accuracy XAFS of Fc and DmFc, the FDMX theory gives clear evidence for the eclipsed conformation for Fc and the staggered conformation for DmFc for frozen solutions at ca. 15 K. This represents the first clear experimental assignment of the solution structures of Fc and DmFc and reveals the potential of high-accuracy XAFS for structural analysis.

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.

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

The complex dielectric function and associated energy loss spectrum of a condensed matter system is a fundamental material parameter that determines both the optical and electronic scattering behavior of the medium. The common representation of the electron energy loss function (ELF) is interpreted as the susceptibility of a system to a single- or bulk-electron (plasmon) excitation at a given energy and momentum and is commonly derived as a summation of noninteracting free-electron resonances with forms constrained by adherence to some externally determined optical standard. This work introduces a new causally constrained momentum-dependent broadening theory, permitting a more physical representation of optical and electronic resonances that agrees more closely with both optical attenuation and electron scattering data. We demonstrate how the momentum dependence of excitation resonances may be constrained uniquely by utilizing a coupled-plasmon model, in which high-energy excitations are able to relax into lower-energy excitations within the medium. This enables a robust and fully self-consistent theory with no free or fitted parameters that reveals additional physical insight not present in previous work. The new developments are applied to the scattering behavior of solid molybdenum and aluminum. We find that plasmon and single-electron lifetimes are significantly affected by the presence of alternate excitation channels and show for molybdenum that agreement with high-precision electron inelastic mean free path data is dramatically improved for energies above 20 eV.

Structure determination from XAFS using high-accuracy measurements of x-ray mass attenuation coefficients of silver, 11 keV-28 keV, and development of an all-energies approach to local dynamical analysis of bond length, revealing variation of effective thermal contributions across the XAFS spectrum.

We use the x-ray extended range technique (XERT) to experimentally determine the mass attenuation coefficient of silver in the x-ray energy range 11 kev-28 kev including the silver K absorption edge. The results are accurate to better than 0.1%, permitting critical tests of atomic and solid state theory. This is one of the most accurate demonstrations of cross-platform accuracy in synchrotron studies thus far. We derive the mass absorption coefficients and the imaginary component of the form factor over this range. We apply conventional XAFS analytic techniques, extended to include error propagation and uncertainty, yielding bond lengths accurate to approximately 0.24% and thermal Debye-Waller parameters accurate to 30%. We then introduce the FDMX technique for accurate analysis of such data across the full XAFS spectrum, built on full-potential theory, yielding a bond length accuracy of order 0.1% and the demonstration that a single Debye parameter is inadequate and inconsistent across the XAFS range. Two effective Debye-Waller parameters are determined: a high-energy value based on the highly-correlated motion of bonded atoms (σ(DW) = 0.1413(21) Å), and an uncorrelated bulk value (σ(DW) = 0.1766(9) Å) in good agreement with that derived from (room-temperature) crystallography.

Full-potential theoretical investigations of electron inelastic mean free paths and extended x-ray absorption fine structure in molybdenum.

X-ray absorption fine structure (XAFS) spectroscopy is one of the most robust, adaptable, and widely used structural analysis tools available for a range of material classes from bulk solids to aqueous solutions and active catalytic structures. Recent developments in XAFS theory have enabled high-accuracy calculations of spectra over an extended energy range using full-potential cluster modelling, and have demonstrated particular sensitivity in XAFS to a fundamental electron transport property-the electron inelastic mean free path (IMFP). We develop electron IMFP theory using a unique hybrid model that simultaneously incorporates second-order excitation losses, while precisely accounting for optical transitions dictated by the complex band structure of the solid. These advances are coupled with improved XAFS modelling to determine wide energy-range absorption spectra for molybdenum. This represents a critical test case of the theory, as measurements of molybdenum K-edge XAFS represent the most accurate determinations of XAFS spectra for any material. We find that we are able to reproduce an extended range of oscillatory structure in the absorption spectrum, and demonstrate a first-time theoretical determination of the absorption coefficient of molybdenum over the entire extended XAFS range utilizing a full-potential cluster model.

Electron inelastic mean free path theory and density functional theory resolving discrepancies for low-energy electrons in copper.

We develop the many-pole dielectric theory of UV plasmon interactions and electron energy losses, and couple our advances with recent developments of Kohn-Sham density functional theory to address observed discrepancies between high-precision measurements and tabulated data for electron inelastic mean free paths (IMFPs). Recent publications have demonstrated that a five standard error difference exists between longstanding theoretical calculations and measurements of electron IMFPs for elemental solids at energies below 120 eV, a critical region for analysis of electron energy loss spectroscopy (EELS), X-ray absorption spectroscopy (XAS), and related technologies. Our implementation of improved optical loss spectra and a physical treatment of second-order excitation lifetimes resolves this problem in copper for the first time for energies in excess of 80 eV and substantially improves agreement for lower energy electrons.

Measurements of electron inelastic mean free paths in materials.

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.