Shigeo Tanuma

Proposed formula for electron inelastic mean free paths based on calculations for 31 materials

A new general formula is proposed for determining electron inelastic mean free paths (IMFPs) for 200–2000 eV electrons in solids. The new formula is based on separate IMFP calculations for 27 elements and 4 compounds using an algorithm due to Penn. This formula is believed useful for determining the IMFP dependence on electron energy for a given material and the material-dependence for a given energy. The new formula should also be a reasonable guide to electron attenuation lengths which have been difficult to determine with the needed accuracy.

Calculations of Electron Inelastic Mean Free Paths (IMFPs)VI. Analysis of the Gries Inelastic Scattering Model and Predictive IMFP Equation

Gries has recently reported [Surf.Interface Anal. 24, 38 (1996)] an atomistic model for inelastic electron scattering relevant to Auger electron spectroscopy and x-ray photoelectron spectroscopy and has derived an equation (designated G1) for the estimation of inelastic mean free paths (IMFPs). We present an analysis of the Gries model and the G1 equation in terms of the similarities and differences of inelastic electron scattering by free atoms and by solids. We also compare the G1 equation with our TPP-2M equation for estimation of IMFPs. The former equation was developed from fits to our published IMFPs over the 200–2000 eV energy range, and is identical in its energy dependence to the Bethe equation for inelastic scattering cross-sections and to a simplification of our TPP-2M equation for the same energy range. Comparison of parameters indicates that the Gries fitting parameterk1 should be approximately 0.0016 and 0.0022 for non-transition and transition elements, respectively. We find that the G1 equation could be improved by allowing the Gries fitting parameterk2 to depend on density (as recommended for the equivalent parameter in TPP-2M). Although we believe that the Gries model is inconsistent with current theories for the electronic structure of metals, semiconductors and inorganic compounds, we find (from sum-rule considerations) that the G1 equation can provide an approximate guide to IMFP values. For some compounds, however, there were unexplained deviations (as found by Gries). In contrast to the G1 equation, the TPP-2M equation provides useful IMFP estimates for all materials over the parameter range that has been explored. Gries claims that the G1 equation can be extrapolated to energies lower than 200 eV on the basis of limited agreement with some experimental IMFPs over the 10–100 eV range for Be and the alkali metals, and has questioned the reliability of our IMFPs for energies below 200 eV. We consider this comparison to be inadequate, and we recommend that the G1 equation not be used in the 50–200 eV range.

Material dependence of electron inelastic mean free paths at low energies

We present and discuss electron inelastic mean free path (IMFP) data for aluminum and gold in the 50–200 eV range. These elements serve as examples of IMFP calculations that have been made for 50–2000 eV electrons in 31 materials (27 elements and 4 compounds). Substantial differences are found in the shapes of the IMFP versus energy curves for Al and Au and these can be understood in terms of the different inelastic scattering mechanisms in the two metals. The minimum IMFP value occurs at 40 eV in aluminum and at 120 eV in gold, a result which is consistent with the trends expected from free‐electron IMFP calculations. This result differs, however, from that expected from the Seah and Dench attenuation length formula which shows essentially no material dependence at low energies. We have extended a general formula derived earlier to describe the calculated IMFPs over the 200–2000 eV energy range to give the IMFP dependences on material and energy from 50 to 2000 eV.

Estimation of surface excitation correction factor for 200–5000 eV in Ni from absolute elastic scattering electron spectroscopy

We have determined the surface plasmon excitation correction (SEC) factor for nickel in the 200-5000 eV range from the ratios of the absolute elastic scattering electron intensities measured by a novel cylindrical mirror analyser and those by the Monte Carlo method. The inelastic mean free paths (IMFPs) of nickel used for the Monte Carlo method in the energy range specified were calculated by the Penn algorithm. The resulting SECs were smaller than the values calculated from Chen and Oswald general equations of surface excitation parameters (SEPs), which describe the influence of surface plasmon excitations by electrons crossing a solid surface. We also found that SEPs (obtained from SECs) could be fitted to the equation P s (α, E) = C/[E n cos(α) + C] or P s (α, E) = aE -b / cos(α) (<7% root-mean-square error) in the 200-5000 eV energy range, where P s is the SEP, a is the surface crossing angle of the electron to the surface normal, n(= 0.41), C(= 5.39), a(= 1.7) and b(= 0.29) are parameters and E is the electron energy.

Use of sum rules on the energy-loss function for the evaluation of experimental optical data

Abstract We present an evaluation of optical data for Al, Si, Ti, Mo, W, and Ir based on two sum rules for the energy-loss function, the familiar f-sum rule and another sum rule based on a limiting form of the Kramers-Kronig integral. These sum rules were used to evaluate sets of energy-loss function data constructed first from tabulated optical data which have been supplemented by interpolations in the 40–100 eV range for Ti, Mo, W, and Ir. A second set of energy-loss function data was constructed for each material by substituting energy-loss function values calculated from the optical data of Windt et al. (Appl. Opt., 27 (1988) 246, 279) in the 10–525 eV range. The deviations in the results of the sum-rule tests with the second set of optical data were about twice those found for the first set. We conclude that the first set of optical data is preferred over the second set.

Electron inelastic mean free paths in solids at low energies

Abstract We have calculated electron inelastic mean free paths (IMFPs) for 50–200 eV electrons in 31 materials (27 elements and 4 compounds). These calculations extend those previously reported for 200–2000 eV electrons in the same materials but avoid an approximation valid for electron energies above 200 eV. IMFP results are presented in this paper for magnesium, aluminum, silicon, nickel, copper, and gold. The IMFP dependence on electron energy in the range 50–200 eV varies considerably from material to material; these variations are associated with substantial differences in the electron energy-loss functions amongst the materials. We have also extended the general IMFP formula derived earlier to describe the calculated IMFPs over the 50–2000 eV energy range.

Calculations of stopping powers of 100eV–30keV electrons in 31 elemental solids

We present calculated electron stopping powers (SPs) for 31 elemental solids (Li, Be, glassy C, graphite, diamond, Na, Mg, K, Sc, Ti, V, Fe, Y, Zr, Nb, Mo, Ru, Rh, In, Sn, Cs, Gd, Tb, Dy, Hf, Ta, W, Re, Os, Ir, and Bi). These SPs were determined with an algorithm previously used for the calculation of electron inelastic mean free paths and from energy-loss functions (ELFs) derived from experimental optical data. The SP calculations were made for electron energies between 100eV and 30keV and supplement our earlier SP calculations for ten additional solids (Al, Si, Cr, Ni, Cu, Ge, Pd, Ag, Pt, and Au). Plots of SP versus atomic number for the group of 41 solids show clear trends. Multiple peaks and shoulders are seen that result from the contributions of valence-electron and various inner-shell excitations. Satisfactory agreement was found between the calculated SPs and values from the relativistic Bethe SP equation with recommended values of the mean excitation energy (MEE) for energies above 10keV. We dete...

Effects of elastic and inelastic electron scattering on quantitative surface analyses by AES and XPS

Abstract A review is given that describes the complications due to elastic and inelastic electron scattering in quantitative surface analyses by Auger-electron spectroscopy and x-ray photoelectron spectroscopy. Four principal topics are addressed. First, the simple formulae for surface analyses are based on a model that ignores elastic scattering. Recent work assessing the effects of elastic scattering is summarized which shows that the simple formulae are valid in certain analytical situations but with an appropriate choice of the parameter describing inelastic scattering. Second, we review measurements of effective attenuation lengths and point out many sources of significant systematic error in these measurements. Third, we describe recent calculations of inelastic mean free paths (IMFPs) in over fifty materials that have been utilized to develop a predictive IMFP formula. Finally, we discuss the complicating effects of inelastic scattering on reliable measurements of AES and XPS intensities.

Modified Predictive Formula for the Electron Stopping Power

We report an improved predictive formula for the electron stopping power (SP) based on an analysis and fit of SPs and electron inelastic mean free paths (IMFPs) calculated from optical data for 37 elemental solids and energies between 200eV and 30keV. The formula is a function of energy, density, and IMFP, and is recommended for solids with atomic numbers larger than 6. While the mean deviation between predicted and calculated SPs was 7.25%, larger deviations were found for four additional materials, Li (22.2%), Be (17.9%), graphite (15.3%), and diamond (15.7%). The predictive SP formula can be applied to multicomponent materials. Test comparisons for two compounds, guanine and InSb, showed average deviations of 16.0% and 19.1%, respectively. The improved SP formula is expected to be useful in simulations of electron trajectories in solids with the continuous slowing-down approximation (e.g., in Auger-electron spectroscopy and electron microprobe analysis).

Measurement of optical constants of Si and SiO2 from reflection electron energy loss spectra using factor analysis method

The energy loss functions (ELFs) and optical constants of Si and SiO2 were obtained from quantitative analysis of reflection electron energy loss spectroscopy (REELS) by a new approach. In order to obtain the ELF, which is directly related to the optical constants, we measured series of angular and energy dependent REELS spectra for Si and SiO2. The λ(E)K(ΔE) spectra, which are the product of the inelastic mean free path (IMFP) and the differential inverse IMFP, were obtained from the measured REELS spectra. We used the factor analysis (FA) method to analyze series of λ(E)K(ΔE) spectra for various emission angles at fixed primary beam energy to separate the surface-loss and bulk-loss components. The extracted bulk-loss components enable to obtain the ELFs of Si and SiO2, which are checked by oscillator strength-sum and perfect-screening-sum rules. The real part of the reciprocal of the complex dielectric function was determined by Kramers–Kronig analysis of the ELFs. Subsequently, the optical constants of...