Inelastic mean free path

About: Inelastic mean free path is a research topic. Over the lifetime, 616 publications have been published within this topic receiving 23317 citations.

Quantitative electron spectroscopy of surfaces: A standard data base for electron inelastic mean free paths in solids

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.

Calculations of electron inelastic mean free paths. III. Data for 15 inorganic compounds over the 50–2000 eV range

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.

Calculations of electorn inelastic mean free paths. II. Data for 27 elements over 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.

Calculations of electron inelastic mean free paths for 31 materials

Abstract: We present new calculations of electron inelastic mean free paths (IMFPs) for 200–2000 eV electrons in 27 elements (C, Mg, Al, Si, Ti, V, Cr, Fe, Ni, Cu, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Os, Ir, Pt, Au and Bi) and four compounds (LiF, SiO2, ZnS and Al2O3). These calculations are based on an algorithm due to Penn which makes use of experimental optical data (to represent the dependence of the inelastic scattering probability on energy loss) and the theoretical Lindhard dielectric function (to represent the dependence of the scattering probability on momentum transfer). Our calculated IMFPs were fitted to the Bethe equation for inelastic electron scattering in matter; the two parameters in the Bethe equation were then empirically related to several material constants. The resulting general IMFP formula is believed to be useful for predicting the IMFP dependence on electron energy for a given material and the material-dependence for a given energy. The new formula also appears to be a reasonable but more approximate guide to electron attenuation lengths.

EELS Log-Ratio Technique for Specimen-Thickness Measurement in the TEM

Abstract: We discuss measurement of the local thickness t of a transmission microscope specimen from the log-ratio formula t = lambda ln (It/I0) where It and I0 are the total and zero-loss areas under the electron-energy loss spectrum. We have measured the total inelastic mean free path lambda in 11 materials of varying atomic number Z and have parameterized the results in the form lambda = 106F (E0/Em)/ln (2 beta E0/Em) where F = (1 + E0/1,022)/(1 + E0/511)2, the incident energy E0 is in keV, the spectrum collection semiangle beta is in mrad, and Em = 7.6Z0.36. This formulation should allow absolute thickness to be determined to an accuracy of +/- 20% in most inorganic specimens.