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.     

Account of photoelectron elastic determination of overlayer thickness,in-depth profiling,escape depth,attenuation coefficients and intensities in surface systems

An analytical connection is found between parameters of Monte Carlo and transport theory methods to account for elastic electron scattering in solids. A simple analytical method is proposed for the intensity calculations in X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy (AES) with account of elastic scattering. The method is applied for solution of many problems in XPS including determination of the overlayer thickness, correction factors for the in-depth profiling, escape depth, attenuation lengths, intensities in layered systems.     

Relative intensities in x-ray photoelectron spectra: Part IV. The effect of elastic scattering in a solid on the free path of electrons and their angular distribution

A new expression for the intensity of X-ray photoelectron spectra is derived with due allowance for multiple elastic scattering of photoelectrons durin     

Escape probability of signal photoelectrons from non-crystalline solids: influence of anisotropy of photoemission

The escape probability of photoelectrons as a function of depth of orgin haa been studied experimentally, analytically and by the Monte Carlo (MS) technique. The depth distribution function (DDF) describing the probability for an electron emitted at a certain depth to leave a surface without being scattered inelastically has been obtained by solving a kinetic equation in the transport approximation. The analytically derived DDF is a universal function of the ratio of the inealstic to the transport mean free paths and the asymmetry parameter. In the directions of minima of the angular distribution, this function is no longer exponential, but it may be essentially nonmonotonic, reaching its maximum value at the depth comparable with the inelastic mean free path. The maximum value of the DDF exceeds its surface value by about 50% for the asymmetry parameter being equal to 2 in the emission directions close to that of X-ray propagation. Under the same conditions, the mean escape depth of electrons may be several times larger than the value predicted by the usual XPS formalism. Such behaviour of the escape probability is explained by elastic scattering of photoelectrons.The solution to the kinetic equation for a uniform target is generalized for a sample with an arbitrary depth profile and depth-dependent elastic and inelastic scattering cross-sections under the condition of the ratio of the inelastic to the transport mean free paths being independent of depth. Analytical formulas for the photoelectron yield from overlayer/substrate structure have been derived and studied in detail. The analytical predictions are compared with the experimental and Monte Carlo simulation data obtained for aluminium oxide/aluminium specimen. A satisfactory agreement is observed between the experimental and theoretical results.     

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 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.     

Relative intensities in X-ray photoelectron spectra: Part VII. The effect of elastic scattering in a solid on the angular distribution of photoelectrons escaping from samples covered with thin films of various thicknesses

The angular distributions of X-ray photoelectron peak intensity for (1) a semi-infinite sample, (2) a substrate sample covered with a film, and (3) an overlayer sample are calculated by the Monte-Carlo method. The elastic as well as the inelastic scattering of electrons in a solid is taken into account. In all cases the elastic scattering is shown to have a significant effect on both the absolute value of peak intensity and the angular distribution of photoelectrons. The electron mean free paths without inelastic collisions (λ_n) calculated using formulas derived without taking account of elastic scattering are shown to differ significantly from the real values. Moreover, the λ_n values calculated in this way are not physical constants at all, but depend for example on the film thickness and the intervals of photoelectron take-off angles under consideration. The elastic scattering effect is shown capable of explaining some difficulties which arise in the interpretation of experimental data reported in the literature on the basis of expressions derived taking into account only the inelastic interactions of photoelectrons with a solid.     

The influence of elastic scattering of electrons on measured X-ray photoelectron signals

The basic equations for quantitative X-ray photoelectron spectroscopy (XPS) of uncovered and covered solid surfaces have to be corrected regarding the effect of elastic scattering processes of photoelectrons in matter. We propose two correction terms which were quantified on an empirical basis from the results of Monte Carlo calculations.     

Extracting electron-ion differential scattering cross sections for partially aligned molecules by laser-induced rescattering photoelectron spectroscopy

We extract large-angle elastic differential cross sections (DCSs) for electrons scattering from partially aligned O2+ and CO2+ molecules using rescattering photoelectrons generated by infrared laser pulses. The extracted DCSs are in good agreement with those calculated theoretically, demonstrating that accurate DCSs for electron-ion scattering can be extracted from the laser-induced rescattering spectra, thus paving the way for dynamic imaging of chemical reactions by rescattering photoelectron spectroscopy.     

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.     

X-ray photoelectron spectroscopy: Exact solution to the problem with internal sources

A fundamentally new model of multiple photoelectron scattering in solids is described in this paper. It takes into account the nonuniform depth distribution of photoelectron sources and the anisotropic character of single scattering and yields an exact solution to the problem of multiple elastic scattering. Highly accurate and fast algorithms for calculating X-ray photoelectron spectroscopy signals can be developed on the basis of this model.     

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 escape from iron oxide

Iron oxide of nanometer thickness were grown in situ by step-by-step oxidation of an iron foil to measure the escape probabilities of O 1s photoelectrons as a function of depth of origin, the so-called emission depth distribution function (EDDF), and the mean escape depth (MED). To record photoelectron spectra for a wide range of emission angles, the X-ray excitation source was positioned on the opposite side of the iron foil with respect to the analyzer. To excite photoelectrons on the side of the foil surface adjacent to the analyzer, the foil was made thin enough to be semitransparent to the X-ray radiation. The O 1s spectra were recorded for a wide range of oxide thicknesses until no features of metallic iron were recognized in the photoelectron spectra. The escape probability of the O 1s photoelectrons in the iron oxide was derived from the oxide-thickness dependence of the O 1s peak areas. The resulting EDDF reached a maximum beneath the oxide surface for X-ray incidence and electron-emission angles located along the surface normal. For the same incidence angle and an emission angle of 60°, the escape probability could be well approximated by a simple exponential function. The mean escape depths were obtained for both experimental geometries and agreed well with the available theory.     

Experimental retrieval of target structure information from laser-induced rescattered photoelectron momentum distributions

We have measured two-dimensional photoelectron momentum spectra of Ne, Ar, and Xe generated by 800-nm, 100-fs laser pulses and succeeded in identifying the spectral ridge region (back-rescattered ridges) which marks the location of the returning electrons that have been backscattered at their maximum kinetic energies. We demonstrate that the structural information, in particular the differential elastic scattering cross sections of the target ion by free electrons, can be accurately extracted from the intensity distributions of photoelectrons on the ridges, thus effecting a first step toward laser-induced self-imaging of the target, with unprecedented spatial and temporal resolutions.     

Emission-depth-selective auger photoelectron coincidence spectroscopy

The collision statistics of the energy dissipation of Auger and photoelectrons emitted from an amorphized Si(100) surface is studied by measuring the Si 2p photoelectron line as well as the first plasmon loss peak in coincidence with the Si-LVV Auger transition and the associated first plasmon loss. The Si 2p plasmon intensity decreases when measured in coincidence with the Si-LVV peak. If measured in coincidence with the Si-LVV plasmon the decrease is significantly smaller. The results agree quantitatively with calculations accounting for surface, volume, and intrinsic losses as well as elastic scattering in a random medium. In this way one can determine the average emission depth of individual electrons by means of Auger photoelectron coincidence spectroscopy, which therefore constitutes a unique tool to investigate interfaces at the nanoscale level.     

Role of elastic scattering in high-order above threshold ionization

We investigate the target and intensity dependence of plateau in high-order above threshold ionization(HATI) by simulating the two-dimensional(2D) momentum distributions and the energy spectra of photoelectrons in HATI of rare gas atoms through using the quantitative rescattering model. The simulated results are compared with the existing experimental measurements. It is found that the slope of the plateau in the HATI photoelectron energy spectrum highly depends on the structure of elastic scattering differential cross section(DCS) of laser-induced returning electron with its parent ion. The investigations of the long- and short-range potential effects in the DCSs reveal that the short-range potential, which reflects the structure of the target, plays an essential role in generating the HATI photoelectron spectra.     

Delay in atomic photoionization

We analyze the time delay between emission of photoelectrons from the outer valence ns and np subshells in noble gas atoms following absorption of an attosecond extreme ultraviolet pulse. Various processes such as elastic scattering of the photoelectron on the parent ion and many-electron correlation affect the apparent "time zero" when the photoelectron leaves the atom. This qualitatively explains the time delay between photoemission from the 2s and 2p subshells of Ne as determined experimentally by attosecond streaking [Science 328, 1658 (2010)]. However, with our extensive numerical modeling, we were only able to account for less than half of the measured time delay of 21 ± 5 as. We argue that the extreme ultraviolet pulse alone cannot produce such a large time delay and it is the streaking IR field that is most likely responsible for this effect.     

Application of high-energy synchrotron-radiation XPS to determine the thickness of SiO2 thin films on Si(100)

The escape depth of photoelectrons depends on their kinetic energy. We apply this relationship to measure film thicknesses from X-ray photoelectron spectroscopy (XPS) measurements with tunable-energy synchrotron radiation (SR). For this purpose, a “high-energy SR-XPS” instrument has been constructed and used to characterize thermally oxidized thin films on Si(100) single crystals. In order to observe photoelectrons emitted from deeper regions than with conventional XPS, Si 1s photoelectrons with an energy up to 4000 eV were measured with X-ray energies up to 5800 eV. The oxide thickness was estimated from measurements of the relative Si intensities from the oxide and the substrate at various photon energies. Our results suggest that the SR-XPS system is useful for measuring the thickness of thin films.     

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.