Subshell photoionization cross-sections,electron mean free paths and quantitative X-ray photoelectron spectroscopy

Subshell photoionization cross-sections (SPC) for elements of atomic number in the range 3?, z ? 82 have been determined from measurement of relative photoelectron intensities at a photon energy of 1486.6 eV (Al Kα). A correction procedure has been developed which permits such determinations even when sample surfaces are not atomically clean. The results obtained suggest that Scofield's SPC calculations [2] are reasonably reliable for 1s, 2p and 3d subshells but that the present, experimentally derived data are to be preferred for quantitative use. As a result of this work, a rapid method of quantitative surface-constituent analysis, accurate to ± 20%, has also been developed, which is expected to be of value particularly in industrial situations. A semi-empirical method of extracting electron mean free paths from measurements of relative photoelectron intensities is also illustrated.     

Relative partial photoionization cross-sections and photoelectron branching ratios of ethylene

Relative partial photoionization cross-sections and photoelectron branching ratios of the valence bands (~10–25 eV binding energy) of ethylene are reported over the photon energy ranges 18–100 eV and 21–100 eV, respectively. The four lowest ionization energy bands (1b⁻¹_1u, 1b⁻¹_1g, 3a⁻¹_g, and 1b⁻¹_2u) show monotonic cross-section decreases with photon energy from 33 eV, the 1b⁻¹_1u CC π band showing the least rapid decline. In contrast, the 2b⁻¹_3u and 2a⁻¹_g bands show almost constant cross-sections up to ~50 eV photon energy, followed by similar, although slower, monotonic decreases. This is attributed to the substantial carbon 2s character of the 2b_3u and 2a_g orbitais. The cross-section behaviour of all bands is interpreted with the aid of SCF-LCAO-MO calculations on the neutral molecule using the Gaussian-80 series of programs.     

Photoelectron mean free paths in barium stearate layers

Barium stearate monolayers were deposited on polished clean germanium and copper substrates using the Blodget technique. Film thicknesses were determined by ellipsometry by assuming the films were optically isotropic with a refractive index of 1.5 and an absorption coefficient of zero. X-ray photoelectron spectroscopy intensity ratios, obtained at 223 K to minimize vaporization, were used to determine electron inelastic mean free paths (IMFP) in the barium stearate layers. The substrate photoelectron lines cover a binding energy range of 1200 eV. IMFP values range from approximately 27 ± 5 Å at about 230 eV to 65 ± 12 Å at about 1480 eV kinetic energy. The approximately linear shape of this function, together with the throughput function of the instrument, suggests that over the binding energy range of 0–600 eV, the photoelectron mean free paths and throughput effects in the Hewlett-Packard instrument approximately cancel.     

Relative intensities in X-ray photoelectron spectra. Part IX. Estimates for photoelectron mean free paths taking into account elastic collisions in a solid

By means of the Monte Carlo method the angular dependences of photoelectron peak intensities have been calculated for substrates covered with films of various thicknesses D. The calculations have been carried out for several sets of parameters of the elastic and inelastic interactions of electrons with solids and for various experimental geometries. On the basis of numerical theoretical results, analytical expressions are derived for estimating the difference between the effective mean free path of photoelectrons (λ_eff) and the inelastic mean free path (λ_n) in solids. These expressions are used to analyse experimental data for the determination of thin-film thicknesses by means of ESCA. It is concluded that the values determined experimentally are apparently D/λ_eff ratios — not D/λ_n, as is usually assumed. The importance of the results obtained is discussed with reference to the determination of photoelectron mean free paths in solids and of thin-film thicknesses by means of ESCA.     

Interaction mean free paths of He fragments from ultrahigh-energy nucleus-nucleas collisions in emulsion

The interaction mean free paths of He fragments produced by the collisions of ³²S and ¹⁶O at 200 GeV/n in nuclear emulsion have been investigated. 906 He fragments giving rise to 374 secondary interactions have been used in the present analysis. Within the present statistics, we do not observe any anomalous behavior in the mean free paths of He fragments. The interaction mean free paths are found to be independent of the projectile mass and the impact parameter of collision, at the highest available beam energies.     

Inelastic mean free paths for electrons in bulk jellium

Bulk inelastic mean free paths, λ, of electrons in jellium are given in graphical form as a function of the electron spacing parameter r_s and the electron energy E, based on self-energy results of Lundqvist. The results are suggested as a useful guide to the dependence of λ on the material in the energy range near the minimum of λ.     

Comments on nucleon mean free paths in nuclear matter

It is suggested that recent evidence cited for a fourfold increase in the mean free path of nucleons in nuclear matter results from an error in formulation of the exciton model. The literature cited as being in support of the longer mean free path is reviewed and found to be in disagreement with the new value, and in quite reasonable agreement with results used over the past 30 years.     

Reflected electron-energy-loss spectra,differential inverse inelastic mean free paths,and angular resolved X-ray photoelectron spectra of a niobium sample

A technique for recovering the differential inverse inelastic mean free paths (DIIMFP) of electrons in Nb from the reflected electron energy loss spectra (REELS) at initial energies of 5 to 40 keV using a threelayer model of the sample surface is presented. The recovered DIIMFP are used for analyzing X-ray photoelectron spectra measured at different viewing angles. Comparison with experimental data is carried out.     

Observations on the determination of electron mean free paths from RF size effect measurements

Numerical calculations of the line shape of the rf size effect for 0.1 mm thick potassium plates in the transmission geometry at 1.25 MHz, show that the amplitude of the fundamental resonance is proportional to exp (?1.22d/l), while that of the second resonance is proportional to exp (?0.92d/l), whered andl are the plate thickness and electron mean-free path, respectively. In the case of the fundamental, our result differs significantly from the exp (?1.57d/l) dependence usually assumed for the purpose of determiningl, and indicates that the conventional analysis leads to an overestimate ofl by approximately 30%. The amplitude dependence found here can be explained physically in terms of the finite skin depth, and in the case of the second resonance, in terms of the strength of the electric field splash at the center of the plate.     

Thermal conductivity spectroscopy technique to measure phonon mean free paths

Size effects in heat conduction, which occur when phonon mean free paths (MFPs) are comparable to characteristic lengths, are being extensively explored in many nanoscale systems for energy applications. Knowledge of MFPs is essential to understanding size effects, yet MFPs are largely unknown for most materials. Here, we introduce the first experimental technique which can measure MFP distributions over a wide range of length scales and materials. Using this technique, we measure the MFP distribution of silicon for the first time and obtain good agreement with first-principles calculations.     

Above-threshold ionization photoelectron spectrum from quantum trajectory

Many nonlinear quantum phenomena of intense laser-atom physics can be intuitively explained with the concept of trajectory. In this paper, Bohmian mechanics (BM) is introduced to study a multiphoton process of atoms interacting with the intense laser field: above-threshold ionization (ATI). Quantum trajectory of an atomic electron in intense laser field is obtained from the Bohm-Newton equation first and then the energy of the photoelectron is gained from its trajectory. With energies of an ensemble of photoelectrons, we obtain the ATI spectrum which is consistent with the previous theoretical and experimental results. Comparing BM with the classical trajectory Monte-Carlo method, we conclude that quantum potential may play a key role to reproduce the spectrum of ATI. Our work may present a new approach to understanding quantum phenomena in intense laser-atom physics with the image of trajectory.     

Electron inelastic mean free paths in solids: A theoretical approach

In the present paper, the inelastic mean free path (IMFP) of incident electrons is calculated as a function of energy for silicon (Si), oxides of silicon (SiO2 ), SiO, and Al2O3 in bulk form by employing atomic/molecular inelastic cross sections derived by using a semi-empirical quantum mechanical method developed earlier. A general agreement of the present results is found with most of the available data. It is of great importance that we have been able to estimate the minimum IMFP, which corresponds to the peak of inelastic interactions of incident electrons in each solid investigated. New results are presented for SiO, for which no comparison is available. The present work is important in view of the lack of experimental data on the IMFP in solids.     

Relationships between electron inelastic mean free paths, effective attenuation lengths, and mean escape depths

The terms inelastic mean free path (IMFP), effective attenuation length (EAL), and mean escape depth (MED) are frequently used to specify the surface sensitivity of Auger-electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). These terms are different conceptually because of the effects of elastic-electron scattering, and generally have different numerical values for a specified material and electron energy. In addition, values of the EAL and MED depend on the instrumental configuration. We give an historical overview of efforts to measure EALs by the overlayer method and of work to investigate elastic-scattering effects in AES and XPS. We then apply an analytical formalism developed from a solution of the kinetic Boltzmann equation within the transport approximation to demonstrate the relationships between the IMFP, EAL, and MED for selected elemental solids and for common measurement conditions. Examples are given to show the magnitude of elastic-scattering effects on MED values for angle-resolved XPS and AES. If XPS or AES data are acquired for emission angles between zero and 60°, the ratio of the MED to that found with elastic scattering neglected is approximately constant (to within 10%), and this ratio can be used to determine an average value for the EAL. This EAL value can then be used to establish the depth scale in the data analysis. Finally, we show ratios of the EAL to the IMFP for XPS from the Au 4s subshell with Mg K X-rays as a function of emission angle and depth; this ratio has a weak dependence on emission angle from zero to 40° but a more pronounced dependence for larger emission angles.     

An analytical expression for the calculation of electron mean free paths in solids

A simple analytical expression for the calculation of the inelastic-scattering mean free path for electrons in free-electron-like metals has been derived on the basis of a dielectric formalism. Good agreement with experimental data for energies greater than 200 eV has been demonstrated. By extending the concept of a one-mode excitation spectrum, an analogous formula applicable to semiconductors, insulators and non-free-electron-like metals has been derived which also compares well with experimental data.