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.     

Influence of octupole photoionization transitions on the angular distribution of photoelectrons from solids with account for elastic scattering

Using the transport theory approach, equations are derived for the angular dependence of XPS intensities from semi-infinite solids taking into account elastic scattering of photoelectrons and non-dipolar transitions up the second-order corrections. The unpolarized excitation source is considered. The elastic scattering is the main term smearing the non-dipolar contribution in complete analogy with smearing of dipole contribution. Some additional terms are shown to be negligible in comparison with the main term for complete sets of emission and azimuth angles, three representative single scattering albedo values and several representative sets of the second-order non-dipolar parameters. The photoelectron angular distributions are calculated for Al 2s and Ag 3d lines using transport theory and Monte-Carlo simulation. The Monte-Carlo calculations are in agreement with transport theory approach.     

On the influence of elastic scattering on asymmetric xp-signal distribution

In the standard equation for the strength of photoelectron signals the angular dependence of emitted photoelectrons is represented by the asymmetry parameter. As the geometry has a number of characteristic angles, γ, for example due to a finite solid angle of electron detection, one expects an effective asymmetry parameter β* instead of the theoretical β. But elastic electron scattering causes much more of a spread from the characteristic angle γ to a spectrum of possible γ-values. This paper aims to obtain quantitative results allowing a quantification of the influence of elastic scattering on the theoretical asymmetry parameter β. For photoelectrons with kinetic energies within 1–1.5 keV and elements up to Z = 46 the result is β* = (1.0688 ?0.0235Z+0.000188Z²)β     

Photoelectron emission from thin overlayers

Photoelectron signal intensities calculated for a thin overlayer from theoretical models taking elastic photoelectron collisions into account are shown to be very weakly dependent on the substrate material. This result has been obtained for photoelectrons analyzed in XPS spectrometers equipped with typical X-ray sources, i.e. sources of Mg Kα and Al Kα radiation. Low sensitivity to the substrate material is due to the fact that trajectories of photoelectrons emitted in the overlayer and entering the substrate have a low probability to reach the analyzer without energy loss. On the other hand, the signal intensity of photoelectrons emitted in the overlayer is found to be distinctly affected by elastic photoelectron scattering. Consequently, a theoretical model that can accurately describe the photoelectron intensity from an overlayer deposited on any material (e.g. on a substrate of the same material as the overlayer) can be a useful basis for a universal and convenient method for determination of the overlayer thickness. It is shown that the formalism derived from the kinetic Boltzmann equation within the so-called transport approximation satisfies these requirements. This formalism is postulated for use in overlayer-thickness measurements to avoid time-consuming Monte Carlo simulations of photoelectron transport, and also to circumvent problems with determining the effective attenuation lengths for overlayer/substrate systems.     

Photoelectron elastic scattering effects in XPS

The photoelectron elastic scattering effects in XPS are reviewed. Using the transport theory approach and Monte-Carlo calculations as well experimental data, the influence of elastic scattering is demonstrated for the escape probability of the photoelectrons from solids, the intensities from bulk and surface systems, the angular intensity dependence including dipole and quadrupole transitions, attenuation lengths from various definitions, mean escape depths, the path-length distribution of photoelectrons in solids, the overlayer thickness determination, in-depth profiling and photoelectron diffractions patterns from single crystals.     

The influence of relaxation and nondipole effects on the intensity of X-ray photoelectron spectra

The photoionization cross sections; dipole and nondipole parameters of the angular distribution of photoelectrons; and the spectroscopic factors for the main X-ray photoelectron lines, which are used in quantitative analysis of the surface and most of atoms, have been calculated. It is shown that consideration of nondipole effects leads to a significant (up to 10%) change in the photoelectron angular distribution. Therefore, neglect of nondipole transitions may lead to an error above 10% when MgK _α and AlK _α X-ray lines are used for surface analysis. Consideration of the spectroscopic factors leads to a decrease in the absolute line intensity by about 20%. Calculations showed that this value weakly depends on the atomic number and quantum shell numbers.     

Influence of elastic-scattering processes on an X-ray photoelectron spectroscopy signal: Effect of the underlying surface

The boundary-value problem for the transfer equation with internal sources and without them is solved using the invariant embedding method. The influence of processes of photoelectron elastic scattering on the energy spectra of photoelectron emission is analyzed. The focus of attention is on the analysis of variations in the intensity and the spectral composition of the ascending flow of the photoelectron emission of a layer when underlying layers with different compositions appear. The physical fundamentals of the influence of elastic scattering on the formation of X-ray photoelectron spectra are demonstrated. The peak intensities for homogeneous Au 4s _1/2 and Si 2s _1/2 targets are calculated with and without the inclusion of reflection processes. The error appearing as a result of neglecting elastic scattering processes, which transform the descending motion into ascending type, is determined.     

Anomaly in α-scattering from 6Li between 35 and 45 MeV

The elastic scattering of α-particles on ⁶Li nuclei has been measured from 20° to 170° (c.m.) and the inelastic scattering to the first excited state of ⁶Li has been measured for forward and backward angles. The elastic scattering angular distributions are calculated (i) in terms of pure potential scattering, (ii) in terms of potential scattering with an l-cut-off on the imaginary part of the potential and (iii) in terms of the coherent addition of the potential scattering amplitude and of the exchange amplitude. The third method gives the best fit to the data. The inelastic angular distributions are compatible with the macroscopic calculations, except in the very backward region where exchange phenomena are also shown to dominate.     

XPS Study of Niobium and Niobium-Nitride Nanofilms

A new, XPS-based approach to quantitative and nondestructive determination of the chemical and phase layer composition of multicomponent multilayer films is proposed. It includes a new method for subtracting the background of repeatedly inelastically scattered photoelectrons, taking into account the inhomogeneity of inelastic scattering over depth; a new way of decomposing a photoelectron line into component peaks, taking into account the physical nature of various decomposition parameters; solution of the problem of subtracting the background and decomposing the photoelectron line simultaneously; and determination of the thickness of the layers of a multilayer target using a simple equation. The phase-layer composition of nanoscale Nb and NbN films is determined, and the thicknesses of these layers are calculated.     

Leed intensity calculations for finite instrumental transfer width caused by the angular aperture of the primary beam

The influence of the angular divergence of the primary beam on the dynamic intensities in LEED is investigated. It is shown that the corresponding finite instrument transfer width restricts the area of dynamic scattering within one layer. For usual angular apertures of about 1° reductions considerably below the area determined by inelastic processes result. This reduces the lattice sum to be executed in intralayer scattering. For a typical value of the imaginary part of the optical potential, v_0i=4 eV, changes up to a few percent of the intensity result. Hence more realistic intensity spectra are calculated with a simultaneous considerable saving of computing time.     

Channel coupling and exchange of an alpha-particle cluster in deuteron scattering on 6Li nuclei

Existing experimental data on elastic and inelastic deuteron scattering on ⁶Li nuclei in the energy range from 8 to 50 MeV were analyzed within the approach of coupled reaction channels. The coupling of elastic scattering and inelastic scattering accompanied by the transition to the 3⁺ state at E _x = 2.186 MeV and the mechanism involving the exchange of an alpha-particle cluster were taken into account in respective calculations. The phenomenological potentials obtained from the present analysis describe well experimental angular distributions at all energies and in full angular ranges. The depths of the real and imaginary parts of the potentials in question depend smoothly on energy at fixed values of the remaining parameters. The energy dependence of relevant volume integrals agrees well with similar data for the p + ⁶Li, ?? + ⁶Li, and ¹²C + ¹²C systems and with the predictions of a microscopic theory.     

Study of parameters of the angular distribution of photoelectrons in the relativistic quadrupole approximation

Relativistic calculations of differential cross sections for photoionization are performed and the behavior of parameters β, γ, and δ describing the angular distribution of photoelectrons in the quadrupole approximation is studied. The calculations were carried out for a number of atoms for kinetic energies of photoelectrons E _k ≈50 000 eV. The electronic wave functions of the initial and final states are calculated by the Dirac-Fock method taking into account the exchange interaction and a hole produced in the atomic shell upon photoionization. The dependence of parameters β, γ, and δ on the physical assumptions used in the calculations is studied. Comparison with nonrelativistic calculations shows that relativistic values of the nondipole parameters γ and δ can be substantially different even at low energies of photoelectrons. Our calculations of nondipole parameters γ and δ for the 2p-shell of the Kr atom better agree with the recent experimental data than nonrelativistic calculations performed earlier taking approximately into account the exchange interaction and neglecting a hole.     

Dynamic spin susceptibility of hole-doped high-temperature superconductors in a singlet-correlated conduction band model

We have derived an expression for the dynamical spin susceptibility of a hole-doped high-temperature superconductor taking into account a strong correlation between the magnetization of spins of the localized and itinerant electrons. This formula has been used to calculate the imaginary part of the susceptibility as a function of the frequency and wave vector. The results are compared to experimental data on the inelastic neutron scattering in compounds of the YBa₂Cu₃O_6+y type. A peak in the scattering intensity observed at an energy of about 40 meV in the region of wave vectors Q = (π, π) and an arc-shaped dispersion relief are interpreted as manifestations of the collective spin excitations in the system, the energy of which falls within a superconducting gap (spin exciton). The U-shaped divergent relief observed in the neutron scattering intensity is assigned to collective short-rage-order spin oscillations.     

Influence of the processes of multiple elastic scattering on the angular distributions of X-ray photoelectrons

Based on the boundary-value problem for the transport equation, the angular distributions of photoelectrons are analyzed using the method of invariant immersion. Monte Carlo (MC) simulation of the process of photoelectron emission is carried out. The determining influence of the process of multiple elastic scattering on the photoelectron spectra is shown. Simple analytical formulas for the angular distributions of photoelectrons are obtained in the small-angle approximation. The results of MC simulation and those of other authors are compared.     

Photoelectron emission for layers of finite thickness

Basic tools that describe the energy and angular distributions of photoelectrons emitted by inhomogeneous targets are presented. These are the functions of reflection and transmission, the function of photoelectron emission, the equation for photoelectron flow, and the equation for the transmission function, which describes the dynamics of the angular and energy spectra of photoelectrons when they move in the tar-get. The determining influence of the effects of multiple elastic scattering on the angular distribution of photoelectrons is shown. It is demonstrated in which way and by how much the effect of brightness body rotation, well known in optics, influences the X-ray photoelectron spectroscopy signal. Along with analytical solutions, the results of simulation of the X-ray photoelectron spectroscopy signals are presented.     

Influence of elastic scattering on the measurement of core-level binding energy dispersion in X-ray photoemission spectroscopy

We explore the interplay between the elastic scattering of photoelectrons and the surface core level shifts with regard to the determination of core level binding energies in Au(111) and Cu₃Au(100). We find that an artificial shift is created in the binding energies of the Au 4f core levels, that exhibits a dependence on the emission angle, as well as on the spectral intensity of the core level emission itself. Using a simple model, we are able to reproduce the angular dependence of the shift and relate it to the anisotropy in the electron emission from the bulk layers. Our results demonstrate that interpretation of variation of the binding energy of core-levels should be conducted with great care and must take into account the possible influence of artificial shifts induced by elastic scattering.     

Die Winkelabhängigkeit der Resonanzstreuung niederenergetischer Elektronen an N2

Results of scattering experiments with monochromatic electrons in the energy range from a few tenth of an eV to about 16 eV are reported. Below 1.8 eV collision energy no resonance structures have been found either in the total scattering (transmitted current) or in the elastic and inelastic differential cross sections. The resonances above 1.8 eV have been measured in the elastic and inelastic channels (up to vibrational quantum numberν=8 of the N₂-molecule) in the angular range from 10° to 110°. In the inelastic channelsν≧2 especially the first resonance peak appears asymmetric, as predicted by calculations of the associated Franck-Condon-factors. In all inelastic channels the angular dependence (due to the pure resonance scattering) shows maxima at 0° and 90° and a minimum around 55°, probably indicating gerade-symmetry of the associated N ₂ ^? -state. Excitation functions of three states of N₂ were measured between their thresholds (between 11 and 12 eV) and 15 eV, one of them showing several new resonance structures.     

Analysis of elastic and inelastic α + <Superscript>24</Superscript>Mg scattering within the <Emphasis Type="Italic">S</Emphasis> matrix model involving regge poles

A generalization of the phenomenological S-matrix model taking into account isolated Regge poles is proposed for simultaneously describing refractive effects in the cross sections for the elastic and inelastic scattering of light nuclei. The cross sections for elastic α + ²⁴Mg scattering are analyzed at energies of 50, 54, 65.7, 81, and 119 MeV. The analysis of the cross sections for elastic scattering is supplemented with an analysis of the inelastic scattering of alpha particles that is accompanied by the excitation of the first excited state (2⁺) of ²⁴Mg nuclei. It is shown that the proposed model makes it possible to describe satisfactorily all of the aforementioned cases of elastic and inelastic scattering, correctly reproducing the refraction Airy structures and anomalous large-angle scattering that are observed at large scattering angles.