Quantitative electron spectroscopy of surfaces: A standard data base for electron inelastic mean free paths in solids
TL;DR: In this paper, a compilation of all published measurements of electron inelastic mean free path lengths in solids for energies in the range 0-10 000 eV above the Fermi level is presented.
Abstract: A compilation is presented of all published measurements of electron inelastic mean free path lengths in solids for energies in the range 0–10 000 eV above the Fermi level. For analysis, the materials are grouped under one of the headings: element, inorganic compound, organic compound and adsorbed gas, with the path lengths each time expressed in nanometers, monolayers and milligrams per square metre. The path lengths are vary high at low energies, fall to 0.1–0.8 nm for energies in the range 30–100 eV and then rise again as the energy increases further. For elements and inorganic compounds the scatter about a ‘universal curve’ is least when the path lengths are expressed in monolayers, λm. Analysis of the inter-element and inter-compound effects shows that λm is related to atom size and the most accuratae relations are λm = 538E−2+0.41(aE)1/2 for elements and λm=2170E−2+0.72(aE)1/2 for inorganic compounds, where a is the monolayer thickness (nm) and E is the electron energy above the Fermi level in eV. For organic compounds λd=49E−2+0.11E1/2 mgm−2. Published general theoretical predictions for λ, valid above 150 eV, do not show as good correlations with the experimental data as the above relations.
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TL;DR: A review of the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds is presented in this article, with the purpose of providing an updated summary of the extensive literature.
Abstract: The last decade witnessed significant progress in angle-resolved photoemission spectroscopy (ARPES) and its applications. Today, ARPES experiments with 2-meV energy resolution and $0.2\ifmmode^\circ\else\textdegree\fi{}$ angular resolution are a reality even for photoemission on solids. These technological advances and the improved sample quality have enabled ARPES to emerge as a leading tool in the investigation of the high-${T}_{c}$ superconductors. This paper reviews the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds, with the purpose of providing an updated summary of the extensive literature. The low-energy excitations are discussed with emphasis on some of the most relevant issues, such as the Fermi surface and remnant Fermi surface, the superconducting gap, the pseudogap and $d$-wave-like dispersion, evidence of electronic inhomogeneity and nanoscale phase separation, the emergence of coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function due to the interaction of the charge with magnetic and/or lattice degrees of freedom. Given the dynamic nature of the field, we chose to focus mainly on reviewing the experimental data, as on the experimental side a general consensus has been reached, whereas interpretations and related theoretical models can vary significantly. The first part of the paper introduces photoemission spectroscopy in the context of strongly interacting systems, along with an update on the state-of-the-art instrumentation. The second part provides an overview of the scientific issues relevant to the investigation of the low-energy electronic structure by ARPES. The rest of the paper is devoted to the experimental results from the cuprates, and the discussion is organized along conceptual lines: normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. Within each topic, ARPES data from the various copper oxides are presented.
3,077 citations
Cites background from "Quantitative electron spectroscopy ..."
...As the photoelectron mean free path increases from approximately 5 to almost 20 Å when the photon energy is increased from 120 to 880 eV (Seah and Dench, 1979), it was concluded that the 4d-4f spectra mainly reflect the surface 4f electronic states....
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...The mean free path for unscattered photoelectrons is characterized by a minimum of approximately 5 Å at 20–100 eV kinetic energies (Seah and Dench, 1979), which are typical values in ARPES experiments....
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TL;DR: Recent advances in the understanding and application of plasmon-induced hot carrier generation are discussed and some of the exciting new directions for the field are highlighted.
Abstract: The discovery of the photoelectric effect by Heinrich Hertz in 1887 set the foundation for over 125 years of hot carrier science and technology. In the early 1900s it played a critical role in the development of quantum mechanics, but even today the unique properties of these energetic, hot carriers offer new and exciting opportunities for fundamental research and applications. Measurement of the kinetic energy and momentum of photoejected hot electrons can provide valuable information on the electronic structure of materials. The heat generated by hot carriers can be harvested to drive a wide range of physical and chemical processes. Their kinetic energy can be used to harvest solar energy or create sensitive photodetectors and spectrometers. Photoejected charges can also be used to electrically dope two-dimensional materials. Plasmon excitations in metallic nanostructures can be engineered to enhance and provide valuable control over the emission of hot carriers. This Review discusses recent advances in the understanding and application of plasmon-induced hot carrier generation and highlights some of the exciting new directions for the field.
2,511 citations
TL;DR: In this article, the electron inelastic mean free paths (IMFPs) of 14 organic compounds were computed for a group of 14 compounds: 26-n-paraffin, adenine, β-carotene, bovine plasma albumin, deoxyribonucleic acid, diphenylhexatriene, guanine, kapton, polyacetylene, poly(butene-1-sulfone), polyethylene, polymethylmethacrylate, polystyrene and poly(2-vinyl
Abstract: We report calculations of electron inelastic mean free paths (IMFPs) of 50–2000 eV electrons for a group of 14 organic compounds: 26-n-paraffin, adenine, β-carotene, bovine plasma albumin, deoxyribonucleic acid, diphenylhexatriene, guanine, kapton, polyacetylene, poly(butene-1-sulfone), polyethylene, polymethylmethacrylate, polystyrene and poly(2-vinylpyridine). The computed IMFPs for these compounds showed greater similarities in magnitude and in the dependences on electron energy than was found in our previous calculations for groups of elements and inorganic compounds (Papers II and III in this series). Comparison of the IMFPs for the organic compounds with values obtained from our predictive IMFP formula TPP-2 showed systematic differences of ∼40%. These differences are due to the extrapolation of TPP-2 from the regime of mainly high-density elements (from which it had been developed and tested) to the low-density materials such as the organic compounds. We analyzed the IMFP data for the groups of elements and organic compounds together and derived a modified empirical expression for one of the parameters in our predictive IMFP equation. The modified equation, denoted TPP-2M, is believed to be satisfactory for estimating IMFPs in elements, inorganic compounds and organic compounds.
2,383 citations
TL;DR: In the light of recent experimental evidence, two common assumptions are re-examine: that the amount of radiation damage is proportional to the electron dose and is independent of beam diameter; and that the extent of the damage is proportionate to theamount of energy deposited in the specimen.
1,756 citations
Cites background from "Quantitative electron spectroscopy ..."
...Instead, collateral damage might be caused by slow secondaries, for which the inelastic mean free path can exceed 2 nm in some materials if their starting energy is less than 10 eV (Seah and Dench, 1979; Cartier et al., 1997; Bass and Sanche, 1998)....
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TL;DR: In this article, a modified version of the Bethe equation for inelastic electron scattering in matter has been used to estimate IMFPs in the 50-2000 eV range.
Abstract: We report calculations of electron inelastic mean free paths (IMFPs) for 50–2000 eV electrons in a group of 27 elements (C, Mg, Al, Si, Ti, V, Cr, Fe, Ni, Cu, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Ta, W, Re, Os, Ir, Pt, Au and Bi). This work extends our previous calculations (Surf. Interface Anal. 11, 57 (1988)) for the 200–2000 eV range. Substantial variations were found in the shapes of the IMFP versus energy curves from element to element over the 50–2000 eV range and we attribute these variations to the different inelastic scattering properties of each material. Our calculated IMFPs wee fitted to a modified form of the Bethe equation for inelastic electron scattering in matter; this equation has four parameters. These four parameters could be empirically related to several material parameters for our group of elements (atomic weight, bulk density and number of valence electron per atom). IMFPs and those initially calculated was 13%. The modified Bethe equation and our expressions for the four parameters can therefore be used to estimate IMFPs in other materials. The uncertainties in the algorithm used for our IMFP calculation are difficult to estimate but are believed to be largely systematic. Since the same algorithm has been used for calculating IMFPs, our predictive IMFP formula is considered to be particularly useful for predicting the IMFP dependence on energy in the 50–2000 eV range and the material dependence for a given energy.
1,082 citations
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TL;DR: In this paper, the electron mean free path for inelastic scattering as a function of energy for all elemental solids (with the exception of the rare earths and the actinides) and formulae for the calculation of the mean free paths for compounds were given.
780 citations
TL;DR: In this article, a compilation of measured attenuation lengths of low-energy electrons in solids in the energy range (40 to 2000 eV) normally employed in X-ray photoelectron and Auger-electron spectroscopy is presented.
610 citations
TL;DR: In this article, a self-energy approach was used to calculate the energy of a single excited electron with the sea of conduction electrons in a metal, and an expression for the instantaneous rate of energy loss of the excited electron as a function of its initial energy was derived.
Abstract: The energy of interaction of a single excited electron with the sea of conduction electrons in a metal has been calculated by a self-energy approach. The imaginary part of the self-energy of the excited electron can be interpreted in terms of a total rate of real collisions with the sea of conduction electrons. By weighting the differential scattering rate by the amount of energy lost in each scattering event, one obtains an expression for the instantaneous rate of energy loss of the excited electron as a function of its initial energy. The extremely strong dependence of this rate on the initial energy is the main result of this paper. For slow electrons, by which we mean those of initial energy smaller than the sum of the Fermi energy and the plasma energy of the electron gas, the rate of energy loss is determined by the small imaginary part of the dielectric constant. For electrons close to the Fermi surface this rate is proportional to ${(p\ensuremath{-}{p}_{0})}^{3}$, where $p$ is the momentum of the excited electron and ${p}_{0}$ the Fermi momentum; therefore in this range the rate of energy loss is very sensitive to the initial energy. For fast electrons, a new contribution to the rate of energy loss arises due to a pole of the inverse dielectric constant. This new process corresponds to the excitation of plasma oscillations by the excited electron, and causes fast electrons to lose energy very rapidly.
417 citations
TL;DR: In this paper, a simple theory relating the Auger electron range to this dependence and to the quantitative use of electron spectroscopy is developed, and the range between 2 and 7 monolayers is obtained.
344 citations
TL;DR: In this paper, the energy dependence of the escape depth and its implications for interpretation of photoemission and Auger-electron data are discussed for twenty different materials in the energy range 0-3000 eV.
340 citations